Elizabeth Aston

Mutation rate plasticity in rifampicin resistance depends on Escherichia coli cell–cell interactions

Variation of mutation rate at a particular site in a particular genotype, in other words mutation rate plasticity (MRP), can be caused by stress or ageing. However, mutation rate control by other factors is less well characterized. Here we show that in wild-type Escherichia coli (K-12 and B strains), the mutation rate to rifampicin resistance is plastic and inversely related to population density: lowering density can increase mutation rates at least threefold. This MRP is genetically switchable, dependent on the quorum-sensing gene luxS—specifically its role in the activated methyl cycle—and is socially mediated via cell–cell interactions. Although we identify an inverse association of mutation rate with fitness under some circumstances, we find no functional link with stress-induced mutagenesis. Our experimental manipulation of mutation rates via the social environment raises the possibility that such manipulation occurs in nature and could be exploited medically.

Spontaneous mutation rate is a plastic trait associated with population density across domains of life

Rates of random, spontaneous mutation can vary plastically, dependent upon the environment. Such plasticity affects evolutionary trajectories and may be adaptive. We recently identified an inverse plastic association between mutation rate and population density at 1 locus in 1 species of bacterium. It is unknown how widespread this association is, whether it varies among organisms, and what molecular mechanisms of mutagenesis or repair are required for this mutation-rate plasticity. Here, we address all 3 questions. We identify a strong negative association between mutation rate and population density across 70 years of published literature, comprising hundreds of mutation rates estimated using phenotypic markers of mutation (fluctuation tests) from all domains of life and viruses. We test this relationship experimentally, determining that there is indeed density-associated mutation-rate plasticity (DAMP) at multiple loci in both eukaryotes and bacteria, with up to 23-fold lower mutation rates at higher population densities. We find that the degree of plasticity varies, even among closely related organisms. Nonetheless, in each domain tested, DAMP requires proteins scavenging the mutagenic oxidised nucleotide 8-oxo-dGTP. This implies that phenotypic markers give a more precise view of mutation rate than previously believed: having accounted for other known factors affecting mutation rate, controlling for population density can reduce variation in mutation-rate estimates by 93%. Widespread DAMP, which we manipulate genetically in disparate organisms, also provides a novel trait to use in the fight against the evolution of antimicrobial resistance. Such a prevalent environmental association and conserved mechanism suggest that mutation has varied plastically with population density since the early origins of life.

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.

Critical Mutation Rate Has an Exponential Dependence on Population Size in Haploid and Diploid Populations

Understanding the effect of population size on the key parameters of evolution is particularly important for populations nearing extinction. There are evolutionary pressures to evolve sequences that are both fit and robust. At high mutation rates, individuals with greater mutational robustness can outcompete those with higher fitness. This is survival-of-the-flattest, and has been observed in digital organisms, theoretically, in simulated RNA evolution, and in RNA viruses. We introduce an algorithmic method capable of determining the relationship between population size, the critical mutation rate at which individuals with greater robustness to mutation are favoured over individuals with greater fitness, and the error threshold. Verification for this method is provided against analytical models for the error threshold. We show that the critical mutation rate for increasing haploid population sizes can be approximated by an exponential function, with much lower mutation rates tolerated by small populations. This is in contrast to previous studies which identified that critical mutation rate was independent of population size. The algorithm is extended to diploid populations in a system modelled on the biological process of meiosis. The results confirm that the relationship remains exponential, but show that both the critical mutation rate and error threshold are lower for diploids, rather than higher as might have been expected. Analyzing the transition from critical mutation rate to error threshold provides an improved definition of critical mutation rate. Natural populations with their numbers in decline can be expected to lose genetic material in line with the exponential model, accelerating and potentially irreversibly advancing their decline, and this could potentially affect extinction, recovery and population management strategy. The effect of population size is particularly strong in small populations with 100 individuals or less; the exponential model has significant potential in aiding population management to prevent local (and global) extinction events.

Where antibiotic resistance mutations meet quorum-sensing

We do not need to rehearse the grim story of the global rise of antibiotic resistant microbes. But what if it were possible to control the rate with which antibiotic resistance evolves by de novo mutation? It seems that some bacteria may already do exactly that: they modify the rate at which they mutate to antibiotic resistance dependent on their biological environment. In our recent study [Krašovec, et al. Nat. Commun. (2014), 5, 3742] we find that this modification depends on the density of the bacterial population and cell-cell interactions (rather than, for instance, the level of stress). Specifically, the wild-type strains of Escherichia coli we used will, in minimal glucose media, modify their rate of mutation to rifampicin resistance according to the density of wild-type cells. Intriguingly, the higher the density, the lower the mutation rate (Figure 1). Why this novel density-dependent ‘mutation rate plasticity’ (DD-MRP) occurs is a question at several levels. Answers are currently fragmentary, but involve the quorum-sensing gene luxS and its role in the activated methyl cycle.

