Universite de Provence(Aix-Marseille I)

Memoire presente par

Christophe Legeren vue d’obtenir l’habilitation a diriger des recherches

Etudes fonctionnelles d’enzymes redox

par electrochimie directe

Soutenance le 18 juin 2007 devant le jury compose de :

Patrick Bertrand, professeur, universite de Provence, rapporteur,

Marc Fontecave, professeur, universite Joseph Fourier,

Bruno Guigliarelli, professeur, universite de Provence,

Yvan Massiani, professeur, universite de Provence,

A. William Rutherford, directeur de recherche, CNRS, rapporteur,

Jean-Michel Saveant, directeur de recherche emerite, CNRS, rapporteur.

Unite de Bioenergetique et Ingenierie des Proteines, CNRS, Marseille.

C. Leger. UPR 9036. Memoire d’HDR. 2007.

Unite de Bioenergetique et Ingenierie des Proteines (CNRS UPR 9036, Dir. Mireille Bruschi)Institut de Biologie Structurale et Microbiologie (IFR 88, Dir. Mireille Bruschi)31, Chemin Joseph Aiguier,13402 Marseille Cedex 20E-mail : christophe.leger@ibsm.cnrs-mrs.frTel : 04 91 16 45 29,Fax : 04 91 16 45 78

La version pdf, couleur, et cliquable de ce document est disponible a l’adressehttp://bip.cnrs-mrs.fr/bip07/pdf/leger_hdr.pdf

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C. Leger. UPR 9036. Memoire d’HDR. 2007.

Table des matieres

1 Curriculum Vitæ 4

2 Diffusion des travaux de recherche 4

2.1 Publications dans des revues a comite de lecture . . . . . . . . . . . . . . . . 42.2 Communications a des colloques, conferences, seminaires . . . . . . . . . . . . 9

3 Enseignement, formation, encadrement 13

4 Responsabilites collectives et management de la recherche 15

5 Description breve des travaux jusqu’a la these 16

5.1 L’hydroxyde de nickel : materiau electroactif d’intercalation (1995–1996) . . . 165.2 Instabilites morphologiques au cours d’experiences d’electrodeposition (1996–

1999) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

6 Travaux post-doctoraux (1999–2002) 22

6.1 Contexte . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226.2 La fumarate reductase de E. coli . . . . . . . . . . . . . . . . . . . . . . . . . 266.3 L’hydrogenase d’A. vinosum . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286.4 La DMSO reductase de E. coli . . . . . . . . . . . . . . . . . . . . . . . . . . 32

7 Insertion au BIP 35

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357.2 Soutiens financiers obtenus . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

8 Resultats obtenus au BIP (2002–2006) 37

8.1 Transferts d’electrons dans les enzymes multicentres . . . . . . . . . . . . . . 378.2 Mecanismes catalytiques au site actif . . . . . . . . . . . . . . . . . . . . . . . 448.3 Sensibilite a l’oxygene des hydrogenases . . . . . . . . . . . . . . . . . . . . . 488.4 Etude du transport de matiere intramoleculaire . . . . . . . . . . . . . . . . . 518.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

9 Objectifs 54

9.1 Vers une vision integree du mecanisme des enzymes multicentres . . . . . . . 549.2 Directionnalite des hydrogenases . . . . . . . . . . . . . . . . . . . . . . . . . 559.3 Specificite des molybdoenzymes de la famille de la DMSO reductase . . . . . 58

10 Articles choisis 60

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C. Leger. UPR 9036. Memoire d’HDR. 2007.

1 Curriculum Vitæ

– Charge de Recherche au Laboratoire de Bioenergetique et Ingenierie des Proteines,2002–Marseille.

– Post-doctorant, dans le groupe de bioelectrochimie dirige par Fraser Armstrong, au1999–2002laboratoire de Chimie Inorganique de l’Universite d’Oxford, U.K. Financement BBSRC.

– These de Doctorat de l’Universite de Bordeaux I, specialite Chimie-Physique, soutenue1996–1999le 20 septembre 1999, dirigee au Centre de Recherche Paul Pascal (UPR 8641, Pessac)par Francoise Argoul. Financement MRT.Etude d’instabilites morphologiques dans des systemes electrochimiques.Titre du memoire : “L’electrodeposition en cellule mince sous l’œil d’un interferometre :une etude experimentale et theorique de processus limites par la diffusion.”Composition du Jury : Christian Vidal, Alain Arneodo, Francoise Argoul, Juan Elezgaray,Gabriel Faivre, Daniel Lincot, Michel Rosso.Le manuscrit (9.6Mb) est disponible a l’adresse : http://bip.cnrs-mrs.fr/bip07/pdf/leger_these.pdf

– Stage pre-doctoral, Scientifique du contingent a l’Institut de Chimie de la Matiere1995–1996Condensee de Bordeaux (UPR 9048), dans le groupe dirige par Claude Delmas.Etude electrochimique et structurale de l’electrode d’hydroxyde de nickel pour batteriesalcalines.

– D.E.A. de Chimie-Physique (mention TB), Universite de Bordeaux I.1995– Agregation de Sciences physiques, option chimie.1994– Cursus universitaire de Chimie-Physique a l’Universite de Bordeaux I.1989–1993– Ne le 12/08/1971.

2 Diffusion des travaux de recherche

2.1 Publications dans des revues a comite de lecture

“*” = auteur correspondant.

Publications liees a l’activite pre-doctorale

P1. C. Leger, C. Tessier, M. Menetrier, C. Denage and C. Delmas,?

“Investigations of the second discharge plateau of the β(III)-NiOOH/β(II)-Ni(OH)2system,”J. Electrochem. Soc. 146-3, 924–932 (1999).http://dx.doi.org/10.1149/1.1391701

P2. C. Leger et C. Delmas,“L’electrode positive d’hydroxyde de nickel pour batteries alcalines,”Bulletin de l’Union des Physiciens 93-811, 291–301 (1999).

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Publications liees a la these

P3. F. Argoul,? E. Freysz, A. Kuhn, C. Leger and L. Potin,“Interferometric characterization of growth dynamics during dendritic electrodepositionof zinc,”Phys. Rev. E. 53, 1777–1787 (1996).http://dx.doi.org/10.1103/PhysRevE.53.1777

P4. C. Leger, J. Elezgaray and F. Argoul,?

‘‘Experimental demonstration of diffusion-limited dynamics in electrodeposition expe-riments,”Phys. Rev. Lett. 78-26, 5010–5013 (1997).http://dx.doi.org/10.1103/PhysRevLett.78.5010

P5. F. Texier, G. Gadret, C. Leger and F. Argoul,?

“Convection induced self-organization in electroless deposition experiments,”J. Phys. II France 7, 663–675 (1997).http://dx.doi.org/10.1051/jp2:1997150

P6. C. Leger, J. Elezgaray and F. Argoul,?

‘‘Dynamical characterization of one dimensional stationary growth regimes in diffusion-limited electrodeposition processes,”Phys. Rev. E 58-6, 7700–7709 (1998).http://dx.doi.org/10.1103/PhysRevE.58.7700

P7. J. Elezgaray,? C. Leger and F. Argoul,‘‘Linear stability analysis of unsteady galvanostatic electrodeposition in the 2D diffusionlimited regime,”J. Electrochem. Soc. 145-6, 2016–2024 (1998).http://dx.doi.org/10.1149/1.1838592

P8. C. Leger, L. Servant, J.-L. Bruneel and F. Argoul,?

‘‘Growth patterns in electrodeposition,”Physica A 263(1-4), 305–314 (1999).http://dx.doi.org/10.1016/S0378-4371(98)00484-1

P9. C. Leger, F. Argoul? and M. Z. Bazant,“Front dynamics during diffusion-limited corrosion of ramified electrodeposits,”J. Phys. Chem. B 103-28, 5841–5851 (1999).http://dx.doi.org/10.1021/jp990486+

P10. C. Leger, J. Elezgaray and F. Argoul,?

“Probing interfacial dynamics by phase-shift interferometry in thin cell electrodeposition,”J. Electroanal. Chem. 486, 204–219 (2000).http://dx.doi.org/10.1016/S0022-0728(00)00143-1

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P11. J. Elezgaray, C. Leger and F. Argoul,?

“Dense branching morphology in electrodeposition experiments : characterization andmean-field modeling,”Phys. Rev. Lett. 84-14, 3129–3132 (2000).http://dx.doi.org/10.1103/PhysRevLett.84.3129

P12. C. Leger, J. Elezgaray and F. Argoul,?

“Internal structure of dense electrodeposits,”Phys. Rev. E. 61-5, 5452–5463 (2000).http://dx.doi.org/10.1103/PhysRevE.61.5452

P13. C. H. Chen, C. A. Miller, J. M. Walsh, P. B. Warren, J. N. Ruddock, P. R. Garrett,?

F. Argoul and C. Leger,‘‘Dissolution rates of pure nonionic surfactants,”Langmuir 16-12, 5276-5283 (2000).http://dx.doi.org/10.1021/la9913497

Publications liees a l’activite post-doctorale

P14. F. A. Armstrong,? R. Camba, H. A. Heering, J. Hirst, L. J. C. Jeuken, A. K. Jones,C. Leger and J. P. McEvoy,“Fast voltammetric studies of the kinetics and energetics of coupled electron-transferreactions in proteins,”Faraday Discuss., 116, 191–203 (2000).http://dx.doi.org/10.1039/b002290j

P15. C. Leger, K. Heffron, H. Pershad, E. Maklashina, C. Luna-Chavez, G. Cecchini, B. A.C. Ackrell and F. A. Armstrong,?

“Enzyme electrokinetics : energetics of succinate oxidation by fumarate reductase andsuccinate dehydrogenase,”Biochemistry 40-37, 11234–11245 (2001)http://dx.doi.org/10.1021/bi010889b

P16. K. Heffron, C. Leger, R. A. Rothery, J. H. Weiner and F. A. Armstrong,?

“Determination of an optimal potential window for catalysis by E. coli dimethyl sul-foxide reductase, and hypothesis on the role of MoV in the reaction pathway,”Biochemistry, 40-10, 3117–3126 (2001).http://dx.doi.org/10.1021/bi002452u

P17. L. Bateman, C. Leger, D. B. Goodin and F. A. Armstrong,?

“A distal histidine mutant (H52Q) of yeast cytochrome c peroxidase catalyses theoxidation of H2O2 instead of its reduction,”J. Am. Chem. Soc., 123-38, 9260–9263 (2001).http://dx.doi.org/10.1021/ja0158612

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P18. S. J. Elliott, C. Leger, H. R. Pershad, J. Hirst, K. Heffron, F. Blasco, R. A. Rothery,J. W. Weiner and F. A. Armstrong,?

“Detection and interpretation of redox potential optima in the catalytic activity ofenzymes,”Biochim. Biophys. Acta (Bioenergetics), 1555-1/3, 54–59 (2002)http://dx.doi.org/10.1016/S0005-2728(02)00254-2

P19. C. Leger, A. K. Jones, W. Roseboom, S. P. J. Albracht and F. A. Armstrong,?

“Enzyme electrokinetics : hydrogen evolution and oxydation by A. vinosum NiFe-hydrogenase,”Biochemistry, 41-52, 15736–15746 (2002).http://dx.doi.org/10.1021/bi026586e

P20. C. Leger, A. K. Jones, S. P. J. Albracht and F. A. Armstrong,?

“Effect of a dispersion of interfacial electron transfer rates on steady state catalyticelectron transport in NiFe-hydrogenase and other enzymes,”J. Phys. Chem. B, 106-50, 13058–13063 (2002).http://dx.doi.org/10.1021/jp0265687

P21. C. Leger, S. J. Elliott, K. J. Hoke, L. J. C. Jeuken, A. K. Jones and F. A. Armstrong,?

“Enzyme electrokinetics : using protein film voltammetry to investigate redox enzymesand their mechanisms”,Biochemistry, “Current Topics” 42-29, 8653–8662 (2003).http://dx.doi.org/10.1021/bi034789c

Reprints pdf : http://pubs.acs.org/cgi-bin/download.pl?bi034789c/z6oE

P22. V. Yankovskaya, R. Horsefield, S. Tornroth, C. Luna-Chavez, H. Miyoshi, C. Leger,B. Byrne, G. Cecchini and S. Iwata,?

“Molecular architecture of succinate dehydrogenase (Complex II) prevents reactive oxy-gen species generation,”Science, 299, 700–704 (2003).http://dx.doi.org/10.1126/science.1079605

Publications liees a l’activite au BIP

P23. B. Frangioni, P. Arnoux, M. Sabaty, D. Pignol, P. Bertrand, B. Guigliarelli and C. Leger,?

“In Rhodobacter sphaeroides respiratory nitrate reductase, the kinetics of substrate bin-ding favors intramolecular electron transfer,”J. Am. Chem. Soc., 126-5, 1328–1329 (2004).http://dx.doi.org/10.1021/ja0384072

Reprints pdf : http://pubs.acs.org/cgi-bin/download.pl?ja0384072/z3vt

P24. C. Leger,? S. Dementin, P. Bertrand, M. Rousset and B. Guigliarelli,“Inhibition and aerobic inactivation kinetics of Desulfovibrio fructosovorans NiFe hy-drogenase studied by Protein Film voltammetry,”

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C. Leger. UPR 9036. Memoire d’HDR. 2007.

J. Am. Chem. Soc., 126-38, 12162–12172 (2004).http://dx.doi.org/10.1021/ja046548d

Reprints pdf : http://pubs.acs.org/cgi-bin/download.pl?ja046548d/J7Cs

P25. M. Guiral, P. Tron, V. Belle, C. Aubert, C. Leger, B. Guigliarelli and M.-T. Giudici-Orticoni,?

“Hyperthermostable and oxygen resistant hydrogenases from a hyperthermophilic bac-terium Aquifex aeolicus : physicochemical properties,”Int. J. Hydrogen. Energ. 31-11, 1414–1431 (2006).http://dx.doi.org/10.1016/j.ijhydene.2006.06.007

P26. C. Leger,? F. Lederer, B. Guigliarelli and P. Bertrand,“Electron flow in multicenter enzymes : theory, applications and consequences on thenatural design of redox chains,”J. Am. Chem. Soc., 128-1, 180–187 (2006).http://dx.doi.org/10.1021/ja055275z

Reprints pdf : http://pubs.acs.org/cgi-bin/download.pl?ja055275z/e2tm

P27. S. Dementin, V. Belle, P. Bertrand, B. Guigliarelli, G. Adryanczyk-Perrier, A. Delacey,V. M. Fernandez, M. Rousset and C. Leger.?

“Changing the ligation of the distal [4Fe4S] cluster in NiFe hydrogenase impairs inter-and intramolecular electron transfers,”J. Am. Chem. Soc. 128-15, 5209–5218 (2006).http://dx.doi.org/10.1021/ja060233b

Reprints : http://pubs.acs.org/cgi-bin/download.pl?ja060233b/K4LW

P28. M. G. Almeida, C. M. Silveira, B. Guigliarelli, P. Bertrand, J. J. G. Moura, I. Mouraand C. Leger.?

“A needle in a haystack : the active site of the membrane-bound complex cytochromec nitrite reductase.”FEBS Letters 581-2, 284–288 (2007).http://dx.doi.org/10.1016/j.febslet.2006.12.023

En preparation :– C. Leger? and P. Bertrand.

“Direct electrochemistry of redox enzymes as a tool for mechanistic studies,”En preparation pour le numero de Chemical Reviews intitule “Molecular and Biomole-cular Electrochemistry,” edite par J.-M. Saveant (Juin 2008).

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2.2 Communications a des colloques, conferences, seminaires

Communications orales dans des conferences et reunions internationales

C1. 29/08–2/09/2004 7th European Biological Inorganic Chemistry Conference (EUROBIC7), Garmisch - Partenkirchen, Allemagne.Communication orale intitulee : “In Rhodobacter sphaeroides respiratory nitrate reduc-tase, the kinetics of substrate binding favors intramolecular electron transfer”Resume : http://www.uni-dortmund.de/eurobic7/session_lectures.html (SL44)

C2. 3-5/12/2004 Seminar on “Structure and function of metalloenzymes,” Goa, Inde.Organise par le CEFIPRA, Centre Franco-Indien pour la Promotion de la RechercheAvancee, coordonne en Inde par le Dr. Shymalava Mazumdar, du Tata Institute ofFundamental Research, Bombai et en France par J. Fontecilla-Camps et M. Fontecave(IMBG).Communication orale intitulee “Enzyme electrokinetics : using protein film voltammetryto investigate redox enzymes and their mechanisms”http://www.cefipra.org,Programme : http://www.tifr.res.in/~bic/INDOFENCH.htm

C3. 28/08–01/09/2005 15th IUPAB & 5th EBSA International Biophysics Congress, Mont-pellier, F.Communication orale intitulee : “Fragile design of the electron transfer chain in NiFehydrogenase.”http://worldbiophysics2005.sfbiophys.org/.Programme : http://worldbiophysics2005.sfbiophys.org/scientific_program.

pdf.

C4. 2–6/07/2006 8th European Biological Inorganic Chemistry Conference (EUROBIC 8),Aveiro, Portugal.Communication orale intitulee “Intramolecular electron transfers in NiFe hydrogenaseand other respiratory enzymes : new methods, new concepts”http://www.eurobic8.com/

Programme : http://www.eurobic8.com/programme.php (S5.5)

C5. 24-27/09/2006 Second International Meeting of the Institute of Metals in Biology ofGrenoble, Autrans, F. “Metals in Biocatalysis : from metalloenzymes to bio-inspiredsystems.”Communication orale invitee intitulee “The global catalytic properties of NiFe hydro-genases may be controlled by sites that are remote from the active site.”http://imbg.ujf-grenoble.fr/IMBG2006/

Programme : http://imbg.ujf-grenoble.fr/IMBG2006/lectures.htm

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C6. 18-20/10/2006 4th France-China workshop on surface electrochemistry of molecules ofbiological interest & biosensor applications, Ceret, France. Comite scientifique francais :C. Amatore, M. Comtat, S. Cosnier, A. Deronzier & J.-L. Marty.Communication orale intitulee “Using protein film voltammetry to investigate the ca-talytic mechanism of hydrogenases.”

A venir :

C7. 05-10/08/2007 2007 Hydrogenase Conference, Breckinridge, Colorado, USA.Communication orale intitulee “The mechanism of NiFe hydrogenase : beyond active-site chemistry.”http://www.chem.tamu.edu/hydrogenase

Seminaires de laboratoires et autres communications orales

C8. 14/04/1999 Seminaire du Groupe de Physique des Solides, Universite de Jussieu, Paris.“Croissance et corrosion d’agregats ramifies electrodeposes.”

C9. 29/11/2000 Seminaire du Centre de Recherche Paul Pascal, Bordeaux.“Etude d’enzymes redox par voltamperometrie.”

C10. 23/11/2000 Seminaire de l’Institut de Biologie Structurale et Microbiologie, Marseille.“Etude d’enzymes redox par voltamperometrie, principe et applications a quelques en-zymes respiratoires d’Escherichia coli.”

C11. 3/12/2001 Seminaire de la Section de Bioenergetique, CEA Saclay, Gif-sur-Yvette.

C12. 12/2001 Seminaire de l’Institut de Biologie Structurale et Microbiologie, Marseille.

Depuis mon recrutement au BIP :

C13. 28/03/2003 Seminaire du Departamento de Quımica (Dir. J. Moura), Universite Nou-velle de Lisbonne, Portugal.“Enzyme electrokinetics : using protein film voltammetry to investigate redox enzymesand their mechanisms.”

C14. 14–17/09/2003 Reunion annuelle du Club Metalloproteines et Modeles, Carry-le-Rouet.Communication orale intitulee “Etude par electrochimie directe d’une nitrate reductaseperiplasmique et considerations sur le cycle catalytique des enzymes de la famille de laDMSO reductase”http://clubmetallo.u-3mrs.fr/

C15. 5–10/09/2004 1st German-French summer school on electrochemistry and nanotechnology,Porquerolles, F.Communication orale intitulee “Studies of redox enzymes by protein film voltammetry :examples”Programme : http://www.lko.uni-erlangen.de/summer_school/static/program.

html

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C16. 31/05–04/06/2004 Ecole Thematique Biohydrogene, Cargese, Corse, F.Communication orale intitulee “Inhibition et cinetique de l’inactivation aerobie de l’hy-drogenase NiFe de D. fructosovorans : role du residu glutamate E25.”

C17. 23/03/2005 Seminaire Laboratoire des Interactions Moleculaires et Reactivite Chimiqueet Photochimioque (IMRCP), UMR 5623, Dir. I. Rico-Lattes, Universite Paul Sabatier,Toulouse.“Etude d’enzymes redox par electrochimie directe : exemples.”http://imrcp.ups-tlse.fr

C18. 13/10/2005 Seminaire du Departamento de Quımica (Dir. J. Moura), Universite Nou-velle de Lisbonne, Portugal.“Fragile design of the electron transfer chain in NiFe hydrogenase.”

C19. 23/01/2006 Seminaire du laboratoire d’Electrochimie Moleculaire de Paris, UMR 7591,Universite Paris 7.“Deux utilisations de l’electrochimie directe pour l’etude du transfert d’electron intra-moleculaire dans les enzymes multicentres.”http://www.lemp7.cnrs.fr/Index.htm

C20. 4/05/2006 Seminaire de l’Institut de Chimie Moleculaire et des Materiaux d’Orsay,Universite Paris-Sud 11.“Transferts d’electrons dans les enzymes respiratoires : nouvelles methodes, nouveauxconcepts.”http://www.icmo.u-psud.fr/

C21. 5–9/06/2006 GDR biohydrogene, Aussois, F.Communication orale intitulee “Effet de mutations sur la cinetique de transport dematiere dans les canaux de l’hydrogenase NiFe de D. fructosovorans.”

C22. 29/06/2006 Seminaire du Laboratoire de Bioenergetique Cellulaire, UMR 163, CEACadarache.Communication orale intitulee “Deux exemples d’utilisation de l’electrochimie directepour etudier les transferts d’electrons intramoleculaires dans les enzymes respiratoiresmulticentres.http://www-dsv.cea.fr/content/cea/d_dep/d_devm/d_lbc/

C23. 29–30/01/2007 Reunion BioH2 du CEA, Cadarache, F.Communication orale intitulee “Etude electrochimique du transport de matiere dansl’hydrogenase NiFe.”

C24. 11/04/2007 Seminaire du laboratoire Joliot-Curie, ENS Lyon, F.“Sur le fonctionnement des enzymes redox multicentres et leur etude par electrochimiedirecte.”http://www.ens-lyon.fr/Joliot-Curie/?id=seminaires

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Affiches

C25. 09/1997, Poster, Meeting of the Electrochemical Society, Paris.“High accuracy measurement of concentration fields in electrodeposition experiments.”This poster won the competition of the best student poster.

C26. 07/1998, Poster, Stat. Phys. 20, Paris.“Interfacial velocity and wavelength selection of dense electrodeposited patterns”.

C27. 08/1998, Poster, Gordon Conference on electrodeposition, New Hampshire USA.“Dynamical investigation on stationary growth regimes in electrodeposition experi-ments.”

C28. 07/1999, Poster, EUROBIC 5, Toulouse.“Energetics and dynamics of enzyme switches probed by Protein Film Voltammetry.”

C29. 08/2001, Poster, ICBIC 10 (International Conference on Bioinorganic Chemistry), Flo-rence, Italie.“Energetics of succinate oxidation by E. coli Fumarate reductase.” (J. Inorg. Biochem.86-1, 312 (2001)).

C30. 11/2001, Poster, Symposium of the collaborative research center SFB498 on “Protein-cofactor-interactions in biological processes”, Berlin, Germany.

C31. 27–30/09/2003, COST meeting on hydrogenase, Mulheim, AllemagneAffiche intitulee “Studies of NiFe hydrogenases by Protein Film Voltammetry”

C32. 08/2002, Poster, EUROBIC 6, Lund, Suede.

C33. 28/08–01/09/2005, 15th IUPAB & 5th EBSA International Biophysics Congress, Mont-pellier, F.Affiche reprenant ma communication orale, intitulee : “Fragile design of the electrontransfer chain in NiFe hydrogenase.”http://worldbiophysics2005.sfbiophys.org/.Programme : http://worldbiophysics2005.sfbiophys.org/scientific_program.

pdf.

C34. 2–6/07/2006, 8th European Biological Inorganic Chemistry Conference (EUROBIC 8),Aveiro, Portugal.Affiche reprenant ma communication orale, intitulee “Intramolecular electron transfersin NiFe hydrogenase and other respiratory enzymes : new methods, new concepts”http://www.eurobic8.com/

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3 Enseignement, formation, encadrement

Enseignementannee volume niveau Universite de theme

1994–1995 10h TD/TP Prepa. Agreg. Bordeaux I Chimie physique

1996–1997 15h TD DEUG Bordeaux I Chimie physique

1997–1998 Monitorat DEUG Bordeaux I Chimie physiqueet 1998–1999 2×64h ETD

2001 2×(2h de cours doctorat(a) Louvain, B Biolectrochemistryet 2002 + 16h TP)

2002–2003 8h de cours DEA Provence BioelectrochimiePhysicochimie(b)

2003–2004 8h de cours DEA Provence BioelectrochimiePhysicochimie(b)

2004–2005 8h de cours M2 Orsay Transfert d’electronsBiophysique(c) dans les sytemes biologiques

8h de TP M1 Provence Introduction a laChimie Bioenergetique

2005–2006 8h de cours M2 Orsay Transfert d’electronsBiophysique(c) dans les sytemes biologiques

1h de cours formation cont.(d) Lisbonne, P Introduction toProtein Film Voltammetry

8h de TP M1 Provence Introduction a laChimie Bioenergetique

2006–2007 3×4h TD/TP Math-spe. Encadrement de TIPE (e)

(a)Dans le cadre d’une ecole thematique europeenne intitulee “Metals in biology” et or-ganisee par R. Chrichton & C. Veeger a l’Universite de Louvain la Neuve, Belgique. Ellereunissait chaque annee pendant 10 jours 30 a 40 doctorants de tous les pays d’Europe et unedouzaine d’enseignants. Les enseignements concernaient les techniques qui permettent l’etudedes metalloproteines (spectroscopies, electrochimie, biologie moleculaire. . . ), des TP par pe-tits groupes et une deuxieme serie de cours sur les differentes familles de metalloproteines.Deux generations d’etudiants ont eu la chance de suivre cette formation qui n’a pas ete re-conduite, faute de subventions, depuis 2003.

(b) Resp. J.-P. Aycard, Universite de Provence.

(c) Resp. J.-P. Mahy, Universite d’Orsay.

(d) Dans le cadre d’un ecole thematique “bioelectrochimie” organisee par J. Moura al’Universite Nouvelle de Lisbonne, Portugal.

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(e) “Travaux d’Initiative Personnelle Encadres,” dont l’un des objectifs est l’initiationa la demarche de recherche scientifique. http://prepas.org/renseignementselevescpge/tipe.htm

Encadrement de jeunes chercheurs

– Coencadrement d’etudiants en these a Oxford : K. Heffron [P16] et L. Bateman [P17].– Coencadrement du DEA et de la These de Bettina Frangioni, 2002–2006. A la suite

de l’enseignement au DEA “Physicochimie, Analyse et Spectrometrie Moleculaire,” uneetudiante, Bettina Frangioni, a effectue un stage de DEA, puis une these (financementMRT) dans notre equipe ; elle y a developpe le couplage des approches electrochimiqueset spectroscopiques dans l’etude des enzymes de la famille DMSO reductase (nitratereductase, TMAO reductase). Sa these, coencadree par Bruno Guigliarelli pour la par-tie spectroscopie, et moi meme pour les etudes par electrochimie, a ete soutenue le11/10/2006.Bettina a obtenu les felicitations du Jury, que l’Universite de Provence accorde a environ50% des nouveaux docteurs.

– These de Fanny Leroux, 2006–2009 (coencadrement). L’ecole doctorale de chimie del’Universite de Provence nous a attribue une bourse de these (Ministere), sur un pro-jet lie aux etudes par electrochimie du fonctionnement des hydrogenases (transfertd’electrons, sensibilite a l’oxygene, etc.). Fanny Leroux a ete recrutee et a commenceson travail de these en octobre 2006.

– Post-doc ANR, 2007–2010 Dans le cadre du projet ANR-PCV que j’ai porte, un post-doctorant physicien et electrochimiste, Vincent Fourmond, a ete recrute a compter du15/04/2007.

Formation permanente

– Ecole de formation a la RPE organisee par l’ARPE, 14–20/05/2006, Carry-le-rouet.– Formation ACMO 16–18/03/2005 et 5–7/04/2005, Montpellier.

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4 Responsabilites collectives et management de la recherche

R1. Porteur d’un projet finance par l’ANR (2006-2009) associant deux autres laboratoires(A. Magalon, LCB, CNRS Marseille et D. Pignol, LBC, CEA Cadarache).

R2. Membre de la Commission de Specialistes groupe VII (Chimie), a l’Universite de Pro-vence, depuis 2004. Participation aux CSP liees au recrutement de 13 maıtres de confe-rence en chimie (sections 31–33), dont 2 pour etre affectes au BIP (B. Burlat, C. Baffert).

R3. Membre de la Commission Enseignement de l’UFR de Sciences de la Matiere a l’Uni-versite de Provence, 2004–2006.

R4. ACMO de l’Unite, depuis 2005. Formation (6 jours). Aide a la mise en place d’experiencescomportant un risque chimique important dans l’unite (arsenic, selenium). Controles,remises en etat, ramonages des sorbonnes. Gestion des petits incidents. Installations denouveaux equipements de securite.

R5. Rapporteur de 7 articles soumis a JACS, J. Phys. Chem. B, BBA-Bioenergetics etBioelectrochemistry.

R6. Rapporteur- d’un projet ANR blanc 2006 dans la CSD Chimie, a la demande de A. Deronzier- d’un projet soumis en 2007 a la “Technology Foundation STW” hollandaise, elle memefinancee par la “Netherlands Organisation for Scientific Research,” et le “Dutch Ministryof Economic Affairs.”- d’un projet soumis a la Region Midi-Pyrenees en 2007.

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5 Description breve des travaux jusqu’a la these

5.1 L’hydroxyde de nickel : materiau electroactif d’intercalation (1995–

1996)

Scientifique du contingent pendant l’annee scolaire 1995–1996, j’ai ete affecte dans legroupe “Energie - Materiaux pour batteries”1 alors dirige par Claude Delmas a l’Institut deChimie de la Matiere Condensee de Bordeaux (ICMB), pour y etudier le fonctionnement dumateriau des electrodes positives de plusieurs types d’accumulateurs alcalins : l’hydroxyde denickel. Dans ces electrodes, le stockage d’energie se fait schematiquement via la transformationde l’hydroxyde de nickel Ni(OH)2 en oxyhydroxyde NiOOH. Alors que le premier brevet surl’utilisation de l’hydroxyde de nickel a ete depose au tout debut du siecle dernier, les differentesphases solides impliquees au cours du cyclage n’ont ete identifiees que dans les annees 1960,et le fonctionnement de l’electrode de nickel n’est encore connu aujourd’hui que de facon tresschematique.

Les reaction electrochimiques et les transformations structurales mises en jeu sont en effetcomplexes. L’hydroxyde de nickel existe sous deux formes, anhydre et hydratee, auxquellescorrespondent respectivement deux phases solides oxydees. Ces quatre phases solides sontsusceptibles d’etre impliquees simultanement ou successivement au cours du cyclage d’unaccumulateur commercial. Les etudes de l’hydroxyde sont difficiles pour deux raisons. Toutd’abord, les phases qui interviennent en cours de cyclage sont mal cristallisees, ce qui rend leuranalyse par des techniques de rayons X malaisee. D’autre part, les phases oxydees decomposentspontanement le solvant ; le potentiel de l’electrode est donc mixte (et donc relie de facon nontriviale a la composition de la matiere active) et le plus souvent non-stationnaire. La plupartdes etudes rapportees dans la litterature portent sur l’effet de l’addition a la matiere activede certains “dopants” susceptibles d’augmenter les performances de la batterie, alors que lefonctionnement de l’hydroxyde pur est encore aujourd’hui mal compris. C’etait l’objectif demon travail que de reprendre l’etude fondamentale de l’hydroxyde de nickel non substitue.

Principaux resultats Au cours de cette annee, nous nous sommes interesses aux struc-tures cristallines des differentes phases solides impliquees, mais l’essentiel de notre travaila porte sur la capacite residuelle a bas potentiel (fig. 1), appelee “second plateau,” parcequ’elle se manifeste par un palier a bas potentiel en fin de reduction galvanostatique del’oxyhydroxyde (la duree de ce palier peut atteindre 30% de la capacite faradique totale del’electrode). Des explications divergentes ont ete enoncees depuis les annees 1960. Contraire-ment a ce qui etait propose dans la litterature, nous avons prouve que ce second plateau endecharge n’etait pas lie a la reduction de l’oxygene et qu’il pouvait etre observe en l’absence dela phase oxydee hydratee. Il etait aussi propose que le second plateau soit une caracteristique

1http://www.icmcb-bordeaux.cnrs.fr/groupes/groupe2.html

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Fig. 1: Illustration de la capaciteresiduelle a bas potentiel de l’electrodepositive d’hydroxyde de nickel. (a) Volt-amperogramme cyclique (regime poten-tiostatique) de l’hydroxyde de nickel. Lareduction de l’oxyhydroxyde NiOOH enhydroxyde Ni(OH)2 s’effectue a deux po-tentiels distincts 0.35 et −0.2 V vs. HgO.Cette deuxieme etape de reduction cor-respond a la capacite residuelle. (b) Encyclage galvanostatique, les deux paliersde potentiels observes pendant la chargede l’electrode correspondent a l’oxydationde l’hydroxyde en oxyhydroxyde et audegagement d’oxygene. Lorsque le courantest inverse (a t > 30 h ici), la reductionde l’oxyhydroxyde s’effectue a deux poten-tiels distincts, marques par deux plateaux[P1].

thermodynamique de la matiere active et que sa duree soit liee au diagramme de phase dusysteme NiOOH/Ni(OH)2. En effectuant des mesures de diffraction des rayons X tres precises,nous avons montre que ce diagramme de phase est tres different de celui qui etait admis jus-qu’alors et que le domaine de solution solide qui existe pres de la composition Ni(OH)2 esttrop etroit pour etre simplement lie a l’apparition du second plateau. Nous avons ensuiteinterprete la forme inhabituelle des courbes de relaxation de potentiel a l’arret du courant,et la caracterisation des courbes de decharge sur une large gamme de courant (4 ordres degrandeur) nous a finalement permis de proposer une interpretation du phenomene basee surl’existence d’heterogeneites spatiales de structure lors du processus de decharge [P1].

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Anode

Cath

ode

Fig. 2: Representation schematique de lacellule d’electrolyse et du depot (celui-cin’est pas a l’echelle). Typiquement, la dis-tance entre les electrodes est 10cm, la lar-geur des plaques de verre 5cm, le diametredes electrodes, qui fixe la distance entre lesplaques 30µm−1mm. La cellule est rem-plie par capillarite d’une solution aqueusedu sel d’un cation metallique en concen-tration 0.01 − 1M, et les densites decourant imposees peuvent atteindre 100mA/cm−2.

5.2 Instabilites morphologiques au cours d’experiences d’electrodeposition

(1996–1999)

Le sujet de mon DEA et de ma these etait l’etude de processus de structuration interfacialedans des systemes electrochimiques. Depuis les travaux de Mandelbrot sur les objets fractals,2

de nombreux systemes physiques, chimiques ou biologiques qui permettent de generer en coursde croissance des formes complexes ont ete etudies.3 Des travaux sur la digitation visqueuse, lescroissances bacteriennes, la solidification de corps purs surfondus ou d’alliages, la combustionet l’electrodeposition ont permis de montrer que leur caracteristique commune est que leprocessus de transport qui “nourrit” l’interface au cours de la croissance est l’etape limitanteen vitesse. On parle de “croissance laplacienne” lorsque ce processus de transport est de typediffusif.

Dans ce contexte, l’electrodeposition en cellule mince est l’un des systemes experimentauxles plus etudies. Cet enthousiasme4 tient autant a l’invraisemblable diversite des morpholo-gies obtenues qu’a l’apparente simplicite avec laquelle ces experiences peuvent etre mises enœuvre. Il s’agit d’electrolyser une solution aqueuse du sel binaire d’un cation metallique (sanselectrolyte support) dans une cellule quasi-bidimensionnelle constituee de deux plaques deverre espacees de quelques centaines de microns par deux fils metalliques, qui jouent aussi lerole d’electrodes (fig. 2). Un depot metallique ramifie croıt alors sur la cathode.

Si l’experience est aisee, son interpretation reste difficile parce que de nombreux processusphysiques et chimiques interagissent au cours de la croissance et influent sur la forme dudepot. Pendant les annees 1990, des etudes systematiques menees par de nombreuses equipesont permis de mettre a jour certains d’entre eux. Il a par exemple ete possible de mettre enevidence l’effet sur la morphologie de reactions chimiques parasites (qui entrent en competition

2Mandelbrot, “Les Objets fractals : forme, hasard et dimension, survol du langage fractal,” coll. Poche(1999).

3Ben-Jacob & Garik, Nature 343 523 (1990) “The formation of patterns in non-equilibrium growth.” http:

//dx.doi.org/10.1038/343523a0.4Brady et al., Nature 309 225 (1984) “Fractal growth of copper electrodeposits” http://dx.doi.org/10.

1038/309225a0

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(a)

(b)

(c)

(d)

(e)

Fig. 3: Visualisation par interferometriedu champ de concentration en electrolyteautour d’un depot de cuivre dans une cel-lule de tres faible epaisseur (50 µm). Ledepot est represente en noir, a gauchede chacune des images et le champ deconcentration mesure par interferometrieest code sous forme de lignes de niveaux.L’electrolyte est concentre a droite, loindu depot, et sa concentration diminuepres du depot. L’electrolyte utilise ici estdu chlorure cuivrique. Taille des images :2 × 7 mm et 0.4 mm × 0.4 mm pourles deux agrandissements des figures (a)et (b). (a) Depletion, (b) Destabilisationlorsque la concentration interfaciale de-vient tres petite, (c) Selection, (d) Crois-sance, (e) Corrosion, lorsque les gra-dients de concentration relaxent et que lesions cuivriques et chlorures reagissent aucontact du cuivre pour former du chlorurecuivreux.

avec la reduction du cation metallique) et de reveler des phenomenes de transport complexes(convectifs en particulier), mais il n’est pas encore possible de prevoir la forme du depot enfonction des parametres experimentaux.

Principaux resultats Pour avancer dans la comprehension de ces processus, il noussemblait que deux conditions devaient etre remplies. D’une part, il fallait determiner desconditions experimentales pour lesquelles la complexite du systeme est reduite ; c’est ce quenous avons fait en choisissant des conditions telles que tous les processus convectifs sontamortis. D’autre part, il est tres utile d’utiliser des techniques de caracterisation in situ desprocessus mis en jeu ; c’est pour cette raison que nous avons mis au point au CRPP, etutilise tout au long de notre travail, un dispositif d’interferometrie a modulation de phase,permettant de mesurer, de facon precise et resolue en temps, les champs de concentrationbidimensionnels en electrolyte autour des depots, pendant leur croissance (fig. 3) ; la mise enœuvre de cette technique est decrite dans l’encart page 21.

Nous avons analyse successivement, et de facon quantitative, les differentes phases du

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processus d’electrodeposition, a savoir la depletion de l’interface cathodique (figure 3a, [P4]),sa destabilisation (fig. 3b, [P7]), la croissance des depots ramifies (fig. 3d, [P6, P12]) et leurcorrosion apres l’arret du courant (fig. 3e, [P9]). L’interpretation des certains resultats n’auraitsans doute pas ete possible sans une etroite collaboration avec des theoriciens : Juan Elezgarayau CRPP et Martin Z. Bazant au MIT ont en particulier montre beaucoup d’interet pour cesetudes.

Sans entrer dans le detail de nos resultats, nous voudrions ici resumer les idees essentiellesqui emergent de ce travail.(i) Dans la plupart des etapes que nous avons etudiees, il est a ete possible de rendre comptede la forme du champ de concentration experimental en resolvant une equation de diffusionpour le champ de concentration equivalente.5 Notre approche se distingue donc de nombreuxtravaux anterieurs dans lesquels les auteurs supposaient que la migration pouvait assurer seulele transport.6

(ii) Notre etude a repose la question du role de la rupture de l’electroneutralite dans ladynamique du systeme7 : la destabilisation de l’electrode [P7] et la vitesse d’avancee del’interface du depot [P6] peuvent etre interpretees en faisant abstraction de tels effets, memes’il existe des cas ou la presence d’electroconvection temoigne de l’existence de charges noncompensees pres de l’interface.(iii) Une caracteristique essentielle du depot est son extreme porosite. Il est remarquable quela concentration moyenne en atomes de metal dans la partie de la cellule envahie par le depotsoit du meme ordre de grandeur que la concentration en ions metalliques dans la solution. Sicette propriete du depot avait ete etablie bien avant le debut de mon travail de these, nousavons montre quelles pouvaient en etre les implications lors de la modelisation des etapes decroissance [P6, P11, P12] et de corrosion [P9] des depots. Nous avons pu donner des imagestres satisfaisantes de ces processus a l’aide de modeles dans lesquels il est fait abstraction de lastructure microscopique de l’interface metallique. Dans ces approches “champ moyen,” il suffitde caracteriser le depot par sa concentration locale en atomes de metal, independamment de sastructure interne et la cinetique interfaciale peut etre decrite a l’aide de lois de type cinetiquehomogene. Cette demarche, totalement originale dans le contexte de l’electrodeposition encellule mince, est illustree par le premier des articles inseres a la fin de ce memoire.8

5Dans le cas d’une solution d’un electrolyte binaire (contenant des cations et des anions d’un seul type,CuCl2 par exemple), la concentration equivalente est C = z+C+ = −z−C−, ou C+/− est la concentration encation/anion, et z+/− sa charge algebrique.

6“In the thin-cell electrochemical deposition of metals, the interfacial velocity is shown, in the regimedominated by migration transport, to match the drift velocity of the counterion. . . ” (les italiques sont lesnotres), dans l’abstract de Melrose et al., Phys. Rev. Lett. 65 3009 (1990) “Interfacial velocity in electrochemicaldeposition and the hecker transition” http://dx.doi.org/10.1103/PhysRevLett.65.3009

7Avant notre travail, il etait considere que “(. . . ) ramified growth is a direct consequence of the creationof a space charge upon anion depletion in the vicinity of the cathode,” cf l’abstract de Chazalviel, Phys.Rev. A 42 7355 (1990) “Electrochemical aspects of the generation of ramified metallic electrodeposits” http:

//dx.doi.org/10.1103/PhysRevA.42.73558Le manuscrit (9.6Mb) est disponible a l’adresse : http://bip.cnrs-mrs.fr/bip07/pdf/leger_these.pdf

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Les variations locales de concentration dansla cellule d’electrolyse entraınent des variationsproportionnelles d’indice optique de la solutionet de trajet optique pour un faisceau qui la tra-verse, qui peuvent etre mises en evidence parinterferometrie. Le schema de principe de l’in-terferometre de type Mach-Zehnder que nousavons mis au point est represente ci-dessous.

CCD

LASERFS

CSM1

M2S1

λ/4

λ/4

CCDL2

L1 OPZT

GBF

Le faisceau lumineux monochromatique estsepare en deux bras dont l’un se reflechit sur lemiroir M1 et traverse la cellule d’electrochimie.L’intensite detectee en chaque point x, y dudetecteur CCD s’ecrit :

Ix,y = I0x,y

(1 + mx,y cos

[ϕx,y + ϕref

x,y

])(1)

ou ϕx,y est le dephasage proportionnel au che-min optique dans la cellule, et donc a la concen-tration locale en electrolyte que nous cher-chons a mesurer. Une ligne de meme inten-site (une frange d’interference) correspond doncen premiere approximation a une zone d’iso-concentration dans la cellule, mais la relationentre I et (ϕ + ϕref) n’est pas univoque parce

que dans l’equation 1, les termes I0 et msont aussi des inconnues. On peut resoudre ceclassique “probleme de phase” en enregistrantpar exemple cinq images (indicees i) pour desdephasages additionnels i2π

5 entre les deux brasde l’interferometre.

Iix,y = I0

x,y

(1 + mx,y cos

[ϕx,y + ϕref

x,y + i2π

5

])(2)

(La facon la plus simple d’introduire cedephasage est de deplacer le miroir M2 a l’aided’un translateur piezo electrique.) Pour chaquepoint x, y, le systeme d’equations 2 contientmaintenant 5 observables Ii pour seulement 3inconnues (I0, m et (ϕ + ϕref)) ; le dephasageentre les bras de l’interferometre est calcule sim-plement par inversion :

ϕx,y + ϕrefx,y = tan−1

2(I2x,y − I4

x,y)2I3

x,y − I5x,y − I1

x,y

(3)

La phase de reference ϕref peut etre enre-gistree dans une experience preliminaire et sous-traite des phases determinees en cours de crois-sance du depot ; cette technique permet doncde faire de l’interferometrie holographique avecbeaucoup de souplesse, une bonne exactitude(environ 1% d’erreur sur la concentration enelectrolyte et un bruit < 4mM, dans une cel-lule de 50µm d’epaisseur), mais aussi une bonneresolution spatiale dans le plan (x, y) (quelquesµm) et temporelle (typiquement, des salvesd’images etaient enregistrees en moins d’une se-conde toutes les 30s au cours d’une experiencequi durait plus d’une heure).

(i=1) (i=2) (i=3) (i=4) (i=5)

Ci-dessus, de gauche a droite, serie d’images dephasees d’environ 2π/5, image du depot enregistreealors que l’obturateur “O” est ferme, et champ de concentration calcule, code en utilisant deslignes de niveau. Taille de l’image : 5× 5 mm.

Encart 5.1: Mesure du champ de concentration bidimensionnel dans une cellule d’electrolysepar une technique d’interferometrie a modulation de phase temporelle.

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6 Travaux post-doctoraux (1999–2002)

6.1 Contexte

J’ai passe trois ans dans le groupe de Fraser Armstrong, au laboratoire de Chimie Inorga-nique de l’Universite d’Oxford. Pendant cette periode, l’equipe comptait trois post-doctorants,sept doctorants et quatre stagiaires “under-graduate.”

F. Armstrong s’est illustre depuis le debut des annees 1980, alors qu’il etait lui-memepost-doctorant a Oxford dans le groupe d’un pionnier de la bioelectrochimie, H. Allen O.Hill,9 par ses etudes electrochimiques de ferredoxines.10 A cette epoque, pour de nombreusesequipes qui travaillaient dans le domaine de la bioelectrochimie faradique, la voltammetrieetait au mieux un outil permettant de mesurer des potentiels de reduction. La contributionscientifique d’Armstrong est exceptionnelle parce qu’il a au contraire demontre a de nom-breuses reprises qu’elle permettait d’obtenir des informations cinetiques, toujours originaleset souvent pertinentes d’un point de vue mecanistique ou physiologique. Je pense en parti-culier aux etudes de metallation de clusters [3Fe4S],11 aux conversions [4Fe4S]→[3Fe4S] dansdes conditions electrochimiques qui miment le stress oxydant,12 ou a la serie de travaux tresspectaculaires sur les transferts de protons.13

Parmi les nombreuses possibilites offertes par les techniques electrochimiques, Armstronga demontre les avantages de la configuration appelee “protein film voltammetry” dans laquelleun transfert d’electrons (TE) direct se produit entre l’electrode et la proteine adsorbee : dansles cas favorables, les quantites de materiel biologique necessaires sont minuscules, les signauxsont de faible amplitude, mais mieux definis et plus simples a analyser que lorsque la reponseest convoluee par un processus de transport de type diffusif et la fenetre temporelle est elargieparce que de plus hautes vitesses de balayage sont aisement accessibles.

Au debut des annees 1990, il a ete parmi les premiers a obtenir des signaux electrochimiquescatalytiques avec des enzymes adsorbees sur des electrodes. Le changement d’etat redox del’enzyme resultant de la transformation du substrat est continuellement compense par unflux d’electrons qui se produit entre le site actif et l’electrode. Ce flux est simplement mesurecomme un courant dont la valeur est proportionnelle a la vitesse de turnover de l’enzyme(voir l’encart page 23).

9http://www.chem.ox.ac.uk/researchguide/haohill.html10Des petites proteines de transfert d’electrons, de masse moleculaire voisine de 15 kDa, contenant un ou

deux centres FeS.11Butt et al., JACS 119 9729 (1997) “Electrochemical potential and pH dependences of [3Fe4S]→[M3Fe4S]

cluster transformations (M=Fe, Zn, Co, and Cd) in ferredoxin III from Desulfovibrio africanus and detectionof a cluster with M=Pb” http://dx.doi.org/10.1021/ja971403a

12Camba et al., Biochemistry 39 10587 (2000) “Investigations of the Oxidative disassembly of Fe-S clustersin Clostridium pasteurianum 8Fe ferredoxin using pulsed-protein-film voltammetry” http://dx.doi.org/10.

