Collective Dynamics of Biomolecules using ProDy & Elastic Network Models

Transcription

1 Collective Dynamics of Biomolecules using ProDy & Elastic Network Models Ivet Bahar Department of 1 Computational and Systems Biology School of Medicine, University of Pittsburgh, Pittsburgh, PA 15260

2 MMBioS Resources Eyal et al., Bioinformatics 2015 Li et al., Nucleic Acids Res 2016

3 MMBioS Resources Bakan et al., Bioinformatics 2011; 2014 Li et al Nucleic Acids Res 2016

4 NMWiz Cihan Kaya She (John) Zhang Dr. Ying Liu Dr. Timothy R Lezon Assistant Prof, DCSB, Pitt Reference: Drs. Ahmet Bakan and Anindita Dutta Bakan A, Meireles LM, Bahar I. (2011) ProDy: Protein dynamics inferred from theory and experiments Bioinformatics 27: Bakan, A., Dutta, A., Whenzi, M., Liu, Y., Chennubhotla, C., Lezon, T.R., & Bahar, I. (2014) Bioinformatics in press. Dr. Chakra Chennubhotla Assist Prof, DCSB, Pitt 4

5 ProDy References Bakan A,* Dutta A,* Mao W, Liu Y, Chennubhotla C, Lezon TR, Bahar I (2014) Evol and ProDy for Bridging Protein Sequence Evolution and Structural Dynamics Bioinformatics 30: Bakan A, Meireles LM, Bahar I (2011) ProDy: Protein dynamics inferred from theory and experiments Bioinformatics 27:

6 ProDy: Usage and dissemination statistics Date Releases Downloads 1 Visits 2 Unique 3 Pageviews 2 Countries 5 Nov 10 - Oct ,530 8,678 2,946 32, Nov 11 - Oct * 35,108 16,472 6,414 71, Nov 12 - Oct 13 8 * 87,909 19,888 8,145 86, Nov 13 - Oct 14 5 * 140,101 24,134 11, , Nov 14 - May 15 1* 68,230 15,941 8,479 66, June 15- June 16 5* 124,613 32,491 15, , June 16- June 17 31,374 16, , Total , ,978 68, , * Indicates software release made during the grant period. 1 Download statistics retrieved from PyPI ( using ( 2 Google Analytics ( was used to track: 3 Unique indicates number of unique visitors; 5 Country of origin for visits.

7 Usage in the last year Google Analytics June 1, 2016 June 1, 2017

8 Who? Where? June 1, 2016 June 1,

9 Tutorials Day 2 Day 1 Evol ProDy NMWiz Druggability

10 Workshop files on ProDy website 10

11 Representation of structure as a network Why network models? for large systems collective motions & long time processes beyond the capability of full atomic simulations to incorporate structural data in the models at multiple levels of resolution to take advantage of theories developed in other disciplines: polymer physics, graph theory, spectral graph methods, etc. 11

12 Proteins are not static: They move, breath, work, dance, interact with each other Local motions

13 Proteins are not static: They move, breath, work, dance, interact with each other Global motions

14 Many proteins are molecular machines And mechanical properties become more important in complexes/assemblies STMV dynamics (Zheng Yang)

15 Each structure encodes a unique dynamics Structure Dynamics Function Signaling dynamics of AMPARs and NMDARs domain/subunit motions Concerted movements of signaling molecules DuttaA, Krieger J, Lee JY, Garcia-Nafria J, Greger IH, Bahar I (2015) Cooperative Dynamics of Intact AMPA and NMDA Glutamate Receptors: Similarities and Subfamily-Specific DifferencesStructure 23:

16 13nm Spatio-temporal scale/resolution Information transfer GOAL: TO GENERATE DATA FOR MESOSCOPIC SCALE Developing integrated methodology to enable information transfer across scales Microphysiological simulations to subcellar events Cell/Tissue: Images/circuits (Cell Organizer, SLML & VVFS) Subcellular: Spatial/network (MCELL & BioNetGen) from molecules Molecular modeling & Sim (ENM, PGM, WE) Analytical methods & Critical assessment from 6 x 6 x 5 μm 3 sample of adult rat hippocampal stratum radiatum neuropil 16

