Mutation rate variability as a driving force in adaptive evolution

Mutation rate is a key determinant of the pace as well as outcome of evolution, and variability in this rate has been shown in different scenarios to play a key role in evolutionary adaptation and resistance evolution under stress caused by selective pressure. Here we investigate the dynamics of resistance fixation in a bacterial population with variable mutation rates, and we show that evolutionary outcomes are most sensitive to mutation rate variations when the population is subject to environmental and demographic conditions that suppress the evolutionary advantage of high-fitness subpopulations. By directly mapping a biophysical fitness function to the system-level dynamics of the population, we show that both low and very high, but not intermediate, levels of stress in the form of an antibiotic result in a disproportionate effect of hypermutation on resistance fixation. We demonstrate how this behavior is directly tied to the extent of genetic hitchhiking in the system, the propagation of high-mutation rate cells through association with high-fitness mutations. Our results indicate a substantial role for mutation rate flexibility in the evolution of antibiotic resistance under conditions that present a weak advantage over wildtype to resistant cells.

Figure 1

Schematic indicating the allowed single-step transitions and their rates between phenotypes.

Figure 2

The sensitivity of evolution success to hypermutation $\left[R_r(f>1)/R_r(f=1)\right]$ is negatively correlated with the baseline-mutation rate evolutionary advantage $R_r(f=1)$ of the resistant mutant and is optimized at a mutation rate increase ($f$) that depends on the extent of advantage, diminishing upon further increases in this rate. (a) $R_r(f>1)/R_r(f=1)$ vs $R_r(f=1)$ curves for individual parameters $\vec{\rho }$ affecting the resistant mutant's evolutionary advantage at $f=150$. (b) Averages of the single-${\rho }_i$ curves in the appropriate ranges put through a low-pass filter for smoothness shown at multiple values of $f$ (on a log-linear scale, for clarity of resolution between different mutation rates). The dashed black line (parity in $R_r$ at baseline and elevated $f$) indicates the point of no benefit from hypermutation; initial increases in $f$ yield significant benefit at low-advantage conditions, which decreases and eventually becomes negligible at high-advantage conditions $\left[R_r(f=1)\to 1\right]$. At very high $f$ (here $f\gtrsim 700$) even low-advantage mutants experience diminishing benefit from hypermutation. (c) and (d) $R_r(f>1)/R_r(f=1)$ contours corresponding to plot (b) in $f-R_r(f=1)$ space. The green curve shows the optimal [i.e., yielding highest $R_r(f>1)/R_r(f=1)$] mutation rate increase factor $f$ as a function of $R_r(f=1)$. The probability of deleterious mutations was set at $P_{\text{del}}=0.9$ for plots (a)–(c) and at $P_{\text{del}}=0.6$ in plot (d). When held constant, $\vec{\rho }$ parameters were set at $g_r/g_{\text{wt}}=3$, $K/x_{\text{tot}}(t=0)={10}^2$, $p_{\text{wt},r}=0.01$, and $x_r(t=0)=0$. Wildtype E. coli growth was set at $g_{\text{wt}}=0.34{\text{h}}^{-1}$ and ${\mu }_{\text{bl}}=2\times {10}^{-10}\times N_g$, with $N_g$ the size of the E. coli genome.

Figure 3

(a) Hypermutation has a strong impact on resistance fixation at low and at very high levels of inhibition that is optimized at a mutation rate that depends on the inhibition level. (b) Genetic hitchhiking on resistant mutations is most pronounced in intermediate levels of inhibition. The black contour ($=1$) indicates no hitchhiking on resistant mutations. Parameters were set at $g_{0,r}=g_{0,\text{wt}}=0.34{\text{h}}^{-1}$, $g_{r,I}=5g_{\text{wt},I}$, where $g_{\text{wt},I}=3.6\mu \text{g}/\text{mL}$, $P_{\text{del}}=0.9$; and $K$, $p_{\text{wt},r}$, and $x_r(t=0)$ as in Fig. 2.

Figure 4

While the intrinsic selection coefficient $g_r/g_{\text{wt}}-1$ increases monotonically as a function of inhibition (a), the difference in growth rates $g_r-g_{\text{wt}}$ is maximized at intermediate levels of inhibition (b).

Figure 5

Computed values of $r_{\mu }$ from the system (2) for different expected steady-state proportions of resistant cells as the availability of resources is varied. Across a wide range of carrying capacities, $r_{\mu }$ only varies from $\sim 0.5\%$ to $\sim 1.5\%$. Plots in the main text employ $r_{\mu }=0.25\%$, corresponding to an initial hypermutant population of $1\%$ of the total population.