Computational Molecular Modeling

Transcription

1 Computational Molecular Modeling & Structural Bioinformatics Lecture 5: Protein-Protein Interactions (Molecular Recognition) Chandrajit Bajaj University of Texas at Austin 2012

2 Structural Analysis of Molecular Function Computational Problems Binding Affinities Energy Minimization Forward Dynamics Techniques nfft, KiFMM for fast summations Fast Dynamic Neighborhood Queries Docking Tiling Challenges Protein Flexibility Protein Folding, Rotamer Packing Spontaneous Assembly University of Texas at Austin 2012

3 Thermodynamic Free Energy: Empirical Model Covalent Bonds Dispersion Hydrogen Bonds Electrostatic Hydrophobic E = E mm + E sol TS E sol = E area + E vol + E disp + E pol : covalent bond variation bonded : valence angle variation : torsion angle variation nonbonded : Lennard-Jones parameters : distance between atoms : atomic charge Generalized Born E pol E pol Poisson Boltzmann University of Texas at Austin : molecular surface 2012

4 Binding Affinity Measure Equilibrium Dissociation constant defined by: K d = [R][L] [RL] Ligand concentration Receptor concentration Complex concentration Equilibrium Dissociation constant is related to free energy through: K d = exp ΔG E kt Minimum Binding free energy Boltzmann s constant Temperature University of Texas at Austin 2012

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6 Predicting Molecular Recognition : Conformational Docking with Minimum Binding Free Energy Given two molecules, search for the best rela5ve transforma5on and rela5ve conforma5on that yields a complex with the minimum binding free energy. Docking Search is based on an adaptively sampled Search space (Translation + Rotation + Flexibility) Energetics Docking Score [Bajaj, et al, TCBB 2008 ] [Chowdhury, et al 2011] University of Texas at Austin 2012

7 The Energe5c SCORING in Protein- Protein Docking Major components Shape complementarity: Lennard- Jones poten5al ( ΔE vdw ) AFrac5on between atoms Repulsion due to steric clashes Curvature complementarity Electrosta5c interac5ons Long range ( ΔE elec ) Short range: Hydrogen bonds Desolva5on free energy ( ΔE sol ) Displacing water from interface Hydrophobic patches Dispersion & Polariza5on Calmodulin closed and open ( 1CLL.PDB ) Pep5de For flexible proteins Calmodulin complexed with pep5de Energy change due to conforma5onal changes ( 2BBM.PDB ) University of Texas at Austin 2012

8 Modeling Flexibility Conformational changes occur due to changes in torsional angles: φ, ψ and χ hinge-type bending and shearing movements Conformational changes in Calmodulin: open ( 1CLL.PDB ) closed ( 2BBM.PDB ) 2012

9 Affinity Func5ons I: Shape Complementarity ( ΔE vdw ) [ Wang 91, Katchalski- Katzir et al. 92, Chen et al. 03 ] To maximize skin- skin overlaps and minimize core- core overlaps assign posi5ve real weights to skin atoms assign posi5ve imaginary weights to core atoms Let A denote molecule A with the pseudo skin atoms. For molecule P {A, B} with M P atoms, affinity func5on: where, with β = 2.3. University of Texas at Austin 2012

10 Docking with Shape Complementarity Affini5es ( ΔE vdw ) For rota5on r and transla5on t of molecule B, the interac5on score, Max t,r Non-Convex Optimization over Rigid Body Motion : = skin- skin overlap score core- core overlap score = skin- core overlap score University of Texas at Austin 2012

11 Affinity Based Rigid Body Scoring Op5miza5on University of Texas at Austin 2012

12 Affinity Based Scoring Op5miza5on University of Texas at Austin 2012

13 Transla5onal Search using FFT (alterna5vely nfft) M A atoms M B atoms rotate discre5ze discre5ze Forward FFT mul5ply frequency maps Forward FFT complex conjugate Inverse FFT University of Texas at Austin 2012

