Effects of gene duplication, epistasis, recombination and gene conversion on the fixation time of compensatory mutations.

Gene duplication is one of the major mechanisms of molecular evolution. Gene duplication enables copies of a gene to accumulate mutations through functional redundancy. If a gene encodes a specific protein that interacts with other proteins, RNA, or DNA, the relaxation of selective constraints caused by gene duplication might contribute to the fixation of compensatory mutations that occur at the interacting sites. In this study, we investigate the effect of gene duplication, epistasis among the duplicated copies and gene conversion on the fixation time of compensatory mutations by extending the original model of compensatory evolution proposed by Kimura in 1985. Our simulation results reveal that the time to fixation of compensatory mutations can be decreased remarkably by gene duplication if one of the duplicated loci can completely mask the deleterious effects of a mutation that occurs at the other locus. Conversely, the fixation time can be increased by gene duplication if such functional compensation is weak. We also show that the combination of the degree of functional compensation and the rate of gene conversion between duplicate loci have contrasting effects on the time to fixation of compensatory mutations.

A model of compensatory molecular evolution involving multiple sites in RNA molecules.

Consider two sites under compensatory fitness interaction, such as a Watson-Crick base pair in an RNA helix or two interacting residues in a protein. A mutation at any one of these two sites may reduce the fitness of an individual. However, fitness may be restored by the occurrence of a second mutation at the other site. Kimura modeled this process using a two-locus haploid fitness scheme with two alleles at each locus. He predicted that compensatory evolution following this model is very rare unless selection against the deleterious single mutations is weak and linkage between the interacting sites is tight. Here we investigate the question whether the rate of compensatory evolution increases if we take the context of the two directly interacting sites into account. By "context", we mean the effect of neighboring sites in an RNA helix. Interaction between the focal pair of sites under consideration and the context may lead to so-called indirect compensation. Thus, extending Kimura's classical model of compensatory evolution, we study the effects of both direct and indirect compensation on the rate of compensatory evolution. It is shown that the effects of indirect compensation are very strong. We find that recombination does not slow down the rate of compensatory evolution as predicted by the classical model. Instead, compensatory substitutions may be relatively frequent, even if linkage between the focal interacting sites is loose, selection against deleterious mutations is strong, and mutation rate is low. We compare our theoretical results with data on RNA secondary structures from vertebrate introns.

Models of compensatory molecular evolution: effects of back mutation.

Compensatory mutations are individually deleterious but appropriate combinations of mutants are harmless. For several models of compensatory molecular evolution, we consider the effects of back mutation. It is shown that the effects of back mutation on the rate of compensatory molecular evolution are weak. Further we estimate the values of selection parameter of deleterious single mutants for the models of compensatory molecular evolution both with and without back mutation using sequence data of folded RNA molecules and compare them with the previous results.

Compensatory evolution in diploid populations.

Compensatory mutations are individually deleterious but harmless in appropriate combinations either at more than two sites within a gene or on separate genes. Considering that dominance effects of selection and heterodimer formation of gene products may affect the rate of compensatory evolution, we investigate compensatory neutral mutation models for diploid populations. Our theoretical analysis on the average time until fixation of compensatory mutations shows that these factors play an important role in reducing the fixation time of compensatory mutations if mutation rates are not low. Compensatory evolution of heterodimers is shown to occur more easily if the deleterious effects of single mutants are recessive.