Etude de systèmes moléculaires complexes

Développement d'outils de modélisation moléculaire à basse

résolutionLaurence Leherte

Laboratoire de Physico-Chimie Informatique (PCI)Groupe de Chimie Physique Théorique et Structurale

Séminaire résidentiel de la Faculté des Sciences des FUNDP« Les systèmes complexes »Blankenberge, Janvier 2009

All-atom description of a moleculeHuge number of degrees of freedomMultiple minima problem

I. Reduced Molecular Representations

All-atom model Coarse-grain model

Coarse-grain modelsCα Center-of-mass

Cα representation of lysozyme (green spheres). Interactions are represented by springs (red).[K. Hinsen, http://dirac.cnrs-orleans.fr/plone/Members/hinsen/elastic-network-models-for-proteins, 2007]

[Basdevant et al., J. Phys. Chem. B 111 (2007) 9390]

44

Coarse-grain models Uses (1)

Lowest frequency normal mode of adenylate kinase obtained with elastic network normal mode analysis [http://ctbp.ucsd.edu/summer_workshop04/elastic_network/html/elastic_network.htm]

Slow & large amplitude dynamicsNormal Mode Analysis

55

Coarse-grain models Uses (2)

Open-to-closed transition of adenylate kinase [Chu & Voth, Biophys. J. 93 (2007) 3860 ]

Conformational changes in proteinsElastic Network Models

66

Time-dependent trajectoriesMolecular Dynamics

Coarse-grain MD simulation (350 ns) of Kv channel embedded in a lipid bilayerhighlighting the overall conformational rearrangement of the model during theclosing process [Treptow et al. J. Phys. Chem. B 112 (2008) 3277]

Coarse-grain models Uses (3)

77

Coarse-grain models Uses (4)Protein docking

Prediction of the configuration of molecular complexes

88

[Becue, A. Development of an original genetic algorithm method dedicated to complementarity studies between protein-protein and protein-nucleic acid macromolecular partners, PhD Thesis, FUNDP, 2004]

99

Coarse grain molecular descriptions :

- Faster calculations forconformational analysisdynamical properties

- Need of specific interaction potentials

II. Topological Features of 3D Scalar Fields

Molecular Electron Density (1)

Topology characterized by the number and type of critical points

)()(

)()( tpeakttpeakttpeaktpeak ρ

ρ∇

Δ−Δ

+Δ−= rr

[Leung et al., IEEE T. Pattern Anal. 22 (2000) 1396][Leherte et al., J. Phys. Chem. A 107 (2003) 9875]

t = 0.0 bohr2

Contours : 0.1, 0.5 e-/bohr3t = 1.5 bohr2

Contours : 0.1, 0.15 e-/bohr3

Gly-Tyr-Ser

Molecular Electrostatic Potential

)()(

)()( tpVttpV

ttptp ∇Δ−

Δ+Δ−= rr [Leung et al., IEEE T. Pattern

Anal. 22 (2000) 1396]

t = 0.0 bohr2, isoMEP: -0.1, 0.1 e-/bohr

t = 0.95 bohr2, isoMEP: -0.03, 0.03 e-/bohr

t = 1.35 bohr2, isoMEP: -0.03, 0.03 e-/bohr

β-Gly15

1313

CG descriptions from topological features ofsmoothed 3D scalar fields:

- Molecular Electron Density (PASA)CG = ED peaksMolecular decomposition into fragments

- Molecular Electrostatic Potential (Coulomb)CG = MEP peaks and pitsFragment description is possible (but not physically relevant)

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? ?1DWB.pdb 1WAY.pdb

Trypsin Inhibitors

[Martin et al., Do structurally similar molecules have similar biological activity ? J. Med. Chem. 45 (2002) 4350]

III. Molecular Similarity

molecular superposition/alignment through similarity degreeoptimization

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•• Molecular descriptorsMolecular descriptors1D properties (experimental or calculated): MW, volume, 1D properties (experimental or calculated): MW, volume, pKapKa, , logPlogP, …, …

