Evolutionary Dynamics on Protein Bi-stability Landscapes can Potentially Resolve Adaptive Conflicts

Experimental studies have shown that some proteins exist in two alternative native-state conformations. It has been proposed that such bi-stable proteins can potentially function as evolutionary bridges at the interface between two neutral networks of protein sequences that fold uniquely into the two different native conformations. Under adaptive conflict scenarios, bi-stable proteins may be of particular advantage if they simultaneously provide two beneficial biological functions. However, computational models that simulate protein structure evolution do not yet recognize the importance of bi-stability. Here we use a biophysical model to analyze sequence space to identify bi-stable or multi-stable proteins with two or more equally stable native-state structures. The inclusion of such proteins enhances phenotype connectivity between neutral networks in sequence space. Consideration of the sequence space neighborhood of bridge proteins revealed that bi-stability decreases gradually with each mutation that takes the sequence further away from an exactly bi-stable protein. With relaxed selection pressures, we found that bi-stable proteins in our model are highly successful under simulated adaptive conflict. Inspired by these model predictions, we developed a method to identify real proteins in the PDB with bridge-like properties, and have verified a clear bi-stability gradient for a series of mutants studied by Alexander et al. (Proc Nat Acad Sci USA 2009, 106:21149–21154) that connect two sequences that fold uniquely into two different native structures via a bridge-like intermediate mutant sequence. Based on these findings, new testable predictions for future studies on protein bi-stability and evolution are discussed.     

Genetic instability and the quasispecies model

Genetic instability is a defining characteristic of cancers. Microsatellite instability (MIN) leads to by elevated point mutation rates, whereas chromosomal instability (CIN) refers to increased rates of losing or gaining whole chromosomes or parts of chromosomes during cell division. CIN and MIN are, in general, mutually exclusive. The quasispecies model is a very successful theoretical framework for the study of evolution at high mutation rates. It predicts the existence of an experimentally verified error catastrophe. This catastrophe occurs when the mutation rates exceed a threshold value, the error threshold, above which replicative infidelity is incompatible with cell survival. We analyse the semiconservative quasispecies model of both MIN and CIN tumors. We consider the role of post-methylation DNA repair in tumor cells and demonstrate that DNA repair is fundamental to the nature of the error catastrophe in both types of tumors. We find that CIN introduces a plateau in the maximum viable mutation rate for a repair-free model, which does not exist in the case of MIN. This provides a plausible explanation for the mutual exclusivity of CIN and MIN.     

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.     

GENETIC VARIATION AND DNA REPLICATION TIMING,OR WHY IS THERE LATE REPLICATING DNA?

Mutation rates vary significantly within the genome and across species. Recent studies revealed a long suspected replication-timing effect on mutation rate, but the mechanisms that regulate the increase in mutation rate as the genome is replicated remain unclear. Evidence is emerging, however, that DNA repair systems, in general, are less efficient in late replicating heterochromatic regions compared to early replicating euchromatic regions of the genome. At the same time, mutation rates in both vertebrates and invertebrates have been shown to vary with generation time (GT). GT is correlated with genome size, which suggests a possible nucleotypic effect on species-specific mutation rates. These and other observations all converge on a role for DNA replication checkpoints in modulating generation times and mutation rates during the DNA synthetic phase (S phase) of the cell cycle. The following will examine the potential role of the intra-S checkpoint in regulating cell cycle times (GT) and mutation rates in eukaryotes. This article was published online on August 5, 2011. An error was subsequently identified. This notice is included in the online and print versions to indicate that both have been corrected October 4, 2011.     

A large variation in the rates of synonymous substitution for RNA viruses and its relationship to a diversity of viral infection and transmission modes

RNA viruses successfully adapt to various environments by repeatedly producing new mutants, often through generating a number of nucleotide substitutions. To estimate the degree of variation in mutation rates of RNA viruses and to understand the source of such variation, we studied the synonymous substitution rate because synonymous substitution is exempt from functional constraints at the protein level, and its rate reflects the mutation rate to a great extent. We estimated the synonymous substitution rates for a total of 49 different species of RNA viruses, and we found that the rates had tremendous variation by 5 orders of magnitude (from 1.3 x 10(-7) to 6.2 x 10(-2) /synonymous site/year). Comparing the synonymous substitution rates with the replication frequencies and replication error rates for the RNA viruses, we found that the main source of the rate variation was differences in the replication frequency because the rates of replication error were roughly constant over different RNA viruses. Moreover, we examined a relationship between viral life strategies and synonymous substitution rates to understand which viral life strategies affect replication frequencies. The results show that the variation of synonymous substitution rates has been influenced most by either the difference in the infection modes or the differences in the transmission modes. In conclusion, the variation of mutation rates for RNA viruses is caused by different replication frequencies, which are affected strongly by the infection and transmission modes.     

