| Correlations between amino acids at different sites in protein sequences of the same protein family may yield important information on the protein three-dimensional structure and its evolution. We recently proposed an analytical approach which allows to quantitatively predict correlations that arise from selective constraints on unfolding and misfolding stabilities. Our approach is based on a cluster expansion of sequence entropy up to pairwise terms, with stability constraints represented through Lagrange multipliers. These Lagrange multipliers can be obtained either directly from data of correlated mutations or via the constraints on the cumulants of the partition function of the native and the misfolded ensemble, yielding very similar values. We show that in the latter case, the constraints can be written in good approximation as linear functions of the Lagrange multipliers, and that the coefficients quantify the strength of selective constraints on unfolding and misfolding stabilities on the correlation. |
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