Protein side-chain fluctuations: A computational study of entropy and correlation

Despite the high density within a typical protein fold, the ensemble of sterically permissible side-chain repackings is vast. Motion within this crowded environment can be accommodated in part through correlated fluctuations, and experimental evidence suggests that wide-spread changes in side-chain fluctuations can result from ligand-binding or point mutations. Here we examine the extent of the available side-chain packing 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 quantify the torsional entropy of this native state ensemble, relative to that of a noninteracting reference system. The reduction in entropy per rotatable bond due to each kind of interaction is remarkably consistent across a set of twelve small proteins. To assess the biophysical importance of these fluctuations, we estimate side-chain entropic 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 · 308 K). We also quantify correlations among side-chain inter-rotameric motions. Results indicate that long range correlations of side-chain fluctuations can arise independently from several different types of interactions. These robust correlations persist across the entire protein and can propagate long-range changes in side-chain variability in response to single residue perturbations. As the protein is cooled, these fluctuations die away. We examine the equilibrium behavior of side-chain torsional fluctuations over a range of temperatures from 100 K to 345 K. We find that just as the distribution of entropy amongst the residues at physiological temperature is heterogeneous, so too is their equilibrium behavior upon cooling. Within a limited temperature range, the side-chain variability of a few residues even increases upon cooling.