1021/bi000832+13Chen et al., Nature 405 814 (2000) “Atomically defined mechanism for proton transfer to a buried redox

centre in a protein” http://dx.doi.org/10.1038/35015610

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Une enzyme redox multicentre est constituee d’un site actif (SA) implique dans la partie purementchimique de la reaction catalytique et le plus souvent enfoui au cœur de la proteine. Le processuscatalytique complet fait schematiquement intervenir deux etapes : l’oxydation/la reduction dusubstrat change l’etat redox du site actif, et celui-ci est regenere suite a une serie de transfertsd’electrons (TE) depuis/vers un partenaire redox soluble. Les electrons sont transferes a l’interieurde la proteine via un ou plusieurs centres redox (par exemple des centres FeS ou des hemes) dontl’un est expose a la surface de la proteine. La facon classique de mesurer l’activite d’une enzymeredox consiste a utiliser un partenaire redox dont on peut suivre le changement de concentrationpar spectroscopie optique.En electrochimie directe au contraire, une electrode se substitue au partenaire redox soluble.L’enzyme est adsorbee sur une surface conductrice dans une configuration telle que le centredistal peut etre oxyde ou reduit suite a une etape de TE interfacial. Il en resulte un flux d’electronqui est simplement mesure comme un courant dont la valeur est directement proportionnelle a lafrequence de turnover de l’enzyme. Dans une experience typique, l’electrode est tournante (pourforcer le flux de substrat vers la surface de l’electrode et idealement s’affranchir de la limitationdue a la diffusion) et le potentiel d’electrode est balaye pour enregistrer un voltamperogrammecomme celui qui est trace ci-dessous.

Encart 6.1: Principe de la mesure d’activite en electrochimie directe.

Le gain d’information par rapport a toutes les autres techniques de mesure d’activite estimmense puisque la vitesse est maintenant mesuree en fonction du potentiel d’electrode, quipermet d’imposer la force motrice pour le processus catalytique et de faire varier (indirecte-ment) l’etat redox de l’enzyme tout en maintenant des conditions stationnaires de turnover.La figure 4 montre les voltamperogrammes catalytiques pour les sous-unites solubles de deuxenzymes homologues, la succinate deshydrogenase (Succinate-Quinol oxydoreductase, SQRou Complexe II) et la fumarate reductase (Quinol-Fumarate oxydoreductase, QFR). Dansle premier cas, l’activite est mesuree en presence de succinate et de fumarate, et le courantnegatif a bas potentiel resulte de la reduction du fumarate alors que le succinate est oxyde

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Fig. 4: Signaux catalytiques typiques ob-tenus pour les parties solubles du com-plexe II (succinate deshydrogenase), pa-nel A, et de la fumarate reductase, pa-nel B, dont les structures sont super-posees dans la fig. 5. NB : Dans tousles exemples discutes dans ce memoire,les donnees sont enregistrees en utilisantune electrode tournante et le transport dematiere n’est pas limitant. Dans le panelA, le signal est enregistre en presence desuccinate et de fumarate, alors que pour lafumarate reductase (panel B), l’experienceest realisee en presence de fumarate seule-ment. La fleche a −310mV dans le pa-nel B indique le potentiel de reduction ducentre [4Fe4S] median dans la chaıne deTE (fig. 5). Les formes complexes de cessignaux restent mal comprises.

a haut potentiel d’electrode. Le courant negatif dans la figure 4B revele la dependance enpotentiel de la vitesse de reduction du fumarate par la fumarate reductase.

Avec les premiers signaux catalytiques en electrochimie directe vinrent aussi les premieressurprises et difficultes d’interpretation. La forme du signal catalytique de la succinate deshydro-genase montre que l’activite fumarate reductase decroıt lorsque les conditions sont tropreductrices (a bas potentiel d’electrode, pour E < 100mV, fig. 4A). Cette decouverte ma-jeure, communiquee dans le journal Nature en 1992,14 a ete suivie de nombreuses autresetudes electrochimiques.15 Mais, alors que je commencais mon post-doctorat sept ans plustard, de l’aveu meme des auteurs, les bases moleculaires de cette extinction d’activite a baspotentiel restaient incomprises.16

Dans le cas de la fumarate reductase, les donnees electrochimiques publiees en 1993, puis

14Sucheta et al., Nature 356 361–362 (1992) “Diode-like behaviour of a mitochondrial electron-transportenzyme” http://dx.doi.org/10.1038/356361a0

15(a) Hirst et al., JACS 118 5031 (1996) “Electrocatalytic voltammetry of succinate dehydrogenase : directquantification of the catalytic properties of a complex electron-transport enzyme” http://dx.doi.org/10.

1021/ja9534361,(b) Hirst et al., JACS 119 7434 (1997) “Global observation of hydrogen/deuterium isotope effects on bi-

directional catalytic electron transport in an enzyme : direct measurement by protein-film voltammetry ”http://dx.doi.org/10.1021/ja9631413,(c) Pershad et al., BBA-Bio 1412 262 (1999) “Voltammetric studies of bidirectional catalytic electron trans-port in Escherichia coli succinate dehydrogenase : comparison with the enzyme from beef heart mitochondia”http://dx.doi.org/10.1016/S0005-2728(99)00066-3.

16“. . . the origin of the effect remains unclear.” Hirst et al., JACS (1996), op. cit., note 15a.

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Fig. 5: Superposition des structures desparties solubles de deux enzymes qui ca-talysent la conversion succinate/fumaratechez E. coli : la fumarate reductase (pdb1FUM) et la succinate deshydrogenase(pdb 1NEN, [P22]). Le site actif consisteen un groupe flavine (a gauche), leselectrons sont transferes le long d’unechaıne de centres FeS. On note la co-ordination inhabituelle du centre [2Fe2S]par un aspartate dans la succinatedeshydrogenase. Alors que les structuresde ces deux enzymes sont tres voisines,leurs proprietes catalytiques et en particu-lier electrochimiques sont tres differentes(fig. 4).

1997 montraient deja que l’activite n’augmente pas simplement lorsque les conditions sontrendues de plus en plus reductrices (fig. 4B). La vitesse de reduction du fumarate sembleacceleree (“boostee”) en-dessous d’un potentiel d’electrode qui correspond au potentiel dereduction du cluster median dans la chaıne de TE qui relie le site actif enfoui de l’enzyme ala surface de la proteine.17 L’origine de cet effet n’est toujours pas clarifiee.18

Peu avant mon arrivee a Oxford, H. Heering (alors post-doctorant chez Armstrong) avaitpose les bases d’une interpretation quantitative des vagues catalytiques a l’aide d’un modelecinetique incluant 9 constantes de vitesse.19 Le modele incluait les etapes de TE direct entrel’electrode et le site actif, la fixation du substrat a un seul des etats redox du site actif, etle transport du substrat vers l’electrode tournante sur laquelle l’enzyme est supposee etreadsorbee. En depit du nombre important de parametres, ce modele n’a pas la complexitesuffisante pour expliquer l’un des signaux reels obtenus a ce jour.

En l’absence de modele cinetique approprie, l’usage etait de caracteriser la largeur desvagues catalytiques par le parametre napp, mesure en parametrant le signal catalytique par

17(a) Sucheta et al., Biochemistry 32 5455 (1993) “Reversible electrochemistry of fumarate reductase immo-bilized on an electrode surface. Direct voltammetric observations of redox centers and their participation inrapid catalytic electron transport” http://dx.doi.org/10.1021/bi00071a023

(b) Heering et al., JACS 119 11628 (1997) “Direct detection and measurement of electron relays in a multicen-tered enzyme : voltammetry of electrode-surface films of Escherichia coli fumarate reductase, an Iron-Sulfurflavoprotein” http://dx.doi.org/10.1021/ja9723242

18Hudson et al., JACS 127 6977 (2005) “Electron transfer and catalytic control by the iron-sulfur clustersin a respiratory enzyme, E. coli fumarate reductase” http://dx.doi.org/10.1021/ja043404q.

19Heering et al., J. Phys. Chem. B 102 6889 (1998) “Interpreting the catalytic voltammetry of electroactiveenzymes adsorbed on electrodes” http://dx.doi.org/10.1021/jp981023r

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une sigmoıde centree sur un potentiel Ecat :

i =ilim

1 + exp[±nappF

RT (E − Ecat)] (4)

Des combinaisons ad hoc de sigmoıdes pouvaient etre utilisees pour decrire des signaux auxformes complexes.15 Les valeurs de napp typiques sont dans la fourchette 0.8–1.8, les plusgrandes valeurs correspondant aux vagues les plus abruptes. En depit du fait que des valeursnon-entieres de napp aient pu etre mesurees, ce parametre etait interprete comme etant lenombre d’electrons impliques dans l’etape limitante en vitesse du processus catalytique.20

Quant a Ecat, le “potentiel de l’enzyme,”15 seule sa dependance en pH pouvait etre discutee.

Dans l’equipe de Fraser Armstrong, je me suis convaincu que l’electrochimie directe seraitune bonne technique pour etudier le mecanisme d’enzymes redox a condition que l’on progressedans l’interpretation quantitative des signaux ; c’est avec cet objectif que j’ai travaille depuis.

6.2 Le cas le plus simple de l’oxydation du succinate par la fumarate

reductase de E. coli

Parmi tous les systemes qui etaient etudies a Oxford, j’ai d’abord choisi de m’interesser al’oxydation du succinate par la fumarate reductase de coli parce qu’elle donnait des signauxelectrochimiques apparemment simples (fig. 6). La raison fondamentale pour laquelle leurmodelisation a effectivement ete aisee est que cette enzyme reduit le fumarate tres efficacement(c’est la reaction physiologique), alors que la reaction inverse d’oxydation du succinate au siteactif flavinique est tellement lente que tout se passe comme si l’equilibre redox entre le siteactif et l’electrode n’etait pas perturbe par le processus catalytique, qui pourtant consommela forme oxydee du site actif. Dans cette limite, l’etat redox du site actif est simplement lieau potentiel d’electrode par la loi de Nernst meme si le systeme n’est pas a l’equilibre.

L’apparition du courant a haut potentiel d’electrode reflete la formation de l’etat redoxdu site actif competent pour oxyder le succinate et la courbe courant/potentiel peut etreinterpretee comme une simple courbe de titrage potentiometrique de la forme oxydee du siteactif. L’equation du courant en fonction du potentiel d’electrode est deduite en combinant deslois d’action de masse : le courant est egal au produit de la fraction du site actif qui est dansla forme oxydee par la fraction liee au substrat, multiplie enfin par le courant limite maximumcorrespondant a la vitesse de transformation du succinate dans le complexe enzyme-substratcompetent :

i =imaxlim /(1 + S

KO)

1 + exp[f(EQ/SQ − E)

]+ exp

[2f(EQ/HQ − E)

] (5)

S est la concentration en succinate, KO la constante de dissociation pour le site actif oxyde,

20“The n-value corresponds to the number of electrons in the rate-determining enzyme step.” Hirst et al.,JACS (1997), op. cit., note 15b.

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Fig. 6: Signaux catalytiques pour l’oxy-dation du succinate par la fumaratereductase de E. coli adsorbee sur uneelectrode tournante. Avant (A) et apres(B) correction du courant capacitif. Lesdifferents traits correspondent a desconcentrations croissantes en succinate[P15].

imaxlim = 2FAΓkcat, EQ/SQ et EQ/HQ les potentiels de reduction des couples quinone/ semiqui-

none et quinone/ hydroquinone du site actif flavinique, AΓ la quantite d’enzyme adsorbee surl’electrode, F la constante de Faraday, kcat est la frequence maximale de turnover (dans lesconditions les plus oxydantes et lorsque la concentration en substrat est saturante), f = F/RT .

Le numerateur de cette equation s’identifie au courant limite atteint a haut potentield’electrode pour une concentration en substrat donnee ; il impose l’amplitude globale du si-gnal et varie avec S selon une loi de type Michaelis-Menten, ilim = imax

lim /(1+S/KO). Une ob-servation plus interessante est que la dependance en potentiel de l’activite (au denominateur)est directement liee aux potentiels de reduction du site actif, qui peuvent ainsi etre determinesa partir d’un seul voltamperogramme, enregistre pour un pH et une concentration en sub-strat donnes. L’electrochimie directe apparaıt donc comme une technique unique en ce qu’ellepermet de mesurer le potentiel du site actif dans des conditions de turnover, alors que lesexperiences traditionnelles de titrage redox a l’equilibre ne sont pas compatibles avec lapresence de substrat, mais qu’on soupconne que sa fixation puisse changer significativementles proprietes de site actif.21

La figure 7A est un diagramme de Pourbaix representant les potentiels de reduction dusite actif flavine a une concentration en succinate donnee en fonction du pH. De la memefacon que ce diagramme permet de determiner la stœchiometrie electron/proton pour chaqueprocessus redox et les constantes d’acidite des differentes especes, l’interpretation de la facondont les potentiels de reduction du site actif dependent de la concentration en succinate a pH

21“Redox properties generally match catalytic function and when they do not, substrate binding often regu-lates the redox properties” M. Stankovitch, a propos des deshydrogenases, dans “Chemistry and Biochemistryof Flavoenzymes”, Franz Muller, ed. (1991).

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Fig. 7: Panel A : diagramme de Pour-baix pour les potentiels de reduction dusite actif flavine de la fumarate reductasede E. coli en presence de succinate1mM, determines en parametrant les si-gnaux catalytiques par l’equation 5. Leslignes continues sont les modelisations desdependances en pH, qui permettent dedeterminer les etats de protonation etles constantes d’acidite des differents in-termediaires. Panel B : variation des memepotentiels en fonction de la concentrationen succinate a pH 7. Q = flavine dansl’etat Quinone (oxyde), SQ = Semiqui-none (semi reduit), HQ = Hydroquinone(reduit) [P15].

fixe (fig. 7B) est simplement liee a l’affinite relative des differents etats redox du site actif pourle substrat. En dernier lieu, l’interpretation des donnees electrochimiques permet d’eluciderla succession d’evenements (transferts d’electrons, de protons, liaison avec le substrat) qui seproduisent au cours du demi-cycle catalytique conduisant a l’oxydation du site actif.

Cette etude n’a pas apporte d’information saisissante sur le fonctionnement de l’enzyme.Elle a cependant eu le merite de proposer une interpretation complete et intuitive d’un signalelectrochimique dans un cas limite simple. Elle a servi de base au fil des ans pour ajouter lesingredients physiques supplementaires dans des modeles permettant de modeliser des signauxplus complexes. Notre analyse relativisait surtout l’utilite de la description des signaux a l’aidede sigmoıdes caracterisees par des largeurs apparentes (l’equation 5 ne s’identifie pas a celled’une sigmoıde), et bat en breche l’idee que la valeur de napp est liee au nombre d’electronsimpliques dans l’etape limitante en vitesse dans le cycle catalytique20 : cet enonce n’a aucunsens dans ce cas precis.

6.3 L’effet du transfert d’electron interfacial et le cas de l’hydrogenase de

A. vinosum.

L’hypothese que l’activite de l’enzyme est faible, qui justifie le modele simple precedent,est contraignante d’un point de vue experimental : on prefere habituellement les enzymestres actives, et une enzyme dont l’activite est faible ne donnera de toutes facons un signal

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Fig. 8: Les signaux catalytiques pourl’oxydation de l’hydrogene par l’hy-drogenase NiFe de A. vinosum : on observeune transition entre une vague presquesigmoıdale a basse temperature vers uneforme etonnamment lineaire quand l’ac-tivite de l’enzyme augmente. Ces formespeuvent etre expliquees si l’on considereque les molecules d’enzyme ne sont pastoutes adsorbees sur l’electrode dans lameme orientation [P20].

detectable que si sa concentration surfacique est tres elevee, ce qui n’est pas toujours possiblea realiser. Pour elaborer un modele plus general et plus utile, il semblait alors naturel de leverl’hypothese que le turnover de l’enzyme est lent devant le transfert d’electron interfacial.

Dans l’appendice de la reference [P19], nous montrons qu’on peut considerer explicitementla cinetique de TE interfacial en imposant que les vitesses des transformations redox du siteactif suivent une loi de type Butler-Volmer. Par exemple :

kox = k0 exp[f

2(E − E0)

](6)

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Fig. 9: Diagrammes de Pourbaix pourles potentiels de reduction du site ac-tif de l’hydrogenase de A. vinosum,determines en parametrant les signauxcatalytiques de production d’hydrogene.Les lignes continues sont les modelisationsdes dependances en pH, qui permettentde determiner les etats de protonation etles constantes d’acidite des differents in-termediaires [P19].

ou E0 est le potentiel de reduction de la transition consideree et k0 la constante de vitesse asurtension nulle. Un TE interfacial lent (k0 < kcat) fait s’elargir la vague catalytique.

A lui seul, ce raffinement ne permet cependant pas de rendre compte des nombreusesdonnees experimentales qui ressemblent a celles representees sur la figure 8. Ce qui est sur-prenant dans ces signaux, c’est l’absence de plateau de courant a haut potentiel d’electrode.Lorsqu’on augmente E, la vitesse d’oxydation de l’enzyme augmente exponentiellement (se-lon la theorie de Butler-Volmer, eq. 6) puis sature (theorie de Marcus-Hush).22 Dans les deuxcas, on s’attend a ce que l’activite de l’enzyme tende vers une limite, soit parce que le TEinterfacial n’est plus limitant en vitesse, soit parce que sa vitesse ne depend plus du potentield’electrode ; ce n’est pas ce qui est observe sur la fig. 8.

Nous avons montre qu’on peut expliquer ce phenomene en considerant a la fois quele TE interfacial est partiellement limitant en vitesse (d’autant plus que l’enzyme est in-trinsequement active), et que la vitesse de TE interfacial n’est pas la meme pour toutesles molecules d’enzyme [P20]. Nous avons propose que cela resulte d’une distribution desorientations des enzymes sur l’electrode, qui entraıne une distribution des distances a traverslesquelles se produit le TE (la vitesse de TE decroıt typiquement de maniere exponentielleavec la distance sur laquelle il se produit). Selon ce modele, les enzymes pour lesquelles le TEinterfacial est lent ne contribuent qu’a des surtensions d’autant plus grandes que k0 est petit.La modelisation des donnees requiert qu’on se munisse d’une loi precise pour la densite deprobabilite de distance : nous justifions celle que nous avions choisie dans l’encart page 31.

En utilisant la nouvelle equation de courant, nous avons pu mettre en œuvre la mememethodologie que celle qui nous avait permis de determiner la sequence de reactions chi-miques couplees au TE vers le site actif dans le cas de la fumarate reductase : nous avonsparametre les voltammogrammes pour l’oxydation de l’hydrogene et la reduction des protonspar l’hydrogenase de A. vinosum a differents pH pour determiner les potentiels de reductionet les constantes d’acidite des intermediaires dans le cycle catalytique (fig. 9).

L’objectif de proposer une equation de courant “utile” a ete atteint puisque ce modele a

22Saveant “Elements of molecular and biomolecular electrochemistry : an electrochemical approach to elec-tron transfer chemistry,” Wiley-Interscience (2006).

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servi ulterieurement a interpreter les donnees obtenues pour deux enzymes tres differentes :arsenite oxydase23 et Complexe I.24

23Hoke et al., Biochemistry 43 1667 (2004) “Electrochemical studies of arsenite oxidase : an unusual exampleof a highly cooperative two-electron molybdenum center” http://dx.doi.org/10.1021/bi0357154

24Hirst & Reda, J. Phys. Chem. B 10 1394 (2006) “Interpreting the catalytic voltammetry of an adsorbedenzyme by considering substrate mass transfer, enzyme turnover and interfacial electron transport” http:

//dx.doi.org/10.1021/jp054783s

Le TE entre l’electrode et le site actif se produitvia une chaıne de clusters FeS. Habituellement,l’un de ces centres (celui qui est “distal” vis avis du site actif) est expose a la surface de laproteine et echange des electrons directementavec l’electrode. Si toutes les enzymes ne sontpas orientees de la meme facon sur l’electrode,cela entraıne une distribution des distances dsur lesquelles se produisent les TE interfaciaux,et une distribution des valeurs de k0, qui sontproportionnelles a exp(−βd).Dans la reference [P20], nous avons utilise sansla justifier vraiment une densite de probabiliteuniforme pour la distance sur laquelle s’effectuele transfert d’electron interfacial. C’est en effetla seule distribution qui permette de predire unerelation lineaire entre le courant et le potentield’electrode (fig. 8). Nous exposons ici le modelegeometrique qui nous a conduit a l’utiliser.

δd

φ

dd

θ0

electrode surface

R

On imagine que l’enzyme est une sphere, poseesur un plan (l’electrode) dans une orientationaleatoire. On repere a la surface de la sphere unpoint (le cluster distal) par lequel on supposeque les electrons vont etre transferes depuis/versl’electrode, et on cherche la probabilite que lepoint marque soit a une altitude comprise entre

d et d + δd.Cette probabilite est proportionnelle a l’aire dela portion de la sphere comprise entre ces deuxaltitudes (car la probabilite que le point marquearrive dans une region est proportionnelle a l’airede cette region). Pour calculer la surface dela region consideree, on la parametre en co-ordonnees spheriques par φ ∈ [0, 2π] (inva-riance par rotation autour de l’axe vertical) etθ ∈ [θ0, θ0 + δθ] ou θ0, l’angle avec la verticale(θ ∈ [0, π]), est defini par

R(1− cos θ0) = d (7)

L’aire se calcule ainsi en coordonneesspheriques :

A =∫ 2π

φ=0

∫ θ0+δθ

θ=θ0

R2 sin θdθdφ (8)

En utilisant R sin θ0δθ = δd on montre quecette probabilite est bien independante de d :

proba =12

δd

R(9)

(NB : ce n’est pas le cas si on fait le calcul en di-mension 2, avec un cercle au lieu d’une sphere).Il n’est certes pas raisonnable de faire l’hy-pothese que l’orientation de l’enzyme surl’electrode est completement aleatoire, mais laconclusion est identique si les orientations pos-sibles de l’enzyme sont restreintes, par exemplea un cone centre sur le centre de la sphere(pourvu que toutes ces orientations restentequiprobables).

Encart 6.1: Justification de la loi de densite de probabilite de distance, utilisee pour modeliserla distribution de constantes de vitesse de TE interfacial.

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Fig. 10: Les enzymes de la famille de la DMSO reductase sont caracterisees par un site actif

molybdene mononucleaire coordinne par deux molybdopterines et le plus souvent par un 5eme

ligand proteique. Elles catalysent des reactions variees (par exemple la reduction du DMSO,du TMAO, du nitrate, ou l’oxydation du formate, du nitrite ou de l’arsenite) mais les basesmoleculaires de la selectivite et directionnalite de ces enzymes ne sont pas comprises. Figurerealisee par Pascal Arnoux (pdb 1DMR, 1G8K, 1OGY, 1Y4Z).

6.4 Un signal catalytique complexe : celui de la DMSO reductase de E. coli

La famille de la DMSO reductase rassemble de nombreuses enzymes (DMSO, TMAOet nitrate reductases, formate, nitrite et arsenite oxydases etc.) tres variees en termes destructures quaternaires et de contenus en centres metalliques (fig. 10), mais qui catalysent leplus souvent des reactions de transfert de groupement oxo et ont en commun un site actifcontenant un ion molybdene coordinne par les quatre thiolates de deux molybdopterines. Unesous-classification differencie ces enzymes selon la nature du cinquieme ligand du molybdene(serine, (seleno)cysteine, aspartate ou molecule d’eau). Les enzymes les plus simples de cettefamille ne contiennent que le cofacteur a Mo, toutes les autres possedent en plus un clusterFeS “proximal” (vis-a-vis du Mo). Parmi les plus complexes en structure et composition, laDMSO reductase et la nitrate reductase membranaire de coli contiennent 5 clusters FeS etdeux hemes b ; cette derniere enzyme est etudiee de longue date a Marseille.25

25e.g. Guigliarelli et al., EJB 207 61 (1992) “EPR and redox characterization of iron-sulfur centers in nitratereductases A and Z from Escherichia coli. Evidence for a high-potential and a low-potential class and theirrelevance in the electron-transfer mechanism” http://dx.doi.org/10.1111/j.1432-1033.1992.tb17020.x

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Fig. 11: Signaux catalytiques pour lareduction du DMSO par la DMSOreductase (membranaire) de coli. Nousavons propose le premier modele cinetiqueexpliquant qualitativement que l’activitereductase n’est pas maximale dans lesconditions les plus reductrices [P16].

MoV

k4[H+]

MoV:H MoIV:H

k5[H+]

MoIVMoVI

k2

fast

Fig. 12: Schema minimal permettantd’expliquer qualitativement les signauxcatalytiques de la fig 11. Le site actif dela DMSO reductase est un atome de mo-lybdene qui peut exister dans trois degresd’oxydation : VI, V et IV. Le Mo reduitpeut transformer le DMSO en DMS, ce quiregenere le Mo dans sa forme oxydee.

La figure 11 montre les signaux catalytiques obtenus a Oxford avec la DMSO reductasemembranaire de E. coli. Dans des conditions alcalines, lorsque le potentiel d’electrode estrendu de plus en plus negatif, on observe une augmentation de l’activite avant qu’elle nedecroisse a plus bas potentiel, et la forme du signal rappelle celui obtenu dans le cas de lasuccinate deshydrogenase (fig. 4A) alors que ces enzymes n’ont rien en commun. L’attenuationde l’activite a bas potentiel n’est pas observee dans des conditions acides.

Nous avons note l’analogie qui existe entre l’existence d’une fenetre de potentiel danslaquelle l’activite de la DMSO reductase est maximale et les habituelles courbes en clocherepresentant l’activite d’une enzyme en fonction du pH. De la meme facon qu’une activiteenzymatique optimale requiert habituellement que le pH soit modere, des etapes importantesdans le cycle catalytique d’une enzyme redox pourraient se produire quand le site actif estdans un etat redox intermediaire. C’est l’hypothese qui est formalisee dans la figure 12 :nous considerons qu’une etape de protonation cruciale dans le mecanisme et partiellementlimitante en vitesse, schematisee verticalement, peut se produire avant ou apres la reductiondu MoV, mais qu’elle est plus rapide dans le premier cas (k5 > k4). Selon ce schema, l’ordre desevenements dans le cycle catalytique depend de la force motrice appliquee26 : si la reductiondu MoV est lente, a potentiel moderement bas, l’etape de protonation fait intervenir le MoV,alors qu’a plus bas potentiel, le Mo est reduit rapidement avant d’etre protone lentement, ce

26Il a ete propose ulterieurement par Bray et al que la reduction du DMSO et l’oxydation du DMS procedentselon deux mecanismes differents. Biochemistry 40 9810 (2001) “Reactions of dimethylsulfoxide reductase inthe presence of dimethyl sulfide and the structure of the dimethyl sulfide-modified enzyme” http://dx.doi.

org/10.1021/bi010559r

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qui entraıne une diminution de l’activite.C’etait la premiere fois que l’explication d’une forme de signal catalytique complexe etait

basee sur un schema cinetique, mais nous avons du nous contenter d’une interpretation qua-litative des donnees, en particulier en raison de problemes experimentaux compliquant leuracquisition (les signaux etaient difficiles a enregistrer parce que le film de DMSO reductase esttres instable), et le projet a finalement ete abandonne. Nous n’avons pu reprendre ce travailde modelisation que recemment, en etudiant une autre enzyme de la meme famille (la nitratereductase periplasmique), dont les signaux catalytiques sont relativement similaires mais plussimples a acquerir (cf page 45).

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7 Insertion au BIP

7.1 Introduction

A Marseille, l’Institut Federatif de Recherche en Biologie Structurale et Microbiologie(IBSM) regroupe sur un meme campus CNRS sept unites de recherche, dont l’UPR 9036,Unite de Bioenergetique et Ingenierie des Proteines (BIP), dirigee par Mireille Bruschi, quicomptera a son renouvellement en 2008 20 chercheurs et enseignants-chercheurs. Cette unitea pour champ thematique la caracterisation des chaınes respiratoires bacteriennes et desmetalloenzymes qui y sont impliquees (hydrogenases, en particulier). Le BIP developpe uneapproche pluridisciplinaire qui inclut des techniques physiques, chimiques, genetiques, ainsique de biologie moleculaire et structurale pour l’etude des relations structure-fonction dansles metalloenzymes.

J’ai ete recrute a l’automne 2002 au BIP, dans l’equipe “Biophysique des Metalloproteines,”dirigee par le professeur Bruno Guigliarelli. Cette equipe regroupe sept enseignants-chercheurset un ingenieur de l’Universite de Provence,27 une technicienne CNRS,28 trois etudiants enthese et moi-meme. Les spectroscopies de Resonance Paramagnetique Electronique (RPE)multifrequence, ENDOR et MCD sont les techniques experimentales principalement utiliseesdans ce groupe. Elles permettent l’etude du mecanisme catalytique de plusieurs enzymes res-piratoires, etude basee sur l’analyse des proprietes structurales, electroniques et redox descentres presents dans ces systemes complexes et d’intermediaires reactionnels, qu’ils soientthermodynamiquement stables ou pieges. Mon recrutement avait pour objectif de developperdans ce groupe une strategie d’etude complementaire, de type cinetique, en important lescompetences que j’avais pu acquerir au cours de mon post-doc.

Nous avons tourne nos efforts vers des oxydoreductases dont les sites actifs et les architec-tures sont completement distincts, en collaboration avec diverses equipes du BIP ou d’autreslaboratoires en France et a l’etranger, dont j’ai fait la liste ci-dessous.Enzyme / Origine Equipes partenaires Laboratoire Pubs.

Hydrogenase NiFe, D. fructosovorans M. Rousset BIP Marseille [P24,P27]J. Fontecilla-Camps CEA GrenobleL. Cournac CEA CadaracheV. Fernandez CSIC Madrid

Hydrogenase I (thermophile), Aquifex M.-Th. Giudici-Orticoni BIP Marseille [P25]Nitrate reductase, R. sphaeroides D. Pignol CEA Cadarache [P23]Nitrite reductase, D. desulfuricans I. Moura & G. Almeida Lisbonne [P28]Flavocytochrome b2, Levure F. Lederer CNRS Gif [P26]

27Bruno Guigliarelli (Pr), Patrick Bertrand (Pr), Andre Fournel (Mcf), Valerie Belle (Mcf), Stephane Gri-maldi (Mcf, depuis 2003), Benedicte Burlat (Mcf, depuis 2005), Carole Baffert (Mcf, depuis 2006), EmilienEtienne (Ingenieur, depuis 2006).

28Mireille Woudstra.

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C. Leger. UPR 9036. Memoire d’HDR. 2007.

De nouvelles collaborations sont en train de se mettre en place :

Hydrogenase a Fer / C. acetobutilicum P. Soucaille & L. Girbal CNRS/INRA ToulouseNitrate reductase membranaire, E. coli A. Magalon LCB/CNRS MarseilleArsenite oxydases meso- et thermophiles W. Nitschke BIP Marseille

La mise en place de l’equipement scientifique necessaire a la realisation des experiencesd’electrochimie directe s’est effectuee en collaboration avec les services communs de l’IBSM etl’equipe “Electrochimie et spectroelectrochimie des proteines et de leurs modeles” du BIP.29

7.2 Soutiens financiers obtenus

L’achat du materiel necessaire au demarrage des experiences a ete possible grace a unedotation specifique a notre projet de la part de la Ville de Marseille (en janvier 2004), et ausoutien financier au laboratoire de l’Universite de Provence.

Notre travail a ete associe a deux programmes ACI lies a des financements sur la periode2004–2006 : L’ACI “energie et conception durable,” dans le cadre du programme “Hydro-lux” coordonne par M. Rousset, au BIP ; l’ACI “Dynamique et reaction des assemblagesmembranaires,” dans le cadre du programme “Metabolisme du soufre” coordonne par M. T.Guidici-Orticoni, au BIP.

Nous sommes partenaires du programme BioH2 (2005–) du CEA “Controle de la reactivitedes hydrogenases vis-a-vis de l’oxygene,” coordonne par C. Cavazza (IBS/LCCP, Grenoble).

Notre etude de la nitrite reductase pentahemique a ete soutenue dans le cadre des “ActionsUniversitaires Integrees luso-francaises” 2005–2006 (il s’agit du produit d’une cooperationentre la CPU et son homologue portugais, le CRUP, avec le soutien de l’Ambassade de Franceau Portugal) ; d’autre part, l’Universite de Provence a finance l’accueil en juillet 2005 deM. G. Almeida, avec qui nous collaborons sur ce projet, comme “Maıtre de Conference Invite.”

Nous sommes partenaires de l’ANR PNRB portee par L. Cournac (CEA Cadarache) en2006, labelisee par le pole de competitivite Energie, intitulee “Biodiversite des hydrogenases,”et financee.30

J’ai porte le projet ANR PCV intitule “Engineering the reactivity of complex molybdoen-zymes,” et selectionne.31 Il associe notre equipe a celles de W. Nitschke (BIP), A. Magalon(LCB, CNRS Marseille) et D. Pignol (CEA Cadarache). Ce projet est decrit brievementpage 58.

29Pierre Bianco (DR, maintenant a la retraite), Doris Lexa (DR, maintenant a la retraite) et Elisabeth Lojou(CR, section 12, maintenant dans l’equipe de Marie-Therese Giudici-Orticoni).

30http://www.agence-nationale-recherche.fr/documents/aap/2006/selection/pnrb.pdf31http://www.agence-nationale-recherche.fr/documents/aap/2006/selection/pcv.pdf

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8 Resultats obtenus au BIP (2002–2006)

Mes etudes ces quatre dernieres annees se sont articulees autour de trois problematiques :le transfert d’electrons (TE) a longue distance dans les enzymes respiratoires multicentres, lemecanisme catalytique de metalloenzymes, et la sensibilite a l’oxygene des hydrogenases.

8.1 Transferts d’electrons (TE) dans les enzymes multicentres

Les TE a longue distance sont fondamentaux en bioenergetique : selon le principe de latheorie chimiosmotique de Peter Mitchell,32 operationel dans l’ensemble du monde vivant, lasynthese d’ATP est couplee a un flux de protons a travers une membrane ; ce flux est possiblegrace a un gradient de potentiel electrochimique du proton, qui est construit et entretenu parles enzymes respiratoires ou photosynthetiques ; ces enzymes couplent la translocation de pro-tons a des processus d’oxydation et de reduction qui se produisent souvent de part et d’autrede la membrane. Les electrons sont transferes a travers ces enzymes sur des distances pouvantatteindre 80 A33 par des chaınes de centres redox, souvent constituees de chlorophylles et depheophytines dans les enzymes photosynthetiques, ou de centres FeS, a cuivre ou hemiquesdans les enzymes respiratoires.

La figure 13 montre la chaıne de TE intramoleculaire dans l’hydrogenase NiFe, une enzymequi catalyse la reaction reversible 2H+ + 2e− ⇀↽ H2. Cette chaıne est constituee d’un centre[4Fe4S] “proximal” (vis-a-vis du site actif), d’un cluster median [3Fe4S], et d’un cluster distal[4Fe4S]. Le potentiel de reduction du cluster median est tres eleve (fig. 14), ce qui est peufavorable au TE depuis ce centre vers l’un ou l’autre des centres [4Fe4S] (selon que l’enzymecatalyse la reduction des protons ou l’oxydation du dihydrogene). Cette enzyme a beaucoupete citee pour illustrer les regles qui regissent le design des chaınes de TE,34 alors qu’il n’y ajamais eu de mesure de vitesse de TE intramoleculaire dans l’hydrogenase. En fait, il n’y a eude mesure de vitesse de TE entre centres FeS dans aucune enzyme respiratoire,35 et cela estdu a deux principales limitations : (1) les centres FeS n’ont pas les signatures UV-Vis clairesqui permettraient le suivi des reactions de TE par des methodes spectroscopiques resoluesen temps et (2) le TE est le plus souvent difficile a synchroniser dans les enzymes respira-toires (contrairement aux systemes photosynthetiques ou la separation de charge initiale est

32Nicholls & Ferguson, “Bioenergetics 3,” Academic Press (2002).33C’est le cas dans le complexe mitochondrial I. Sazanov et al., Science 311 1430 (2006) http://dx.doi.

org/10.1126/science.112380934Voir par exemple Dutton et al., Nature 402 47 (1999) “Natural engineering principles of electron tunneling

in biological oxidation-reduction,” http://dx.doi.org/10.1038/4697235Des vitesses de TE intramoleculaires entre centres FeS n’ont ete determinees que dans quelques ferredoxines

a deux centres [4Fe4S], en utilisant la RMN du proton, voir le travail de Moulis et al., JBIC 6 446 (2001)“Intramolecular ET in [4Fe4S] proteins : estimates of the reorganization energy and ectronic coupling inChromatium vinosum ferredoxin,” http://dx.doi.org/10.1007/s007750100228.Des resultats sur le TE entre centres FeS dans le Photosysteme I ont ete publies tres recemment par Rappaportet al BBA-Bioenergetics 1757 1529 (2006) “Assignment of a kinetic component to electron transfer betweeniron-sulfur clusters FX and FA/B of Photosystem I” http://dx.doi.org/10.1016/j.bbabio.2006.06.016.

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Fig. 13: La chaıne de transfert d’electron(TE) dans l’hydrogenase NiFe de D. fruc-tosovorans (pdb 1YQW). Constituee de 3centres FeS, elle connecte le site actif NiFe(a droite) au partenaire redox de l’enzyme,un cytochrome c3, qui interagit avec lecluster “distal” expose a la surface de laproteine (a gauche).

Fig. 14: Energetique de la chaıne deTE intramoleculaire dans l’hydrogenaseNiFe. La litterature suggere34 que memel’etape de TE intramoleculaire du [3Fe4S]median vers le [4Fe4S] distal est rapide,mais il n’y a eu de mesure de vitesse deTE entre centres FeS dans aucune en-zyme respiratoire.35 Nous avons montrepar electrochimie directe que ce TE estlent dans un mutant de l’enzyme de D.fructosovorans [P27].

declenchee par un flash).

La consequence de ce manque crucial d’informations experimentales est que l’essentiel dece que nous croyons savoir sur la cinetique de TE entre FeS dans les enzymes respiratoires aete extrapole a partir des connaissances acquises sur les systemes photosynthetiques.

On croit ainsi que les TE, meme thermodynamiquement defavorables, sont toujours ra-pides par rapport a la vitesse de turnover de l’enzyme, pourvu que les centres soient a moinsde 14 A les uns des autres ;36 on neglige souvent leur reversibilite (les TE sont effectivementirreversibles dans les enzymes photosynthetiques) ; et on ne pense l’efficacite de la chaınede TE qu’en terme de vitesse.37 Dans les centres reactionnels (photosynthetiques), le TEdoit en effet etre tres rapide pour que la separation de charge l’emporte sur les processus defluorescence/ retour/ recombinaison, qui entraıneraient un gaspillage de l’energie lumineuseabsorbee. Dans les enzymes respiratoires au contraire, il n’est pas indispensable que le TE soitrapide ; pourtant, il n’a jamais ete propose qu’il puisse y avoir un avantage a ce qu’il soit lent.

36“Electrons can travel up to 14 A between redox centres (. . . ) This redox centre proximity alone is sufficientto allow tunnelling of electrons at rates far faster than the substrate redox reactions it supports” dans l’abstractde Dutton et al., Nature 1999 op. cit. (note 34).

37“Electron tunneling times must be in the millisecond to microsecond range for biological redox machines tofunction properly. (. . . ) Requirement for functionnal hopping [i.e. electron transfer] include optimal positioningof redox centers and fine-tuning of reaction driving forces,” Gray & Winkler PNAS 102 3534 (2005) “Long-range Electron transfer” http://dx.doi.org/10.1073/pnas.0408029102

ou encore : “(. . . ) electron tunneling distances of 14 A or less (. . . ) assure that tunneling rates are faster thanthe typical millisecond bond-breaking at catalytic sites” Dutton et al., Curr. Op. Chem. Biol. 7 551 (2003)“Mechanism for electron transfer within and between proteins” http://dx.doi.org/10.1016/j.cbpa.2003.

08.005

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Recemment, nous avons montre a deux reprises [P26, P27] que l’electrochimie directe deproteines pouvait apporter des informations quantitatives sur les cinetiques de TE intramole-culaire dans les enzymes respiratoires ; cela nous a amene a remettre en cause certaines desidees preconcues que nous venons d’enoncer.

Cinetique du TE intramoleculaire dans des mutants de l’hydrogenase NiFe Lecluster distal dans la chaıne de TE de l’hydrogenase (fig. 13) presente une coordination in-habituelle par 3 cysteines et une histidine (H184) (au lieu de la coordination habituelle par4 cysteines). Ce type de coordination n’a ete etabli sans ambiguıte que dans quatre famillesd’enzymes : les hydrogenases NiFe du groupe 1 (hydrogenases respiratoires selon la classifica-tion de P. Vignais38), les hydrogenases FeFe de type Clostridium, le Complexe I mitochondrialet certaines molybdoenzymes membranaires de la famille de la DMSO reductase. Dans cestrois derniers cas, des experiences de mutagenese dirigee ont montre que l’histidine est indis-pensable a l’activite, mais son role n’avait pas ete determine.

Nous avons etudie deux mutants de l’hydrogenase de D. fructosovorans (produits parSebastien Dementin, dans l’equipe de Marc Rousset au BIP) : un mutant His/Cys concupour recreer une coordination canonique (par 4 cysteines), et un mutant His/Gly. Un cluster[4Fe4S] distal est assemble dans les deux mutants, mais l’activite de ces deux enzymes pourl’oxydation du dihydrogene est d’environ 1.5 et 3 % de celle de l’enzyme sauvage. Nous avonscompare les activites des enzymes (sauvage et mutantes) pour l’oxydation du dihydrogene, lareduction des protons et l’echange isotopique H/D dans des conditions variees : (1) soit enelectrochimie directe (avec l’enzyme adsorbee sur une electrode), soit en cinetique homogeneen presence de differents partenaires redox solubles et (2) en presence de ligands exogenesdont nous pensions que la liaison a l’atome de fer expose du cluster distal du mutant His/Glymodifierait ses proprietes.

L’electrochimie directe s’est averee particulierement utile pour discriminer simplementl’effet des mutations et de la liaison avec les ligands exogenes sur les vitesses de TE inter- etintramoleculaire. Cette approche est expliquee dans l’encart page 40.

Nous avons demontre que changer la coordination du cluster distal n’a pas d’effet surl’assemblage du cluster, la stabilite de la proteine, la chimie au site actif et les transferts deprotons. En revanche, les mutations diminuent les vitesses de TE depuis et vers ce cluster.Dans le cas du mutant H184C, nous n’avons pas pu obtenir d’informations sur le TE in-tramoleculaire, mais nous avons montre que la coordination par quatre cysteines ralentit lesTE intermoleculaires. Dans le cas du mutant H184G, nous avons demontre que le TE intra-moleculaire (“uphill”) entre le [3Fe4S] median et le [4Fe4S] distal dans le mutant His/Gly estlimitant en vitesse lorsque l’enzyme oxyde l’hydrogene. Cela montre que, bien que les clustersFeS soient des assemblages robustes d’un point de vue chimique, les ligands proteiques directs

38Vignais, FEMS Microbiol. Rev. 25 455 (2001) “Classification and phylogeny of hydrogenases” http://dx.

doi.org/10.1016/S0168-6445(01)00063-8.

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C. Leger. UPR 9036. Memoire d’HDR. 2007.

jouent un role essentiel pour leur conferer la capacite a transferer des electrons.C’est la premiere fois qu’une information experimentale est obtenue sur le TE entre centres

FeS dans une enzyme et nous opposons un contre exemple a l’idee repandue selon laquelleles TE d’electrons entre centres separes de moins de 14 A sont toujours plus rapides que lachimie au site actif et ne peuvent donc pas etre limitants en vitesse.36

Dans les deux figures ci-dessous, un signal experimental typique pour l’oxydation de l’hydrogene par l’hy-drogenase NiFe est represente (carres, le signal est sous-echantillonne), et superpose a des signaux calculesavec le modele presente dans la section 6.3, page 28. Selon ce modele la forme du signal depend beaucoupdu rapport de constantes de vitesse kcat/k0, ou kcat est une constante de vitesse du premier ordre quiincorpore toutes les etapes intramoleculaires (chimie, TE intramoleculaire, transfert de protons) alors quela vitesse de TE interfacial est proportionnelle au parametre k0 (equation 6, page 29). Les signaux sur lesfigures gauche et droite ont ete recalcules en faisant varier kcat ou k0, respectivement : l’amplitude du signalest bien sur modifiee dans les deux cas, mais la facon dont la forme evolue est completement differente. Ensuivant l’evolution experimentale de la forme d’un signal, on peut donc distinguer des variations d’activitequi resulteraient de variations de vitesses de TE intramoleculaire (kcat) ou interfacial (k0).

Le mutant H184G de l’hydrogenase NiFe de fructosovorans est “repare” par l’addition d’imidazole exogene,mais les mesures d’activite en solution ne permettent pas de determiner s’il s’agit d’un effet sur le TEinter- ou intramoleculaire. Les figures ci-dessous montrent que l’addition d’imidazole augmente l’activite del’enzyme pour l’oxydation de l’hydrogene (a gauche) ou la reduction des protons (a droite) et en analysantcomment la forme des signaux se modifie, nous avons pu demontrer que la coordination du cluster distal parl’imidazole a deux effets distincts : (1) augmenter les vitesses de TE interfacial et (2) augmenter la vitessede TE intramoleculaire entre le cluster median et le cluster distal lorsque l’enzyme oxyde l’hydrogene. Cetteetape, qui est thermodynamiquement defavorable dans l’enzyme sauvage (fig. 14) est limitante en vitessedans le mutant H184G.

Encart 8.1: Utilisation de l’electrochimie directe pour l’etude du TE intramoleculaire dans lemutant H184G de l’hydrogenase de D. fructosovorans [P27].

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C. Leger. UPR 9036. Memoire d’HDR. 2007.

Fig. 15: Detail de la structure du flavo-cytochrome b2 de la levure (pdb 1FCB).L’oxydation du lactate se produit au siteactif flavine (a droite), qui donne seselectrons a un cytochrome apres echangeintramoleculaire avec l’heme de type b (agauche sur la figure). Quel est le potentielde reduction du partenaire redox le moinsoxydant qui permet quand meme d’en-tretenir l’oxydation catalytique du lactatepar cette enzyme ? [P26]

Sur la reversibilite du TE intramoleculaire dans les enzymes respiratoires, et les

principes qui regissent leur design naturel Si l’on pense a la situation ou une enzymemulticentre est en presence d’un substrat oxydable, on peut se poser la question suivante :pour entretenir le processus catalytique, le potentiel de reduction du partenaire redox del’enzyme qui accepte les electrons doit etre suffisamment eleve, mais plus eleve que quoi ?Le potentiel de reduction de l’accepteur doit-il etre superieur a celui du site actif ? a celuidu centre avec lequel il interagit a la surface de la proteine ? au plus grand des potentielsde reduction de tous les relais dans l’enzyme ? Cette question simple, qui se pose de faconsimilaire dans le cas ou l’enzyme echange des electrons avec une electrode sur laquelle elle estadsorbee, semble n’avoir jamais ete posee.

Nous avons montre qu’on ne peut baser la reponse a cette question que sur un modelecinetique dans lequel on prend en compte tous les etats redox de l’enzyme, et les transitionsreversibles entres ces etats (encart page 42). On peut alors demontrer que la “force motri-ce” necessaire pour oxyder l’enzyme dans des conditions stationnaires de turnover depend dela cinetique et de la thermodynamique de la chaıne de TE dans l’enzyme. Si le TE intra-moleculaire est rapide, la chaıne de TE ne fait que transmettre au site actif la force motricedisponible a partir du partenaire redox, et il suffit que celui-ci ait un potentiel de reductionsuperieur a celui du site actif. Si au contraire le TE intramoleculaire est limitant en vitessedans le cycle catalytique, tout se passe comme si le site actif avait un potentiel de reductionapparent qui depend de la cinetique du TE intramoleculaire ; cela nous a permis de suggererune alternative a l’idee que les chaınes de TE sont toujours optimisees en terme de vitesse :dans certains cas, la lenteur du TE pourrait conferer un avantage a l’enzyme, en modulantles proprietes redox apparentes de son site actif.

En dehors de ces considerations sur le design naturel des chaınes de TE, il se trouveque l’electrochimie directe, en donnant la possibilite de mesurer continument l’activite del’enzyme en fonction du potentiel d’electrode, permet d’acceder directement a cette forcemotrice minimale a partir de laquelle le flux d’electron stationnaire se produit, et il est pos-sible dans certains cas de deduire les vitesses de TE intramoleculaires a partir de mesures

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C. Leger. UPR 9036. Memoire d’HDR. 2007.

d’electrochimie directe catalytique. Nous n’avons encore developpe cette theorie que dans lecas d’enzymes qui ne contiennent qu’un seul relais, et nous l’avons appliquee avec succes adifferents exemples, en particulier la sulfite oxydase et le flavocytochrome b2 (fig. 15) ; pourcela nous avons developpe une collaboration avec Florence Lederer, au Laboratoire d’Enzy-mologie et Biochimie Structurales CNRS, Gif-sur-Yvette.

