How frequent are correlated changes in families of protein sequences?

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Abstract
A loss-of-function point mutation in a protein is often rescued by an additional mutation that compensates for the original physical change. According to one hypothesis, such compensation would be most effective in maintaining a structural motif if the two mutated residues were spatial neighbors. If this hypothesis were correct, one would expect that many such compensatory mutations have occurred during evolution and that present-day protein families show some degree of correlation in the occurrence of amino acid residues at positions whose side chains are in contact. Here, a statistical theory is presented which allows evaluation of correlations in a family of aligned protein sequences by assigning a scalar metric (such as charge or side-chain volume) to each type of amino acid and calculating correlation coefficients of these quantities at different positions. For the family of myoglobins it is found that there is a high correlation between fluctuations in neighboring charges. The correlation is close to what would be expected for total conservation of local charge. For the metric side-chain volume, on the other hand, no correlation could be found.