Calculation of proteins' total side-chain torsional entropy and its influence on protein-ligand interactions

Despite the high density within a typical protein fold, the ensemble of sterically permissible side-chain repackings is vast. Here, we examine the extent of this variability that survives energetic biases due to van der Waals interactions, hydrogen bonding, salt bridges, and solvation. Monte Carlo simulations of an atomistic model exhibit thermal fluctuations among a diverse set of side-chain arrangements, even with the peptide backbone fixed in its crystallographic conformation. We have quantified the torsional entropy of this native-state ensemble, relative to that of a noninteracting reference system, for 12 small proteins. The reduction in entropy per rotatable bond due to each kind of interaction is remarkably consistent across this set of molecules. To assess the biophysical importance of these fluctuations, we have estimated side-chain entropy contributions to the binding affinity of several peptide ligands with calmodulin. Calculations for our fixed-backbone model correlate very well with experimentally determined binding entropies over a range spanning more than 80 kJ/(mol x 308 K).