Advanced in silico drug design
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1 Advanced in silico drug design RNDr. Martin Lepšík, Ph.D. Lecture: Advanced scoring Palacky University, Olomouc
2 Outline 1. Scoring Definition, Types 2. Physics-based Scoring: Master Equation Terms 3. Molecular Mechanics (MM) 4. Solvation Models 5. Quantum Mechanics (QM) 6. Water Thermodynamics (WaterMap) 7. Molecular Dynamics (MD) 8. MM-PBSA 9. Alchemical Simulations (FEP, TI) 2
3 Scoring - protein ligand affinity prediction - master equation = scoring function - Requirements: quick and accurate 1) Empirical/Statistical (Glide, ChemScore) - regression-based, arbitrary terms (H-bonds, hydrophobic contacts) 2) Knowledge (DrugScore) rules from experimental data pseudopotentials 3) Physics (DOCK, Autodock, GoldScore) molecular/quantum mechanics 3
4 Score = ΔE int + ΔΔG solv + ΔG conf (P,L) - TΔS Affinity = Interactions + Solvation + Entropy
5 Supramolecular Approach What is the weight of Popeye, the sailor?
6 Supramolecular Interaction Energy Weigh him on a ship and subtract the weight of the ship. Problem: Subtracting large numbers to get a small difference prone to inaccuracies
7 ΔE int by Molecular Mechanics (MM) Atom = point charge, radius and mass Molecule = atoms connected by springs, classical mechanics, parameters Non-bonded terms: electrostatic and van der Waals (dispersion) ΔE int = ΔE coulomb + ΔE vdw
8 Score = ΔE int + ΔΔG solv + ΔG conf (P,L) - TΔS Affinity = Interactions + Solvation + Entropy
9 Solvation Free Energy Implicit = Continuum - MM: generalized Born, Poisson-Boltzmann - QM: PCM, COSMO, SMD Explicit - MM: TIP3P, SPC,.TIP5P, SPC/E - QM: H 3 O +
10 Poisson-Boltzmann Surface Area (PBSA) PB: describes the electrostatic effect of solvent SA: linear relations between Gibbs free energy of transfer and the surface area of a solute molecule
11 Skore [kcal/mol] Skore [kcal/mol] Scoring Function Problems I Soft Repulsion Electrostatics original DOCK 6.6 DOCK 6.6 with exponential repulsion RMSD [A] -60 RMSD [A] Bazgier V, Banáš P, Berka K, Otyepka M, in preparation 11
12 Scoring Function Problems II Qualitative: Missing Quantum Effects (proton/charge transfer, polarization, halogen-bonding, metals, inorganic ligands) Quantitative: Accuracy QM Implicit Solvation Kolar, Hobza. J. Phys Chem. B, 2013, 117, Dobes, Hobza. J Phys Chem B, 2011, 115,
13 QM-based Scoring Function QM Interactions and solvation Score = ΔE int + ΔΔG solv + ΔG conf (P,L) TΔS ΔE int - PM6-D3H4X (corrected semiempirical QM) ΔΔG solv - COSMO (PM6), SMD (HF, ligand only) Lepsik, Fanfrlik. ChemPlusChem 2013, 78,
14 Quantum Chemistry Covalent Reactions electron rearrangements Noncovalent Interactions - proton/charge transfer - sigma-hole bonding - metals - ligands (no parametrization) System size Accuracy Time 14
15 Ab initio Quantum Mechanics (QM) mathematical description of dual particle-wave duality Time independent Schrődinger equation: Eψ = Ĥψ E - energy ψ - Wave function Ĥ Hamilton operator Ab initio QM methods ( from first principles of QM ) Hartree-Fock electronic effects as mean field, H-bond described, not dispersion (electron correlation) Møler-Plesset perturbation theory (MP2, MP3,.) CCSD(T) coupled-cluster, singles doubles triples Scaling HF (N 4 ), MP2 (N 5 ), CCSD(T) (N 6 ) 15
