Testing for spatial clustering of amino acid replacements within protein tertiary structure

Widely used models of protein evolution ignore protein structure. Therefore, these models do not predict spatial clustering of amino acid replacements with respect to tertiary structure. One formal and biologically implausible possibility is that there is no tendency for amino acid replacements to be spatially clustered during evolution. An alternative to this is that amino acid replacements are spatially clustered and this spatial clustering can be fully explained by a tendency for similar rates of amino acid replacement at sites that are nearby in protein tertiary structure. A third possibility is that the amount of clustering exceeds that which can be explained solely on the basis of independently evolving protein sites with spatially clustered replacement rates. We introduce two simple and not very parametric hypothesis tests that help distinguish these three possibilities. We then apply these tests to 273 homologous protein families. The null hypothesis of no spatial clustering is rejected for 102 of 273 families. The explanation of spatially clustered rates but independent change among sites is rejected for 43 families. These findings need to be reconciled with the common practice of basing evolutionary inferences on models that assume independent change among sites.