17 Spatio-temporal scale/resolution Spatio-temporal scale/resolution Information transfer Developing integrated methodology for complex systems dynamics, to enable information transfer across scales Coarse-grained approaches Elastic Network Models Subcellular: Spatial/network (MCELL & BioNetGen) Molecular modeling & Sim (ENM, PGM, WE) Analytical methods & Critical assessment Subcellular: Spatial/network (MCELL & BioNetGen) Molecular simulations Accelerated MD, Brownian simulations Analytical methods & Critical assessment 17

18 Length scales (m) Each structure encodes a unique dynamics 10-7 Structure X-ray Dynamics Function 10-8 Cooperative machinery 10-9 domain/subunit motions loop motions sidechain motions NMR bond vibrations time scales fs ps ns ms ms s QC/MM atomic simulations Coarse-grained computations 18

19 Summary 1. Theory a. Gaussian Network Model (GNM) b. Anisotropic Network Model (ANM) c. Resources/Servers/Databases (ProDy, DynOmics) 2. Allosteric Changes in Structure 3. Ensemble analysis. Experiments vs Predictions Adaptability/evolution 4. Recent Extensions and Applications a. Membrane Proteins b. AMPA Receptor c. Chromatin 19

20 Two elastic network models: Gaussian Network Model (GNM) o Li H, Chang YY, Yang LW, Bahar I (2016) ignm 2.0: the Gaussian network model database for bimolecular structural dynamics Nucleic Acids Res 44: D o Bahar I, Atilgan AR, Erman B (1997) Direct evaluation of thermal fluctuations in protein Folding & Design 2: Anisotropic Network Model (ANM) o Eyal E, Lum G, Bahar I (2015) The Anisotropic Network Model web server at 2015 (ANM 2.0) Bioinformatics 31: o Atilgan AR, Durrell SR, Jernigan RL, Demirel MC, Keskin O, Bahar I (2001) Anisotropy of fluctuation dynamics of proteins with an elastic network model Biophys J 80:

21 Physics-based approach Statistical Mechanics of Polymers Theory of Rubber Elasticity Elastic Network Model for Proteins Paul J. Flory ( ) Nobel Prize in Chemistry 1974 And Pearson (1976), Eichinger (1980), Klockzkowski, Erman & Mark (1989)

22 Collective motions A R ij j B i Eigenvalue decomposition of Kirchhoff/Hessian matrix mode 1 mode 2 GNM: Bahar et al Fold & Des 1996; Haliloglu et al. Phys Rev Lett1997 ANM: Doruker et al. Proteins 2000; Atilgan et al, Biophys J 2001 Based on theory of elasticity for polymer networks by Flory, 1976 Bahar, Lezon, Yang & Eyal (2010) Global Dynamics of Proteins: Bridging Between Structure and Function Annu Rev Biophys 39: 23-42

23 Gaussian Network Model (GNM) Each node represents a residue Residue positions, Ri, identified by a-carbons coordinates R k k Springs connect residues located within a cutoff distance (e.g., 10 Å) Nodes are subject to Gaussian fluctuations DR i Inter-residue distances R ij also undergo Gaussian fluctuations DR ij = DR j - DR i Fluctuations in residue positions Bahar, Atilgan & Erman, Fold & Des

24 Gaussian Network Model (GNM) Fluctuation vector: DR 1 R k k DR = DR 2 DR 3 DR DR N Fluctuations in residue positions Bahar, Atilgan & Erman, Fold & Des

25 Z R ij (k) DR i (k) - d ij /2 DR j (k) R i 0 R ij 0 R j 0 d ij /2 Y X DR ij = DR j - DR i

26 Fluctuation with respect to starting structure R(0) Instantaneous deviation for atom i DR i (t k ) = R i (t k ) - R i (0) Under equilibrium conditions: Average displacement from equilibrium: < DR i (t k )> = 0 But the mean-square fluctuation (MSF), < (DR i (t k )) 2 > 0 5/30/2017

27 Rouse model for polymers Classical bead-and-spring model Kirchhoff matrix = DR 12 = R 12 - R 0 Force constant 12 V tot = (g/2) [ (DR 12 ) 2 + (DR 23 ) (DR N-1,N ) 2 ] = (g/2) [ (DR 2 DR 1 ) 2 + (DR 3 DR 2 )

