Error-threshold exists in fitness landscapes with lethal mutants

BACKGROUND: One of the important insights of quasi-species theory is an error-threshold. The error-threshold is the error rate of replication above which the sudden onset of the population delocalization from the fittest genotype occurs despite Darwinian selection; i.e., the break down of evolutionary optimization. However, a recent article by Wilke in this journal, after reviewing the previous studies on the error-threshold, concluded that the error-threshold does not exist if lethal mutants are taken into account in a fitness landscape. Since lethal mutants obviously exist in reality, this has a significant implication about biological evolution. However, the study of Wagner and Krall on which Wilke's conclusion was based considered mutation-selection dynamics in one-dimensional genotype space with the assumption that a genotype can mutate only to an adjoining genotype in the genotype space. In this article, we study whether the above conclusion holds in high-dimensional genotype space without the assumption of the adjacency of mutations, where the consequences of mutation-selection dynamics can be qualitatively different. RESULTS: To examine the effect of mutant lethality on the existence of the error-threshold, we extend the quasi-species equation by taking the lethality of mutants into account, assuming that lethal genotypes are uniformly distributed in the genotype space. First, with the simplification of neglecting back mutations, we calculate the error-threshold as the maximum allowable mutation rate for which the fittest genotype can survive. Second, with the full consideration of back mutations, we study the equilibrium population distribution and the ancestor distribution in the genotype space as a function of error rate with and without lethality in a multiplicative fitness landscape. The results show that a high lethality of mutants actually introduces an error-threshold in a multiplicative fitness landscape in sharp contrast to the conclusion of Wilke. Furthermore, irrespective of the lethality of mutants, the delocalization of the population from the fittest genotype occurs for an error rate much smaller than random replication. Finally, the results are shown to extend to a system of finite populations. CONCLUSION: High lethality of mutants introduces an error-threshold in a multiplicative fitness landscape. Furthermore, irrespective of the lethality of mutants, the break down of evolutionary optimization happens for an error rate much smaller than random replication

The Effect of Stochasticity on the Lac Operon: An Evolutionary Perspective

The role of stochasticity on gene expression is widely discussed. Both potential advantages and disadvantages have been revealed. In some systems, noise in gene expression has been quantified, in among others the lac operon of Escherichia coli. Whether stochastic gene expression in this system is detrimental or beneficial for the cells is, however, still unclear. We are interested in the effects of stochasticity from an evolutionary point of view. We study this question in the lac operon, taking a computational approach: using a detailed, quantitative, spatial model, we evolve through a mutation–selection process the shape of the promoter function and therewith the effective amount of stochasticity. We find that noise values for lactose, the natural inducer, are much lower than for artificial, nonmetabolizable inducers, because these artificial inducers experience a stronger positive feedback. In the evolved promoter functions, noise due to stochasticity in gene expression, when induced by lactose, only plays a very minor role in short-term physiological adaptation, because other sources of population heterogeneity dominate. Finally, promoter functions evolved in the stochastic model evolve to higher repressed transcription rates than those evolved in a deterministic version of the model. This causes these promoter functions to experience less stochasticity in gene expression. We show that a high repression rate and hence high stochasticity increases the delay in lactose uptake in a variable environment. We conclude that the lac operon evolved such that the impact of stochastic gene expression is minor in its natural environment, but happens to respond with much stronger stochasticity when confronted with artificial inducers. In this particular system, we have shown that stochasticity is detrimental. Moreover, we demonstrate that in silico evolution in a quantitative model, by mutating the parameters of interest, is a promising way to unravel the functional properties of biological systems

