Protein-ligand binding enthalpies from near-millisecond simulations: Analysis of a preorganization paradox

Calorimetric studies of protein-ligand binding sometimes yield thermodynamic data that are difficult to understand. Today, molecular simulations can be used to seek insight into such calorimetric puzzles, and, when simulations and experiments diverge, the results can usefully motivate further improvements in computational methods. Here, we apply near-millisecond duration simulations to estimate the relative binding enthalpies of four peptidic ligands with the Grb2 SH2 domain. The ligands fall into matched pairs, where one member of each pair has an added bond that preorganizes the ligand for binding and thus may be expected to favor binding entropically, due to a smaller loss in configurational entropy. Calorimetric studies have shown that the constrained ligands do in fact bind the SH2 domain more tightly than the flexible ones, but, paradoxically, the improvement in affinity for the constrained ligands is enthalpic, rather than entropic. The present enthalpy calculations yield the opposite trend, as they suggest that the flexible ligands bind more exothermically. Additionally, the small relative binding enthalpies are found to be balances of large differences in the energies of structural components such as ligand and the binding site residues. As a consequence, the deviations from experiment in the relative binding enthalpies represent small differences between these large numbers and hence may be particularly susceptible to error, due, for example, to approximations in the force field. We also computed first-order estimates of changes in configurational entropy on binding. These too are, arguably, paradoxical, as they tend to favor binding of the flexible ligands. The paradox is explained in part by the fact that the more rigid constrained ligands reduce the entropy of binding site residues more than their flexible analogs do, at least in the simulations. This result offers a rather general counterargument to the expectation that preorganized ligands should be associated with more favorable binding entropies, other things being equal.