14 F 2 Dock: Search & Scoring START INPUT MOLECULES A & B UNIFORMLY DISTRIBUTED EULER ANGLES NEXT ROTATION R SAMPLE ROTATION SPACE FIRST ROTATION R Q RETAINS ONLY THE TOP 2000 SCORES ACROSS ALL ROTATIONS ROTATE B TO B R SCORE TRANSLATIONS OF B R W.R.T. A USING FFT TOP 1-5 TRANSLATIONS ( T ) AFFINITY FUNCTIONS SHAPE COMPLEMENTARITY ELECTROSTATICS & CHARGE COMPLEMENTARITY HYDROPHOBICITY / INTERFACE PROPENSITY H- BOND CORRECTION PHASE I ( F 2 Dock ) PUSH EACH R, T, S INTO PRIORITY QUEUE Q ( S = SCORE OF THE POSE ) YES MORE ROTATIONS? FILTERS PROXIMITY CLUSTERING #CLASHES LENNARD- JONES POTENTIAL HYDROPHOBICITY / INTERFACE PROPENSITY INTERFACE AREA ANTIBODY CONTACT GLYCINE RICHNESS INTERFACE CONTACT PREFERENCES NO PENALIZE POTENTIAL FALSE POSITIVES IN Q BASED ON VARIOUS FILTERS RERANK THE DOCKING POSES IN Q BASED ON CHANGE IN SOLVATION ENERGY OUTPUT THE RERANKED DOCKING POSES R, T PHASE II ( GB- rerank ) END 2012

15 F 2 - Dock s Shape Complementarity ( ΔE vdw ) University of Texas at Austin 2012

16 F 2 - Dock s Shape Complementarity Func5on: Weights Assigned to Skin Atoms of ( Sta5c ) Molecule A Recall that the centers of A s skin atoms are at a constant distance d from its van der Waal s surface S. Let s enlarge S by d so that it passes through the skin atom centers, and let V be the volume enclosed by it. Let B k be a ball of radius δ at the center of atom k, and. Define, Weight assigned to skin atom k of molecule A, We approximate ρ( k ) from a 3D grid embedding molecule A and its grown skin layer. University of Texas at Austin 2011

17 F 2 - Dock s Shape Complementarity Func5on: Weights Assigned to Core Atoms of ( Sta5c ) Molecule A Weight assigned to core atom k of molecule A,, where, j is the layer containing atom k, and α 1 is a constant. University of Texas at Austin 2012

18 F 2 - Dock s Shape Complementarity Func5on: Weights Assigned to Atoms of ( Moving ) Molecule B layer 2 layer 3 layer 1 Weight assigned to atom k of molecule B, University of Texas at Austin 2012

19 F 2 - Dock s Shape Complementarity ( ΔE vdw ) Let, w ss = reward for skin- skin overlap w cc = penalty for core- core overlap w sc = reward/penalty for skin- core overlap Weight assigned to atom k,. Affinity func5on,, where, with β = 2.3. Overall interac5on score, where, University of Texas at Austin 2012

20 Let, w E = weight for electrosta5c interac5on Affinity func5ons for molecules A and B: Electrosta5cs Complementarity ( ΔE elec ) ( Gabb et al. 97 ) Each charge is treated as a Gaussian ball of constant radius. Overall interac5on score, where, University of Texas at Austin 2012

21 Hydrophobicity Similarity Let, w b = reward for hydrophobic- hydrophobic interac5on w l = penalty for hydrophilic- hydrophilic interac5on w bl = reward/penalty for hydrophobic- hydrophilic interac5on Weight assigned to each atom is, where Overall interac5on score, University of Texas at Austin 2012

22 Hydrogen Bond Interac5on Let, w hb = weight for hydrogen- bonding interac5on Weight assigned to each atom is. For molecule A, For molecule B, Overall interac5on score, University of Texas at Austin 2012

23 F 2- Dock On- the- fly Score and Search using FFT F 2- Dock computes the following set: For any given rota5on r, the FFT- based scoring takes O( M A + M B + N 3 log N ) 5me, where N 3 is the size of the FFT grid. University of Texas at Austin 2012

