1、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,Binding Free Energy Methods,Free Energy Perturbation (FEP/TI),Double
2、Decoupling (DDM),McCammon, Jorgensen, Kollman (1980s present),Jorgensen, Gilson, Roux, Dill (2000s 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 energ
3、y 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 solva
4、tion (Pratt, Widom, etc.),Ligand in binding site in absence of ligand-receptor interactions,Choice of Vsite,Entropic work to place the ligand in binding site from a solution at concentration C Gets more favorable as Vsite is increased,Free energy gain for turning on ligand-receptor interactions Gets
5、 less 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,The Binding Energy Distribution Analysis Method (BEDAM),P0 (E): encodes all enthalpic and entropic effects,Solution: Hamiltonian Rep
6、lica Exchange +WHAM Biasing potential = E,E kcal/mol,P0(E ) kcal/mol-1,P0(E),Integration problem: region at favorable Es is seriously undersampled.,Main contribution to integral,Ideal for cluster computing.,Better sampling at 1 BEDAM/HREM less sensitive to initial conditions than BEDAM/MD,X-ray pose
7、,“Bad” pose,Uncouple-MD,Coupled-HREM,time ns,Fb 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 E,E,k(E),Spread indicative of multiple poses
8、,Average binding energy (“enthalpic” component),E,k(E),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, 2544-2564 (2009). Gallicch
9、io, Levy. JCC, 25, 479-499 (2004).,First-Shell Hydration,Non-Polar Hydration,Analytical intermolecular HB potential,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 a
10、nd NMR.,Results for Binding to Mutants of T4 Lysozyme,BEDAM: 2ns HREM, 12 replicas =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 Apolar,L99A/M102Q Polar,Binders,Binders,Non-Binders,Non-Binders,phenol,4-vinylpiridine,phenylhydrazin
11、e,2-aminophenol,3-chlorophenol,4-chloro-1h-pyrazole,catechol,toluene,benzene,1,3,5-trimethylbenzene,cyclohexane,ter-butylbenzene,indole,toluene,phenol,iso-butylbenzene,Binders vs. Non-Binders,L99A T4 Lysozyme, Apolar Cavity,L99A/M102Q T4 Lysozyme, Polar Cavity,Free Energy vs. Energy-based Predictors
12、,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,E kcal/mol,k(E) kcal/mol-1,Energetically favored,Entropically favored,Entropically favored:,Polar Receptor,Apolar Recepto
13、r,Computed Binding affinity densities,k(E) functions provide insights on the driving forces for binding,Conformational Decomposition,Observed binding constant is a weighted average of the binding constants of individual macrostates i,Macrostate population at =0,Macrostate-specific binding constant,O
14、bserved affinity due to multiple binding poses,Reorganization (ligand and receptor),Reorganization refers to the free energy cost to restrict the system to the bound conformation -coupling in BEDAM is a partial solution, Additional ways to accelerate sampling of unbound states using (multi-dimension
15、al) replica exchange are available,Okumura, Gallicchio, Levy, JCC, 2010,Example: TMC278 HIV-RT Inhibitor,Bound conformation,P3%,Temperature replica exchange + WHAM,Frenkel, Gallicchio, Das, Levy, Arnold. JMC (2009),Reorganization: large scale studies,146 ligands for 4 target receptors: ABL-kinase, P
16、38-kinase, nn-HIVRT, PDE4 Temperature RE calculations,F(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),T,0,Precomputed receptor a
17、nd ligand T-REM conformational reservoirs at =0.,Sampling Enhancements for reorganization,(, T)-replica exchange with conformation reservoirs,Reservoirs at =0 provide conformational diversity Calculations for ligand reservoirs are inexpensive Receptor =0 reservoir needs to be computed only once Can
18、include a “knowledge-based” set from crystal structures,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
19、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,
