Selection and mutation at a diallelic X-linked locus

Equilibria and convergence of gene frequencies are studied in the case of a diallelic X-linked locus under the influence of selection and mutation. The model used is that of an infinite diploid population with nonoverlapping discrete generations and random mating. It is proved that if the mutation rates and fitnesses are constant and the mutation rates are less than one-third, then global convergence of gene frequencies to equilibria occurs. The phase portraits of the dynamical system describing the change of allelic frequencies from one generation to the next are determined. Convergence of gene frequencies is monotone from a certain generation on if every other generation is skipped. In the case without mutation, our proof of this monotone convergence simplifies G. Palm's original proof [37].     

Selection at a diallelic autosomal locus in a dioecious population

The model used is that of an infinite dioecious population with nonoverlapping discrete generations and random mating. If the fitnesses are constant and heterozygotes are viable, it is proved that the allelic frequencies converge to equilibria as the number of generations tend to infinity. The results complement those of Karlin and Lessard [1] and Selgrade and Ziehe [5] in that hyperbolicity of equilibria is not assumed, use of index theory is avoided and it is determined how the number of equilibria and phase portraits depend on the fitnesses in the most general case. Lessard [2] gives, in the same situation, a condensed proof of convergence of allelic frequencies off the separatrix under the hypothesis that 1 is not an eigenvalue at any equilibrium. Our method of study is elementary.     

A stochastic model for estimation of mutation rates in multiple-replication proliferation processes

In this paper we propose a stochastic model based on the branching process for estimation and comparison of the mutation rates in proliferation processes of cells or microbes. We assume in this model that cells or microbes (the elements of a population) are reproduced by generations and thus the model is more suitably applicable to situations in which the new elements in a population are produced by older elements from the previous generation rather than by newly created elements from the same current generation. Cells and bacteria proliferate by binary replication, whereas the RNA viruses proliferate by multiple replication. The model is in terms of multiple replications, which includes the special case of binary replication. We propose statistical procedures for estimation and comparison of the mutation rates from data of multiple cultures with divergent culture sizes. The mutation rate is defined as the probability of mutation per replication per genome and thus can be assumed constant in the entire proliferation process. We derive the number of cultures for planning experiments to achieve desired accuracy for estimation or desired statistical power for comparing the mutation rates of two strains of microbes. We establish the efficiency of the proposed method by demonstrating how the estimation of mutation rates would be affected when the culture sizes were assumed similar but actually diverge.      

Mathematical analysis of a model describing evolution of an asexual population in a changing environment

We investigate a mathematical model for an asexual population with non-overlapping (discrete) generations, that exists in a changing environment. Sexual populations are also briefly discussed at the end of the paper. It is assumed that selection occurs on the value of a single polygenic trait, which is controlled by a finite number of loci with discrete-effect alleles. The environmental change results in a moving fitness optimum, causing the trait to be subject to a combination of stabilising and directional selection.This model is different from that investigated by Waxman and Peck [Genetics 153 (1999) 1041] where overlapping generations and continuous effect alleles were considered. In this paper, we consider non-overlapping generations and discrete effect alleles. However in [Genetics 153 (1999) 1041] and the present work, there is the same pattern of environmental change, namely a constant rate of change of the optimum.From [Genetics 153 (1999) 1041], no rigorous theoretical conclusion can be drawn about the form of the solutions as t grows large. Numerical work carried out in [Genetics 153 (1999) 1041] suggests that the solution is a lagged travelling wave solution, but no mathematical proof exists for the continuous model. Only partial results, regarding existence of travelling wave solutions and perturbed solutions, have been established (see [Nonlin. Anal. 53 (2003) 683; An integral equation describing an asexual population in a changing environment, Preprint]). For the discrete case of this paper, under the assumption that the ratio between the unit of genotypic value and the speed of environment change is a rational number, we are able to give rigorous proof of the following conclusion: the population follows the environmental change with a small lag behind, moreover, the lag is represented using a calculable quantity.     