Nous decrivons ici la facon dont la position d’un si-gnal catalytique depend de la cinetique du TE intra-moleculaire.Dans les modeles ou le TE intramoleculaire n’est pasconsidere, on postule que tout se passe comme si leTE entre l’electrode et le site actif etait direct [P19],et l’equation de courant est determinee a l’aide d’unschema cinetique qui ne fait intervenir que les tran-sitions entre les differents etats redox du site actif(AO, AI et AR pour site actif oxyde, intermediaireet reduit, dans le schema (A), ci-dessous), avec desvitesses qui dependent du potentiel d’electrode selonl’equation de Butler-Volmer.

��� ���

��� ���

��� ���

��������

� ��� �

��� ��

���

� �� ��

��

�����

��

� ��

������

������

������

������

������

������

��

��� �

Dans ce cas, et dans la limite ou le TE interfacial esttres rapide, l’equation de courant est :

i =ilim

1 + exp [f(E1 − E)] + exp [2f(E2 − E)](10)

ou E1 = E0O/I et E2 = E0

O/R sont les potentiels dereduction du site actif.Si on veut considerer explicitement les etapes detransfert d’electron intramoleculaire, on doit incluredans le schema cinetique tous les etats redox del’enzyme. Par exemple, une enzyme comme le fla-vocytochrome b2, dont le site actif qui peut existerdans 3 etats redox differents est connecte a un seulrelais R (un heme), peut exister dans 3 × 2 = 6etats redox (schema B). L’equation de Butler-Volmerest alors utilisee pour decrire le TE entre l’electrodeet le relais (et non le site actif) et les rapports de

constantes de vitesse pour le TE intramoleculaire(k1/k−1, k′1/k′−1) sont contraints par les differencesde potentiel de reduction entre le relais et le siteactif.Ce qui est interessant, c’est que l’equation de cou-rant pour ce schema peut se mettre exactementsous la forme de l’equation 10, mais avec des po-tentiels E1 et E2 qui dependent simplement de lacinetique de TE intramoleculaire, et en particulierdu rapport kcat/ki ou ki est la plus lente des etapesde TE intramoleculaire entre le site actif et le relais(1/ki = 1/k1 + 1/k′1).Par exemple dans le cas ou E0

O/I > E0I/R, si le TE

intramoleculaire est tres rapide (kcat/ki ≈ 0), la po-sition de la vague catalytique est celle du site actif(E1 = E0

O/I) alors que si le TE est limitant en vitesse

(kcat/ki ≈ 1), la vague est centree sur le potentiel dereduction du relais (E1 = E0

R). Dans une situationintermediaire, le rapport kcat/ki peut etre deduit dela position de la vague catalytique :

E1 = E0O/I +

1f

ln(

1+[expf(E0

R−E0O/I)−1

] kcat

ki

)(11)

Dans le cas d’une enzyme comme l’hydrogenaseNiFe, qui contient trois relais, le calcul est plus dif-ficile parce qu’on doit considerer 3× 23 = 24 etats.Ce travail est actuellement en cours.

Encart 8.1: Sur la cinetique de TE intramoleculaire stationnaire dans les enzymes multicentres,en lien avec la forme des voltamperogrammes obtenus pour des enzymes adsorbees [P26].

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Perspectives de nos travaux sur le TE d’electrons dans les enzymes respiratoires

Nous avons propose deux strategies originales d’utilisation de l’electrochimie directe pourl’etude du transfert d’electron intramoleculaire dans les enzymes respiratoires, en particulierdans des cas ou ces informations ne sont pas accessibles par des techniques classiques, et ap-porte les premiers resultats experimentaux sur les cinetiques de TE dans l’hydrogenase NiFe.Cela nous a amene a remettre en question certaines idees dogmatiques, et a faire remarquerle besoin urgent de donnees cinetiques nouvelles.

Nos efforts se poursuivent pour generaliser notre modele cinetique a des systemes compre-nant plusieurs relais, ceci afin d’etudier le TE intramoleculaire dans l’hydrogenase sauvage.Notre collaboration avec Marc Rousset nous permettra d’etudier d’autres variants de l’hy-drogenase NiFe ; des doubles mutants de la chaıne de TE sont en cours de purification. Nousnous interesserons en particulier a un double mutant P238C-H184G dans lesquels le cluster[3Fe4S] median de haut potentiel est converti en un cluster [4Fe4S] de bas potentiel,39 etl’histidine du cluster distal est simultanement supprimee pour permettre la reparation del’enzyme par des ligands exogenes (c’est l’effet de cette reparation sur la forme du signalelectrochimique qui nous a permis de demontrer simplement que le TE intramoleculaire estlimitant en vitesse dans le mutant His/Gly, encart page 40).

Notre objectif a court terme est de repondre a une question qui n’a obtenu qu’une reponsehative40 dans le passe : les potentiels de reduction des centres FeS dans l’hydrogenase sauvagerendent-ils le TE intramoleculaire limitant en vitesse ?

39Rousset et al., PNAS 95 11625 (1998) “[3Fe4S] to [4Fe4S] cluster conversion in Desulfovibrio fructosovoransNiFe hydrogenase by site-directed mutagenesis” http://www.pnas.org/cgi/content/abstract/95/20/11625

40Par exemple dans Dutton et al., Nature (1999) op. cit. (note 34), la valeur numerique de 5× 104s−1 pourla vitesse de TE dans l’hydrogenase de D. fructosovorans est calculee pour un ∆G de 0.40eV, une energie dereorganisation λ = 0.7eV et une distance qui n’est pas precisee. En utilisant l’“ET rates calculator” de Dutton(http://www.uphs.upenn.edu/biocbiop/local_pages/dutton_lab/golden.html), on realise que la distanceutilisee (5.66 A) est significativement plus petite que la distance bord-a-bord mesuree sur le fichier pdb del’hydrogenase de D. gigas qui etait disponible a l’epoque (8.55 A). Les auteurs ont peut-etre mesure la pluscourte distance “soufre de cysteine ligand a soufre de cysteine,” qui est de 5.35 A.Plus generalement, on peut aussi s’interroger sur le sens a donner a cette mesure lorsqu’il s’agit d’objets dontla taille est justement du meme ordre de grandeur que la distance qui les separe.

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Fig. 16: Detail sur la structure de lanitrite reductase penta-hemique de W.succinogenes (pdb 1FS7). Le nombred’hemes en interaction magnetique danscette enzyme rend difficile l’interpretationdes donnees RPE. L’utilisation del’electrochimie directe nous a permis desonder selectivement les proprietes redoxdu site actif [P28].

8.2 Reactions chimiques couplees au TE et mecanismes catalytiques au

site actif

C’est la chimie au site actif qui fait en general l’objet de l’attention la plus soutenue, peut-etre parce que le modele de catalyse enzymatique “lock and key” propose par Fischer en 1894est encore tres present dans les esprits. Dans les systemes que nous etudions, des reactionschimiques (protonations, liaison avec le substrat) sont tres souvent couplees au changementd’etat redox du site actif et peuvent modifier ses proprietes (par exemple, son potentiel dereduction, ses constantes d’acidite). Ainsi, les grandeurs thermodynamiques mesurees dansdes experiences a l’equilibre, en l’absence de substrat, ne peuvent pas toujours etre utiliseesdirectement pour comprendre le fonctionnement du systeme. La technique que nous utilisonsa, au contraire, l’avantage de donner des informations sur la succession d’evenements quise produisent au site actif dans des conditions de turnover, et permet la caracterisation desproprietes de certains intermediaires reactionnels, sans qu’il soit necessaire de les isoler parpiegeage, comme cela est illustre dans les exemples qui suivent.

Une aiguille dans une botte de foin : le site actif de la nitrite reductase penta-

hemique. La nitrite reductase penta-hemique catalyse la reduction a six electrons du nitriteen ammonium : NO−2 + 6e− + 8H+ → NH+

4 + 2H2O.

Dans cette enzyme, le site actif est un heme haut-spin dont un site axial accueille le sub-strat pendant le turnover ;41 ce site actif recoit des electrons via quatre autres hemes de typec (fig. 16). Dans les organismes de type Desulfovibrio, l’enzyme est purifiee avec son parte-naire redox tetrahemique, sous forme d’un complexe α2β qui contient 14 hemes.42 Le nombred’hemes dans cette enzyme, leur proximite et les interactions magnetiques qui en resultent,rendent tres difficile la caracterisation du site actif par des techniques spectroscopiques clas-

41Neese et al., JACS 124 11737 (2002) “Mechanism of the six-electron reduction of nitrite to ammonia bycytochrome c nitrite reductase” http://dx.doi.org/10.1021/ja0206487

42Archer et al., EMBO J. 25 5951 (2006) “X-Ray structure of the membrane-bound cytochrome c quinoldehydrogenase NrfH reveals novel haem coordination” http://dx.doi.org/10.1038/sj.emboj.7601439 (pdb2J7A).

44

C. Leger. UPR 9036. Memoire d’HDR. 2007.

Fig. 17: Detail de la structure de la nitratereductase de R. sphaeroides (pdb 1OGY).La sous unite NapA (en jaune) contientle cofacteur a molybdene qui caracteriseles enzymes de la famille de la DMSOreductase. Nous avons montre commentdans les conditions de turnover, les etapeslentes de liaison avec le substrat rendentexergonique l’etape de TE vers le Mo[P23]. Figure realisee par Pascal Arnoux.

siques (UV-vis, EPR, Mossbauer. . . ).

En collaboration avec Gabriella Almeida et Isabel Moura, a l’Universite Nouvelle de Lis-bonne, nous avons entrepris l’etude de l’enzyme de D. desulfuricans. Nous avons propose unemethode simple et originale d’utilisation de l’electrochimie directe permettant la detectionselective de l’heme catalytique et la mesure de son potentiel de reduction. Pour cela, nousavons demontre que seul le site actif lie le CO, et exploite le fait que cette coordination modifiefortement le potentiel de reduction du site actif, qu’on peut alors determiner en examinant ladifference entre les signaux electrochimiques enregistres avec et sans CO [P28].

Nous avons repete ces mesures sur une large gamme de pH pour demontrer que la reductiondu site actif est couplee au transfert d’un proton. Le site actif reduit se protone avec un pKaqui suggere que le proton est porte par l’histidine conservee dans les enzymes de cette familleet representee en haut a gauche sur la fig. 16.

Notre collaboration avec le laboratoire d’Isabel Moura se poursuit, dans le but d’obtenirdes informations supplementaires sur le mecanisme catalytique. Les signaux electrochimiquescatalytiques obtenus sont de qualite, mais nous buttons encore sur leur complexite.43 Au prixd’un important effort de modelisation, ils permettront peut-etre a moyen terme de tester lespropositions de mecanisme obtenues par des approches de type DFT.

La nitrate reductase periplasmique de Rhodobacter sphaeroides. En collaborationavec Pascal Arnoux et David Pignol, au CEA-Cadarache, nous avons entrepris l’etude d’unenitrate reductase periplasmique, une enzyme de la famille de la DMSO reductase (fig. 10c,page 32). Celle-ci a ete purifiee et cristallisee au CEA sous deux formes : le monomere NapAcontient le site actif et un cluster [4Fe4S] ; dans l’heterodimere NapAB, deux hemes de type c

participent en plus au TE intramoleculaire vers le molybdene (fig. 17). Les etudes com-paratives de NapA et NapAB a Cadarache et dans notre equipe ont mis en evidence desdifferences spectaculaires dans la cinetique de reduction du nitrate et le potentiel de reduction

43L’interpretation de ces signaux dans la litterature est encore tres speculative ; Butt et al., JACS 127 14964(2005) “Diode or tunnel-diode characteristics ? resolving the catalytic consequences of proton coupled electrontransfer in a multi-centered oxidoreductase” http://dx.doi.org/10.1021/ja054160s

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C. Leger. UPR 9036. Memoire d’HDR. 2007.

du cluster [4Fe4S].44 Ce systeme est unique en ce qu’il permet d’etudier comment les inter-actions entre les cofacteurs influencent leurs proprietes redox, electroniques et magnetiques,et plus generalement comment certaines proprietes des enzymes de la famille de la DMSOreductase sont influencees par l’architecture supra-moleculaire de l’enzyme, et non pas seule-ment par la structure locale du site actif.

Les signaux electrochimiques que nous avons obtenus sont complexes mais particulierementbien definis et tres similaires a ceux obtenus a Oxford pour la DMSO reductase de coli, ouplus recemment par d’autres groupes45 avec des enzymes de la meme famille. Nous avons pules premiers interpreter quantitativement la facon contre-intuitive dont l’activite depend del’etat redox de l’enzyme, en utilisant un modele base sur des hypotheses tres simples (encartpage 47). Nous avons mis en avant le caractere general de ce modele qui s’applique a toutesles enzymes multicentres de la famille de la DMSO reductase, et nous avons discute ce qu’im-pliquent nos resultats vis-a-vis des mecanismes de TE intramoleculaires. Nous avons montrecomment l’existence dans le cycle catalytique d’etapes lentes de liaison avec le substrat,couplees au TE vers le molybdene, rend exergonique l’etape de TE entre le cluster [4Fe4S]proximal et le molybdene [P23]. Cela illustre l’idee importante — mais peu repandue — selonlaquelle les potentiels de reduction (mesures dans des conditions d’equilibre thermodyna-mique) ne peuvent pas toujours etre utilises directement pour comprendre le fonctionnementd’un systeme enzymatique dans des conditions de turnover.

44Arnoux et al., NSB 10 928 (2003) “Structural and redox plasticity in the heterodimeric periplasmic nitratereductase,” http://dx.doi.org/10.1038/nsb994

45(a) Anderson et al., Biochemistry 40 11294 (2001) “Catalytic protein film voltammetry from a respiratorynitrate reductase provides evidence for complex electrochemical modulation of enzyme activity” http://dx.

doi.org/10.1021/bi002706b

(b) Jepson et al., JBC 279 32212 (2004) “Tuning a nitrate reductase for function” http://dx.doi.org/10.

1074/jbc.M402669200

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Nous avons interprete les donnees obtenues avecla nitrate reductase de sphaeroides a l’aide duschema ci-dessous, qui est legerement modifiepar rapport a celui que nous avions propose lorsde l’etude de la DMSO reductase (page 33).

MoV

k4s

MoV:S MoIV:S

k5s

MoIV

E2

E1

P

k2

MoV:S

MoVI

E3

fast

Il est possible de determiner l’equation de cou-rant pour ce schema en faisant l’hypothese quele TE est rapide et que les etapes de liaisonavec le substrat sont irreversibles (a l’echelle detemps du turnover). On obtient :

2FAΓk2

i= 1 + e2(1 + e3) +

k2

k4s

1 + e1

1 + (k5/k4)e1

(12)ou nous utilisons la notation compacte ej =exp[f(E−Ej)], j = 1–3. Les figures ci-dessousmontrent le parametrage de signaux cataly-tiques stationnaires enregistres pour des concen-trations en substrat croissantes, et pour 4 va-leurs du pH.

Dans une deuxieme etape, les dependances enpH des potentiels de reduction deduits du pa-rametrage des signaux sont interpretees a l’aidedu diagramme de Pourbaix ci-dessous, pourdeterminer les etats de protonation et les pKade chacun des intermediaires.

Il est remarquable que l’hypothese d’irrever-sibilite des etapes de liaison avec le substratentraıne que le potentiel Ecat auquel l’activiteapparaıt est lie au potentiel de reduction du siteactif lie au substrat meme lorsque la concentra-tion en substrat tend vers 0, alors que le poten-tiel ou l’activite s’attenue Esw depend principa-lement de la valeur du potentiel de reduction dusite actif libre (sans substrat).

Ecat = E2 +RT

Fln

(1 +

k2

k5s

)(13a)

Esw = E1 +RT

Fln

(k2 + k4s

k2 + k5s

)(13b)

En ce qui concerne le mecanisme catalytique,l’image qui emerge de notre etude est qu’aucours du demi-cycle catalytique qui conduit ala reduction du site actif, se produit la liaisonirreversible du nitrate au MoV et celle-ci est sui-vie d’etapes de protonation. Ces reactions chi-miques couplees au TE ont pour consequenced’augmenter largement le potentiel de reductiondu couple MoV/IV, qui devient reductible par lecluster [4Fe4S] proximal.

Encart 8.2: Interpretation des signaux catalytiques de la nitrate reductase de R. sphaeroides.[P23] et these de Bettina Frangioni, article en preparation.

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8.3 Sensibilite a l’oxygene des hydrogenases

Les hydrogenases sont etudiees pour des raisons tres diverses : mecanisme catalytique,transferts de protons et d’electrons a longue distance (page 39 et fig. 13), phylogenese,bioenergetique, aspects environnementaux et technologiques. La comprehension des processusd’oxydation et de production du dihydrogene est en particulier de toute premiere importancedans le contexte de la production d’energie propre.

Une part importante des etudes des hydrogenases porte aujourd’hui sur la sensibilite deces enzymes a l’oxygene, parce que l’inhibition par l’oxygene est un obstacle a la valorisationde ces enzymes dans des piles a combustible ou pour la photo-production biologique dudihydrogene. Nous collaborons etroitement avec Sebastien Dementin46 et Marc Rousset (BIP,CNRS Marseille), dont un projet vise a utiliser la biologie moleculaire pour construire desmutants de l’hydrogenase NiFe qui seront insensibles a l’oxygene.

Un obstacle a ces etudes etait qu’il n’existe pas de methode de mesure d’activite deshydrogenases en presence d’oxygene : celui-ci oxyde directement les accepteurs d’electrons so-lubles (viologenes ou cytochromes) utilises pour la mesure d’activite hydrogenase en cinetiquehomogene.47 Ce verrou peut etre leve simplement en utilisant l’electrochimie directe, puisquele potentiel de l’electrode qui joue le role d’accepteur peut etre maintenu a une valeur suffi-samment elevee pour que l’hydrogene soit oxyde par l’hydrogenase sans que le dioxygene nesoit reduit sur l’electrode.

Resultats sur l’enzyme sauvage Nous avons propose une methodologie originale per-mettant d’etudier par electrochimie directe la reaction d’enzymes redox avec leurs substratsou inhibiteurs gazeux. Dans le cas de l’hydrogenase sauvage de D. fructosovorans, nous avonsmontre que des mesures d’activite non stationnaires, pendant que decroıt la concentrationen H2, CO ou O2, permettent de determiner de facon simple et virtuellement instantanee lesconstantes de Michaelis, les constantes d’inhibition et les vitesses d’inactivation, respective-ment (encarts pages 49 et 52). Cela est remarquable parce que ces parametres sont habituelle-ment difficiles, voire impossibles a determiner dans le cas des hydrogenases : independemmentdes difficultes que nous venons de discuter (liees a la presence d’oxygene), une mesure pardes methodes traditionnelles de constante de Michaelis ou d’inhibition par le CO requiert quel’on maintienne constantes, precisement et simultanement, les pressions partielles en chacundes gaz pendant la mesure d’activite, ce qui n’est pas possible en routine [P24].

46Sebastien dementin a ete recrute CR2 au BIP en 2006.47Il est cependant possible de tester en conditions aerobies l’activite des hydrogenases qui reduisent le

NAD+. Voir par exemple Albracht et al., JBC 279 46686 (2004) “The auxiliary protein HypX provides oxygentolerance to the soluble NiFe hydrogenase of Ralstonia eutropha H16 by way of a cyanide ligand to nickel”http://Dx.doi.org/10.1074/jbc.M406942200.

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Selon la methode que nous avons mise aupoint pour etudier la cinetique d’inhibition del’hydrogenase par l’oxygene, le potentiel del’electrode tournante sur laquelle l’enzyme estadsorbee est maintenu a une valeur telle qu’uncourant catalytique est mesure, et des aliquotsde solution saturee en air sont injectes dansla cellule electrochimique. La concentration enoxygene augmente en une fraction de secondevers une valeur initiale [O2]0, puis decroıt expo-nentiellement vers zero avec une constante detemps τ .

[O2](t) = [O2]0 exp(−t/τ) (14)

Dans ces conditions experimentales, le proces-sus d’inactivation est irreversible, de telle sorteque l’evolution temporelle de la concentrationen enzyme active Γa obeit a :

dΓa(t)dt

= −kinact(t)Γa(t) (15)

La dependance temporelle de la vitesse glo-bale d’inactivation kinact resulte du fait quela concentration en oxygene varie au cours dutemps.Les donnees peuvent etre analysees sans faired’hypothese a priori sur kinact(t) en remarquantque puisque les processus d’inactivation sont dupremier ordre en enzyme, l’equation 15 se trans-forme en

− kinact(t) =d log Γa(t)

dt(16)

Enfin, puisque le courant mesure est proportion-nel a Γa(t), la vitesse instantanee d’inactivationpeut simplement etre mesuree en transformantle courant :

kinact(t) = −d log i(t)dt

(17)

La figure B montre les variations de cou-rant (d’activite) qui resultent des variations deconcentration en oxygene schematisees sur la fi-

gure A. La transformee du courant sur la fig. Cdonne directement les vitesses instantanees d’in-activation qui peuvent etre parametrees par

kinact(t) = ka × exp(−t/τ) + kb (18)

ou kb est la vitesse d’un processus d’inactivationindependant de la presence d’oxygene, et ka,dont la valeur est proportionnelle a la quantited’oxygene injectee (fig. D), s’interprete commeune constante de vitesse pseudo-premier ordrepour le processus bimoleculaire de reaction avecl’oxygene.

Cette interpretation est est accord avec ce quel’on sait des processus d’inactivation de l’hy-drogenase dans des conditions oxydantes. Enparticulier, la formation de l’espece inactive etoxydee appelee “NiB” peut se produire dans desconditions anaerobies, alors que l’exposition al’oxygene entraıne la formation d’un melanged’especes inactives (NiA+NiB) (Lamle et al.,JACS 126 14899 (2004) http://dx.doi.org/10.1021/ja047939v).

Encart 8.3: Mesure des vitesses d’inactivation anaerobie de l’hydrogenase NiFe de fructoso-vorans [P24].

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C. Leger. UPR 9036. Memoire d’HDR. 2007.

NiFe

Figures adaptees de Friedrich et al.48

Fig. 18: Detail de la structure de l’hy-drogenase de D. gigas (A) et du ca-nal d’acces du substrat (represente parune grille fine). Les residus volumi-neux conserves dans les hydrogenases detype gigas (F et I), sont remplaces pardes residus plus petits (V et L) dansles enzymes resistantes a l’oxygene. Lamodelisation (Panel B) suggere48 que lecanal de ces enzymes est naturellementobstrue (a l’endroit encercle), ce qui per-mettrait le passage selectif de H2.

Figures realisees par Anne Volbeda.

Fig. 19: L’extremite du canal a H2, ducote du site actif, dans l’hydrogenase deD. fructosovorans sauvage (a gauche) etun double mutant (a droite) dans lesquelsdes aminoacides conserves (L et V) ontete substitues par des methionines. Lastructure du mutant montre que le canalest partiellement obstrue. Nos etudes per-mettent d’en mesurer l’effet sur les vitessesde diffusion vers et depuis le site actif.

Vers le design et l’identification d’enzymes moins sensibles a l’oxygene Une pistede travail a ete recemment suggeree par la comparaison des sequences des enzymes “respi-ratoires” (comme celles que nous etudions) et “senseur.” Ces dernieres sont tres peu activespour l’oxydation de H2, mais elles sont insensibles a l’oxygene ; cette insensibilite pourraitresulter en partie du fait que les canaux hydrophobes qui permettent l’acces du dihydrogene(mais aussi du dioxygene) vers le site actif semblent obstrues par des residus plus volumineuxque ceux qui sont presents dans les enzymes sensibles (fig. 18). Des experiences de mutagenesesur l’enzyme senseur de R. eutropha ont en effet demontre qu’il est possible de rendre cetteenzyme sensible a l’oxygene en augmentant la taille de ses canaux.48 Il faut encore determinersi l’inverse est aussi possible, c’est-a-dire obstruer par mutagenese les canaux de l’enzyme defructosovorans pour rendre celle-ci insensible a l’oxygene. . . sans qu’elle ne perde son activite.

Nous avons effectivement identifie recemment un double mutant du canal qui, dans desconditions aerobies, s’inactive plus lentement que l’enzyme sauvage (fig. 19). C’est le premierpas jamais realise en direction du design d’une enzyme resistante a l’oxygene [C21].Il n’est pas certain cependant que les enzymes de types “senseurs” ne soient resistantes a l’O2

48Friedrich et al., JBC 280 23791 (2005) “Oxygen tolerance of the H2-sensing [NiFe] hydrogenase fromRalstonia eutropha H16 is based on limited access of oxygen to the active site” http://dx.doi.org/10.1074/

jbc.M503260200.

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C. Leger. UPR 9036. Memoire d’HDR. 2007.

que parce que leurs canaux sont plus etroits, et au-dela de la strategie que nous avons testee,il faudra perseverer dans l’etude du processus d’inactivation, pour suggerer de nouvelles pistesaux biologistes moleculaires avec qui nous collaborons.

8.4 Etude du transport de matiere intramoleculaire

Nous avons etudie les cinetiques d’inhibition par le CO pour tester un inhibiteur plus“simple” (en terme de reactivite au site actif), identifie plusieurs mutants du canal de diffusiondu substrat pour lesquels les vitesses de transport vers et depuis le site actif sont ralenties[C21], et mis au point la methodologie qui permet de mesurer finement les vitesses de diffusionvers et depuis le site actif, le long des canaux modifies (voir l’encart page 52).

Cela nous permet d’aborder un autre aspect du fonctionnement enzymatique sur lequel lesdonnees cinetiques manquent encore singulierement, le transport intramoleculaire de petitesmolecules, qui s’effectue le long de canaux dont il est propose que la geometrie et la dyna-mique49 permettent aux enzymes de selectionner un substrat (vis-a-vis d’un substrat alternatifou d’un inhibiteur). Depuis la premiere mise en evidence d’un tunnel dans une enzyme (ils’agissait de la tryptophane synthase en 1988), des experiences ont permis d’identifier certainsmecanismes par lesquels les sites actifs d’enzymes bifonctionnelles echangent un intermediaire(l’indole ou l’ammonium dans de nombreux exemples)50 en evitant son accumulation ou sadiffusion vers le solvant. Dans le cas des enzymes redox dans lesquelles des canaux ont eteidentifies ou proposes sur la base de structures cristallographiques statiques (ACS-CODH,51

hydrogenase FeFe49 et NiFe,52 nitrogenase, cytochrome-c oxydase53), en depit de nombreusesetudes theoriques (en particulier sur les hydrogenases), on ne sait pas a quelle vitesse lessubstrats diffusent, ni comment la structure detaillee du canal influence son efficacite et saspecificite. La methodologie que nous avons mise au point permet de mesurer les vitesses detransport le long des canaux de l’hydrogenase NiFe par electrochimie ; lorsque nous auronsexamine les liens entre la nature (au-dela de la taille) des residus qui entravent la diffusiondu CO et les vitesses de diffusion, ce seront des resultats spectaculaires et originaux sur ladynamique du transport de matiere dans ces geometries confinees.

49Schulten et al., Structure 13 1321 (2005) “Finding gas diffusion pathways in proteins : application to O2

and H2 transport in CpI FeFe-hydrogenase and the role of the packing defects” http://dx.doi.org/10.1016/

j.str.2005.05.01350(a) Holden et al., Acc. Chem. Res. 36 539 (2003) “Enzymes with molecular tunnels” http://dx.doi.org/

10.1021/ar020047k

(b) Raushel et al., Curr. Op. Chem. Biol. 10 465 (2006) “Tunneling of intermediates in enzyme-catalyzedreactions” http://dx.doi.org/10.1016/j.cbpa.2006.08.008

51Lindhal et al., JACS 127 5833 (2005) “The tunnel of acetyl-coenzyme A synthase-CO dehydrogenaseregulates delivery of CO to the active site” http://dx.doi.org/10.1021/ja043701v

52Fontecilla-Camps et al., NSB 4 523 (1997) “Gas access to the active site of NiFe hydrogenase probed byX-ray crystallography and molecular dynamics” http://dx.doi.org/10.1038/nsb0797-523

53(a) Brzezinski et al., PNAS 101 11617 (2004) “A single-amino-acid lid renders a gas-tight compartmentwithin a membrane-bound transporter” http://dx.doi.org/10.1073/pnas.0402242101

(b) Ferguson-Miller et al., PNAS 100 15539 (2003) “A discrete water exit pathway in the membrane proteincytochrome c oxidase” http://dx.doi.org/10.1073/pnas.2633243100

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Pour etudier la cinetique d’inhibition par leCO, le potentiel de l’electrode tournante surlaquelle l’enzyme est adsorbee est maintenu aune valeur telle qu’un courant catalytique estmesure, et une petite quantite de solution sa-turee en CO est injectee a t = 0 dans lacellule electrochimique. Sa concentration aug-mente en une fraction de seconde vers une va-leur initiale [CO]0, puis tend exponentiellementvers zero avec une constante de temps τ [P24].L’evolution temporelle de la concentration d’en-zyme dans la forme libre (active) obeit a :

dΓa(t)dt

= −ki[CO]0e−t/τΓa(t) + ka[1− Γa(t)]

(19)ou ki est la constante de vitesse du secondordre pour l’inhibition par le CO et ka est laconstante de vitesse du 1er ordre pour l’activa-tion (liberation du CO).Si ki et ka sont grands devant 1/τ , comme c’estle cas pour l’hydrogenase sauvage de fructoso-vorans, la fraction d’enzyme inhibee est instan-tanement et continuellement en equilibre avec laquantite de CO presente en solution. Le courantvarie alors de facon sigmoıdale avec le temps :

i(t)i(0)

=1

1 + [CO]0KI

e−tτ

(20)

et seule la constante d’inhibition apparenteKI = ka/ki peut etre mesuree [P24] (fig. A).Au contraire, si ki et ka sont petits, commec’est le cas pour le double mutant L122M-V74M (fig. 19), la variation d’activite au coursdu temps est alors lente (qu’il s’agisse de l’in-activation initiale ou du recouvrement d’acti-vite lorsque le CO s’est echappe de la cel-lule) et c’est ce retard qui contient l’infor-mation sur les constantes de vitesse de diffu-sion du CO a l’interieur de l’enzyme. ki et ka

peuvent alors etre determines independammenten parametrant les donnees avec la solution de

l’equation 19 [P28] (fig. B) :

i(t)i(0)

= eki[CO]0τe−tτ −kat

×(

e−ki[CO]0τ+∫ t

0

kae−ki[CO]0τe−uτ +kaudu

)(21)

Encart 8.4: Mesure des vitesses de diffusion intramoleculaire le long des canaux de l’hy-drogenase de fructosovorans [P24,P28].

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C. Leger. UPR 9036. Memoire d’HDR. 2007.

8.5 Conclusion : sur l’utilisation de l’electrochimie directe pour l’etude des

metalloenzymes

Je me suis familiarise avec la technique de l’electrochimie directe, et j’ai contribue a ladevelopper, au cours d’un post-doctorat de trois ans dans le laboratoire de Fraser Armstrong,a Oxford.

Cette technique a l’avantage de ne demander que de tres petites quantites de proteines,et permet d’obtenir des informations originales pour deux raisons principales. La premiereest qu’il est possible de mesurer continument l’activite de l’enzyme en fonction du potentield’electrode qui influe sur son etat redox. D’autre part, la mesure d’activite comme un courantest virtuellement instantanee, ce qui permet d’etudier precisement les variations d’activite quiresultent de modifications rapides des parametres experimentaux. La possibilite pour certainssystemes d’utiliser la mutagenese dirigee offre un degre de liberte supplementaire.

Depuis mon arrivee au BIP, nous avons pu developper de nouvelles methodologies per-mettant d’utiliser cette technique pour obtenir des informations originales sur chacune desetapes du cycle catalytique. Des informations quantitatives precieuses peuvent parfois etreobtenues au prix d’un certain effort de modelisation (cette technique est recente et encore encours de developpement) et c’est une des caracteristiques de notre equipe que de mettre aussil’accent sur les aspects methodologiques formels. Cet aspect du travail a ete possible gracea l’enthousiasme et aux competences des physiciens de l’equipe de Bruno Guigliarelli et toutparticulierement de Patrick Bertrand avec qui j’ai etroitement collabore.

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9 Objectifs

9.1 Vers une vision integree du mecanisme des enzymes multicentres

La nouvelle equipe “Dynamique reactionnelle des enzymes redox multicentres” sera creeea l’occasion du renouvellement du laboratoire en janvier 2008, et comprendra des anciensmembres de l’equipe de Biophysique des Metalloproteines (Patrick Bertrand PR1 UP et moimeme), une nouvelle electrochimiste au BIP, Carole Baffert, recrutee comme Mcf a l’Uni-versite de Provence a l’automne 2006, et deux non-permanents, un post-doctorant, VincentFourmond, a partir de mars 2007 et Fanny Leroux, monitrice et doctorante a l’Universite deProvence, qui a commence sa these a l’automne 2006.

Il s’agira, en complement de l’approche spectroscopique de l’equipe dirigee par BrunoGuigliarelli, de mettre particulierement l’accent sur les aspects dynamiques du fonctionnementd’enzymes respiratoires. Dans ces proteines, la reactivite chimique est localisee au niveaudu site actif, mais le fonctionnement global fait aussi intervenir des etapes de transfert deprotons (depuis et vers le solvant), d’electrons (depuis et vers un partenaire redox), ainsi quele transport de matiere (substrat et produit de la reaction) entre le site actif et le milieuexterieur. Ces etapes se produisent sur des sites de l’enzyme qui sont distincts et quelquefoisdistants de plusieurs dizaines d’Angstroms, de telle sorte qu’il faut repenser le mecanismed’une enzyme multicentre comme un processus largement delocalise. Ces etapes sont difficilesa etudier a l’aide de techniques classiques, mais notre objectif est de caracteriser chacuned’elles dans un petit nombre de systemes modeles, et surtout de comprendre la facon dont ellesconcourent a donner a l’enzyme ses proprietes catalytiques globales, en termes de specificiteet de directionnalite. Il n’y a en effet pas de raison de supposer que la chimie au site actif estl’evenement le plus lent dans le cycle catalytique, et pour chaque enzyme etudiee fonctionnantdans des conditions experimentales particulieres, on ne sait pas a priori quelle etape estdeterminante en vitesse pour le processus catalytique global. Il est aussi possible que l’etapelimitante en vitesse ne soit pas la meme lorsque l’enzyme fonctionne en oxydation ou enreduction : chacune de ces etapes a donc potentiellement un role dans la determination du“biais catalytique” de l’enzyme (defini par exemple comme un rapport de vitesses maximalespour les reactions en sens opposes).

La technique d’electrochimie directe est particulierement adaptee a l’etude des hydrogenasespour lesquelles elle permet de lever certains des verrous qui empechent sa caracterisation, maisnous avons aussi choisi d’autres systemes pour la variete de leurs sites actifs, architectureset proprietes catalytiques (nitrite reductase penta-hemique, nitrate reductases au molybdene,flavocytochrome b2). Ces etudes se feront en collaboration avec plusieurs equipes de biochi-mistes :

– Marc Rousset (BIP-MRS-CNRS)– Marie-Therese Giudici (BIP-MRS-CNRS),

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C. Leger. UPR 9036. Memoire d’HDR. 2007.

– Isabel Moura (Lisbonne),– David Pignol (LBC-Cadarache-CEA),– Florence Lederer (LEBS-Gif-CNRS),– Philippe Soucaille et Laurence Girbal (LBB-Toulouse-CNRS/INRA/INSA).

Partenaires de deux consortiums differents qui regroupent des equipes travaillant sur l’hy-drogenase NiFe, d’une part et sur des enzymes de la famille de la DMSO reductase, d’autrepart, nous nous interesserons aux developpements methodologiques et a l’utilisation de latechnique d’electrochimie directe pour :

– l’etude detaillee de certaines etapes des cycles catalytiques de metalloenzymes quipeuvent etre difficiles a sonder specifiquement par des techniques classiques, et

– la comprehension des bases moleculaires de certaines proprietes globales de ces cataly-seurs, liees par exemple a la directionnalite des reactions catalysees et a la specificitevis-a-vis du substrat.

9.2 Directionnalite des hydrogenases

Nous nous interesserons particulierement a l’elucidation des determinants moleculaires du“biais catalytique” des metalloenzymes bi-directionnelles, qu’on peut quantifier, par exemple,par le rapport des vitesses maximales pour les reactions en sens opposes. Il est remarquableque cet aspect du fonctionnement ait ete tres peu aborde dans le cas des oxydoreductases.

Dans le cas des oxydoreductases, l’examen de la litterature montre que diverses hypothesessont avancees pour expliquer le biais des enzymes. S’agissant des flavoenzymes, l’explicationla plus frequente21 (mais a ma connaissance jamais reellement testee) est que celui-ci estdetermine par l’ecart de potentiel de reduction entre le site actif et le substrat. Au contraire,au cours de l’etude de nombreux mutants de l’hydrogenases NiFe initialement construits poursonder l’une ou l’autre des etapes du mecanisme, nous avons identifie plusieurs mutants pourlesquels des acides amines distants du site actif ont ete modifies (et pour deux d’entre eux, nousavons verifie que les proprietes electroniques et redox du site actif NiFe etaient inchangees)avec un effet spectaculaire sur le biais catalytique. Dans l’un des ces deux cas, nous avons crutrouver la raison pour laquelle un tel effet est observe (voir l’encart page 57).

Notre explication a tout d’abord ete tres critiquee par un reviewer dont nous citons icile commentaire parce qu’il illustre une certaine confusion au sujet de l’utilisation dans cecontexte de la loi d’action de masse :

“Enzymes cannot alter the overall thermodynamics of the reactions they ca-talyze (First Law of Thermodynamics) and in lowering the activation barrier inone direction they must necessarily accelerate the reaction in reverse. It is a well-established principle that enzymes simply accelerate the rate of equilibration bet-ween substrate and product and cannot influence which is preferentially formed.(. . . ) it is not correct to speak of the enzyme itself as being biased toward H2

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Fig. 20: Catalyse reversible de la conver-sion fumarate/succinate par la fumaratereductase de coli. [S] = 1.2mM et [F ] =4µM. Le potentiel en circuit ouvert estmarque d’un rond noir. Il correspond aupotentiel du couple F/S, qui peut etre cal-cule pour un rapport de concentrationsdonne a partir de l’equation de Nernst etde la valeur publiee E0′

F/S ≈ +20mV a

pH 7 ; EF/S = E0′

F/S + RT2F ln([F ]/[S]) =

−46mV [P15].

production or consumption, as the authors do. On the basis of the First Law, thissimply cannot be.”

Le malaise disparait lorsque l’on realise que nous definissons le biais comme un rapport devitesses maximales mesurees dans des experiences qui se deroulent chacune dans des conditionsdifferentes : ce rapport de vitesse la ne s’identifie pas a une constante d’equilibre et n’est pasdetermine par la thermodynamique. La loi d’action de masse selectionne dans des conditionsexperimentales particulieres la direction dans laquelle une reaction peut se produire ; elle neprejuge pas de l’existence d’un catalyseur pour cette reaction, ni ne prevoit la cinetique decette reaction.54

Dans le cas d’une enzyme bidirectionnelle, le signal electrochimique catalytique est naturel-lement tres illustratif de cette difference entre la thermodynamique et la cinetique parce qu’ilest une mesure de la vitesse de turnover de l’enzyme en fonction de la force motrice (thermody-namique) et le biais de l’enzyme peut etre evalue au cours d’une seule experience (un balayagede potentiel). Cela est illustre sur la fig. 20, qui montre la conversion fumarate/succinate parla fumarate reductase, lorsque ces deux molecules sont presentes simultanement en solution.La thermodynamique ne predit que la valeur du potentiel d’electrode (marque d’un rond noir)pour lequel les reactions en sens inverses se compensent exactement et le courant s’annule

54Dans la section appelee “One-way enzymes” de son livre “Fundamental of enzyme kinetics” (PortlandPress, 2004), Athel Cornish-Bowden ecrit :

“Some enzymes are much more effective catalysts for one direction than the other. As a strikingexample, the limiting rates of the forward reaction catalyzed by methionine adenosyltransferaseis about 105 greater than that for the reverse direction, even though the equilibrium constantis close to unity. Even after a thorough discussion of this type of behavior by W. P. Jencks(1975), many biochemists remain rather uneasy about it, suspecting that it may violate the lawsof thermodynamics.”

Jencks explique cette observation par un effet qu’il appelle “Circe,” d’apres le nom de la magicienne quiseduit et retient Ulysse dans l’Odyssee. Selon Jencks, le biais catalytique est la consequence de l’existence d’undifferentiel d’affinite pour le substrat et le produit de l’enzyme, “Binding energy, specificity and enzymaticcatalysis : the Circe effect,” dans “Advances in enzymology and related areas of molecular biology,” ed. AltonMeister, vol 43, p. 219–410 (1975).

Ce travail concerne les enzymes a un seul substrat, et ne s’applique pas directement aux oxydoreductasesqui nous interessent.

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(il s’agit du potentiel de reduction formel du couple succinate/fumarate, a ce pH et pources concentrations en substrat et produit). Cette valeur n’est pas une propriete de l’enzyme,contrairement au reste du signal electrochimique qui montre des courants d’oxydation et dereduction d’amplitudes comparables alors que dans cette experience le succinate est 300 foisplus concentre que le fumarate ; cela montre et quantifie le biais de l’enzyme dans le sensphysiologique.

Nous avons l’intention d’approfondir ces aspects sur deux systemes modeles (hydrogenasesNiFe et FeFe), pour lesquels nous disposons de mutants. Au dela de l’aspect fondamental lieau metabolisme de l’hydrogene dans le monde vivant, ce travail pourra avoir des retombeesen terme de valorisation des enzymes, puisque la plupart des applications des hydrogenasesrequierent que l’enzyme fonctionne preferentiellement dans l’un ou l’autre sens.

Le tableau ci-dessous resume un certain nombre deresultats cinetiques caracterisant l’hydrogenase sau-vage de D. fructosovorans et les mutants H184G etH184C. La vitesse maximale de reduction des pro-tons est peu influencee par les mutations (un facteurdeux) alors que les vitesses d’oxydation de H2 parMV et MB varient beaucoup plus fortement (envi-ron d’un facteur 100). Dans ces mutants, les pro-prietes spectroscopiques et redox du site actif sont in-changees, et effectivement, la vitesse d’echange iso-topique n’est pas influencee par la mutation. Cettereaction de formation de HD a partir de D2 impliquele site actif et les processus de transfert de protons,mais pas les centres FeS.La raison fondamentale pour laquelle la mutationchange le biais de l’enzyme est que l’etape limitanteen vitesse dans le processus catalytique n’est pas lameme lorsque l’enzyme oxyde l’hydrogene et lors-qu’elle reduit les protons, et que les mutations ralen-tissent la vitesse d’une etape qui n’est limitante quedans le premier cas.

En effet, c’est le TE intermoleculaire qui est limi-tant en vitesse pour le processus d’oxydation de l’hy-drogene, comme le prouve le fait que le turnoverdepend beaucoup de la nature du partenaire redox ;il est meme au moins un ordre de grandeur plus elevelorsque l’enzyme echange des electrons avec uneelectrode, d’apres Pershad & Armstrong, Bioche-mistry 38 8992 (1999) http://dx.doi.org/10.1021/bi990108v. Le fait que la mutation P238Cqui accelere le TE intramoleculaire n’a pas d’ef-fet sur la vitesse de turnover dans des experiencesde cinetique homogene est aussi une indication quele TE intramoleculaire n’est pas limitant en vitesselorsque le MV accepte les electrons.39 La forma-tion de H2 est limitee par une etape de transfertde protons, Bertrand et al., JBIC 5 682 (2000)http://dx.doi.org/10.1007/s007750000152.D’autre part, l’etude electrochimique a montre que lavitesse du TE interfacial (et donc aussi, vraisembla-blement, intermoleculaire) est largement influenceepar les mutations.

Reaction : oxydation de H2 echange isotopique reduction de H+

Partenaire redox : MV oxyde 100µM MB none MV reduitKm

(a) vm(b) v (c) v (d) Km

(a) vm(b)

WT 9 500 1000 87 0.02 130H184G 2.2 15 23 74 0.044 96H184C 16 8.4 7 70 0.033 61

Pour les vitesses, 1 Unit ≈ 1.5 mol de gaz/s/mole d’enzyme (a) Km en mM (b) vitesses maximales (a

concentration en partenaire redox infinie) (c) vitesses en presence de 100 µM MB oxyde (� Km) (d) vitesse

de formation de HD dans la reaction d’echange H+/D2. pH 8 pour l’oxydation de H2 et l’echange H+/D2,

pH 7 pour la formation d’H2. D’apres [P27].

Encart 9.1: Comment l’histidine 184 ligand du cluster distal des hydrogenases NiFe (fig. 13)influence le biais catalytique de l’enzyme.

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9.3 Specificite des molybdoenzymes de la famille de la DMSO reductase

Dans le cadre d’une demande de financement ANR “Physique et Chimie du Vivant,”j’ai porte un projet intitule “Engineering the Reactivity of Complex Molybdoenzymes,” encollaboration avec les equipes de Wolfgang Nitschke au BIP, David Pignol au CEA/Cadaracheet Axel Magalon, au LCB/CNRS/Marseille.

Notre objectif est d’identifier les determinants moleculaires qui pilotent le fonctionnementcatalytique des enzymes de la famille de la DMSO reductase (fig. 10 et texte page 32), gracea une strategie integree combinant des approches de biologie moleculaire, de biophysique(spectroscopies avancees, electrochimie) et de modelisation. Ces approches seront mises enœuvre sur un petit nombre de molybdoenzymes modeles, bien maıtrisees sur le plan de laproduction. Notre but sera de controler leur reactivite en agissant sur les facteurs que nousaurons identifies. A terme, il s’agira d’orienter, grace a une ingenierie moleculaire raisonnee,la reactivite d’enzymes de type nitrate reductase vers l’oxydation ou la reduction d’oxydestoxiques.

Nous avons selectionne parmi les enzymes de la famille de la DMSO reductase deux nitratereductases et une arsenite oxydase comme systemes modeles sur la base des criteres suivants :

– Elles illustrent la diversite de reactivite, de structure du site actif et d’architectureoligomerique des enzymes de cette famille.

– Les reactions catalysees sont liees a des preoccupations d’ordre environnemental.– Leurs structures 3D sont connues (deux d’entre elles ont ete determinees dans les labo-

ratoires associes a ce projet).– Nous possedons les capacites de production et de purification a grande echelle de ces

proteines, permettant la mise en œuvre de techniques spectroscopiques exigeantes quanta la quantite de materiel biologique disponible.

– Nous sommes capables de les modifier selectivement par des techniques de biologiemoleculaire.

Nous etudierons ces systemes complexes sur la base d’une approche interdisciplinaire al-liant des techniques electrochimiques modernes, des spectroscopies optiques et magnetiquesavancees (EPR, ENDOR, MCD) ou resolues en temps, la cristallographie, la biochimie, lamutagenese dirigee.

Nous nous interesserons a tous les aspects de leur fonctionnement : proprietes structurales,electroniques et redox des sites actifs, dynamique du transfert intramoleculaire d’electrons etde protons, TE intermoleculaires impliquant les sites redox membranaires d’interaction avecles quinones. Au-dela de l’etude detaillee de chacun des systemes, c’est la comparaison de leursproprietes specifiques qui constituera le fil conducteur et l’approche originale de ce projet.Nous chercherons surtout a aborder les questions transversales et ambitieuses, qui debordentlargement le champ thematique des molybdoenzymes, liees a la specificite des enzymes vis-a-vis de leurs substrats, a la directionnalite de la reaction catalysee, et aux aspects integres et

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dynamiques du fonctionnement.Ces etudes apporteront un ensemble de connaissances nouvelles sur les determinants struc-

turaux de la reactivite de ces oxydoreductases complexes, connaissances que nous mettrons al’epreuve en utilisant la mutagenese dirigee afin de reorienter le fonctionnement d’une nitratereductase, pour inverser le sens de la catalyse et/ou augmenter sa reactivite vis-a-vis de sub-strats alternatifs, comme des oxydes toxiques. Le fait que les enzymes qui ont une activitephysiologique et specifique de bioremediation (y compris les arsenite oxydases) appartiennenttoutes a la famille de la DMSO reductase suggere que les nitrates reductases que nous etudionssont, en effet, les gabarits ideaux pour induire de facon raisonnee ce type de reactivite.