Determinants of simulated RNA evolution

Models of RNA secondary structure folding are widely used to study evolution in theory and simulation. However, systematic studies of the parameters involved are rare. In this paper, we study by simulation how RNA evolution is influenced by three different factors, namely the mutation rate, scaling of the fitness function, and distance measure. We found that for low mutation rates the qualitative evolutionary behavior is robust with respect to the scaling of the fitness function. For efficient mutation rates, which are close to the error threshold, scaling and distance measure have a strong influence on the evolutionary behavior. A global distance measure that takes sequence information additively into account lowers the error threshold. When using a local sequence-structure alignment for the distance, we observed a smoother evolution of the fitness over time. Finally, in addition to the well known error threshold, we identify another threshold of the mutation rate, called divergence threshold, where the qualitative transient behavior changes from a localized to an exploratory search.     

A deterministic approach for the estimation of mutation rates in cultured mammalian cells

Unequal growth rates between mutant and wild-type cells in a large population constitute a problem for the estimation of mutation rate. Over a period of cell growth, a selective advantage of one cell type over the other might lead to considerable error in the estimation of mutation rate if equal growth rates are assumed. In this study, we propose a formula and apply it to the estimation of spontaneous mutation rate in a growing population of Chinese hamster V79 cells in which ouabain-resistant mutant cells exhibit a slower growth rate than the wild-type cells. The formula is a generalization of that previously presented by Armitage (1953), and this is the first attempt to apply the deterministic approach for mutation rate estimation to cultured mammalian cells. The value of the estimated rate is compared with that derived from a parallel experiment using the fluctuation test of Luria and Delbrück (1943). The limitations and advantages of taking the deterministic approach to mutation rate estimation in mammalian cell systems are discussed.     

Rapid mutational declines of viability in Drosophila

High rates of mildly deleterious mutation could cause the extinction of small populations, reduce neutral genetic variation and provide an evolutionary advantage for sex. In the first attempts to estimate the rate of mildly deleterious mutation, Mukai and Ohnishi allowed spontaneous mutations to accumulate on D. melanogaster second chromosomes shielded from recombination and selection. Viability of the shielded chromosomes appeared to decline rapidly, implying a deleterious mutation rate on the order of one per zygote per generation. These results have been challenged, however; at issue is whether Mukai and Ohnishi may have confounded viability declines caused by mutation with declines resulting from environmental changes or other extraneous factors. Here, using a method not sensitive to non-mutational viability changes, I reanalyse the previous mutation-accumulation (MA) experiments, and report the results of a new one. I show that in each of four experiments, including Mukai's two experiments, viability declines due to mildly deleterious mutations were rapid. The results give no support for the view that Mukai overestimated the declines. Although there is substantial variation in estimates of genomic mutation rates from the experiments, this variation is probably due to some combination of sampling error, strain differences and differences in assay conditions, rather than to failure to distinguish mutational and non-mutational viability changes.     

Ultrasensitive detection of rare mutations using next-generation targeted resequencing

With next-generation DNA sequencing technologies, one can interrogate a specific genomic region of interest at very high depth of coverage and identify less prevalent, rare mutations in heterogeneous clinical samples. However, the mutation detection levels are limited by the error rate of the sequencing technology as well as by the availability of variant-calling algorithms with high statistical power and low false positive rates. We demonstrate that we can robustly detect mutations at 0.1% fractional representation. This represents accurate detection of one mutant per every 1000 wild-type alleles. To achieve this sensitive level of mutation detection, we integrate a high accuracy indexing strategy and reference replication for estimating sequencing error variance. We employ a statistical model to estimate the error rate at each position of the reference and to quantify the fraction of variant base in the sample. Our method is highly specific (99%) and sensitive (100%) when applied to a known 0.1% sample fraction admixture of two synthetic DNA samples to validate our method. As a clinical application of this method, we analyzed nine clinical samples of H1N1 influenza A and detected an oseltamivir (antiviral therapy) resistance mutation in the H1N1 neuraminidase gene at a sample fraction of 0.18%.     