24 Near Uniform Sampling for Rota5onal Search [ Mandell et al., 2001 ] Non-uniform Sampling Interval Number of Samples ( N R ) Mul5ple of Samples ( w.r.t. 20 sampling ) 20 1, , , , , , , University of Texas at Austin 2012

25 F 2 Dock: Search & Scoring START INPUT MOLECULES A & B UNIFORMLY DISTRIBUTED EULER ANGLES NEXT ROTATION R SAMPLE ROTATION SPACE FIRST ROTATION R Q RETAINS ONLY THE TOP 2000 SCORES ACROSS ALL ROTATIONS ROTATE B TO B R SCORE TRANSLATIONS OF B R W.R.T. A USING FFT TOP 1-5 TRANSLATIONS ( T ) AFFINITY FUNCTIONS SHAPE COMPLEMENTARITY ELECTROSTATICS & CHARGE COMPLEMENTARITY HYDROPHOBICITY / INTERFACE PROPENSITY H- BOND CORRECTION PHASE I ( F 2 Dock ) PUSH EACH R, T, S INTO PRIORITY QUEUE Q ( S = SCORE OF THE POSE ) YES MORE ROTATIONS? FILTERS PROXIMITY CLUSTERING #CLASHES LENNARD- JONES POTENTIAL HYDROPHOBICITY / INTERFACE PROPENSITY INTERFACE AREA ANTIBODY CONTACT GLYCINE RICHNESS INTERFACE CONTACT PREFERENCES NO PENALIZE POTENTIAL FALSE POSITIVES IN Q BASED ON VARIOUS FILTERS RERANK THE DOCKING POSES IN Q BASED ON CHANGE IN SOLVATION ENERGY OUTPUT THE RERANKED DOCKING POSES R, T PHASE II ( GB- rerank ) END 2012

26 F 2 Dock Filters Proximity Clustering: A configura5on is penalized if similar configura5ons with higher score exist(s). Similarity is measured as geometric distance D between the mass centers of the ligand molecule in the two configura7ons The score of the configura5on with score is further reduced By 80% if there is 1 configura7on with D < δ By 50% if there are 3 configura7ons with D < 2δ By 10% if there are 6 configura7ons with D < 3δ δ is a user specified parameter Using Dynamic Packing Grids Takes O( N Q log N Q ) 5me in total, where, N Q is the number of configura5ons University of Texas at Austin 2011

27 Dynamic Data Structures n n Dynamic Packing Grids (DPG) Dynamic updates in O(1) w.h.p. Neighborhood query in O(1) w.h.p. O(n) space Does not support multi-resolution directly Not cache efficient Dynamic Octree Dynamic updates in O(lgn) amortized Neighborhood queries in O(lgn) O(n) space Supports multi-resolution Cache efficient grid ( level 3 ) grid- planes ( level 2 ) grid- lines ( level 1 ) grid- cells ( level 0 ) balls ( leaves ) University of Texas at Austin 2012

28 Solvation Energetics based Re-Ranking Computing interface related scoring terms using Octree and DPG Construct two octrees for the proteins A and B. Given a pose defined by a transformation T call computeinteractions(roota, rootb, T, d) compute Interactions(na, nb, T, d) score = 0 if dist(na,nb) < d if both na and nb are leaves score = pairwise interactions within the atoms in na and nb elseif na is a leaf for each child nb j of nb do score += computeinteractions(na, nb j, T, d) elseif nb is a leaf for each child nai of na do score += computeinteractions(na i, nb, T, d) else return score for each each child na i of na and each child nb j of nb do score += computeinteractions(na i, nb j, T, d) University of Texas at Austin

29 Fast Re-Ranking Computations Approxima5ng Lennard- Jones Poten5al ( 1 + ε ) - Approxima5on in O( M / ε 2 ) 5me Approxima5ng Coulomb Poten5al ( 1 + ε ) - Approxima5on in O( M / ε 2 ) 5me Approxima5ng Solva5on Energy O( M) Sparse Triangula5on & Sampling of Analy5c Molecular Surfaces in O( M log M) 5me ( 1 + ε ) - Approxima5on of Born Radii in O( M/ ε 2 ) 5me ( 1 + ε ) - Approxima5on of GB Polariza5on Energy in O( M log M / ε ) 5me ( 1 + ε ) - Approxima5on of PB Polariza5on Energy in O( M / ε ) 5me [Bajaj, Zhao, SIAM J Sci Comp. 2010] [Chowdhury, Bajaj, SIAM J Sci Comp in review] University of Texas at Austin 2012