28 Rouse model for polymers Kirchhoff matrix = Force constant V tot = (g/2) [ (DR 12 ) 2 + (DR 23 ) (DR N-1,N ) 2 ] = (g/2) [ (DR 2 DR 1 ) 2 + (DR 3 DR 2 )

29 Rouse model for polymers Fluctuation vector Kirchhoff matrix (g/2) [DR 1 DR 2 DR 3. DR N ] Force constant = DR 1 DR 2 DR 3 DR V tot = (g/2) DR T DR N = V tot = (g/2) [ (DR 12 ) 2 + (DR 23 ) (DR N-1,N ) 2 ] = (g/2) [ (DR 2 DR 1 ) 2 + (DR 3 DR 2 )

30 Kirchhoff matrix for inter-residue contacts For a protein of N residues 1 N 1 = ik= ii = - Sk ik -1 if rik < rcut 0 if rik > rcut V tot = (g/2) DR T DR N provides a complete description of contact topology! 30

31 Statistical mechanical averages For a protein of N residues D V k T D D D B R. R Z R. / (1/ ) ( R ) e d D R i j N i j (3 k B T / g ) 1 ij provides a complete description of contact topology! 31

32 Kirchhoff matrix determines the mean-square fluctuations [ -1 ] ii ~ <(DR i ) 2 > And cross-correlations between residue motions [ -1 ] ij ~ <(DR i.dr j )>

33 Comparison with B factors X-ray crystallographic structures deposited in the PDB also report the B-factors (Debye- Waller factors) for each atom, in addition to atomic coordinates B-factors scale with mean-square fluctuations (MSFs), i.e. for atom i, B i = [8p 2 /3] <(DR i ) 2 > How do residue MSFs compare with the B-factors? 33

34 Output from DynOmics 1vaa Example: 1vaa PDB title: CRYSTAL STRUCTURES OF TWO VIRAL PEPTIDES IN COMPLEX WITH MURINE MHC CLASS I H-2KB 34

35 Output from DynOmics 1vaa 35

36 B-factors are affected by crystal contacts Two X-ray structures for a designed sugar-binding protein LKAMG

37 B-factors are affected by crystal contacts Particular loop motions are curtailed by intermolecular contacts in the crystal environment causing a discrepancy between theory and experiments FOR MORE INFO... Liu, Koharudin, Gronenborn & Bahar (2009) Proteins 77,

38 Agreement between theory and experiments upon inclusion of crystal lattice effects into the GNM theory Crystal contacts Particular loop motions are curtailed by intermolecular contacts in the crystal environment causing a discrepancy between theory and experiments FOR MORE INFO... Liu, Koharudin, Gronenborn & Bahar (2009) Proteins 77,

39 C. Xu, D. Tobi and I. Bahar (2003) J. Mol. Biol. 2003, Application to hemoglobin 50 theoretical B-factor a-subunit -subunit experimental B-factor Intradimer cooperativity Symmetry rule (Yuan et al. JMB 2002; Ackers et al. PNAS 2002.) residue number B- factors Comparison with experiments

40 Cross-correlations - Provide information on the relative movements of pairs of residues - Purely orientational correlations (correlation cosines) are obtained by normalizing cross-correlations as Fully anticorrelated <(DR i.dr j )> -1 1 [<(DR i ) 2 > <(DR i ) 2 >] 1/2 Fully correlated 40

41 Output from ignm 1cot Li, Chang, Yang and Bahar (2016) Nucleic Acids Res 44: D

42 Output from DynOmics - ENM 1vaa Li et al (2017) Nucleic Acids Res 44: D

43 Cross-Correlations may be organized in a Covariance Matrix C -1 ~ C Covariance scales with the inverse of the Kirchhoff matrix. The proportionality constant is 3kT/g 43

44 Covariance matrix (NxN) C = DR 1. DR 1 > DR 1. DR 2 > DR 1. DR N > DR 2. DR 1 > DR 2. DR 2 > = DR DR T DR N. DR 1 > DR N. DR N > DR = N-dim vector of instantaneous fluctuations DR i for all residues (1 i N) < DR 1. DR 1 > = ms fluctuation of site 1 averaged over all m snapshots.