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10 Articles choisis

“Front dynamics during diffusion-limited corrosion of ramified electrodeposits,” C. Leger,F. Argoul? and M. Z. Bazant, J. Phys. Chem. B, 103-28, 5841–5851 (1999).Cet article illustre mon travail de these, et concerne l’interpretation de la relaxation du champde concentration equivalente dans une cellule d’electrodeposition bidimensionnelle apres lacroissance d’un depot presque 1D. Nous demontrons et utilisons l’analogie avec un problemede reaction-diffusion tres classique : celui ou dans une geometrie 1D, deux reactifs sont ini-tialement separes et soudainement autorises a diffuser l’un vers l’autre et reagir. Le problemeest simple a poser, mais sa non-linearite entraıne une grande richesse d’un point de vueexperimental et theorique. C’etait la premiere etude experimentale d’un tel probleme dans lecas ou l’un des reactifs (ici, le depot) est immobile.http://dx.doi.org/10.1021/jp990486+

“Enzyme electrokinetics : energetics of succinate oxidation by fumarate reductase and suc-cinate dehydrogenase,” C. Leger, K. Heffron, H. Pershad, E. Maklashina, C. Luna-Chavez,G. Cecchini, B. A. C. Ackrell and F. A. Armstrong,? Biochemistry, 40-10, 3117–3126 (2001).Cet article demontre dans un exemple tres simple (du point de vue de la modelisation) legain substantiel d’information que permet l’electrochimie directe par rapport aux techniquesde mesures d’activite classiques.http://dx.doi.org/10.1021/bi010889b

“Effect of a dispersion of interfacial electron transfer rates on steady state catalytic elec-tron transport in NiFe-hydrogenase and other enzymes,” C. Leger, A. K. Jones, S. P. J.Albracht and F. A. Armstrong,? J. Phys. Chem. B, 106-50, 13058–13063 (2002).Cet article propose la seule explication a ce jour d’un phenomene observe dans de nombreuxcas de signaux electrochimiques obtenus avec des catalyseurs adsorbes : l’absence de plateaude courant a haute surtension (fig. 8, page 29). Nous l’attribuons a l’existence d’une distri-bution d’orientations pour le transfert d’electron (TE) interfacial.http://dx.doi.org/10.1021/jp0265687

“Electron flow in multicenter enzymes : theory, applications and consequences on the na-tural design of redox chains,” C. Leger,? F. Lederer, B. Guigliarelli and P. Pertrand, J. Am.Chem. Soc., 128-1, 180–187 (2006).Une difference fondamentale entre les enzymes respiratoires et photosynthetiques est que dansle deuxieme cas, l’absorption d’un photon declenche le TE (la separation de charge) sans fairevarier le nombre total d’electrons dans l’enzyme,55 alors que le fonctionnement d’une enzyme

55Pour un exemple de traitement rigoureux de la cinetique de TE intramoleculaire transitoire dans letetraheme du centre reactionnel de viridis, voir Alric et al., JACS 128 4136 (2006) “Kinetic performance

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redox fait potentiellement intervenir autant d’etat redox “macroscopiques” qu’il y a de centresredox. Pour etudier la cinetique de TE dans un tel systeme, il faut considerer tous les etats“microscopiques” de l’enzyme, et autant d’equations differentielles couplees : on en denombre3 × 2 = 6 dans une enzyme simple comme le flavocytochrome b2 qui ne contient qu’un seulrelais, 3 × 23 = 24 dans l’hydrogenase NiFe et 3 × 29 = 1536 dans le Complexe I.56 Nous nenous attaquons ici qu’au probleme le plus simple.http://dx.doi.org/10.1021/ja055275z

“Changing the ligation of the distal [4Fe4S] cluster in NiFe hydrogenase impairs inter-and intramolecular electron transfers” S. Dementin, V. Belle, P. Bertrand, B. Guigliarelli, G.Adryanczyk-Perrier, A. Delacey, V. M. Fernandez, M. Rousset and C. Leger.? J. Am. Chem.Soc. 128-15, 5209–5218 (2006).L’un des clusters [4Fe4S] de l’hydrogenase NiFe est coordinne par trois cysteines et une histi-dine, alors que l’immense majorite des clusters [4Fe4S] sont coordinnes par quatre cysteines.Nous avons eu la chance de pouvoir etudier des mutants dans lequel cette histidine est sub-stituee sans que cela n’affecte le repliement de la proteine ou la nuclearite du cluster.57 Notretravail rapporte la premiere etude fonctionnelle du role d’un tel ligand et les seuls resultatsexperimentaux sur la cinetique de TE intramoleculaire entre clusters FeS dans une enzymerespiratoire.35

http://dx.doi.org/10.1021/ja060233b

and energy profile in a roller coaster electron transfer chain : a study of modified tetraheme-reaction centerconstructs” http://dx.doi.org/10.1021/ja058131t.

56Dans le cas du Complexe I, nous ignorons comment le calcul a pu etre mene dans Dutton et al., BBABioenergetics 1757 1096 (2005) “Electron tunneling chains of mitochondria” http://dx.doi.org/10.1016/j.

bbabio.2006.04.01557Pour de nombreux contre-exemples, voir Moulis, JBIC 1 2 (1996) “The coordination sphere of iron-sulfur

clusters : lessons from site-directed mutagenesis experiments” http://dx.doi.org/10.1007/s007750050017.

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Front Dynamics during Diffusion-Limited Corrosion of Ramified Electrodeposits

Christophe Leger and Francoise Argoul*Centre de Recherche Paul Pascal, AVenue Schweitzer, 33600 Pessac, France

Martin Z. BazantDepartment of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

ReceiVed: February 9, 1999; In Final Form: May 1, 1999

Experiments on the diffusion-limited corrosion of porous copper clusters in thin gap cells containing cupricchloride are reported. By carefully comparing corrosion front velocities and concentration profiles obtainedby phase-shift interferometry with theoretical predictions, it is demonstrated that this process is well-describedby a one-dimensional mean-field model for the generic reaction A + B (static) f C (inert) with only onediffusing reactant (cupric chloride) and one static reactant (copper) reacting to produce an inert product (cuprouschloride). The interpretation of the experiments is aided by a mathematical analysis of the model equations,which allows the reaction order and the transference number of the diffusing species to be inferred. Physicalarguments are given to explain the surprising relevance of the one-dimensional mean-field model in spite ofthe complex (fractal) structure of the copper clusters.

I. Introduction

Diffusion-limited processes are ubiquitous in physics,1 chem-istry,2 and biology.3 Reaction-diffusion processes have beenthe subject of intense and continuous interest since the work ofSmoluchowski.4-6 A crucial feature of many such processescontrolling pattern formation and reaction efficiency is the“reaction front”, a dynamic but localized region where reactionsare most actively occurring and which separates regions rich inthe individual reactants. The simplest theoretical model of areaction front, introduced more than a decade ago by Galfi andRacz,7 is the “mean-field” model for two initially separatedspecies A and B reacting to produce an inert species C. Sincethen, the case of two diffusing reactants A and B has beenthoroughly studied analytically7-10 and numerically,11-21 andsome predictions of the mean-field model have been checkedin the experiments.21-30

In contrast, the case of only one diffusing reactant A andone static reactant B (confined on a fixed matrix) has not yetbeen studied experimentally. We show in this paper that thecorrosion of a porous solid (B) immersed in a chemically activefluid suspension (A) can also be described by such a mean-field model. Some analytical10,31 and numerical11,32 studies existfor this case as well, but since it is more microscopicallycomplex (for a real porous interface) than the case of twodiffusing reactants (in a homogeneous medium) an experimentaltest of the model is needed.

The mean-field model of a planar reaction front for thechemical reaction

postulates that the concentrations FA(X, T) and FB(X, T) ofspecies A and B, respectively, evolve according to a pair ofcoupled partial differential equations10,31

where DA is the diffusion constant for species A and R(FA,FB)is the reaction rate density. The most frequently used initialconditions assume that the reactants are uniformly distributedand completely separated at first, FA(X,0) ) F°AH(X) andF°B(X,0) ) F°BH(-X), where H(X) is the Heaviside unit stepfunction. Such initial conditions are easier to reproduce inexperiments than those involving uniformly mixed reactants.There are several assumptions behind eqs 2 and 3: (i) Theproduct C is generated in small enough quantities that itspresence does not significantly affect the dynamics. (ii) Theconcentrations are dilute enough that the diffusivities areconstant. (iii) The fixed matrix containing reactant B (static) isporous enough that reactant A can freely diffuse through it. (iv)The reaction rate is a function of only the local concentrationsand not any fluctuations or many-body effects (which is the“mean-field approximation”). It is common to make the mean-field approximation under the assumption R(FA,FB) ) kFA

m FBn ,

but in the interpretation of our experiments we will not assumeanything about the form of R(FA,FB) a priori since the reactiontakes place at a solid-liquid interface. Moreover, this interfaceis highly ramified, and therefore, the underlying microscopicdynamics is expected to be more complex than for simplehomogeneous kinetics.

In this paper we carefully test the validity of these assump-tions with experiments on a particular porous-solid corrosionsystem: copper clusters corroded by a cupric chloride (CuCl2)electrolyte. The clusters are obtained by thin gap cell elec-trodeposition from a CuCl2 electrolyte at fixed current. Thisprocess builds a depletion layer of CuCl2 ahead of the copper

A (diffusing) + B (static)f C (inert) (1)

∂FA

∂T ) DA∂

2FA

∂X2 - R(FA,FB) (2)

∂FB

∂T ) -R(FA,FB) (3)

5841J. Phys. Chem. B 1999, 103, 5841-5851

10.1021/jp990486+ CCC: $18.00 © 1999 American Chemical SocietyPublished on Web 06/25/1999

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deposit. When the current is switched off, the CuCl2 depletionlayer relaxes toward the copper cluster, bringing Cu2+ cationsthat react with copper according to

where the cuprous chloride (CuCl) is produced in the form ofsmall (white) crystallites that drop down to the bottom of thecell.

In section II we describe the experimental setup and themethod used to prepare the porous clusters to be corroded. Insection III we report the experimental evidence that ourcorrosion system behaves like a 1D diffusion-reaction processwith one static reactant. In section IV, a mathematical analysisis presented that makes quantitative predictions based on theexperimental data of section II, within the theoretical frameworkof the mean-field model, eqs 2 and 3. Also in section IV, theexperimental results are revisited to refine the comparison withthe theoretical model and to discuss in some detail its physicallimitations.

II. Experimental MethodsA. Apparatus. The experiments are performed in a thin gap

electrodeposition cell, which is depicted schematically in Figure1. The cell consists of an unsupported, aqueous solution of CuCl2confined to a narrow region of dimensions W ) 5 cm × L )8 cm × δ ) 50 µm between two closely spaced, optically flatglass plates (λ/4 over 80 mm × 50 mm). Two parallel, ultrapurecopper and silver wires (50 µm diameter, Goodfellow 99%purity) are inserted between the two glass plates to act both asspacers and as electrodes. During the electrodeposition (priorto corrosion) the wires are polarized so that the silver wire actsas the cathode and the copper wire as the anode. The solutionsof CuCl2 (ACS reagent) are prepared from deionized water,carefully cleaned of any trace of dissolved oxygen by bubblingnitrogen through it for 1 h. The anodic part of the cell (notshown in Figure 1) is filled by a dilute solution of CuCl2 topostpone the precipitation of the salt due to saturation effectsby dissolution of the anode. The copper electrodeposits are allgrown at constant current, and the entire experiment isperformed at room temperature (≈20 °C).

Digitized color pictures of the copper clusters are obtainedby direct imaging of the cluster through a lens, using a three-CDD camera coupled with an 8-bit frame grabber from DataTranslation driven by the public domain software IMAGE,33

which successively captures three RGB frames and from themreconstructs the color image.

A phase-shift Mach Zehnder interferometer is used indepen-dently to resolve the concentration field, averaged over the depthof the cell. A sketch of the interferometer can be found in ref

34. The interference patterns are recorded through a CCDcamera coupled to the same frame grabber33 with a 768 × 512pixel resolution. Phase-shift interferometry offers several sig-nificant advantages over traditional interferometry in that itprovides an accurate reconstruction of the entire concentrationfield, using a set of successive interference pictures recordedfor shifted values of the phase difference between two opticalwavefronts and can also be used as an holographic interferom-eter.35

B. Preparation of Copper Clusters by Electrodeposition.When current flows from the anode to the cathode, chargetransfer occurs at the cathode, leading to the reduction of coppercations into copper metal according to34,36,37

The actual mechanism of deposition is much more complex thanthis two-electron transfer process since competitive reactionsinvolving the solvent species are likely to occur. Nevertheless,in CuCl2 electrolytes, we have observed that the formation ofcuprous oxide (Cu2O) in competition with copper by reductionof Cu2+ cations is not favored, contrary to what is observed incopper sulfate (CuSO4) solutions,38-40 which can be partlyexplained by the strong adsorption and complexation propertiesof chloride anions.37 This reduction process on the cathodeimplies a local depletion of the copper cations close to thecathode and also their replenishment by a global transportprocess, namely diffusion. Although electromigration alsocontributes to transport, it does not act independently of diffusionin regions where electroneutrality is maintained,41 which meanseverywhere in the cell outside the 10-100 Å thick doublelayer.42,43 This often misunderstood fact was given a firmtheoretical basis by Newman over 30 years ago in his asymptoticanalysis of the transport equations for a rotating disk electrode,44

but only recently has it been quantitatively verified in experi-ments (by our group) for the case of constant boundary flux ata fixed cathode.34,36 In summary, the theoretical and experi-mental evidences indicate that in the absence of convection theconcentration FA of a dilute, binary electrolyte evolves accordingto the classical diffusion equation

where DA is the “ambipolar diffusion coefficient” for theelectrolyte given by a certain weighted average of the diffusionconstants of the individual ions.41

When the interfacial concentration of metal cation Cu2+

approaches zero, the interface becomes unstable and developsinto a forest of fine spikes that compete with each other to invadethe cell.45,46 In some cases, a “dense-branched” pattern isselected.36,47-50 This morphology is characterized by a densearray of branches of invariant width advancing at constantvelocity V through the cell, whose tips delimit a nearly planarfront between the copper salt electrolyte and the deposit zone.We have shown recently that this growth regime can be modeledvia a 1D diffusion model through the measurement of the coppersalt concentration field ahead of the growing deposit byinterferometry.36,50 The experimental concentration field closelyfits the “traveling-wave” solution to eq 5,

where Ld ) DA/V, and X is the distance to the front edge of thecopper deposit, in the direction normal to the front, oriented

Figure 1. Schematic diagram of the thin gap electrodeposition cellcontaining a ramified, metallic copper deposit. Note that the size ofthe deposit has been enlarged for clarity.

CuCl2 (aq) + Cu (solid, red)f 2CuCl (solid, white) (4)

Cu2+ + 2e-f Cu

∂FA

∂t ) DA∇2FA (5)

FA(X) ) F°A (1 - exp-X/Ld) (6)

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toward the bulk electrolyte. The diffusion length Ld is propor-tional to F°A/j, where F°A is the initial bulk concentration incopper cations and j is the current density. This diffusion lengthtends to zero as j/F°A increases, and in that limit the concentra-tion profile looks like a step function. Note that FA(Xe0) ≈ 0and FA(X.Ld) ≈ F°A; i.e., the metallic copper deposit leavesbehind it a region entirely depleted in copper cations, pushingin front of it a diffusion layer of constant width extending intothe bulk electrolyte. Due to the conservation of copper duringthe deposition process, a linear relation exists between thevelocity V of the growth and the interfacial flux of cations J,namely VFB ) J, where FB is the mean concentration of(metallic) copper in the region of the deposit.

Using the relation V ) DA/Ld, the ratio of the copperconcentration in the bulk electrolyte F°A (where it takes theform of cupric ions) to that in the region of the deposit F°B(where it mostly takes the metallic form) is easily calculatedfrom the basic properties of the electrolyte36,48-50

where t+ is the transference number41,43 of the copper cation ina CuCl2 electrolyte. Practically, t+ is a characteristic of theelectrolyte and therefore q will not be a free parameter in ourexperiments (neither t+ nor q depend on the current density j).The closer t+ is to 1, the greater the concentration of copperinside the cluster. In CuCl2 electrolytes, t+ is expected to besmaller than 0.5, which implies that the copper composition ofthe deposited zone will not go beyond twice the originalconcentration of CuCl2 in the electrolyte. Therefore, the copperclusters obtained by thin gap electrodeposition in CuCl2 are infact highly porous.

The large porosity of the deposited copper clusters is offundamental importance in our subsequent study of the corrosionof the copper deposits once the current has been switched off(and the electrodeposition halted) because, as a consequence,the cupric ions are able to diffuse freely through the dendriteswith approximately their bulk diffusivity and then react with alarge exposed surface of metallic copper. The low density ofthe deposit also suggests that the product of the corrosionreaction, cuprous chloride (CuCl) crystal, is produced in smallenough quantities that its presence should not significantly affectthe dynamics of the reaction-diffusion process. Therefore, byinterrupting the current during electrodeposition, we can observea simple reaction-diffusion system with two initially separatedreactants, copper chloride (A) and metallic copper (B), onlyone of which is free to diffuse. Since the initial interface betweenthe bulk electrolyte and the ramified electrodeposit is planarand the deposit is disordered, it is likely that the dynamics ofthe corrosion process will be effectively “one-dimensional” (1D),in the sense that there might be nearly perfect translationalsymmetry in the two spatial directions (Y and Z) perpendicularto direction of the front propagation. Moreover, since thedynamics occurs in three dimensions (as opposed to two for asurface or one for a molecular channel), it is also likely that amean-field, continuum model will be valid, although this maynot seem obvious a priori in light of the complex geometry ofthe electrodeposits, which is known to be fractal.51-54

The rest of the paper is devoted to a careful, experimentalvalidation of these hypotheses, showing that our system is indeedaccurately described by a one-dimensional, mean-field modelfor the generic chemical reaction, A + B (static)f C. We begin

in the next section by describing the scaling behavior of thereaction front and accompanying depletion layer of CuCl2. Inthe following section, a mathematical analysis of the one-dimensional, mean-field model is presented, which incorporatesthe observed scalings and makes quantitative predictions regard-ing the reaction front speed and the concentration evolution.Finally, these predictions are checked with a more detailedanalysis of the experimental data in the last section, andarguments are given to explain the relevance of the one-dimensional, mean-field model for our experimental system.

III. Preliminary Experimental Results

A. Temporal Evolution of the Corrosion Front. At themoment when the current is switched off, the region of thecopper deposit is entirely depleted of cupric ions, which arethus initially separated from the metallic copper in the deposit.At later times, cupric ions diffuse amidst the copper dendritesand react at the metal surfaces, leaving behind cuprous chloride(CuCl) crystallites. In Figure 2a,b are shown images of a copperdeposit just prior to corrosion and after 30 min of corrosion,respectively. Note that in Figure 2b the interfacial regionbetween the red copper (the gray color in this picture) and thewhite CuCl is rather flat and thin.

Focusing on the temporal evolution of this red/white interface,we have observed that, while at first the white layer of CuClappears at the tips of the copper-deposit branches, it graduallybecomes flatter and flatter. As a result, the system approachestranslational invariance along the Y direction, normal to thegrowth direction X, thus justifying a one-dimensional modelfor the system involving the single spatial coordinate X (normalto the reaction front).

By carefully comparing the concentration field of cupric ionsobtained by phase-shift interferometry and the red/white, Cu/CuCl interface observed on the deposit, the location and extentof the reaction front, where there is a significant overlap ofmetallic copper and cupric ions, can be identified. Following atransient regime (which we describe in the last section), it isobserved that the reaction front approaches a constant width w

q ≡F°AF°B

) 1 - t+ (7)Figure 2. (a) Photograph of a copper deposit grown from a 0.5 mol‚L-1

CuCl2 solution at j ) 40 mA‚cm-2 for approximately 15 min. (b)Photograph of the same deposit 0.5 h after the current had been switchedoff. (The white zone is CuCl.) (c) The montage shows a sequence ofphotographs of a small region of the deposit including the reactionfront taken every 30 min after the interruption of the current.

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∼ TR with R ) 0, which is consistent with certain mean-fieldmodels.10,11,31 Using the theoretical methods pioneered by Galfiand Racz7 in the case of two diffusing reactants, this scalingwas first predicted by Jiang and Ebner11 using physicalarguments supported by computer simulations and later byKoza31 using asymptotic analysis.

Recently, Bazant and Stone10 have considered the case ofhigher-order reactions mA + nB (static) f C represented bythe mean-field reaction rate R(FA,FB) ) kFA

m FBn and proved that

the scaling exponent for the front width is given (uniquely) bythe formula

which holds for any real number m g 1. (The scaling solutiondoes not exist for m < 1.) In light of this result, the experimentalobservation R ) 0 is consistent with the usual one-dimensional,mean-field theory only in the case m ) 1. If higher-orderreactions were present, m > 1, the theory would predict thatthe reaction front width increases in time (R > 0) althoughalways more slowly than diffusion (R < 1/2).

The position of the reaction front Xf(T) during the corrosionof a copper deposit (grown from a 0.5 M CuCl2 solution at j )40 mA/cm2) is plotted in Figure 3. Note that, after initialtransients have vanished (T > 500 s), the reaction front itself“diffuses” with its position given by the scaling, Xf ∼ Tσ withσ ) 1/2, which is is also consistent with predictions of the one-dimensional mean-field model.7,11,31

B. Temporal Evolution of the Diffusion Layer. At T ) 0when the current is interrupted, the reactants Cu and CuCl2 arecompletely separated, since the concentration of CuCl2 isnegligibly small in the immediate vicinity of the metallic Cuelectrodeposit. During the subsequent corrosion process theconcentration of CuCl2 remains very small in the reaction front,which leads to the modification of the initial depletion layer ofCuCl2 (produced by the electrodeposition process) into a regionwhere the concentration smoothly interpolates to the value ofthe bulk solution far behind the front. The term “diffusion layer”is used to describe this region because it is characterized bythe transport of fresh CuCl2 by diffusion from the bulk, relativelyunaffected by chemical reactions due to the negligible (orvanishing) concentration of metallic Cu remaining behind thereaction front.

The temporal evolution of the diffusion layer is revealed byprecise interferometric measurements of the concentration profileof CuCl2. In Figure 4 are shown three contour plots of theconcentration field computed from the integrated index alongthe depth of the cell. Since the experiments are performed inthin gap cells (50 µm) and the depletion layer spreads overdistances larger than this gap, it is safely assumed that theconcentration of CuCl2 does not change appreciably along theZ direction (parallel to the laser beam36). In Figure 4, the shadowof the Cu/CuCl cluster is also clearly seen. A close inspectionof the panels (b) and (c), which correspond to eroded clusters,reveals that in the zone of the copper cluster where CuCl2 hasdiffused (recognizable where the leftmost isoconcentrationcontours have moved through the cluster), the cluster has beenbroken down into smaller crystallites, which, as indicated bytheir color in Figure 2, are made of CuCl.

Typical experimental concentration profiles of CuCl2 mea-sured at different times (averaged along the Y direction, normalto the growth direction) are shown in Figure 5. The shape ofthese concentration profiles is discussed in the next two sections,but here we focus on the scaling of the width Wd(T) of thediffusion layer (defined as the region of non-negligible gradi-ents). Figure 6 shows that at long times (T > 500 s), thediffusion layer approaches a self-similar structure, with thediffusive flux entering the reaction front obeying the scaling

Figure 3. log-log plot of the position of the reaction front Xf as afunction of time T for two different experimental runs in CuCl2 0.5mol‚L-1 for deposits grown at j ) 40 mA‚cm-2. The solid lines ofslope 1/2 represent the predictions of the one-dimensional, mean-fieldtheory, given by eq 41, with D ) 10-5 cm2‚s-1, in the cases q ) 0.6and q ) 0.73.

R )m - 1

2(m + 1)(8)

Figure 4. Interferometric characterization of the concentration fieldaround a copper deposit during its dissolution (a) just before theinterruption of the current, (b) 15 min later, and (c) 1 h later. (∆F ≈F°A/10 between adjacent isoconcentration lines.) The deposit grown in0.5 mol‚L-1 CuCl2 solution at j ) 40 mA‚cm-2 for 20 min. Theconcentration of CuCl2 is negligibly small inside and ahead (to theleft) of the reaction front and approaches the bulk value of 0.5 mol‚L-1

far behind (to the right of) the front.

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law Jd ∝ (∂FA/∂X)|X)Xf ∼ T-δ, and that, therefore, the width ofthe diffusion layer has the familiar scaling7,9,11,31 Wd ∼ Tδ withδ ) 1/2, which is another robust feature of the mean-fieldmodels.10

A physical argument based on mass conservation betweenthe diffusion layer and reaction front7,11 can be used to predictthe scaling of the reaction rate (per unit volume) in the front R∼ T-â from the preceding experimental observations. The totalreaction rate in the front (per unit area) scales as wR ∼ TR-â,and this flux of cupric ions due to reactions must balance thediffusive flux entering the front Jd ∼ T-δ, which yields thescaling relation, â ) R + δ ) 0 + 1/2 ) 1/2. It is important topoint out, however, that while R ) 0 and δ ) 1/2 are the resultsof direct experimental observations, the scaling exponent â )1/2 is only inferred by a physical argument, based on theassumption that chemical reactions are negligible in the diffusionlayer. Although this assumption has been checked numerically

and analytically for various mean-field models, the reaction rateis not directly measured in our experiments.

In the general case R(FA,FB) ) kFAm FB

n mentioned above, itcan be shown10 that â is given (uniquely) by

so that once again m ) 1 is suggested by the inferred value â) 1/2. However, given that the experimental system has acomplex fractal structure and three-dimensional transport in thereaction front, it is not obvious a priori that R(FA,FB) ) kFA

m FBn

is a reasonable approximation within a spatially averaged one-dimensional model. Instead, we will make no ad hoc assump-tions about the functional form of the reaction rate R(FA,FB)and then explore consequences of only our direct experimentalobservations, R ) 0 and δ ) σ ) 1/2, within the framework ofa one-dimensional mean-field model.

IV. Theoretical Predictions of the Mean-Field ModelA. Dimensionless Model Equations. The model equations

have a dimensionless form involving only the parameter, q ≡F°A/F°B, defined in eq 7,

with boundary and initial conditions

where

These initial conditions are closest to the actual ones used inthe experiments when the copper deposit is grown at largecurrent, which corresponds to small Ld in eq 6. The initial-boundary-value problem of eqs 10-14 involves an idealized,infinite system possessing no natural length or time scale, andtherefore, it is expected that asymptotic similarity solutions existin which distance and time appear coupled by power-lawscalings.55 The experimental system, on the other hand, pos-sesses several relevant length scales, but they turn out not toaffect the evolution of the reaction front, at least for some rangeof times. For example, the spatial scales of the copper deposit,such as the typical dendrite spacing and dendrite width, surelyaffect the dynamics at early times since these length scales areof the same order as the diffusion length Ld,36 but it is observedthat during corrosion the system quickly approaches planarsymmetry, averaged across scales much larger than individualdendrites. Likewise, the length scale of the gap spacing is not

Figure 5. One-dimensional concentration profiles extracted from thetwo-dimensional data. The deposit has been grown from a 1 mol‚L-1

CuCl2 solution at j ) 68 mA‚cm-2 over 15 min. The concentrationprofiles are shown every 15 min after the current had been switchedoff. The different symbols are added on each profile to differentiatethe recording times. These symbols will be used on the next representa-tions of the concentration profiles in Figures 9 and 10.

Figure 6. log-log plot of the temporal evolution of the derivative ofa(X,T) at X ) 0 as a function of T. Same parameters as in Figure 5.The plain line corresponds to the prediction of eq 45 with D ) 10-5

cm2‚s-1 and q ) 0.79.

â )m

m + 1 (9)

∂a∂t )

∂2a

∂x2 - r(a,b) (10)

∂b∂t ) -qr(a,b) (11)

a(-∞,t) ) 0, a(∞,t) ) 1 (12)b(-∞,t) ) 1, b(∞,t) ) 0 (13)

a(x,0) ) H(x), b(x,0) ) H(-x) (14)

a ≡FA

F°A, b ≡

FB

F°B(15)

r(a, b) ≡R(aF°A,bF°B)R(F°A,F°B)

(16)

t ≡R(F°A,F°B)T

F°A, x ≡ X x

R(F°A,F°B)(DAF°A)

(17)

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expected to greatly influence the corrosion dynamics becausevertical (buoyancy-driven) convection, which has been observedduring the growth phase56 is suppressed in 50 µm depth cells.34,57

However, the settling of the reaction product, CuCl crystallites,could have some effect on the front dynamics at this scale.Finally, the largest length scales, namely the distances from theouter edge of the deposit to the two electrodes, also should notaffect corrosion dynamics until the reaction front gets close tothe cathode and/or the diffusion layer approaches the anode.Therefore, during intermediate times, after three-dimensionaltransient effects have subsided but before the system size beginsto matter, the corrosion dynamics should be well described bya self-similar solution to the one-dimensional mean-field equa-tions.

B. The Diffusion Layer. Motivated by these arguments, weconsider the transformation

for the concentration of CuCl2 in the diffusion layer (definedby ú > 0) with power-law expressions for xf(t) and Wd(t). Inlight of the experimental results from the previous section wemake the definitions Wd(t) ) 2xt and

where ν(q)2 is an effective diffusion constant for the reactionfront to be determined during the analysis. Substituting theseexpressions into eq 10, we have

which simply amounts to a change of variables from (x,t) to(ú,t).

The starting point for our analysis is the experimentalobservation (see below) that the concentration of CuCl2 ap-proaches a single, continuous profile in the ú coordinate

which has been called the “quasistationary approximation” inthe physics literature.9,15,31,58 This is not really an “approxima-tion” but is rather an exact asymptotic property of a certain classof solutions to eqs 10-13, which happens to fit the experimentaldata. To find such solutions from eq 21, we must assume t(∂A/∂t) f 0, ∂A/∂ú f A′(ú), and ∂2A/∂ú2

f A′′(ú) for fixed ú > 0.At this point it is customary31 to further assume ad hoc that thereaction term in eq 21 vanishes relative to the diffusion term

and that the concentration of the nondiffusing species alsovanishes in the diffusion layer, i.e., where the reaction fronthas already passed,

but Bazant and Stone have shown that these limits are actuallynecessary consequences of the assumed quasistationarity.10

With these arguments we are led to an ordinary differentialequation for A(ú) by taking the limit tf ∞ with fixed ú > 0 ineq 21:

The solution of this equation subject to the boundary conditionA(∞) ) 1 can be written in terms of error functions,59

where Ao ≡ A(0) is a constant to be determined by asymptoticmatching with the reaction front as úf 0. The function A(ú) isshown in Figure 7 for different values of ν. The slope of A(ú)at ú ) 0 given by

is the (dimensionless) diffusive flux into the reaction front.On the length scale Wd(t) ∝ t1/2 appropriate for the diffusion

layer, the limiting concentration fields just derived appear notto be differentiable at ú ) 0,

as t f ∞ with ú * 0 fixed, but as we have already observedexperimentally, that is only because in the reaction front(at ú ) 0) the concentrations are smoothly interpolated acrossthese apparent discontinuities on a much smaller length scalew ∝ tR ) o(Wd) since R < δ. In mathematical terms, theasymptotic approximations in eq 28 are not uniformly valid forall (x,t) as t f ∞, but rather are valid only for ú * 0, i.e. xt )O(|x + 2νxt|).

C. The Reaction Front. We now explore the consequencesof the experimental results R ) 0 and δ ) σ ) 1/2 within thepresent mathematical model. Although the physical argumentsmade above for the lack of a natural length scale are much moretenuous in the reaction front because the observed front width(about 0.2 mm) is comparable to the average dendrite thickness(0.1 mm) and spacing (0.4 mm) as well as the gap (0.05 mm),the nearly perfect planar symmetry of the corrosion process leadsus to nevertheless seek another asymptotic similarity solutionto the one-dimensional, mean-field equations in the vicinity of

a(x,t) ) A(ú,t), b(x,t) ) B(ú,t), ú )x - xf(t)

Wd(t)(18)

xf(t) ) -2νxt (19)

ú )x

2xt+ ν (20)

∂A∂t + (ν - ú

2t ) ∂A∂ú

) ( 14t)∂

2A∂ú2 - r(A,B) (21)

limtf∞

A(ú,t) ) A(ú) (ú > 0) (22)

limtf∞

t‚r(A,B) ) 0 (ú > 0) (23)

limtf∞

B(ú,t) ) 0 (ú > 0) (24)

Figure 7. Asymptotic similarity function a(x,t) ∼ A(ú), where ú )(x/2xt) + ν, shown for Ao ) 0 and ν ) 0, 0.5, 1, 1.5, 2, 2.5 from leftto right.

A′′ + 2(ú - ν)A′ ) 0 (25)

A(ú) ) Ao + (1 - Ao)erf(ú - ν) + erf(ν)

1 + erf(ν)(26)

A′(0) )2(1 - Ao)e

-ν2

xπ(1 + erf(ν))(27)

a(x,t) ∼ A(ú) H(ú), b(x,t) ∼ H(-ú) (28)

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the reaction front, x - xf(t) ) O(1). The predictions of the modelwill be carefully tested against the experimental data in the nextsection.

Since R ) 0 and σ ) 1/2, we consider the transformation

where η is a new similarity variable for the reaction front definedby

The exponent γ g 0 is introduced to allow for the possibilitythat a(x,t) f 0 in the reaction front, which is suggested by theresult r(a,b) ∼ t-â with â ) 1/2 inferred earlier from theexperimental data. In contrast, no such prefactor multipliesB˜(η,t) in the reaction front since b(x,t) must remain finitethere in order to interpolate between the limiting values of 0and 1, respectively, behind and ahead of the front.

Making these transformations in eq 10 yields

As before, we explore the possibility of self-similar quasi-stationarity in the reaction front: A (η,t) ∼ A (η) and B˜(η,t) ∼B (η) as t f ∞ with |η| < ∞ fixed. The consequence of thequasistationarity assumption in eq 31 is

Since A ′′(η) ) 0 cannot satisfy the boundary conditionA (-∞) ) 0 (except in the trivial case A (η) ) 0), the limit onthe right-hand side of eq 32 must be nonzero (and finite), whichis possible only if r(a,b) is linear in a, i.e.

for some function f(b). Therefore, the experimental facts w(t)∼ t0 and xf(t) ∼ t1/2 are consistent with the one-dimensional,mean-field model only if the reaction rate is first order in thediffusing species.

Next we make the same transformation in eq 11 and replacethe reaction term with eq 33 to obtain

By inspection, quasistationarity is possible only if γ ) 1/2, whichwould imply r(a,b) ∼ t-1/2A (η) f(B (η)). Therefore, we concludeâ ) 1/2 once again, and the physical argument given in theprevious section is found to have sound mathematical justifica-tion.

With these results we arrive at a third-order system ofnonlinear ordinary differential equations for the concentrationfields in the reaction front,

These equations may be combined to eliminate the reaction termand integrated once using the boundary conditions ahead of thefront, A (-∞) ) 0 and B (-∞) ) 1 to obtain

Before proceeding with another integration, however, a third

boundary condition is needed, which comes from asymptoticmatching with the diffusion layer.

D. Asymptotic Matching. In mathematical terms, our equa-tions possess an “internal boundary layer”.60 The reaction front,defined by |x + 2νxt| ) O(1), acts as the “inner region”,while the diffusion layer, defined by xt ) O(|x + 2νxt|), actsas the “outer region”. For consistency, the “inner limit” (ú f0) of the outer approximation, eq 18, must match the “outerlimit” (η f ∞) of the inner approximation, eq 29. We haveshown that γ > 0 is required to describe the experimental data,which means that a(x,t) approaches zero uniformly in thereaction front. Therefore, by matching at zeroth order, we obtainA(0) ) Ao ) 0, but this does not provide the missing boundarycondition for the reaction front. At the next (linear) order wehave, as t f ∞,

and by matching, we conclude A ′(∞) ) A 1, where A 1(ν) ≡A′(0)/2 can be expressed in terms of ν(q) using eq 27. In lightof eq 24, the matching condition for b(x,t) is B (∞) ) 0.

The matching conditions allow us to derive an exact expres-sion for ν(q) and hence the asymptotic front position xf(t) )2νxt. Taking the limit ηf ∞ in eq 37 using A ′(∞) ) A 1 andB (∞) ) 0, we obtain qA 1(ν) ) ν. By substituting A 1(ν) fromeq 27, we obtain the desired expression for ν(q),

which has also been derived by Koza.31 The relation q ) F(ν)is plotted in Figure 8 and will be used in the next section toestimate q from the experimentally measured value of ν.

With these results, we are led to a second-order, nonlinear-boundary-value problem for the reaction front concentration ofthe diffusing species:

Note that eq 40 is invariant to translation η f η + ηo, whereηo is an undetermined constant depending on the initialconditions that precisely defines the location of the reaction front(e.g., as the point of maximal reaction rate).

a(x,t) ) t-γ A (η,t), b(x,t) ) B (η,t) (29)

η ) x + 2νt1/2 ) 2t1/2ú (30)

∂ A ˜∂t + νt-1/2 ∂ A ˜

∂η- γt-1 A ˜) ∂

2 A ˜∂η2 - tγr(t-γA ˜ ,B ) (31)

A ′′(η) ) limtf∞

tγr(t-γA (η),B (η)) (|η| < ∞) (32)

r(a,b) ) a‚f(b) (33)

∂B∂t + νt-1/2 ∂B

∂η) -qt-γA f(B ) (34)

A ′′ - A ‚f(B ) ) 0 (35)νB ′ + qA ‚f(B ) ) 0 (36)

qA ′ ) ν(1 - B ) (37)

Figure 8. Exact asymptotic dependence of ν, the square root of thedimensionless diffusion constant of the reaction front, on the asymmetryparameter q, predicted by eq 39.

∂a∂x ) {∂A

∂ú

∂ú

∂x ∼A′(ú)2xt

0 < ú < ∞

1xt

∂A∂η

∂η

∂x ∼A ′(η)

xt|η| < ∞

(38)

ν ) F-1(q) where F(x) ≡ xπxex2[1 + erf(x)] (39)

A ′′ ) A ‚f(1 - A ′/A 1), A (-∞) ) 0, A ′(∞) ) A 1(40)

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Since it is difficult to accurately measure the reaction-frontconcentration fields in our experiments, we stop here and referthe reader to the article of Bazant and Stone10 for the integrationof this boundary-value problem and other analytical results inthe case f(b) ) bm, m g 1.

V. Experimental Test of the Theoretical ModelA. Check of the Exact Asymptotic Predictions. In section

III we showed that as corrosion proceeds, the reaction frontmoves with the time as Xf(T) ∼ T1/2 and does not spread (w(T)∼ TR with R ) 0) and the width Wd of the depletion layerincreases with the time as Wd(T) ∼ T1/2. In section IV we showedthat these observations are consistent with the predictions of aone-dimensional A + B (static) f C (inert) mean-field modelwith a reaction rate that is first order in the diffusing speciesA. By solving the mean-field equations, we derived not onlythe scaling exponents for Xf(T) and W(T) but also the prefactorsand the exact asymptotic shape of the concentration profile ofthe diffusing reactant as a function of the reduced coordinate ú

) [X - Xf(T)]/2xDT. In this section, we quantitatively testthese theoretical predictions against the experimental results.

1. MoVement of the Front. In dimensional units eq 19 reads

Therefore, from a log-log plot of Xf as a function of T onegets the value of ν, and q can then be deduced from eq 39. Inour experimental system, q is linearly related to a characteristicproperty of the electrolyte, namely the transference number ofthe cation, through q ) 1 - t+. To derive the values of q andt+ from eq 41, we need an accurate value of the diffusioncoefficient of the electrolyte. D is likely to depend on theconcentration of CuCl2, but to our knowledge, has not beentabulated for CuCl2. Hereafter, we use the value D ) (1.0 (0.1) × 10-5 cm2‚s-1, determined independently by our inter-ferometric technique.

The two sets of experimental data in of Figure 3 give 2νxD) (1.7 ( 0.1) × 10-3 cm‚s-1/2, therefore ν ) 0.27 ( 0.02 andt+ ) 0.33 ( 0.05 from eq 39, q ) F(ν). Note that t+ ≈ 0.3 (fora 0.5 mol‚L-1 electrolyte) is quite consistent with the corre-sponding value at infinite dilution t+

∞ ) 0.4, since t+ is likely tobe a decreasing function of the concentration.49 Although wehave not directly measured the transference number t+ of theCu2+ cation, its reasonable value just inferred from the observedfront speed via eq 39 constitutes a successful prediction of theone-dimensional mean-field model.

2. Width of the Depletion Zone and Whole ConcentrationProfile. In this section, we analyze the experiments performedwith a higher electrolyte concentration, namely 1.0 mol‚L-1

CuCl2. The concentration profile in the laboratory frame canbe written in dimensional units using eq 26 and the definitionof ú:

Note that a(X,T) is used in the experimental parts to denoteFA(X,T)/F°A. A characteristic feature of these profiles (and theexperimental data in Figure 5) is that they exhibit a fixed pointwith ordinate

Since a(0,T) depends only on q, a value of q can be deducedfrom Figure 5, which shows the concentration profiles duringthe corrosion of a copper deposit obtained by electrodepositionfrom a 1.0 mol‚L-1 CuCl2 solution. We find a(X)0,T) ) 0.25( 0.01, which implies ν ) 0.30 ( 0.01. From eq 39 the mean-field model would predict q ) 0.79 ( 0.06. As expected, theinferred value of the transference number, t+ ) 1 - q ) 0.21( 0.06, for this 1.0 mol‚L-1 CuCl2 solution is lower than thevalue of 0.33 ( 0.05 at 0.5 mol‚L-1 computed above. This valueis somewhat smaller than expected on the basis of concentrationeffects (see below). Note that we have not directly measuredthe ratio q ) F°A/F°B or the transference number t+ in theexperiments described in this paper, but the value of q ) 0.79just obtained from eq 43 is necessary for comparison with themean-field model (without any other adjustable parameters).Therefore, we will use q ) 0.79 in the following analysis ofthe experimental runs in 1 mol‚L-1 CuCl2 electrolyte.

From eq 26 the width Wd of the diffusion layer (withdimensions) is given by

From an experimental point of view, it is simpler to measurea(X,T) at X ) 0 rather than at X ) Xf(T), so we consider thetemporal evolution of the gradient of a(X,T) at X ) 0. From eq42 we obtain

and Wd(T) ) exp(ν2)/∂Xa(X,T)|X)0. Figure 6 shows the quantita-tive agreement between the experimental values of ∂Xa|X)0 andthe function of eq 45 plotted for D ) 10-5 cm2‚s-1 and q )0.79. Note that D and q are deduced from previous analysisand are not adjustable parameters.

Continuing our quantitative analysis of the experimentalconcentration field, we plot in Figure 9 the asymptotic shapeof the concentration profile. To determine a(ú) from a(X,T),we compute ú using ú ) (X/2xDT) + ν(q), with q ) 0.79 andD ) 10-5 cm2‚s-1 and adjust the origin of the abscissa to theinitial front of copper position, to ensure that A(ú)0,T) ) 0 forall T. For comparison we also show in the same plot thetheoretically predicted A(ú) function computed from eqs 26 and39 with q ) 0.79.

To focus on the region of the reaction front, the experimentaldata are plotted in Figure 10 according to the linearized versionof eq 26

Since (X - Xf)/2 is proportional to the reaction-front similarityvariable η in eq 30, the mean-field model would predict acollapse of this data to a single curve given by the solution ofeq 40.

Unfortunately, the noise in the experimental data washes outthe exact concentration profiles in the reaction front on this scale,but it is clear that the width of the reaction front has theasymptotic scaling w ∼ tR with R ) 0. Moreover, the asymptoticshape of the concentration distribution is quite consistent withthe solutions to eq 40 given in ref 10. Note that the decay ofslope of the reaction-front concentration A ′(η) toward itslimiting value in the diffusion layer A 1 in Figure 10 appears to

-Xf ) 2ν(q)xDT (41)

a(X,T) )erf(X/2xDT) + erf(ν)

1 + erf(ν)(42)

a(X)0,T) )erf(ν)

1 + erf(ν)(43)

Wd(T) ) (∂Xa(X,T)|X)Xf)-1 ) ( exp(-ν2)

xπDT(1 + erf(ν)))-1

(44)

∂a(X,T)∂X |X)0

)1

xπDT(1 + erf(ν))(45)

axDT ) A′(0)X - Xf

2 )2e-ν2

xπ(1 + erf(ν))

X - Xf

2 (46)

5848 J. Phys. Chem. B, Vol. 103, No. 28, 1999 Leger et al.

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C. Leger. UPR 9036. Memoire d’HDR. 2007.

be quite fast. If this decay were exponential rather than a (muchslower) power law, then according to the mean-field model10

the reaction rate would have to be first order in the static reactantm ) 1, i.e., f(b) ) b or r(a,b) ) ab, but it is impossible toreach this conclusion definitively from our data.

As shown in Figures 9 and 10, all of the measured concentra-tion profiles collapse to the single asymptotic curve predictedfor q ) 0.79 over the whole length scales investigated in theexperiment. This quantitative agreement between the experi-

mental and theoretical concentration profiles of the diffusingreactant independent of the length scale strongly support ourmodeling of this corrosion experiment with a one-dimensionalA + B (static) f C(inert) mean-field model.

B. The Transient. The A + B f C mean-field model withtwo diffusing reactants exhibits many surprising and nontrivialbehaviors at short times (see refs 30 and references therein, 26,and 61). In this case, some microscopic parameters like thereaction constant(s) can be determined from these short timebehaviors. In particular, at a time inversely proportional to themicroscopic reaction constant, the global reaction rate switchesfrom an initial t1/2 increase to a subsequent t-1/2 decrease.30

Moreover, in the reversible A + B h C system, a crossoverbetween irreversible and reversible regimes can be observed atlong times61 and the value of the backward reaction constantcan be inferred from the crossover time.26

In the present case of one static reactant, it is also possibleto express the transient decay to the asymptotic solution in termsof the reaction orders m and n for the one-dimensional mean-field model.10 In our experiment, however, the transient behavioris determined by a superposition of different mechanisms sinceour system is not really one-dimensional or homogeneous. Wenow show that the transient behavior appears to be governedby two-dimensional geometric effects that hide the kineticfeatures by analyzing the detail of the experimental runs.

Looking at Figure 4a, note that the concentration field is notone-dimensional at the early stages of the corrosion experi-ment: the isoconcentration lines closely follow the jaggedoutline of the deposit in the region near the tips. The amplitudeG of the modulation of the leftmost isoconcentration line (theclosest to the copper cluster) is about 0.4 mm. This systemclearly cannot be viewed as one-dimensional until the front hastraveled at least a distance on the order of G. In Figure 3, notethat the time of the transient regime (before the asymptotic t1/2

behavior sets in) closely corresponds to the time needed forthe front to move across a distance G ∼ 0.4 mm. (This two-dimensional geometric effect also may explain why the initialmovement of the front is slower than the asymptotic behavior,as shown in Figure 3.)

To further support this hypothesis, we now study therelaxation dynamics of the concentration field. In Figure 11a,is plotted the isoconcentration line corresponding to a ) Fa/F°a) 0.1, just after the current has been switched off. This line isnot continuous, because the concentration field cannot beextracted by interferometry in the zones containing the deposit.This line defines a function X(Y), roughly periodic, of amplitudeG(T) and period λ ∼ 1 mm. It is reasonable to expect that thecharacteristic time for the relaxation of this modulation of theconcentration field toward a flat two-dimensional profile is thetime τf needed for the front of copper to move from its startingposition (Xf(T ) 0)) on the length scale G(T ) 0) ) 0.3 mm )2νxDτf, which yields the estimate τf ) G(0)2/4ν2D ∼ 250 s.Moreover, in light of the analysis of Krug62 described below, itis also reasonable to expect that the functional form of the decaywill be exponential.

In Figure 11b, we plot log(G(T)/G(0)) as a function of thedimensionless time T/τf. The relaxation is well fitted by anexponential function, with a characteristic time close to τf, whichsupports our hypothesis. Therefore in our experiments, thetransient behavior is directly linked to the relaxation of the initialtwo-dimensional concentration field toward a Y-invariant profileand cannot provide information on the kinetics independently.

C. Physical Relevance of the One-Dimensional Mean-FieldModel. In the previous sections, we have demonstrated the

Figure 9. Collapse of the experimental concentration data in thediffusion layer plotted versus the similarity variable (X - Xf)/2xDTcompared with the theoretically predicted asymptotic experimentalsimilarity function A(ú) (the solid line). The profiles are the same asthose plotted in Figure 5, but only one point out of 20 is shown on thisplot for clarity.

Figure 10. Collapse of the experimental concentration data in thereaction front plotted versus the similarity variable (X - Xf)/2. Thesolid line shows the linearized extension of the similarity function A(ú)from the diffusion layer (see Figure 9) extended into the reaction front.These profiles are the same as those plotted in Figure 5, but only onepoint out of 4 is shown on this plot for clarity. The negativeconcentration values are artifacts of the interferometric technique andhave no physical meaning.

Diffusion-Limited Corrosion of Electrodeposits J. Phys. Chem. B, Vol. 103, No. 28, 1999 5849

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C. Leger. UPR 9036. Memoire d’HDR. 2007.

quantitative agreement between the behavior of our thin gapcorrosion system and various predictions of a one-dimensionalmean-field model. This agreement is not obvious a priori, andtherefore we close in this section by giving physical argumentsto explain this surprising fact.