2D “fingerprints”2D “fingerprints”:

3D surfaces or fields: molecular surfaces, MEP, ED, …3D surfaces or fields: molecular surfaces, MEP, ED, …

•• Type of molecular similarityType of molecular similarityStructural similarity (global or partial)Structural similarity (global or partial)

Geometrical/Shape similarity (“)Geometrical/Shape similarity (“)

Property SimilarityProperty Similarity

•• Similarity measure and index/degreeSimilarity measure and index/degree

Phenyl prim. Amine Amide Methyl (Ar) Carboxy (Ar)

Molecule A 1 1 1 1 0

Dice (Dice (Carbo),TanimotoCarbo),Tanimoto, , KulczinskiKulczinski, …, …

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NH2

OHNH

NH

O

O

NH

O

O

Superposition of small molecules using smoothed ED

1717

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0 2.5r (A)

S AB

kinetic @ 1.5

kinetic @ 0.0

∫= )()( ,,, rrr tBtAOverlapAB dZ ρρ

Similarity measures

∫= )( T )( ,,, rrr tBtAKineticAB dZ ρρ

Similarity indices

BBAA

ABCarboAB ZZ

ZS =,

ABBBAA

ABTanimotoAB ZZZ

ZS−+

=,

H C N

Objective function in a Monte Carlo/SA approach

[Leherte, J. Comp. Chem. 27 (2006) 1800]

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Literature case: superposition of DFKi on TurkeyOvoMucoid Inhibitor

ZOverlap – STanimoto @ t = 1.5 bohr2 RMSD = 14.0 ÅZKinetic – STanimoto @ t = 1.5 bohr2 RMSD = 0.7 ÅExpected (from PDB)

[Masek et al., Proteins 17 (1993) 193][Richards, Molecular Informatics, Beilstein Workshop (2002)]

TOMI

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Low-Resolution ED and Molecular Similarity:

- Less local solutions vs. atomic resolution

- Simple superposition algorithms

- Zkinetic seems to performs well due to its sensitivity to ED skeleton alignments(and type of atoms)

- Useful for superposing systems withdifferent sizes

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IV. Dynamics of ProteinsCoarse-Grained Elastic Network Models

LargeLarge--scale Motionsscale MotionsProtein = elastic network of atoms Cα

- Gaussian Network Model- Anisotropic Network Model (Normal Mode Analysis)

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Web servers

K. Suhre, Y.-H. Sanejouand, Nucleic Acids Res. 32 (2004) W610 ;http://www.igs.cnrs-mrs.fr/elnemo/

Z. W. Cao, Y. Xue, L. Y. Han et al., Nucleic Acids Res. 32 (2004) W679 ; http://ang.cz3.nus.edu.sg/cgi-bin/prog/norm.pl

L.-W. Yang, X. Liu, Ch. J. Jursa et al., Bioinformatics 21 (2005) 2978 ; http://ignm.ccbb.pitt.edu/

S. M. Hollup, G. Salensminde, N. Reuter, BMC Bioinformatics 6 (2005) 52 ; http://www.bioinfo.no/tools/normalmodes

E. Eyal, L.-W. Yang, I. Bahar, Bioinformatics 22 (2006) 2619 ; http://ignmtest.ccbb.pitt.edu/cgi-bin/anm/anm1.cgi

J. I. Garzó, J. Kovacs, R. Abagyan et al., Bioinformatics 23 (2007) 901 ; http://sbg.cib.csis.es/Software/DFprot

…

ElNémo

oANM

DFprot

WEBnm@

MoViES

iGNM

2222

2323[Hinsen,

PROTEINS 33 ( 1998) 417]HinsenHinsen

19981998

[Hinsen et al., Chem. Phys. 261 (2000) 25]

