Review Goal: • Given a protein structure, Protein-Ligand predict its ligand bindings Docking Methods Applications: • Function prediction • Drug discovery Thomas Funkhouser • etc. Princeton University CS597A, Fall 2007 1hld Review Protein-Ligand Docking Questions: Questions: • Where will the ligand bind? • Where will the ligand bind? • Which ligand will bind? • Which ligand will bind? • How will the ligand bind? • How will the ligand bind? • When? • When? • Why? • Why? • etc. • etc. Ligand 1hld 1hld Protein-Ligand Docking Protein-Ligand Docking Goal 1: Goal 2: • Given a protein and a ligand, • Predict the binding affinity of any protein-ligand complex determine the pose(s) and conformation(s) minimizing the total energy of the protein-ligand complex Virtual Screening High Throughput (Computational Docking & Scoring) Screening http://www.molsoft.com/ 1 Protein-Ligand Docking Protein-Ligand Docking Challenges: Challenges: • Predicting energetics of protein-ligand binding Predicting energetics of protein-ligand binding • Searching space of possible poses & conformations • Searching space of possible poses & conformations Protein-Ligand Docking Protein-Ligand Docking Challenges: Challenges: • Predicting energetics of protein-ligand binding • Predicting energetics of protein-ligand binding • Searching space of possible poses & conformations • Searching space of possible poses & conformations Relative position (3 degrees of freedom) § Relative position (3 degrees of freedom) Relative orientation (3 degrees of freedom) Protein-Ligand Docking Protein-Ligand Docking Challenges: Challenges: • Predicting energetics of protein-ligand binding • Predicting energetics of protein-ligand binding • Searching space of possible poses & conformations • Searching space of possible poses & conformations § Relative position (3 degrees of freedom) § Relative position (3 degrees of freedom) § Relative orientation (3 degrees of freedom) § Relative orientation (3 degrees of freedom) Rotatable bonds in ligand (n 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 Outline Outline Introduction Introduction Scoring functions Scoring functions • Molecular mechanics • Molecular mechanics • Empirical functions • Empirical functions • Knowledge-based • Knowledge-based Searching poses & conformations Searching poses & conformations • Systematic search • Systematic search • Molecular dynamics • Molecular dynamics • Simulated annealing • Simulated annealing • Genetic algorithms • Genetic algorithms • Incremental construction • Incremental construction • Rotamer libraries • Rotamer libraries Results & Discussion Results & Discussion Scoring Functions Scoring Functions Goal: estimate binding affinity for given Goal: estimate binding affinity for given protein, ligand, pose, and conformations protein, ligand, pose, and conformations HIV-1 protease complexed with an hydroxyethylene isostere inhibitor [Marsden04] Scoring Functions Scoring Functions + + Binding Equations: Binding Equations: [R'L'] [R'L'] Ka K = K -1= Ka K = K -1= R + L R'L' a d [R][L] R + L R'L' a d [R][L] Kd Kd Free Energy Equations: o o o o G = -RTln(Ka) G = H - TS 3 Scoring Functions Scoring Functions + + Binding Equations: Binding Equations: [R'L'] [R'L'] Ka K = K -1= Ka K = K -1= R + L R'L' a d [R][L] R + L R'L' a d [R][L] Kd Kd Free Energy Equations: Free Energy Equations: o o o o o o o o G = -RTln(Ka) G = H - TS G = -RTln(Ka) G = H - TS -2 -12 Ka : 10 – 10 M enthalpy entropy Go : -10 to -70 kcal/mol enthalpy entropy Factors Affecting Go Scoring Functions Intramolecular Forces Intermolecular Forces Molecular mechanics force fields: (covalent) (noncovalent) • CHARMM [Brooks83] • Bond lengths • Electrostatics • AMBER [Cornell95] • Bond angles • Dipolar interactions • Dihedral angles • Hydrogen bonding Empirical methods: • Hydrophobicity • ChemScore [Eldridge97] • van der Waals • GlideScore [Friesner04] • AutoDock [Morris98] Knowledge-based methods H and S work against each other in many situations. • PMF [Muegge99] • Bleep [Mitchell99] • DrugScore [Gohlke00] Scoring Functions Molecular Mechanics Force Fields Molecular mechanics force fields: CHARMM: • CHARMM [Brooks83] • AMBER [Cornell95] Empirical methods: • ChemScore [Eldridge97] • GlideScore [Friesner04] • AutoDock [Morris98] Knowledge-based methods • PMF [Muegge99] • Bleep [Mitchell99] • DrugScore [Gohlke00] [Brooks83] 4 Molecular Mechanics Force Fields Scoring Functions AMBER: Molecular mechanics force fields: • CHARMM [Brooks83] • AMBER [Cornell95] Empirical methods: • ChemScore [Eldridge97] • GlideScore [Friesner04] • AutoDock [Morris98] Knowledge-based methods • PMF [Muegge99] • Bleep [Mitchell99] • DrugScore [Gohlke00] [Cornell95] Empirical Scoring Functions