可控高突变率枯草芽孢杆菌工程菌株的构建及应用

[背景]适应性实验室进化是运用于菌株改良的定向进化方法之一.适应性进化已成功应用于扩大底物利用范围和提高底物(产物)耐受性.由于微生物存在错配修复机制,使得菌株自然突变率水平极低,实验室适应性进化周期长,容易导致传代过程染菌而失败.[目的]获得可控高突变率的枯草芽孢杆菌工程菌株.[方法]采用无痕等位基因置换系统,将枯草...     

Panel discussion on submammalian systems

A test of X-ray-induced recessive lethal mutations in mouse spermatogonia (500 rad) was carried out. The test was based on familial analysis, which allowed division on the P pairs into those with lethal heterozygous members and in others assumed to be lethal-free. The F1 males from the latter group, in back-crosses to their daughters, gave an excessive rate of intra-uterine death in comparison with lethal-free males. The excessive death is assumed to reflect the rate of new (induced + spontaneous) recessive lethals or rather lethal equivalents.Three ways of estimating the rate of new recessive lethal mutations gave a mean of 5.5% per genome. From previous tests we can assume that 1% are spontaneous mutations. Thus the data indicate that the mutation rate per rad per gamete is 9 × 10^?5. This value is identical with a previous estimate.The results are discussed in relation to population tests performed in the early 60'2. It is concluded that the lack of observable deterioration in the populations after several consecutive generations of exposure is in accord with the estimates in the present analysis which are more than an order of magnitude lower than assumed at the start of the population tests.It is also stressed that species with different DNA contents show similarities in point estimates of doubling dosages.     

On fluctuation analysis: a new,simple and efficient method for computing the expected number of mutants

Fluctuation analysis, which is often used to demonstrate random mutagenesis in cell lines (and to estimate mutation rates), is based on the properties of a probability distribution known as the Luria-Delbrück distribution (and its generalizations). The two main new results reported in this paper are (i) a simple, completely general, and computationally efficient procedure for calculating probability distributions arising from fluctuation analysis and (ii) the formula for this procedure when cells in a colony have only grown for a finite number of generations after initial seeding. It is also shown that the procedure reduces to one that was developed earlier when an infinite number of generations is assumed. The derivation of the generating function of the distribution is also clarified. The results obtained should also be useful to experimentalists when only a relatively short time elapses between seeding and harvestint cultures for fluctuation analysis.     

A Study on a Nearly Neutral Mutation Model in Finite Populations

As a nearly neutral mutation model, the house-of-cards model is studied in finite populations using computer simulations. The distribution of the mutant effect is assumed to be normal. The behavior is mainly determined by the product of the population size, N, and the standard deviation, sigma, of the distribution of the mutant effect. If 4N sigma is large compared to one, a few advantageous mutants are quickly fixed in early generations. Then most mutation becomes deleterious and very slow increase of the average selection coefficient follows. It takes very long for the population to reach the equilibrium state. Substitutions of alleles occur very infrequently in the later stage. If 4N sigma is the order of one or less, the behavior is qualitatively similar to that of the strict neutral case. Gradual increase of the average selection coefficient occurs and in generations of several times the inverse of the mutation rate the population almost reaches the equilibrium state. Both advantageous and neutral (including slightly deleterious) mutations are fixed. Except in the early stage, an increase of the standard deviation of the distribution of the mutant effect decreases the average heterozygosity. The substitution rate is reduced as 4N sigma is increased. Three tests of neutrality, one using the relationship between the average and the variance of heterozygosity, another using the relationship between the average heterozygosity and the average number of substitutions and Watterson's homozygosity test are applied to the consequences of the present model. It is found that deviation from the neutral expectation becomes apparent only when 4N sigma is more than two. Also a simple approximation for the model is developed which works well when the mutation rate is very small.     

Microsatellite evolution: Markov transition functions for a suite of models

This paper takes from the collection of models considered by Whittaker et al. [2003. Likelihood-based estimation of microsatellite mutation rates. Genetics 164, 781-787] derived from direct observation of microsatellite mutation in parent-child pairs and provides analytical expressions for the probability distributions for the change in number of repeats over any given number of generations. The mathematical framework for this analysis is the theory of Markov processes. We find these expressions using two approaches, approximating by circulant matrices and solving a partial differential equation satisfied by the generating function. The impact of the differing choice of models is examined using likelihood estimates for time to most recent common ancestor. The analysis presented here may play a role in elucidating the connections between these two approaches and shows promise in reconciling differences between estimates for mutation rates based on Whittaker's approach and methods based on phylogenetic analyses.     