30 Benchmark Dataset and Measures of Performance Dataset: 60 rigid- body protein- protein complexes from ZDock Benchmark 2.0 #atoms per molecule: ,000 ( avg: 3,700, median: 3,200) enzyme- substrate/enzyme- inhibitor: 21 an5body- an5gen: 9, an5body- bound an5gen: 9 other: 21 Two Types of Experiments Bound- Bound: both molecules come from the same complex ( co- crystallized ) Unbound- Unbound: extracted from different complexes or crystallized separately Quality of Solu5ons RMSD: computed between the ( interface ) atoms of B in the target and predicted solu5ons ayer superimposing the two A s Hit: A predicted solu5on with RMSD less than 5Å University of Texas at Austin 2012

31 Performance Results ( Bound- Bound Docking ) University of Texas at Austin 2012

32 Performance Results ( Bound- Bound Docking ) University of Texas at Austin 2012

33 Performance Results ( Bound- Bound Docking ) An5body- An5gen An5gen - Bound An5body Enzyme- Inhibitor or Enzyme- Substrate Others University of Texas at Austin 2011

34 University of Texas at Austin 2012

35 n Performance of F2Dock 2.0 Measured as number of test cases where a correct solution was found within a top few results University of Texas at Austin 2012

36 Neurotoxin Fasciculin2-Acetylcholinesterase Docking Fasciculin2-Acetylcholinesterase complex Acetylcholinesterase Fasciculin 2 Surface Area mache: A 2 Fasciculin: 3348 A 2 Interface Area mache: 845 A 2 Fasciculin: 842 A 2 Binding Interfaces University of Texas at Austin 2012

37 Complexes predicted by F2Dock Different Scores of F2Dock Binding interfaces and interface areas (3A cutoff) Fas2-AChE Complex (bound) Shape Comp = Electrostatic = Interface Prop = Charge Comp = Pseudo Gsol = 3.31 Interface RMSD = 3.1 A Rank 1 solution A A 2 Unbound ligand Shape Comp = Electrostatic = Interface Prop = Charge Comp = Pseudo Gsol = 2.98 Interface RMSD = 14.7 A Rank 2 solution A A 2 F2Dock Shape Comp = Electrostatic = Interface Prop = Charge Comp = Pseudo Gsol = 3.88 Interface RMSD = 4.4 A Rank 3 solution A A 2 Unbound receptor Shape Comp = Electrostatic = Interface Prop = Charge Comp = Pseudo Gsol = 1.65 Interface RMSD = 30.5 A Rank 4 solution A A 2

38 Electrostatic complementarity Near the interfaces Complexes predicted by F2Dock Different Scores of F2Dock Binding interfaces and interface areas (3A cutoff) Shape Comp = Electrostatic = Interface Prop = Charge Comp = Pseudo Gsol = 3.31 Interface RMSD = 3.1 A Rank 1 solution A A 2 Shape Comp = Electrostatic = Interface Prop = Charge Comp = Pseudo Gsol = 2.98 Interface RMSD = 14.7 A Rank 2 solution A A 2 Shape Comp = Electrostatic = Interface Prop = Charge Comp = Pseudo Gsol = 3.88 Interface RMSD = 4.4 A Rank 3 solution A A 2 Shape Comp = Electrostatic = Interface Prop = Charge Comp = Pseudo Gsol = 1.65 Interface RMSD = 30.5 A Rank 4 solution A A 2

