Protein-Ligand Docking Methods

Transcription

1 Review Goal: Given a protein structure, predict its ligand bindings Protein-Ligand Docking Methods Applications: Function prediction Drug discovery etc. Thomas Funkhouser Princeton University S597A, Fall hld Review Questions: Questions: Where will the ligand bind? Which ligand will bind? ow will the ligand bind? When? Why? etc. Where will the ligand bind? Which ligand will bind? ow will the ligand bind? When? Why? etc. Ligand 1hld 1hld Goal: Metric: Given a protein and a ligand, determine the pose(s) and conformation(s) minimizing the total energy of the protein-ligand complex ow well do the predicted poses and conformations match measured ones (e.g., RMSD) [Jones97] 1

2 hallenges: Predicting energetics of protein-ligand binding Searching space of possible poses & conformations hallenges: Predicting energetics of protein-ligand binding Searching space of possible poses & conformations hallenges: Predicting energetics of protein-ligand binding Searching space of possible poses & conformations Relative position (3 degrees of freedom) hallenges: Predicting energetics of protein-ligand binding Searching space of possible poses & conformations Relative position (3 degrees of freedom) Relative orientation (3 degrees of freedom) hallenges: Predicting energetics of protein-ligand binding Searching space of possible poses & conformations Relative position (3 degrees of freedom) Relative orientation (3 degrees of freedom) Rotatable bonds in ligand (n degrees of freedom) hallenges: Predicting energetics of protein-ligand binding Searching space of possible poses & conformations Relative position (3 degrees of freedom) Relative orientation (3 degrees of freedom) Rotatable bonds in ligand (n degrees of freedom) Rotatable bonds in protein (m degrees of freedom) Side chain movements Large-scale movements 2

3 utline Introduction Scoring functions Molecular mechanics Empirical functions Knowledge-based Searching poses & conformations Systematic search Molecular dynamics Simulated annealing Genetic algorithms Incremental construction Rotamer libraries Results & Discussion utline Introduction Scoring functions Molecular mechanics Empirical functions Knowledge-based Searching poses & conformations Systematic search Molecular dynamics Simulated annealing Genetic algorithms Incremental construction Rotamer libraries Results & Discussion Scoring Functions Goal: estimate binding affinity for given protein, ligand, pose, and conformations Scoring Functions Goal: estimate binding affinity for given protein, ligand, pose, and conformations IV-1 protease complexed with an hydroxyethylene isostere inhibitor [Marsden04] Fundamental Forces of Binding Fundamental Forces of Binding Binding Equations: K a R L R'L' K d -1 K a = K d = [R'L'] [R] [L] Binding Equations: K a R L R'L' K d Free Energy Equations: -1 K a = K d = [R'L'] [R] [L] G o = -RTln(K a ) G o = o - TS o 3

4 Fundamental Forces of Binding Fundamental Forces of Binding Binding Equations: K a R L R'L' K d Free Energy Equations: -1 K a = K d = [R'L'] [R] [L] Binding Equations: K a R L R'L' K d Free Energy Equations: -1 K a = K d = [R'L'] [R] [L] G o = -RTln(K a ) G o = o - TS o G o = -RTln(K a ) G o = o - TS o enthalpy entropy K a : M G o : -10 to -70 kcal/mol enthalpy entropy Factors Affecting G o Intramolecular Forces Intramolecular Forces (covalent) Bond lengths Bond angles Dihedral angles Intermolecular Forces (noncovalent) Electrostatics Dipolar interactions ydrogen bonding ydrophobicity van der Waals Bond lengths (Å): N 1.47 N 1.01 = and S work against each other in many situations. Intramolecular Forces Bond lengths (Å): N 1.47 N 1.01 = Intramolecular Forces Bond lengths (Å): N 1.47 N 1.01 = Bond angles: o 120 o 180 o N ~109.5 o Bond angles: o 120 o 180 o N ~109.5 o staggered Dihedral angles: eclipsed 4