Empirical Scoring Functions ChemScore: GlideScore: ∆ ∆α + ∆ ∆ + ∆ Chbond −neut−neut g( r)h( ) Gbind = G0 Gbind = ∆ ∆α + ∆ ∆ ∆α + C − − g( r)h( ) Ghbond g1( r)g2 ( ) hbond neut ch arg ed iI ∆ ∆α + Chbond −ch arg ed −ch arg ed g( r)h( ) ∆G f r + metal ( aM ) ∆α + aM Cmax −metal−ion f (rlm )h( ) ∆ + + Glipo f (riL ) Clipo−lipo f (rlr ) iL [Marsden04] C H + ∆ rotb rotb Grot H rot Cpolar− phobVpolar− phob + Ccoul Ecoul + CvdW EvdW solvationterms [Eldridge97] [Friesner04] Empirical Scoring Functions Scoring Functions AutoDock 3.0: Molecular mechanics force fields: • CHARMM [Brooks83] ∆ ∆ ∆ ∆ Gbinding = GvdW + Gelec + Ghbond + • AMBER [Cornell95] ∆ ∆ Gdesolv + Gtors ∆ Empirical methods: GvdW 12-6 Lennard-Jones potential • ChemScore [Eldridge97] ∆ Gelec • GlideScore [Friesner04] Coulombic with Solmajer-dielectric • AutoDock [Morris98] ∆ Ghbond 12-10 Potential with Goodford Directionality Knowledge-based methods ∆ Gdesolv Stouten Pairwise Atomic Solvation Parameters • PMF [Muegge99] ∆ Gtors • Bleep [Mitchell99] Number of rotatable bonds • DrugScore [Gohlke00] [Huey & Morris, AutoDock & ADT Tutorial, 2005] 5 Knowledge-Based Scoring Functions Scoring Functions DrugScore: Molecular mechanics force fields: • CHARMM [Brooks83] »ƒ∆W (SAS,SAS ) + » ÿ … i 0 • AMBER [Cornell95] ∆ = γ ∆ + −γ × ki W …ƒƒ Wi j (r)Ÿ (1 ) … , ∆Wj SAS SAS … ki l j ⁄Ÿ …ƒ ( , 0 ) Empirical methods: l j • ChemScore [Eldridge97] How to compute • GlideScore [Friesner04] score efficiently? Protein-Ligand Solvent Atom Accessible • AutoDock [Morris98] Distance Surface Term Terms Knowledge-based methods • PMF [Muegge99] • Bleep [Mitchell99] • DrugScore [Gohlke00] [Gohlke00] Computing Scoring Functions Computing Scoring Functions Point-based calculation: Grid-based calculation: • Sum terms computed at positions of ligand atoms • Precompute “force field” for each term of scoring function (this will be slow) for each conformation of protein (usually only one) • Sample force fields at positions of ligand atoms p X Accelerate calculation of scoring function by 100X i r p Xi r [Huey & Morris] Outline Systematic Search Introduction Uniform sampling of search space • Relative position (3) Scoring functions The search space • Relative orientation (3) • Molecular mechanics has dimensionality n m • Empirical functions • Rotatable bonds in ligand (n) 3 + 3 + r + r • Knowledge-based • Rotatable bonds in protein (m) Searching poses & conformations • Systematic search • Molecular dynamics Rotations Translations • Simulated annealing • Genetic algorithms • Incremental construction • Rotamer libraries tstep rstep Results & Discussion FRED [Yang04] 6 Systematic Search Systematic Search Uniform sampling of search space Uniform sampling of search space • Exhaustive, deterministic • Exhaustive, deterministic • Quality dependent on granularity of sampling • Quality dependent on granularity of sampling • Feasible only for low-dimensional problems • Feasible only for low-dimensional problems § Example: search all rotations – Wigner-D-1 Maximum Correlation n o i Rotations t Translations a l e r r X o C Rotation Correlation in Rotational Frequency Correlation Domain Molecule 3D Grid Spherical Harmonic Functions Decompositions tstep rstep FRED [Yang04] Molecular Mechanics Simulated Annealing Energy minimization: Monte Carlo search of parameter space: • Start from a random or specific state • Start from a random or specific state (position, orientation, conformation) (position, orientation, conformation) • Move in direction indicated • Make random state changes, accepting up-hill moves by derivatives of energy function with probability dictated by “temperature” • Stop when reach • Reduce temperature after each move local minimum • Stop after temperature gets very small [Marai04] AutoDock 2.4 [Morris96] Genetic Algorithm Incremental Extension Genetic search of parameter space: Greedy fragment-based construction: • Start with a random population of states • Partition ligand into fragments • Perform random crossovers and mutations to make children • Select children with highest scores to populate next generation • Repeat for a number of iterations Gold [Jones95], AutoDock 3.0 [Morris98] FlexX [Rarey96] 7 Incremental Extension Incremental Extension Greedy fragment-based construction: Greedy fragment-based construction: • Partition ligand into fragments • Partition ligand into fragments • Place base fragment (e.g., with geometric hashing) • Place base fragment (e.g., with geometric hashing) • Incrementally extend ligand by attaching fragments FlexX [Rarey96] FlexX [Rarey96] Rotamer Libraries Rigid Docking Rigid docking of This is just like matching binding sites (complement) many conformations: • Can use same methods we used for matching