1. No Inhibition of Diffusion or Reaction by CuCl. In Figure4 we see that the product of the reaction does not seem to disturbthe concentration field of the diffusing reactant A. To understandthis fact, we consider the volume occupied by the product CuClin the cell. We know from eq 7 that the mean concentration ofcopper before the dissolution is ≈2F°A. We deduce from eq 4that if CuCl does not diffuse (which is verified in ourexperiments), the mean concentration of CuCl is twice the initialconcentration of copper, which is approximately 4 times theinitial concentration of CuCl2 in the bulk, i.e., 2 mol‚L-1. Sincethe density and molecular weight of CuCl are 3.38 g‚cm-3 and99 g‚mol-1, respectively, the volume occupied by the solid CuClafter the dissolution is roughly 5% of the total local volume.Therefore, the small crystals of CuCl do not significantly alterthe volume free for the diffusion of CuCl2. Moreover, becausethe CuCl crystallites do not adhere to the copper metal branchesand fall to the bottom of the thin gap cell, the surface of thecopper cluster is constantly renewed and “ready” for corrosionby CuCl2.

2. Stable Front, Asymptotically One-Dimensional. The factthat the dissolution process builds a stable (flat) interface canbe understood by considering that diffusion-limited corrosionis the “time-reversed” process of diffusion-limited aggregationand that the fluctuations of the interface decay rather than grow

to reach a stable flat front asymptotically. Krug62 showed thatperiodic perturbations of a flat front of wavelength λ in thedirection perpendicular to the direction of motion of the interfacewould decay with a characteristic time τ ) λ/V. The stability ofthe corrosion front can therefore be qualitatively understood withthe following argument: the electrolyte most easily reaches themost exposed or least screened parts of the copper deposit. Thesebulges are dissolved first, and the interface is smoothed.

3. ReleVance of 1D Approximation of the Concentration Field.In the long-time asymptotic regime, the modulation of the initialconcentration of reactant A (CuCl2 ) relaxes toward a flatconcentration profile along the direction Y whose shape is givenby eq 26. However, the concentration of the static reactant B(Cu), as well as the concentration of the product C (CuCl) keepa periodic shape along the Y direction, which somehow doesnot alter the one-dimensional asymptotic solution. The largestcharacteristic length of the deposit in the direction parallel tothe front (Y) is the mean distance λ between the trees. Thispuzzling observation can be understood by comparing therelaxation time of the perturbations of FA(X,Y) along Y, τd ∼λ2/D, with the time needed by the front of copper to move onthe same length, τf ∼ λ/Xf ) λxT/νxD. Since τf increaseswith time T, in the asymptotic regime it will be much greaterthan τd. Therefore, whereas FB is highly correlated along the Ydirection due to the structure of the solid deposit, there areeventually no fluctuations in FA along this direction.

4. Departure from Pure Diffusion in the Reaction Zone. Thefact that the transference number t+ deduced from t+ ) 1 - qand the inferred value of q ) F(ν) from eq 39 decreasessignificantly from 0.33 to 0.21 when the concentration of CuCl2is increased from 0.5 to 1 mol‚L-1 is unlikely to be caused solelyby a pure salt-concentration effect. It is also possible thatconvection produced by the sedimentation of CuCl crystallitestoward the bottom of the cell could artificially increase theeffective diffusion coefficient close to the reaction front byconvective mixing. This would cause an increase of ν(q) (theprefactor for the speed of the reaction front), which could atleast partly explain the difference in the inferred q values, andtherefore also in the effective t+ values.

VI. Conclusion

We have shown that after long times the corrosion of highlyporous copper clusters can be understood as a one-dimensional,homogeneous, mean-field A + B f C reaction-diffusionprocess with one diffusing and one static reactant. This is thefirst experimental analysis of such a situation where only onereactant is free to diffuse through the other one. Whereas onewould expect highly complex dynamics and a possible break-down of the mean-field approximation when the reaction isconfined to a porous (fractal) interface, we show that in thisparticular corrosion system, the dynamics are equivalent to thoseexpected for a homogeneous system. The strength of ourdemonstration is built on precise measurements of the concen-tration field of the diffusing species by interferometry, whichare compared quantitatively with analytical predictions of theone-dimensional mean-field model.

Acknowledgment. We are very grateful to Y. Sorin and G.Gadret for their technical assistance with the optical setup. Wealso thank H. A. Stone, E. Clement, J. Elezgaray, and A.Arneodo for stimulating and fruitful discussions. This work wassupported (mainly) by the Centre National d’Etudes Spatialesunder Grant No. 97/CNES/071/6850 and also (partially) by anNFS infrastructure grant to the MIT Department of Mathematics.

Figure 11. Relaxation of the two-dimensional initial concentration fieldat the beginning of the dissolution. (a) Isoconcentration line a ) 0.1,for T ) 27 s. The deposit has been grown from a 1 mol‚L-1 CuCl2solution, at j ) 68 mA‚cm-2 over 15 min. (b) log-linear plot of theevolution of the amplitude G of the modulation of A concentration, asshown in (a), versus the reduced time T/τf ) 4ν2DT/G(0)2.

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Enzyme Electrokinetics: Energetics of Succinate Oxidation by Fumarate Reductaseand Succinate Dehydrogenase†

Christophe Leger,‡ Kerensa Heffron,‡ Harsh R. Pershad,§ Elena Maklashina,| Cesar Luna-Chavez,|,⊥ Gary Cecchini,|Brian A. C. Ackrell,| and Fraser A. Armstrong*,‡

Inorganic Chemistry Laboratory, Oxford OX1 3QR, U.K., Department of Chemistry, UniVersity of California at Berkeley,Berkeley, California 94720, Molecular Biology DiVision, VA Medical Center and Department of Biochemistry and Biophysics,

UniVersity of California, San Francisco, California 94121

ReceiVed May 1, 2001; ReVised Manuscript ReceiVed July 6, 2001

ABSTRACT: Protein film voltammetry is used to probe the energetics of electron transfer and substratebinding at the active site of a respiratory flavoenzymesthe membrane-extrinsic catalytic domain ofEscherichia coli fumarate reductase (FrdAB). The activity as a function of the electrochemical drivingforce is revealed in catalytic voltammograms, the shapes of which are interpreted using a Michaelis-Menten model that incorporates the potential dimension. Voltammetric experiments carried out at roomtemperature under turnover conditions reveal the reduction potentials of the FAD, the stability of thesemiquinone, relevant protonation states, and pH-dependent succinate-enzyme binding constants for allthree redox states of the FAD. Fast-scan experiments in the presence of substrate confirm the value of thetwo-electron reduction potential of the FAD and show that product release is not rate limiting. The sequenceof binding and protonation events over the whole catalytic cycle is deduced. Importantly, comparisonsare made with the electrocatalytic properties of SDH, the membrane-extrinsic catalytic domain ofmitochondrial complex II.

Fumarate reductase (FrdAB)1 and succinate dehydrogenase(SDH) are the closely related water-soluble cytoplasm/matrix-facing domains of menaquinol:fumarate reductase(QFR) and succinate:ubiquinone oxidoreductase (SQR, orcomplex II), respectively (1-5), that catalyze redox inter-conversion between the dicarboxylates fumarate and succi-nate (EF/S

0′) 0-30 mV at pH 7).

In bacteria, QFR catalyses the final step in anaerobicrespiration on fumarate, coupling its reduction to succinateto the oxidation of menaquinol to menaquinone (EMQ/MQH2

0′

) -74 mV). In mitochondria and other systems, SQR linksthe citric acid cycle to the aerobic electron-transport respira-tory chain by passing the electrons from succinate to thequinone pool (ubiquinone/ubiquinol, EUQ/UQH2

0′) 70-110

mV). In vitro, both enzymes oxidize succinate or reducefumarate using artificial electron partners. In vivo, they canreplace one another functionally, following genetic manipu-lation of the organism (6, 7).

The matrix/cytoplasm-facing peripheral domain comprisestwo tightly associated subunits, one containing three iron-sulfur clusters, and the other containing a 8R-(N3-histidyl)covalently bound flavin adenine dinucleotide (FAD) and thesite for dicarboxylate binding. Whereas the crystal structureof SQR has not yet been determined, those of two QFRs[from Escherichia coli (8, 9) and Wolinella succinogenes(10-12)] and of four soluble fumarate reductases (13-16)have been solved recently. In all these enzymes, dicarboxy-

† This work was supported by funds from the U.K. EPSRC andBBSRC (Grant number 43/B10492), the Department of VeteransAffairs, the National Science Foundation (MCB 9728778) and the NIH(HL-16251), and by a Fulbright-AstraZeneca award to H.R.P.

* To whom correspondence should be addressed. Phone 44-1865-272647. Fax 44-1865-272690. E-mail: fraser.armstrong@icl.ox.ac.uk.

‡ Inorganic Chemistry Laboratory.§ Department of Chemistry.| Molecular Biology Division.⊥ Current address: Center for Biophysics and Computational Biol-

ogy, University of Illinois, Urbana, Illinois 61801.

1 Abbreviations: A, electrode area; CHES, 2-[N-cyclohexylamino]-ethenesulfonic acid; DTT, threo-1,4-dimercapto-2,3-butandiol dithio-threitol; E, electrode potential; EGTA, ethylene glycol-bis(â-aminoethylether)-N′,N′,N′,N′-tetraacetic acid; EO/H, EH/R, One-electron reductionpotentials for the two redox transitions of the flavin, see caption ofScheme 1; ET, electron transfer; [F], fumarate bulk concentrations; F,Faraday constant; FAD, flavin adenine dinucleotide; FrdAB, fumaratereductase; Γ, electroactive coverage; HEPES, N-(2-hydroxyethyl)-piperazine-N′-[2-ethanesulfonic acid]; i, current; ilim, limiting current(at high or low potential); K, Dissociation constant from FAD; thesuperscript stands for the species which binds/dissociates (e.g., “OAA”,“succ”, or “fum”). The subscript tells the redox state of the FAD [O,H, or R, for oxidized (quinone), half-reduced (semiquinone), andreduced (hydroquinone)]; Ka, acidity constant for the semiquinone formof the FAD; Km

succ, Kmfum, Michaelis constants for succinate oxidation of

fumarate reduction; k2succ, k2

fum, first-order potential-independent rateconstants for chemical transformations in the enzyme-substrate complex(succinate oxidation by oxidized FAD or fumarate reduction dependingon the superscript); κ, disproportionation constant, κ ) exp(2F /RT(EO/H- EO/R)); the maximal fraction of FAD in the semiquinone form,occurring at E ) EO/R, is xκ/(2+ xκ); M-M, Michaelis-Menten; ν,scan rate; OAA, oxaloacetate; ω, electrode rotation rate in units rpm(revolution per minute); PFV, protein film voltammetry; QFR,menaquinol:fumarate reductase; R, gas constants; [S], succinate bulkconcentration; SDH, succinate dehydrogenase; SQR, succinate:u-biquinone oxidoreductase (complex II); T, temperature; TAPS, N-tris-[hydroxymethyl]methyl-3-aminopropanesulfonic acid.

11234 Biochemistry 2001, 40, 11234-11245

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late binding utilizes hydrogen bonds from highly conservedresidues, and the hydrogenation reaction is thought to involvehydride transfer between N5 of the FAD isoalloxazine ringand the substrate, followed by proton transfer (10). Proto-nation may occur via a hydrogen-bonded water moleculefound in the Wolinella enzyme (11), although the Shewanellaputrefaciens (13) and Shewanella frigidimarina (14, 15)structures, along with site-directed mutagenesis (12, 17-19), suggest that the proton donor is a conserved arginine.

The one- and two-electron reduction potentials of theactive-site FAD and the resulting thermodynamic and kineticcharacteristics of catalytic activity are modulated by covalentbonds with histidine (20, 21) and interactions with nearbyresidues. Of interest here is the intrinsic bias of the enzymetoward reduction of fumarate or oxidation of succinate, animportant factor being the difference between the E0′s forFAD and fumarate: for example, in soluble fumaratereductases, the lower E0′ of the noncovalently bound FADcontributes to make these enzymes poor catalysts of succinateoxidation. A more detailed description of the reactionrequires knowing how the FAD one- and two-electronpotentials depend on substrate binding (22-27). These valueshave been measured in equilibrium titrations but not, so far,under turnover conditions.

Protein film voltammetry (PFV) is emerging as a powerfultool to investigate redox enzymes (28, 29). In this technique,the protein is adsorbed up to monolayer coverage at anelectrode which effectively substitutes for the redox partnerand is able to rapidly donate or abstract electrons from theenzyme depending on the electrode potential. Withoutsubstrate in solution, at slow scan rates, PFV yields equi-librium reduction potentials directly, while kinetic informa-tion can be obtained by using fast modulations of thepotential (30). With substrate in solution, catalytic turnoverproduces an amplified response, the shape of which revealsdetails of the active-site redox transformations and the roleof the driving force in controlling activity.

PFV studies of E. coli FrdAB (31, 32) and bovinemitochondrial (33-35) and E. coli (36) SDH, as well asstudies of the soluble fumarate reductases from S. frigidi-marina (37-40) have revealed substantial differences be-tween succinate dehydrogenases and fumarate reductases.These succinate dehydrogenases efficiently catalyze fumaratereduction, but only over a narrow potential range becauseactivity decreases abruptly once a critical driving force isreached, i.e., at sufficiently low potential (33-36, 41). Thisreversible “switch” (of possible physiological relevance) mayarise from a conformational change linked to the oxidationstate of FAD. By contrast, the fumarate reduction activitiesof E. coli FrdAB (at high pH) (31, 32) and soluble fumaratereductases (40, 42) are marked by complex sigmoidalincreases upon successive reductions of the prosthetic groups.

In this paper, we describe experiments that probe andcompare the catalytic energetics of FrdAB and SDH duringturnover. In particular the studies reveal effects of substratebinding and roles of the different FAD redox states incatalysis.

EXPERIMENTAL METHODS

Purification of FrdAB and SDH. E. coli strain DW35 [43]was transformed with plasmid pFAB-HT (frdA+B+) derived

from plasmid pH3 (frdA+B+C+D+) (44). Plasmid pFAB-HTwas constructed using pH3 as a template and utilizing ExSitePCR based mutagenesis (Stratagene, La Jolla, CA) to addan 8-amino acid extension (Leu-Glu-6His) to the C-terminusof the iron-sulfur protein subunit (FrdB) of fumaratereductase. The plasmid construct also resulted in deletionof the frdCD genes from plasmid pFAB-HT. Thus, pFAB-HT encodes soluble E. coli fumarate reductase with a 6His-Tag on the iron-sulfur protein subunit. To express thesoluble FrdAB enzyme, E. coli DW35 transformed withpFAB-HT was used to inoculate 150 mL of Terrific broth(45) containing 150 µg/mL ampicillin in a 1-L flask andgrown with vigorous aeration for 6 h. The culture was thenused to inoculate 1.2 L of Terrific broth plus antibiotic in2-L flasks and the cultures were grown with moderateaeration (200 rpm in a New Brunswick G25 rotary shaker)for 18 h at 37 °C before harvesting by centrifugation (15min at 6000 × g). The cells were resuspended in buffer A[50 mM potassium phosphate pH 7.0, 500 mM NaCl, 1%glycerol (w/v)] and one “Complete Protease Inhibitor” tabletwithout EDTA (Roche, Indianapolis, IN) was added per 50mL of suspended cells. The cells were disrupted by onepassage through an Avestin homogenizer (Ottawa, Canada)at 15 000 PSI at 4 °C.

Cells and membrane fractions were removed by centrifu-gation at 120000×g in a Beckman Ti60 rotor for 35 min,and the supernatant was applied to nickel affinity resin(Qiagen, Chatsworth, CA) (2 × 11 cm) equilibrated withbuffer A. The column was washed with 3-5 bed vol ofbuffer A and 2 bed volumes of buffer A with 80 mMimidazole, then FrdAB was eluted with 0.5 M imidazole.The dark-brown fractions containing the soluble FrdAB wereconcentrated to 2-4 mL (15-20 mg/mL) using an Amiconcell with a YM30 membrane under nitrogen, then diluted8-fold with 20 mM histidine, 0.5 mM EDTA, 0.5 mM DTT,in 1% glycerol, pH 7.5. The resulting solution was appliedto a Mono Q HR 10/10 column (Amersham Pharmacia)equilibrated with the same histidine buffer used to dilute theenzyme. The column was washed with 2 bed vol of 0.1 MKCl in the histidine buffer, then a gradient of KCl (0.1-1.0M) was appliedsthe FrdAB fraction eluting at approximately0.35 M KCl. The dark-brown fractions were pooled andbrought to 60% saturation with ammonium sulfate, thenprecipitated by centrifugation at 20000 × g at 4 °C and storedat -80 °C. A last FPLC step was found to greatly enhancethe signal intensity, resolution, and stability of the voltam-metry. After passing through a PD10 column (AmershamPharmacia) to remove ammonium sulfate, the samples werefurther purified anaerobically with a FPLC Mono Q columnusing a 0 to 0.5 M NaCl gradient (20 mM HEPES, 10%glycerol, 0.1 mM EGTA, 0.5 mM DTT, pH 7.4). Elution ofthe FrdAB, monitored using UV-Vis, occurred at ap-proximately 0.3 M NaCl. Electrochemical experiments didnot reveal any significant difference between the wild-typeand His-tagged enzymes.

The methyl viologen-fumarate reductase assay of purifiedFrdAB was performed in a 2 mL cuvette, containing anargon-saturated solution of 10 mM fumarate, 200 µM methylviologen, with glucose (10 mM), glucose oxidase andcatalase to maintain anaerobiosis. Dithionite was added toreduce the viologen, and the reaction was initiated by additionof enzyme. The decrease in absorbance at 602 nm was

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C. Leger. UPR 9036. Memoire d’HDR. 2007.

monitored and the rate of the reaction was calculated usingan extinction coefficient of 9.6 mM-1 cm-1. The succinate-ferricyanide reductase activity was determined at 420 nm(ε )1 mM-1 cm-1) with 20 mM succinate and 200 µMferricyanide. (In each case, the concentration of substratewas much greater than the Michaelis constant.) Solutionassays were carried out in 50 mM potassium phosphate atpH 7.0 and at 25 °C. We obtained the turnover numbersk2

succ) 12 s-1 and k2

fum) 450 s-1 for FrdAB activity toward

succinate oxidation and fumarate reduction, respectively.Beef heart SQR was isolated from mitochondria by the

method of Beginsky and Hatefi (46), and pure fractions ofsoluble SDH were obtained by resolution with perchlorate(47).

Electrochemistry. Experiments were performed with amixed buffer system consisting of 10 mM in each of CHES,HEPES, and TAPS (Sigma) containing 0.1 M NaCl asadditional supporting electrolyte. Mixtures were titrated withNaOH or HCl to the desired pH at 20 °C. Substrates (fumaricor succinic acid, Fluka 99.5%) were added from 50 mM stocksolutions prepared in the same mixed buffers. Polymyxin Bsulfate (Sigma), which enhances the adsorption of FrdABon the electrode, was prepared as a 20 mg/mL stock solutionin water.

A pyrolytic graphite edge (PGE) rotating disk workingelectrode (31) (geometric area A ) 0.03 cm2) was used inconjunction with an EG&G model 636 electrode rotator. Aplatinum wire was used as counter electrode, and a saturatedcalomel electrode (SCE) in a Luggin sidearm containing0.1M NaCl was used as reference. All potentials are quotedagainst the standard hydrogen electrode (SHE), using ESHE) ESCE + 241 mV at 20 °C (48). The electrochemical cellwas thermostated at 20 °C using a Neslab circulator andhoused in a Faraday cage. Voltammetry was performed usingan Autolab electrochemical analyzer (Eco Chemie, Utrecht,The Netherlands) controlled by GPES software and equippedwith analogue scan generator and electrochemical detection(increased sensitivity) modules. For fast-scan experiments,the effects of uncompensated cell resistance were minimizedby using the positive-feedback iR compensation function ofthe potentiostat (49).

All voltammetric experiments and handling of enzymesolutions were carried out in a glovebox (Vacuum Atmo-spheres) under a N2 atmosphere (O2 < 3 ppm). Prior to eachexperiment the PGE electrode was polished with an aqueousslurry of alumina (1 µm, Buehler) and sonicated thoroughly.For FrdAB, 5 µL of enzyme stock (approximately 50 µM)and 10 µL of polymyxin solution were mixed and appliedto the surface of the electrode which was then inserteddirectly into the cell whose large volume (4 mL) minimizedthe influence of fumarate formation during slow scans at highpotentials. To study substrate-concentration dependences, asingle film of FrdAB was used at each pH and transferredinto solutions of increasing succinate concentration. ForSDH, the enzyme samples were freed of residual ammoniumsulfate and perchlorate by diafiltration, using a micro-dialyzer(Spectrum Micro DispoDialyzer 1356021) against a mixedbuffer containing 0.5 mM succinate. Aliquots of the enzymesolution were added to the electrolyte (1 mL) to give a finalconcentration of 1 µM. Film formation was then initiatedby poising the electrode potential at -200 mV for 30 s, the

electrode rotating at 100 rpm. After each experiment, thecell solution was retained, and its pH was checked at 20 °C.

The voltammetric data were analyzed using an in-houseprogram. The noncatalytic data were filtered using a Fouriertransform (50) and corrected for charging current byinterpolating the baseline on each side of the voltammetricpeaks using a cubic spline procedure (50); deconvolution ofthe signals was then performed by least-squares fitting tothe sum of four independent2 redox transitions. The peaksassociated with each center were assumed to have thenernstian shapes given in ref 48 and 55 for the one- andtwo-electron signals, respectively. Six parameters weresimultaneously adjusted: four reduction potentials (three[Fe-S] clusters and the FAD), the disproportionationconstant of the FAD (κ) and the electroactive coverage (AΓ).The assignment of each one-electron peak to an Fe-S clusterhas been done as in ref 32. The catalytic voltammogramswere corrected for charging current by subtracting a second-order polynomial from the wave, such that at the low- andhigh-potential limits the corrected current was constant (32).

RESULTS AND MODELING

Noncatalytic Voltammetry. Figure 1A shows a voltam-mogram of FrdAB adsorbed at a PGE electrode. In theabsence of substrate, sweeping across the potential range

2 This assumption should be questioned, but the relatively low-intensity noncatalytic peak currents observed for large enzymesadsorbed on an electrode seems to to preclude the investigation ofpossible cooperativity between the different redox centers. For discus-sions of these effects in the context of ET in multicentered enzymes,see, e.g., refs 51-54.

FIGURE 1: (A) Noncatalytic voltammograms obtained for FrdABadsorbed at a PGE electrode in the absence of substrate. The rawvoltammogram (outer dash-dot line) is not to scale. The insetshows the background corrected current (small dots) and decon-voluted data. [2Fe2S]2+/+, Em,7 ) -35 mV; [3Fe4S]+/0, -67 mV;[4Fe4S]2+/+, -310 mV; FAD quinone/hydroquinone: -50 mV(dashed lines for individual contributions and plain lines for theirsum). Stationary (non-rotating) electrode, area A ) 0.03 cm2, scanrate ν ) 10 mV/s, temperature T ) 20 °C, pH 7. (B) Catalyticwave showing reversible succinate oxidation and fumarate reductionby adsorbed FrdAB in a solution containing succinate and fumaratein concentrations [S] ) 1.2 mM and [F] ) 4 µM, respectively.The scan was started from the open circuit potential marked witha filled circle. ν ) 1 mV/s, T ) 20 °C, pH 7, electrode rotationrate ω ) 3000 rpm.

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produces current peaks due to electron transfer between theelectrode and the different redox centers in the enzyme. Inthe limiting case of an active site undergoing a fullycooperative transfer of n electrons, the peak current variesas n2 and the half-height width varies as n-1 (28).

In the potential range -600 to +200mV, four signals (pairsof oxidation and reduction peaks) are observed (31, 32):these are the one-electron transitions of the three Fe-Sclusters, and the prominent two-electron transition of theFAD (quinone/hydroquinone, -50 mV at pH 7) whichclearly exhibits some cooperativity. In Figure 1A, the outertrace is a cyclic voltammogram recorded at pH 7. Aftersubtracting the charging current, the resulting faradaicvoltammogram can be deconvoluted to determine the con-tributions of the individual centers. Integrating the currentover half a cycle yields the total number of electronstransferred, and thus the electroactive enzyme coveragesinthis experiment, Γ ≈ 13 pmol/cm2.

Steady-State Catalysis. Figure 1B shows a voltammogramrecorded for an FrdAB film in contact with a solutioncontaining both succinate and fumarate, at concentrations[S] ) 1.2 mM and [F] ) 4 µM, respectively. A low scanrate was used (ν ) 1 mV/s) to ensure steady state (k2 forsuccinate oxidation is low, vide infra).

The resulting voltammogram is a “direct read-out” of therate of catalysis in either direction as a function of theelectrode potential (driving force). At an applied potential(E) higher than the fumarate/succinate equilibrium potential(EF/S), electrons flow from succinate to electrode via the FADand Fe-S clusters; the resulting (positive) current is directlyproportional to the rate of succinate oxidation. At lowpotential the net direction of electron flow is reversed; anegative current is now observed that is proportional to therate of fumarate reduction. The limiting currents at very highor very low potential (ilim

succ and ilimfum) reflect the maximal rate

of turnover in either direction, for given concentration ofsubstrates, when regeneration of the active site by theelectrode is not limiting.

The filled circle in Figure 1B indicates the potential ofzero net current (or “open circuit potential”) at -51 mV.This should correspond to EF/S which can be calculated forany concentration ratio using the Nernst equation and thepublished value EF/S

0′ ≈ +20 mV at 25 °C, pH 7 (57); EF/S )

EF/S0′

+ RT/2F ln([F]/[S]) ) -46 mV (F is the Faradayconstant, R the gas constant, and T the temperature).

The direction and rate of catalysis depend on the electrodepotential and the concentrations of reactants and on theenzyme’s intrinsic catalytic bias which is defined as the ratioof the potential-independent first-order rate constants forsuccinate or fumarate conversion in the enzyme-substratecomplex (k2

succ and k2fum). In Figure 1B, ilim

succ/ilimfum is approxi-

mately 1 for a [S]/[F] ratio of 300, suggesting that FrdAB issignificantly biased in the direction of fumarate reduction.However, as explained below, quantitative analysis requiresconsideration of binding effects.

Figure 2 shows as-measured (panel A) and baseline-subtracted (panel B) cyclic voltammograms for succinateoxidation in fumarate-free solutions at pH 7.5. The experi-ments have been performed with the same FrdAB filmsuccessively transferred to pH-buffered solutions of increas-ing succinate concentration in the range [S] ) 20 µM to 16mM. The electrode rotation rate was sufficiently high that

raising it further produced no noticeable increase in current;thus there is neither substrate depletion nor product ac-cumulation near the interface (56). Importantly, in additionto the expected increase in catalytic current as the succinateconcentration is raised, the position of the wave shifts tomore negative potentials.

A second important feature becomes apparent in thecorresponding Heyrovsky-Ilkovich plot shown in Figure 2C.This plot of log10 [(ilim - i)/i] against E is usually used toanalyze sigmoidal polarographic waves recorded understeady-state diffusion-limited conditions (58). For an n-electron electrochemical reaction that is reversible (i.e., theNernst equation is obeyed at all times), the plot is linearwith a slope -nF /2.3RT. By contrast, Figure 2C shows asignificant upward curvature over the entire range of suc-cinate concentration.

DeriVation of a Potential-Dependent Michaelis-MentenModel. The first-order rate constant for succinate oxidationby FrdAB can be estimated immediately from the magnitudeof the catalytic currents in Figure 2 using

[The 2F AΓ term arises because the current is proportionalto the total electroactive coverage (AΓ) and the fumarate/succinate transformation involves two electrons.] Assumingan electroactive coverage of AΓ ≈ 10-13 mol, k2

succ is of theorder of a few (seconds)-1; therefore, catalytic oxidation canbe described by a Michaelis-Menten (M-M) scheme, in

FIGURE 2: Substrate-concentration dependence of catalytic voltam-metry for succinate oxidation by FrdAB. Raw catalytic voltammo-grams (A), baseline subtracted data (B) and semilogarithmic plotof the catalytic waves (C). pH 7.5, scan rate ν ) 1 mV/s, electroderotation rate ω ) 3000 rpm, temperature T ) 20 °C, succinateconcentration [S] ) 20 µM to 16 mM (no fumarate).

ilim

2F AΓ)

k2succ

1 +Km

succ

[S]

(2)

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which all binding steps are fast relative to reactions withinthe enzyme-substrate complex. The limiting current dependson the (surface) concentration of substrate-bound enzyme,which is proportional to [S]/([S] + KO

succ), where KOsucc is the

dissociation constant from the oxidized active site. ThusKO

succ and k2succ can be determined from the variation in

limiting current with substrate concentration shown in Figure2B.

To interpret the shapes of the voltammograms anddetermine the energetics of the catalytic mechanism, we mustadd the “potential dimension” to the M-M model andincorporate the Nernst equation to relate the populations ofthe different redox forms of the FAD to the electrodepotential (E). We consider only the states of the FAD, andassume that the role of the Fe-S clusters is to mediate theelectrons. In Scheme 1, EO/H is the reduction potential forthe one-electron interconversion between oxidized and half-reduced forms, and EO/R is the average two-electron reductionpotential. We get

by assuming that the current is proportional to the concentra-tion of oxidized, substrate-bound enzyme.3

The denominator of eq 3 hides a substrate-concentrationdependence: the potentials of the redox transitions are relatedto their values in a succinate-free solution [EO/R([S] ) 0)and EO/H([S] ) 0)], to the succinate concentration ([S]), andto the dissociation constant from the oxidized, semi-reduced,and reduced forms of the FAD (KO

succ, KHsucc, and KR

succ)according to

An equation similar to 4a was used previously to determinethe dissociation constants KO

OAA and KROAA from the oxalo-

acetate-concentration-dependent potential of the FAD inFrdAB, measured using noncatalytic voltammetry (32).

At high potential, the exponential terms in eq 3 vanish(FAD is fully oxidized), and the current equation reduces toa M-M form, with limiting current current (ilim) given by

From eqs 3 and 5, we obtain the logarithmic transform ofthe wave,

which is expected to show a crossover between two limitingbehaviors: the plot should be linear at high potential with aslope -F /2.3RT decade/mV and also linear at lowerpotential, but with a slope -2F /2.3RT decade/mV (-58 and-29 mV/decade, respectively, at 20 °C).

Data Analysis. Figure 3 demonstrates that the modelaccounts for both the change in limiting current as a functionof succinate concentration (eq 5) and for the waveshape (eq6).

Figure 3A shows a plot of ilim as a function of ilim/[S] atpH 7.5; this is an Eadie-Hofstee plot, slope ) -Km

succ (59).The best fit gives Km

succ) (83 ( 5) µM for succinate

oxidation by FrdAB.Logarithmic transforms of two catalytic voltammograms

are plotted in Figure 3B. The average slopes are - nappF /2.3RT, where napp is an apparent number of electrons greaterthan one (31): this qualitatively conveys the cooperativecharacter of electron transfer at the FAD.4 As predicted bythe model, each plot shows upward curvature and tendstoward limiting slopes - F /2.3RT and -2F /2.3RT decade/mV at high and low potentials, respectively. Moreover, eq6 accounts well for the data in the entire potential range (plainlines in Figure 3B), with only two adjustable parameters.For a given substrate concentration and pH, the fit yieldsvalues of the FAD reduction potentials, EO/R and EO/H, shownas filled and empty squares, respectively.

3 Applying the Nernst equation, the fraction of FAD in the oxidizedform equates to (1 + exp[F/RT(EO/H - E)] + exp[2F/RT(EO/R - E)])-1.This has to be multiplied by [S]/([S] + KO

succ) to obtain the fraction ofoxidized, succinate-bound enzyme, and then by k2

succ to obtain theturnover number, and by 2F AΓ to obtain the catalytic current.

4 There is a formal analogy between the Heyrovsky-Ilkovich plotand the Hill plot used in studies of cooperative binding in allostericproteins. From the measurement of the saturation (Y) as a function ofthe substrate concentration ([S]), the cooperativity is evidenced in aHill plot of log10(Y/(1 - Y)) against log10([S]). Y is analogous to thecurrent (which is proportional to the fraction of oxidized enzyme), andlog10(Y/(1 - Y)) is analogous to log10((ilim - i)/i). The average slopeof a Hill plot or a Heyrovsky-Ilkovich plot exceeds one when bindingor ET, respectively, is a cooperative event.

Scheme 1: Catalytic Cycle for the Oxidation of Succinateby SDH and FrdABa

a Ox, HR (half-reduced) and Red are used to denote the three redoxstates of the FAD (quinone, semiquinone and hydroquinone respec-tively). EO/H and EH/R are the one-electron reduction potentials for thequinone/semiquinone and semiquinone/hydroquinone transformations.The average two-electron reduction potential quinone/hydroquinone isEO/R ) (EO/H + EH/R)/2.

i2F AΓ

)

k2succ/(1 +

KOsucc

[S] )1 + exp[ F

RT(EO/H - E)] + exp[2F

RT(EO/R - E)](3)

EO/R ) EO/R([S] ) 0) + 2.3RT2F

log101 + [S]/KR

succ

1 + [S]/KOsucc (4a)

EO/H ) EO/H([S] ) 0) + 2.3RTF

log101 + [S]/KH

succ

1 + [S]/KOsucc (4b)

ilim

2F AΓ)

k2succ

1 +KO

succ

[S]

(5)

log10 (ilim - ii ) )

log10 (exp[ F

RT(EO/H - E)] + exp[2F

RT(EO/R - E)]) (6)

≈ { F

2.3RT(EO/H - E) at high potential,2F

2.3RT(EO/R - E) at low potential,

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Thermodynamic Properties of the FAD from CatalyticVoltammetry. Experiments were conducted at several pHs(7-9.5) for a range of succinate concentrations 20 µM to50 mM, and in each case, values of EO/R and EO/H weredetermined from the fits to eq 6. Figure 4 shows that bothEO/R and the stability of the semiquinone state (related toEO/H - EO/R) depend on pH and succinate concentration.

For each pH, values of EO/R([S] ) 0), KOsucc and KR

succ weredetermined by fitting the values EO/R against [S] to eq 4a,then the fit of EO/H to eq 4b gave EO/H([S] ) 0) and KH

succ.The best parameters are reported in Table 1. The mostpronounced pH dependence is observed for KH

succ whichdecreases 30-fold between pH 7 and 9. As found also forSDH (5, 60) the dissociation constants for succinate decrease(binding is enhanced) when the FAD is oxidized.

The pH dependence of the FAD reduction potentials (Table1) yields the number of protons involved in the redoxtransformations of the active site. Figure 5 shows that EO/Rdecreases by about 30 mV/pH unit in the pH range

investigated 7-9.5, thus, one proton is transferred for thetwo-electron reaction, i.e., the active site operates betweenneutral quinone (FAD) and anionic hydroquinone (FADH-)states. In 1 mM succinate, EO/R shifts by about -25 mVwithout changing the pH dependences of the redox processes.

Table 1: Thermodynamics Properties of FAD in FrdAB Measured at 20 °C from the Analysis of Voltammograms

pH Kmsucc a KO

succ b,c KHsucc b,c KR

succ b,c EO/Rd,e EO/R

c,e EO/Hc,e

7 0.14 0.31 8 -50 -42 -457.5 0.083 ( 0.005 0.18 0.63 9 -65 -59 -668 0.130 ( 0.01 0.25 1.8 12 -80 -78 -888.5 0.71 6.3 16 -97 -109 -1039 0.8 10 11 -118 -124 -1109.5 0.8 ndf 8 -142 -141 ndf

a Michaelis constant in mM. From Eadie-Hofstee plots (as in Figure 3A), provided the films were sufficiently stable. b Dissociation constants arein mM. Since fitting the data with eq 4 gives the log of the dissociation constants with an error (0.1, the error on a dissociation constant K is (0.1× 2.3 × K. c From catalytic data. d From noncatalytic data. Reproducibility (3 mV. e All potentials correspond to succinate-free FAD, and are inmillivolts vs SHE. The good agreement between the values of EO/R obtained from noncatalytic and catalytic data suggests that the error on the latteris lower than 10 mV. The errors on pKH

succ and EO/H are correlated: an error (0.1 on pKHsucc results in an additional error of (0.1 × 60 mV on EO/H.

f At pH 9.5, the data are too noisy to be fitted with eq 4b, therefore these values could not be determined.

FIGURE 3: Analysis of steady-state catalytic waves for succinateoxidation by FrdAB. (A) Eadie-Hofstee plot to determine Km

succ

from the change in limiting current as a function of the substrateconcentration (eq 5). Same conditions as in Figure 2. The best fitto a straight line gives Km

succ) (83 ( 5) µM. (B) Heyrovsky-

Ilkovich plot of two of the voltammograms plotted in Figure 2 (for[S] ) 150 µM and [S] ) 16 mM). The small filled circles are theraw data. At each concentration, the fit to eq 6 (plain line) givesthe values of EO/R (9) and EO/H (0).

FIGURE 4: Changes, observed for FrdAB, in the two-electronreduction potential of FAD quinone/hydroquinone (filled symbols)and one-electron reduction potential of FAD quinone/semiquinone(empty symbols) as a function of the succinate concentration andfor different pHs. These were measured by fitting catalyticvoltammograms with eq 6. T ) 20 °C. The symbols correspond topH 7 (squares), 8 (triangles), and 9 (circles). Lines are best fitswith eqs 4.

FIGURE 5: pH dependences of FrdAB active site FAD reductionpotentials; EO/R (filled symbols) and EO/H (empty symbols) for [S]) 0 (squares) and [S] ) 1 mM (circles). Crosses (×) are values ofEO/R determined from noncatalytic data at [S] ) 0. For EO/R, bestfits (dashed straight lines) give slopes -34 mV/pH. For EO/H fitsto eq 7 (plain lines) give pKa ) 8.15 ( 0.1.

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Fitting the pH dependence of EO/H to

(plain lines in Figure 5), gives pKa ) 8.15 ( 0.10 for thesemiquinone form of the flavin.

In support of the above analysis, the values of severalparameters determined in two independent ways werecompared. With sufficiently stable films, Michaelis constantswere determined by Eadie-Hofstee plots yielding values ofKm

succ, which matched the independently measured KOsucc

(Table 1), as expected from eq 5. Additionally, we comparedthe average two-electron substrate-free potentials of the FADmeasured either (i) by analyzing the catalytic wave andextrapolating the concentration dependence of EO/R to zerosuccinate concentration using eq 4a, or (ii) by deconvolutingthe noncatalytic voltammograms recorded in substrate-freesolution (Figure 1A). The difference was always less than10 mV (see Table 1, and compare the filled squares andcrosses in Figure 5). The cooperativity of the ET process atzero succinate concentration can be estimated by analyzingthe FAD peak in noncatalytic experiments. Fitting the datain Figure 1A at pH 7 yields a disproportionation constant κ

) 0.2 ( 0.1, therefore EO/H - EO/R ) - 22 ( 8 mV. Byextrapolating catalytic data to zero succinate concentration(Table 1) we obtained EO/H - EO/R ) - 3 ( 20 mV. Bothestimates suggest a significant maximal level of semiquinone(respectively, 20 ( 5 and 35 ( 15%) at E ) EO/R, pH 7, inthe absence of substrate.

Product Inhibition and Estimation of the Catalytic Biasof FrdAB. From Scheme 2, the limiting current for succinateoxidation (ilim

succ) in the presence of succinate and fumaratefollows M-M kinetics with the apparent Km

succ increased bya factor (1 + [F]/KO

fum), where KOfum is the fumarate dis-

sociation constant for oxidized FAD. Symmetrical reasoningholds for fumarate reduction inhibition by succinate at lowpotential so that:

Four parameters (Kmsucc, Km

fum, KOfum, and KR

succ) are required toestimate the catalytic bias of FrdAB from eqs 8 and theexperiment plotted in Figure 1B. At pH 7, Km

fum) 160 µM

(31), Kmsucc

) 140 µM and KRsucc

) 8 mM (Table 1). Theremaining parameter is KO

fum, which is likely to be muchhigher than the fumarate concentration used ([F] ) 4 µM).The ratio of limiting current therefore simplifies to5

The limiting currents for succinate oxidation and fumarate

reduction are roughly equal to each other under the conditionsof Figure 1B. Equation 9 gives k2

fum/k2succ ≈ 40, while a

similar value (approximately 37) was obtained in solutionassays at 25 °C, pH 7, based on methyl viologen orferricyanide as the electron partner (Experimental Section).Using the value k2

fum ≈ 840 s-1 obtained for WT FrdABadsorbed onto an electrode (31), we obtain k2

succ ≈ 20 s-1

for succinate oxidation at pH 7.Fast-Scan Voltammetry in the Presence of Substrate. Fast-

scan voltammetry provides another way to study the FADcofactor during catalysis (38). Figure 6 shows how the FADoxidation and reduction peak positions vary with scan ratein the absence of succinate (empty symbols). Because (i)the two electrons transfer cooperatively (55) (see Figure 1A)and (ii) ET to the FAD is fast, the signal is prominent andcould be tracked over 4 orders of magnitude in scan rate (ν) 10 mV/s to 100 V/s). By analyzing the position of peaksas a function of scan rate, information on the rates ofinterfacial ET and coupled chemical processes can beobtained (30, 32).

When succinate is bound, the plot of FAD peak positionsagainst ν (filled symbols in Figure 6) commences at a scanrate that is high enough to outrun catalysis, i.e., allowingthe electrons to be re-injected before transformation of theFADOx-succinate enzyme-substrate complex. The scans inthe presence of substrate were started from a reductive poise,in 50 mM succinate at pH 7. Since KR

succ) 8 mM (Table 1),

the active site is 86% saturated. As seen in Figure 6, theaverage peak position of the FAD at pH 7, [S] ) 50 mM isEO/R ) -80 mV vs SHE. This value matches well thatdetermined from the waveshape in the same conditions (EO/R≈ -88 mV, Figure 4). The shift of about -31 mV seen inFigure 6 is smaller than expected from Figure 4, where 50mM succinate causes a shift of nearly -50 mV. Thisdiscrepancy is likely to arise to the greater error in EO/Rdetermined from catalytic data at very low concentration ofsuccinate (due to the small currents which are then mea-

5 Since the fumarate concentration is very low, it should not inhibitsuccinate oxidation. Moreover, the succinate concentration is muchhigher than KO

succ, so the right-hand side of eq 8a reduces to k2succ.

Regarding the limiting reductive current, the succinate concentrationis much lower than KR

succstoo low to inhibit fumarate reduction. With

the fumarate concentration being lower than Kmfum, the denominator of

eq 8b approximates to Kmfum/[F].

EO/H ) EO/Halk

+2.3RT

Flog10(1 +

[H+]Ka

) (7)

ilimsucc

2F AΓ)

k2succ

1 +Km

succ

[S] (1 +[F]

KOfum)

(8a)

ilimfum

2F AΓ)

-k2fum

1 +Km

fum

[F] (1 +[S]

KRsucc)

(8b)

ilimsucc

ilimfum ≈ -

k2succKm

fum

k2fum[F]

(9)

Scheme 2: Product Inhibition of Succinate Oxidation atHigh Electrode Potential (top) and Fumarate Reduction atLow Potential (bottom)

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sured). Under fast scan conditions, in the presence ofsubstrate, we did not notice any change in the stoichiometryof the FAD signal compared to the one-electron [4Fe-4S]couple.

Comparison with SDH. Figures 7 and 8 emphasize thedifferences in catalytic energetics between SDH and FrdAB.In both figures, the upper plots (Figures 7A and 8A) are thelogarithmic transforms of catalytic voltammograms for SDHadsorbed at PGE, whereas the lower plots (Figures 7B and8B) correspond to catalysis by FrdAB under the sameconditions. For reasons that remain unclear, SDH does notgive a high electroactive coverage at PGE (nonturnoversignals have not been reliably detected) and the films areunstable (33-36). Even so, the data are well-defined enoughto draw comparative insights.

Two catalytic voltammograms for succinate oxidation bySDH are plotted in Figure 7, differing only in pH. Thewaveshape is not distinguishable from a line of slope -F /2.3RT decade/mV that is expected from the above M-M

model if the semiquinone is stable (i.e., EO/H . EO/R). Inthis case, eq 6 reduces to6

and the logarithmic plot intercepts the line for (ilim - i)/i )1 at E ) EO/H, i.e., the mid-wave potential is EO/H (shown asempty squares in Figure 7A). Note that the position of thewave provides no information on EO/R. The one-electronshape of the wave is unambiguous evidence that thesemiquinone form of FAD in SDH is stable over quite alarge range of potential although the conclusion that the mid-wave potential equals EO/H (eq 10) is based on the assumptionthat binding of succinate is a rapidly established equilibrium.7

As seen in Figure 7A, the value of EO/H as determinedfrom the waveshape with eq 10 decreases by approximatively10 mV when the pH is increased from 7 to 8. This pHdependence of the mid-wave potential has been reportedpreviously (34-36) but may now be interpreted. For FrdAB,the -60 mV/pH dependence of EO/H (Figure 7B) shows thatthe FAD is protonated upon reduction to the semiquinonestate; by contrast, for SDH, the very small pH dependenceof EO/H now shows that the semiquinone form is anionic atneutral pH, consistent with EPR results (61).

In the case of FrdAB at pH 9, EO/H shifts by about -55mV when the succinate concentration is raised from 50 µMto 50 mM (empty squares in Figure 8B). This must resultfrom the higher affinity of succinate for the oxidized FADthan for the semiquinone form under alkaline conditions(Table 1). A clear contrast is now evident with SDH, whereEO/H is hardly sensitive to succinate concentration (Figure8A). According to eq 4b this suggests that in SDH, bindingof succinate at high pH does not depend on whether the FADis in the quinone or semiquinone state.

DISCUSSION

In classical enzyme kinetics, turnover is measured as afunction of the concentrations of various reactants (substrate,protons, inhibitors) and a plausible mechanism is derived.Such studies rely on the relationship between the concentra-tion of reactants and their microscopic rates of binding, whichaffect the measurable rate of turnover. PFV adds the“potential dimension” to this investigation since rates ofredox processes depend on the electrode potential. Thisstrong dependence (exponential at low driving force, asopposed to a linear dependence of binding rate on speciesconcentration) enables the rates of redox reactions to be tuned

6 Using κ ) exp(2F/RT(EO/H - EO/R)), eq 6 reads:

log10(ilim - ii ) ) log10(xκ exp[ F

RT(EO/R - E)] +exp[2F

RT(EO/R - E)]) (11)

If the semiquinone is very stable (κ large), the first term is much greaterthan the second (except at extremely low potential, where hardly anycurrent can be measured), and eq 11 simplifies into eq 10.

7 In contrast with FrdAB, this hypothesis is questionable in the caseof SDH since the generally accepted physiological role of the latterenzyme is to catalyze succinate oxidation. Just as in the case of Briggs-Haldane kinetics where the Michaelis constant is not a true dissociationconstant, the one-electron mid-wave potential for succinate oxidationby SDH may have to be interpreted as an “apparent” EO/H.

FIGURE 6: Fast-scan voltammetry of FrdAB without succinate (O)and with 50 mM succinate (b) at pH 7. The prominent high-potential (FAD) peak position is plotted as a function of the scanrate. The arrow marks the value of EO/R in the presence of 50 mMsuccinate. When succinate was present, the cyclic voltammogramswere recorded between -610 and +240 mV, after 5 s equilibrationat low potential.

FIGURE 7: Comparison between SDH (A) and FrdAB (B): pHdependence of EO/H. pH 7 and 8, [S] ) 1.5 mM (FrdAB) and [S]) 0.8 mM (SDH). As in Figure 3, the sets of two squares markthe values of EO/R (9) and EO/H (0). In plot A, EO/R cannot bedetermined from the analysis of the waveshape with eq 10. T ) 20°C, ω ) 1000 rpm (SDH) and 3000 rpm (FrdAB), ν ) 10 mV/s(SDH) and 1 mV/s (FrdAB).

log10 (ilim - ii ) ≈

F

2.3RT(EO/H - E) (10)

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over orders of magnitude, and makes PFV a potentiallypowerful method to investigate the catalytic properties ofcomplex multicentered redox enzymes (28, 31-38, 40, 62).

FrdAB. FrdAB, the principal subject of the present study,gives a stable electrochemical response when it is adsorbedonto a graphite electrode. First, we note that the enzyme isfirmly biased to operate in the direction of fumarate reduction(Figure 1B), with succinate oxidation being slow.8 Thisproves to be a valuable asset in our study of the electro-kinetics. The noncatalytic signal (i.e., in the absence ofsubstrate) is easily deconvoluted to measure the reductionpotentials of the FAD and the Fe-S clusters (Figure 1A).Due to the cooperativity of the two one-electron transfers,the FAD moiety is easily distinguished as a prominent peak;this provides an alternative to optical or EPR titrations todetermine its redox properties and observe its reactions. Thetwo-electron reduction potential of the FAD can even bemeasured from the peak positions in the presence ofsubstrate, provided the scan rate is high enough to outruncatalysis (38). The shift in the FAD noncatalytic signal tolow potential when succinate is present (Figure 6) mirrorsthe shift in the catalytic wave when the concentration ofsuccinate is raised (Figure 2B). As a specific example, Figure6 shows that at pH 7, [S] ) 50 mM, the 2-electron potentialof the FAD moves to -80 mV vs SHE. The good agreementwith the value of EO/R obtained by analyzing catalytic data(EO/R ≈ - 88 mV at pH 7, [S] ) 50 mM, Figure 4) fullysupports the model developed here in which the catalyticwaveshape is linked to the FAD reduction potentials.

