Structural origins of protein conformational entropy

The thermodynamics of molecular recognition by proteins is a central determinant of complex biochemistry. For over a half-century detailed cryogenic structures have provided deep insight into the energetic contributions to ligand binding by proteins1. More recently, a dynamical proxy based on NMR-relaxation methods has revealed an unexpected richness in the contributions of conformational entropy to the thermodynamics of ligand binding2,3,4,5. There remains, however, a discomforting absence of an understanding of the structural origins of fast internal motion and the conformational entropy that this motion represents. Here we report the pressure-dependence of fast internal motion within the ribonuclease barnase and its complex with the protein barstar. Distinctive clustering of the pressure sensitivity correlates with the presence of small packing defects or voids surrounding affected side chains. Prompted by this observation, we performed an analysis of the voids surrounding over 2,500 methyl-bearing side chains having experimentally determined order parameters. We find that changes in unoccupied volume as small as a single water molecule surrounding buried side chains greatly affects motion on the subnanosecond timescale. The discovered relationship begins to permit construction of a united view of the relationship between changes in the internal energy, as exposed by detailed structural analysis, and the conformational entropy, as represented by fast internal motion, in the thermodynamics of protein function.