45 Collective Motions Encoded by the Structure: Normal Modes 45

46 Several modes contribute to dynamics ΔR Contribution of mode k i ΔR j [ΔRi ΔR j ] k k ΔR ΔR (3k T / g ) Γ i j B 1 ij Contribution of mode k [ΔR i 1 ΔR j ] k (3k BT / g ) lk u k u T k ij FOR MORE INFO... expressed in terms of kth eigenvalue lk and kth eigenvector uk of Bahar et al. (1998) Phys Rev Lett. 80,

47 Several modes contribute to dynamics Slowest (global) modes (most collective and softest) function Fastest (local) modes (at highest packing density regions) stability The first mode selects the easiest collective motion FOR MORE INFO... Bahar et al. (1998) Phys Rev Lett. 80,

48 Output from DynOmics 1vaa 48

49 Output from DynOmics 1vaa 49

50 Summary - Gaussian network model (GNM) [ΔR 1 i ΔRi ] k (3k BT / g ) lk u k u T k ii Kirchhoff matrix for inter-residue contacts 1 N 1 Contact: Rij < 10Å = Several modes of motion contribute to dynamics N MSF of residue i = <(DRi) 2 > 2 ( DRi) ( 3 k B T / g ) 1 ii

51 Recipe (GNM) Obtain the coordinates of network nodes from the PDB Write the corresponding Kirchhoff matrix Eigenvalue decomposition of yields the eigenvalues l 1, l 2, l 3,.., l N-1 (and l 0 = 0) and eigenvectors u 1, u 2, u 3,..u N-1 (and u 0 ) Properties the eigenvalues scale with the frequency squared (l i ~ w i2 ) eigenvector u k is an N-dim vectors the i th element of u k represents the displacement of node i in mode k the eigenvectors are normalized, i.e. u k u k = 1 for all k as such, the squared elements of u k represent the mobility distribution dynamics results from the superposition of all modes l k -1/2 serves as the weight of u k low frequency modes have high weights

52 Database of GNM results ignm.ccbb.pitt.edu Li, Chang, Yang and Bahar (2016) Nucleic Acids Res 44: D

53 Why use ignm2.0? Easy access to precomputed results for 95% of the PDB including the largest structures beyond the scope of MD protein-dna/rna complexes biological assemblies (intact, biologically functional structures) Easy to understand, visualize, make functional inferences for any structure 13.9% of the structures in the ignm 2.0 (14,899 out of 107,201) contain >10 3 nodes The biological assembly of 39,505 PDB structures is different from the default structure reported in the PDBs (as asymmetric unit) 53

54 Collective motions are functional Collectivity (2D) for a given mode k is a measure of the degree of cooperativity (between residues) in that mode, defined as (*) Information entropy associated with residue fluctuations in mode k where, k is the mode number and i is the residue index. A larger collectivity value refers to a more distributive mode and vice versa. Usually soft modes are highly collective. (*) Brüschweiler R. Collective protein dynamics and nuclear spin relaxation. J. Chem. Phys. 1995;102:

55 Energy Anisotropic Network Model (ANM) ANM mode 1 (u 1 ) low-frequency ~ global modes ~λ 1 Mode 2 Displacement ~λ 2 H H = g Γ ( ij) ij 3N 6 l i 1 i X ij X Y X ij ui ui T X 0 ( ij ij ij ij ij ij R 2 ij Zij X ij ZijYij ZijZij ij Y Y Y ij X Y ij Z Z ij Mode 20 l 1 < λ 2 < λ 3 < ~λ 20 higher-frequency Doruker et al. (2000) Proteins; Atilgan AR et al. (2001) Biophys J.; Eyal et al. (2006) Bioinformatics 22,

56 3N x 3N Hessian of ANM replaces the NxN Kirchhoff matrix of GNM to yield mode shapes in 3N-d space

57 ANM covariance matrix (3Nx3N) C 3N = C 11 C 21 C 13 C 1N C 12 C 22 C N1 C NN 3N x 3N <DX 1 DX 2 > DX 1 DY 2 > DX 1 DZ 2 > DY 1 DX 2 > DY 1 DY 2 > DY 1 DZ 2 > DZ 1 DX 2 > DZ 1 DY 2 > DZ 1 DZ 2 > 5/30/2017

