  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.