39 Rank 1 solution Shape Comp = Electrostatic = Interface Prop = Charge Comp = Pseudo Gsol = 3.31 Interface RMSD = 3.1 A Negative potential (both molecules) Positive potential (both molecules) Neutral (both molecules) Negative potential on interface (receptor) Positive potential on interface (receptor) Negative potential on interface (ligand) Positive potential on interface (ligand) Rank 2 solution Shape Comp = Electrostatic = Interface Prop = Charge Comp = Pseudo Gsol = 2.98 Interface RMSD = 14.7 A Rank 3 solution Shape Comp = Electrostatic = Interface Prop = Charge Comp = Pseudo Gsol = 3.88 Interface RMSD = 4.4 A Weaker potentials on the interface Rank 4 solution Shape Comp = Electrostatic = Interface Prop = Charge Comp = Pseudo Gsol = 1.65 Interface RMSD = 30.5 A

40 Performance : F2Dock n Complexity of F2Dock 2.0 M A, M B : number of atoms N r : number of rotational sample g: number of translational sample in each axis K: number of solutions Complexity for FFT based scoring O( N r ( g 3 log g ) + max(m A, M B ) + Kg 3 ) Complexity of computing filtering (knowledge-based) terms n Publications [F2Dock] C. Bajaj, R. Chowdhury, V. Siddahanavalli, Fast Fourier Protein Protein Docking, IEEE/ ACM Transactions on Computational Biology and Bioinformatics, 8 (1): 45-58, 2011 [F2Dock2] R. Chowdhury, D. Keidel, M. Rasheed, M. Moussalem, A. Olson, M. Sanner, and C. Bajaj. Protein-protein docking with F2Dock 2.0 and GB-rerank. Under review, 2012 [DPGenergy] C. Bajaj, R. A. Chowdhury, and M. Rasheed. A dynamic data structure for flexible molecular maintenance and informatics. Bioinformatics, 27(1):55 62, 2010 University of Texas at Austin 2012

41 Dynamic Packing Grid (DPG): Neighborhood Queries M = { B 1, B 2,, B n }: a set of n balls in 3-space B i = ( c i, r i ): a ball with center c i and radius r i δ QUERIES: INTERSECT( c, r ): return all balls in M intersecting the query ball B = ( c, r ) UPDATES: RANGE( p, δ ): return all balls in M with centers within distance δ of p EXPOSED( c, r ): return true if B = ( c, r ) M contributes to the outer boundary of the union of balls in M SURFACE( ): return the outer boundary of the union of balls in M ADD( c, r ): add a new ball B = ( c, r ) to M REMOVE( c, r ): remove the ball B = ( c, r ) from M MOVE( c 1, c 2, r ): move the ball B = ( c 1, r ) M to a new center c 2 University of Texas at Austin 2012

42 Performance Bounds of DPG IMPLEMENTATION 1 IMPLEMENTATION 2 QUERY TIMES UPDATE SPACE TIMES RANGE( p, δ ) ( δ = O( r max ) ) INTERSECT( c, r ) EXPOSED( c, r ) ( k = # results returned ) SURFACE( ) ( m = # balls on boundary ) ADD( c, r ) REMOVE( c, r ) MOVE( c 1, c 2, r ) TOTAL SPACE ( n = # balls in the union ) O( log log w + k ) O( log log n + k ) ( w.h.p. ) ( w.h.p. ) O( m ) ( worst case ) O( log w ) O( log n / log log n ) ( w.h.p. ) ( w.h.p. ) O( n ) ( worst case ) Assumptions: (1) union of n balls (2) RAM with w-bit words (3) distance between any pair of atoms is Ω( r max ) [C.Bajaj, R.Chowdhury,,M.Rasheed Bioinformatics 2010] University of Texas at Austin 2012

43 Performance Bounds of DPG IMPLEMENTATION 1 IMPLEMENTATION 2 QUERY TIMES UPDATE SPACE TIMES RANGE( p, δ ) ( δ = O( r max ) ) INTERSECT( c, r ) EXPOSED( c, r ) ( k = # results returned ) SURFACE( ) ( m = # balls on boundary ) ADD( c, r ) REMOVE( c, r ) MOVE( c 1, c 2, r ) TOTAL SPACE ( n = # balls in the union ) O( log log w + k ) O( log log n + k ) ( w.h.p. ) ( w.h.p. ) O( m ) ( worst case ) O( log w ) O( log n / log log n ) ( w.h.p. ) ( w.h.p. ) O( n ) ( worst case ) Assumptions: (1) union of n balls (2) RAM with w-bit words (3) distance between any pair of atoms is Ω( r max ) [C.Bajaj, R.Chowdhury,,M.Rasheed Bioinformatics 2010] University of Texas at Austin 2012

