Shifts in Mutation Bias Promote Mutators by Altering the Distribution of Fitness Effects

Abstract

AbstractRecent experimental evidence demonstrates that shifts in mutational biases-for example, increases in transversion frequency-can change the distribution of fitness effects of mutations (DFE). In particular, reducing or reversing a prevailing bias can increase the probability that a de novo mutation is beneficial. It has also been shown that mutator bacteria are more likely to emerge if the beneficial mutations they generate have a larger effect size than observed in the wild type. Here, we connect these two results, demonstrating that mutator strains that reduce or reverse a prevailing bias have a positively shifted DFE, which in turn can dramatically increase their emergence probability. Since changes in mutation rate and bias are often coupled through the gain and loss of DNA repair enzymes, our results predict that the invasion of mutator strains will be facilitated by shifts in mutation bias that offer improved access to previously undersampled beneficial mutations.

Keywords: bacteria; microbial evolution; mutation bias; mutation rate; mutation spectra; mutator.

Figure 1:

Schematic diagram of simulated invasion tests. For each replicate, we create a new fitness landscape, initiate a new population, and evolve starting at time zero. Populations of initially random genotypes evolve with a fixed mutation rate and fixed transition:transversion bias. The mean population fitness (solid line) increases over time, while the fraction of mutations in the mutation-weighted DFE that are beneficial (dotted line) declines. When the mutation-weighted beneficial fraction, $f_{\beta }$, reaches 30%, we perform the three invasion tests illustrated. The same tests are repeated in new simulations but when the beneficial fraction in the evolving population reaches 15%.

Figure 2:

The mutational bias affects the numbers of Ti/Tv fixations. (a) More transitions (circles) than transversions (stars) fix in a transition-biased population $(\beta =0.7)$ with epistasis $(K=1)$. Hamming distance to the closest ancestor is shown in squares. The two vertical lines indicate when the beneficial fraction reaches 30% and 15%. (b) The fraction of fixations that are transitions (means of 300 replicates) is almost constant for unbiased mutations (squares), while it strongly reflects the bias in other cases. As adaptation proceeds, this fraction decreases for transition-biased and increases for transversion-biased populations. Error bars are smaller than symbol heights and are omitted.

Figure 3:

Beneficial fractions and beneficial effect-sizes decline during the evolution of a transition-biased population, while deleterious fractions increase. (a) Fraction of beneficial transitions (circles) decreases over time, falling more rapidly than beneficial transversions (stars). Overall beneficial fraction of the bias-weighted DFE ($f_{\beta }$, squares) falls in between. (b) Relative difference $\left(f_{\mathrm{T}\mathrm{v}}-f_{\mathrm{T}\mathrm{i}}\right)/f_{\mathrm{T}\mathrm{i}}$ increases over time. Panels (c) and (d) show analogous results for the mean positive effect-sizes, while panels (e) and (f) show the opposite for the deleterious fractions. Means of 300 replicates are shown for $\beta =0.7$ and $K=2$. Error bars in top panels are smaller than symbol heights and are omitted.

Figure 4:

Bias-shifted mutators have higher invasion probabilities (dashed) than mutators without a bias shift (solid). Invading strains are initiated at 5% frequency and have $F$-fold increase in mutation rate; we compare no change in bias, with full bias shift ($\beta =1$ to ${\beta }^{\prime }=0$, top row), or strong bias shift ($\beta =0.9$ to ${\beta }^{\prime }=0.1$, bottom row). Invasion tests occur at two levels of adaptive potential, $f_{\beta }=30\%$ (left) and $f_{\beta }=15\%$ (right). The case of epistasis is shown in red, while for blue lines $K=0$. The horizontal lines represent the neutral expectation 0.05. Results of 500 replicates are shown; shaded regions indicate ± one s.d.

Figure 5:

Mutator invasion probability increases when bias is reversed. Populations evolved with a starting bias $\beta$ until 15% beneficial fraction was reached before invasion tests for mutators $(F=50)$ were initiated. Mutators either have the same bias (solid), or shifted bias (dashed). The vertical line represents the unbiased transition frequency. (a) For $\beta <\alpha$, a shift to ${\beta }^{\prime }=0.9$ reverses the bias and thus increases the invasion probability; the same bias shift tends to reduce the probability if $\beta >\alpha$. (b) The effects are reversed when the bias shifts to ${\beta }^{\prime }=0.1$. Results of 4000 replicates are shown; shaded regions indicate ± one s.d.

Figure 6:

In populations that have evolved with a transition frequency of $\beta =0.9$, the invasion probability of mutators increases when the bias is reduced or reversed. (a) Larger bias reversals increased the invasion probability of mutators with 50-fold higher mutation rate whether the invasion test occurred at a beneficial fraction of 30% (bold lines) or 15% (thin lines), on either smooth ($K=0$, blue circles) or epistasic landscapes ($K=1$, red squares). (b) Results are consistent across different values of the mutation rate multiplier, $F\left(K=0,f_{\beta }=30\%\right.$ illustrated.) Results of 500 replicates are shown; shaded regions indicate ± one s.d.