According to eq 6, the semilogarithmic transform of thecatalytic wave (the Heyrovsky-Ilkovich plot) reveals acrossover between two limiting behaviors. As indeed con-

firmed by Figure 2C, the catalytic current as a function ofthe potential follows a sigmoidal increase with a two- orone-electron shape at low or high driving force, respectively.This can be understood in the following simple terms.According to our hypothesis of rapidly established equilib-rium among the different states shown in Scheme 1, the ratesof ET and binding are all greater than that for transformationof the enzyme-substrate complex. (i) At low potential,reduced FAD accumulates: its oxidation at the electrodeappears as a cooperative two-electron reaction because uponformation of the semiquinone form, the second electron isremoved spontaneously. (ii) At higher potential, the semi-quinone form becomes more prevalent, and the waveshapenow reflects the further one-electron oxidation necessary forturnover. (iii) At Very high potential, the fully oxidized formof the FAD predominates, and turnover is now limited bythe transformation of the FADOx-succinate complex, the rateof which is potential-independent; the catalytic current thusreaches a plateau.

The model developed here is the electrochemical coun-terpart of Michaelis-Menten kinetics. We have assumed thatcatalysis proceeds via hydride transfer between the succinateand FAD. This has the slowest rate constant in the entiresequence of events,9 over the whole potential range, andensures that the other processes are always at equilibrium.Consequently, turnover is proportional to the level of fullyoxidized (quinone) FAD that can be maintained by theelectrode potential. The model would not apply if turnoverwere limited by ET between electrode and FAD; were thisto be the case, the wave would broaden at high driving force(56) whereas the limiting slope of the logarithmic transformdoes not decrease below the nernstian limit of - F /2.3RTdecade/mV (Figure 3B).

Strictly speaking, the net unimolecular rate constant k2succ

that we interpreted as the rate of succinate oxidation in theenzyme-substrate complex could instead be for fumaraterelease. That this is not the case is shown by fast-scan PFV.If fumarate release were rate limiting, the “faradaic capacity”of the active site, evidenced in the shape of the FADcomponent of the signal, should increase to four electrons(the FADRed-fumarate enzyme-substrate complex could befurther oxidized before the scan is reversed). This changeshould be easily quantified using the low-potential [4Fe-4S]one-electron signal as a one-electron reference (Figure 1A).Apart from the shift in potential, there was no change in thestoichiometry of the noncatalytic voltammograms recordedat high scan rate in the presence of succinate; this showsthat the transformation of the FADOx-succinate complex intoFADRed-fumarate is slower than the release of fumarate.

Importantly, while the cooperativity of the two one-electron transfers at the FAD depends on the pH andsuccinate concentration, the semiquinone has a significantstability across the whole experimental range (pH ) 7-9.5,[S] ) 0-50 mM): EO/H - EO/R ranges between -20 and+25 mV (Figure 4); therefore, under turnover conditions,the maximum percentage of semiquinone (at E ) EO/R) is

8 The pH dependence of the limiting current for [S] ) 50 mM (datanot shown) is as expected for a reaction whose rate depends on thebasic form of an acid of pKa ) 6.8 ( 0.2. Thus, k2

succ increases lessthan 2-fold between pH 7 and 9.

9 Accordingly, the oxidation of perdeuteriosuccinate by SDH issignificantly slower than that of succinate, whereas deuteration offumarate has no observable effect (see ref 35 and references therein).In the case of FrdAB, a large decrease in fumarate reduction activityresults upon substitution of H2O by D2O (unpublished results).

FIGURE 8: Comparison between SDH (A) and FrdAB (B):succinate-concentration dependence of EO/H. [S] ) 50 µM (dashedlines) and 50 mM (plain lines). As in Figures 3 and 7, the squaresmark the values of EO/R (9) and EO/H (0). T ) 20 °C, ω ) 1000rpm (SDH) and 3000 rpm (FrdAB), ν ) 10 mV/s (SDH) and 1mV/s (FrdAB).

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20-50%. In the absence of substrate, at pH 7, analysis ofnoncatalytic experiments (the shape of the FAD peak) andextrapolation of catalytic data to zero succinate concentrationboth suggest that the level of semiquinone at E ) EO/R isabout 25%. This contrasts with the previous EPR investiga-tion according to which no significant radical signals wereobserved at 165 K after room-temperature solution titration,and it was concluded that the maximum semiquinone levelmust be <2% (32). The reason for this discrepancy isunclear; however, from the literature, it appears that thestability of the FAD radical in QFR may vary from onepreparation to another, and be sensitive to such factors asthe presence of the membrane anchor domain (FrdCD) andmutations thereof (63, 64).

The catalytic cycle of succinate oxidation consists of (i)oxidation of the FAD and binding of succinate, and (ii)subsequent oxidation of bound succinate and reduction ofthe FAD. The only quantity we measure regarding the latterstep is its rate, k2

succ, and this is also possible with solutionassays. However, PFV reveals the thermodynamic propertiesof the FAD during the reoxidation half-cycle, which is notrate limiting during solution assays with oxidizing dyes.Discrete redox states of the FAD can be probed by PFVbecause it is possible to tune the electrode potential toinfluence their levels during turnover. From the directmeasurement of the FAD reduction potentials as a functionof the succinate concentration and pH, we were able todetermine the succinate-enzyme dissociation constants forthe three redox states of the FAD (Table 1) and the succinate-concentration independent acidity constant of the semi-quinone (pKa ) 8.15 ( 0.10). With respect to the modelflavin 8R-N-imidazolylriboflavin (65), the enzyme environ-ment raises the pKa of the radical by over 1 pH unit. Thesethermodynamic properties of the FAD are relevant to thecatalytic cycle, regarding the protonation and binding statesof the FAD intermediates.

During the catalytic cycle of FrdAB, the two-electronreoxidation of the anionic FAD hydroquinone is associatedwith the loss of one proton. The -60 mV/pH dependencefor EO/H below pH 8 (Figure 5) shows that this proton is lostduring the one-electron reoxidation of the semiquinone tothe quinone. The semiquinone is therefore neutral, and mostlikely protonated at N5. This contrasts with the finding that8R-(N3-histidyl) covalently bound flavins generally giveanionic semiquinone radicals (61, 66).

The data in Table 1 show that at neutral pH, thedissociation constant for the FrdAB enzyme-succinatecomplex containing reduced FAD is very high, whereas thosefor the semiquinone and the quinone forms are low (andequal to Km

succ) (Table 1). Therefore, unless [S] . 1 mM(for KR

succ. [S] . Km

succ), binding of succinate must occurduring the catalytic cycle after the hydroquinone is oxidized,i.e., to semiquinone (or quinone) state. In solution assayswith high-potential dyes, or in voltammetric measurementson the limiting current plateau, the reoxidation may be sofast that binding could occur later, i.e., to the oxidized form,but not to the reduced form since this is not favored from athermodynamic viewpoint. However, determining the se-quence of binding events occurring in vivo would requireto take into account all the dicarboxylates which competefor binding to the active site.

SDH. With SDH, a clear and reproducible noncatalyticsignal has not so far been detected. This may largely be dueto our inability to obtain a sizable coverage. Furthermore,the FAD will not be conspicuous unless the two one-electrontransfers show reasonable cooperativity. That the latter isunlikely is evidenced by the fact that the catalytic currentcan be well fitted to a one-electron sigmoid (Figures 7A and8A). In view of the model described, this implies that thesemiquinone form of the FAD is stable over quite a largepotential range, the oxidation of the semiquinone to thequinone being the step revealed in the one-electron wave-shape. In this respect (and like QFR, see above), EPRinvestigations (in the absence of substrate) have givenconflicting results [the maximal percentage of FAD semi-quinone measured by EPR ranges from 7% (67) to 70% (61,68)]. Despite this, the measurement of EO/R in SDH fromEPR (67) is consistent with results from reductive reactiva-tion experiments (69). Our previous hypothesis that theattenuation of fumarate reduction at low potential is due toreduction of the FAD (34) is not in conflict with the presentwork: this was modeled as a two-electron switch, but thismay well appear at the average two-electron reductionpotential of the FAD if the unimolecular rate constant forfumarate reduction (k2

fum) depends on the ratio of oxidizedto reduced flavin, this quantity being independent of thestability of the semiquinone.

In contrast with FrdAB, reoxidation of the hydroquinonein SDH is thought to involve two protons (34, 36, 67, 70)while the present observations suggest that no proton isreleased during oxidation of the anionic semiquinone.Williamson et al. demonstrated that the interpretation of thepH-dependent reduction potentials of synthetic 8R-N-imi-dazolylriboflavin has to take into account the protonation ofthe imidazole ring and of the N1, N3, and N5 positions onthe isoalloxazine ring (65). In flavoenzymes, this could befurther complicated by the protonation of nearby amino acidresidues and solvent water, and makes doubtful the inter-pretation of any potentiometric data in the absence of reliablecomplementary spectroscopic evidence.

CONCLUDING REMARKS

We have shown previously the SDH activity for fumaratereduction shuts down partly below a certain potential (abovea certain driving force) (33-36, 41). Such behavior may bewidespread for enzymes exhibiting multiple oxidation levels,as evidenced further in our recent report of the catalyticactivity of DMSO reductase from E. coli (62). Just as mostenzymes function in vivo at substrate concentrations lowerthan Km, they are unlikely to be subjected to extremes ofelectrochemical driving force, dictated by the reductionpotential and concentrations of the physiological, membrane-associated electron donor or acceptor. In the case of QFR,the physiologically relevant driving force is given byEMQ/MQH2

0′+ RT/2F ln[MQ]/[MQH2]. With EMQ/MQH2

0′) - 75 mV

at pH 7; therefore, a 400-fold excess of menaquinone overmenaquinol would be required for the activity to lie on theactivity plateau at 0 mV (Figure 2B). The physiologicallymost important region of potential is certainly the reVersibleregion (around the reduction potential of the electron partner)that PFV is able to investigate precisely. The potentialdependence revealed by our studies is therefore not only a

Energetics of Succinate Oxidation Biochemistry, Vol. 40, No. 37, 2001 11243

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C. Leger. UPR 9036. Memoire d’HDR. 2007.

controllable parameter useful in mechanistic studies, but alsoa physiologically relevant quantity that should be exploredas a possible basis for metabolic regulation.

Determining which amino acid residues are responsiblefor the differences in the electrocatalytic properties of FrdABand SDH is an interesting and important task. The distinctionis not trivial since even in a single organism, QFR isexpressed under anaerobic conditions and SQR under aerobicconditions. This occurs not only in E. coli: as a strikingexample, the maturation of the larvae of the liver flukeFasciola hepatica involves moving from a sheep’s lungs toits liver; concomitant with the change from aerobic toanaerobic conditions, the mature fluke stops using SQR andsynthesizes QFR as a separate gene product to use fumarateas a terminal oxidant instead of oxygen (71). Microorganismsmay have evolved separate genes for succinate oxidation andfumarate reduction to obtain directional specificity (toimprove the catalytic bias), and not only to speed up theturnover rate.

ACKNOWLEDGMENT

We thank Sean Elliot, Raul Camba Acosta, Hendrik A.Heering, Lars C. Jeuken, Anne K. Jones, and TomokoOhnishi for fruitful discussions, and Bruce Cochran forassistance in preparing SDH.

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39. Dobbin, P. S., Butt, J. N., Powell, A. K., Reid, G. A.,Richardson, D. J. (1999) Biochem. J. 342, 439-448.

40. Butt, J. N., Thornton, J., Richardson, D. J., and Dobbin, P. S.(2000) Biophys. J. 78, 1001-1009.

41. Ackrell, B. A. C., Armstrong, F. A., Cochran, B., Sucheta,A., and Yu, T. (1993) FEBS Lett. 326, 92-94.

42. Jones, A. K., Chapman, S. K., and Armstrong, F. A.Unpublished results.

43. Westenberg, D. J., Gunsalus, R. P., Ackrell, B. A. C., Sices,H., and Cecchini, G. (1993) J. Biol. Chem. 268, 815-822.

44. Blaut, M. K., Whittaker, K., Valdovinos, A., Ackrell, B. A.C., Gunsalus, R. P., and Cecchini, G. (1989) J. Biol. Chem.264, 13599-13604.

45. Sambrook, J., Fritsh, E. F., and Maniatis, T. (1989) MolecularCloning: a laboratory manual, Cold Spring Harbor Labora-tory, Cold Spring Harbor, NY.

46. Beginsky, M. L., and Hatefi, Y. (1969) J. Biol. Chem. 244,5313-5319.

47. Davis, K. A., and Hatefi, Y. (1971) Biochemistry 10, 2509-2516.

48. Bard, A. J., and Faulkner, L. R. (1980) Electrochemicalmethods. Fundamental and applications, John Wiley & Sons,Inc., New York.

49. Britz, D. (1978) J. Electroanal. Chem. 88, 309-352.

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50. Press, W. H., Teukolsky, S. A., Vetterling, W. T., andFlannery, B. P. (1999) Numerical Recipes in Fortran 77, 2nded., Cambridge University Press, New York.

51. Bertrand, P., Dole, F., Asso, M., and Guigliarelli, B. (2000)J. Biol. Inorg. Chem. 5, 682-691.

52. Guigliarelli, B., and Bertrand, P. (1999) AdV. Inorg. Chem.47, 421-497.

53. Louro, R. O., Catarino, T., Turner, D. L., Picarra-Pereira, M.A., Pacheco, I., LeGall, J., and Xavier, A. V. (1998)Biochemistry 37, 15808-15815.

54. Louro, R. O., Catarino, T., LeGall, J., and Xavier, A. V. (1997)J. Biol. Inorg. Chem. 2, 488-491.

55. Plichon, V., and Laviron, E. (1976) J. Electroanal. Chem. 71,143-156.

56. Heering, H. A., Hirst, J., and Armstrong, F. A. (1998) J. Phys.Chem. B 102, 6889-6902.

57. Clark, W. M. (1960) Oxidation-reduction potentials oforganic systems, Bailliere, Tindal & Cos Ltd., London.

58. Bond, A. M. (1980) Modern polarographic methods inanalytical electrochemistry, Marcel Dekker, Inc.

59. Cornish-Bowden, A. (1995) Fundamental of enzyme kinetics,Portland Press.

60. Kotlyar, A. B., and Vinogradov, A. D. (1984) Biochim.Biophys. Acta 784, 24-34.

61. Ackrell, B. A. C., McIntire, W., Edmondson, D. E., andKearney, E. B. (1982) The semiquinone form of succinate

dehydrogenase and other 8R-substituted flavoenzymes. InFlaVins and FlaVoproteins (Massey, V., and Williams, C. H.,Eds.) Chapter 80, pp 488-491, Elsevier North-Holland, Inc.

62. Heffron, K., Leger, C., Rothery, R. A., Weiner, J. H., andArmstrong, F. A. (2001) Biochemistry 40, 3117-3126.

63. Weiner, J. H., Cammack R., Cole S. T., Condon C., HonoreN., Lemire B. D., and Shaw G. (1986) Proc. Natl. Acad. Sci.U.S.A. 83, 2056-2060.

64. Ohnishi, T. Personnal communication.65. Williamson, G., and Edmondson, D. (1985) Biochemistry 24,

7790-7797.66. Edmondson, D. E., Ackrell, B. A. C., and Kearney, E. B.

(1981) Arch. Biochem. Biophys. 208, 69-74.67. Ohnishi, T., King, T. E., Salerno, J. C., Blum, H., Bowyer, J.

R., and Maida, T. (1981) J. Biol. Chem. 256, 5577-5582.68. Beinert, H., Ackrell, B. A. C., Kearney, E. B., and Singer, T.

P. (1975) Eur. J. Biochem. 54, 185-194.69. Ackrell, B. A. C., Kearney, E. B., and Edmondson, D. (1975)

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BI010889B

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Effect of a Dispersion of Interfacial Electron Transfer Rates on Steady State CatalyticElectron Transport in [NiFe]-hydrogenase and Other Enzymes

Christophe Leger,†,| Anne K. Jones,† Simon P. J. Albracht,‡ and Fraser A. Armstrong*,†

Inorganic Chemistry Laboratory, South Parks Road, Oxford OX1 3QR, United Kingdom, and SwammerdamInstitute for Life Sciences, Biochemistry, UniVersity of Amsterdam, Plantage Muidergracht 12,NL-1018 TV Amsterdam, The Netherlands

ReceiVed: July 19, 2002; In Final Form: October 4, 2002

Redox enzymes can be adsorbed onto electrode surfaces such that there is a rapid and efficient direct electrontransfer (ET) between the electrode and the enzyme’s active site, along with high catalytic activity. In anidealized way, this may be analogous to protein-protein ET or, more significantly, the nonrigid interfacebetween different domains of membrane-bound enzymes. The catalytic current that is obtained when substrateis added to the solution is directly proportional to the enzyme’s turnover rate and its dependence on theelectrode potential reports on the energetics and kinetics of the entire catalytic cycle. Although the current isexpected to reach a limiting value as the electrode potential is varied to increase the driving force, a residualslope in voltammograms is often observed. This slope is significant, as it is unexpected from all simpleconsiderations of electrochemical kinetics. A particularly remarkable result is obtained in experiments carriedout with the [NiFe]-hydrogenase from Allochromatium Vinosum: this enzyme displays high catalytic activityfor hydrogen oxidation and is easily studied up to 60 °C, at which temperature the current-potential responsebecomes completely linear over a range of more than 0.5 V. The explanation for this effect is that the enzymemolecules are not adsorbed in a homogeneous manner but vary in their degree of ET coupling with theelectrode, i.e., through there being many slightly different orientations. Under conditions in which interfacialET becomes rate-limiting, i.e., when turnover number is high at elevated temperatures, the current-potentialresponse reflects the superposition of numerous electrochemical rate constants. This is highly relevant in theinterpretation of the catalytic electrochemistry of enzymes.

IntroductionIn catalytic protein film voltammetry1 (PFV), a redox enzyme

is adsorbed onto an electrode, typically to submonolayercoverage. Direct, long-range electron transfer (ET) occursbetween the electrode and the buried active site, usually throughan intramolecular chain of redox groups, such as iron-sulfurclusters or hemes, that is naturally designed to facilitate fastand efficient intramolecular ET.2 The driving force for thecatalytic reaction is provided through the applied electrodepotential and can be fine-tuned, while the catalytic activity issimultaneously and precisely measured as a steady state, faradaiccurrent that results from the continuous regeneration of the activesite by interfacial ET: importantly, the magnitude of the currentis directly proportional to the turnover rate. This kind ofexperiment presents important opportunities to study enzymekinetics since the resulting voltammograms reveal the exactvariation in activity (current) as a function of driving force(electrode potential) and contain information about the kineticsand energetics of interconversions between catalytic inter-mediates.3-5 Yet, as we now describe, the nature of theinteraction between the electrode and these giant catalysts isunclear and provides a further intriguing dimension to thesestudies.

Hydrogenases are enzymes that catalyze the evolution andoxidation of H2 (see refs 6-10 for recent reviews). The [NiFe]-hydrogenase from the purple sulfur bacterium AllochromatiumVinosum contains a buried active site for H2/H+ interconversion(the [NiFe(CO)(CN)2] center), which is redox-coupled to theprotein surface by a chain of three [FeS] clusters. Whenadsorbed onto a pyrolytic graphite edge (PGE) electrode, theenzyme displays intense catalytic activity.11,12 The turnovernumber, which exceeds 1500 s-1 at 30 °C (ref 11), isconsiderably higher than that measured using soluble redox dyesas electron acceptors, indicating that in these more conventionalsolution experiments, the rate is limited by the reaction withthe mediator. The activity of the enzyme is so high that withoptimized coverage on the electrode, the hydrogen substrate isdepleted near the electrode surface and mass transport-controlledvoltammetry is observed, for which the catalytic currentincreases with the electrode rotation rate.11 However, aninteresting situation arises if the electrode surface onto whichthe enzyme is adsorbed is abraded; for example, with cottonwool, this greatly lowers the coverage of enzyme, and if thepressure of H2 is increased to one bar, mass transport control isremoved.12 The influence of temperature is now strikinglyrevealed, and as shown in Figure 1, the quasi-sigmoidal catalyticwave observed at low temperature converts to a response thatis linear over a potential range of more than 0.5 V when thetemperature is raised. The linearity is unexpected and resemblesthat for a device obeying Ohm’s law. Similar observations, albeitin most cases less dramatic,3-5,12-20 have been made for other

* To whom correspondence should be addressed. Tel: 44-1865-272647.Fax: 44-1865-272690. E-mail: fraser.armstrong@chem.ox.ac.uk.

† Inorganic Chemistry Laboratory.‡ University of Amsterdam.| Current address: Laboratoire de Bioenergetique et Ingenierie des

Proteines, CNRS, Marseille, France.

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10.1021/jp0265687 CCC: $22.00 © 2002 American Chemical SocietyPublished on Web 11/20/2002

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enzymes confined to an electrode surface, leading us to questionits origin and mechanistic significance.

In this paper, we discuss the origin of this behavior and showthat it can be explained by disorder among the adsorbed enzymemolecules, resulting in a dispersion of interfacial ET rateconstants. There are interesting implications both for theinterpretation of catalytic waveshapes for adsorbed enzymes andon the influence of the fidelity of intermacromolecular interac-tions in physiological ET reactions.

Modeling

Ideal Case. The two-electron oxidation of a substrateoccurring at the redox active site of an enzyme normallyinvolves two one-electron oxidations of the active site, followedby product formation and release and substrate binding. Inclassical enzyme kinetics, turnover is measured as a functionof the concentrations of various reactants, whereas PFV addsthe “potential dimension” to this investigation, since rates ofredox processes (and therefore turnover) depend on the electrodepotential. According to the Butler-Volmer model,21,22 the rateof interfacial ET increases exponentially with the driving force(overpotential, η); consequently, the ET rate will alwayseventually exceed the rate of substrate conversion by the

enzyme-substrate complex. According to Marcus theory,22,23 therate of interfacial ET starts to level off once the overpotentialbecomes higher than the reorganization energy of the reaction(η > λ). With these considerations (i.e., whatever the ET model)and assuming that the rate of substrate conversion is independentof potential, the resulting catalytic voltammogram is expectedto show the current increasing with overpotential at moderatedriving force and then leveling off to a limiting value (plateau).

In ref 5, equations were derived for the current correspondingto the steady state, catalytic, two electron oxidation of a substrateby an enzyme adsorbed on an electrode, assuming that masstransport of the substrate to the electrode is not rate-limiting.Further assumptions were that (i) the active site exists in threeredox states termed O (oxidized), I (half-reduced intermediate),and R (reduced). As depicted in Scheme 1, the oxidized,deprotonated, and substrate-bound form of the active siteregenerates R, while the product of the reaction is producedwith a first-order rate constant k2. (ii) (De)protonation andsubstrate binding steps are at equilibrium throughout. (iii) Therate of active site oxidation as a function of the electrodepotential E is predicted by Butler-Volmer formalism,21 i.e.,

with eO/I ) exp[f(E - EO/I)], EO/I is the reduction potential ofthe O/I couple, f ) F/RT, and k0 is the interfacial ET rate atzero overpotential, which is assumed to be the same for alladsorbed enzyme molecules. Analogous equations hold for theI/R transformation.

The model predicts that the current i increases from zero atlow potential to a limiting value ilim at high driving forceaccording to24

where ilim ) 2FAΓk2 (i.e., the limiting current is enzyme-controlled), A is the electrode surface area, and Γ is theelectroactive coverage of enzyme. Four parameters must beadjusted to fit the data to eq 2: two reduction potentials, k2/k0and ilim.

Origin of Nonidealities. Because intramolecular ET alongthe chain of Fe-S clusters in hydrogenase is expected to bevery fast,2 we assume that the overall rate of ET depends onthe distance-related electronic coupling between the electrodeand the surface-exposed [4Fe-4S] cluster that provides theentry/exit point for electrons within the enzyme. The importantextension of the model described above is that we now considerthe effect of disorder in the orientation of enzyme molecules

Figure 1. Catalytic hydrogen oxidation by A. Vinosum [NiFe]-hydrogenase adsorbed at a PGE electrode at pH 7, under one bar H2,as a function of temperature. As the enzyme activity increases, thecatalytic response is transformed from a sigmoid to a line. The electrodegeometric area was A ) 0.03 cm2, the scan rate was ν ) 1 V/s, andthe electrode rotation rate was ω ) 2500 rpm. Increasing ω furtherproduced no change in the voltammetry, showing that it is not masstransport-controlled. The dotted line shows the linear baseline that issubtracted to remove the capacitive current before fitting the data(Figure 5).

SCHEME 1: Generic Scheme for a Two-ElectronCatalytic Oxidationa

a The reduced form of the active site is oxidized to O (via anintermediate species I) following two one-electron transfers and coupleddeprotonation steps. The oxidized, substrate-bound form of the activesite makes and releases the product with a rate k2.

kOfI ) k0 exp[-f2 (E - EO/I)] ) k0eO/I

-1/2 (1a)

kIfO ) k0 exp[ f2(E - EO/I)] ) k0eO/I

1/2 (1b)

ilim

i - 1 ) eO/I-1(1 + eI/R

-1) +k2

k0{eI/R

-1/2+ eO/I

-1/2(1 + eI/R-1)} (2)

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on the electrode: this introduces a dispersion of tunnelingdistances and hence a dispersion of interfacial ET rate constants(Figure 2).

The rate of interfacial ET to the active site decreasesexponentially with the tunneling distance d between theelectrode and the entry point for electrons in the enzymeaccording to the relationship:

where k0max ) k0(d)dmin) and â is a decay constant (Figure 3B),the value of which is typically of the order of 1 Å-1. We assumethat within a certain range of distances [dmin, dmax ) dmin +

d0], all of the values of d occur with the same probability (Figure3A), i.e.,

The square function has been chosen for simplicity, since boththe enzyme molecule and the electrode surface at which it isbound have irregular shapes, and further definition is not useful.

Combining the probability function of d (eq 4) and thedependence of k0 on d (eq 3), the probability of ET occurringwith a given value of k0 is

with k0min ) k0maxexp(-âd0). Equation 5 is derived in theSupporting Information section and is plotted in Figure 3C.

Corrected Waveshape. Starting from an equation for thewaveshape as a function of two reduction potentials and theinterfacial ET rate at zero overpotential k0 (eq 2), the current iseasily integrated across all possible values of k0 in the range[k0min, k0max] (eq 5). As demonstrated in the SupportingInformation section, the corrected current i* is represented by:

The corresponding equation for catalytic reduction is given inthe Supporting Information section.

In Figure 4, eq 6 is plotted as empty squares; the filledsymbols are plots of the ideal waveshapes, given by eq 2, andvalid when there is no distribution of ET rates or when ET isvery fast with respect to turnover number (k2). Panel A

Figure 2. Cartoon illustrating the consequences of two differentorientations of A. Vinosum [NiFe]-hydrogenase on an electrode, resultingin different tunneling distances d for interfacial ET. In the case of A.Vinosum [NiFe]-hydrogenase, ET occurs from the electrode surface tothe enzyme active site through a “wire” of Fe-S clusters. The so-called distal [4Fe-4S] cluster is surface-exposed and is believed to bethe site of interaction with a redox partner, and d is indicated to thiscenter. The structure shown is that of DesulfoVibrio gigas [NiFe]-hydrogenase.25

Figure 3. (A) Probability function of d, the distance over whichtunneling between the electrode surface and the enzyme occurs (eq 4).(B) Dependence of k0 (the interfacial ET rate constant at zerooverpotential) on d (eq 3). (C) Resulting probability function of k0 (eq5).

k0(d) ) k0max exp(-âd) (3)

p(d) ) 1/d0 for d ∈ [dmin, dmin + d0] (4)

Figure 4. Steady state voltammograms calculated according to eq 6(empty squares) and approximations given by eqs 8 (plain lines) and 9(dashed lines) for EO/I ) EI/R ) E1. (A) k2/k0

max ) 101 and from left toright, âd0 ) 100.5, 10, 101.5, and 102 (empty squares); filled symbols,k2/k0

max ) 10 and âd0 f 0 (eq 2 with k2/k0 ) 10). (B) âd0 ) 10 andfrom left to right, k2/k0

max ) 10-3, 10-2, 10-1, 1, and 10. Filled symbols,k2/k0

max f 0 (eq 2 with k2/k0 ) 0).

p(k0) ) {(âd0)-1 k0

-1 for k0 ∈ [k0min, k0

max]0 for any other value

(5)

i*ilim

)1

aïx (1 +1

âd0ln

aïx+ b2

ox

aox+ b1

ox) (6a)

aox) 1 + eO/I

-1(1 + eI/R-1) (6b)

b2ox)

k2

k0max(eI/R

-1/2+ eO/I

-1/2(1 + eI/R-1)) (6c)

b1ox) b2

ox exp(âd0) (6d)

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corresponds to k2/k0max ) 10 and increasing values of âd0 (fromleft to right). A large value of âd0 corresponds to a distributionof tunneling distances (d0) that is wide with respect to â-1. Asâd0 increases, the number of enzyme molecules having a smallvalue of k0 increases, and this results in a transition from asigmoidal wave to a linear current response. If âd0 is small,k0min is very close to k0max, and the effect of the dispersion oftunneling distances is negligible: the limiting case âd0 f 0 isgiven by eq 2 and plotted as filled squares in Figure 4A. Thedeparture from ideal behavior when k2/k0max increases (for agiven value of âd0) is illustrated in Figure 4B. For small valuesof k2/k0max, the limitation due to interfacial ET is relaxed.

Approximations. When the driving force increases, the lastexponential term to vanish in eq 2 is (k2/k0)eO/I

-1/2 or (k2/k0)eI/R-1/2

depending on which of the reduction potentials (EO/I or EI/R) isthe greater. To avoid distinguishing this case (and only in thederivation of eqs 7 and 9), we consider hereafter that EO/I )

EI/R ) E1. For this case, in the high driving force limit (justbefore the exponential terms vanish), the current eq 2 reducesto

At high driving force, the contribution to the current of a givenadsorbed enzyme molecule for which k0 is small appears aroundE ) E1 + (2/f) ln(2k2/k0), i.e., it is shifted to a higher drivingforce by the ET limitation.26 The linear change in current as afunction of electrode potential E, which results from the additionof contributions of all enzyme molecules with a small value ofk0/k2, is therefore expected for E values lying between E1 +

(2/f) ln(2k2/k0max) and E1 + (2/f) ln(2k2/k0min), i.e., over a rangeof electrode potential ≈2RT/F × âd0.

For the data shown in Figure 1, the current does not leveloff in the experimental potential range. This corresponds to E< E1 + (2/f) ln(2k2/k0min), i.e., b1

ïx. aïx. Equation 6a then

simplifies to

with aïx and b2ox as defined in eq 6b,c. The plot of eq 8 is

shown as solid lines in Figure 4 and departs from eq 6 (emptysquares) only at high driving force (when the limiting currentis reached) or when âd0 is small (so that the electrode potentialrange over which the “ohmic” behavior is expected is virtuallynonexistent, panel A).

Similarly, the equation for the linear part of the voltammo-gram at high driving force is given by aïx

≈ 1 and b1ïx

. 1 .

b2ïx, so that eq 6 (with EO/I ) EI/R ) E1) reduces to

(dashed lines in Figure 4), and the slope of the linear part ofthe voltammogram is

ResultsSamples of A. Vinosum [NiFe]hydrogenase were prepared as

described in ref 27, and electrochemical experiments were

conducted as described in refs 5, 11, and 12. Voltammogramsof catalytic H2 oxidation by A. Vinosum [NiFe]hydrogenaseadsorbed at a PGE electrode are plotted as empty squares inFigure 5.28 Comparison with Figure 4B shows that the changein shape as the temperature increases is consistent with arelatively greater increase in enzyme activity as compared tointerfacial ET (an increase of k2 relative to k0 at constant âd0).

The fit of the linear, high driving force part of the data to astraight line is also shown in Figure 5 (dashed lines). Equation10 predicts that the product of the slope times the temperatureis proportional to the limiting current and therefore to the activity(this assumes that the coverage of enzyme remains unchangedas the temperature is varied, but see below); however, note thatwhereas the limiting current cannot be measured from the datain Figure 5, the slope can. Therefore, measuring the slope ofthe voltammogram is equivalent to measuring the activity ofthe enzyme. The exponential increase of (∂i/∂E × T) with T isshown in Figure 6A, and the semilog plot in panel B allowsthe activation energy (Ea) of the catalytic hydrogen oxidationreaction to be measured. The slope of the straight line in Figure6B equates to -Ea/R and gives Ea ≈ 50 kJ/mol, a value that iscommon to many enzymes.

Equation 8 can be used to fit the whole waveshape byadjusting two reduction potentials, k2/k0max and ilim/âd0. Remark-ably, adding a dispersion of ET rate constants to the model doesnot increase the number of adjustable parameters. The fits ofthe voltammograms in Figure 1 to eq 8 are shown as plain linesin Figure 5.29 Because the temperature dependence of k0(involving electron tunneling) is much lower than that of k2(involving changes in covalent bonding), the change in k2/k0max

determined by fitting the catalytic voltammograms to eq 8 as afunction of T is an additional measure of the temperaturedependence of activity. The adjusted value of k2/k0max is plottedin Figure 6C and gives Ea ≈ 60 kJ/mol. This measure of k2/k0max is independent of the slope of the voltammograms because,as shown in Figure 4B, changing k2/k0max affects the shape ofthe low driving force part of the voltammogram, whereas theslope is measured at the high potential limit. Therefore, theagreement between the values of Ea deduced from Figure 6B,Cis a check of the consistency of the model.

From an experimental point of view, the comparison of theresidual slopes of different voltammograms relies on theassumption that the electroactive coverage is unchanged (eq 10shows that the slope is proportional to ilim and therefore to Γ).

iilim

≈1

1 +2k2

k0e1-1/2

(7)

i*ilim

≈1

âd0 aïx lnaïx

+ b2ïx

b2ïx (8)

i*ilim

≈1

âd0( f2(E - E1) - ln

2k2

k0max) (9)

∂i*/∂E )ilim

âd0

F2RT (10)

Figure 5. Fits of catalytic voltammograms28 such as those shown inFigure 1 to eq 8 (plain line, enlarged residues are plotted as dottedlines) and fits of the high potential parts of the voltammograms tostraight lines (dashed) according to eq 9.

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No such assumption is made when the change in k2/k0 isdetermined by fitting the voltammograms to eq 8, as thisparameter characterizes the shape (as opposed to the magnitude)of the signals.

Discussion

When a redox enzyme undergoes direct ET with an electrode,the catalytic voltammograms often show a residual slope overa large range of electrode potential at high driving force (Figure1), whereas it is simply predicted that it should reach a plateau.This observation, made with many multicentered redoxenzymes3-5,12-20 and with less complex enzymes such ascytochrome c peroxidase (Bateman, L.; Goodin, D. B.; Arm-strong, F. A. Unpublished results),30 has not been discussedpreviously in the context of enzyme electrocatalysis. In thispaper, we propose a general model based on the idea thatdisorder among the adsorbed enzyme molecules (Figure 2)results in a distribution of tunneling distances and thus adispersion of the interfacial ET rates.

Assuming that the distribution of orientations is such thatwithin a certain range (of width d0) all of the possible distancesbetween the electrode surface and the entry point for electronsin the enzyme occur with the same probability (eq 4 and Figure3A), the resulting distribution of k0 values is given by eq 5(Figure 3C). The catalytic current corresponding to the hetero-geneous assembly of enzymes molecules was derived byaveraging over the distribution of interfacial ET rate constants(eq 6), and a linear change in current as a function of electrodepotential at high driving force was predicted (eq 9).

In simple terms, this behavior results from the contributionof enzyme molecules having low k0 values with respect toturnover (k2), which contribute only at greater driving force.

Because it results from competition between turnover andinterfacial ET, the linear response should become more promi-nent as the activity of the enzyme increases. This is indeed thetrend observed for hydrogen oxidation by A. Vinosum [NiFe]-hydrogenase, for which the catalytic signal changes fromsigmoidal to linear when the temperature is increased (Figure1). Notably, this enzyme is extremely active (high k2), hencethe ease with which this effect is observed. Another interestingexample comes from the study20 of the respiratory nitratereductase from Paracoccus pantotrophus. Here, the greateractivity for chlorate reduction than for nitrate reduction correlateswith a greater residual slope in the voltammogram when chlorateis the substrate.31 The same effect has also been observed withthe nitrate reductase from Escherichia coli (Elliot, S. J.; Weiner,J. H.; Blasco, F.; Armstrong, F. A. Unpublished results).

The model developed here can be used to fit the catalyticdata for hydrogen evolution and oxidation by A. Vinosum [NiFe]-hydrogenase over a large range of experimental conditions(temperature and pH). The study of the pH dependence ofvoltammetry gives insights into the catalytic cycles and isthoroughly discussed in ref 5, whereas here, we have focusedon the temperature dependence of the voltammetry. Theactivation energy of the hydrogen oxidation reaction wasestimated from the change of both the high potential slope andthe shape of the voltammograms as a function of temperature.The fact that these two independent measurements give similarvalues for the activation energy (Ea ) 55 ( 5 kJ/mol) supportsthe consistency of the analysis. The model we propose makesit possible to deconvolute intrinsic properties of the active siteand film/interfacial ET properties and may be applied to otheradsorbed redox enzymes.

The well-defined nature of electrochemical data obtained withadsorbed molecules usually makes deviations from ideal be-haviors rather apparent. For noncatalytic systems, local interac-tions between the redox sites in nearby adsorbed molecules,32-34

spatial distribution of potentials within the electrode doublelayer,35-41 and distribution of ET rate constants exhibited byredox centers in the layer41-54 have all been suggested to accountfor nonideal peak widths or separations.55 In order for theelectrochemical data to depend on the properties of interfacialET, the system must be driven far from equilibrium; this isusually achieved by using transient techniques, such as fast-scan cyclic voltammetry or chronoamperometry. It is importantto note that in the present study, steady-state experiments revealthe nonideal properties of interfacial ET; this is because thecatalytic reaction competes continuously with the redox trans-formation of the active site following ET.

Increasingly inclined plateau currents can be observed whena redox process at a rotating disk electrode involves an adsorbedcatalyst (see ref 56 and references therein). To explain theseobservations, Jiang and Anson proposed a model based on awide, Gaussian distribution of reduction potentials of thecatalyst-substrate complex.56 To test which nonidealities couldexplain the results in Figure 1, we performed (numerical)integrations of the ideal current eq 2 with a distribution ofseveral parameters: Gaussian (i.e., normal) distribution ofreduction potentials and normal, log-normal, and uniformdistributions of distances between the electrode and the electronacceptor. In all cases, this broadens the catalytic wave, but nodistribution apart from that used in the model presented herewas found to result in the linear shape seen in Figure 1.

The observations presented in this paper may suggest howelectron transport catalysis in real biological systems would beaffected in situations where the subunits of an enzyme complex

Figure 6. (A) Plot of the high driving force slope of the voltammo-grams (dashed lines in Figure 5) times the temperature, as a functionof the temperature. (B) Semilog plot allowing the activation energy ofthe H2 oxidation reaction to be measured from the high driving forceslope of the voltammogram. (C) Semilog plot of the value of k2/k0

max

determined by fitting the voltammograms to eq 8 (plain lines in Figure5).

13062 J. Phys. Chem. B, Vol. 106, No. 50, 2002 Leger et al.

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are not connected together in a single, well-defined manner,exemplified by the complexes between myoglobin and cyto-chrome b557,58 and plastocyanin and cytochrome c.59

In a recent paper, reporting how the electrocatalytic oxidationof H2 by A. Vinosum hydrogenase compares with that of a Pt-coated electrode, we identified less than ideal interfacial ET asa possible shortcoming of the enzyme system.12 We can nowsee that ET is not uniformly limiting but that efforts to achievegreater homogeneous high values of k0 may well provide animportant improvement in the performance of enzymes aselectrocatalysts, for example, in the development of hydroge-nases as future biofuel cell catalysts.

Acknowledgment. We thank W. Roseboom for preparingthe purified A. Vinosum enzyme, B. Audit (European Bioinfor-matics Institute, Cambridge, U.K.), V. Guirardel (Departmentof Mathematics, Universite Joseph Fourier, Grenoble, F.), P.N. Bartlett (Department of Chemistry, University of Southamp-ton, U.K.), and J. P. McEvoy (Inorganic Chemistry Laboratory,Oxford) for invaluable discussions. This work was supportedby funds from the UK EPSRC and BBSRC (Grant Nos. 43/B10492 and 43/E16711) and The Netherlands Organization forScientific Research (NWO) division for Chemical Science(CW). A.K.J. thanks the Rhodes Trust and the NSF forscholarships.

Supporting Information Available: Derivation of eqs 5 and6 and corresponding equation for a reductive wave. This materialis available free of charge via the Internet at http://pubs.acs.org.

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402, 47-52.(3) Heffron, K.; Leger, C.; Rothery, R. A.; Weiner, J. H.; Armstrong,

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Chavez, C.; Cecchini, G.; Ackrell, B. A. C.; Armstrong, F. A. Biochemistry2001, 40, 11234-11245.

(5) Leger, C.; Jones, A. K.; Roseboom, W.; Albracht, S. P. J.;Armstrong., F. A. Biochemistry 2002, in press.

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(23) Chidsey, C. E. D. Science 1991, 251, 919-922.(24) Two distinct apparent k2/k0 parameters, corresponding to each of

the ET steps, should appear in eq 2 (see ref 5). From the point of view ofdata analysis, this increases the number of adjustable parameters withoutresulting in better fits to the data. Therefore, we make hereafter theassumption that these two parameters have the same value.

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(28) A linear baseline (dotted line in Figure 1), extrapolated from thepotential range where the faradaic current is zero, was subtracted to removethe contribution from the capacitive current.

(29) When the voltammograms were fit to eq 8, the adjusted value ofEI/R was systematically found to lie below the potential range where acatalytic current is measured. This implies that the value of this reductionpotential cannot be determined from the catalytic voltammograms. There-fore, to fit the data, we used modified versions of eq 6b,c, where the termseI/R-1 and eI/R-1/2 were fixed to zero, leaving three adjustable parameters(EO/I, k2/k0max, and ilim/âd0).

(30) The fact that nonwired enzymessfor which direct interfacial EToccurs from the electrode to the active sitesalso show this behavior makesunlikely the hypothesis that it results from an electric field effect on therate of intramolecular ET (as opposed to interfacial ET).

(31) Anderson, L. J. Thesis, University of East Anglia, 2002.(32) Albery, W. J.; Boutelle, M. G.; Colby, P. J.; Hillman, A. R. J.

Electroanal. Chem. 1982, 133, 135-145.(33) Laviron, E. Electroanal. Chem. Interfacial Electrochem. 1974, 52,

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147, 4584-4588.(55) In the literature, normal52,53 distributions of distances between the

electrode and the redox center and log-normal distribution of ET rates42

have been considered. Although a uniform distribution of distances wasrecently proposed,54 the corresponding distribution of k0 values (eq 5) wasnot explicitly derived.

(56) Jiang, R. Z.; Anson, F. C. J. Electroanal. Chem. 1991, 305, 171-184.

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Electron Transfer to Adsorbed Enzymes J. Phys. Chem. B, Vol. 106, No. 50, 2002 13063

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Electron Flow in Multicenter Enzymes: Theory, Applications,and Consequences on the Natural Design of Redox ChainsChristophe Leger,*,† Florence Lederer,‡ Bruno Guigliarelli,† and Patrick Bertrand†

Contribution from the Laboratoire de Bioenergetique et Ingenierie des Proteines, UPR 9036,CNRS, IBSM and UniVersite de ProVence, 31 chemin Joseph Aiguier, 13402 Marseille Cedex

20, France, and Laboratoire d’Enzymologie et Biochimie Structurales, UPR 9063, CNRS,AVenue de la Terrasse, 91198 Gif-sur-YVette Cedex, France

Received August 3, 2005; E-mail: christophe.leger@ibsm.cnrs-mrs.fr

Abstract: In protein film voltammetry, a redox enzyme is directly connected to an electrode; in the presenceof substrate and when the driving force provided by the electrode is appropriate, a current flow reveals thesteady-state turnover. We show that, in the case of a multicenter enzyme, this signal reports on theenergetics and kinetics of electron transfer (ET) along the redox chain that wires the active site to theelectrode, and this provides a new strategy for studying intramolecular ET. We propose a model whichtakes into account all the enzyme’s redox microstates, and we prove it useful to interpret data for variousenzymes. Several general ideas emerge from this analysis. Considering the reversibility of ET is arequirement: the usual picture, where ET is depicted as a series of irreversible steps, is oversimplifiedand lacks the important features that we emphasize. We give justification to the concept of apparent reductionpotential on the time scale of turnover and we explain how the value of this potential relates to thethermodynamic and kinetic properties of the system. When intramolecular ET does not limit turnover, theredox chain merely mediates the driving force provided by the electrode or the soluble redox partner, whereaswhen intramolecular ET is slow, the enzyme behaves as if its active active site had apparent redox propertieswhich depend on the reduction potentials of the relays. This suggests an alternative to the idea that redoxchains are optimized in terms of speed: evolutionary pressure may have resulted in slowing downintramolecular ET in order to tune the enzyme’s “operating potential”.

1. IntroductionLong-distance electron transfer (ET) is a crucial process in

bioenergetics. Energy conversion via oxidative phosphorylationrequires the existence of a transmembrane proton gradient, thebuilding of which is coupled to a cascade of redox reactions.1,2

In the enzymes that catalyze these transformations, the electronsare transferred over distances sometimes as large as 100 Å alongchains of closely spaced (<15 Å) redox relays: iron-sulfurclusters, copper centers and hemes in respiratory enzymes, orchlorophylls, pheophytins, and quinones in photosyntheticreaction centers.3-8

Most of our knowledge on ET in biology comes fromtransient kinetics studies of reaction centers, where the largedifferential absorption of the porphyrin rings makes it relativelyeasy to detect redox processes synchronized by light flashes

and to measure their rates. These experiments are analyzed usingMarcus theory,9 which relates the first-order rate of ET betweenthe adjacent centers “a” and “b”, the electronic coupling Tab,the thermodynamic driving force ∆G ) F(Ea

0- Eb

0), and thereorganization energy λ:

The magnitude and the dependence on distance of Tab aremodulated by superexchange,10 but it is often considered thatthe detailed structure of the intervening medium matters little,and the simple “ruler” proposed by Dutton and co-workers11,12

is sometimes used to predict the rates of intramolecular ET incases where only the distance between the centers and theirreduction potentials are known, using an arbitrary (but reason-able) value of λ.12,13

Measurements of intramolecular ET rates are difficult andscarce in respiratory systems. When the ET involves a heme,

† Laboratoire de Bioenergetique et Ingenierie des Proteines.‡ Laboratoire d’Enzymologie et Biochimie Structurales.

(1) Saraste, M. Science 1999, 283, 1488-1491.(2) Nicholls, D. G.; Ferguson, S. J. Bioenergetic 3; Academic Press: San Diego,

2002.(3) Baum, R. M. Chem. Eng. News 1993, 71 (Feb 22), 20-23.(4) Stubbe, J.; Nocera, D. G.; Yee, C. S.; Chang, M. C. Y. Chem. ReV. 2003,

103, 2167-2201.(5) Page, C. C.; Moser, C. C.; Dutton, P. L. Curr. Opin. Chem. Biol. 2003, 7,

551-556.(6) Leys, D.; Scrutton, N. S. Curr. Opin. Struct. Biol. 2004, 14, 642-647.(7) Gray, H. B.; Winkler, J. R. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 1534-

1539.(8) Hinchliffe, P.; Sazanov, L. A. Science 2005, 309, 771-774.

(9) Marcus, R. A.; Sutin, N. Biochim. Biophys. Acta 1985, 811, 265-322.(10) Malak, R. A.; Gao, Z.; Wishart, J. F.; Isied, S. S. J. Am. Chem. Soc. 2004,

126, 13888-13889.(11) Moser, C. C.; Keske, J. M.; Warncke, K.; Farid, R. S.; Dutton, P. L. Nature

1992, 355, 796-802.(12) Page, C. C.; Moser, C. C.; Chen, X.; Dutton, P. L. Nature 1999, 402, 47-

52.(13) Unciuleac, M.; Warkentin, E.; Page, C. C.; Boll, M.; Ermler, U. Structure

2004, 12, 2249-2256.

kET ∝ Tab2 exp(- (∆G + λ)2

4λRT ) (1)

Published on Web 12/08/2005

180 9 J. AM. CHEM. SOC. 2006, 128, 180-187 10.1021/ja055275z CCC: $33.50 © 2006 American Chemical Society

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the transformation can still be monitored using time-resolvedspectroscopy, and the enzyme-dependent strategies that havebeen designed to trigger the transfer include the use oftemperature jumps,14 ligand photolysis,15 or reaction withphotoactivated soluble reductants (such as deazaflavin, ruthenium-containing dyes, and modified cytochromes); this is informativemainly if the reaction with the soluble electron donor is fastwith respect to subsequent intramolecular ET.

