Phenotype switching of the mutation rate facilitates adaptive evolution

Abstract

The mutation rate plays an important role in adaptive evolution. It can be modified by mutator and anti-mutator alleles. Recent empirical evidence hints that the mutation rate may vary among genetically identical individuals: evidence from bacteria suggests that the mutation rate can be affected by expression noise of a DNA repair protein and potentially also by translation errors in various proteins. Importantly, this non-genetic variation may be heritable via a transgenerational epigenetic mode of inheritance, giving rise to a mutator phenotype that is independent from mutator alleles. Here, we investigate mathematically how the rate of adaptive evolution is affected by the rate of mutation rate phenotype switching. We model an asexual population with two mutation rate phenotypes, non-mutator and mutator. An offspring may switch from its parental phenotype to the other phenotype. We find that switching rates that correspond to so-far empirically described non-genetic systems of inheritance of the mutation rate lead to higher rates of adaptation on both artificial and natural fitness landscapes. These switching rates can maintain within the same individuals both a mutator phenotype and intermediary mutations, a combination that facilitates adaptation. Moreover, non-genetic inheritance increases the proportion of mutators in the population, which in turn increases the probability of hitchhiking of the mutator phenotype with adaptive mutations. This in turns facilitates the acquisition of additional adaptive mutations. Our results rationalize recently observed noise in the expression of proteins that affect the mutation rate and suggest that non-genetic inheritance of this phenotype may facilitate evolutionary adaptive processes.

Keywords: epigenetics; evolutionary adaptive process; mutation rate; mutation rate phenotype switching; non-genetic inheritance; non-genetic variation.

Fig. 1.

a) Switching between the non-mutator and the mutator phenotypes. The switching rate from non-mutator to the mutator phenotype ${\gamma }_1$ is the probability of an individual having a mutator phenotype given that its parent was a non-mutator. The switching rate from mutator to non-mutator ${\gamma }_2$ is the probability of an individual having a non-mutator phenotype given that its parent was a mutator. b) Fitness landscape motif examples. A fitness landscape motif is a succession of genotypes that are one mutation away from each other. The first genotype is considered the wild-type, and has a relative fitness of 1. The genotype with the highest number of mutations always has the highest fitness and is the adaptive genotype. Depending on the fitness of the intermediate genotypes, a fitness motif can be classified as valley, flat, or monotonic ascent. c) Analysis workflow. The population is initialized at the wild-type genotype. The population is then allowed to reach mutation-selection balance on a fitness landscape where the wild-type genotype has the highest fitness. Next, an environmental change occurs. A genotype that is different from the wild-type genotype now has the highest fitness.

Fig. 2.

Adaptation-optimal switching rate ${\mathit{\gamma }}_1^{\mathbf{\ast }}$ for varying values of $\mathit{U}$, $\mathit{\tau }$, $\mathit{s}$. For each combination of parameters, we calculate the probability of appearance of the adaptive mutant for ${\gamma }_1$ ranging from ${\gamma }_1={10}^{-6}$ to ${\gamma }_1=0.5$, and the value resulting in the higher rate of adaptation is recorded. Other parameters: $n=5000;{\gamma }_2=\alpha {\gamma }_1$.

Fig. 3.

The probability of appearance of the adaptive genotype is maximized for intermediate switching rates. The frequency of mutators $p_M$ increases with the switching rate, while the association between mutants and the mutator phenotype is maximized for intermediate switching rates. The probability of appearance of the adaptive genotype q is computed with Eq. 5 and MSB frequencies obtained numerically for each value of ${\gamma }_1$ and other parameters. The frequency of mutators $p_M$ is obtained directly from the MSB frequencies. The association A is computed from the MSB frequencies using Eq. 8. Parameters: $n=5000$, ${\gamma }_2=\alpha {\gamma }_1$.

Fig. 4.

Adaptation rate for several fitness motifs. For each parameter set, 1,000 runs of the stochastic simulation were performed. The proportion of runs that converged to the adaptive genotype were recorded after 1,000 generations. Parameters: $U=4\cdot {10}^{-5}$, $\tau =100$, $s=0.1$, $N={10}^7$.

Fig. 5.

Dynamics of mutator frequency during an adaptive evolution. The frequency of mutators was recorded over 10,000 simulations during adaptation (that is, the appearance and fixation of a fitter genotype). When either of the switching rates is higher than ${10}^{-3}$, the mutator frequency barely changes from its mutation-selection balance value. However, when switching rates are lower, the mutator hitchhikes with the adaptive genotype, leading to a transient increase in mutator frequency. For a monotone ascent fitness motifs (right column), each appearance and increase in frequency of an adaptive mutation results in an increase of the mutator frequency, thus facilitating the appearance of the next mutation. We suggest that this phenomenon is responsible for the high adaptation rates observed for ${\gamma }_1<\tau U/2$ and ${\gamma }_2<\tau U/2$. Parameters: $U=4\cdot {10}^{-5}$, $\tau =100$, $s=0.03$, $n=5000$, $N={10}^9$. Values of α in each panel: a) $\alpha =2000$; b) $\alpha =1$; c) $\alpha =1$; d) $\alpha =2.5\cdot {10}^{-4}$; e) $\alpha =0.1$; and (F) $\alpha =0.02$.

Fig. 6.

Complex adaptation on Aspergillus Niger landscape. The proportion of runs out of 1,000 that converged upon the fittest genotype in the landscape was recorded after 500 generations. In order to disentangle the different effects of the non-genetic inheritance of the mutation rate on the rate of adaptation, we then rerun the simulation while removing the association of mutator and mutant, limiting the frequency of mutators during the evolution, and eliminating hitchhiking. Limiting the frequency $p_M$ reduces adaptation overall. Parameters: $U=4\cdot {10}^{-5}$, $\tau =100$, $N=1000$.