58 ANM server 58

59 Output from ANM server 1cot 59

60 Softest modes are functional open Experiments closed Theory E coli adenylate kinase dynamics: comparison of elastic network model modes with 15 N- NMR relaxation data. Temiz NA, Meirovitch E, Bahar I. (2004) Proteins 57, 468. T R transition of Hb intrinsically favored by global dynamics Xu, Tobi & Bahar (2003) J. Mol. Biol. 333, 153; tense (T) relaxed (R)

61 Li et al (2017) Nucleic Acids Research (e-pub on May 3). enm.pitt.edu

62 New features sensors effectors sensors and effectors first passage times for signaling mechanically functional sites effect of oligomerization coupling to membrane Perturbation response map Dynamics of Structural Proteomics and Beyond Li et al (2017) Nucleic Acids Research (e-pub on May 3).

63 Plan 1. Theory a. Gaussian Network Model (GNM) b. Anisotropic Network Model (ANM) c. Resources/Servers/Databases (ProDy, DynOmics etc) 2. Allosteric Changes in Structure 3. Ensemble analysis. Experiments vs Predictions Adaptability/evolution 4. Recent Extensions and Applications a. Membrane Proteins b. AMPA Receptors c. Chromatin 63

64 Allosteric changes in conformation Elastic Network Models are particularly useful for exploring the cooperative motions of large multimeric structures Comparison with experimental data shows that the functional movements are those predicted by the ANM to be intrinsically encoded by the structure

65 Proteins exploit pre-existing soft modes for their interactions Structural changes involved in protein binding correlate with intrinsic motions in the unbound state maltodextrin binding protein Unbound/Bound Dror Tobi & I. Bahar (2005) PNAS 102:

66 Substates may be identified along soft modes S1 p 2 p 1 P1 P2 S3 S2 P1 Hybrid ANM/MD methods include atomic details and specificity

67 trans ring cis ring Allosteric dynamics of GroEL Passage between the R and T states (c) R T R R (d) (f) See... Z Yang, P Marek and I Bahar, PLoS Comp Biology 2009

68 What is the overlap between computations and experiments? Computations ANM yields a series of 3N dimensional deformation vectors T Experiments (c) Mode 1 (slowest mode) Mode 2 Mode 3. Mode 3N-6 (fastest mode) (d) Given by eigenvectors u 1, u 2, u 3,.u 3N-6, with respective frequencies of l 1, l 2, l 3,. l 3N-6 (f) d = [Dx 1 Dy 1 Dz 1 Dz N ] T See... Z Yang, P Marek and I Bahar, PLoS Comp Biology 2009

69 Correlation cosine with experimental d trans ring cis ring What is the overlap between computations and experiments? Correlation cosine between u k and d (c) R T R (d) Mode index, k d = [Dx 1 Dy 1 Dz 1 Dz N ] T (f) See... Z Yang, P Marek and I Bahar, PLoS Comp Biology 2009

70 Correlation cosine with experimental d trans ring cis ring The softest mode enables the passage R T (with a correlation of 0.81) (c) R T R (d) Mode index, k d = [Dx 1 Dy 1 Dz 1 Dz N ] T (f) See... Z Yang, P Marek and I Bahar, PLoS Comp Biology 2009

71 Mutations may stabilize conformers along soft modes which may be impair function E461 mutant is a deformed structure along mode 1 E461K mutation causes disruption of inter-ring transfer of ATP-induced signal (Sewell et al NSB 2004) Yang et al. Mol Biosyst 2008

72 Plan 1. Theory a. Gaussian Network Model (GNM) b. Anisotropic Network Model (ANM) c. Resources/Servers/Databases (ProDy, DynOmics etc) 2. Allosteric Changes in Structure 3. Ensemble analysis. Experiments vs Predictions Adaptability/evolution 4. Recent Extensions and Applications a. Membrane Proteins b. AMPA Receptors c. Chromatin 72

73 A better comparison: Consider more than 2 end points for a given structure, but all the known structures for a given protein, or the structurally resolved Ensemble of structures 73