5 Intramolecular Forces Entropic Effects of Ligand Binding Bond lengths (Å): N 1.47 N 1.01 = Bond angles: o 120 o 180 o N ~109.5 o Dihedral angles: staggered eclipsed torsional strain energy (eclipsed: 1 kcal/mol) Entropic Effects of Ligand Binding Intermolecular Forces Electrostatic interactions Dipolar interactions ydrogen bonding ydrophobicity van der Waals associations Loss of degrees of freedom upon binding can cost 60 kcal/mol Electrostatics Electrostatics harge-charge p dependence harge-charge p dependence harge-dipole harge-dipole - harge-induced dipole harge-induced dipole 5

6 Electrostatics oulomb s Law harge-charge p dependence charge-charge harge-dipole - harge-induced dipole Electrostatics harge-charge p dependence harge-dipole harge-induced dipole increasing distance dependence 4-7 kcal/mol oulombic Interactions in Ligand Binding R 2 2 N 3 2 N arginine B ligand ation- Interactions Interactions with Metal Ions δ δ Na δ δ δ δ δ N R 5 6

7 Dipolar Interactions - Dipole-Dipole Interactions - -l - N R kcal/mol ydrogen Bonding -Stacking Interactions: End-to-Face Å highly directional (130 o 180 o ) 2-10 kcal stabilization also -, F-, even - δ δ δ δ δ δ δ 6 -Stacking Interactions: Face to Face ydrogen Bonding in Ligand Binding 7 7

8 Salt Bridges Salt Bridges in Ligand Binding energetics similar to -bonds (2-10 kcal/mol) [Klebe02] Binding of napsagatran to thrombin [Klebe02] ydrophobicity ydrophobicity Binding pocket becomes interior upon complexation with ligand Binding pocket becomes interior upon complexation with ligand Big penalty: charged or polar groups buried but unpaired ydrophobicity van der Waals Interactions Dipole induced dipole Induced dipole induced dipole Binding pocket becomes interior upon complexation with ligand Big penalty: charged or polar groups buried but unpaired Energetic contribution is propotional to the size of the surface buried upon ligand binding e.g. 3 group (25 Å 2 ): 3 to 6 kcal/mol Distance dependent Short-range repulsion stabilization > 1 kcal/mol 8

9 van der Waals Interactions Solvation and Desolvation AutoDock User s Manual AutoDock User s Manual Solvent Effects: ydrogen Bonding Solvation and Desolvation Water tetrahedrally connected network very small volume Enthalpy: 3 4 -bonds at 2 10 kcal/mol each Entropy: flexible matrix (disorder) Rupture -bonds within water matrix Reform -bonds Reorganize water molecules at surface Bury a hydrophobic pocket surface Lose degrees of freedom Some water molecules released AutoDock User s Manual Solvent Effects: Solvent-Assisted Binding Solvent-Assisted Binding interstitial waters [Klebe02] 9

10 Solvent Displacement Protein onformation Fewer degrees of freedom New interaction surfaces Usually driven by hydrophobicity Scoring Functions Molecular mechanics force fields: ARMM [Brooks83] AMBER [ornell95] Empirical methods: hemscore [Eldridge97] GlideScore [Friesner04] AutoDock [Morris98] Knowledge-based methods PMF [Muegge99] Bleep [Mitchell99] DrugScore [Gohlke00] Scoring Functions Molecular mechanics force fields: ARMM [Brooks83] AMBER [ornell95] Empirical methods: hemscore [Eldridge97] GlideScore [Friesner04] AutoDock [Morris98] Knowledge-based methods PMF [Muegge99] Bleep [Mitchell99] DrugScore [Gohlke00] Molecular Mechanics Force Fields ARMM: Molecular Mechanics Force Fields AMBER: [Brooks83] [ornell95] 10

