The mutation process of microsatellites during the polymerase chain reaction.

We build a mathematical model for the mutation process of microsatellites during polymerase chain reaction (PCR) using the theory of branching processes. Based on the model, we develop a method to estimate the mutation rate of microsatellites per PCR cycle and the probability of expansion by maximizing a quasi-likelihood of the observed data. We show by simulations that the proposed estimation method can accurately recover the relationship between the mutation rate and number of repeat units. The theoretical basis for the proposed method is also given. We apply the method to experimental data on poly-A and poly-CA repeats.     

Estimation of the mutation rate during error-prone polymerase chain reaction.

Error-prone polymerase chain reaction (PCR) is widely used to introduce point mutations during in vitro evolution experiments. Accurate estimation of the mutation rate during error-prone PCR is important in studying the diversity of error-prone PCR product. Although many methods for estimating the mutation rate during PCR are available, all the existing methods depend on the assumption that the mutation rate is low and mutations occur at different places whenever they occur. The available methods may not be applicable to estimate the mutation rate during error-prone PCR. We develop a mathematical model for error-prone PCR and present methods to estimate the mutation rate during error-prone PCR without assuming low mutation rate. We also develop a computer program to simulate error-prone PCR. Using the program, we compare the newly developed methods with two other methods. We show that when the mutation rate is relatively low (< 10(-3) per base per PCR cycle), the newly developed methods give roughly the same results as previous methods. When the mutation rate is relatively high (> 5 x 10(-3) per base per PCR cycle, the mutation rate for most error-prone PCR experiments), the previous methods underestimate the mutation rate and the newly developed methods approximate the true mutation rate.     

Benefits and Challenges with Applying Unique Molecular Identifiers in Next Generation Sequencing to Detect Low Frequency Mutations

Indexing individual template molecules with a unique identifier (UID) before PCR and deep sequencing is promising for detecting low frequency mutations, as true mutations could be distinguished from PCR errors or sequencing errors based on consensus among reads sharing same index. In an effort to develop a robust assay to detect from urine low-abundant bladder cancer cells carrying well-documented mutations, we have tested the idea first on a set of mock templates, with wild type and known mutants mixed at defined ratios. We have measured the combined error rate for PCR and Illumina sequencing at each nucleotide position of three exons, and demonstrated the power of a UID in distinguishing and correcting errors. In addition, we have demonstrated that PCR sampling bias, rather than PCR errors, challenges the UID-deep sequencing method in faithfully detecting low frequency mutation.     

Measuring bidirectional mutation

The estimation of mutation rates is usually based on a model in which mutations are rare independent Poisson events. Back-mutation of mutants, an even rarer event, is ignored. In the hypermutating B cells of the immune system, mutation between phenotypes exhibiting, vs. not exhibiting, surface immunoglobulin is common in both directions. We develop three strategies for the estimation of mutation rates under circumstances such as these, where mutation rates in both directions are estimated simultaneously. Our model for the growth of a cell culture departs from the classical assumption of cell division as a memoryless (Poisson) event; we model cell division as giving rise to sequential generations of cells. On this basis, a Monte-Carlo simulation is developed. We develop also a numerical approach to calculating the probability distribution for the proportion of mutants in each culture as a function of forward- and backward-mutation rates. Although both approaches are too computationally intensive for routine laboratory use, they provide the insight necessary to develop and evaluate a third, 'hand-calculator' approach to extracting mutation rate estimators from experiments of this type.     

Influence of mutational and sampling factors on the estimation of demographic parameters in a "continuous" population under isolation by distance

In numerous species, individual dispersal is restricted in space so that "continuous" populations evolve under isolation by distance. A method based on individual genotypes assuming a lattice population model was recently developed to estimate the product Dsigma2, where D is the population density and sigma2 is the average squared parent-offspring distance. We evaluated the influence on this method of both mutation rate and mutation model, with a particular reference to microsatellite markers, as well as that of the spatial scale of sampling. Moreover, we developed and tested a nonparametric bootstrap procedure allowing the construction of confidence intervals for the estimation of Dsigma2. These two objectives prompted us to develop a computer simulation algorithm based on the coalescent theory giving individual genotypes for a continuous population under isolation by distance. Our results show that the characteristics of mutational processes at microsatellite loci, namely the allele size homoplasy generated by stepwise mutations, constraints on allele size, and change of slippage rate with repeat number, have little influence on the estimation of Dsigma2. In contrast, a high genetic diversity (approximately 0.7-0.8), as is commonly observed for microsatellite markers, substantially increases the precision of the estimation. However, very high levels of genetic diversity (>0.85) were found to bias the estimation. We also show that statistics taking into account allele size differences give unreliable estimations (i.e., high variance of Dsigma2 estimation) even under a strict stepwise mutation model. Finally, although we show that this method is reasonably robust with respect to the sampling scale, sampling individuals at a local geographical scale gives more precise estimations of Dsigma2.     

