Compensatory evolution in RNA secondary structures increases substitution rate variation among sites

Abstract

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 (kappa) 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 kappa 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 kappa in paired sites within stems (kappa(p)) and unpaired sites within loops (kappa(u)). 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 kappa(p) > kappa(u). Only the Rev response element from the human immunovirus (HIV) genome showed the reverse pattern, with kappa(p) < kappa(u). Although a variety of evolutionary forces could produce quantitative deviations from the model predictions, the reversal in magnitude of kappa(p) and kappa(u) 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 kappa may have utility as a simple diagnostic to evaluate proposed secondary structures.

FIG. 1.—

RNA secondary structures. Representative (A) mitochondrial tRNA for asparagine (from mammalian); (B) mitochondrial tRNA for glutamine (from amphibian); (C) 5s rRNA; (D) RNaseP (shown is the sequence of Bacillus brevis)—black bars represent a pseudoknot; (E) RRE from HIV-1; (F) IRES; (G) CRE; (H) 12s rRNA (shown is the sequence of Bos taurus). The secondary structures of 16S and 23S rRNA can be found in Cannone et al. (2002).

FIG. 1.—

RNA secondary structures. Representative (A) mitochondrial tRNA for asparagine (from mammalian); (B) mitochondrial tRNA for glutamine (from amphibian); (C) 5s rRNA; (D) RNaseP (shown is the sequence of Bacillus brevis)—black bars represent a pseudoknot; (E) RRE from HIV-1; (F) IRES; (G) CRE; (H) 12s rRNA (shown is the sequence of Bos taurus). The secondary structures of 16S and 23S rRNA can be found in Cannone et al. (2002).

FIG. 2.—

Best-fit nucleotide substitution models for each alignment. Shown is a cartoon illustration of the rate categories of the best-fit nucleotide substitution models for each molecule. Within a molecule, rates were scaled to the maximum rate (black). Diagonal lines depict transitions; the edges of the square depict transversions. The HKY85 model, which was used for the rate ratios reported throughout this article, is shown for comparison on the right.

FIG. 3.—

Transition–transversion rate ratios (κ) for each alignment. The dotted line represents a 1:1 relationship between κ_p and κ_u. The solid line represents the predicted relationship ${\mathrm{\kappa }}_{\text{p}}={\mathrm{\kappa }}_{\text{u}}^2$. Note that the CRE data point is from the analysis of 4-fold degenerate sites in paired and unpaired regions.