74 Dynamics inferred from known structures Comparison of static structures available in the PDB for the same protein in different form has been widely used is an indirect method of inferring dynamics. Bahar et al. J. Mol. Biol. 285, 1023, Different structures resolved for HIV-1 reverse transcriptase (RT)

75 Ensembles of structures Structural changes accompanying substrate (protein) binding Structural changes induced by, or stabilized upon, ligand binding Ubiquitin 140 structures 1732 models

76 Ensembles of structures Structural changes accompanying substrate (protein) binding Structural changes induced by, or stabilized upon, ligand binding p38 MAP kinase (182 structures) p38 inhibitors Ubiquitin 140 structures 1732 models

77 Ensembles of structures Structural changes accompanying substrate (protein) binding Structural changes induced by, or stabilized upon, ligand binding Alternative conformations sampled during allosteric cycles Yang et al. PLoS Comp Biol 2009

78 Ensembles of structures Structural changes accompanying substrate (protein) binding Structural changes induced by, or stabilized upon, ligand binding Alternative conformations sampled during allosteric cycles Yang et al. PLoS Comp Biol 2009

79 Correlation cosine with experimental d trans ring cis ring What is the overlap between computations and experiments? Correlation cosine between u k and d (c) R T R (d) Mode index, k d = [Dx 1 Dy 1 Dz 1 Dz N ] T (f) See... Z Yang, P Marek and I Bahar, PLoS Comp Biology 2009

80 Correlation cosine with experimental d trans ring cis ring The softest mode enables the passage R T (with a correlation of 0.81) (c) R T R (d) Mode index, k d = [Dx 1 Dy 1 Dz 1 Dz N ] T (f) See... Z Yang, P Marek and I Bahar, PLoS Comp Biology 2009

81 Global motions inferred from theory and experiments PCA of the ensemble of resolved structures ANM analysis of a single structure from the ensemble

82 Global motions inferred from theory and experiments Reference: Bakan & Bahar (2009) PNAS 106,

83 What is Ensemble Analysis? Input: An ensemble of structures for a given protein NMR models (~40) X-ray structures resolved under different conditions (ligand-bound/unbound, different stages of molecular machinery or transport cycle MD snapshots/frames Principal component analysis Output: Principal modes of conformational variations/differences between NMR models rearrangements/changes under different functional states dynamics/fluctuations observed in simulations 83

84 What is Ensemble Analysis? Method: Superimpose of the structures Evaluate the covariance matrix (differences between individual coordinates and mean coordinates) Decompose it into a series of modes of covariance (3N-6 eigenvectors) Principal component analysis Output: Principal modes of conformational variations/differences between NMR models rearrangements/changes under different functional states dynamics/fluctuations observed in simulations 84

85 Covariance matrix (NxN) C = DR 1. DR 1 > DR 1. DR 2 > DR 1. DR N > DR 2. DR 1 > DR 2. DR 2 > = DR DR T DR N. DR 1 > DR N. DR N > DR = N-dim vector of instantaneous fluctuations DR i for all residues (1 i N) < DR 1. DR 1 > = ms fluctuation of site 1 averaged over all m snapshots.

86 Covariance matrix (3Nx3N) C 11 C 21 C 13 C 1N C 12 C 22 C 3N = C N1 C NN 3N x 3N <DX 1 DX 2 > DX 1 DY 2 > DX 1 DZ 2 > DY 1 DX 2 > DY 1 DY 2 > DY 1 DZ 2 > DZ 1 DX 2 > DZ 1 DY 2 > DZ 1 DZ 2 > 5/30/2017

87 Principal Component Analysis (PCA) D D D D D D D D D D D D D D D D D D j i j i j i j i j i j i j i j i j i ij z z y z x z z y y y x y z x y x x x ) ( C N i i T 3 1 PSP C p i p it PC1 (f1 = 47%) NNRTI bound Apo DNA/RNA

88 ANM 2 (Å) Fingers Induced Dynamics or Intrinsic Dynamics? Thumb RNase H 1HQE 1N6Q 1VRT r = 0.99 Experiments Theory References: PC1 (Å) Bakan & Bahar (2009) PNAS 106,

89 ANM 2 (Å) Fingers Soft modes enable functional movements Thumb RNase H 1HQE 1N6Q 1VRT r = 0.99 Experiments Theory References: PC1 (Å) Bakan & Bahar (2009) PNAS 106,