The mutation rate of the human mtDNA deletion mtDNA4977.

The human mitochondrial mutation mtDNA4977 is a 4,977-bp deletion that originates between two 13-bp direct repeats. We grew 220 colonies of cells, each from a single human cell. For each colony, we counted the number of cells and amplified the DNA by PCR to test for the presence of a deletion. To estimate the mutation fate, we used a model that describes the relationship between the mutation rate and the probability that a colony of a given size will contain no mutants, taking into account such factors as possible mitochondrial turnover and mistyping due to PCR error. We estimate that the mutation rate for mtDNA4977 in cultured human cells is 5.95 x 10(-8) per mitochondrial genome replication. This method can be applied to specific chromosomal, as well as mitochondrial, mutations.     

The rate of adaptation in asexuals

I study the population genetics of adaptation in asexuals. I show that the rate of adaptive substitution in an asexual species or nonrecombining chromosome region is a bell-shaped function of the mutation rate: at some point, increasing the mutation rate decreases the rate of substitution. Curiously, the mutation rate that maximizes the rate of adaptation depends solely on the strength of selection against deleterious mutations. In particular, adaptation is fastest when the genomic rate of mutation, U, equals the harmonic mean of selection coefficients against deleterious mutations, where we assume that selection for favorable alleles is milder than that against deleterious ones. This simple result is independent of the shape of the distribution of effects among favorable and deleterious mutations, population size, and the action of clonal interference. In the course of this work, I derive an approximation to the probability of fixation of a favorable mutation in an asexual genome or nonrecombining chromosome region in which both favorable and deleterious mutations occur.     

A multipoint method for detecting genotyping errors and mutations in sibling-pair linkage data

The identification of genes contributing to complex diseases and quantitative traits requires genetic data of high fidelity, because undetected errors and mutations can profoundly affect linkage information. The recent emphasis on the use of the sibling-pair design eliminates or decreases the likelihood of detection of genotyping errors and marker mutations through apparent Mendelian incompatibilities or close double recombinants. In this article, we describe a hidden Markov method for detecting genotyping errors and mutations in multilocus linkage data. Specifically, we calculate the posterior probability of genotyping error or mutation for each sibling-pair-marker combination, conditional on all marker data and an assumed genotype-error rate. The method is designed for use with sibling-pair data when parental genotypes are unavailable. Through Monte Carlo simulation, we explore the effects of map density, marker-allele frequencies, marker position, and genotype-error rate on the accuracy of our error-detection method. In addition, we examine the impact of genotyping errors and error detection and correction on multipoint linkage information. We illustrate that even moderate error rates can result in substantial loss of linkage information, given efforts to fine-map a putative disease locus. Although simulations suggest that our method detects 相似文献   

Deleterious mutations can surf to high densities on the wave front of an expanding population

There is an increasing recognition that evolutionary processes play a key role in determining the dynamics of range expansion. Recent work demonstrates that neutral mutations arising near the edge of a range expansion sometimes surf on the expanding front leading them rather than that leads to reach much greater spatial distribution and frequency than expected in stationary populations. Here, we extend this work and examine the surfing behavior of nonneutral mutations. Using an individual-based coupled-map lattice model, we confirm that, regardless of its fitness effects, the probability of survival of a new mutation depends strongly upon where it arises in relation to the expanding wave front. We demonstrate that the surfing effect can lead to deleterious mutations reaching high densities at an expanding front, even when they have substantial negative effects on fitness. Additionally, we highlight that this surfing phenomenon can occur for mutations that impact reproductive rate (i.e., number of offspring produced) as well as mutations that modify juvenile competitive ability. We suggest that these effects are likely to have important consequences for rates of spread and the evolution of spatially expanding populations.     

