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 (κ(p)) and unpaired sites within loops (κ(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 κ(p) > κ(u). Only the Rev response element from the human immunovirus (HIV) genome showed the reverse pattern, with κ(p) < κ(u). Although a variety of evolutionary forces could produce quantitative deviations from the model predictions, the reversal in magnitude of κ(p) and κ(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.越来越多的证据表明，生物分子（biological molecules）间的相互作用（例如RNA-RNA相互作用、蛋白质-蛋白质相互作用、RNA-蛋白质相互作用）会限制分子进化的速率与演化轨迹。 本研究通过拓展相互作用位点处的木村资生补偿性进化模型（Kimura's model of compensatory evolution），证明了相互作用位点上的转换（transition）与颠换（transversion）替换率比值（κ）应等于独立位点上该比值的平方。由于转换突变的发生速率普遍高于颠换突变，该模型预测相互作用位点的κ值应高于独立位点。 我们通过比对茎区配对位点（paired sites within stems，记为κ(p)）与环区非配对位点（unpaired sites within loops，记为κ(u)）的系统发育推导κ估计值，在10个RNA二级结构中验证了这一预测。10个结构中有8个与该模型的定量预测结果高度吻合，9个符合κ(p) > κ(u)的定性预测。仅来自人类免疫病毒（human immunovirus）基因组的Rev应答元件（Rev response element）呈现出相反模式，即κ(p) < κ(u)。 尽管多种进化动力可导致该模型预测值出现定量偏差，但κ(p)与κ(u)的大小逆转，仅能通过违背模型假设得以实现——该假设认为分子的配对与非配对区域中，基础转换（或颠换）突变率完全一致。我们探究了APOBEC3酶（APOBEC3 enzymes）——一种针对逆转录病毒（retroviruses）的宿主防御机制——的作用能力，该酶可优先在人类免疫病毒基因组的单链区域（single-stranded regions）诱导转换突变，以此解释这一反常现象。 综合来看，本研究结果表明，κ可作为一种简便的诊断工具，用于评估已提出的RNA二级结构的合理性。