Bridging Structure and Function, Experiments and Computations. Ivet Bahar

Transcription

1 Day 2 Bridging Structure and Function, Experiments and Computations Ivet Bahar Department of 1 Computational and Systems Biology School of Medicine, University of Pittsburgh, Pittsburgh, PA 15260

2 Summary 1. Theory a. Gaussian Network Model (GNM) b. Anisotropic Network Model (ANM) c. Resources/Servers/Databases (ProDy, DynOmics) 2. Bridging Structure and Function a. Allosteric changes in structure b. Ensemble analysis using the ANM c. Perturbation Response Scanning (PRS) Sensors and Effectors d. Mechanical Stiffness 3. Bridging Sequence, Structure and Interactions a. System-environment: Membrane Proteins b. Sequence evolution and co-evolution c. Druggability simulations 2

3 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:

4 Allosteric changes in conformation Elastic Network Models are particularly useful for exploring the cooperative motions of large multimeric structures HIV Reverse Transcriptase (RT) Red: most mobile Blue: most constrained Comparison with experimental data shows that the functional movements are those predicted by the ANM to be intrinsically encoded by the structure 4

5 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 5

6 Fingers Induced Dynamics or Intrinsic Dynamics? Thumb RNase H 1HQE 1N6Q 1VRT Experiments Theory References: Bakan & Bahar (2009) PNAS 106,

7 Substates may be identified along soft modes S1 p 2 p 1 P1 P2 S3 S2 P1 7

8 Bacterial chaperonin GroEL: an allosteric machine 8

9 trans ring cis ring GroEL Allosteric Dynamics 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

10 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 ANM eigenvectors v 1, v 2, v 3,.v 3N-6, with respective frequencies proportional to k 1, k 2, k 3,. k 3N-6 (f) d = [Dx 1 Dy 1 Dz 1 Dz N ] T See... Z Yang, P Marek and I Bahar, PLoS Comp Biology

11 What is the overlap between computations and experiments? Correlation cosine with experimental d trans ring cis ring Correlation cosine between v 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

12 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

13 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

14 Correlation cosine of 0.75 ± 0.15 between one of the softest modes and the experimentally observed change in structure Significant decrease in RMSD between the endpoints upon moving along a single soft mode (out of 3N-6 modes) See... Bahar, Lezon, Yang and Eyal (2010) Annual Rev Biophys 39,

15 Summary 1. Theory a. Gaussian Network Model (GNM) b. Anisotropic Network Model (ANM) c. Resources/Servers/Databases (ProDy, DynOmics) 2. Bridging Structure and Function a. Allosteric changes in structure b. Ensemble analysis using the ANM c. Perturbation Response Scanning (PRS) Sensors and Effectors d. Mechanical Stiffness 3. Bridging Sequence, Structure and Interactions a. System-environment: Membrane Proteins b. Sequence evolution and co-evolution c. Druggability simulations 15

16 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 16

17 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) 17

18 RESEARCH ARTICLES Recognition Dynamics Up to Microseconds Revealed from an RDC-Derived Ubiquitin Ensemble in Solution Oliver F. Lange,, Jens Meiler, Helmut Grubmüller, Christian Griesinger, Bert L. de Groot The ensemble covers the complete structural heterogeneity observed in 46 ubiquitin crystal structures, mostly complexes with other proteins. Conformational selection, rather than induced-fit explains the molecular recognition dynamics of ubiquitin. A concerted mode accounts for molecular recognition heterogeneity Reference Lange et al. (2008) Science 320:

19 Ensembles of structures Structural changes accompanying substrate (protein) binding Structural changes induced by, or stabilized upon, ligand binding Ubiquitin 140 structures 1732 models 19

20 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 20

21 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

22 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

23 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 23

24 What is Ensemble Analysis? ANM analysis Select a representative structure (e.g. with minimal RMSD from others) Evaluate the ANM Hessian, or its inverse Theoretical (i.e. the ANM covariance matrix C) Decompose either H or C into a series of modes (3N-6 eigenvectors) Principal component analysis PCA Superimpose/align the structures Evaluate the covariance matrix Experimental (differences between individual coordinates and mean coordinates) Decompose it into a series of modes of covariance (3N-6 eigenvectors) 24

25 Global motions inferred from theory and experiments PCA of the ensemble of resolved structures ANM analysis of a single structure from the ensemble 25

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

27 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. 27

28 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 > 28

29 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 29

30 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,

31 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 r = 0.84 paths 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:

32 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 950,000+ 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,