Eco-evolutionary dynamics, coding structure and the information threshold

<p>Abstract</p> <p>Background</p> <p>The amount of information that can be maintained in an evolutionary system of replicators is limited by genome length, the number of errors during replication (mutation rate) and various external factors that influence the selection pressure. To date, this phenomenon, known as the information threshold, has been studied (both genotypically and phenotypically) in a constant environment and with respect to maintenance (as opposed to accumulation) of information. Here we take a broader perspective on this problem by studying the accumulation of information in an ecosystem, given an evolvable coding structure. Moreover, our setup allows for individual based as well as ecosystem based solutions. That is, all functions can be performed by individual replicators, or complementing functions can be performed by different replicators. In this setup, where both the ecosystem and the individual genomes can evolve their structure, we study how populations cope with high mutation rates and accordingly how the information threshold might be alleviated.</p> <p>Results</p> <p>We observe that the first response to increased mutation rates is a change in coding structure. At moderate mutation rates evolution leads to longer genomes with a higher diversity than at high mutation rates. Thus, counter-intuitively, at higher mutation rates diversity is reduced and the efficacy of the evolutionary process is decreased. Therefore, moderate mutation rates allow for more degrees of freedom in exploring genotype space during the evolutionary trajectory, facilitating the emergence of solutions. When an individual based solution cannot be attained due to high mutation rates, spatial structuring of the ecosystem can accommodate the evolution of ecosystem based solutions.</p> <p>Conclusions</p> <p>We conclude that the evolutionary freedom (eg. the number of genotypes that can be reached by evolution) is increasingly restricted by higher mutation rates. In the case of such severe mutation rates that an individual based solution cannot be evolved, the ecosystem can take over and still process the required information forming ecosystem based solutions. We provide a proof of principle for species fulfilling the different roles in an ecosystem when single replicators can no longer cope with all functions simultaneously. This could be a first step in crossing the information threshold.</p

The role of genome and gene regulatory network canalization in the evolution of multi-trait polymorphisms and sympatric speciation

<p>Abstract</p> <p>Background</p> <p>Sexual reproduction has classically been considered as a barrier to the buildup of discrete phenotypic differentiation. This notion has been confirmed by models of sympatric speciation in which a fixed genetic architecture and a linear genotype phenotype mapping were assumed. In this paper we study the influence of a flexible genetic architecture and non-linear genotype phenotype map on differentiation under sexual reproduction.</p> <p>We use an individual based model in which organisms have a genome containing genes and transcription factor binding sites. Mutations involve single genes or binding sites or stretches of genome. The genome codes for a regulatory network that determines the gene expression pattern and hence the phenotype of the organism, resulting in a non-linear genotype phenotype map. The organisms compete in a multi-niche environment, imposing selection for phenotypic differentiation.</p> <p>Results</p> <p>We find as a generic outcome the evolution of discrete clusters of organisms adapted to different niches, despite random mating. Organisms from different clusters are distinct on the genotypic, the network and the phenotypic level. However, the genome and network differences are constrained to a subset of the genome locations, a process we call genotypic canalization. We demonstrate how this canalization leads to an increased robustness to recombination and increasing hybrid fitness. Finally, in case of assortative mating, we explain how this canalization increases the effectiveness of assortativeness.</p> <p>Conclusion</p> <p>We conclude that in case of a flexible genetic architecture and a non-linear genotype phenotype mapping, sexual reproduction does not constrain phenotypic differentiation, but instead constrains the genotypic differences underlying it. We hypothesize that, as genotypic canalization enables differentiation despite random mating and increases the effectiveness of assortative mating, sympatric speciation is more likely than is commonly suggested.</p

Adapting the engine to the fuel: mutator populations can reduce the mutational load by reorganizing their genome structure

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Phenotypic error threshold; additivity and epistasis in RNA evolution

BACKGROUND: The error threshold puts a limit on the amount of information maintainable in Darwinian evolution. The error threshold was first formulated in terms of genotypes. However, if a genotype-phenotype map involves redundancy ("mutational neutrality"), the error threshold should be formulated in terms of phenotypes since there is no unique fittest genotype. A previous study formulated the error threshold in terms of phenotypes, and their results showed that a rather low degree of mutational neutrality can increase the error threshold unlimitedly. RESULTS: We obtain an analytical formulation of the phenotypic error threshold by considering the "additive assumption", in which base substitutions do not influence each other (no epistasis). Our formulation shows that an increase of the error threshold due to mutational neutrality is limited. Computer simulations of RNA evolution are conducted to verify our formulation, and the results show a good agreement between the analytical prediction and the simulations. The comparison with the previous formulation illustrates that it is important for the prediction of the error threshold to consider that the number of base substitutions per replication is rather large near the error threshold. To examine the additive assumption, a detailed analysis of additivity and epistasis in RNA folding of a particular sequence is performed. The results show a high degree of epistasis in RNA folding; furthermore, the analysis also elucidates the reason of the success of the additive assumption. CONCLUSIONS: We conclude that an increase of the error threshold by mutational neutrality is limited, and that the additive assumption achieves a good prediction of the error threshold in spite of a high degree of epistasis in RNA folding because the average number of base substitutions of sequences retaining the phenotype per replication is sufficiently small to avoid of the effect of epistasis

Modeling Complex Biological Systems: Tackling the Parameter Curse Through Evolution

