Horizontal gene transfer can rescue prokaryotes from Muller's ratchet: benefit of DNA from dead cells and population subdivision

Abstract

Horizontal gene transfer (HGT) is a major factor in the evolution of prokaryotes. An intriguing question is whether HGT is maintained during evolution of prokaryotes owing to its adaptive value or is a byproduct of selection driven by other factors such as consumption of extracellular DNA (eDNA) as a nutrient. One hypothesis posits that HGT can restore genes inactivated by mutations and thereby prevent stochastic, irreversible deterioration of genomes in finite populations known as Muller's ratchet. To examine this hypothesis, we developed a population genetic model of prokaryotes undergoing HGT via homologous recombination. Analysis of this model indicates that HGT can prevent the operation of Muller's ratchet even when the source of transferred genes is eDNA that comes from dead cells and on average carries more deleterious mutations than the DNA of recipient live cells. Moreover, if HGT is sufficiently frequent and eDNA diffusion sufficiently rapid, a subdivided population is shown to be more resistant to Muller's ratchet than an undivided population of an equal overall size. Thus, to maintain genomic information in the face of Muller's ratchet, it is more advantageous to partition individuals into multiple subpopulations and let them "cross-reference" each other's genetic information through HGT than to collect all individuals in one population and thereby maximize the efficacy of natural selection. Taken together, the results suggest that HGT could be an important condition for the long-term maintenance of genomic information in prokaryotes through the prevention of Muller's ratchet.

Keywords: competence; environmental DNA; evolution of transformation; soil bacteria; structured population.

Figure 1

Operation of Muller’s ratchet in the model in the absence of HGT ($r=0$). (A, B, D, E) The number of deleterious mutations is plotted against time: the population average (gray); the number of mutations fixed in the population (black); and the number of mutations in the least-loaded class (red). (C and F) The average gene diversity of the least-loaded class $H_{m_{\text{LLC}}}$ (green), that of the one but the least-loaded class $H_{m_{\text{LLC}}+1}$ (blue), and the eDNA quality $q_{\text{eDNA}}$ (orange) are plotted against time (see the main text for how these quantities are defined). Parameters were as follows: s = 0.01, N = 10⁵, d_eDNA = 1, l = 100. In the slow ratchet regime, $s{\overline{n}}_{m_{\text{LLC}}}=10$, $U=4.6052\times {10}^{-2}$ (A−C); in the fast ratchet regime, $s{\overline{n}}_{m_{\text{LLC}}}=1$, $U=6.9078\times {10}^{-2}$ (D−F).

Figure 2

Schematic diagram depicting accumulation of mutations in the model. Horizontal bars indicate the genomes of the least-loaded class (genomes of the other classes in the population are not shown). Crosses on the bars indicate deleterious mutations.

Figure 3

The effect of HGT on the operation of Muller’s ratchet. The rate of mutation accumulation Δm_fix/Δt is plotted as a function of the rate of HGT r. The accumulation rate was estimated as m_fix/t, where m_fix is the number of fixed mutations at the end of a simulation and t is the duration of a simulation (e.g., t >10⁶ for N = 10⁶ and t >10⁹ for N = 2 × 10³). The error bars indicate standard error of means estimated as $\sqrt{m_{\text{fix}}/t^2}$. The parameters were as follows: s = 0.01, d_eDNA = 1, l = 100. In the slow ratchet regime, $s{\overline{n}}_{m_{\text{LLC}}}=10$ (filled circles): N = 10⁶ and $U=6.9078\times {10}^{-2}$ (black), N = 10⁵ and $U=4.6052\times {10}^{-2}$ (red), N = 10⁴ and $U=2.3026\times {10}^{-2}$ (green), N = 2 × 10³ $U=6.9315\times {10}^{-3}$ (blue). In the fast ratchet regime, $s{\overline{n}}_{m_{\text{LLC}}}=1$ (open circles): N = 10⁶ and $U=9.2103\times {10}^{-2}$ (black), N = 10⁵ and $U=6.9078\times {10}^{-2}$ (red), N = 10⁴ and $U=3.6052\times {10}^{-2}$ (green), $N=2\times {10}^3$ and $U=2.9957\times {10}^{-2}$ (blue).

