One Plus One Makes Three: Triangular Coupling of Correlated Amino Acid Mutations

Correlated mutations have played a pivotal role in the recent success in protein fold prediction. Understanding nonadditive effects of mutations is crucial for altering protein structure, as mutations of multiple residues may change protein stability or binding affinity in a manner unforeseen by the investigation of single mutants. While the couplings between amino acids can be inferred from homologous protein sequences, the physical mechanisms underlying these correlations remain elusive. In this work we demonstrate that calculations based on the first-principles of statistical mechanics are capable of capturing the effects of nonadditivities in protein mutations. The identified thermodynamic couplings cover the short-range as well as previously unknown long-range correlations. We further explore a set of mutations in staphyloccocal nuclease to unravel an intricate interaction pathway underlying the correlations between amino acid mutations.