Critical Mutation Rate has an Exponential Dependence on Population Size for Eukaryotic-Length Genomes

The critical mutation rate (CMR) determines the shift between survival-of-the-fittest and the survival of individuals with greater mutational robustness (the flattest). Small populations are more likely to exceed the CMR and become less well adapted; understanding the CMR is crucial to understanding the potential fate of small populations under threat of extinction. Here we present a simulation model capable of utilising input parameter values within a biologically relevant range. A previous study identified an exponential fall in CMR with decreasing population size, but the parameters and output were not directly relevant outside artificial systems. The first key contribution of this study is the identification of an inverse relationship between CMR and gene length when the gene length is comparable to that found in biological populations. The exponential relationship is maintained, and the CMR is lowered to between two to five orders of magnitude above existing estimates of per base mutation rate for a variety of organisms. The second key contribution of the study is the identification of an inverse relationship between CMR and the number of genes. Using a gene number in the range for Arabidopsis thaliana produces a CMR close to its known mutation rate; per base mutation rates for other organisms are also within one order of magnitude. This is the third key contribution of the study as it represents the first time such a simulation model has used input and produced output both within range for a given biological organism. This novel convergence of CMR model with biological reality is of particular relevance to populations undergoing a bottleneck, under stress, and subsequent conservation strategy for populations on the brink of extinction.

Critical mutation rate in a population with horizontal gene transfer.

Horizontal gene transfer (HGT) enables segments of DNA to be transferred between individuals in a population in addition to from parent to child. It is a prominent process in bacterial reproduction. Existing in silico models have succeeded in predicting when HGT will occur in evolving bacterial populations, and have utilised the concept of HGT in evolutionary algorithms. Here we present a genetic algorithm designed to model the process of bacterial evolution in a fitness landscape in which individuals with greater mutational robustness can outcompete those with higher fitness when a critical mutation rate (CMR) is exceeded. We show that the CMR has an exponential dependence on population size and can be lowered by HGT in both clonal and non-clonal populations. A population reproducing clonally has a higher CMR than one in which individuals undergo crossover. Allowing HGT only from donors with a non-zero fitness prevents HGT from lowering the CMR. In all cases the change in CMR with population size is grea...

Opposing effects of final population density and stress on Escherichia coli mutation rate

Evolution depends on mutations. For an individual genotype, the rate at which mutations arise is known to increase with various stressors (stress-induced mutagenesis—SIM) and decrease at high final population density (density-associated mutation-rate plasticity—DAMP). We hypothesised that these two forms of mutation-rate plasticity would have opposing effects across a nutrient gradient. Here we test this hypothesis, culturing Escherichia coli in increasingly rich media. We distinguish an increase in mutation rate with added nutrients through SIM (dependent on error-prone polymerases Pol IV and Pol V) and an opposing effect of DAMP (dependent on MutT, which removes oxidised G nucleotides). The combination of DAMP and SIM results in a mutation rate minimum at intermediate nutrient levels (which can support 7 × 108 cells ml−1). These findings demonstrate a strikingly close and nuanced relationship of ecological factors—stress and population density—with mutation, the fuel of all evolution.

Environmental pleiotropy and demographic history direct adaptation under antibiotic selection

Evolutionary rescue following environmental change requires mutations permitting population growth in the new environment. If change is severe enough to prevent most of the population reproducing, rescue becomes reliant on mutations already present. If change is sustained, the fitness effects in both environments, and how they are associated—termed ‘environmental pleiotropy’—may determine which alleles are ultimately favoured. A population’s demographic history—its size over time—influences the variation present. Although demographic history is known to affect the probability of evolutionary rescue, how it interacts with environmental pleiotropy during severe and sustained environmental change remains unexplored. Here, we demonstrate how these factors interact during antibiotic resistance evolution, a key example of evolutionary rescue fuelled by pre-existing mutations with pleiotropic fitness effects. We combine published data with novel simulations to characterise environmental pleiotropy and its effects on resistance evolution under different demographic histories. Comparisons among resistance alleles typically revealed no correlation for fitness—i.e., neutral pleiotropy—above and below the sensitive strain’s minimum inhibitory concentration. Resistance allele frequency following experimental evolution showed opposing correlations with their fitness effects in the presence and absence of antibiotic. Simulations demonstrated that effects of environmental pleiotropy on allele frequencies depended on demographic history. At the population level, the major influence of environmental pleiotropy was on mean fitness, rather than the probability of evolutionary rescue or diversity. Our work suggests that determining both environmental pleiotropy and demographic history is critical for predicting resistance evolution, and we discuss the practicalities of this during in vivo evolution.

Critical mutation rate has an exponential dependence on population size for eukaryotic-length genomes with crossover

The critical mutation rate (CMR) determines the shift between survival-of-the-fittest and survival of individuals with greater mutational robustness (“flattest”). We identify an inverse relationship between CMR and sequence length in an in silico system with a two-peak fitness landscape; CMR decreases to no more than five orders of magnitude above estimates of eukaryotic per base mutation rate. We confirm the CMR reduces exponentially at low population sizes, irrespective of peak radius and distance, and increases with the number of genetic crossovers. We also identify an inverse relationship between CMR and the number of genes, confirming that, for a similar number of genes to that for the plant Arabidopsis thaliana (25,000), the CMR is close to its known wild-type mutation rate; mutation rates for additional organisms were also found to be within one order of magnitude of the CMR. This is the first time such a simulation model has been assigned input and produced output within range for a given biological organism. The decrease in CMR with population size previously observed is maintained; there is potential for the model to influence understanding of populations undergoing bottleneck, stress, and conservation strategy for populations near extinction.