44 Prior Work [ Eyal & Halperin, 2005 ] A data structure based on dynamic graph connectivity that maintains the molecular surface under conformational changes and supports queries involving single atoms in O( log n ) amortized time updates of individual atoms in O( log 2 n ) amortized time Opera5on Eyal & Halperin (2005) DPG Results Queries Updates O( log n ) ( amor5zed ) O( log 2 n ) ( amor5zed ) O( log log w ) = O( 1 ) ( w.h.p. ) O( log log n ) ( w.h.p. ) O( log w ) = O( 1 ) ( w.h.p. ) O( log n / log log n ) ( w.h.p. ) In theory, the new query bounds are exponentially better! University of Texas at Austin 2012

45 A Fully Dynamic 1D Integer Range Reporting Data Structure for word-ram [ Mortensen et al., 2005 ] This data structure is at the heart of our DPG data structure. It maintains a set S of integers under updates, and answers queries: report any or all integers in S in a given range Performance bounds on a RAM with w-bit words: space: O( n ), where n is the number of integers in S update time: O( t u ) with high probability (w.h.p.) query time: O( t q + k ) w.h.p., where k is the number of items reported Depending on implementation: t u = O( log w ) and t q = O( loglog w ) t u = O( log n / loglog n ) and t q = O( loglog n ) University of Texas at Austin 2012

46 The DPG Data Structure We decompose the entire 3-space into an axis-parallel infinite grid structure of cells of size 2r max 2r max 2r max. We store the non-empty grid cells (i.e., containing at least one atom center) into the DPG data structure. University of Texas at Austin 2012

47 Hierarchical Layout of the DPG Data Structure grid ( level 3 ) grid-planes ( level 2 ) grid-lines ( level 1 ) grid-cells ( level 0 ) balls ( leaves ) For i { 1, 2, 3 }, each level i data structure can identify each of its children at level i 1 by a unique integer, and stores them in an integer range reporting data structure. University of Texas at Austin 2012

48 The Leaf Level Ball Data Structure Stores the center and radius of the given ball B. A Boolean flag exposed, which is set to true if B contributes to the outer boundary of the union of balls in M. The circular intersections of all balls intersecting B define a 2D arrangement A on the surface of B. All exposed faces of A are stored in a set F. With each face f F, we store pointers to other Ball data structures that share faces with f. University of Texas at Austin 2012

49 Step 1: Level 3 Range Query Implementation of RANGE ( p, δ ) Consider a sphere of radius δ at point p inside the level 3 grid p δ University of Texas at Austin 2012

50 Step 1: Level 3 Range Query Implementation of RANGE ( p, δ ) Consider a sphere of radius δ at point p inside the level 3 grid The level 3 grid is a collection of level 2 grid-planes University of Texas at Austin 2012

51 Implementation of RANGE ( p, δ ) Step 1: Level 3 Range Query Consider a sphere of radius δ at point p inside the level 3 grid The level 3 grid is a collection of level 2 grid-planes Perform a range query on the range reporting data structure to collect all relevant non-empty level 2 grid-planes University of Texas at Austin 2012

52 Implementation of RANGE ( p, δ ) Step 1: Level 3 Range Query Consider a sphere of radius δ at point p inside the level 3 grid The level 3 grid is a collection of level 2 grid-planes Perform a range query on the range reporting data structure to collect all relevant non-empty level 2 grid-planes University of Texas at Austin 2012

53 Implementation of RANGE ( p, δ ) Step 2: Level 2 Range Query (on each grid-plane from step 1) The sphere from step 1 cuts a circular slice of possibly different radius from each grid-plane University of Texas at Austin 2012

