The look-ahead effect of phenotypic mutations

According to a central principle of molecular evolution, the likelihood that a given mutation occurs is independent of the mutation’s phenotypic consequences. Organisms cannot choose specific mutations. This tenet was challenged by Cairns et al. (1988), who observed that under a certain selective pressure, E. coli cells appeared to acquire an excess of beneficial mutations. The idea that cells can somehow ‘direct’ evolution was thought provoking, and stimulated many investigations (for reviews see Bridges (1998); Foster (1999); Cairns (1998); Hall (1998); Rosenberg (2001)). While the notion that cells can directly decide in which genomic regions to increase their mutation rate has been mostly abandoned (Foster, 1998; Cairns, 1998), the original observations by Cairns et al. (1988) have been corroborated (see above reviews).

If mutations arise independently of their phenotypic consequences, then how can adaptations occur that require multiple amino acid mutations and for which the intermediate stages are either selectively neutral or disadvantageous? Large populations can climb multiple fitness peaks, even with disadvantageous intermediate alleles (Behe and Snoke, 2004; Weinreich and Chao, 2005). Although no new mechanisms are therefore required to explain the evolution of complex proteins (Lynch, 2005), we propose that errors in transcription and translation (phenotypic mutations) allow the selection of the intermediate mutations of a multiple-mutation requiring trait, and can thus speed up the evolution of complex traits.

Studies on the phenotypic mutation rate indicate that it is orders of magnitude larger than the genotypic mutation rate (Springgate and Loeb, 1975; Edelmann and Gallant, 1977): the global phenotypic non-synonymous mutation rate has been estimated to be $4.5\times 10^{-4}$ mistranslations per codon (Ellis and Gallant, 1982; Shaw et al., 2002), compared with a genotypic mutation rate of between $\sim 10^{-7}$ to $10^{-11}$ (Drake et al., 1998). Consequently, for a protein of 300 residues, on average more than 1 in 10 copies of the protein will contain a mutation. Using mutation rates derived from the literature and conservative biological assumptions, we show via mathematical modeling and simulations that phenotypic mutations allow evolution to select for neutral intermediate alleles of a multi-mutation trait, actually selecting for proteins whose exact DNA sequence is not in the organism under selection. Evolution is then able to look ahead for evolutionary jackpots in sequence space.

Our theory is based on the following hypothetical scenario. A protein can increase the fitness of an individual if it evolved a specific trait. This trait requires two mutations, for example a disulphide bridge between two cysteine residues. Having only one of the required mutations is either selectively neutral or deleterious, however when an individual has only one mutation, small amounts of the protein with both mutations will be produced due to phenotypic mutations. If the presence of both mutations at low concentrations provides even a small fitness improvement then the allele with one mutation will spread though the population. As the frequency of the intermediate allele increases, there is a greater probability that if the second mutation occurs, it will be the presence of the first mutation, and thus provide the full fitness benefit.

The aim of this article is to show that adaptive phenotypic mutations can undergo positive selection under biologically plausible conditions, allowing proteins greater access to features involving multiple mutations. We thus introduce the notion of a ”look-ahead” effect. The name indicates that seemingly unsurmountable evolutionary barriers can be overcome thanks to phenotypic mutations which are not yet present in the genome. We wish to emphasize that the look-ahead concept is firmly grounded on the idea of chance and necessity and by no means insinuates a teleological feature of molecular evolution.

We have described a model demonstrating the consequences of positive phenotypic mutations on the evolution of a single gene. We have compared numerical simulations with the analytical approximations and found them to be in good agreement. When phenotypic mutations exert an effect on fitness, selection can operate on the intermediate allele of a complex trait, which otherwise (without phenotypic mutations) would be neutral. We refer to selection for the intermediate allele as the look-ahead effect, because this effect allows evolution to select for sequences not yet in the genome.

The approximation for small $s\beta$, Eq.(6), shows most clearly the relationship between the parameters. The look-ahead effect is proportional to $N$, $s$, and $\beta$, and sets in when $N$ is on the order of $1/(s\beta)$. For large $Ns\beta$, the look-ahead effect saturates. The asymptotic value of $\xi$ is approximately $N$ for $NU\ll 1$. Therefore, large populations have two advantages over small populations in terms of the look-ahead effect: the effect sets in for smaller values of $s$, and saturates at a larger asymptotic value $\xi$. Of course, even in the absence of the look-ahead effect, larger populations can more easily traverse multiple local fitness peaks (Weinreich and Chao, 2005).

Because the selection coefficient $s$ depends on the environment, a valid question is how often does $s$ reach sufficiently high levels so that the look-ahead effect can operate. For microbial species such as bacteria, sufficiently large $s$ should be reasonably common. Many bacteria experience highly fluctuating (Smit et al., 2001) and structured (Baquero and Negri, 1997) environments, where growth is limited by the lack of a key trait. An obvious and extreme example is antibiotic resistance. Evolving a defense against an antibiotic molecule can involve only a few amino acids (Palzkill et al., 1994), and those individuals that can generate an enzyme capable of degrading the antibiotic, even if briefly or weakly, will have a very large fitness increase. In fact, if the efficacy of the antibiotic is 100% on susceptible genotypes, a mutation providing only moderate resistance has an infinite selective advantage. And even for very small antibiotic concentrations, mutants differing by only two amino acids at a single $\beta$-lactamase gene can be selected effectively (Baquero et al., 1997, 1998). Thus, bacteria may frequently experience environments in which a large fitness increase (large $s$) is only a few mutations away. Similarly, in bacteriophages, selective coefficients $s$ of 10 or more are not uncommon, even for individual mutations (Bull et al., 2000).