WEBnmWEBnm@@

[[GarzGarzóó et alet al., ., BioinformaticsBioinformatics 23 (2007) 901]23 (2007) 901]

DFPROTDFPROT

[Atilgan et al., Biophys. J. 80 (2001) 505]

StepStep functionfunctionrrc = 11.5 = 11.5 ÅÅ

ANMANM

[Bahar et al., Folding & Design 2 (1997) 173][Haliloglu et al., Phys. Rev. Lett. 79 (1997) 3090]

StepStep functionfunctionrrc = 7.3 = 7.3 ÅÅ

GNMGNM

∫= )()( ,,, rrr tjtitij d ρργ

Force constants [Leherte & Vercauteren, J. Comp. Chem. 29 (2008) 1472Comp. Phys. Commun. 179 (2008) 171]

28.3

2 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

ij

ij

rγ

nm 4.0 ; 128

nm 4.0 ;10 )39.26.8(6

5

≥

<−= −

ijij

ijijij

rr

rrγ

22 0.7/ijrij e−=γ

i, j = ED peaks

i, j = Cα

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Pancreatic Trypsin Inhibitor (5PTI.pdb)

58 aa residues3 disulfide bridges

[Brooks & Karplus, PNAS USA 80 (1983) 6571][Levitt et al., J. Mol. Biol. 181 (1985) 423]

[MacKerell et al. J. Phys. Chem. B 102 (1998) 3586]

2525

5

15

25

35

0 10 20 30 40 50Residue #

B (A

2 )

Experimental DFPROTγ ~ r-2

Corr = 0.816

peaks@1.4 /ANMγ = 1 ; rc = 11.5 ÅCorr = 0.804

Isotropic Displacement Parameters B <∆Ri.∆Ri>

Cα /ANMγ = 1 ; rc = 11.5Corr = 0.633

[Leherte & Vercauteren, J. Comp. Chem. 29 (2008) 1472, Comp. Phys. Commun. 179 (2008) 171]

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Low-Resolution ED and Protein Dynamics:

- Coarse-grain force constant ~ ED overlapintegral

- Justification of commonly used rc cut-offvalues

- Lowest limit for force constants smoothing of the B profile

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V. Electrostatics of Proteins

Determination of protein coarse-grain charges from smoothed electron density distribution functions and molecular electrostatic potentials[Leherte & Vercauteren, accepted in Computational Chemistry: New Research, NovaPublishers]

Construction of Gly7-AA-Gly7 in a β conformation withvarious AA rotamers

Conformation χ1 (°) χ2 (°) χ3 (°) χ4 (°) Occurrence (%)

Arg g-, t, g-, g- 300 180 300 300 9.5

g-, t, g-, t 300 180 300 180 11.9

g-, t, g+, t 300 180 60 180 12.2

g-, t, t, t 300 180 180 180 12.2

Asn t, Nt 180 0 11.1

t, Og- 180 300 21.3

t, Og+ 180 60 23.6

Identification of CG points obtained at t = 1.35 bohr2

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Lys

CG Charge fitting vs. unsmoothed MEP grid withconstraints:

- Gly15 charges except for the CG points located on the central AA- Total charge- Molecular dipole moment

Thr

2929

Application to KcsA channel – 388 AA (1BL8.pdb)

3030-350

-300

-250

-200

-150

-100

-50

0

50

-15 -10 -5 0 5 10 15 20 25 30

Distance vs . K3 (A)

MEP

(kca

l/mol

)

All-atom (5888)MEP peaks and pits (1494)ED peaks (494)

3131

Low-Resolution MEP and Protein Electrostatics:

- Design of AA CG templates

- Better approximation of all-atom MEP (to be confirmed by transferability tests)

- CG interaction potentials may becharacterized by steric centers that are different from electrostatic centers

[Leherte et al., in: “Quantum Theory of Atoms in Molecules - FromSolid State to DNA and Drug Design”, Eds C. F. Matta, R. J. Boyd, Wiley (2007)]