90 p38 MAP kinase ANM 3 (Å) CaM-MLCK ANM 1 (Å) Experimental structures (for a given protein) are mainly variants along soft modes Pre-existing paths r = 0.84 PC1 ANM1 C-ter MLCK N-ter NMR model (160) PC1 (Å) B N-lobe C-lobe r = 0.95 PC1 ANM3 Unbound (3) +Inhibitor (56) +Protein (5) +Glucoside (10) PC1 (Å) Meireles L, Gur M, Bakan A, Bahar I (2011) Pre-existing soft modes of motion uniquely defined by native contact topology facilitate ligand binding to proteins Protein Science 20:

91 Theoretical Modes for exploring conformational space Experiment/Theory Overlap table User inputs a protein sequence p38 ensemble (PCA) >1A9U:A PDBID CHAIN GSSHHHHHHSSGLVPRGSHMSQER PTFYRQELNKTIWEVPERYQNLSPV GSGAYGSVCAAFDTKTGLRVAVKK LSRPFQSIIHAKRTYRELRLLKHMKH ENVIGLLDVFT... Experimental Modes identifies, retrieves, aligns, and analyzes (PCA) structures that match the input sequence p38 network model (ANM) User can compare experimental and theoretical models ANM 500,000+ downloads User can sample an ensemble of conformations along ANM modes for docking simulations ProDy-ANM sampling of conformational space is more complete than that of MD MD Source Bakan & Bahar, PSB 2011,

92 Major advantages of ProDy: Simplicity Visualizing the global dynamics Applicability to large systems Assessing cooperative motions Efficiency immediate results Relevance to observables, to functional mechanisms & allostery 92

93 Disadvantages Low resolution approach No specific interactions Lack of atomic details Linear theory applicable near energy minimum Requires structural data not a tool for structure prediction 93

94 Co-MD: Guiding MD simulations by ANM modes ANM-guided transition pathways Isin B, Schulten K, Tajkhorshid E, Bahar I (2008) Biophysical J 95: Yang Z, Májek P, Bahar I (2009) PLoS Comput Biol 5: e Gur M, Madura JD, Bahar I (2013) Biophys J 105: Dr. Mert Gur Das A, Gur M, Cheng MH, Jo S, Bahar I, Roux B (2014) PLoS Comput Biol 10: e comd trajectories proceed along the minima of free energy landscape 94

95 Session I: Plotting <(DR i ) 2 > and contributions of selected modes from prody import * from pylab import * anm = calcanm('1cot', selstr='calpha') anm, cot = calcanm('1cot', selstr='calpha') anm cot figure() showprotein(cot) Application to cytochrome c PDB: 1cot A protein of 121 residues figure() showsqflucts(anm) figure() showsqflucts(anm[:10]) figure() showsqflucts(anm[:10], label='10 modes') cmd ipython 95

96 Session 2: Viewing color-coded animations of individual modes writenmd('cot_anm.nmd', anm, cot) Start VMD select Extensions Analysis Normal Mode Wizard Select Load NMD File 96

97 Session 3: Cross-correlations <(DR i.dr j )> between fluctuations cross_corr = calccrosscorr? cross_corr = calccrosscorr(anm[0]) figure() showcrosscorr(anm[0])

98 Session 4: Viewing cross-correlations using VMD writeheatmap('anm_cross1.hm', cross_corr) VMD Load file Select cot_anm.nmd (from your local folder) Load HeatMap open anm_cross1.hm (from your local folder) 98

99 Support from NIGMS, NLM, NIDDK & NIAID Acknowledgment Dr. Lee-Wei Yang Assoc Prof, T singhua U, T aiwan Dr. Ahmet Bakan Kabbage, Inc. Dr. Ying Liu Google, Inc Dr. Tim Lezon Comp & Systems Biol, U of Pittsburgh Anindita Dutta Agilent Technologies Dr. Eran Eyal Cancer Research Institute Sheba Medical Center, Israel Cihan Kaya Dr. James Krieger Dr. Karolina Mikulska-Dr. Hongchun Li Ruminska Dr. JiYoung Lee She (John)Zhang