33 ProDy: An Interactive Tool 33

34 Suite of tools Elastic Network Model (ANM/GNM) Analysis Principal component analysis of experimentally resolved structures Multiple Sequence Alignment Sequence conservation Correlated Mutation Computational Drug Discovery Binding Site Prediction Affinity Estimation A VMD plugin Visualization of collective motions Animations/movies 34

35 3 Suite of tools Modeling coupled protein-lipid dynamics Useful for membrane proteins Response to external forces Identification of mechanical stiffness ENM guided MD simulations Efficient sampling of energy landscape

36 Tutorials: ProDy & Structure Analysis Retrieving PDB Files BLAST-Searching the PDB Constructing Biomolecular Assemblies Determining functional motions Aligning and Comparing Structures Identifying Intermolecular Contacts 36

37 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 37

38 Caveats Low resolution approach No specific interactions Lack of atomic details Linear theory applicable near an energy minimum not a tool for structure prediction (could be used for refinement) 38

39 Hybrid methods combining MD simulations and ANM modes ANM-guided transition pathways Implemented in ProDy are: Co-MD for hybrid simulations EVOL for sequence analyses DRUGUI for druggability simulations (pre- and postprocessing coupled to NAMD) 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: Das A, Gur M, Cheng MH, Jo S, Bahar I, Roux B (2014) PLoS Comput Biol 10: e

40 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 40

41 PRS Perturbation-Response Scanning Sensors and Effectors of allosteric signals General, Liu, Blackburn, Mao, Gierasch & Bahar I (2014) ATPase subdomain IA is a mediator of interdomain allostery in Hsp70 molecular chaperones. PLoS Comp Bio. 10: e

42 GNM Basics - Linear theory Single spring F = k Dx E = ½ k (x x 0 ) 2 Dx = x - x 0 F = de/dx Network of springs (bead-and-spring model) F = g G DR V = ½ g DR T GDR DR T = (DR 1 DR 2 DR 3 DR N ) G = Kirchhoff matrix 42

43 Perturbation-response scanning (PRS) theory Linear theory F = g G DR perturbation g -1 G -1 F = DR response F 1 F 2 DR 1 g -1 G -1 DR 2 You can evaluate the response of the structure to any external force F N DR N Atilgan & Atilgan (2009) PLoS Comp Biol 5(10):e

44 Covariance matrix g -1 G -1 In NMA, the covariance matrix is given by C 3N = k B T H -1 C N = (3k B T/g) G -1 where k B is the Boltzmann constant, T is the absolute temperature and H is the (Hessian) matrix of the second derivatives of the potential. In the GNM, H is replaced by the Kirchhoff matrix gg. 44

45 Perturbation-response scanning (PRS) theory We replace g -1 G -1 on the lefthand side by (3k B T) -1 C: <DR 1. DR 1 > <DR 1. DR 2 > <DR 1.DR N > (3k B T) -1 <DR 2. DR 1 > <DR 2. DR 2 > F 1 F 2 <DR N.DR 1 > <DR N.DR N > F N The response is defined by the covariance matrix 45

46 Perturbation-response scanning (PRS) theory Start perturbation from residue 1, by applying a force F1 on node 1: <DR 1. DR 1 > <DR 1. DR 2 > <DR 1.DR N > (3k B T) -1 <DR 2. DR 1 > <DR 2. DR 2 > F 1 0 DS 11 DS 21 <DR N.DR 1 > <DR N.DR N > 0 DS N1 Due to perturbation of node 1 46

47 Perturbation-response scanning (PRS) theory Continue with the perturbation of residue 2, by applying a force F2 on node 2: (3k B T) -1 <DR 1. DR 1 > <DR 1. DR 2 > <DR 1.DR N > <DR 2. DR 1 > <DR 2. DR 2 > F 2 DS 12 DS 22 <DR N.DR 1 > <DR N.DR N > 0 DS N2 Due to perturbation of node 2 47

48 Perturbation-response scanning (PRS) theory Repeat with all nodes and organize in a matrix Response matrix S (3k B T) -1 <DR 1. DR 1 > <DR 1. DR 2 > <DR 1.DR N > <DR 2. DR 1 > <DR 2. DR 2 > F F 2 DS 11 DS 21 DS 12 DS 22 <DR N.DR 1 > <DR N.DR N > 0 0 DS N1 DS N2 48

49 Response matrix S = S 1,1 S 1,2 S 1,3 S 2,1 S 2,2 S 2,3 S 3,1 S 3,2 S 3,3 N N Response of residue 1 to perturbation at all other residues Strong response to Effectors all others residue 1 communicates effectively with all other residues. The row average is the effector propensity of residue 1 Division by diagonal element ensure the removal of the intrinsic effect of residue 1 Response of all residues to perturbation at residue 1; shows the influence of residue 1 on all others. Sensors May be reduced to a single number for each residue, by averaging out over the elements. The most influential residue serves as a sensor to efficiently send signals to all other residues S i,j = response of residue i to perturbation at residue j 49