The frequency of shifts between alternative equilibria

We derive a formula giving the frequency with which random drift shifts a population between alternative equilibria. This formula is valid when such shifts are rare (Ns much greater than 1), and applies over a wide range of mutation rates. When the number of mutations entering the population is low (4 N mu much less than 1), the rate of stochastic shifts reduces to the product of the mutation rate and the probability of fixation of a single mutation. However, when many mutations enter the population in each generation (4 N mu much greater than 1), the rate is higher than would be expected if mutations were established independently, and converges to that given by a gaussian approximation. We apply recent results on bistable systems to extend this formula to the general multidimensional case. This gives an explicit expression for the frequency of stochastic shifts, which depends only on the equilibrium probability distribution near the saddle point separating the alternative stable states. The plausibility of theories of speciation through random drift are discussed in the light of these results.     

On Method of Moments Estimation in Linear Mixed Effects Models with Measurement Error on Covariates and Response with Application to a Longitudinal Study of Gene-Environment Interaction

We study a linear mixed effects model for longitudinal data, where the response variable and covariates with fixed effects are subject to measurement error. We propose a method of moment estimation that does not require any assumption on the functional forms of the distributions of random effects and other random errors in the model. For a classical measurement error model we apply the instrumental variable approach to ensure identifiability of the parameters. Our methodology, without instrumental variables, can be applied to Berkson measurement errors. Using simulation studies, we investigate the finite sample performances of the estimators and show the impact of measurement error on the covariates and the response on the estimation procedure. The results show that our method performs quite satisfactory, especially for the fixed effects with measurement error (even under misspecification of measurement error model). This method is applied to a real data example of a large birth and child cohort study.     

The relationship between microsatellite slippage mutation rate and the number of repeat units

Microsatellite markers are widely used for genetic studies, but the relationship between microsatellite slippage mutation rate and the number of repeat units remains unclear. In this study, microsatellite distributions in the human genome are collected from public sequence databases. We observe that there is a threshold size for slippage mutations. We consider a model of microsatellite mutation consisting of point mutations and single stepwise slippage mutations. From two sets of equations based on two stochastic processes and equilibrium assumptions, we estimate microsatellite slippage mutation rates without assuming any relationship between microsatellite slippage mutation rate and the number of repeat units. We use the least squares method with constraints to estimate expansion and contraction mutation rates. The estimated slippage mutation rate increases exponentially as the number of repeat units increases. When slippage mutations happen, expansion occurs more frequently for short microsatellites and contraction occurs more frequently for long microsatellites. Our results agree with the length-dependent mutation pattern observed from experimental data, and they explain the scarcity of long microsatellites.     

Joint inference of microsatellite mutation models, population history and genealogies using transdimensional Markov Chain Monte Carlo

We provide a framework for Bayesian coalescent inference from microsatellite data that enables inference of population history parameters averaged over microsatellite mutation models. To achieve this we first implemented a rich family of microsatellite mutation models and related components in the software package BEAST. BEAST is a powerful tool that performs Bayesian MCMC analysis on molecular data to make coalescent and evolutionary inferences. Our implementation permits the application of existing nonparametric methods to microsatellite data. The implemented microsatellite models are based on the replication slippage mechanism and focus on three properties of microsatellite mutation: length dependency of mutation rate, mutational bias toward expansion or contraction, and number of repeat units changed in a single mutation event. We develop a new model that facilitates microsatellite model averaging and Bayesian model selection by transdimensional MCMC. With Bayesian model averaging, the posterior distributions of population history parameters are integrated across a set of microsatellite models and thus account for model uncertainty. Simulated data are used to evaluate our method in terms of accuracy and precision of estimation and also identification of the true mutation model. Finally we apply our method to a red colobus monkey data set as an example.     

The probability that beneficial mutations are lost in populations with periodic bottlenecks

Population bottlenecks affect the dynamics of evolution, increasing the probability that beneficial mutations will be lost. Recent protocols for the experimental study of evolution involve repeated bottlenecks-when fresh media are inoculated during serial transfer or when chemostat tubes are changed. Unlike population reductions caused by stochastic environmental factors, these bottlenecks occur at known, regular intervals and with a fixed dilution ratio. We derive the ultimate probability of extinction for a beneficial mutation in a periodically bottlenecked population, using both discrete and continuous approaches. We show that both approaches yield the same approximation for extinction probability. From this, we derive an approximate expression for an effective population size.     