Our work is entirely theoretical, but we expect that it will be possible to experimentally verify our predictions in future work. For experimentally observing the look-ahead effect, we would need a system where $s$ and $N$ are both large, while $\beta$ (the phenotypic mutation rate) can be modified. The values of both $N$ and $s$ used in this work are well within biologically realistic ranges achievable in a microbiological laboratory. Conditions for large $s$ may be created with e.g. antibiotic resistance, which is a common laboratory workhorse. Unfortunately, many antibiotics function by reducing translation fidelity (Ogle and Ramakrishnan, 2005), and thus would conflate $s$ and $\beta$. Changing $\beta$ could involve a mutated ribosome. Ribosomes appear to be optimized for accurate and efficient translation of mRNA (Baxter-Roshek et al., 2007), and several examples of altered ribosome fidelity exist, both increasing (Vila-Sanjurjo et al., 2003) and decreasing fidelity (Friedman et al., 1968). Specific regions of the ribosome rRNA sequence have been identified as influencing fidelity (O’Connor et al., 1997), and various agents can reduce fidelity, e.g., streptomycin, magnesium, and ethanol (Friedman et al., 1968). Few mutations may be sufficient to alter the fidelity of a ribosome, for example, a single mutation in the S5 ribosomal protein in E. coli increases frameshifting and nonsense mutations (Kirthi et al., 2006). In yeast, mutations in the 18S RNA have been found that both increase and decrease translational fidelity (Konstantinidis et al., 2006).

In this work, we have calculated the look-ahead effect from a comparison between the two cases of $\beta>0$ and $\beta=0$. The latter may not be experimentally possible; any experiment will likely compare two different positive values of $\beta$. Nevertheless, Figure 5 shows that a larger look-ahead effect can be achieved with a higher $\beta$, where increasing $\beta$ by one order of magnitude both increases the look-ahead effect by an order of magnitude and lowers the smallest $s$ where an effect is observed. Of course, our model does not take into account the loss of fitness or other confounding effects from a higher phenotypic mutation rate. Thus, a balance must be found in having two different values of $\beta$ that are different enough to measure, while at the same time minimizing the confounding effects. The most obvious consequence of increasing the phenotypic mutation rate is that overall fitness may be reduced, for example in E. coli, where a higher translational error rate activates stress responses (Fredriksson et al., 2007), or in mouse, where such errors are implicated in neurodegeneration caused by misfolded proteins that aggregate (Lee et al., 2006). Increasing translational fidelity may not come without fitness cost either. The hyperaccurate mutations in the 18S RNA in yeast (Konstantinidis et al., 2006) cause an increase in oxidative stress. This observation suggests that cells consume more energy to achieve hyperaccuracy. It may also partially explain why the phenotypic error rate is much higher than the genotypic error rate, as there is possibly a direct disadvantage in reducing the phenotypic error rate, rather than only reducing the selective advantage that occurs if the phenotypic error rate is reduced, as discussed in Buerger et al. (2006).

Buerger et al. (2006) asked whether evolution has selected for the current phenotypic error rate, which does not differ significantly between eukaryotes and prokaryotes (Ellis and Gallant, 1982; Shaw et al., 2002) even though the source of errors is different. They suggested that the increase in fitness becomes incrementally smaller for improvements to transcription and translation fidelity. We would like to speculate that the phenotypic error rate is on the border between minimal costs (of e.g. misfolded proteins) and maximum payoff (via the look-ahead effect).

The goal of our analysis was to demonstrate that the look-ahead effect is theoretically possible, and as such, we intentionally excluded confounding factors for the sake of clarity. There are several aspects not considered in our model that may play important roles. For example, in this work we did not consider the expression level. For low expressed genes, the mutation from allele 1 to allele 2 will occur less frequently compared to highly expressed genes. However, if allele 2 is produced it will be at a higher concentration (of allele 2 mutant proteins in a population of allele 1 proteins), as the overall copy number of allele 1 is low. This difference in expression levels is likely reduced in a large population, where beneficial mutations occur with sufficient frequency. Another factor related to the expression level is translational robustness. It has been proposed that highly expressed genes are under selection to properly fold despite phenotypic mutations, and consequently evolve slower (Drummond et al., 2005; Wilke and Drummond, 2006). If a gene is robust to translational errors, then it can tolerate a larger variety of mutations, of which some may be intermediates to a new adaptive multi-residue trait. Thus, translational robustness may increase the sequences available for experimentation at the phenotypic level. However, if the intermediate allele is itself not robust to errors in translation, then it will not be neutral, and may be selected against. The location of the protein trait will also influence the viability of the intermediate allele: mutations near the surface of the protein are less likely to disrupt the protein compared to mutations in the core (Tokuriki et al., 2007).

In conclusion, we propose that organisms can experiment with protein sequences that are mutationally close to the current sequence, but not yet in the genome. This effect allows selection for intermediates of complex traits, opening up a more direct route to the trait and thus reducing the time needed for fixation in the population.

D.J.W. would like to thank January Weiner for stimulating discussions and Maya Amago for helpful suggestions. D.J.W. and E.B.B. were supported by an HFSP program grant. C.O.W. was supported by NIH grant AI 065960.