Equilibrium Distribution of Mutators in the Single Fitness Peak Model

This paper develops an analytically tractable model for determining the equilibrium distribution of mismatch repair deficient strains in unicellular populations. The approach is based on the single fitness peak (SFP) model, which has been used in Eigen's quasispecies equations in order to understand various aspects of evolutionary dynamics. As with the quasispecies model, our model for mutator-nonmutator equilibrium undergoes a phase transition in the limit of infinite sequence length. This "repair catastrophe" occurs at a critical repair error probability of $\epsilon_r = L_{via}/L$, where $L_{via}$ denotes the length of the genome controlling viability, while $L$ denotes the overall length of the genome. The repair catastrophe therefore occurs when the repair error probability exceeds the fraction of deleterious mutations. Our model also gives a quantitative estimate for the equilibrium fraction of mutators in {\it Escherichia coli}.Comment: 4 pages, 2 figures (included as separate PS files

Coevolutionary Landscape Inference and the Context-Dependence of Mutations in Beta-Lactamase TEM-1

The quantitative characterization of mutational landscapes is a task of outstanding importance in evolutionary and medical biology: It is, for example, of central importance for our understanding of the phenotypic effect of mutations related to disease and antibiotic drug resistance. Here we develop a novel inference scheme for mutational landscapes, which is based on the statistical analysis of large alignments of homologs of the protein of interest. Our method is able to capture epistatic couplings between residues, and therefore to assess the dependence of mutational effects on the sequence context where they appear. Compared with recent large-scale mutagenesis data of the beta-lactamase TEM-1, a protein providing resistance against beta-lactam antibiotics, our method leads to an increase of about 40% in explicative power as compared with approaches neglecting epistasis. We find that the informative sequence context extends to residues at native distances of about 20 Å from the mutated site, reaching thus far beyond residues in direct physical contact

The Conserved nhaAR Operon Is Drastically Divergent between B2 and Non-B2 Escherichia coli and Is Involved in Extra-Intestinal Virulence

The Escherichia coli species is divided in phylogenetic groups that differ in their virulence and commensal distribution. Strains belonging to the B2 group are involved in extra-intestinal pathologies but also appear to be more prevalent as commensals among human occidental populations. To investigate the genetic specificities of B2 sub-group, we used 128 sequenced genomes and identified genes of the core genome that showed marked difference between B2 and non-B2 genomes. We focused on the gene and its surrounding region with the strongest divergence between B2 and non-B2, the antiporter gene nhaA. This gene is part of the nhaAR operon, which is in the core genome but flanked by mobile regions, and is involved in growth at high pH and high sodium concentrations. Consistently, we found that a panel of non-B2 strains grew faster than B2 at high pH and high sodium concentrations. However, we could not identify differences in expression of the nhaAR operon using fluorescence reporter plasmids. Furthermore, the operon deletion had no differential impact between B2 and non-B2 strains, and did not result in a fitness modification in a murine model of gut colonization. Nevertheless, sequence analysis and experiments in a murine model of septicemia revealed that recombination in nhaA among B2 strains was observed in strains with low virulence. Finally, nhaA and nhaAR operon deletions drastically decreased virulence in one B2 strain. This effect of nhaAR deletion appeared to be stronger than deletion of all pathogenicity islands. Thus, a population genetic approach allowed us to identify an operon in the core genome without strong effect in commensalism but with an important role in extra-intestinal virulence, a landmark of the B2 strains

A case of adaptation through a mutation in a tandem duplication during experimental evolution in Escherichia coli

Background DNA duplications constitute important precursors for genome variation. Here we analyzed an unequal duplication harboring a beneficial mutation that may provide alternative evolutionary outcomes. Results We characterized this evolutionary event during experimental evolution for only 100 generations of an Escherichia coli strain under glucose limitation within chemostats. By combining Insertion Sequence based Restriction Length Polymorphism experiments, pulsed field gel electrophoresis and two independent genome re-sequencing experiments, we identified an evolved lineage carrying a 180 kb duplication of the 46? region of the E. coli chromosome. This evolved duplication revealed a heterozygous state, with one copy harboring a 2668 bp deletion that included part of the ogrK gene and both the yegR and yegS genes. By genetically manipulating ancestral and evolved strains, we showed that the single yegS inactivation was sufficient to confer a frequency dependent fitness increase under the chemostat selective conditions in both the ancestor and evolved genetic contexts, implying that the duplication itself was not a direct fitness contributor. Nonetheless, the heterozygous duplicated state was relatively stable in the conditions prevailing during evolution in chemostats, in striking contrast to non selective conditions in which the duplication resolved at high frequency into either its ancestral or deleted copy

Exact phase diagram of quasispecies model with mutation rate modifier

We consider an infinite asexual population with a mutator allele which can elevate mutation rates. With probability $f$, a transition from nonmutator to mutator state occurs but the reverse transition is forbidden. We find that at $f=0$, the population is in the state with minimum mutation rate and at $f=f_c$, a phase transition occurs between a mixed phase with both nonmutators and mutators and a pure mutator phase. We calculate the critical probability $f_c$ and the total mutator fraction $Q$ in the mixed phase exactly. Our predictions for $Q$ are in agreement with those seen in microbial populations in static environments.Comment: Revised versio