Estimation of the rate and effect of new beneficial mutations in asexual populations

The rate and effect of available beneficial mutations are key parameters in determining how a population adapts to a new environment. However, these parameters are poorly known, in large part because of the difficulty of designing and interpreting experiments to examine the rare and intrinsically stochastic process of mutation occurrence. We present a new approach to estimate the rate and selective advantage of beneficial mutations that underlie the adaptation of asexual populations. We base our approach on the analysis of experiments that track the effect of newly arising beneficial mutations on the dynamics of a neutral marker in evolving bacterial populations and develop efficient estimators of mutation rate and selective advantage. Using extensive simulations, we evaluate the accuracy of our estimators and conclude that they are quite robust to the use of relatively low experimental replication. To validate the predictions of our model, we compare theoretical and experimentally determined estimates of the selective advantage of the first beneficial mutation to fix in a series of ten replicate populations. We find that our theoretical predictions are not significantly different from experimentally determined selection coefficients. Application of our method to suitably designed experiments will allow estimation of how population evolvability depends on demographic and initial fitness parameters.     

The evolution of two mutations during clonal expansion

Knudson's two-hit hypothesis proposes that two genetic changes in the RB1 gene are the rate-limiting steps of retinoblastoma. In the inherited form of this childhood eye cancer, only one mutation emerges during somatic cell divisions while in sporadic cases, both alleles of RB1 are inactivated in the growing retina. Sporadic retinoblastoma serves as an example of a situation in which two mutations are accumulated during clonal expansion of a cell population. Other examples include evolution of resistance against anticancer combination therapy and inactivation of both alleles of a metastasis-suppressor gene during tumor growth. In this article, we consider an exponentially growing population of cells that must evolve two mutations to (i) evade treatment, (ii) make a step toward (invasive) cancer, or (iii) display a disease phenotype. We calculate the probability that the population has evolved both mutations before it reaches a certain size. This probability depends on the rates at which the two mutations arise; the growth and death rates of cells carrying none, one, or both mutations; and the size the cell population reaches. Further, we develop a formula for the expected number of cells carrying both mutations when the final population size is reached. Our theory establishes an understanding of the dynamics of two mutations during clonal expansion.     

Missense mutations in disease genes: a Bayesian approach to evaluate causality.

The problem of interpreting missense mutations of disease-causing genes is an increasingly important one. Because these point mutations result in alteration of only a single amino acid of the protein product, it is often unclear whether this change alone is sufficient to cause disease. We propose a Bayesian approach that utilizes genetic information on affected relatives in families ascertained through known missense-mutation carriers. This method is useful in evaluating known disease genes for common disease phenotypes, such as breast cancer or colorectal cancer. The posterior probability that a missense mutation is disease causing is conditioned on the relationship of the relatives to the proband, the population frequency of the mutation, and the phenocopy rate of the disease. The approach is demonstrated in two cancer data sets: BRCA1 R841W and APC I1307K. In both examples, this method helps establish that these mutations are likely to be disease causing, with Bayes factors in favor of causality of 5.09 and 66.97, respectively, and posterior probabilities of .836 and .985. We also develop a simple approximation for rare alleles and consider the case of unknown penetrance and allele frequency.     

The degeneration of asexual haploid populations and the speed of Muller's ratchet

The accumulation of deleterious mutations due to the process known as Muller's ratchet can lead to the degeneration of nonrecombining populations. We present an analytical approximation for the rate at which this process is expected to occur in a haploid population. The approximation is based on a diffusion equation and is valid when N exp(-u/s) > 1, where N is the population size, u is the rate at which deleterious mutations occur, and s is the effect of each mutation on fitness. Simulation results are presented to show that the approximation estimates the rate of the process better than previous approximations for values of mutation rates and selection coefficients that are compatible with the biological data. Under certain conditions, the ratchet can turn at a biologically significant rate when the deterministic equilibrium number of individuals free of mutations is substantially >100. The relevance of this process for the degeneration of Y or neo-Y chromosomes is discussed.     

A mathematical model for experimental gene evolution

The purpose of this paper is to determine the optimal mutation rate for random mutagenesis procedures used to make mutant libraries for subsequent screening. When the mutation rate is low, the probability of achieving a rare beneficial mutation is low. When the mutation rate is high, the probability of producing lethal mutations which result in loss of function is also high. We demonstrate that between these two extremes, an optimal mutation rate exists for experimental gene improvement. This rate depends strongly on the number of simultaneous mutations required for a beneficial change of the gene, but only weakly on the number of possible lethal mutations. This model predicts that when mutagenesis is performed at the optimum mutation rate, at least 63% (1--e(-1)) of the cloned genes in a mutant library will be non-functional.