  Here we present an approximate analytical theory for the relationship between
a protein structure's contact matrix and the shape of its energy spectrum in
amino acid sequence space. We demonstrate a dependence of the number of
sequences of low energy in a structure on the eigenvalues of the structure's
contact matrix, and then use a Monte Carlo simulation to test the applicability
of this analytical result to cubic lattice proteins. We find that the lattice
structures with the most low-energy sequences are the same as those predicted
by the theory. We argue that, given sufficiently strict requirements for
foldability, these structures are the most designable, and we propose a simple
means to test whether the results in this paper hold true for real proteins.
