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Binding Energy Distribution Analysis Method (BEDAM) for estimating protein-ligand affinities

Ronald Levy Emilio Gallicchio , Mauro Lapelosa Chemistry Dept &BioMaPS Institute, Rutgers University. Binding Energy Distribution Analysis Method (BEDAM) for estimating protein-ligand affinities. Ways of Estimating Binding Affinities. Binding Free Energy Methods.

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Binding Energy Distribution Analysis Method (BEDAM) for estimating protein-ligand affinities

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  1. Ronald Levy Emilio Gallicchio, Mauro Lapelosa Chemistry Dept &BioMaPS Institute, Rutgers University Binding Energy Distribution Analysis Method (BEDAM) for estimating protein-ligand affinities

  2. Ways of Estimating Binding Affinities

  3. Binding Free Energy Methods • In principle they account for: • Total binding free energy • Entropic costs • Ligand/receptor reorganization Free Energy Perturbation (FEP/TI) Double Decoupling (DDM) McCammon, Jorgensen, Kollman (1980’s – present) Jorgensen, Gilson, Roux, Dill (2000’s – to present) • : • Challenges: • Dissimilar ligand sets • Dependence on starting conformations • Multiple bound poses • Numerical instability • Slow convergence

  4. Statistical Thermodynamics Theory of Binding [Gilson et al., (1997)] Binding “energy” of a fixed conformation of the complex. W(): solvent PMF Ligand in binding site in absence of ligand-receptor interactions Probability distribution of binding energy in “0” ensemble Formalism homologous to Particle Insertion for solvation (Pratt, Widom, etc.)

  5. Choice of Vsite • Free energy gain for turning on ligand-receptor interactions • Gets less favorable as Vsite is increased • Entropic work to place the ligand in binding site from a solution at concentration C° • Gets more favorable as Vsite is increased • The two effects cancel each other out • Result insensitive to choice of Vsite as long as it contains all of the bound conformations

  6. The Binding Energy Distribution Analysis Method (BEDAM) P0 (ΔE): encodes all enthalpic and entropic effects Integration problem: region at favorable ΔE’s is seriously undersampled. P0(ΔE) P0(ΔE ) [kcal/mol-1] • Solution: • Hamiltonian Replica Exchange +WHAM • Biasing potential = λ ΔE • Ideal for cluster computing. Main contribution to integral ΔE [kcal/mol]

  7. Improved Sampling with HREM Uncouple-MD • Better sampling at λ≈1 • BEDAM/HREM less sensitive to initial conditions than BEDAM/MD Phenol bound to L99A/M102Q T4 Lysozyme X-ray pose ΔFb [kcal/mol] Coupled-HREM “Bad” pose time [ns]

  8. Binding Affinity Density Can write: with “Binding Affinity Density” Measures contribution to binding constant from conformations at ΔE k(ΔE) Spread indicative of multiple poses entropically favored k(ΔE) Average binding energy (“enthalpic” component) ΔE ΔE

  9. H H H The AGBNP2 Implicit Solvent Model OPLS-AA/AGBNP Non-Polar Hydration First-Shell Hydration Analytical Generalized Born Parameter-free pairwise descreening implementation Analytical intermolecular HB potential Cavity/vdW dispersion decomposition. Gallicchio, Paris, Levy, JCTC, 5, 2544-2564 (2009). Gallicchio, Levy. JCC, 25, 479-499 (2004).

  10. Improved Intramolecular Interactions • MD simulations of mini-proteins with the AGBNP 2.0 model • Number of intramolecular hydrogen bonds now agrees with explicit solvent and NMR. FSD TrpCage PSV

  11. L99A Hydrophobic cavity L99A/M102Q Polar cavity Brian Matthews Brian Shoichet Benoit Roux David Mobley Ken Dill John Chodera Graves, Brenk and Shoichet, JMC (2005) Results for Binding to Mutants of T4 Lysozyme BEDAM: 2ns HREM, 12 replicas λ={10-6, 10-5, 10-4, 10-3, 10-2, 0.1, 0.15, 0.25, 0.5, 0.75, 1, 1.2} IMPACT + OPLS-AA/AGBNP2

  12. Isosteric Ligand Set L99A – Apolar L99A/M102Q – Polar Binders Binders benzene iso-butylbenzene phenol 3-chlorophenol indole toluene catechol toluene Non-Binders Non-Binders phenol 1,3,5-trimethylbenzene 4-vinylpiridine phenylhydrazine cyclohexane ter-butylbenzene 2-aminophenol 4-chloro-1h-pyrazole

  13. Binders vs. Non-Binders L99A T4 Lysozyme, Apolar Cavity L99A/M102Q T4 Lysozyme, Polar Cavity

  14. Free Energy vs. Energy-based Predictors L99A/M102Q T4 Lysozyme, Polar Cavity • The minimum binding energy is poorly correlated to binding free energy • Average binding energy is a somewhat better predictor

  15. 3-chlorophenol ΔF°b=-3.47 kcal/mol Kb = (1.77 + 0.71 + 0.28)  103 catechol ΔF°b=-3.44 kcal/mol Kb = (1.48 + 1.31)  103 k(ΔE) [kcal/mol-1] Xtal1 52% Xtal2 46% Xtal 62% pose2 25% pose3 10% ΔE [kcal/mol] ΔE [kcal/mol] Conformational Decomposition Observed binding constant is a weighted average of the binding constants of individual macrostates i Macrostate-specific binding constant Macrostate population at λ=0 Observed affinity due to multiple binding poses

  16. Reorganization (ligand and receptor) • Reorganization refers to the free energy cost to restrict the system to the bound conformation • λ-coupling in BEDAM is a partial solution, • Additional ways to accelerate sampling of unbound states using (multi-dimensional) replica exchange are available Example: TMC278 HIV-RT Inhibitor Temperature replica exchange + WHAM Bound conformation P3% Frenkel, Gallicchio, Das, Levy, Arnold. JMC (2009) Okumura, Gallicchio, Levy, JCC, 2010

  17. Reorganization: large scale studies Ligand Receptor • 146 ligands for 4 target receptors: • ABL-kinase, P38-kinase, nn-HIVRT, PDE4 • Temperature RE calculations HIV-RT (non-nucleoside site) Analysis of ~100 crystal structures Count ΔF(reorg) [kcal/mol] • The majority of ligands have reorganization free energy > 1 kcal/mol Paris, Haq, Felts, Das, Arnold, Levy. JMC (2009)

  18. Sampling Enhancements for reorganization • (λ, T)-replica exchange with conformation reservoirs Precomputed receptor and ligand T-REM conformational reservoirs at λ=0. λ 0 T • Reservoirs at λ=0 provide conformational diversity • Calculations for ligand reservoirs are inexpensive • Receptor λ=0 reservoir needs to be computed only once • Can include a “knowledge-based” set from crystal structures

  19. Conclusions • BEDAM: binding affinities from probability distributions of binding energies in a special ensemble (l=0) • Full account of entropic effects • Efficient implementation based on parallel HREM sampling and WHAM; well matched to underlying theory • Illustrative calculations on T4 Lysozyme • Enhancements needed to fully treat ligand/receptor reorganization

  20. Ronald Levy Emilio Gallicchio, Mauro Lapelosa Chemistry Dept &BioMaPS Institute, Rutgers University Binding Energy Distribution Analysis Method (BEDAM) for estimating protein-ligand affinities

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