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.2011 Jan 18;108(3):1082-7.
doi: 10.1073/pnas.1012918108. Epub 2011 Jan 3.

Evolution of molecular error rates and the consequences for evolvability

Affiliations

Evolution of molecular error rates and the consequences for evolvability

Etienne Rajon et al. Proc Natl Acad Sci U S A..

Abstract

Making genes into gene products is subject to predictable errors, each with a phenotypic effect that depends on a normally cryptic sequence. Many cryptic sequences have strongly deleterious effects, for example when they cause protein misfolding. Strongly deleterious effects can be avoided globally by avoiding making errors (e.g., via proofreading machinery) or locally by ensuring that each error has a relatively benign effect. The local solution requires powerful selection acting on every cryptic site and so evolves only in large populations. Small populations with less effective selection evolve global solutions. Here we show that for a large range of realistic intermediate population sizes, the evolutionary dynamics are bistable and either solution may result. The local solution facilitates the genetic assimilation of cryptic genetic variation and therefore substantially increases evolvability.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Fig. 1.
Fig. 1.
Evolutionary dynamics of the read-through error rate ρ. (A) Coevolution of ρ and of the number of cryptic sequences that are deleterious,Ldel. The optimal value of ρ as a function ofLdel, calculated as the value maximizing Eq.2 (Methods), is represented by a thick gray line, and ρ evolves toward this line whenLdel is fixed. The equilibrium values ofLdel as functions of log10(ρ) are represented by thin lines, for population sizesN = 103 andN = 105.Ldel evolves toward these lines when ρ is fixed. The values of ρ andLdel obtained by simulation are represented by solid crosses (centered on the mean, ±2 SD across replicate populations), each matching the intersection of the thick and one thin line.Movie S1 shows the simulated coevolutionary dynamics. (B) The evolved error rate ρ is low in small populations, high in large populations, and bistable for intermediate populations. Solid and open symbols (error bars ±2 SD;x values were slightly changed to avoid superposition) represent the results of simulations starting with (log10(ρ),Ldel) = (−5, 400) and (−2, 0), respectively. (C) The ranges ofN at which ρ is low or bistable increase with the total number of loci,Ltot. Bistable outcomes were identified by comparing the results of simulations obtained with the same initial conditions as inB, using at test with critical value 0.005. Parameter values: γ = 0.01,pdel = 0.4,pdel = 0.1, δ = 10−2.5, μ = 10−8, andLtot = 500 (A andB).
Fig. 2.
Fig. 2.
The mean population trait value,x, changes faster after an environmental change with the high -ρ (log10(ρ) = −1.71) than with the low-ρ attractor (log10(ρ) = −2.96). (A) One simulation in which the population with the high-ρ attractor (dashed line) reaches the new optimum before the low-ρ attractor (solid line). A change in the optimal trait value, from −1.5 to 1.5, is simulated att = 20,000. (B) The time before the population reaches a mean trait value near the optimum (1.4) after an environmental change (time to adaptation) increases with the number of loci coding for the trait,K. The time to adaptation is consistently lower for the high-ρ attractor whenK > 5. The size of mutations decreases withK (see text), which explains that the time to fixation of advantageous mutants increases. Keeping the size of mutations independent ofK leads to a decreasing time to adaptation withK (Fig. S7), but leads to the sameK > 5 condition for high-ρ attractor advantage. The error bars represent the first and third quartiles in the distribution of the time to adaptation, calculated from 20 simulations for each set of parameter values. The two attractors are those shown in Fig. 1A andB forN = 105. Parameter values:N = 105, σm = 0.5,a = 750; other values are the same as in Fig. 1A andB.
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References

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