16 Density Functional Theory (DFT) Alternative (non-ψ) description Electron Density Partial description of dispersion Exchange-correlation Functionals: B3LYP, PBE, BP86, M06 Missing Dispersion - Empirical 16
17 Basis Sets Set of functions representations of molecular orbitals (MO-LCAO) Slater - Gaussian - Minimal basis set (one function per orbital) - Polarization functions - Diffuse functions - STO-3G, 3-21G, 6-31G*, G**, SVP, aug-cc-pvtz 17
18 Semiempirical QM Integrals parameters Simplified HF, no dispersion AM1, PM6 - MOPAC Linear scaling (N): MOZYME Underestimate H-bonds, repulsion subminimal basis, only valence orbitals, core-core Stewart J, MOPAC
19 Corrected Semiempirical QM D3H4X reliable: corrections for H-bonding, D-dispersion, X-bonding Řezáč,, Hobza J. Chem. Theory Comput. 2009, 5, 1749 Řezáč, Hobza, Chem. Phys.Lett. 2011, 506, 286 Řezáč, Hobza, J. Chem. Theory Comput. 2012, 8,
20 Parametrization Model systems Consistent Datasets CCSD(T)/CBS H-bonding, dispersion, stacking (S22, S66) Nonequilibrium geometries (S22x5, S66x8) X-bonding (X40) Large dispersion (L7) 20
21 Limitations of QM Scoring - PM6-D3H4X vs. DFT-D - Implicit solvent - Single-Conformer Approach Solutions: QM/SQM Hybrid explicit/implicit solvent model Dynamics and Snapshot rescoring 21
22 Water Thermodynamics WaterMap (Schrodinger), GRID, JAWS, HINT, Vorlová, Nachtigallová, Lepšík Eur. J. Med. Chem. 2015, 89,
23 Molecular Dynamics Solving Newton s equations of motion MM (no electrons, only nuclei!) E (x) = E covalent + E noncovalent E covalent = E bond + E angle + E dihedral torsion E noncovalent = E electrostatic + E vanderwaals -de/dx = F = m * a = m * dv/dt = m * (dx/dt)/dt Trajectory - x, v (t): initial (x-structure, v - Gaussian) Integrator (Leap-frog, Verlet) time step (1-4 fs) 23
24 Thermodynamic Ensembles, Heat, Pressure, Solvent NVE (microcanonical) NVT (canonical, isothermal isochoric) NPT (Isothermal isobaric) Temperature, pressure coupling to external (heat, pressure) baths Solvent implicit (dielectric), explicit (water box) 24
25 Periodic Boundary Condition unit cell infinite system Boxes - rectangular, - truncated octahedron Long-range electrostatics 25
26 MD Analyses Fluctuations of energy, volume, pressure, temperature Root-mean square deviations (RMSD): protein backbone, ligand Heating, Equilibration, Production Atomic fluctuations: B-factors, Order parameters Atom-atom Distances 26
27 MD-MM/GBSA ca. 100 Snapshots from Explicit MD strip water - ΔG - average ΔG = ΔE MM + ΔG solv TΔS ΔE MM = E bond + E angle + E dihedral torsion + E electrostatic + E vanderwaals ΔG solv = ΔG solv-pol (GB,PB) + ΔG solv-nonpol (SA) TΔS loss of translation, rotation, vibration kcal/mol 27
28 Alchemical Simulations Relative free energies of solvation, binding - only small changes Thermodynamic Cycle ΔG state function ΔG(D+A) = ΔG(B+C) ΔG(A-B) = ΔG(C-D) Experimental binding Alchemical Simulations Chemical accuracy (+/- 1 kcal/mol) Forward-reverse hysteresis, sampling, convergence, force-field limitations 28
29 Conclusions 1. Scoring Definition, Types 2. Physics-based Scoring: Master Equation Terms 3. Molecular Mechanics (MM) 4. Solvation Models 5. Quantum Mechanics (QM) 6. Water Thermodynamics (WaterMap) 7. Molecular Dynamics (MD) 8. MM-PBSA 9. Alchemical Simulations (FEP, TI) 29
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