54 Implementation of RANGE ( p, δ ) Step 2: Level 2 Range Query (on each grid-plane from step 1) The sphere from step 1 cuts a circular slice of possibly different radius from each grid-plane Consider any such grid-plane University of Texas at Austin 2012

55 Implementation of RANGE ( p, δ ) Step 2: Level 2 Range Query (on each grid-plane from step 1) The sphere from step 1 cuts a circular slice of possibly different radius from each grid-plane Consider any such grid-plane University of Texas at Austin 2012

56 Implementation of RANGE ( p, δ ) Step 2: Level 2 Range Query (on each grid-plane from step 1) The sphere from step 1 cuts a circular slice of possibly different radius from each grid-plane Consider any such grid-plane A level 2 grid-plane is a collection of level 1 grid-lines University of Texas at Austin 2012

57 Implementation of RANGE ( p, δ ) Step 2: Level 2 Range Query (on each grid-plane from step 1) The sphere from step 1 cuts a circular slice of possibly different radius from each grid-plane Consider any such grid-plane A level 2 grid-plane is a collection of level 1 grid-lines Perform a range query on the range reporting data structure to find all relevant non-empty grid-lines University of Texas at Austin 2012

58 Implementation of RANGE ( p, δ ) Step 3: Level 1 Range Query (on each grid-line from step 2) The circle from step 2 cuts a slice of possibly different length from each grid-line University of Texas at Austin 2012

59 Implementation of RANGE ( p, δ ) Step 3: Level 1 Range Query (on each grid-line from step 2) The circle from step 2 cuts a slice of possibly different length from each grid-line Consider any such grid-line University of Texas at Austin 2012

60 Implementation of RANGE ( p, δ ) Step 3: Level 1 Range Query (on each grid-line from step 2) The circle from step 2 cuts a slice of possibly different length from each grid-line Consider any such grid-line A level 1 grid-line is a collection of level 0 grid-cells University of Texas at Austin 2012

61 Implementation of RANGE ( p, δ ) Step 3: Level 1 Range Query (on each grid-line from step 2) The circle from step 2 cuts a slice of possibly different length from each grid-line Consider any such grid-line A level 1 grid-line is a collection of level 0 grid-cells Perform a range query on the range reporting data structure to find all relevant non-empty grid-cells University of Texas at Austin 2012

62 Performance of DPG Intersec5on Query ( without surface updates ) University of Texas at Austin 2012

63 Performance of DPG Update times Query times [DPG] C. Bajaj, R. A. Chowdhury and M. Rasheed, A Dynamic Data Structure for Flexible Molecular Maintenance and Informatics, Proceedings of the ACM Symposium on Solid and Physical Modeling, , 2009,Final version in Bioinformatics 2011, 2 7, Free software download University of Texas at Austin 2012

64 Performance of DPG Surface Genera5on ( space ) RDV outer capsid ( P8 ) RDV outer capsid ( cut view ) RDV inner capsid ( P3 ) RDV inner capsid ( cut view ) Images produced by CVC Lab TexMol Software

65 TexMol Client to F2Dock Free Software Download University of Texas at Austin 2012

66 TexMol & F 2 Dock F2d file generation: Includes generation of atomic charges and radii, identification of protein skin regions./texmol -f2dgen <>.inp.inp file contains staticmoleculepdb <>.pdb movingmoleculepdb <>.pdb resolution <int> 64, 128, 256 specifies size of grid Quad file generation: Includes generation of molecular surfaces and quadrature point computation./texmol -quadgen <>.inp.inp file contains parameters Docking./TexMol -dock <>.inp.inp file contains parameters Re-ranking./TexMol -rerank <>.inp.inp file contains parameters University of Texas at Austin 2012

67 WebMol (work in progress) receptorid=1acb_r_u.pdb&ligandid=1acb_l_u.pdb&jobid= University of Texas at Austin 2012

68 Structural Analysis of Molecular Function Computational Problems Binding Affinities Energy Minimization Forward Dynamics Techniques nfft, KiFMM for fast summations NEXT Fast Dynamic Neighborhood Queries Docking Tiling Challenges Protein Flexibility Protein Folding, Rotamer Packing Spontaneous Assembly University of Texas at Austin 2012