Iron-sulfur clusters lack the spectroscopic handles thatfacilitate the studies of ET to or from porphyrin rings, but NMRcan be used provided |∆G| is small and kET ranges in the kineticwindow of the spectrometer.16-19

Noncatalytic protein film voltammetry (PFV) has also beenused to study biological ET.20-23 In this approach, a multicenterenzyme is adsorbed onto an electrode in such a way that ETto/from the enzyme is direct (i.e., not mediated by solubledyes).24-26 Interfacial ET occurs between the electrode and theredox site that is exposed at the surface of the protein, and theelectrons are transferred between this redox center and the activesite, either in one step or via a chain of relays. In the case oftwo fumarate reductases,20-23 the enzyme can be adsorbed withhigh coverage, and the active-site flavin gives a prominentnoncatalytic peak in the absence of substrate.27,28 In thisfavorable situation, when electron transfer is triggered bysweeping the electrode potential, the transient current responseincorporates the delays that result from the finite rates of ET.

Using PFV, even if the electroactive coverage is too low fornoncatalytic studies, a catalytic current can still be detected inthe presence of substrate. Such data were obtained recently fora variety of multicenter enzymes, including mitochondrialcomplexes I, II, and IV,29-31 hydrogenases,32-36 copper,37

heme,38-40 and molybdenum enzymes,41-45 to cite but a few.The steady-state current develops when the driving forceprovided by the electrode potential is high enough that the redoxstate of the active site is continuously regenerated followingthe transformation of the substrate. This signal (the “catalyticwave”) is a direct read-out of the activity of the enzyme as afunction of driving force or, more precisely, as a function ofthe rate of reduction/oxidation of the exposed relay. In somecases, the wave is centered on the reduction potential of theactive site34,43,46 (the change in current seems to simply revealthe formation of the redox state of the active site that iscompetent to transform the substrate). There are also exampleswhere the position of the wave is closer to the reduction potentialof a relay,31,40,44 a situation which was sometimes said to revealrate-limiting ET to or from this mediating redox site.25,40,44

However, a theoretical study is lacking to support theseinterpretations, as the models developed so far to interpret thecatalytic data for multicenter enzymes have never describedintramolecular electron transfer in a realistic manner. Most often,it was assumed that the active site is simply in redox equilibriumwith46,47 or directly connected to the electrode.34,48-51 When therelays were explicitly taken into account, the assumption wasmade that intramolecular ET between the relay and the activesite follows second-order kinetics,22,48,52 whereas eq 1 refers tothe first-order rate constant for the reversible transition betweentwo distinct redox states of the protein, characterized by theelectrons residing on either center “a” or center “b”. Therequirement that all redox (micro) states of a multicenter enzymebe considered has certainly hindered the developpement of morepertinent models.

Hereafter, we provide the first rigorous and fully analyticaltreatment of the kinetics of reversible ET in a catalytic systemin the case of a minimal redox chain, consisting of a singleone-electron relay connecting the electrode to a two-electronactive site. We show that the precise shape and position of thecatalytic wave depend not only on the redox properties of theactive site but also on the thermodynamics and kinetics of ETalong the entire redox chain. Conversely, such data can give

(14) Tegoni, M.; Silvestrini, M. C.; Guigliarelli, B.; Asso, M.; Brunori, M.;Bertrand, P. Biochemistry 1998, 37, 12761-12771.

(15) Jasaitis, A.; Rappaport, F.; Pilet, E.; Liebl, U.; Vos, M. H. Proc. Natl.Acad. Sci. U.S.A. 2005, 102, 10882-10886.

(16) Bertini, I.; Capozzi, F.; Luchinat, C.; Messori, L.; Monnanni, R.; Scozzafava,A.; Vallini, G. Eur. J. Biochem. 1992, 204, 831-839.

(17) Kyritsis, P.; Huber, J. G.; Quinkal, I.; Gaillard, J.; Moulis, J. M.Biochemistry 1997, 36, 7839-7846.

(18) Kummerle, R.; Kyritsis, P.; Gaillard, J.; Moulis, J.-M. J. Inorg. Biochem.2000, 79, 83-91.

(19) Kummerle, R.; Gaillard, J.; Kyritsis, P.; Moulis, J.-M. J. Biol. Inorg. Chem.2001, 6, 446-451.

(20) Heering, H. A.; Weiner, J. H.; Armstrong, F. A. J. Am. Chem. Soc. 1997,119, 11628-11638.

(21) Jones, A. K.; Camba, R.; Reid, G. A.; Chapman, S. K.; Armstrong, F. A.J. Am. Chem. Soc. 2000, 122, 6494-6495.

(22) Jeuken, L. J. C.; Jones, A. K.; Chapman, S. K.; Cecchini, G.; Armstrong,F. A. J. Am. Chem. Soc. 2002, 124, 5702-5713.

(23) Hudson, J. M.; Heffron, K.; Kotlyar, V.; Sher, Y.; Maklashina, E.; Cecchini,G.; Armstrong, F. A. J. Am. Chem. Soc. 2005, 127, 6977-6989.

(24) Armstrong, F. A.; Heering, H. A.; Hirst, J. Chem. Soc. ReV. 1997, 26, 169-179.

(25) Leger, C.; Elliott, S. J.; Hoke, K. R.; Jeuken, L. J. C.; Jones, A. K.;Armstrong, F. A. Biochemistry 2003, 42, 8653-8662.

(26) Armstrong, F. A. Curr. Opin. Chem. Biol. 2005, 9, 110-117.(27) Plichon, V.; Laviron, E. J. Electroanal. Chem. 1976, 71, 143-156.(28) Laviron, E. J. Electroanal. Chem. 1979, 101, 19-28.(29) Zu, Y.; Shannon, R. J.; Hirst, J. J. Am. Chem. Soc. 2003, 125, 6020-

6021.(30) Hirst, J.; Sucheta, A.; Ackrell, B. A. C.; Armstrong, F. A. J. Am. Chem.

Soc. 1996, 118, 5031-5038.(31) Haas, A. S.; Pilloud, D. L.; Reddy, K. S.; Babcock, G. T.; Moser, C. C.;

Blasie, J. K.; Dutton, P. L. J. Phys. Chem. B 2001, 105, 11351-11362.(32) Butt, J. N.; Filipiak, M.; Hagen, W. R. Eur. J. Biochem. 1997, 245, 116-

122.(33) Pershad, H. R.; Duff, J. L. C.; Heering, H. A.; Duin, E. C.; Albracht, S. P.

J.; Armstrong, F. A. Biochemistry 1999, 38, 8992-8999.(34) Leger, C.; Jones, A. K.; Roseboom, W.; Albracht, S. P. J.; Armstrong, F.

A. Biochemistry 2002, 41, 15736-15746.(35) Lamle, S. L.; Albracht, S. P. J.; Armstrong, F. A. J. Am. Chem. Soc. 2005,

127, 6595-6604.(36) Leger, C.; Dementin, S.; Bertrand, P.; Rousset, M.; Guigliarelli, B. J. Am.

Chem. Soc. 2004, 126, 12162-12172.

(37) Johnson, D. L.; Thompson, J. L.; Brinkmann, S. M.; Schuller, K. A.; Martin,L. L. Biochemistry 2003, 42, 10229-10237.

(38) Angove, H. C.; Cole, J. A.; Richardson, D. J.; Butt, J. N. J. Biol. Chem.2002, 277, 23374-23381.

(39) Bradley, A. L.; Chobot, S. E.; Arciero, D. M.; Hooper, A. B.; Elliott, S. J.J. Biol. Chem. 2004, 279, 13297-13300.

(40) Heering, H. A.; Wiertz, F. G. M.; Dekker, C.; de Vries, S. J. Am. Chem.Soc. 2004, 126, 11103-11112.

(41) Aguey-Zinsou, K. F.; Bernhardt, P. V.; Leimkuhler, S. J. Am. Chem. Soc.2003, 15, 15352-15358.

(42) Jepson, B. J. N.; Anderson, L. J.; Rubio, L. M.; Taylor, C. J.; Butler, C.S.; Flores, E.; Herrero, A.; Butt, J. N.; Richardson, D. J. J. Biol. Chem.2004, 279, 32212-32218.

(43) Hoke, K. R.; Cobb, N.; Armstrong, F. A.; Hille, R. Biochemistry 2004, 43,1667-1674.

(44) Elliott, S. J.; McElhaney, A. E.; Feng, C.; Enemark, J. H.; Armstrong, F.A. J. Am. Chem. Soc. 2003, 124, 11612-11613.

(45) Frangioni, B.; Arnoux, P.; Sabaty, M.; Pignol, D.; Bertrand, P.; Guigliarelli,B.; Leger, C. J. Am. Chem. Soc. 2004, 126, 1328-1329.

(46) Leger, C.; Heffron, K.; Pershad, H. R.; Maklashina, E.; Luna-Chavez, C.;Cecchini, G.; Ackrell, B. A. C.; Armstrong, F. A. Biochemistry 2001, 40,11234-11245.

(47) Limoges, B.; Saveant, J.-M. J. Electroanal. Chem. 2004, 562, 43-52.(48) Heering, H. A.; Hirst, J.; Armstrong, F. A. J. Phys. Chem. B 1998, 102,

6889-6902.(49) Leger, C.; Jones, A. K.; Albracht, S. P. J.; Armstrong, F. A. J. Phys. Chem.

B 2002, 106, 13058-13063.(50) Honeychurch, M. J.; Bernhardt, P. V. J. Phys. Chem. B 2005, 109, 5766-

5773.(51) The assumption that ET is direct is made when the Butler-Volmer

formalism55 is used to relate the rates of oxidation/reduction of the activesite to the electrode potential.

(52) See eqs 12 and B1 in ref 48, and eq 7 in ref 22.

Electron Flow in Multicenter Enzymes A R T I C L E S

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information on the intramolecular ET kinetics, provided thereduction potentials of the centers are known. We use this modelto interpret new and previously published data for variousenzymes, and we provide experimental evidence that theconcepts that emerge from this theoretical analysis may begeneralized to multicenter enzymes comprising several electronrelays. We demonstrate that, depending on how fast intramo-lecular ET is with respect to the active-site chemistry, theposition of the catalytic wave can indeed match either thereduction potential of the relay that receives or gives electronsin the slow step or the reduction potential of the active site. Inthe latter case only, ET between the electrode and the activesite can, indeed, be treated as direct.

Importantly, the model is not restricted to enzymes adsorbedat electrode surfaces, and we discuss the physiological implica-tions regarding reversible ET along redox chains. We demon-strate that, when intramolecular ET is not much faster thanturnover, the active site can have apparent redox properties underturnover conditions which differ from those determined atequilibrium. This may explain why evolutionary pressure hasselected relays whose properties do not favor fast intramolecularET: optimization of a redox chain may not necessarily implyacceleration of ET.

2. Experimental MethodsSamples of Saccharomyces cereVisiae flavocytochrome b2 (fb2) were

prepared as described in ref 53.We used the electrochemical setup and equipment described in ref

36. The protein films were made by painting the surface of a pyrolyticgraphite edge (PGE) electrode with 1 µL of 300 µM neomycin solution(Sigma) and then with 0.5 µL of stock solution of enzyme (380 µM).The buffer was a mixture of MES, HEPES, sodium acetate, TAPS,and CHES (5 mM of each component), 1 mM EDTA, and 0.1 M NaCl,titrated to pH 7 with NaOH. L-Lactate (Sigma) was added to the cell(at T ) 25 °C) from a concentrated solution made in the same bufferand titrated to the appropriate pH.

As in the case of most enzymes for which PFV data are available,no reliable noncatalytic signals could be observed in the absence ofsubstrate, and this is a direct consequence of electroactive coveragebeing low.25

The catalytic data in Figure 2 have been recorded with the sameenzyme film, and the substrate concentration was varied by injectingaliquots of a concentrated solution of L-lactate. In such experiments,the plot of activity against substrate concentration is usually easilydistorted due to film loss. In contrast, the very good fit to theMichaelis-Menten equation in Figure 3A proves that the film of fb2was perfectly stable over the time course of the experiment (despitethe use of a slow scan rate) and rules out a decrease in the enzyme’sactivity over time resulting, for example, from a slow release of thenoncovalently bound active-site flavin.

The electrode rotation rate ω was sufficiently high that raising itfurther produced no increase in current; thus, there was no complicationdue to substrate depletion near the interface or product inhibition.25

The scan rate ν was small enough to achieve steady state: the shapeof the baseline-subtracted signal was independent of scan direction.

All potentials are quoted against the standard hydrogen electrode(SHE).

3. Modeling

A Two-Electron Active Site Directly Wired to the Elec-trode. To show how the intramolecular ET kinetics affects the

shape of a voltammogram for a two-electron oxidation catalyzedby an adsorbed enzyme, we first recall the current equation thatapplies when ET occurs directly from the active site to theelectrode.34,46 We consider that the active site exists in threeredox states, termed O (oxidized), I (half-reduced intermediate),and R (reduced). As depicted in Figure 1A, the oxidized formof the active site is transformed into AR with an apparent first-order rate constant k2 (which incorporates the rates of substratebinding/transformation and product release). We assume that(i) the active site is fully saturated with substrate at steady state54

(this is the case under saturating conditions, provided thatbinding of substrate and release of product are fast and thatthere is neither inhibition by nor back-reaction with the product),(ii) substrate mass transport is not limiting, and (iii) the rate ofactive-site oxidation as a function of electrode potential E isgiven by the Butler-Volmer (BV) formalism,55 i.e., kb )

k0 exp[(-f/2)(E - EI/R0 )] and kf ) k0 exp[(f/2)(E - EI/R

0 )],where EI/R

0 is the reduction potential of the I/R couple, f )

F/RT, and k0 is the interfacial ET rate at zero overpotential.Analogous equations hold for k′f and k′b and the O/I transfor-mation. The catalytic current i is proportional to the steady-state concentration of the oxidized state; it increases from naughtat low electrode potential to a limiting value ilim at high drivingforce according to34

where A is the electrode surface and Γ is the electroactivecoverage of enzyme. The four terms un are proportional toexp(-nfE) and are defined in Table 1. The terms with smallern values contribute increasingly to the sum when the drivingforce increases, so that the i against E curve described by eq 2is a sigmoidal wave which broadens at high electrode potential.

The terms u1 and u2 (Table 1, left) are nernstian contributionswhose meaning is straightforward: a catalytic current appearswhen the electrode potential is high enough that the oxidizedform of the active site is present.46 The terms u3/2 and u1/2 reveal

(53) Dubois, J.; Chapman, S. K.; Mathews, F. S.; Reid, G. A.; Lederer, F.Biochemistry 1990, 29, 6393-6400.

(54) Taking into account substrate binding in scheme 1B is not straightforward,because this increases from 6 to 12 the number of states of the enzymethat must be considered (each state in Figure 1 should be considered freeand bound to substrate).

(55) The “Marcus-like” theory of interfacial ET (ref 56) predicts how the rateof the redox process changes with the driving force η ) E - E0 for agiven reorganization energy (λ). In the limiting case where |η| < λ, therates of interfacial ET become independent of λ and are equally predictedby the BV formalism.

(56) Chidsey, C. E. D. Science 1991, 251, 919-922.

Figure 1. Catalytic schemes for a two-electron oxidation at an enzymeactive site “A” directly connected to an electrode (panel A) or when a relay“R” mediates the ET between the electrode and the active site (panel B).Subscripts O, I, R, f, and b stand for oxidized, intermediate, reduced,forward, and backward, respectively.

ilim

i - 1 ) u2 +k2

k0u3/2 + u1 +

k2

k0u1/2 (2a)

ilim ) 2FAΓk2 (2b)

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the deviation from nernstian equilibrium which results from thesteady-state competition between the reduction of the active site,with rate k2, and its reoxidation following interfacial ET, witha rate proportional to k0;34 hence, the greater k2/k0, the morethe steady-state concentrations of species depart from theirequilibrium values, and the broader the wave.

Effect of a One-Electron Relay. We now consider thecase where interfacial ET occurs between the electrode anda relay whose reduction potential is ER

0 , with rates kb )

k0R exp[(-f/2)(E - ER

0 )] and kf ) k0R exp[(f/2)(E - ER

0 )]. Weassume that the redox state of one center has no effect on theredox properties of others; hence, a single pair of rate constantskf and kb describes the electron exchange between the electrodeand the exposed relay, independently of the redox state of theactive site. The intramolecular electron exchange between therelay and the active site is described by the rate constantsk1, k-1, k′1, and k′

-1 (see Figure 1B), with K1 ) k1/k-1 )

exp[f(ER0- EO/I

0 )] and K′1 ) k′1/k′-1 ) exp[f(ER

0- EI/R

0 )]. Thecatalytic current equates 2FAk2 times the steady-state concentra-tion of the enzyme with the active site in the oxidized state; weshow in the Supplementary Information that it can be writtenin the form

At infinite driving force, i tends to a limiting value ilim whichincorporates irreversible intramolecular ET and catalytic trans-formation at the active site. The terms un are written in Table1, so as to facilitate the comparison with the case where thereis no relay. Instead of writing the current as a function of theseven rate constants defined in Figure 1B, it is convenient tochoose as independent parameters kcat, kcat/k0

R, the three reduc-tion potentials EO/I

0 , EI/R0 , and ER

0 , and the quantities ∆E1 and∆E2 defined in Table 1.

Is is remarkable that, despite the much greater complexityof the second kinetic scheme, the rate equation takes onessentially the same form as when there is no relay. However,some significant differences appear, as discussed below.

The terms u1 and u2 are no longer centered on EO/I0 and (EO/I

0

+ EI/R0 )/2, respectively. When a relay is considered, E1 and E2

are effective reduction potentials, which are shifted away fromthe reduction potentials of the active site. The magnitude of

the shifts ∆E1 ) E1 - EO/I0 and ∆E2 ) E2 - (EO/I

0+ EI/R

0 )/2depends on kcat and on the rate constants for intramolecular ET,and this is discussed in detail hereafter. We note already that,since ∆E1 g 2∆E2, the presence of the relay always increasesthe difference E1 - E2 and thus tends to make the catalyticsignal more closely resemble a one-electron wave.

The two terms that convey the competition with interfacialET are now naturally weighted by kcat/k0

R instead of k2/k0. Theterm ux is a complex function of E, but we explain in theAppendix (Supporting Information) why, in most cases, weexpect it to contribute to the wave as a term u1/2. In contrast,we have also identified some situations where this termsimultaneously affects the wave shape (i.e., is large in theelectrode potential range of the wave) and deviates from beingproportional to e(-f/2)E. We give in the Appendix counter-intuitive examples where the catalytic wave sharpens as thedriving force increases, or where the change in activity againstdriving force is far from being sigmoidal; this provides aspectacular demonstration that the kinetics allowed by scheme1B (Figure 1) can be just as complex as its mathematicaltreatment is straightforward. However, none of the catalyticsignals reported to date illustrate these peculiar situations.

Fast Intramolecular ET. In the limiting case where theintramolecular electron transfers are much faster than k2 (therate of reduction of the active site), the values of ∆E1 and ∆E2tend to zero,57 the terms u1 and u2 are centered on EO/I

0 and(EO/I

0+ EO/I

0 )/2, respectively, and the wave shape reports on thereduction potentials of the active site, independently of theproperties of the relays which merely act as an extension of theelectrode toward the active site.

Slow Intramolecular ET. The opposite limiting case occurswhen the reduction of the active site is much faster thanintramolecular ET. When k2 is much greater than both k1 andk′1, 1/kcat reduces to 1/k1 + 1/k′1 and the shifts ∆En tend to thefollowing limits:

According to eq 4a, exp(2f∆E2lim) e K1, and this sets an upper

limit for the position of the two-electron wave at E2 e (EI/R0

+

ER0 )/2. Likewise, the quantity exp(f∆E1

lim) is greater than K1,

(57) kcat reduces to k2 and the terms ∆En vanish if all the following conditionsapply: k1, k′1 . k2; k1, k′1 . k2|K1 - 1|; k1 . k2|K1 - 1 + K1/K′1 |.

Table 1. Steady-State Rate Equations for a Two-Electron Catalytic Oxidation: Comparisons between the System without (Left) and with(Right) a One-Electron Relaya

a These equations are derived in the Supporting information.

ilim

i - 1 ) u2 +kcat

k0R u3/2 + u1 +

kcat

k0R ux (3a)

ilim ) 2FAΓkcat (3b)1/kcat ) 1/k1 + 1/k′1 + 1/k2 (3c)

exp(2f∆E2lim) ) K1k′1/(k1 + k′1) (4a)

exp(f∆E1lim) ) K1{1 + k′1/[K′1(k1 + k′1)]} (4b)

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which implies that the one-electron term is centered on E1 g

ER0 .General Case. In the most general situation, the values of

E1 and E2 depend on k2 and on the intramolecular ET rateconstants, and it is convenient to write the shifts in the form

where 1/ki ) 1/k1 + 1/k′1, 1/kcat ) 1/k2 + 1/ki, and ∆Enlim are

defined by eqs 4. Equations 5 show that the shifts vary in amonotonic way from ∆En ) 0 when intramolecular ET is fast(ki . kcat) to ∆En ) ∆En

lim when it is rate limiting (ki ) kcat),and this is why the position of the wave can give quantitativeinformation on the kinetics of intramolecular ET, as illustratedhereafter.

4. ApplicationsFast Intramolecular ET. The literature provides several

examples that illustrate the limiting case of fast intramolecularET. For example, in Allochromation Vinosum NiFe hydrogenase,the electrons are mediated by a linear chain consisting of threeFeS clusters, and the electrochemical data for proton reductioncould be modeled assuming that direct ET occurs between theelectrode and the active site,34 the oxidation and reduction ofwhich follows Butler-Volmer kinetics. Our model shows thatthis is not in contradiction with the electron being transferredby hopping between adjacent centers.

The oxidation of succinate by Escherichia coli fumaratereductase,46 which contains an active-site flavin wired by threeFeS clusters,23 exemplifies the case where k2 is so small (theenzyme is actually tuned to operate in the reverse direction)that the active site is in redox equilibrium with the electrodepotential.

In both cases, intramolecular ET is so fast that it does notaffect the dependence of activity on driving force. Thus, theelectrochemical data can be used to gain insights into thechemistry that occurs at the active site, but they hold noinformation on the kinetics of intramolecular ET.

Intramolecular ET in Flavocytochrome b2. In flavocyto-chrome b2 (fb2),58 the electrons produced upon oxidation ofL-lactate at the FMN active site are transferred to the redoxpartner via a single heme. When adsorbed onto a PGE electrode,this enzyme displays catalytic activity, as shown in Figure 2.

At high electrode potential, we observe a residual slope inthe voltammogram, whereas eqs 2 and 3 predict a plateau. Thishas been observed for many enzymes and explained on the basisof disorder among the adsorbed enzyme molecules, resultingin a dispersion of interfacial ET rate constants.25,49 Thus, themethod proposed in ref 49 was used to analyze the voltammo-grams, and eq S14 (Supplementary information) was usedinstead of eq 3 to fit the data. As discussed previously, thischanges neither the number nor the qualitative meaning of theparameters that need to be adjusted; the main difference is thata quantity proportional to ilim (termed ilim/âd0) is adjusted inplace of the true limiting current, which is not reached in theexperimental range of electrode potential. The procedure used

to analyze the data is explained in detail in the SupportingInformation.

The best fits of the voltammograms overlay perfectly the datain Figure 2; no systematic deviation was observed. The adjustedvalue of ilim/âd0 is proportional to the turnover rate V, and itsdependence on substrate concentration can be fit to measurethe Michaelis constant25,43,49 and a quantity proportional to Vmax

(Figure 3A). We found Km ) 200 µM (in solution assays,59 theKm value for lactate oxidation depends on the electron acceptor,ionic strength, and temperature, and it ranges from 240 to 600µM). Figure 3B shows the best values of E1 and E2 plotted asa function of V/Vmax.

Intramolecular ET in fb2 has been previously characterizedby performing redox titrations and temperature jump experi-

(58) Lederer, F. Flavocytochrome b2. Chemistry and Biochemistry of FlaVoen-zymes; CRC Press: Boca Raton, FL, 1991; pp 153-241.

(59) Rouviere, N.; Mayer, M.; Tegoni, M.; Capeillere-Blandin, C.; Lederer, F.Biochemistry 1997, 36, 7126-7135.

∆E2 ) (2f)-1 ln(1 + [exp(2f∆E2lim) - 1]kcat/ki) (5a)

∆E1 ) f-1 ln(1 + [exp(f∆E1lim) - 1]kcat/ki) (5b)

Figure 2. Substrate concentration dependence of catalytic voltammogramsfor lactate oxidation by flavocytochrome b2 (black lines), and fits to eqS14 (red lines). Equation S14 is given in the Supporting Information; it isequivalent to eq 3 after the dispersion of k0

R values is accounted for.49 Thedata have been corrected only by subtracting a voltammogram recorded inthe absence of substrate. T ) 25 °C, pH 7, ω ) 1000 rpm, ν ) 5 mV/s,lactate concentration as indicated.

Figure 3. Result of the fits of voltammograms for lactate oxidation to eqS14 (Supporting Information). Panel A: The change in ilim/âd0 againstlactate concentration is fit to the Michaelis-Menten equation. Panel B:Values of E1 (0 and left axis) and E2 (9 and right axis) plotted againstV/Vmax. Error bars show the difference between the parameters determinedfor scanning in the oxidative and reductive directions.

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ments.14 At pH 7, EO/I0

) -45 mV, EI/R0

) -135 mV, and ER0)

-3mV. The rate k′1 of ET from reduced FMN to heme is muchfaster than k1 from semiquinone to heme (thus, ki ≈ k1) and K′1. 1. Equations 4 give exp(f∆E1

lim) ) exp(2f∆E2lim) ) K1; thus,

E1lim

) ER0) -3 mV and E2

lim) (ER

0+ EI/R

0 )/2 ) -69 mV.Therefore, E1 and E2 should range in the intervals [EO/I

0 , ER0 ]

and [(EO/I0

+ EI/R0 )/2, (ER

0+ EI/R

0 )/2], respectively, the exactvalue depending on how fast k2 is with respect to intramolecularET.

In Figure 3B, the values of E1 ) -15 mV and E2 ) -53mV under saturating conditions are close to the values E1

lim)

-3 mV and E2lim

) -69 mV. According to eqs 5, this impliesthat intramolecular ET is not very fast with respect to kcat.Indeed, kcat ≈ 270 s-1 at 30 °C from ref 59, while values of k1were found in the range 80-500 s-1, depending on experimentalconditions (buffer composition and temperature).14 This is alsoconsistent with the isotope effect under steady-state conditionsbeing significant but smaller than that for flavin reduction,measured using stopped flow.59

Although the model cannot predict accurately the change inEn against substrate concentration because it does not explicitlyconsider the steps for substrate binding, the trends seen in Figure3B are qualitatively consistent with eqs 5: both E1 and E2increase with increasing turnover rate, and this is expectedbecause ER

0 is slightly more positive than EO/I0 .

This is our first illustration that, under turnover conditions,the apparent redox properties of an enzyme depend not onlyon the reduction potential of the active site but also on thethermodynamics and kinetics of intramolecular ET.

Intramolecular ET in Sulfite Oxidase. In chicken liversulfite oxidase,60 the molybdenum active site passes on electronsto cytochrome c via a small heme domain that is tethered tothe molybdenum domain by a flexible loop. The values of EO/I

0

and EI/R0 (for Mo(VI)/(V) and Mo(V)/(IV), respectively), inter-

polated at pH 8 from the data in Table 1 of ref 61, are ∼0 mVand ∼ -200 mV, respectively. When the enzyme is adsorbedonto an electrode, a one-electron noncatalytic peak at ER

0)

+90 mV, pH 8, reveals the reduction potential of the heme (seeFigure 1 in ref 44); under saturating concentrations of substrate,a one-electron catalytic wave is observed whose position (E1) +65 mV at pH 8, 20 °C) is shifted from EO/I

0 and shows littledependence on pH (Figure 2 in ref 44); this contrasts with whatis observed for the reduction potentials of the molybdenumcouples (Table 1 in ref 61). These observations were said toreveal rate-limiting ET from Mo to heme.25,44 In contrast, otherauthors have interpreted the results of kinetic studies of the sameenzyme assuming that intramolecular ET was rapid.62 We willnow show how our model can be used to gain more quantitativeinformation in this respect.

From the values of the reduction potentials above, K′1 . 1;in eq 4b this sets ∆E1

lim) f -1 ln K1 ) ER

0- EO/I

0) 90 mV.

Using the value of ∆E1 ) E1 - EO/I0

) 65 mV in eq 5b giveski/kcat ) 2.9 (this ranges from 2.7 to 4.8, depending on the exactvalue of EO/I

0 in the interval [-60 mV, +60 mV]). This showsthat intramolecular ET is neither very fast nor fully rate-

limiting: the rates of ET from Mo to heme and of chemicaltransformation at the active site must be of the same order ofmagnitude.

Using the value of kcat ) 95 s-1 determined under saturatingconcentrations of sulfite and oxidized cytochrome c, at pH 8,25 °C (ref 62), we determine ki ) k1k′1/(k1 + k′1) in the range250-450 s-1. Since the driving force for k′1 (ET from MoIV tooxidized heme) is much larger than that for k1 (from MoV toheme), we expect k′1 . k1, and thus k1 ≈ ki ≈ 250-450 s-1.This can be compared to kET ) k1 + k-1 ) 800 s-1, determinedat pH 8 using flash photolysis on the same enzyme (see Table1 in ref 63).64

It should be emphasized that we estimated the efficacy ofintramolecular ET from data obtained with the enzyme sulfiteoxidase affixed to an electrode surface, most likely by the hemedomain.44 This adsorption may hinder the domain-domainmotion that plays an important role in the ET process,65 andthis could make ET slower than when the enzyme is free in adilute, uncrowded66 solution.

Interprotein ET. The complex between complex IV andcytochrome c adsorbed on a modified Au electrode31 is anexample where the catalytic process leading to the reduction ofO2 is limited by interprotein ET, and, as discussed in ref 25,this is apparent from the position of the catalytic wave, whichis centered on the reduction potential of the cytochrome (Figure8 in ref 31).

An Artificial Wire. The model we propose also applies toman-made, one-dimensional redox chains linking electrodes toenzymes. For example, in ref 67, Willner and co-workers reporton the reconstitution of apo-glucose oxidase (Gox) on a FADcofactor linked to a pyrroquinoline quinone (PQQ) phenylbo-ronic acid monolayer self-assembled on a gold electrode. Fastinterfacial ET to/from the PQQ moiety is observed. The positionof the catalytic wave for glucose oxidation shows littledependence on substrate concentration (Figure 4 in ref 67) andis centered slightly above the reduction potential of the PQQ(ER

0) 110 mV vs SHE at pH 7, from Figure 2 in ref 67; this

is much greater than the reduction potential of the FAD in Gox,68

EO/I0

) -60 mV at pH 5.3), which we now interpret in terms ofET from FAD to PQQ being rate-limiting during turnover. ThatPQQ is a two-electron relay prevents further analysis of thesedata with the model we developed.5. Discussion

The kinetics of ET along redox chains in multicenter enzymesis very often thought of as a series of irreversible steps.69 Thisis certainly a good approximation in reaction centers, wherebackward electron transfers and charge recombinations areavoided. However, the substrates of respiratory enzymes often

(60) Kisker, C.; Schindelin, H.; Pacheco, A.; Wehbi, W. A.; Garrett, R. M.;Rajagopalan, K. V.; Enemark, J. H.; Rees, D. C. Cell 1997, 91, 973-983.

(61) Spence, J. T.; Kipke, C. A.; Enemark, J. H.; Sundespence, R. A. Inorg.Chem. 1991, 30, 3011-3015.

(62) Brody, M. S.; Hille, R. Biochemistry 1999, 38, 6668-6677.

(63) Sullivan, E. P.; Hazzard, J. T.; Tollin, G.; Enemark, J. H. Biochemistry1993, 32, 12465-12470.

(64) In ref 63, the experimental temperature is not stated, and as the authorspoint out, the determined value of K1 ) k1/k-1 is not consistent with thereduction potentials of the centers. This prevented us from determining k1and k-1 from the values of kET and K1.

(65) Feng, C.; Kedia, R. V.; Hazzard, J. T.; Hurley, J. K.; Tollin, G.; Enemark,J. H. Biochemistry 2002, 41, 5816-5821.

(66) Ellis, R. J. Trends Biochem. Sci. 2001, 26, 597-604.(67) Zayats, M.; Katz, E.; Willner, I. J. Am. Chem. Soc. 2002, 124, 14724-

14735.(68) Stankovich, M.; Massey, L. S. V. J. Biol. Chem. 1978, 253, 4971-4979.(69) The assumption that intramolecular ET is irreversible is made when the

overall rate of ET through a chain is estimated by summing the reciprocalsof the rates calculated or measured for the successive ET steps. For example,see the calculations related to the heme chain of the cytochrome ofRhodopseudomonas Viridis, Figure 2 in ref 12.

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provide only moderate driving forces,70 and neglecting thereverse reactions leads to an oversimplified picture of the ETkinetics which lacks the important features that we discuss here.

The technique called protein film voltammetry (PFV)24-26

makes the driving force a natural experimental parameter: whena multicenter redox enzyme is adsorbed onto an electrode, inthe presence of substrate, the activity of the enzyme is measuredas a current as a function of the electrode potential, which affectsthe rate of oxidation and reduction of the redox relay that isexposed at the surface of the protein. Every point along thevoltammogram is an initial rate for a given driving force, andwe have shown how the entire shape of the catalytic wave relatesto both the active-site chemistry and intramolecular ET.

We have considered the case where a single relay connectsthe active site to the electrode (Figure 1B). At infinite drivingforce (high potential for a catalytic oxidation), the steady-stateconcentration of enzyme in which the relay is reduced tends tozero and the activity depends only on the rates of forward ET;in this case only, the kinetics is adequately described by asuccession of independent, irreversible steps:

Therefore, the magnitude of the wave, which is proportional tokcat, does not depend on the rates of backward ET and containsno information on the energetics of the ET chain. In contrast,at moderate (and thus physiological) driving force, forward andbackward transitions between all the enzyme’s redox microstatesmust be considered, the turnover rate is necessarily lower thanthat predicted by eq 6, and the position and shape of thevoltammogram hold the information about intramolecular ET.

We have shown on several examples that PFV can be usedto diagnose slow intramolecular ET: for a catalytic oxidation,this results in a broad (n ) 1) wave, centered close to thereduction potential of the relay that accepts the electrons in theslow step (E1 g ER

0 ), and the position of the wave is expectedto show little dependence on the experimental parameters thatmay affect the reduction potential of the active site alone (e.g.the concentrations of substrate, product, and inhibitor, andpossibly the pH): our model supports the concept of “controlcenter” introduced in ref 25, and gives it theoretical grounds.

It is remarkable that schemes 1A and 1B (Figure 1) lead torate equations that take on essentially the same form (eq 3 issimilar to eq 2, since we showed in the Appendix that, in mostcases, the term ux behaves like u1/2). Therefore, regarding thefit of the PFV data, considering direct or mediated ET does notchange the number of parameters that have to be adjusted.However, this changes the physical meaning of these param-eters: when ET is mediated by a relay, the position and shapeof the catalytic wave depend on apparent reduction potentials,E1 and E2, which can depart from the reduction potentials ofthe active site.71 These shifts occur when intramolecular ET isnot fast enough to compete successfully with the reaction ofthe active site with substrate. The values of E1 and/or E2 canbe measured by fitting the catalytic wave shapes, and the

comparison with the true reduction potentials of the active sitecan be used to gain information about the ET kinetics: themethod was illustrated by discussing data obtained withflavocytochrome b2 and sulfite oxidase.

So far, we have considered the cases where the enzyme giveselectrons to an electrode, but our main conclusions also applywhen a soluble redox partner accepts the electrons. In the lattercase, Marcus theory,56 rather than Butler-Volmer theory, shouldbe used to describe the rate constants kf and kb in Figure 1B.However, provided the driving force is small, eq 1 reads

That is, the dependence of kET on driving force is the same asthat predicted by the BV formalism for interfacial ET, whichapplies when |E - ER

0| < λ (ref 55):

This shows that, in PFV experiments, the overpotential F(E -

ER0 ) has the same meaning as the driving force ∆G ) Epartner

0-

ER0 in more traditional (homogeneous) kinetics.42,73

Regarding biological ET, we have shown that the usualpicture, where the kinetics is represented as a series ofirreversible steps, is oversimplified. When reversibility isconsidered, the thermodynamics and kinetics of the entire redoxchain (including the active site) must be taken into account,and this gives an integrated picture of the ET dynamics, wherethe behavior of the enzyme as a whole depends on every relay.Two cases are naturally distinguished on the basis of how fastintramolecular ET is with respect to the chemical transformationat the active site. When intramolecular ET does not limitturnover, everything happens as if electrons were transferreddirectly between the redox partner and the active site, and theonly effect of the redox chain is to transmit the driving forceacross the enzyme. In contrast, if intramolecular ET is not veryfast with respect to turnover, the driving force that is requiredto trigger catalysis depends on both the reduction potentials ofthe relays and the kinetics of intramolecular ET: under turnoverconditions, everything happens as if the active site had redoxproperties that are controlled, or tuned, by the ET chain.

There has been a considerable debate regarding whether theredox chains in multicenter enzymes have been optimized toincrease the rates of intramolecular ET.7,12 This was questionnedby the numerous examples where electrons do not simply flowtoward relays of increasing reduction potentials and statisticalstudies did not detect the higher packing density of the proteinin the region between the centers, which would have led to anenhancement of ET.5,12 Our work gives an alternative point ofview, according to which optimization of the ET chain neednot be considered in terms of speed: the properties of the relays,and thefore the ET kinetics, may well have been optimized, insome cases, to tune the apparent reduction potential of the activesite. There can be no such effect in a particular enzyme (andno evolutionary pressure)5 if the rate of ET is much faster than

(70) Osyczka, A.; Moser, C. C.; Daldal, F.; Dutton, P. L. Nature 2004, 427,607-612.

(71) This is reminiscent of a common situation in enzyme kinetics. For example,very complex kinetic models lead to the Michaelis-Menten rate equation,which is a function of only two independent parameters (Km and kcat), andthe Michaelis constant is only an apparent dissociation constant.72

(72) Cornish-Bowden, A. Fundamentals of Enzyme Kinetics, 3rd ed.; PortlandPress: London, 2004.

(73) Elliott, S. J.; Leger, C.; Pershad, H. R.; Hirst, J.; Heffron, K.; Blasco, F.;Rothery, R.; Weiner, J.; Armstrong, F. A. Biochim. Biophys. Acta 2002,1555, 54-59.

1kcat

)1k1

+1k′1

+1k2

(6)

kET ∝ Tab2 exp(- λ

4RT) exp(( ∆G2RT) (7)

kET ) k0R exp(( F

2RT(E - ER0)) (8)

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turnover, but in contrast to reaction centers where charges mustbe separated on the microsecond time scale, very fast ET is nota requirement in respiratory systems.

Acknowledgment. We thank Alexander Kuhn (University ofBordeaux I, France) and Wolfgang Nitschke (CNRS, Marseilles)for fruitful dicussions. This work was supported by the CNRS,the University of Provence, and the City of Marseilles.

Supporting Information Available: The Appendix, deriva-tions of eqs 2 and 3, figure showing the raw data for lactateoxidation by fb2, and description of the procedure used to fitthese data. This material is available free of charge via theInternet at http://pubs.acs.org.

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Changing the Ligation of the Distal [4Fe4S] Cluster in NiFeHydrogenase Impairs Inter- and Intramolecular Electron

TransfersSebastien Dementin,† Valerie Belle,† Patrick Bertrand,† Bruno Guigliarelli,†

Geraldine Adryanczyk-Perrier,† Antonio L. De Lacey,‡ Victor M. Fernandez,‡Marc Rousset,† and Christophe Leger*,†

Contribution from the Laboratoire de Bioenergetique et Ingenierie des Proteines, CNRS UPR9036, IBSM and UniVersite de ProVence, 31 chemin Joseph Aiguier, 13402 Marseille Cedex 20,France, and Instituto de Catalisis, CSIC, C/Marie Curie 2, Cantoblanco, 28049 Madrid, Spain

Received January 24, 2006; E-mail: christophe.leger@ibsm.cnrs-mrs.fr

Abstract: In NiFe hydrogenases, electrons are transferred from the active site to the redox partner via achain of three Iron-Sulfur clusters, and the surface-exposed [4Fe4S] cluster has an unusual His(Cys)3ligation. When this Histidine (H184 in Desulfovibrio fructosovorans) is changed into a cysteine or a glycine,a distal cubane is still assembled but the oxidative activity of the mutants is only 1.5 and 3% of that of theWT, respectively. We compared the activities of the WT and engineered enzymes for H2 oxidation, H+

reduction and H/D exchange, under various conditions: (i) either with the enzyme directly adsorbed ontoan electrode or using soluble redox partners, and (ii) in the presence of exogenous ligands whose bindingto the exposed Fe of H184G was expected to modulate the properties of the distal cluster. Protein filmvoltammetry proved particularly useful to unravel the effects of the mutations on inter and intramolecularelectron transfer (ET). We demonstrate that changing the coordination of the distal cluster has no effect oncluster assembly, protein stability, active-site chemistry and proton transfer; however, it slows down thefirst-order rates of ET to and from the cluster. All-sulfur coordination is actually detrimental to ET, andintramolecular (uphill) ET is rate determining in the glycine variant. This demonstrates that although [4Fe4S]clusters are robust chemical constructs, the direct protein ligands play an essential role in imparting theirability to transfer electrons.

IntroductionHydrogenases are present in some eukaryotes and in virtually

all bacteria.1-3 These enzymes catalyze a reaction that isessential in the energetics of these organisms and has promisingtechnological applications:4 the reversible oxidation of H2. Thehydrogenases that contain iron-sulfur (FeS) clusters5 have beenclassified according to whether their active site is a dinuclearcluster of nickel and iron7 or iron only.8 In both cases, theelectrons produced upon H2 oxidation at the active site aretransferred to the redox partner via a chain of closely spacedFeS clusters, one of which is exposed at the surface of the

enzyme. Similar redox chains occur in many respiratoryenzymes, including mitochondrial complexes I9,10 and II,11 butthere have been no measurements of electron transfer (ET) ratesbetween FeS clusters in these enzymes;12 this is a directconsequence of two experimental limitations: FeS clusters lackthe well-resolved UV-vis features that are required for time-resolved spectroscopic studies, and ET can be difficult to triggerin non-light-driven enzymes.16 Nevertheless, it is generallybelieved that intramolecular ET is fast with respect to the activesite chemistry, so that it does not limit turnover,17 and NiFehydrogenases are actually cited as a paradigm in this respect.18

Vignais and co-workers have classified NiFe hydrogenaseson the basis of sequence homologies.1 In group 1 NiFe† Laboratoire de Bioenergetique et Ingenierie des Proteines, CNRS.

‡ Instituto de Catalisis, CSIC.(1) Vignais, P. M.; Billoud, B.; Meyer, J. FEMS Microbiol. ReV. 2001, 25,

455-501.(2) Cammack, R.; Frey, M.; Robson, R.; Eds. Hydrogen as a Fuel, Learning

from Nature; Taylor and Francis: London and New York, 2001.(3) Armstong, F. A. Curr. Op. Chem. Biol. 2004, 8, 133-140.(4) Vincent, K. A.; Cracknell, J. A.; Lenz, O.; Zebger, I.; Friedrich, B.;

Armstrong, F. A. Proc. Natl. Acad. Sci., U.S.A. 2005, 102, 16951-16954.(5) A third class of hydrogenase, formerly known as “metal-free” is character-

ized by having no FeS clusters and a single Fe atom at the active site. Seeref 6.

(6) Shima, S.; Lyon, E. J., Thauer, R. K.; Mienert B.; Bill E. J. Am. Chem.Soc. 2005, 127, 10430-10435.

(7) Volbeda, A.; Charon, M. H.; Piras, C.; Hatchikian, E. C.; Frey, M.;Fontecilla-Camps, J. C. Nature 1995, 373, 580-587.

(8) Peters, J. W.; Lanzilotta, W. N.; Lemon, B. J.; Seefeldt, L. C. Science 1998,282, 1853-1858.

(9) Hinchliffe, P.; Sazanov, L. A. Science 2005, 309, 771-774.(10) Sazanov, L. A.; Hinchliffe, P. Science 2006, 311, 1430-1436.(11) Yankovskaya, V.; Horsefield, R.; Tornroth, S.; Luna-Chavez, C.; Miyoshi,

H.; Leger, C.; Byrne, B.; Cecchini, G.; Iwata, S. Science 2003, 299, 700-704.

(12) Only in selected ferredoxins could NMR be used to measure intramolecularET rates between [4Fe4S] clusters. See refs 13-15.

(13) Kyritsis, P.; Huber, J. G.; Quinkal, I.; Gaillard, J.; Moulis, J. M.Biochemistry 1997, 36, 7839-7846.

(14) Kummerle, R.; Kyritsis, P.; Gaillard, J.; Moulis, J.-M. J. Inorg. Biochem.2000, 79, 83-91.

(15) Kummerle, R.; Gaillard, J.; Kyritsis, P.; Moulis, J.-M. J. Biol. Inorg. Chem.2001, 6, 446-451.

(16) Leger, C.; Lederer, F.; Guigliarelli, B.; Bertrand, P. J. Am. Chem. Soc.2006, 128, 180-187.

Published on Web 03/23/2006

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hydrogenases, defined as respiratory (i.e., H2-uptake) enzymes,the redox chain that mediates the electron transfer between theactive site and the redox partner consists of a proximal (to theactive site) [4Fe4S] cluster, a medial [3Fe4S] and a distal[4Fe4S] (Figure 1).

The activity of NiFe hydrogenases can be quantified in severalways that each probe a distinct set of steps in the catalytic cycle.2The rates of hydrogen oxidation and proton reduction can bemeasured using either artificial redox dyes or the natural partnercytochrome c3 as electron acceptors or donors; this reactioninvolves intermolecular ET at the exposed FeS site, intramo-lecular ET along the redox chain, proton transfers and hydrogenactivation. In contrast, the activity for the “isotope exchange”reaction (D2 + H+ h HD + D+) does not involve ET.

In the H2 oxidation process, the rate-limiting step is theoxidation of the enzyme by the redox partner (i.e., intermolecularET). This is obvious from experiments where the rate of H2consumption is highly dependent on the nature of the electronacceptor22-24 and some correlation was observed between theturnover rate and the reduction potential of the redox dye thataccepts the electrons in the assay.23 Consistently, when theenzyme is adsorbed on a “friendly” electrode poised at highpotential, H2 oxidation is at least an order of magnitude fasterthan with any soluble electron acceptor.3,24

The relatively high reduction potential of the medial [3Fe4S]cluster makes intramolecular ET to the distal center veryendergonic. Yet the P238C mutant, which has a nearly iso-potential redox chain with a medial [4Fe4S] cluster, is just asactive as the WT enzyme in solution assays of H2 oxidation:20

since intermolecular ET limits the turnover rate, speeding upintramolecular ET does not increase the overall activity.

The distal cluster is unusual in that one of the Fe atoms iscoordinated by the N atom of a histidine which is exposed at

the surface of the protein.7 This type of coordination is rare: itwas also demonstrated by X-ray crystallography only in someenzymes from the DMSO-reductase family, including themembrane-bound nitrate reductase from Escherichia coli (Ec),25

in clostridial-type Fe-only hydrogenases,8 and in respiratoryComplex I.10 Site-directed mutagenesis experiments have shownthat the conserved histidine ligand is required for activity, butits potential function in tuning the properties of the cluster hasnot been defined further. The His to Cys variant of Clostridiumacetobutylicum Fe-only hydrogenase was not produced inquantities large enough for structural and thermodynamic studies(M. Demuez, P. Soucaille, and L. Girbal, unpublished results).The activity of the His to Cys mutant of {\em Ec} nitratereductase is 0.5% of that of the WT enzyme.27

The histidinyl ligation of [4Fe4S] clusters seems to have nomajor effect on their redox properties. In NiFe hydrogenases,the two cubanes appear to have approximately the samereduction potential (∼-350 mV) despite their distinct coordina-tions,20,21 and this also seems to be the case in Fe-onlyhydrogenases. Regarding Ec nitrate reductase, Rothery and co-workers have shown that the histidinyl cluster has moderatelyhigh reduction potential (-55mV);28 the properties of theengineered all-cysteinyl cluster27 have not been reported yet.The attempts to use site-directed mutagenesis to engineerhistidine ligands to [4Fe4S] clusters were mostly unsuccessful(see ref 29 and refs therein): often, either the cluster is convertedto a [3Fe4S] form or the protein is not produced. Only in theDNA-repair enzyme MutY could a histidinyl ligation of a[4Fe4S] cluster be engineered:30,31 one peculiar Cys/His muta-tion, which leaves the activity unchanged, decreases thereduction potential of the DNA-bound, [4Fe4S]3+/2+ couple.32

However, the 70 mV negative shift is small compared, forexample, to the difference between the reduction potentials ofRieske-type and all-cysteinyl [2Fe2S] clusters.