The relationship between the error catastrophe, survival of the flattest, and natural selection

Background  

The quasispecies model is a general model of evolution that is generally applicable to replication up to high mutation rates. It predicts that at a sufficiently high mutation rate, quasispecies with higher mutational robustness can displace quasispecies with higher replicative capacity, a phenomenon called "survival of the flattest". In some fitness landscapes it also predicts the existence of a maximum mutation rate, called the error threshold, beyond which the quasispecies enters into error catastrophe, losing its genetic information. The aim of this paper is to study the relationship between survival of the flattest and the transition to error catastrophe, as well as the connection between these concepts and natural selection.     

Impact of taxon sampling on the estimation of rates of evolution at sites

The function of individual sites within a protein influences their rate of accepted point mutation. During the computation of phylogenetic likelihoods, rate heterogeneity can be modeled on a site-per-site basis with relative rates drawn from a discretized Gamma-distribution. Site-rate estimates (e.g., the rate of highest posterior probability given the data at a site) can then be used as a measure of evolutionary constraints imposed by function. However, if the sequence availability is limited, the estimation of rates is subject to sampling error. This article presents a simulation study that evaluates the robustness of evolutionary site-rate estimates for both small and phylogenetically unbalanced samples. The sampling error on rate estimates was first evaluated for alignments that included 5-45 sequences, sampled by jackknifing, from a master alignment containing 968 sequences. We observed that the potentially enhanced resolution among site rates due to the inclusion of a larger number of rate categories is negated by the difficulty in correctly estimating intermediate rates. This effect is marked for data sets with less than 30 sequences. Although the computation of likelihood theoretically accounts for phylogenetic distances through branch lengths, the introduction of a single long-branch outlier sequence had a significant negative effect on site-rate estimates. Finally, the presence of a shift in rates of evolution between related lineages can be diagnostic of a gain/loss of function within a protein family. Our analyses indicate that detecting these rate shifts is a harder problem than estimating rates. This is so, partially, because the difference in rates depends on two rate estimates, each with an intrinsic uncertainty. The performances of four methods to detect these site-rate shifts are evaluated and compared. Guidelines are suggested for preparing data sets minimally influenced by error introduced by sequence sampling.     

Crow-Kimura模型中位点突变率对误差阈的随机效应

为了补充Eigen模型和Crow-Kimura模型的随机效应研究,Crow-Kimura模型中的位点突变率被处理成高斯分布随机变量,从而研究误差阈值的特征以及误差阈值的扩展与随机突变率涨落强度之间的关系. 准物种浓度和群体序参数分析表明,在位点突变率涨落较大时,误差阈值不再是相变点,而是平滑的转变区域. 定量分析表明,随机Crow-Kimura模型中转变区宽度与涨落强度之间的关系是非线性的. 将Crow-Kimura模型与Eigen模型的随机特征进行比较发现,在两个模型中适应值随机化使得转变区域的宽度和随机变量涨落强度之间的关系是线性的,而位点突变率随机化中两者的关系是非线性的（指数）. 对于随机化的Crow-Kimura模型,适应值随机化与位点突变率随机化引起的误差阈扩展效应相当. 对于随机Eigen模型,误差阈的扩展效应则主要是由位点突变率的随机化引起的. 之后,本文概述了Eigen模型和Crow Kimura模型中适应值和位点突变率随机化对误差阈值随机效应的影响,并讨论了上述结果对抗病毒策略、癌症治疗和动植物育种的重要意义.     

Genetic identity between populations when mutation rates vary within and across loci

A formula is derived for the probability that two genes taken at random from the same locus in two populations isolated at time t ago are of the same allelic type. The model assumed is a neutral one where there are possibly different mutation rates between different alleles. Inequalities are derived for this probability. A particular result is that for a fixed overall mutation rate, the probability is least for the infinite alleles model. Inequalities and approximations are found for Nei's genetic identity at one locus when mutation rates vary, and also for the identity across loci when the overall mutation rates per locus vary. Genetic identity at the molecular level is considered and a probability generating function found for the number of segregating sites between two randomly chosen gametes from two divergent populations, under various models.     