Models of Evolution of Reproductive Isolation

Mathematical models are presented for the evolution of postmating and premating reproductive isolation. In the case of postmating isolation it is assumed that hybrid sterility or inviability is caused by incompatibility of alleles at one or two loci, and evolution of reproductive isolation occurs by random fixation of different incompatibility alleles in different populations. Mutations are assumed to occur following either the stepwise mutation model or the infinite-allele model. Computer simulations by using It?'s stochastic differential equations have shown that in the model used the reproductive isolation mechanism evolves faster in small populations than in large populations when the mutation rate remains the same. In populations of a given size it evolves faster when the number of loci involved is large than when this is small. In general, however, evolution of isolation mechanisms is a very slow process, and it would take thousands to millions of generations if the mutation rate is of the order of 10(-5) per generation. Since gene substitution occurs as a stochastic process, the time required for the establishment of reproductive isolation has a large variance. Although the average time of evolution of isolation mechanisms is very long, substitution of incompatibility genes in a population occurs rather quickly once it starts. The intrapopulational fertility or viability is always very high. In the model of premating isolation it is assumed that mating preference or compatibility is determined by male- and female-limited characters, each of which is controlled by a single locus with multiple alleles, and mating occurs only when the male and female characters are compatible with each other. Computer simulations have shown that the dynamics of evolution of premating isolation mechanism is very similar to that of postmating isolation mechanism, and the mean and variance of the time required for establishment of premating isolation are very large. Theoretical predictions obtained from the present study about the speed of evolution of reproductive isolation are consistent with empirical data available from vertebrate organisms.     

Supporting the structural basis of prion strains: induction and identification of [PSI] variants

The [PSI] genetic element, which enhances the nonsense suppression efficiency in the yeast Saccharomyces cerevisiae, is thought to be amyloid-like aggregates of the Sup35 protein, and to self-propagate by a prion-like mechanism. Analogous to strains of the mammalian prion, variants of [PSI], with different nonsense suppression efficiencies and mitotic stabilities, can be isolated from the same yeast genetic background. In the framework of the "protein-only" hypothesis, variants of prion are assumed to be distinct conformers of the same prion polypeptide. This study aims to provide further support for the structural basis of [PSI] variation. Three variants of [PSI] were induced and distinguished by a panel of 11 single point mutations of the Sup35 protein. The variant phenotypes are intrinsically associated with [PSI] elements, presumably structurally different amyloids, rather than produced from variations in the genetic background. Differential incorporation to [PSI] variants of a Sup35 point mutation as well as N and C-terminally truncated Sup35 fragments is further demonstrated in vivo, suggesting that distinct patches of amino acid residues are involved in the assembly of [PSI] variants. These results establish a method for [PSI] variant-typing and indicate that heritable variations of amyloid structures can be derived from the same polypeptide.     

Expected frequencies of codon use as a function of mutation rates and codon fitnesses

Summary A method is shown to determine the expected pattern of codon use for any given set of mutation rates between nucleotides and any set of fitnesses for the codons. If it is assumed that mutations to stop codons are lethal then those codons which can mutate in one step to a stop codon tend to be used less frequently. This tendency is however, a very small one and is not likely to be observable within a single gene. Nor is it necessarily a general tendency. For example, the leucine pretermination codons may be used preferentially when mutations to proline are deleterious. It is shown that different mutation rates (eg: transitions occuring more frequently than transversions) may have as large an effect on codon usage as would strong selection for particular codons. For the model presented, an increase in the rate of transitions strongly decreases the expected frequency of UGG and CRR codons. Other codes are moderately affected by such a change in the mutation rates. Many other models can be examined using this method.     

Mismatch repair is diminished during stationary-phase mutation.

