Efficient Computation of Small-Molecule Configurational Binding Entropy and Free Energy Changes by Ensemble Enumeration

Here we present a novel, end-point method using the dead-end-elimination and A* algorithms to efficiently and accurately calculate the change in free energy, enthalpy, and configurational entropy of binding for ligand-receptor association reactions. We apply the new approach to the binding of a series of human immunodeficiency virus (HIV-1) protease inhibitors to examine the effect ensemble reranking has on relative accuracy as well as to evaluate the role of the absolute and relative ligand configurational entropy losses upon binding in affinity differences for structurally related inhibitors. Our results suggest that most thermodynamic parameters can be estimated using only a small fraction of the full configurational space, and we see significant improvement in relative accuracy when using an ensemble versus single-conformer approach to ligand ranking. We also find that using approximate metrics based on the single-conformation enthalpy differences between the global minimum energy configuration in the bound as well as unbound states also correlates well with experiment. Using a novel, additive entropy expansion based on conditional mutual information, we also analyze the source of ligand configurational entropy loss upon binding in terms of both uncoupled per degree of freedom losses as well as changes in coupling between inhibitor degrees of freedom. We estimate entropic free energy losses of approximately +24 kcal/mol, 12 kcal/mol of which stems from loss of translational and rotational entropy. Coupling effects contribute only a small fraction to the overall entropy change (1-2 kcal/mol) but suggest differences in how inhibitor dihedral angles couple to each other in the bound versus unbound states. The importance of accounting for flexibility in drug optimization and design is also discussed.