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

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

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

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

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

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.

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

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

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, (2009). Gallicchio, Levy. JCC, 25, (2004). First-Shell Hydration Non-Polar Hydration Analytical intermolecular HB potential H H H

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.

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

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

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

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

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

Conformational Decomposition ΔE [kcal/mol] Xtal 62% pose3 10% pose2 25% 3-chlorophenol ΔF° b =-3.47 kcal/mol K b = ( )  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 = ( )  10 3

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)

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)

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

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

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