Estimation of spontaneous mutation rates

Spontaneous or randomly occurring mutations play a key role in cancer progression. Estimation of the mutation rate of cancer cells can provide useful information about the disease. To ascertain these mutation rates, we need mathematical models that describe the distribution of mutant cells. In this investigation, we develop a discrete time stochastic model for a mutational birth process. We assume that mutations occur concurrently with mitosis so that when a nonmutant parent cell splits into two progeny, one of these daughter cells could carry a mutation. We propose an estimator for the mutation rate and investigate its statistical properties via theory and simulations. A salient feature of this estimator is the ease with which it can be computed. The methods developed herein are applied to a human colorectal cancer cell line and compared to existing continuous time models.     

Environmental tuning of mutation rates

Through their life cycles, bacteria experience many different environments in which the relationship between available energy resources and the frequency and the nature of various stresses is highly variable. In order to survive in such changeable environments, bacteria must balance the need for nutritional competence with stress resistance. In Escherichia coli natural populations, this is most frequently achieved by changing the regulation of the RpoS sigma factor-dependent general stress response. One important secondary consequence of altered regulation of the RpoS regulon is the modification of mutation rates. For example, under nutrient limitation during stationary phase, the high intracellular concentration of RpoS diminishes nutritional competence, increases stress resistance, and, by downregulating the mismatch repair system and upregulating [corrected] the expression of the dinB gene (coding for PolIV translesion synthesis polymerase) increases mutation rates. The reduction of the intracellular concentration of RpoS has exactly opposite effects on nutritional competence, stress resistance and mutation rates. Therefore, the natural selection that favours variants having the highest fitness under different environmental conditions results in high variability of stress-associated mutation rates in those variants.     

Statistical inference of sequence-dependent mutation rates

Several lines of research are now converging towards an integrated understanding of mutational mechanisms and their evolutionary implications. Experimentally, crystal structures reveal the effect of sequence context on polymerase fidelity; large-scale sequencing projects generate vast amounts of sequence polymorphism data; and locus-specific databases are being constructed. Computationally, software and analytical tools have been developed to analyze mutational data, to identify mutational hot spots, and to compare the signatures of mutagenic agents.     

Estimating mutation rates in low-replication experiments

Since mutation rate is a key biological parameter, its proper estimation has received great attention for decades. However, instead of the mutation rate, many authors opt for reporting the average mutant frequency, a less meaningful quantity. This is because the standard methods to estimate the mutation rate, derived from the Luria and Delbrück's fluctuation analysis, ideally require high-replication experiments to be applied; a requirement often unattainable due to constraints of time, budget or sample availability. But the main problem with mutant frequency, apart from being less informative, is its poor reproducibility; an especially marked defect when the chosen average is the arithmetic mean. Several authors tried to avoid this by employing other averages (such as the median or the geometric mean) or discarding outliers, though as far as we know nobody has evaluated which method performs best under low-replication settings. Here we use computer simulations to compare the performance of different methods used in low-replication experiments (≤4 cultures). Besides the customary averages of mutant frequency, we also tested two well-known fluctuation methods. Contrary to common practice, our results support that fluctuation methods should be applied in such circumstances, as they perform as well as or better than any average of mutant frequency. In particular, experimentalists will benefit from using MSS maximum likelihood in low-replication experiments because it: (i) provides more reproducible results, (ii) allows for direct estimation of mutation rate and (iii) allows for the application of conventional statistics.     

Fitness-dependent mutation rates in finite populations

Mutation rate may be condition dependent, whereby individuals in poor condition, perhaps from high mutation load, have higher mutation rates than individuals in good condition. Agrawal (J. Evol. Biol.15, 2002, 1004) explored the basic properties of fitness-dependent mutation rate (FDMR) in infinite populations and reported some heuristic results for finite populations. The key parameter governing how infinite populations evolve under FDMR is the curvature (k) of the relationship between fitness and mutation rate. We extend Agrawal's analysis to finite populations and consider dominance and epistasis. In finite populations, the probability of long-term existence depends on k. In sexual populations, positive curvature leads to low equilibrium mutation rate, whereas negative curvature results in high mutation rate. In asexual populations, negative curvature results in rapid extinction via 'mutational meltdown', whereas positive curvature sometimes allows persistence. We speculate that fitness-dependent mutation rate may provide the conditions for genetic architecture to diverge between sexual and asexual taxa.     

Determining mutation rates in bacterial populations

When properly determined, spontaneous mutation rates are a more accurate and biologically meaningful reflection of underlying mutagenic mechanisms than are mutant frequencies. Because bacteria grow exponentially and mutations arise stochastically, methods to estimate mutation rates depend on theoretical models that describe the distribution of mutant numbers among parallel cultures, as in the original Luria-Delbr]uck fluctuation analysis. An accurate determination of mutation rate depends on understanding the strengths and limitations of these methods, and how to design fluctuation assays to optimize a given method. In this paper we describe a number of methods to estimate mutation rates, give brief accounts of their derivations, and discuss how they behave under various experimental conditions.     

Likelihood-based estimation of microsatellite mutation rates

Microsatellites are widely used in genetic analyses, many of which require reliable estimates of microsatellite mutation rates, yet the factors determining mutation rates are uncertain. The most straightforward and conclusive method by which to study mutation is direct observation of allele transmissions in parent-child pairs, and studies of this type suggest a positive, possibly exponential, relationship between mutation rate and allele size, together with a bias toward length increase. Except for microsatellites on the Y chromosome, however, previous analyses have not made full use of available data and may have introduced bias: mutations have been identified only where child genotypes could not be generated by transmission from parents' genotypes, so that the probability that a mutation is detected depends on the distribution of allele lengths and varies with allele length. We introduce a likelihood-based approach that has two key advantages over existing methods. First, we can make formal comparisons between competing models of microsatellite evolution; second, we obtain asymptotically unbiased and efficient parameter estimates. Application to data composed of 118,866 parent-offspring transmissions of AC microsatellites supports the hypothesis that mutation rate increases exponentially with microsatellite length, with a suggestion that contractions become more likely than expansions as length increases. This would lead to a stationary distribution for allele length maintained by mutational balance. There is no evidence that contractions and expansions differ in their step size distributions.     

