Void Distributions and Vibrational Response in Protein Cores*

Proteins derive much of their stability from densely packed, hydrophobic residues that are shielded from solvent in protein cores. Our previous studies have shown that the packing fraction in protein cores is the same as that for jammed packings of purely repulsive, residue-shaped particles, which suggests that the protein backbone does not significantly affect how core residues pack. Here, we investigate the distribution of void space in protein cores and packings of residue-shaped particles. We show that packings of residue-shaped particles and protein cores possess similar connected void and free volume distributions. We also calculate the density of vibrational modes for packings of residue-shaped particles, and find an abundance of low frequency vibrational modes, which suggests the presence of low-energy collective motions of residues in protein cores. These results suggest that jammed packings of residue-shaped particles can serve as a mechanical analog for residues in protein cores, which can give insight into the response of protein cores to mutations.