50 Results from PRS analysis of HSP70 General, Liu, Blackburn, Mao, Gierasch & Bahar I (2014) ATPase subdomain IA is a mediator of interdomain allostery in Hsp70 molecular chaperones. PLoS Comp Bio. 10: e

51 Effector propensity (from PRS) Hitting time as receiver Effectors are efficient propagators of signals GNM 10 modes, cutoff=7.3 Å Small hit time efficient communication Chennubhotla & Bahar, PLoS Comp Bio,

52 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). 52

53 Eyal E, Bahar I Toward a Molecular Understanding of the Anisotropic Response of Proteins to External Forces: Insights from Elastic Network ModelsBiophys J (9):

54 The mechanical response of proteins Probed by AFM experiments Usually involves partial or total unfolding Depends on - the application points of tension - or the direction of deformation -The structural change is accommodated by the collective motions of the protein - If soft modes can accommodate the change, then the effective resistance to stress, or the effective mechanical stiffness of the protein is smaller. 54

55 Constructing a mechanical resistance map for the entire protein ANM permits us to calculate an effective stiffness/resistance against deformation, under uniaxial tension applied to residues i and j. The idea is simple: if i and j already undergo large distance fluctuations by virtue of the intrinsically accessible slow modes, the molecule is yielding. < kij > is the average force constant < kij > = S k d ij (k) λ k / S k d ij (k) where d ij (k) is the contribution of mode k to the change DR ij given by the projection of DR ij k) onto R ij0, i.e., d ij (k) = DR ij (k) cos(r ij0, DR ij k) ) 55

56 Information-Theoretic Methods Information theory and spectral graph methods, e.g. Markov transfer of signals Chennubhotla C, Bahar I (2007) Signal propagation in proteins and relation to equilibrium fluctuations PLoS Comput Biol 3, 17: Reconcile concepts/methods of IS/graph theory and physical sciences, applied to biomolecules 56

57 Markov propagation of signals P(t) = M P(0) P(t) is instantaneous distribution of information/energy Non stationary process local signal/perturbation at t = 0 Distribution/dissipation after k steps P(k) = M k P(0) Chennubhotla & Bahar, PLoS Comp Bio,

58 Affinity matrix A defines a priori probabilities a ij ~ affinity between residues i and j i a ij j aij = N ij /(N i N j ) 1/2 N ij = # of atom-atom contacts between i and j N i = # of atoms belonging to residue i N j = # of atoms belonging to residue j aij is equivalent to joint probability of j at a given step and i at the next step. A ij = a ij (1 - d ij ) 58

59 Transition probabilities defined by affinities II I i a ij j d j = S i a ij m ij = a ij /d j = probability of passage M = AD -1 from j to i; conditional probability of interaction with i, given residue j 59

60 Messengers/Paths S = - S i p i ln p i ATP binding sites are the highest entropy regions most effective propagation of signals to the entire molecule from ATP binding sites Centers of communication: E461, S463, V464, T30-K34 Red: highest entropy highest Communication ability Chennubhotla & Bahar (2006), Molecular Systems Biology. 60

61 Fluctuations vs communication Commute distance ~ <(DR ij ) 2 > Chennubhotla & Bahar, PLoS Comp Bio,

62 Commute times C(i,j) = H(i,j) + H(j, i) B W31 C 11.5 Å H48 I Å D K69 E H Å 12.9 Å See also N125 Nadler, Lafon, Kevrekidis & Coifman (2005) Diffusion Maps, Spectral Clustering and Eigenfunctions of Fokker-Planck Operators, NIPS 18; Coifman et al (2005) PNAS 102,

63 Commute distance (Å) Standard deviation (steps) Catalytic residues are fast and precise A Asp99 B His48 Tyr52 <Hitting time> (number of steps) Chennubhotla & Bahar, PLoS Comp Bio,

64 Information-Theoretic Methods IS/graph theory Relationship to Physical Quantitites Laplacian L, Affinity matrix A Information theory and spectral graph D A = methods, G di = degree of node I (diag element of D) e.g. Markov transfer of signals Markov transition matrix M = AD -1 Hitting time H(j, i) Rate matrix M-1 = AD -1 DD -1 = (A D)D -1 = - G D -1 Commute time C(i,j) C(i,j) ~ <(DRij 2 )> Reconcile concepts/methods of IS/graph theory and physical sciences, applied to biomolecules Chennubhotla C, Bahar I (2007) PLoS Comput Biol 3, 17:

65 Thank you! 65