Evolution of mutation rates in bacteria

Evolutionary success of bacteria relies on the constant fine-tuning of their mutation rates, which optimizes their adaptability to constantly changing environmental conditions. When adaptation is limited by the mutation supply rate, under some conditions, natural selection favours increased mutation rates by acting on allelic variation of the genetic systems that control fidelity of DNA replication and repair. Mutator alleles are carried to high frequency through hitchhiking with the adaptive mutations they generate. However, when fitness gain no longer counterbalances the fitness loss due to continuous generation of deleterious mutations, natural selection favours reduction of mutation rates. Selection and counter-selection of high mutation rates depends on many factors: the number of mutations required for adaptation, the strength of mutator alleles, bacterial population size, competition with other strains, migration, and spatial and temporal environmental heterogeneity. Such modulations of mutation rates may also play a role in the evolution of antibiotic resistance.     

Optimal mutation rates in dynamic environments

In this paper, we study the evolution of the mutation rate for simple organisms in dynamic environments. A model based on explicit population dynamics at the gene sequence level, with multiple fitness coding loci tracking a moving fitness peak in a random fitness background, is developed and an analytical expression for the optimal mutation rate is derived. The optimal mutation rate per genome is approximately independent of genome length, something that has been observed in nature. Furthermore, the optimal mutation rate is a function of the absolute, not relative, replication rate of the superior gene sequences. Simulations confirm the theoretical predictions.     

Fine-tuning germline mutation rates across evolution

The germline mutation rate (GMR) sets the pace at which mutations, the raw material of evolution, are introduced into the genome. By sequencing a dataset of unprecedently broad phylogenetic scope, Bergeron et al. estimated species-specific GMR, offering numerous insights into how this parameter shapes and is shaped by life-history traits.     

Sex-specific mutation rates in salmonid fish

If germline mutations arise because of replication errors, the mutation rate may differ between males and females given that they differ in their number of germ cell divisions. As males of many higher organisms produce more gametes than females, this has led to the idea of "male-driven evolution." The extent of such male bias to the mutation rate is currently debated. For human some recent data suggest a very low bias, at a factor 1.7 only, while other approaches have given values of alpha(m) (the male-to-female mutation rate ratio) of 5, which is more close to what might be expected from male and female germ cell biology. Comparative analyses of sex-specific mutation rates in other organisms may be necessary for understanding the generality of an effect of sex and the number of germline DNA replications on the mutation rate. In this study we estimate for the first time sex-specific mutation rates in fish. Comparing the intronic substitution rates of the autosomal GH- 2 gene and its duplicated Y-linked and male-specific copy GH- 2Y (447-468 bp of each gene), we estimate alpha(m) to be 5.35-6.60 in salmonid fish of the genus Oncorhynchus. To the observations previously made among mammals and birds, this adds evidence from another class of vertebrates showing that a majority of mutations are of paternal origin. This would suggest that replication errors play a major role for the generation of new mutations.     

The influence of hitchhiking and deleterious mutation upon asexual mutation rates

The question of how natural selection affects asexual mutation rates has been considered since the 1930s, yet our understanding continues to deepen. The distribution of mutation rates observed in natural bacteria remains unexplained. It is well known that environmental constancy can favor minimal mutation rates. In contrast, environmental fluctuation (e.g., at period T) can create indirect selective pressure for stronger mutators: genes modifying mutation rate may "hitchhike" to greater frequency along with environmentally favored mutations they produce. This article extends a well-known model of Leigh to consider fitness genes with multiple mutable sites (call the number of such sites alpha). The phenotypic effect of such a gene is enabled if all sites are in a certain state and disabled otherwise. The effects of multiple deleterious loci are also included (call the number of such loci gamma). The analysis calculates the indirect selective effects experienced by a gene inducing various mutation rates for given values of alpha, gamma, and T. Finite-population simulations validate these results and let us examine the interaction of drift with hitchhiking selection. We close by commenting on the importance of other factors, such as spatiotemporal variation, and on the origin of variation in mutation rates.     

Two optimal mutation rates in obligate pathogens subject to deleterious mutation

Pathogen species with high mutation rates are likely to accumulate deleterious mutations that reduce their reproductive potential within the host. By altering the within-host growth rate of the pathogen, the deleterious mutation load has the potential to affect epidemiological properties such as prevalence, mean pathogen load, and the mean duration of infections. Here, I examine an epidemiological model that allows for multiple segregating mutations that affect within-host replication efficiency. The model demonstrates a complex range of outcomes depending on pathogen mutation rate, including two distinct, widely separated mutation rates associated with high pathogen prevalence. The low mutation rate prevalence peak is associated with small amounts of genetic diversity within the pathogen population, relatively stable prevalence and infection dynamics, and genetic variation partitioned between hosts. The high mutation rate peak is characterized by considerable genetic diversity both within and between hosts, relatively frequent invasions by more virulent types, and is qualitatively similar to an RNA virus quasispecies. The two prevalence peaks are separated by a valley where natural selection favors evolution toward the optimal within-host state, which is associated with high virulence and relatively rapid host mortality. Both chronic and acute infections are examined using stochastic forward simulations.