Void distributions reveal structural link between jammed packings and protein cores

Dense packing of hydrophobic residues in the cores of globular proteins determines their stability. Recently, we have shown that protein cores possess packing fraction $\phi \approx 0.56$, which is the same as dense, random packing of amino acid-shaped particles. In this article, we compare the structural properties of protein cores and jammed packings of amino acid-shaped particles in much greater depth by measuring their local and connected void regions. We find that the distributions of surface Voronoi cell volumes and local porosities obey similar statistics in both systems. We also measure the probability that accessible, connected void regions percolate as a function of the size of a spherical probe particle and show that both systems possess the same critical probe size. By measuring the critical exponent $\tau$ that characterizes the size distribution of connected void clusters at the onset of percolation, we show that void percolation in packings of amino acid-shaped particles and protein cores belong to the same universality class, which is different from that for void percolation in jammed sphere packings. We propose that the connected void regions of proteins are a defining feature of proteins and can be used to differentiate experimentally observed proteins from decoy structures that are generated using computational protein design software. This work emphasizes that jammed packings of amino acid-shaped particles can serve as structural and mechanical analogs of protein cores, and could therefore be useful in modeling the response of protein cores to cavity-expanding and -reducing mutations.