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Mutagenesis is responsive to many environmental factors. Evolution therefore depends on the environment not only for selection but also in determining the variation available in a population. One such environmental dependency is the inverse relationship between mutation rates and population density in many microbial species. Here, we determine the mechanism responsible for this mutation rate plasticity. Using dynamical computational modelling and in culture mutation rate estimation, we show that the negative relationship between mutation rate and population density arises from the collective ability of microbial populations to control concentrations of hydrogen peroxide. We demonstrate a loss of this density-associated mutation rate plasticity (DAMP) when Escherichia coli populations are deficient in the degradation of hydrogen peroxide. We further show that the reduction in mutation rate in denser populations is restored in peroxide degradation-deficient cells by the presence of wild-type cells in a mixed population. Together, these model-guided experiments provide a mechanistic explanation for DAMP, applicable across all domains of life, and frames mutation rate as a dynamic trait shaped by microbial community composition., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2024 Green et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

Agent-based models were used to describe electrical signaling in bacterial biofilms in three dimensions. Specifically, wavefronts of potassium ions in Escherichia coli biofilms subjected to stress from blue light were modeled from experimental data. Electrical signaling occurs only when the biofilms grow beyond a threshold size, which we have shown to vary with the K^{+} ion diffusivity, and the K^{+} ion threshold concentration, which triggered firing in the fire-diffuse-fire model. The transport of the propagating wavefronts shows superdiffusive scaling on time. K^{+} ion diffusivity is the main factor that affects the wavefront velocity. The K^{+} ion diffusivity and the firing threshold also affect the anomalous exponent for the propagation of the wavefront determining whether the wavefront is subdiffusive or superdiffusive. The geometry of the biofilm and its relation to the mean-square displacement (MSD) of the wavefront as a function of time was investigated for spherical, cylindrical, cubical, and mushroom-like structures. The MSD varied significantly with geometry; an additional regime to the kinetics occurred when the potassium wavefront leaves the biofilm. Adding cylindrical defects to the biofilm, which are known to occur in E. coli biofilms, also gave an extra kinetic regime to the wavefront MSD for the propagation through the defect.

Spontaneous mutations are the ultimate source of novel genetic variation on which evolution operates. Although mutation rate is often discussed as a single parameter in evolution, it comprises multiple distinct types of changes at the level of DNA. Moreover, the rates of these distinct changes can be independently influenced by genomic background and environmental conditions. Using fluctuation tests, we characterized the spectrum of spontaneous mutations in Escherichia coli grown in low and high glucose environments. These conditions are known to affect the rate of spontaneous mutation in wild-type MG1655, but not in a Δ luxS deletant strain - a gene with roles in both quorum sensing and the recycling of methylation products used in E. coli 's DNA repair process. We find an increase in AT>GC transitions in the low glucose environment, suggesting that processes relating to the production or repair of this mutation could drive the response of overall mutation rate to glucose concentration. Interestingly, this increase in AT>GC transitions is maintained by the glucose non-responsive Δ luxS deletant. Instead, an elevated rate of GC>TA transversions, more common in a high glucose environment, leads to a net non-responsiveness of overall mutation rate for this strain. Our results show how relatively subtle changes, such as the concentration of a carbon substrate or loss of a regulatory gene, can substantially influence the amount and nature of genetic variation available to selection.

Negative capacitance at low frequencies for spiking neurons was first demonstrated in 1941 (K. S. Cole) by using extracellular electrodes. The phenomenon subsequently was explained by using the Hodgkin-Huxley model and is due to the activity of voltage-gated potassium ion channels. We show that Escherichia coli ( E. coli ) biofilms exhibit significant stable negative capacitances at low frequencies when they experience a small DC bias voltage in electrical impedance spectroscopy experiments. Using a frequency domain Hodgkin-Huxley model, we characterize the conditions for the emergence of this feature and demonstrate that the negative capacitance exists only in biofilms containing living cells. Furthermore, we establish the importance of the voltage-gated potassium ion channel, Kch, using knock-down mutants. The experiments provide further evidence for voltage-gated ion channels in E. coli and a new, low-cost method to probe biofilm electrophysiology, e.g., to understand the efficacy of antibiotics. We expect that the majority of bacterial biofilms will demonstrate negative capacitances.

Fluctuation assays are widely used for estimating mutation rates in microbes growing in liquid environments. Many cultures are each inoculated with a few thousand cells, each sensitive to a selective marker that can be assayed phenotypically. These parallel cultures grow for many generations in the absence of the phenotypic marker. A subset of cultures is used to estimate the total number of cells at risk of mutations (i.e., the population size at the end of the growth period, or Nt). The remaining cultures are plated onto the selective agar. The distribution of observed resistant mutants among parallel cultures is then used to estimate the expected number of mutational events, m, using a mathematical model. Dividing m by Nt gives the estimate of the mutation rate per locus per generation. The assay has three critical aspects: the chosen phenotypic marker, the chosen volume of parallel cultures, and ensuring that the surface on the selective agar is completely dry before the incubation. The assay is relatively inexpensive and only needs standard laboratory equipment. It is also less laborious than alternative approaches, such as mutation accumulation and single-cell assays. The assay works on organisms that go through many generations rapidly and it depends on assumptions about the fitness effects of markers and cell death. However, recently developed tools and theoretical studies mean these issues can now be addressed analytically. The assay allows mutation rate estimation of different phenotypic markers in cells with different genotypes growing in isolation or in a community. By conducting multiple assays in parallel, assays can be used to study how an organism's environmental context affects spontaneous mutation rate, which is crucial for understanding antimicrobial resistance, carcinogenesis, aging, and evolution.

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 × 10 8  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.

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.

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.

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.

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.