Known mutator alleles do not markedly increase mutation rate in clinical Saccharomyces cerevisiae strains

Natural selection has the potential to act on all phenotypes, including genomic mutation rate. Classic evolutionary theory predicts that in asexual populations, mutator alleles, which cause high mutation rates, can fix due to linkage with beneficial mutations. This phenomenon has been demonstrated experimentally and may explain the frequency of mutators found in bacterial pathogens. By contrast, in sexual populations, recombination decouples mutator alleles from beneficial mutations, preventing mutator fixation. In the facultatively sexual yeast Saccharomyces cerevisiae, segregating alleles of MLH1 and PMS1 have been shown to be incompatible, causing a high mutation rate when combined. These alleles had never been found together naturally, but were recently discovered in a cluster of clinical isolates. Here we report that the incompatible mutator allele combination only marginally elevates mutation rate in these clinical strains. Genomic and phylogenetic analyses provide no evidence of a historically elevated mutation rate. We conclude that the effect of the mutator alleles is dampened by background genetic modifiers. Thus, the relationship between mutation rate and microbial pathogenicity may be more complex than once thought. Our findings provide rare observational evidence that supports evolutionary theory suggesting that sexual organisms are unlikely to harbour alleles that increase their genomic mutation rate

Interplay between pleiotropy and secondary selection determines rise and fall of mutators in stress response

Dramatic rise of mutators has been found to accompany adaptation of bacteria in response to many kinds of stress. Two views on the evolutionary origin of this phenomenon emerged: the pleiotropic hypothesis positing that it is a byproduct of environmental stress or other specific stress response mechanisms and the second order selection which states that mutators hitchhike to fixation with unrelated beneficial alleles. Conventional population genetics models could not fully resolve this controversy because they are based on certain assumptions about fitness landscape. Here we address this problem using a microscopic multiscale model, which couples physically realistic molecular descriptions of proteins and their interactions with population genetics of carrier organisms without assuming any a priori fitness landscape. We found that both pleiotropy and second order selection play a crucial role at different stages of adaptation: the supply of mutators is provided through destabilization of error correction complexes or fluctuations of production levels of prototypic mismatch repair proteins (pleiotropic effects), while rise and fixation of mutators occur when there is a sufficient supply of beneficial mutations in replication-controlling genes. This general mechanism assures a robust and reliable adaptation of organisms to unforeseen challenges. This study highlights physical principles underlying physical biological mechanisms of stress response and adaptation

The Error and Repair Catastrophes: A Two-Dimensional Phase Diagram in the Quasispecies Model

This paper develops a two gene, single fitness peak model for determining the equilibrium distribution of genotypes in a unicellular population which is capable of genetic damage repair. The first gene, denoted by $\sigma_{via}$, yields a viable organism with first order growth rate constant $k > 1$ if it is equal to some target ``master'' sequence $\sigma_{via, 0}$. The second gene, denoted by $\sigma_{rep}$, yields an organism capable of genetic repair if it is equal to some target ``master'' sequence $\sigma_{rep, 0}$. This model is analytically solvable in the limit of infinite sequence length, and gives an equilibrium distribution which depends on \mu \equiv L\eps , the product of sequence length and per base pair replication error probability, and \eps_r , the probability of repair failure per base pair. The equilibrium distribution is shown to exist in one of three possible ``phases.'' In the first phase, the population is localized about the viability and repairing master sequences. As \eps_r exceeds the fraction of deleterious mutations, the population undergoes a ``repair'' catastrophe, in which the equilibrium distribution is still localized about the viability master sequence, but is spread ergodically over the sequence subspace defined by the repair gene. Below the repair catastrophe, the distribution undergoes the error catastrophe when $\mu$ exceeds \ln k/\eps_r , while above the repair catastrophe, the distribution undergoes the error catastrophe when $\mu$ exceeds $\ln k/f_{del}$, where $f_{del}$ denotes the fraction of deleterious mutations.Comment: 14 pages, 3 figures. Submitted to Physical Review

Monotonicity of Fitness Landscapes and Mutation Rate Control

A common view in evolutionary biology is that mutation rates are minimised. However, studies in combinatorial optimisation and search have shown a clear advantage of using variable mutation rates as a control parameter to optimise the performance of evolutionary algorithms. Much biological theory in this area is based on Ronald Fisher's work, who used Euclidean geometry to study the relation between mutation size and expected fitness of the offspring in infinite phenotypic spaces. Here we reconsider this theory based on the alternative geometry of discrete and finite spaces of DNA sequences. First, we consider the geometric case of fitness being isomorphic to distance from an optimum, and show how problems of optimal mutation rate control can be solved exactly or approximately depending on additional constraints of the problem. Then we consider the general case of fitness communicating only partial information about the distance. We define weak monotonicity of fitness landscapes and prove that this property holds in all landscapes that are continuous and open at the optimum. This theoretical result motivates our hypothesis that optimal mutation rate functions in such landscapes will increase when fitness decreases in some neighbourhood of an optimum, resembling the control functions derived in the geometric case. We test this hypothesis experimentally by analysing approximately optimal mutation rate control functions in 115 complete landscapes of binding scores between DNA sequences and transcription factors. Our findings support the hypothesis and find that the increase of mutation rate is more rapid in landscapes that are less monotonic (more rugged). We discuss the relevance of these findings to living organisms