England, Jeremy L.Shakhnovich, Eugene I.2019-09-272003England, Jeremy L., and Eugene I. Shakhnovich. 2003. “Structural Determinant of Protein Designability.” Physical Review Letters 90 (21). https://doi.org/10.1103/physrevlett.90.218101.0031-90071079-71141092-0145http://nrs.harvard.edu/urn-3:HUL.InstRepos:41417287Here 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.en-USJournal Article2019-09-2710.1103/PhysRevLett.90.218101