This paper is an invited Response to a recent Commentary [P.L. Foster, Rev. Mut. Res. 436 (1999) 179-184] entitled "Are adaptive mutations due to a decline in mismatch repair? The evidence is lacking". The Commentary argues that no evidence exists supporting the idea that mismatch repair is limiting specifically during stationary-phase mutation. A primary concern of the author is to question the method that we used previously to measure growth-dependent mutation. In this method, mutation rates are calculated using counts of mutant colonies taken at times when those colonies arise, rather than at a predetermined, fixed time. Here we show further data that illustrate why this must be done to ensure accurate mutation measurements. Such accuracy was necessary for our published determination that mismatch repair proteins are not limiting during growth-dependent mutation, but become so during stationary-phase mutation. We review the evidence supporting the idea that stationary-phase reversion of a lac frameshift mutation occurs in an environment of decreased mismatch repair capacity. Those data are substantial. The data presented in the Commentary, in apparent contradiction to this idea, do not justify the conclusion presented there.     

Are economic selection indices always superior to a desired gains index?

Conclusions The comparison of different selection indices is justified only if the indices are constrated to achieve the same profit function, even when each index is not optimized with respect to that profit function.When a profit function is known and is non-linear, the desired gains index may be more efficient than the economic index. The optimum desired gains index should be determined by iterative techniques over several generations to compare the genetic progress with the economic index, because gains by the economic index are not linear and the changes observed in the initial generations of selection are not the same rates in future generations, although those changes are linear in the case of the desired gains index.     

Coalescent theory for a completely random mating monoecious population

Consider a large random mating monoecious diploid population that has N individuals in each generation. Let us assume that at time 0 a random sample of ninfinity. It is then possible to obtain a generalization of coalescent theory for haploid populations if the distribution of G1 has a finite second moment and E[G(1)(3)]/N-->0 as N-->infinity.     

Advantages of a mechanistic codon substitution model for evolutionary analysis of protein-coding sequences

BACKGROUND: A mechanistic codon substitution model, in which each codon substitution rate is proportional to the product of a codon mutation rate and the average fixation probability depending on the type of amino acid replacement, has advantages over nucleotide, amino acid, and empirical codon substitution models in evolutionary analysis of protein-coding sequences. It can approximate a wide range of codon substitution processes. If no selection pressure on amino acids is taken into account, it will become equivalent to a nucleotide substitution model. If mutation rates are assumed not to depend on the codon type, then it will become essentially equivalent to an amino acid substitution model. Mutation at the nucleotide level and selection at the amino acid level can be separately evaluated. RESULTS: The present scheme for single nucleotide mutations is equivalent to the general time-reversible model, but multiple nucleotide changes in infinitesimal time are allowed. Selective constraints on the respective types of amino acid replacements are tailored to each gene in a linear function of a given estimate of selective constraints. Their good estimates are those calculated by maximizing the respective likelihoods of empirical amino acid or codon substitution frequency matrices. Akaike and Bayesian information criteria indicate that the present model performs far better than the other substitution models for all five phylogenetic trees of highly-divergent to highly-homologous sequences of chloroplast, mitochondrial, and nuclear genes. It is also shown that multiple nucleotide changes in infinitesimal time are significant in long branches, although they may be caused by compensatory substitutions or other mechanisms. The variation of selective constraint over sites fits the datasets significantly better than variable mutation rates, except for 10 slow-evolving nuclear genes of 10 mammals. An critical finding for phylogenetic analysis is that assuming variable mutation rates over sites lead to the overestimation of branch lengths.     

High mutation rate of a long microsatellite allele in Drosophila melanogaster provides evidence for allele-specific mutation rates

Within recent years, microsatellite have become one of the most powerful genetic markers in biology. For several mammalian species, microsatellite mutation rates have been estimated on the order of 10(- 3)-10(-5). A recent study, however, demonstrated mutation rates in Drosophila melanogaster of at least one order of magnitude lower than those in mammals. To further test this result, we examined mutation rates of different microsatellite loci using a larger sample size. We screened 24 microsatellite loci in 119 D. melanogaster lines maintained for approximately 250 generations and detected 9 microsatellite mutations. The average mutation rate of 6.3 x 10(-6) is identical to the mutation rate from a previous study. Most interestingly, all nine mutations occurred at the same allele of one locus (DROYANETSB). This hypermutable allele has 28 dinucleotide repeats and is among the longest microsatellite reported in D. melanogaster. The allele-specific mutation rate of 3.0 x 10(-4) per generation is within the range of mammalian mutation rates. Future microsatellite analyses will have to account for the dramatic differences in allele-specific mutation rates.      

