Compensatory Evolution in RNA Secondary Structures Increases Substitution Rate Variation among Sites

There is growing evidence that interactions between biological molecules (e.g., RNA-RNA, protein-protein, RNA-protein) place limits on the rate and trajectory of molecular evolution. Here, by extending Kimura's model of compensatory evolution at interacting sites, we show that the ratio of transition to transversion substitutions (κ) at interacting sites should be equal to the square of the ratio at independent sites. Because transition mutations generally occur at a higher rate than transversions, the model predicts that κ should be higher at interacting sites than at independent sites. We tested this prediction in 10 RNA secondary structures by comparing phylogenetically derived estimates of κ in paired sites within stems (κp) and unpaired sites within loops (κu). Eight of the 10 structures showed an excellent match to the quantitative predictions of the model, and 9 of the 10 structures matched the qualitative prediction κp > κu. Only the Rev response element from the human immunovirus (HIV) genome showed the reverse pattern, with κp < κu. Although a variety of evolutionary forces could produce quantitative deviations from the model predictions, the reversal in magnitude of κp and κu could be achieved only by violating the model assumption that the underlying transition (or transversion) mutation rates were identical in paired and unpaired regions of the molecule. We explore the ability of the APOBEC3 enzymes, host defense mechanisms against retroviruses, which induce transition mutations preferentially in single-stranded regions of the HIV genome, to explain this exception to the rule. Taken as a whole, our findings suggest that κ may have utility as a simple diagnostic to evaluate proposed secondary structures.