As we all know, “Nothing in biology makes sense except in the light of evolution” Dobzhansky (Am Biol Teach 35(3):125–129, 1973). Among the challenges of modeling complex biological systems is to determine the relevant parameters. The common practice is to extract parameters from the literature, or to determine them from ongoing experiments, or by collectively fitting the parameters to the experimental results the model tries to explain. Doing so ignores, or at least does not exploit, Dobzhansky’s wisdom. In this perspective paper, we argue and demonstrate the importance of using evolutionary methods to derive relevant parameters. We show that by doing so, we can debug experimental and modeling artifacts

Moving Forward Moving Backward: Directional Sorting of Chemotactic Cells due to Size and Adhesion Differences

Differential movement of individual cells within tissues is an important yet poorly understood process in biological development. Here we present a computational study of cell sorting caused by a combination of cell adhesion and chemotaxis, where we assume that all cells respond equally to the chemotactic signal. To capture in our model mesoscopic properties of biological cells, such as their size and deformability, we use the Cellular Potts Model, a multiscale, cell-based Monte Carlo model. We demonstrate a rich array of cell-sorting phenomena, which depend on a combination of mescoscopic cell properties and tissue level constraints. Under the conditions studied, cell sorting is a fast process, which scales linearly with tissue size. We demonstrate the occurrence of “absolute negative mobility”, which means that cells may move in the direction opposite to the applied force (here chemotaxis). Moreover, during the sorting, cells may even reverse the direction of motion. Another interesting phenomenon is “minority sorting”, where the direction of movement does not depend on cell type, but on the frequency of the cell type in the tissue. A special case is the cAMP-wave-driven chemotaxis of Dictyostelium cells, which generates pressure waves that guide the sorting. The mechanisms we describe can easily be overlooked in studies of differential cell movement, hence certain experimental observations may be misinterpreted

The evolution of strand preference in simulated RNA replicators with strand displacement: Implications for the origin of transcription

<p>Abstract</p> <p>Background</p> <p>The simplest conceivable example of evolving systems is RNA molecules that can replicate themselves. Since replication produces a new RNA strand complementary to a template, all templates would eventually become double-stranded and, hence, become unavailable for replication. Thus the problem of how to separate the two strands is considered a major issue for the early evolution of self-replicating RNA. One biologically plausible way to copy a double-stranded RNA is to displace a preexisting strand by a newly synthesized strand. Such copying can in principle be initiated from either the (+) or (-) strand of a double-stranded RNA. Assuming that only one of them, say (+), can act as replicase when single-stranded, strand displacement produces a new replicase if the (-) strand is the template. If, however, the (+) strand is the template, it produces a new template (but no replicase). Modern transcription exhibits extreme strand preference wherein anti-sense strands are always the template. Likewise, replication by strand displacement seems optimal if it also exhibits extreme strand preference wherein (-) strands are always the template, favoring replicase production. Here we investigate whether such strand preference can evolve in a simple RNA replicator system with strand displacement.</p> <p>Results</p> <p>We first studied a simple mathematical model of the replicator dynamics. Our results indicated that if the system is well-mixed, there is no selective force acting upon strand preference per se. Next, we studied an individual-based simulation model to investigate the evolution of strand preference under finite diffusion. Interestingly, the results showed that selective forces "emerge" because of finite diffusion. Strikingly, the direction of the strand preference that evolves [i.e. (+) or (-) strand excess] is a complex non-monotonic function of the diffusion intensity. The mechanism underlying this behavior is elucidated. Furthermore, a speciation-like phenomenon is observed under certain conditions: two extreme replication strategies, namely replicase producers and template producers, emerge and coexist among competing replicators.</p> <p>Conclusion</p> <p>Finite diffusion enables the evolution of strand preference, the direction of which is a non-monotonic function of the diffusion intensity. By identifying the conditions under which strand preference evolves, this study provides an insight into how a rudimentary transcription-like pattern might have emerged in an RNA-based replicator system.</p> <p>Reviewers</p> <p>This article was reviewed by Eugene V Koonin, Rob Kinght and István Scheuring (nominated by David H Ardell). For the full reviews, please go to the Reviewers' comments section.</p

Evolution of mutator populations in constant environments

International audienceWe simulate the evolution of mutator strains using the aevol simulator. These strains show a striking resistance to mutational burden. Analysis of their genomes show that this resistance is obtained through two different mechanisms: contraction of the coding part of the genome (directly reducing the burden) and expansion of the non-coding part of the genome (undirectly favoring the reproduction of the best individuals)