11 Scoring Functions Molecular mechanics force fields: ARMM [Brooks83] AMBER [ornell95] Empirical methods: hemscore [Eldridge97] GlideScore [Friesner04] AutoDock [Morris98] Knowledge-based methods PMF [Muegge99] Bleep [Mitchell99] DrugScore [Gohlke00] Empirical Scoring Functions hemscore: G bind = G 0 G G G G hbond metal lipo rot am il ii rot g r) g ( α) 1 ( 2 f ( r il am ) f ( r ) [Marsden04] [Eldridge97] Empirical Scoring Functions GlideScore: G bind = hbond neut neut hbond neut ch arg hbond ch arg ed ch arg max lipo lipo rotb coul vdw metal ion polar phob E E ed ed lm f ( rlr ) rotb coul vdw V solvationterms g( r) h( α ) g( r) h( α ) g( r) h( α ) f ( r ) h( α) polar phob Empirical Scoring Functions AutoDock 3.0: G binding = G vdw G elec G hbond G desolv G tors G vdw12-6 Lennard-Jones potential G elecoulombic with Solmajer-dielectric G hbond Potential with Goodford Directionality G desolv Stouten Pairwise Atomic Solvation Parameters G torsnumber of rotatable bonds [Friesner04] [uey & Morris, AutoDock & ADT Tutorial, 2005] Scoring Functions Molecular mechanics force fields: ARMM [Brooks83] AMBER [ornell95] Empirical methods: hemscore [Eldridge97] GlideScore [Friesner04] AutoDock [Morris98] Knowledge-based methods PMF [Muegge99] Bleep [Mitchell99] DrugScore [Gohlke00] Knowledge-Based Scoring Functions DrugScore: W = γ ki l j W Protein-Ligand Atom Distance Term k j( r) (1 ) l i, γ i j Wi ( SAS, SAS0) Wj( SAS, SAS0) Solvent Accessible Surface Terms [Gohlke00] 11

12 Scoring Functions Molecular mechanics force fields: ARMM [Brooks83] AMBER [ornell95] Empirical methods: hemscore [Eldridge97] GlideScore [Friesner04] AutoDock [Morris98] Knowledge-based methods PMF [Muegge99] Bleep [Mitchell99] DrugScore [Gohlke00] ow to compute score efficiently? omputing Scoring Functions Point-based calculation: Sum terms computed at positions of ligand atoms (this will be slow) X i r p omputing Scoring Functions Grid-based calculation: Precompute force field for each term of scoring function for each conformation of protein (usually only one) Sample force fields at positions of ligand atoms Accelerate calculation of scoring function by 100X X i r p [uey & Morris] utline Introduction Scoring functions Molecular mechanics Empirical functions Knowledge-based Searching poses & conformations Systematic search Molecular dynamics Simulated annealing Genetic algorithms Incremental construction Rotamer libraries Results & Discussion Systematic Search Uniform sampling of search space Relative position (3) Relative orientation (3) Rotatable bonds in ligand (n) Rotatable bonds in protein (m) The search space has dimensionality 3 3 r n r m Systematic Search Uniform sampling of search space Exhaustive, deterministic Quality dependent on granularity of sampling Feasible only for low-dimensional problems Rotations Translations Rotations Translations tstep rstep FRED [Yang04] tstep rstep FRED [Yang04] 12

13 Systematic Search Uniform sampling of search space Exhaustive, deterministic Quality dependent on granularity of sampling Feasible only for low-dimensional problems Example: search all rotations Wigner-D -1 Maximum orrelation Molecular Mechanics Energy minimization: Start from a random or specific state (position, orientation, conformation) Move in direction indicated by derivatives of energy function Stop when reach local minimum X orrelation orrelation in Frequency Domain Rotation Rotational orrelation Molecule 3D Grid Spherical armonic Functions Decompositions [Marai04] Simulated Annealing Monte arlo search of parameter space: Start from a random or specific state (position, orientation, conformation) Make random state changes, accepting up-hill moves with probability dictated by temperature Reduce temperature after each move Stop after temperature gets very small Genetic Algorithm Genetic search of parameter space: Start with a random population of states Perform random crossovers and mutations to make children Select children with highest scores to populate next generation Repeat for a number of iterations AutoDock 2.4 [Morris96] Gold [Jones95], AutoDock 3.0 [Morris98] Incremental Extension Greedy fragment-based construction: Partition ligand into fragments Incremental Extension Greedy fragment-based construction: Partition ligand into fragments Place base fragment (e.g., with geometric hashing) FlexX [Rarey96] FlexX [Rarey96] 13

