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

2. Ways of Estimating Binding Affinities Docking & ScoringScreening & Enrichment1000’s of compounds MM-PB/SA Linear Interaction Energy Ranking100’s of compounds Absolute/Relative Binding Free Energy Methods Ranking, Optimization, Specificity, Resistance 10’s of compounds

3. Binding Free Energy Methods 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 In principle they account for: Total binding free energy Entropic costs Ligand/receptor reorganization

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

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

6. The Binding Energy Distribution Analysis Method (BEDAM) P 0 ( ΔE) : encodes all enthalpic and entropic effects Solution: Hamiltonian Replica Exchange +WHAM Biasing potential = λ ΔE ΔE [kcal/mol] P 0 ( Δ E ) [kcal/mol -1 ] P0(ΔE)P0(ΔE) Integration problem: region at favorable ΔE’s is seriously undersampled. Main contribution to integral Ideal for cluster computing.

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

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

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

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

11. Results for Binding to Mutants of T4 Lysozyme 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) 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 – ApolarL99A/M102Q – Polar Binders Non-Binders phenol 4-vinylpiridinephenylhydrazine 2-aminophenol 3-chlorophenol 4-chloro-1h-pyrazole catecholtoluene benzene 1,3,5-trimethylbenzene cyclohexaneter-butylbenzene indoletoluene phenol iso-butylbenzene

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

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

15. Role of Entropy ΔE [kcal/mol] k( Δ E) [kcal/mol -1 ] Energetically favored Entropically favored Entropically favored: Polar Receptor Apolar Receptor Computed Binding affinity densities k(ΔE) functions provide insights on the driving forces for binding

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

17. 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 Okumura, Gallicchio, Levy, JCC, 2010 Example: TMC278 HIV-RT Inhibitor Bound conformation P  3% Temperature replica exchange + WHAM Frenkel, Gallicchio, Das, Levy, Arnold. JMC (2009)

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

19. λ T 0 Precomputed receptor and ligand T-REM conformational reservoirs at λ=0. Sampling Enhancements for reorganization (λ, T)-replica exchange with conformation reservoirs 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

20. Conclusions BEDAM: binding affinities from probability distributions of binding energies in a special ensemble ( =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

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