etude de systèmes moléculaires complexes développement d ... · [leherte et al., in: “quantum...
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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)
1414
? ?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
1515
•• 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, …, …
1616
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
1919
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
2020
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)
2121
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
2424
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
[email protected] /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]
2626
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
2727
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
2828
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)]