Over the last years, we have designed molecular biologyprocedures to clone and express in D. fructosoVorans (Df) aStrep-tag construct of NiFe-hydrogenase. This allows us topurify mutant enzymes in amounts usually compatible withmaterial-demanding techniques.20,33-35 To study the function ofthe histidine that ligates the distal [4Fe4S] cluster in Df NiFehydrogenase (H184), we have exchanged it for a cysteine or aglycine. By comparing the properties of the WT and varianthydrogenases, we demonstrate the essential function of thisresidue in increasing the rates of inter and intramolecular ETto and from the distal cluster.

(17) Page, C. C.; Moser, C. C.; Dutton, P. L. Curr. Op. Chem. Biol. 2003, 7,551-556.

(18) Page, C. C.; Moser, C. C.; Chen, X.; Dutton, P. L. Nature 1999, 402, 47-52.

(19) Volbeda, A.; Martin, L.; Cavazza, C.; Matho, M.; Faber, B. W.; Roseboom,W.; Albracht, S. P. J.; Garcin, E.; Rousset, M.; Fontecilla-Camps, J. C. J.Biol. Inorg. Chem. 2005, 10, 239-249, Erratum 2005, 10, 591.

(20) Rousset, M.; Montet, Y.; Guigliarelli, B.; Forget, N.; Asso, M.; Bertrand,P.; Fontecilla-Camps, J. C.; Hatchikian, E. C. Proc. Natl. Acad. Sci., U.S.A.1998, 95, 11625-11630.

(21) Teixeira, M.; Moura, I.; Xavier, A. V.; Moura, J. J. G.; Legall, J.;Dervartanian, D. V.; Peck, H. D.; Huynh, B. H. J. Biol. Chem. 1989, 264,16435-16450.

(22) Bertrand, P.; Dole, F.; Asso, M.; Guigliarelli, B. J. Biol. Inorg. Chem. 2000,5, 682-691.

(23) Delacey, A. L.; Santamaria, E.; Hatchikian, E. C.; Fernandez, V. M.Biochim. Biophys. Acta 2000, 1481, 371-380.

(24) Pershad, H. R.; Duff, J. L. C.; Heering, H. A.; Duin, E. C.; Albracht, S. P.J.; Armstrong, F. A. Biochemistry 1999, 38, 8992-8999.

(25) Bertero, M. G.; Rothery, R. A.; Palak, M.; Hou, C.; Lim, D.; Blasco, F.;Weiner, J. H.; Strynadka, N. C. J. Nat. Struct. Biol. 2003, 10, 681-687.

(26) Albracht, S. P.; Mariette, A.; de Jong, P. Biochim. Biophys. Acta 1998,1318, 92-106.

(27) Magalon, A.; Asso, M.; Guigliarelli, B.; Rothery, R. A.; Bertrand, P.;Giordano, G.; Blasco, F. Biochemistry 1998, 37, 7363-7370.

(28) Rothery, R. A.; Bertero, M. G.; Cammack, R.; Palak, M.; Blasco, F.;Strynadka, N. C. J.; Weiner, J. H. Biochemistry 2004, 43, 5324-5333.

(29) Moulis, J.-M.; Davasse, V.; Golinelli, M.-P.; Meyer, J.; Quinkal, I. J. Biol.Inorg. Chem. 1996, 1, 2-14.

(30) Golinelli, M. P.; Chmiel, N. H.; David, S. S. Biochemistry 1999, 38, 6997-7007.

(31) Messick, T. E.; Chmiel, N. H.; Golinelli, M.-P.; Langer, M. R.; Joshua-Tor, L.; David, S. S. Biochemistry 2002, 41, 3931-3942.

(32) Boon, E. M.; Livingston, A. L.; Chmiel, N. H.; David, S. S.; Barton, J. K.Proc. Natl. Acad. Sci., U.S.A. 2003, 100, 12543-12547.

(33) DeLacey, A. L.; Fernandez, V. M.; Rousset, M.; Cavazza, C.; Hatchikian,E. C. J. Biol. Inorg. Chem. 2003, 8, 129-134.

(34) Dementin, S.; Burlat, B.; DeLacey, A. L.; Pardo, A.; Adryanczyk-Perrier,G.; Guigliarelli, B.; Fernandez, V. M.; Rousset, M. J. Biol. Chem. 2004,279, 10508-10513.

(35) DeLacey, A. L.; Fernandez, V. M.; Rousset, M. Coord. Chem. ReV. 2005,249, 1596-1608.

Figure 1. Biological wire which links the active site to the redox partnerin NiFe hydrogenases (PDB file 1YQW).19 In the enzyme from D.fructosoVorans, the reduction potentials of the centers are ∼-340 mV vsSHE for the two [4Fe4S] clusters and +65 mV for the [3Fe4S] cluster.20

In the enzyme from D. gigas, the reported values are -290 and -340 mVfor the two [4Fe4S] clusters, and -70 mV for the medial cluster.21

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Experimental Procedures

Bacterial Strains, Plasmids and Growth Conditions. Escherichiacoli strain DH5R, F-, endA1, hsdR17 (rK

- mK+), supE44, thi-1, λ-,

recA1, gyrA96, relA1, ∆(argF- lacZYA) U169, φ80dlacZ∆M15 wasused as a host in the cloning of recombinant plasmids. The bacteriumwas routinely grown at 37 °C in LB medium. Ampicillin at 100 µg/mL or gentamycin at 20 µg/mL was added when cells harbored pUC18or pBGF4 derivatives, respectively. The pBGF4 plasmid reporting thegentamycin resistance gene,36 was used to carry the [NiFe] hydrogenaseoperon from Df.20 The strain Df MR400 [hyn::npt ∆hynABC] carryinga deletion in the [NiFe] hydrogenase operon37 was grown anaerobicallyat 37 °C in SOS medium.36 Large culture volumes were performed asdescribed previously.20 Kanamycin at 50 µg/mL was present routinely,and 20 µg/L gentamycin was added only when cells harbored theplasmid pBGF4.

Site-Directed Mutagenesis. The QuikChange TM XL site-directedmutagenesis kit (Stratagene, Amsterdam, The Netherlands) was usedto generate point mutations in the small subunit hynA. The PstI-HindIIIfragment from pBGF4 was subcloned in pUC18 to generate the templatethat was used in mutagenesis experiments. After mutagenesis, the PstI-HindIII fragment was fully sequenced and inserted in the PstI-HindIIIdigested pBGF4. The recombinant plasmid was introduced into Df strainMR400 by electrotransformation.36

Protein Purification. The Strep tag II sequence (IBA Gmbh,Gottingen, Germany) was introduced in the hydrogenase gene, and thetagged protein was purified on a Strep-Tactin(R) column (IBA Gmbh),as described previously.34 An additional purification step using a HiLoadTM 26/60 Superdex TM 200 prep grade column (Amersham Bio-sciences, Uppsala, Sweden) was performed. The purification yield wasabout 0.7 mg of pure hydrogenase per liter of culture for both the WTand H184C enzymes, but only 5 µg/L for the H184G mutant. Theuntagged Df NiFe hydrogenase was prepared as described in ref 20.

Redox Titrations and Spectroscopies. The redox titration of theH184C mutant was carried out at 25 °C in a specially designedanaerobic cell containing a solution of purified enzyme (34 µM) in 50mM HEPES buffer at pH 8 under an argon atmosphere. Redoxpotentials were measured with a combined Pt-Ag/AgCl/KCl (3 M)microelectrode, in the presence of a cocktail of mediators consistingof 15 µM in each of 1,2 naphthoquinone, methylene blue, resorufine,indigo carmine, phenosafranine, neutral red, and methyl viologen. Thetitration was conducted by stepwise additions of small amounts ofsodium dithionite solution (20 mM in oxygen-free HEPES buffer). Allpotentials are quoted against the standard hydrogen electrode (SHE).

For the H184G mutant only 150 µL of enzyme at 10 µM wasavailable, precluding a redox titration of the protein. The reduced statewas obtained by adding in the EPR tube an excess of dithionite (1:200) under anaerobic conditions.

The EPR spectra were recorded on a Bruker ELEXSYS E500spectrometer fitted with an Oxford Instruments ESR 900 helium flowcryostat. For spin quantitation, the double integration of the signalrecorded under non saturating conditions was compared with that givenby a CuSO4 standard at the same temperature.

The metal content of the variants was measured using ICP-MSanalysis (spectrometer HP 4500, calibrated using external standards).

Solution Assays. Unless otherwise stated, the purified enzymes wereactivated for 1h at 37 °C in an anaerobic cuvette containing 500 µL of100 mM Tris/HCl buffer at pH 8 with 0.2 mM methyl viologen (MV).Before adding the enzyme, oxygen was removed under vacuum, thecuvette was flushed with H2 and 1 µL of a 1M dithionite solution wasadded to eliminate the residual oxygen.

H2-oxidation activity was measured at 30 °C in a UV cuvettecontaining 1 mL of buffer Tris/HCl 100 mM at pH 8 with 0.5-500mM MV and the exogenous ligand as required. Oxygen was removedunder vacuum, the cuvette was flushed with H2, and dithionite wasadded to eliminate the residual oxygen. The reaction was started bythe addition of 5-20 µL of stock solution of activated enzyme (30-55 nM), and the rate of MV reduction was measured at 604 nm witha UV 1601 spectrophotometer (Shimadzu). The H2/methylene blue assaywas performed under the same conditions except that 50-100 µMmethylene blue (MB) substituted for MV. The reduction of MB wasdetected at 600 nm.

The assays of H2-evolution were performed in a thermostated (30°C) anaerobic vessel connected through a 14 µm Teflon membrane toa mass spectrometer (Masstorr DX 200, VG Quadrupoles Ltd.), andcontaining 10 mL of buffer (50 mM HEPES, 0.01-1 mM MV, pH 7)flushed with nitrogen until dissolved O2 was eliminated (this wasfollowed by the decrease of mass-32 signal). Then, 75 µL of 2 Msodium dithionite were injected into the vessel in order to reduce thedye. Finally, 5-20 µL of activated hydrogenase (4.5-6.5 µM) wereinjected, and the evolution of H2 was detected as an increase in mass-2signal. The assays of H+/D2 exchange were performed as described inref 33.

Protein Film Voltammetry. We used the same electrochemicalsetup and equipment as described in ref 38. The mixed buffer consistedof MES, HEPES, sodium acetate, TAPS, and CHES (5 mM of eachcomponent), 1 mM EDTA, and 0.1 M NaCl as supporting electrolyte.The H184G variant of hydrogenase was adsorbed onto a pyrolyticgraphite edge electrode by painting the surface with about 0.5 µL ofstock solution of enzyme (∼2 µM in 50 mM HEPES.Na, pH 8). Toactivate the H184G variant, the enzyme-coated electrode was theninserted in the electrochemical cell containing the buffer at pH 7, 40°C, with 10 mM imidazole, under an atmosphere of H2, and poised at-560 mV vs SHE for about 1 h. The extent of activation was monitoredby taking the electrode potential to -160 mV to measure the H2

oxidation current. The electrode could then be rinsed and transferredto an imidazole-free solution. Buffered solutions of 1 M imidazole,1-propanol and 3-mercapto-1-propanol were added to the cell to givethe desired final concentrations. Although we observed that imidazoleis directly reduced on graphite at potentials below 0V vs SHE at pH 7,the reductive current was small enough not to interfere with theelectrochemical measurements.

Origin of Chemicals and Cautions. Imidazole, 1-methyl-imidazoleand methylene blue were from Fluka. 1-propanol was from Prolabo.Methyl viologen (caution: toxic and suspected mutagen), and 3-mer-captopropanol (caution: toxic) were from Aldrich. Sodium dithionitewas from Merck.

Results

Spectroscopy. To analyze the influence of the H184 mutationon the properties of the metal centers, the two mutants and theWT enzyme were studied by EPR spectroscopy.

In the oxidized state, both mutants exhibited spectra identicalwith those previously reported for the WT enzyme:20,34,39 amajor Ni-A (g ) 2.32, 2.23, 2.01) and a minor Ni-B (g )

2.34, 2.16, 2.01) signals (not shown), and a weakly anisotropicsignal centered at g ) 2.02, accounting for 1 spin per moleculeand arising from the medial [3Fe4S]+ center (Figure 2A). Noother signal was detected sweeping from 0 to 600 mT, over thetemperature range 6-100 K; this showed that no centers withspin S > 1/2 contributed to the spectrum.

(36) Rousset, M.; Casalot, L.; Rapp-Giles, B. J.; Dermoun, Z.; de Philip, P.;Belaich, J. P.; Wall, J. D. Plasmid 1998, 39, 114-122.

(37) Rousset, M.; Dermoun, Z.; Chippaux, M.; Belaich, J. P. Mol. Mic. 1991,5, 1735-1740.

(38) Leger, C.; Dementin, S.; Bertrand, P.; Rousset, M.; Guigliarelli, B. J. Am.Chem. Soc. 2004, 126, 12162-12172.

(39) Hatchikian, C. E.; Traore, A. S.; Fernandez, V. M.; Cammack, R. Eur. J.Biochem. 1990, 187, 635-643.

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When the H184C variant was titrated from +150 mV to -420mV, the spectral changes were very similar to those observedfor the WT enzyme. The [3Fe4S]+ signal was no longer visiblebelow ∼-100 mV, and the Ni-A and Ni-B signals decreasedprogressively and disappeared at about -270 mV. Below -300mV, these signals were replaced by the usual Ni-C signal (g) 2.19, 2.14, 2.01), the amplitude of which exhibited a bell-shaped variation against potential, with a maximum at ≈ -340mV, as observed in the WT enzyme.20 At low temperature (6K), this signal was split by the magnetic interactions with theproximal [4Fe4S]+ center, and showed major features at g )

2.21 and 2.10, as for the WT enzyme20 (Figure 2B). The minorfeatures observed at lower field result from a small proportionof the active site being in the Ni-L state (compare with Figure1 in ref 40). In addition, a broad and fast-relaxing signalappeared, which was similar to the broad spectrum observedfor the fully reduced WT enzyme,20 arising from the two[4Fe4S]+ clusters interacting magnetically with the S ) 2reduced [3Fe4S]0 cluster (Figure 2C).

Still for the H184C enzyme, a midpoint potential of -310mV was deduced from the titration of the positive peak in theg ) 2.20 region (Figure 2D); this value is close to that of -340mV found for the [4Fe4S] centers in the WT hydrogenase.20

The comparison of the spin-integration measurements performedin the fully reduced WT enzyme and in the sample of H184Cpoised at -420 mV indicated that 1.4 [4Fe4S] cluster permolecule is reduced at this potential in the mutant. Since theNi-C signal was completely in the split form below -340 mV,the proximal [4Fe4S] center was fully reduced in this sample.This implies that a distal [4Fe4S] cluster is present and at leastpartly reduced. Although its reduction potential could not bedetermined accurately, it can be concluded that it cannot be

more negative than ∼-450 mV. Therefore, all of the FeSclusters are present in the H184C mutant. This was confirmedby ICP-MS elemental analysis which gave an Fe to Ni ratio of12.7 ( 2. Attempts to determine the crystal structure of thismutant are now being made; the result will indicate whetherconformational changes around the distal culster are inducedby the substitution.

The H184G was not available in high enough amounts toperform a complete titration. The elemental analysis gave anFe to Ni ratio identical to that in H184C (12 ( 2), showingthat a distal cluster was assembled, and the fact that no new[3Fe4S] signal was detected in the oxidized state demonstratesthat the glycine mutation has not induced cluster conversion(Figure 2A). In the reduced state, the thin lines of the “Ni-Csplit” signal in Figure 2B revealed an intact active site, and thebroad pattern resulting from the magnetically interacting clusterswas essentially identical to that observed for the WT and H184Cenzymes (g ) 1.5-1.9, Figure 2C). The presence of a distal[4Fe4S] cluster in this mutant was also clearly demonstratedby our kinetic data (see below).

Solution Kinetics. The enzymes were assayed for hydrogenoxidation at pH 8, 30 °C, under an atmosphere of H2, usingmethyl viologen (MV) as electron acceptor. The comparisonof the first two lines in Table 1, shows that engineering a Strep-tag increases 3-fold the Michaelis-Menten constant for MV(despite the fact that we positioned the tag on the side of theenzyme opposite to the distal cubane where the MV interacts)but has only a small effect (-20%) on the rate of H2 oxidationunder saturating conditions.

The data in Table 1 (rows 2, 4 and 6) show that the mutationshave only a small effect on the Michaelis constants relative toMV2+, whereas the maximal rates of H2 oxidation by H184Gand H184C are only 3% and 1.7% of that of the WT,respectively. The rates of H2 oxidation in the presence of 100µM methylene blue (MB) to accept the electrons are given inTable 1. The high absorbance of oxidized MB made itimpossible to perform the assay with greater concentrations ofacceptor. In the accessible concentration range, the rate was

Figure 2. EPR spectra of hydrogenases in the oxidized (Panel A) andreduced (B and C) states. Panel D: potentiometric titration curve of thepositive peak around g ) 2.20 in H184C. Experimental conditions were asfollows. Microwave frequency: 9.42 GHz. (A) T ) 15 K, microwave powerP ) 0.1 mW, modulation amplitude MA ) 0.1 mT (WT and H184C) or0.5 mT (H184G); (B) T ) 6 K, P ) 10 mW, MA ) 1 mT, E ) -360 mV(WT) and -340 mV (H184C); (C) T ) 6 K, P ) 10 mW, MA ) 1 mT(WT) and 2 mT (both mutants), E ) -470 mV (WT) and -420 mV(H184C). The H184G sample was reduced without potential control (seetext).

Table 1: Kinetic Properties of Recombinant Df NiFeHydrogenases, Untagged WT, Strep-tagged WT, and Strep-taggedH184G and H184C Variants in the Presence or Absence ofImidazole (Im)a

activity: H2-oxidation exchange H+-reduction

redox partner: oxidized MV100 µM

MB none reduced MV

Kma vm b v c v d Km a vm b

WT (no tag) 3.2 630WT (Strep-tagged) 9 500 1000 87 0.02 130WT + 0.1 M Im 7.2 480 780H184G 2.2 15 23 74 0.044 96H184G + 0.1 M Im 2.7 150 180 82 103H184C 16 8.4 7 70 0.033 61H184C + 0.1 M Im 14 8.5 5

a The rates are in Units of µmol of gas consumed or produced per minand per mg of enzyme (1 Unit ≈ 1.5 mol per second and per mol ofenzyme), and the Km values are in mM. All relative errors are of the orderof 10%. (a) Michaelis constants (relative to the redox partner as indicated).bMaximal rates in the assays of H2 oxidation or production. c Rates of H2-oxidation in the presence of 100 µM oxidized MB (under conditions wherethe activity is proportional to the concentration of redox partner). d Ratesof formation of HD in the H+/D2 exchange assay. The buffer was 100 mMTRIS at pH 8 for H2 oxidation and H+/D2 exchange, or 50 mM HEPES atpH 7 for H+ reduction, T ) 30 °C in all cases

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proportional to the concentration of MB (data not shown), whichdemonstrates that the Michaelis constant for MB is greater than100 µM. Therefore, the H2/MB rates in Table 1 are far belowtheir maximal values; yet they are significantly higher than whenMV accepts the electrons. This confirms that intermolecular ETlimits oxidative turnover.3,22-24

The effect of the mutations does not depend much on whetherMB or MV accepts the electrons in the assay: the His/Gly andHis/Cys mutations decrease the activity 45 and 140-fold,respectively, in the H2/MB assay, compared to 35 and 60-foldin the H2/MV assay.

The maximal rates of proton reduction by H184G and H184Cwith MV as electron donor are about 75% and 45% of that ofthe WT and the mutations have a small effect on the Michaelisconstants for MV+• (the differences between the Km valuesrelative to oxidized versus reduced MV may result, in part, fromthe charge on the dye being dependent on its redox state). Themutations have a much weaker effect on the rates of H+

exchange with D2 than on H2-oxidation. These observationsimply that both mutations leave the active site entirely func-tional.

Chemical Rescue and Inhibition of H184G in SolutionAssays. We repeated the assays in the presence of exogenousligands which were expected to substitute for the histidine inthe H184G variant.

The results of the assays of H+/D2 exchange and H2 oxidationor production with either electron acceptor in the presence of0.1 M imidazole are collected in Table 1. Exogenous imidazoleat 0.1 M has no significant effect on any of the catalyticproperties of the WT and H184C enzymes. Regarding theH184G variant, the only significant effect is on its oxidativeactivity, which increases 10-fold in the presence of imidazole.

Figure 3 shows how the oxidative activity of H184G dependson the concentration of imidazole and 1-methyl-imidazole(methylation is on one of the nitrogen atoms). The changes inturnover number against ligand concentration can be interpretedassuming equilibrium between the free and associated formsof the enzyme. Noting Kd, the dissociation constant betweenthe enzyme and the imidazole derivative, V0 the activity of thefree H184G enzyme and V∞ the activity of the enzyme boundto the ligand, and provided the concentration of ligand C isgreater than the total concentration of enzyme, the activity V(C)reads

For imidazole, the fit of the data in Figure 3 to eq 1 (with V0fixed to 15 Units) gave the values of Kd ) 35 ( 8 mM andV∞/V0 ) 12.2 ( 0.5. For 1-methyl-imidazole, we obtained Kd) 80 ( 10 mM and V∞/V0 ) 13.1 ( 0.5. The dotted lines inFigure 3 illustrate these uncertainties. Control experiments (notshown) were performed to check that neither imidazole (up to0.25 M) nor 1-methyl-imidazole (up to 0.5 M) have an effecton the activity of the WT and H184C enzymes.

Figure 4 shows how the addition of 3-mercapto-1-propanol(MPrOH) affects the rate of viologen reduction during the assayof H184G. In the absence of thiol, the steady-state turnoverresults in a linear change in absorbance against time (dashedline). When 2 mM MPrOH is added to the cuvette just beforethe assay is started, the absorbance change slows down overthe course of minutes, until the enzyme becomes inactive. Nosuch effect was observed with the WT and H184C enzymes(data not shown).

Chronoamperometry. The activation and inhibition ofH184G could be studied with the enzyme adsorbed on anelectrode, in a configuration where electron transfer is direct(no mediator is used) and the turnover rate is simply measuredas a current.3,38,41,42 Figure 5 shows the change in activity againsttime, measured in such configuration, under 1 atm. of H2, theelectrode potential being poised at -160 mV vs SHE,43 andfollowing the addition to the electrochemical cell of 10 mMimidazole, then 2 mM 1-propanol (PrOH) and finally 2 mMMPrOH. The plain line in Figure 5 shows that the addition ofimidazole results in an instantaneous activation, while MPrOHinduces a slow decrease in activity against time, which mirrorsthe behavior in the H2/MV assay (Figure 4). The fact that nochange in activity is observed when PrOH is added (at t ) 150sin Figure 5) proves that the inhibition results from the thiolgroup of 3-mercapto-1-pronanol. Under the same conditions,none of these molecules affects the activity of the WT enzyme(dashed line in Figure 5).

All the control experiments demonstrate that the exogenousligands bind to the Fe atom whose coordination shell isincomplete in H184G.

Using Protein Film Voltammetry (PFV) to Probe theCompetition between Inter- and Intramolecular ET. Theexperiments in Figure 5 confirm the previous observationsregarding the effects of imidazole and thiol on the activity ofH184G, but they do not reveal immediately the reason theactivity varies upon ligand binding. We shall demonstrate thatthis information can be gained from voltammetry experiments,where the activity is measured over a wide range of drivingforce by sweeping the potential E of the electrode onto whichthe enzyme is adsorbed.

Figure 6 shows the voltammetric signature of the WT enzymeadsorbed at a rotating graphite electrode.38 The voltammogram

(40) Dole, F.; Medina, M.; More, C.; Cammack, R.; Bertrand, P.; Guigliarelli,B. Biochemistry 1996, 35, 16399-16406.

(41) Leger, C.; Elliott, S. J.; Hoke, K. R.; Jeuken, L. J. C.; Jones, A. K.;Armstrong, F. A. Biochemistry 2003, 42, 8653-8662.

(42) Armstrong, F. A. Curr. Op. Chem. Biol. 2005, 9, 110-117.(43) Under these conditions, hydrogen is oxidized by the enzyme, but the active

site is not oxidized to one of its inactive states. See refs 38 and 44.

Figure 3. Chemical rescue of H184G hydrogenase: effect on the oxidativeactivity of imidazole (0) and 1-methyl-imidazole (O). The parametersobtained from the fits to eq 1 are given in the text. pH 8, 30 °C, 50 mMMV, 1 atm of H2.

V(C) ) V0

1 +V∞

V0

CKd

1 +CKd

(1)

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plotted with a blue line has been recorded under an atmosphereof Ar, and the negative current at low potential results fromproton reduction by the enzyme. The potential was swept slowlyfrom -150 mV vs SHE down to -550 mV and back, and thefact that the signal is independent of the scan direction (exceptfor the current offset that is due to double layer charging) impliesthat catalysis takes place at steady-state. Under an atmosphereof H2, a positive current (upper, black line in Figure 6) revealsthe oxidative activity at high electrode potential.

The theory that applies to the direct, catalytic electrochemistryof enzymes was developed and applied to several systems inrecent years (refs 16, 42, 45, and refs therein). Here, we onlyrecall the simple rules that allow the semiquantitative interpreta-tion of the electrochemical experiments we shall report. InFigure 7, we decompose the catalytic cycle of NiFe hydrogenaseinto two parts: (i) interfacial ET steps, leading to the oxidationor reduction of the surface exposed [4Fe4S] cluster and (ii) therest of the cycle, described by a pseudo-first-order rate constant

k2 (with subscript “ox” or “red” for H2 oxidation or production,respectively), which incorporates intramolecular ET along thechain of FeS clusters, H2 diffusion and binding, active sitechemistry and proton transfers. The rate of interfacial ET isproportional to a parameter called k0 and depends exponentiallyon the electrode potential E, whereas k2 is independent of E.How the catalytic waveshape depends on k2 and k0 is discussedin ref 46 and illustrated in the Supporting Information: at highdriving force (high electrode potential for a catalytic oxidation,low E for reductive catalysis), the current changes linearly withE, with a slope that is proportional to k2 and independent of k0,whereas the shape of the wave is highly dependent on the ratiok2/k0, fast interfacial ET with respect to chemistry making thewave more sigmoidal.

Therefore, whether the change in coordination of the distalcluster in NiFe hydrogenase affects interfacial or intramolecularET is expected to reflect differently on the shape (as opposedto merely the magnitude) of the catalytic voltammogram andthis makes PFV superior to homogeneous kinetics, where thesteady-state activity is only a measure of the rate of the sloweststep in the catalytic cycle.

Voltammetry: All-Sulfur Coordination Slows InterfacialET. Figure 8A shows the voltammograms recorded with theH184G variant under the same conditions as for the WT enzymein Figure 6, before (dashed lines) and after (plain lines) we addedimidazole. The important observations are that (i) the glycinevariant has a residual activity in the absence of imidazole, (ii)the magnitude of the signal increases upon addition of imidazole(this mirrors the chemical rescue of the enzyme in solutionassays, Table 1 and Figure 3), and (iii) the shape and positionof the voltammogram for the repaired enzyme are very similarto those for the WT.47

The behavior of the H184C enzyme in Panel B is completelydifferent from that of the WT and H184G-imidazole adduct:in this case, there is a large window of electrode potential,

(44) Jones, A. K.; Lamle, S. E.; Pershad, H. R.; Vincent, K. A.; Albracht, S. P.J.; Armstrong, F. A. J. Am. Chem. Soc. 2003, 125, 8505-8514.

(45) Reda, T.; Hirst, J. J. Phys. Chem. B 2006, 10, 1394-1404.(46) Leger, C.; Jones, A. K.; Albracht, S. P. J.; Armstrong, F. A. J. Phys. Chem.

B 2002, 106, 13058-13063.(47) The magnitude of the current in Figure 8A is smaller than that with the

WT enzyme, but since it is proportional to the unknown amount of enzymeadsorbed onto the electrode, this observation does not demonstrate thatthe repaired enzyme has lower activity than the WT (even if we knowfrom solution assays that this is so).

Figure 4. Inhibition of H184G by an alkane thiol: change in absorbanceagainst time resulting from methyl viologen reduction by H184G in theabsence (dashed line) or presence (plain line) of 3-mercapto-1-propanol (2mM). pH 8, 30 °C, 1 atm of H2.

Figure 5. Activation and inhibition of H184G. The activity was measuredas a current with the enzyme adsorbed onto a graphite electrode poised at-160 mV. The current was normalized to its value just before the thiolwas added in the electrochemical cell. Effect of the addition of imidazole(at time t ) 100 s), 1-propanol (t ) 150 s) and 3-mercapto-1-propanol (t) 200 s) on the activity of H184G (plain line) and WT hydrogenase (dashedline). pH 7, 40 °C, 1 atm. of H2, electrode rotation rate 2 krpm.

Figure 6. Voltammograms for WT Df NiFe hydrogenases adsorbed at agraphite electrode, under an atmosphere of H2 (upper, black trace) or Ar(lower, blue trace), pH 7, scan rate ν ) 10 mV/s, electrode rotation rate ω) 1 krpm, T ) 40 °C.

Figure 7. Minimal catalytic cycle for H2 oxidation or production by NiFehydrogenases adsorbed onto an electrode. We note E the electrode potential.

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between -400 and -200 mV, where no activity is detected.The following observations confirm that the current at very lowor very high E results from catalytic H2 production or oxidationcatalyzed by the H184C enzyme: (i) the signal is present onlyif the enzyme is adsorbed (the dotted line shows a blankrecorded with no enzyme adsorbed on the electrode); (ii) theoxidation current (positive) disappears under an atmosphere ofAr (black line) and the reductive current decreases when theatmosphere is switched to H2, which is known to inhibit H+-reduction;38,48 and (iii) we used the method described in ref 38to check that the H+ reduction current is reversibly inhibitedby CO and H2, and that the H2-oxidation current is reversiblyinhibited by CO and irreversibly inhibited by O2, and theinhibition constants and rates of inactivation did not differsignificantly from those measured for the WT (data not shown).

The shapes of the voltammograms for the H184C mutantreveal immediately sluggish interfacial electron transfer: onlyat very high driving force (either very low or very high electrodepotential) is the rate of interfacial ET to or from the enzymehigh enough to result in a turnover rate that can be distinguished

from the background (compare with Figure S1 in the supple-mentary information).

Panel C shows the data for the H184G enzyme, repaired byimidazole (dashed line) and then irreversibly inhibited by adding2 mM thiol in the cell (plain lines). It appears immediately thatthe binding of the thiol to H184G has the same effect as theHis to Cys mutation: it slows interfacial ET.

Voltammetry: Effect of Imidazole Binding on Intramo-lecular ET in H184G. We now examine how the precise shapeof the catalytic signal for the H184G variant is affected byexogenous imidazole. For the experiments in Figure 9, theelectrode potential was cycled repeatedly to monitor thepotential-dependence of the rate of H2 oxidation or production.The concentration of imidazole was increased every other scan,and we checked that the signals increased only following theaddition of imidazole: this implied that the change in activityas a function of time did not result from slow enzyme activation,inactivation or film desorption. The “as-recorded” data are showin the Supplementary Information (Figure S4), while we plotin Figure 9 the voltammograms corrected by subtractingbaselines extrapolated linearly from the region of the voltam-mogram where there is no catalytic current.46

Figure 9A shows how the activity for proton reduction byH184G depends on the concentration of imidazole. Upon

(48) Leger, C.; Jones, A. K.; Roseboom, W.; Albracht, S. P. J.; Armstrong, F.A. Biochemistry 2002, 41, 15736-15746.

Figure 8. Voltammograms for the NiFe hydrogenases variants adsorbedat a graphite electrode, under an atmosphere of H2 (black lines) or Ar (bluelines). Panel A: H184G mutant at pH 7, before (dashed lines) and after theaddition of 20 mM imidazole. Panel B: H184C enzyme, at pH 6. Panel C:H184G mutant, at pH 6, in the presence of 10 mM imidazole, before (dashedline) and after the addition of 2 mM mercapto propanol (MPrOH). ν ) 10mV/s, ω ) 1 krpm (Panel A) or ν ) 20 mV/s, ω ) 2 krpm (Panels B andC). T ) 40 °C in all cases.

Figure 9. Effect of exogenous imidazole on the activity of Df H184G NiFehydrogenase adsorbed at a graphite electrode. Panel A: H2-production under1 atm. of Ar. Panel B: H2-oxidation under 1 atm. of H2. The Panel C showshow the limiting slope of the voltammograms at high driving force (lowpotential for H+ reduction, high potential for H2 oxidation) changes as afunction of the concentration of imidazole. The black line in Panel C is thebest fit of k2

ox to eq 1. pH 7, T ) 40 °C, ν ) 10 mV/s, ω ) 2 krpm.

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increasing the concentration, the waveshape changes fromrevealing sluggish interfacial ET (dashed line) to resemblingthat observed with the WT enzyme (compare with Figure 6);however, the slope of the signal measured in the high drivingforce limit remains unaffected (empty squares in Figure 9C).This change in shape shows that under reducing conditions, thebinding of imidazole increases the rate of interfacial ET (throughk0) but has no effect on k2

red (see the discussion above orcompare with Figure S1, Supporting Information).

The data plotted in Figure 9B were recorded with the solutionunder an atmosphere of H2, and the positive current revealshydrogen oxidation by the enzyme. The magnitude of the currentand the slope at high potential (filled squares in Panel C) bothincrease with increasing ligand concentration. The fit of thehyperbolic dependence of k2

ox on the concentration of imida-zole (eq 1 and black line in Figure 9C) gives a dissociationconstant of 12 mM (at 40 °C, pH 7), in fair agreement with thevalue measured in solution (40 mM at pH 8, 30 °C). Suchincrease in slope of the catalytic data at high driving force isusually observed when an increase in k2 results from the additionof substrate to the solution in contact with the adsorbedenzyme.49,53

Therefore imidazole binding increases k0 and k2ox, but leaves

k2red unchanged. The effect on interfacial ET (k0) mirrors the

chemical rescue of intermolecular ET in solution assays of theenzyme. The observation that k2

ox increases upon imidazolebinding to the distal cluster reveals an acceleration of intramo-lecular ET from the medial [3Fe4S] cluster to the distalcubane: all the other steps which may contribute to k2

ox takeplace far from the distal cluster where imidazole binds andindeed, imidazole has no effect on the active site chemistry andproton transfers (as shown for all three enzymes by theexperiments of isotope exchange and proton reduction in thepresence of imidazole, Table 1).

In summary, imidazole-binding increases all rates of ET toor from the modified distal cluster, except the intramolecular,downhill step from distal to medial cluster in proton reduction,for which we detected no effect. The effect on intermolecularET was revealed by traditional kinetics, while PFV was usedhere to demonstrate the effect on interfacial and intramolecularET.

Discussion

In respiratory NiFe hydrogenases, a histidine ligates one Featom of the [4Fe4S] cluster that is remote from the active siteand exposed at the surface of the protein (Figure 1). To

understand the role of this residue, we have studied the effectof ligand substitution on the catalytic properties of the enzyme.The histidine was changed into a cysteine, to engineer a canonic,all-cysteinyl ligation, or into a glycine, to induce the formationof a [4Fe4S] cluster with a labile and exchangeable ligand. Theessential role of the histidine ligand is demonstrated by the factthat the activities of the variants are only a few percent of thatof the WT enzyme in the assays of H2 oxidation with eitherMB or MV as electron partner.

Our spectroscopic results indicate that a [4Fe4S] distal clusteris assembled in both variants: (i) the elemental analyses showthat a distal clusters is present, (ii) the EPR signatures of theoxidized variants in Figure 2A rule out the presence of a second[3Fe4S] cluster in either mutant (clearly, there has been nocluster conversion), and (iii) the EPR spectra of the reducedenzymes in Figure 2C show patterns of interaction between thereduced clusters that are similar to that for the WT enzyme.We expected the deletion of the imidazole ring of H184 in theglycine variant to open a gap in the coordination shell of an Fethat belongs to the distal cubane, and to make it amenable todirect manipulation through the addition of exogenous ligands.Indeed, we have used the results of activity measurements inthe presence of imidazole derivatives and alkane thiols to bringfurther evidence of the existence of a distal [4Fe4S] cluster inH184G and to investigate how the coordination of the clusteraffects the activity of the enzyme. The control experiments wereport show that these ligands have no effect on the activity ofthe WT and H184C enzymes, both in solution assays (Table 1)and when the activity is measured with the enzyme adsorbedat an electrode surface (Figure 5), whereas they affect stronglythe activity of the H184G enzyme. This demonstrates that theseligands bind to the cluster that is modified by the glycinemutation, most likely to the exposed Fe atom either free orbound to a labile solvent molecule, as already observed in otherFeS-containing proteins. Armstrong and co-workers used PFVto demonstrate that a thiolate (2-mercapto-ethanol) binds to theunique iron of the Asp(Cys)3-ligated [4Fe4S]2+ cluster of D.africanus 8Fe ferredoxin.54 In the case of a hydrogenasematuration protein that houses a [4Fe4S] cluster with only threeproteic ligands, the binding of exogenous imidazole to thecluster’s fourth Fe atom was demonstrated using HYSCOREspectroscopy.55 Such detailed spectroscopic study of the distalcluster in H184G is precluded by the strong inter cluster spin-spin coupling which results in a broad EPR spectrum in thereduced state.

The activity of the H184G variant is intermediate betweenthose of the WT and H184C enzymes, and it can be turned upor down upon binding of imidazole or thiol, respectively(Figures 3-5). It is also significant that these external ligandstransform the electrochemical fingerprint of the H184G enzymeinto that of the WT or H184C enzymes (Figures 6 and 8). Thisdemonstrates that the exogenous ligands can substitute, to someextent, for the cluster’s proteic ligand that is missing in theH184G enzymes. However, our kinetic data also point out theimportance of the attachment of the ligand to the proteinbackbone. Indeed, the H184G-thiol adduct has no detectableoxidative activity in solution assays (whereas the activity of

(49) This was reported in the literature with arsenite oxidase in ref 50, Figure7; sulfite oxidase in ref 51, Figure 5; lactate dehydrogenase in ref 16, Figure2; Complex I in ref 45, Figure 5; nitrite reductase in ref 52, Figure 3 andhydrogenase in ref 48, Figure 2.

(50) Hoke, K. R.; Cobb, N.; Armstrong, F. A.; Hille, R. Biochemistry 2004, 43,1667-1674.

(51) Ferapontova, E. E.; Ruzgas, T.; Gorton, L. Anal. Chem. 2003, 75, 4841-4850.

(52) Angove, H. C.; Cole, J. A.; Richardson, D. J.; Butt, J. N. J. Biol. Chem.2002, 277, 23374-23381.

(53) In H2 oxidation by H184G, Figure 9B, imidazole binding does not onlyincrease k2

ox: the similar effect on k0 is suggested by the fact that the wavedoes not become less sigmoidal as the concentration of ligand is increased,as would be observed if the ratio k2

ox/k0 increased (compare Figure 9B toFigure 1 in ref 46 or Figure 2 in ref 48, or to Figures S2 and S3 in theSupporting Information). This was expected because in discussing Figure9A, we have shown that imidazole binding increases k0 when the enzymereduces protons, and the rate of interfacial ET is proportional to k0 regardlessof the direction of electron flow.

(54) Butt, J. N.; Sucheta, A.; Armstrong, F. A.; Breton, J.; Thomson, A. J.;Hatchikian, E. C. J. Am. Chem. Soc. 1993, 115, 1413-1421.

(55) Brazzolotto, X.; Rubach, J. K.; Gaillard, J.; Ganbarelli, S.; Atta, M.;Fontecave, M. J. Biol. Chem. 2006, 281, 769-774.

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H184C is 1.7% of that of the WT) and the chemical rescue ofH184G by exogenous ligands is incomplete: none of themolecules we tested56 could make the mutant recover more than30% of the oxidative activity of the WT enzyme.

Effect of the Mutations on the Expression and Stabilityof the Proteins. Exchanging a direct ligand of a [4Fe4S] clusteris often destabilizing enough to impair cluster assembly or evenprotein folding (this was comprehensively reviewed by Mou-lis29). In this respect, it is striking that in the case of the H184Gvariant of Df NiFe hydrogenase, the protein is actually properlyfolded but the purification yield is 2 orders of magnitude lowerthan for the WT: this mutant would certainly have escapeddetection if we had not used an affinity purification procedure.The purification yield of the H184C variant was similar to thatfor the WT, suggesting that the absence of the fourth proteicligand in H184G slows down the folding of the protein andmakes the nascent polypeptide prone to degradation by theexpression host. However the mutations did not appear todecrease the “shelf life” of the purified proteins, which couldbe handled with no special care without loss of activity overtime.

Mutations Impair Intermolecular ET. We have shown thatmutating the histidine ligand of the distal cubane impairs neithercofactor incorporation nor protein folding, and has no effecton the structural and electronic properties of the NiFe activesite (the EPR signatures of the active site states are unaffectedby the mutations). Since we do not know the dissociationconstant between the mutants and the physiological electronpartner cytochrome c3, we should not exclude a role of thehistidine in partner recognition. However, we have shown thatchanging the ligation of the distal cluster has a strong effect onthe maximal rate of H2 oxidation (extrapolated to infiniteconcentrations of MV). These maximal rates eliminate effectsof binding: they only incorporate contributions from first-orderinter- and intramolecular ET, proton transfer and hydrogenactivation at the active site. The mutations have no effect onthe latter, since the enzymes retain their H+/D2 exchange activity(Table 1), and we also exclude the involvement of the Nε2 ofH184 in mediating a proton transfer step crucial for catalysis:were this to be the case, 1-methyl-imidazole could not rescuethe H184G variant. Therefore, we conclude that the mutationsimpair electron transfer. Consistent with our earlier finding thatproton-transfer limits reductive turnover,22 the fact that themutations have no significant effect on the rate of protonreduction demonstrates that the distal cluster is not directlyinvolved in the rate-determining step for this reaction.

Considering the H2-oxidation reaction, the fact that the activityis dependent on which electron acceptor is used shows thatintermolecular ET limits oxidative turnover in the WTenzymes3,22-24 and also in the variants. Thus, although ligandsubstitution may have an effect on both intra- and intermolecularET, only the rate of the latter is probed in solution assays of H2oxidation: the decrease in rate of H2 oxidation in Table 1 simplyreveals the fact that the mutations slow ET to the solubleacceptor.

Mutations Slow Interfacial ET. We have used protein filmvoltammetry41,42 to study the effects of the mutation or repair.

In this technique, no soluble redox partner is used: the enzymeis simply adsorbed onto an electrode whose potential can beset to provide whichever driving force is required to sustaincatalysis, and the steady-state activity is measured as a curveof current against electrode potential (E). The reason thistechnique proved useful is that the shape of the catalytic signalreveals the competition between the two processes that lead tothe oxidation and reduction of the distal cluster during cataly-sis: intramolecular and interfacial ET.

The electrochemical results in Figure 8 provide an immediatedemonstration of the detrimental effect of the all-sulfur coor-dination on interfacial ET in both the H184C mutant and in thethiol-inhibited H184G variant. The experiments in Figure 9 alsoshow that imidazole binding to H184G increases the rate ofinterfacial ET. These effects on k0 strongly supports the ideathat impaired intermolecular ET is the reason these enzymeshave so low activity in solution assays.

Intramolecular ET is Slow in H184G. When the electronsproduced upon H2 oxidation at the active site flow toward theelectrode, the effect of imidazole is to increase the parameterk0, that describes interfacial ET, but more surprisingly, it alsoincreases the rate constant k2

ox defined in Figure 7, and this hastwo implications: (i) the imidazole moiety increases the rateof intramolecular ET from the medial to the distal cluster, and(ii) in H184G, this step is slow enough with respect to the activesite chemistry, proton transfer and H2 diffusion, that it is ratedetermining when the enzyme is adsorbed at an electrodesurface. This is in contrast with the general idea17,18 that ETbetween closely spaced (<14 Å) redox centers is necessarilyfaster than the catalytic turnover. The distance between themedial and distal clusters is 8.5 Å in the WT enzyme, and thefact that the distal cubane in H184G remains attached to thestructured protein by three buried cystein ligands makes veryunlikely the hypothesis that it has moved away from the medialcluster; this hypothesis would also be very difficult to reconcilewith the experiments of chemical rescue of the H184G variantby exogenous imidazole.

Why are ET Steps Slow in the Mutants? According toMarcus theory,57 the rate of ET between the distal cluster andits redox partner (depending on which step we consider, thiscan be the electrode, the soluble dye, or the medial cluster) canbe affected by a change in any of the following threeparameters: (i) the reduction potential of the cluster, (ii) theelectronic coupling between the cluster and the partner, and (iii)the reorganization energy of the process.

(i) Regarding intermolecular ET, we can exclude for bothmutants that slow intermolecular ET toward the soluble acceptor(during H2 oxidation) results from a mutation-induced increasein reduction potential of the distal [4Fe4S] cluster. In the caseof H184C, this would be inconsistent with the results of ourpotentiometric titration which shows that the mutation mayinduce a small decrease in reduction potential but not a positiveshift. For H184G, if the reduction potential of the distal clusterwere greater than in the WT, this would speed intramolecularET to the distal cluster, whereas the opposite, detrimental effectis demonstrated by our electrochemical study.

(ii) The low activity of both variants and the chemical rescueof H184G by imidazole56 may reveal a function of the π bondsof H184 in increasing the electronic coupling between the distal(56) The oxidative activity of the H184G variant is also partially rescued by

exogenous pyrazole, triazole, pyridine and 4-ethyl-pyridine, while underidentical conditions, these molecules have no effect on the WT and H184Cenzymes (data not shown). (57) Marcus, R. A.; Sutin, N. BBA 1985, 811, 265-322.

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cluster and its partners. This could result from the change ofcoordination either modifying the valence localization patternwithin the [4Fe4S]+cluster, or altering the electronic pathwayprovided by the network of chemical bonds.

(iii) Last, the decrease in rate of ET to/from the distal clusterin the mutants may result from an increase in reorganizationenergy of the distal cluster. This effect is documented in thecase of azurin58 and copper-containing nitrite reductase,59 whichboth house a surface-exposed, type-I copper site involved inET: when a histidine ligand of the copper is mutated into aglycine, the cluster has much higher reduction potential andincreased reorganization energy. The “redox-inactive” mutantsexhibit extremely slow interfacial58 or intermolecular59 ET rates,unless repaired by exogenous imidazole. A significant increaseof the value of λ in H184G compared to the WT enzyme wouldnot be surprising considering how solvent exposure should affectthe outer-sphere reorganization energy. It may also happen thatthe binding and dissociation of the exogenous ligand on thetime scale of turnover has a considerable retarding influence.An increase in λ would have exactly the effect we observe inH184G: slowing down all ET rates to and from the cluster(intramolecular, intermolecular, and interfacial).

Considering specifically intramolecular ET, we note that theslow step in H184G (from the medial to the distal cluster) isthe step that is very endergonic in the WT enzyme.18,20

Therefore, unfavorable thermodynamics is likely to add to theeffects of the mutation to slow this transfer. Consistently, wedid not detect an acceleration of the reverse step (from the distalto the medial cluster) upon imidazole binding to H184G: thisstep is driven by such large driving force that it is not expectedto be rate determining in proton reduction.

Overall, the fact that the mutations slow ET steps is unlikelyto result from a change in reduction potential of the distal cluster;instead, the contributions of electronic coupling and reorganiza-tion energy must be considered.

Conclusions

Our results suggest that the short distance between FeSclusters in biological redox chains may not always be sufficientto allow rapid intramolecular ET: for very endergonic steps,other structural features, such as the distal cluster’s ligation inNiFe hydrogenase, may have an essential yet undervaluedfunction in making up for the unfavorable thermodynamics.

Whether or not intramolecular ET is also slower thanhydrogen activation in the WT enzyme is still unknown andthis reminds us that measurements of intramolecular ET ratesare difficult and scarce in non-light-driven systems. We haveshown recently that the detailed analysis of the shape of thevoltammograms obtained for enzymes confined at an electrodesurface could give quantitative information in this respect.16 Weare now using this approach to probe the efficacy of ET in WTDf NiFe hydrogenases, and in variants (including H184G,H184C, and P238C) where the ET chain is significantlymodified.

Acknowledgment. We thank C. Hatchikian (BIP, Marseilles)for preparing the untagged Df NiFe hydrogenase, AlejandroBallesteros (CSIC, Madrid) for technical assistance, P. Galliceand F. Chaspoul (Universite de la Mediterranee, Dept. ofPharmacy, Marseilles) for carrying out the ICP-MS measure-ments and K. Meffrou (RMH, London) and F. Baymann (BIP,Marseilles) for fruitful discussions. This work was supportedby the French CNRS, the University of Provence, the City ofMarseilles, the Spanish MCYT (Project BQU2000-0991) andby the Grant G5RD-CT-2002-00750 from the European Unionin the Competitive and Sustainable Growth Program.

Supporting Information Available: Simulations illustratinghow k2 and k0 affect the shapes of the voltammograms.Uncorrected data for Figure 9. This material is available freeof charge via the Internet http://pubs.acs.org.

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