Figure 4

The mean time to extinction of the least-loaded class in the simplified Fisher-Wright model. Below the diagonal lines, HGT decreases the steady-state population size of the least-loaded class (i.e., the condition $r_{10}(1-s^{\prime })U^{\prime }/s^{\prime }<r_{01}(1-U^{\prime })(1-U^{\prime }/s^{\prime })$ is fulfilled). The mean time to extinction is normalized by that obtained in the absence of HGT (i.e., $r_{01}=r_{10}=0$). The parameters were as follows: $s^{\prime }=0.01$, and $s^{\prime }{\overline{n}}_0=10$ where ${\overline{n}}_0=N(1-U^{\prime }/s^{\prime })$. N = 10⁴ and $U^{\prime }=9\times {10}^{-3}$ (A); N = 10⁵ and $U^{\prime }=9.9\times {10}^{-3}$ (B); N = 10⁶ and $U^{\prime }=9.99\times {10}^{-3}$ (C). Each data point was obtained as an average of 100 simulation runs.

Figure 5

The normalized rate of mutation accumulation as a function of the number of loci l. The reference rate is set to the rate obtained for l = 100. The value of l that maximizes the probability P₁₀ (that HGT converts one but the least-loaded class to the least-loaded class) is indicated as $\tilde{l}$ in the graph. The parameters and color coding are the same as in Figure 3 (except for l).

Figure 6

Effect of slow eDNA turnover on the prevention of Muller’s ratchet by HGT. The rate of mutation accumulation Δm_fix/Δt is plotted as a function of the eDNA turnover rate d_eDNA. The parameters and color coding are the same as in Figure 3 (except for d_eDNA).

Figure 7

Effect of slow eDNA turnover on the quality of eDNA q_eDNA . The average gene diversity of the least-loaded class $H_{m_{\text{LLC}}}$ (green), that of the one but the least-loaded class $H_{m_{\text{LLC}}+1}$ (blue), and the quality of eDNA q_eDNA (orange) are plotted against time for various values of eDNA turnover rate d_eDNA. The parameters were as follows: l = 100, s = 0.01, d_eDNA = 0.1 (A and C), 0.01 (B and E), and 0.001 (C and F). In the slow ratchet regime, $sN{e}^{-U/s}=10$, N = 10⁵ and $U=4.6052\times {10}^{-2}$(A−C). In the fast ratchet regime, $sN{e}^{-U/s}=1$, N = 10⁵, and $U=6.9078\times {10}^{-2}$ (D−F).

Figure 8

Effect of population subdivision on the prevention of Muller’s ratchet by HGT when eDNA diffusion is infinitely fast (D_eDNA = ∞). The rate of mutation accumulation $\Delta {\overline{m}}_{\text{fix}}/\Delta t$ is plotted as a function of population migration rate D_pop for various values of HGT rate r. The color coding is as follows: r = 0 (black), r = 10⁻⁴ (red), r = 10⁻³ (green), and r = 10⁻² (blue). The parameters were as follows: in the slow ratchet regime, $sN{e}^{-U/s}=10$, N = 10⁵, and $U=4.6052\times {10}^{-2}$ (A) ; in the fast ratchet regime, $sN{e}^{-U/s}=1$, N = 10⁵ , and $U=6.9078\times {10}^{-2}$ (B). The number of subpopulations was $4\times 4$ with toroidal boundaries (see Materials and Methods).

Figure 9

Effect of population subdivision on the genetic structure of populations and on the contents of eDNA pools. (A) The average gene diversity within subpopulations (H_S) and in the entire population (H_T), and the coefficient of gene differentiation G_ST = (H_T − H_S)/H_T are plotted as a function of D_pop in the absence of HGT (r = 0). The plotted values were obtained as the time average after or nearly after the values reached saturation (all time averages were taken from the last $2\times {10}^4$ generations of simulations). The error bars denote standard deviation. The parameters were the same as in Figure 8A (filled circles) and Figure 8B (open circles) except that r = 0. (B) The quality q_eDNA and toxicity t_eDNA of eDNA are plotted as a function of D_pop in the absence of HGT (r = 0). The values of q_eDNA and t_eDNA were obtained as the time average after the values reached saturation except for D_pop = 0, for which the values indicate lower bounds (all time averages were taken from the last 2 × 10⁵ generations of simulations). The error bars denote standard deviation. The parameters were the same as in Figure 8B except that r = 0.

Figure 10

Effect of population subdivision on the prevention of Muller’s ratchet by HGT when the eDNA diffusion rate is finite. Red squares indicate the combinations of d_eDNA and D_eDNA values for which the rate of mutation accumulation $\Delta {\overline{m}}_{\text{fix}}/\Delta t$ is lower when a population is subdivided (D_pop = 10⁻⁵) than when a population is well-mixed (D_pop = 10⁻¹). Black circles indicate the parameter region where the opposite was the case. The parameters (other than D_eDNA and 2_eDNA) were the same as in Figure 8B with $r=0.01$.