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Four-body potentials reveal protein-specific correlations to stability changes caused by hydrophobic core mutations.

Mutational experiments show how changes in the hydrophobic cores of proteins affect their stabilities. Here, we estimate these effects computationally, using four-body likelihood potentials obtained by simplicial neighborhood analysis of protein packing (SNAPP). In this procedure, the volume of a known protein structure is tiled with tetrahedra having the center of mass of one amino acid side-chain at each vertex. Log-likelihoods are computed for the 8855 possible tetrahedra with equivalent compositions from structural databases and amino acid frequencies. The sum of these four-body potentials for tetrahedra present in a given protein yields the SNAPP score. Mutations change this sum by changing the compositions of tetrahedra containing the mutated residue and their related potentials. Linear correlation coefficients between experimental mutational stability changes, Delta(DeltaG(unfold)), and those based on SNAPP scoring range from 0.70 to 0.94 for hydrophobic core mutations in five different proteins. Accurate predictions for the effects of hydrophobic core mutations can therefore be obtained by virtual mutagenesis, based on changes to the total SNAPP likelihood potential. Significantly, slopes of the relation between Delta(DeltaG(unfold)) and DeltaSNAPP for different proteins are statistically distinct, and we show that these protein-specific effects can be estimated using the average SNAPP score per residue, which is readily derived from the analysis itself. This result enhances the predictive value of statistical potentials and supports previous suggestions that "comparable" mutations in different proteins may lead to different Delta(DeltaG(unfold)) values because of differences in their flexibility and/or conformational entropy.