69 Interface Statistics l l Based on crystal structure l # of atoms on the interface l Distance < 5.0 A # of residues on the interface Any residue having at least one interface atom l # polar residues l # nonpolar residues Based on smooth surface l l l l Interface defined as Distance < 5.0-2*r max Interface area Interface planarity Average distance of the points on the interface from their least squares plane Interface circularity Project the interface points onto the least squares plane Compute the aspect ratio of their convex hull

70 Interface Statistics l Some examples for the 1MAH complex Rank Rank Rank Rank Rank 5 RMSD # of Interface # of Interface # of Polar Res # Res of NonPolar Interface Interface Area Planarity Interface Circularity

71 Machupo Virus Glycoprotein- Human Transferrin Receptor 1 Complex PB Electrostatics Machupo Virus Glycoprotein Human Transferrin Receptor 1 Interface Areas: HT1, 1481 A^2 MVG, 1501 A^2

72 Some Exis5ng Protein- Protein Docking Soyware ZDock ( Boston University, USA ): FFT- based shape- complementarity, electrosta5cs, solva5on; clustering to avoid redundancies DOT ( UCSD, USA ): FFT- based shape- complementarity and Poission- Boltzmann electrosta5cs HEX ( U. Aberdeen, UK ): Spherical polar Fourier correla5on of shape and electrosta5cs ICM ( TSRI,USA ): Rigid- body pseudo- Brownian Monte Carlo simula5on with grid- based energy func5on; refinement and rescoring with a detailed free energy func5on PatchDock ( Tel Aviv U., IL; NIH, USA ): Geometric hashing GAPDOCK ( Sheffield U, UK ): Gene5c algorithm based on shape correla5on and buried area HADDOCK ( Utrecht U, Netherlands): Biochemical Interac5on data driven using NMR 5tra5on/mutagenesis experiments 2012

73 And many more mul7- protein complexes. University of Texas at Austin 2012

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80 Jus5fica5on for the Skin- Core Floa5ng Layer of Sta5c Molecule Distribu5on of Atoms Centers of the Bound Ligand which are within [0, 3Å] from the Receptor vdw Surface Unbound- unbound Docking Bound- bound Docking University of Texas Average at Austin ( Avg + StdDev, Avg StdDev )

81 F2Dock algorithm University of Texas at Austin 2012

82 Experiments with the RanGTPase-RanGAP Complex ( Docking based on Shape Complementarity of Unbound-Unbound complexes extracted from the ZDock benchmark suite 2.0 ) 1DFJ 1GHQ 2PCC 7CEI University of Texas at Austin 2012

83 Electrostatic Potential Experiments with the RanGTPase-RanGAP Complex ( Flexible Docking, Rotational Sampling: 20 ) (a) Ran GTPase (b) Ran GAP (c) Ran GTPase complexed with Ran GAP University of Texas at Austin 2012

84 Experiments with the RanGTPase-RanGAP Complex ( Docking based on Shape & Electrostatics Complementarity ) RanGTPase RMSD 1.6A RMSD 2.9A RanGAP RanGTPase + RanGAP with electrosta5cs without electrosta5cs University of Texas at Austin 2012

85 Some Application of DPG Dynamic Maintenance of the van der Waals Surface PG can be used directly with radius of each atom set to its van der Waals radius Dynamic Maintenance of the Lee-Richards Surface One PG data structure keeps track of the patches on the surface A 2 nd PG data structure detects intersections among concave patches Constructing Mixed Resolution Surfaces We construct a k-level PG data structure HPG( k ) For i [0, k - 1], level i contains a PG data structure PG (i) with parameters r (i) max, d(i) min such that d(i) min = Ω( r(i) max ) For i [0, k - 2], assume r (i+1) max = Θ( r(i) max ) and d(i+1) min = Θ( d(i) min ) PG (0) contains the atomic representation of the molecule Each ball in PG (i+1) is a grouping of several neighboring balls in PG (i) Energetics Computation in Docking We use PG to find all atoms within a constant distance from the sampled quadrature points on the Lee-Richards surface