Forward hysteresis and backward bifurcation caused by culling in an avian influenza model

The emerging threat of a human pandemic caused by the H5N1 avian influenza virus strain magnifies the need for controlling the incidence of H5N1 infection in domestic bird populations. Culling is one of the most widely used control measures and has proved effective for isolated outbreaks. However, the socio-economic impacts of mass culling, in the face of a disease which has become endemic in many regions of the world, can affect the implementation and success of culling as a control measure. We use mathematical modeling to understand the dynamics of avian influenza under different culling approaches. We incorporate culling into an SI model by considering the per capita culling rates to be general functions of the number of infected birds. Complex dynamics of the system, such as backward bifurcation and forward hysteresis, along with bi-stability, are detected and analyzed for two distinct culling scenarios. In these cases, employing other control measures temporarily can drastically change the dynamics of the solutions to a more favorable outcome for disease control.     

Upper-limit mutation rate estimation for a plant RNA virus

It is generally accepted that mutation rates of RNA viruses are inherently high due to the lack of proofreading mechanisms. However, direct estimates of mutation rate are surprisingly scarce, in particular for plant viruses. Here, based on the analysis of in vivo mutation frequencies in tobacco etch virus, we calculate an upper-bound mutation rate estimation of 3×10⁻⁵ per site and per round of replication; a value which turns out to be undistinguishable from the methodological error. Nonetheless, the value is barely on the lower side of the range accepted for RNA viruses, although in good agreement with the only direct estimate obtained for other plant viruses. These observations suggest that, perhaps, differences in the selective pressures operating during plant virus evolution may have driven their mutation rates towards values lower than those characteristic of other RNA viruses infecting bacteria or animals.     

Error thresholds and the constraints to RNA virus evolution

RNA viruses are often thought of as possessing almost limitless adaptability as a result of their extreme mutation rates. However, high mutation rates also put a cap on the size of the viral genome by establishing an error threshold, beyond which lethal numbers of deleterious mutations accumulate. Herein, I argue that a lack of genomic space means that RNA viruses will be subject to important evolutionary constraints because specific sequences are required to encode multiple and often conflicting functions. Empirical evidence for these constraints, and how they limit viral adaptability, is now beginning to accumulate. Documenting the constraints to RNA virus evolution has important implications for predicting the emergence of new viruses and for improving therapeutic procedures.     

Incorporating experimental design and error into coalescent/mutation models of population history

Coalescent theory provides a powerful framework for estimating the evolutionary, demographic, and genetic parameters of a population from a small sample of individuals. Current coalescent models have largely focused on population genetic factors (e.g., mutation, population growth, and migration) rather than on the effects of experimental design and error. This study develops a new coalescent/mutation model that accounts for unobserved polymorphisms due to missing data, sequence errors, and multiple reads for diploid individuals. The importance of accommodating these effects of experimental design and error is illustrated with evolutionary simulations and a real data set from a population of the California sea hare. In particular, a failure to account for sequence errors can lead to overestimated mutation rates, inflated coalescent times, and inappropriate conclusions about the population. This current model can now serve as a starting point for the development of newer models with additional experimental and population genetic factors. It is currently implemented as a maximum-likelihood method, but this model may also serve as the basis for the development of Bayesian approaches that incorporate experimental design and error.     

Mutating away from your enemies: The evolution of mutation rate in a host–parasite system

The rate at which mutations occur in nature is itself under natural selection. While a general reduction of mutation rates is advantageous for species inhabiting constant environments, higher mutation rates can be advantageous for those inhabiting fluctuating environments that impose on-going directional selection. Analogously, species involved in antagonistic co-evolutionary arms races, such as hosts and parasites, can also benefit from higher mutation rates. We use modifier theory, combined with simulations, to investigate the evolution of mutation rate in such a host–parasite system. We derive an expression for the evolutionary stable mutation rate between two alleles, each of whose fitness depends on the current genetic composition of the other species. Recombination has been shown to weaken the strength of selection acting on mutation modifiers, and accordingly, we find that the evolutionarily attracting mutation rate is lower when recombination between the selected and the modifier locus is high. Cyclical dynamics are potentially commonplace for loci governing antagonistic species interactions. We characterize the parameter space where such cyclical dynamics occur and show that the evolution of large mutation rates tends to inhibit cycling and thus eliminates further selection on modifiers of the mutation rate. We then find using computer simulations that stochastic fluctuations in finite populations can increase the size of the region where cycles occur, creating selection for higher mutation rates. We finally use simulations to investigate the model behaviour when there are more than two alleles, finding that the region where cycling occurs becomes smaller and the evolutionarily attracting mutation rate lower when there are more alleles.