Inference of genome-wide mutation rates and distributions of mutation effects for fitness traits: a simulation study.

The properties and limitations of maximum likelihood (ML) inference of genome-wide mutation rates (U) and parameters of distributions of mutation effects are investigated. Mutation parameters are estimated from simulated experiments in which mutations randomly accumulate in inbred lines. ML produces more accurate estimates than the procedure of Bateman and Mukai and is more robust if the data do not conform to the model assumed. Unbiased ML estimates of the mutation effects distribution parameters can be obtained if a value for U can be assumed, but if U is estimated simultaneously with the distribution parameters, likelihood may increase monotonically as a function of U. If the distribution of mutation effects is leptokurtic, the number of mutation events per line is large, or if genotypic values are poorly estimated, only a lower limit for U, an upper limit for the mean mutation effect, and a lower limit for the kurtosis of the distribution can be given. It is argued that such lower (upper) limits are appropriate minima (maxima). Estimates of the mean mutational effect are unbiased but may convey little about the properties of the distribution if it is leptokurtic.     

The imidazopyrrolopyridine analogue AG110 is a novel, highly selective inhibitor of pestiviruses that targets the viral RNA-dependent RNA polymerase at a hot spot for inhibition of viral replication

Ethyl 2-methylimidazo[1,2-a]pyrrolo[2,3-c]pyridin-8-carboxylate (AG110) was identified as a potent inhibitor of pestivirus replication. The 50% effective concentration values for inhibition of bovine viral diarrhea virus (BVDV)-induced cytopathic effect, viral RNA synthesis, and production of infectious virus were 1.2 +/- 0.5 microM, 5 +/- 1 microM, and 2.3 +/- 0.3 microM, respectively. AG110 proved inactive against the hepatitis C virus and a flavivirus. AG110 inhibits BVDV replication at a time point that coincides with the onset of intracellular viral RNA synthesis. Drug-resistant mutants carry the E291G mutation in the viral RNA-dependent RNA polymerase (RdRp). AG110-resistant virus is cross-resistant to the cyclic urea compound 1453 which also selects for the E291G drug resistance mutation. Moreover, BVDV that carries the F224S mutation (because of resistance to the imidazopyridine 5-[(4-bromophenyl)methyl]-2-phenyl-5H-imidazo[4,5-c]pyridine [BPIP]and VP32947) is also resistant to AG110. AG110 did not inhibit the in vitro activity of recombinant BVDV RdRp but inhibited the activity of BVDV replication complexes (RCs). Molecular modeling revealed that E291 is located in a small cavity near the tip of the finger domain of the RdRp about 7 A away from F224. Docking of AG110 in the crystal structure of the BVDV RdRp revealed several potential contacts including with Y257. The E291G mutation might enable the free rotation of Y257, which might in turn destabilize the backbone of the loop formed by residues 223 to 226, rendering more mobility to F224 and, hence, reducing the affinity for BPIP and VP32947. It is concluded that a single drug-binding pocket exists within the finger domain region of the BVDV RdRp that consists of two separate but potentially overlapping binding sites rather than two distinct drug-binding pockets.     

Epigenetic Inheritance,Epimutation, and the Response to Selection

There has been minimal theoretical exploration of the role of epigenetic variation in the response to natural selection. Using a population genetic model, I derive formulae that characterize the response of epigenetic variation to selection over multiple generations. Unlike genetic models in which mutation rates are assumed to be low relative to the strength of selection, the response to selection decays quickly due to a rapid lowering of parent-offspring epiallelic correlation. This effect is separate from the slowing response caused by a reduction in epigenetic variation. These results suggest that epigenetic variation may be less responsive to natural selection than is genetic variation, even in cases where levels of heritability appear similar.