14 Incremental Extension Greedy fragment-based construction: Partition ligand into fragments Place base fragment (e.g., with geometric hashing) Incrementally extend ligand by attaching fragments Rotamer Libraries Rigid docking of many conformations: Precompute all low-energy conformations Dock each precomputed conformations as rigid bodies Ligand Predicted Possible onformations Rigid Docking Best Match FlexX [Rarey96] Protein Glide [Friesner04] Rigid Docking This is just like matching binding sites (complement) an use same methods we used for matching and indexing point, surface, and/or grid representations Ligand Points Surface Grid utline Introduction Scoring functions Molecular mechanics Empirical functions Knowledge-based Searching poses & conformations Systematic search Molecular dynamics Simulated annealing Genetic algorithms Incremental construction Rotamer libraries Results & Discussion Discussion References? [Brooks83] Bernhard R. Brooks, Robert E. Bruccoleri, Barry D. lafson, David J. States, S. Swaminathan, Martin Karplus, "ARMM: A program for macromolecular energy, minimization, and dynamics calculations," J. omp. hem, 4, 2, 1983, pp [Eldridge97] M.D. Eldridge,.W. Murray, T.R. Auton, G.V. Paolini, R.P. Mee, "Empirical scoring functions. I: The development of a fast empirical scoring function to estimate the binding affinity of ligands in receptor complexes," J. omput.- Aided Mol. Des., 11, 1997, pp [Friesner04] R.A. Friesner, J.L. Banks, R.B. Murphy, T.A. algren, J.J. Klicic, D.T. Mainz, M.P. Repasky, E.. Knoll, M. Shelley, J.K. Perry, D.E. Shaw, P. Francis, P.S. Shenkin, "Glide: A New Approach for Rapid, Accurate Docking and Scoring.," J. Med. hem, 47, 2004, pp [Gohlke00]. Gohlke, M. endlich, G. Klebe, "Knowledge-based scoring function to predict protein-ligand interactions," J. Mol. Biol., 295, 2000, pp [uey & Morris] Ruth uey and Garrett M. Morris, "Using AutoDock With AutoDockTools: A Tutorial", [Jones97] G. Jones, P. Willett, R.. Glen, A.R. Leach, R. Taylor, "Development and Validation of a Genetic Algorithm for Flexible Docking," J. Mol. Biol., 267, 1997, pp [Marai04] hristopher Marai, "Accommodating Protein Flexibility in omputational Drug Design," Mol Pharmacol, 57, 2, 2004, p [Marsden04] Marsden PM, Puvanendrampillai D, Mitchell JB and Glen R., "Predicting protein ligand binding affinities: a low scoring game?", rganic Biomolecular hemistry, 2, 2004, p [Mitchell99] J.B.. Mitchell, R. Laskowski, A. Alex, and J.M.Thornton, "BLEEP - potential of mean force describing proteinligand interactions: I. Generating potential", J. omput. hem., 20, 11, 1999, [Morris98] Morris, G. M., Goodsell, D. S., alliday, R.S., uey, R., art, W. E., Belew, R. K. and lson, A. J. "Automated Docking Using a Lamarckian Genetic Algorithm and and Empirical Binding Free Energy Function", J. omputational hemistry, 19, 1998, p [Muegge99] I. Muegge, Y.. Martin, "A general and fast scoring function for protein-ligand interactions: A simplified potential approach," J. Med. hem., 42, 1999, pp [Rarey96] M. Rarey, B. Kramer, T. Lengauer, G. Klebe, "A Fast Flexible Docking Method using an Incremental onstruction Algorithm," Journal of Molecular Biology, 261, 3, 1996, pp