The fixation probability of two competing beneficial mutations

Suppose that a beneficial mutation is undergoing a selective sweep when another beneficial mutation arises at a linked locus. We study the fixation probability of the double mutant, i.e., one (produced by recombination) that carries both mutations. Previous analysis works well for the case where the earlier beneficial mutation confers a greater selective advantage than the later mutation, but not so well in the opposite case. We present an approach to approximating the fixation probability in the case where the later mutation confers a greater selective advantage.     

Effect of changes in population size on the correlation between mutation rate and heterozygosity

Summary The effect of changes in population size on the correlation between mutation rate and heterozygosity was studied by using two models: sudden change in population size and gradual change. It was shown that the results for the two models are close to each other, unless the rate of change for the latter is exceedingly slow. Thus, in many cases, the former model, which is much simpler than the latter, can be used to treat the present problem. Numerical computations showed that the correlation in a population that is expanding or has expanded in the recent past is stronger while the correlation in a population that is decreasing or has experienced a population reduction or bottleneck in the recent past is weaker than that for an equilibrium population with the same mean heterozygosity. However, regardless of whether the population is at equilibrium or not, the proportion of variation in heterozygosity that is attributable to variation in molecular weight over loci is rather small if the mean heterozygosity of the population is low, say of the order 0.05 or smaller.     

A note on the correlation between heterozygosity and recombination rate

Mechanisms responsible for the correlation between heterozygosity and recombination rate have been thought to be background selection and selective sweep. In addition to these two, diversity enhancing selection and/or gene conversion is suggested to be contributing to the correlation, by surveying some examples of highly polymorphic loci that tend to locate in high-recombination regions.     

The effect of tandem substitutions on the correlation between synonymous and nonsynonymous rates in rodents.

Nonsynonymous substitutions in DNA cause amino acid substitutions while synonymous substitutions in DNA leave amino acids unchanged. The cause of the correlation between the substitution rates at nonsynonymous (K(A)) and synonymous (K(S)) sites in mammals is a contentious issue, and one that impacts on many aspects of molecular evolution. Here we use a large set of orthologous mammalian genes to investigate the causes of the K(A)-K(S) correlation in rodents. The strength of the K(A)-K(S) correlation exceeds the neutral theory expectation when substitution rates are estimated using algorithmic methods, but not when substitution rates are estimated by maximum likelihood. Irrespective of this methodological uncertainty the strength of the K(A)-K(S) correlation appears mostly due to tandem substitutions, an excess of which is generated by substitutional nonindependence. Doublet mutations cannot explain the excess of tandem synonymous-nonsynonymous substitutions, and substitution patterns indicate that selection on silent sites is the likely cause. We find no evidence for selection on codon usage. The nature of the relationship between synonymous divergence and base composition is unclear because we find a significant correlation if we use maximum-likelihood methods but not if we use algorithmic methods. Finally, we find that K(S) is reduced at the start of genes, which suggests that selection for RNA structure may affect silent sites in mammalian protein-coding genes.     

Variation in synonymous substitution rates among mammalian genes and the correlation between synonymous and nonsynonymous divergences

Using mammalian gene sequences, the variances in the numbers of synonymous and nonsynonymous substitutions among genes were estimated together with the correlation coefficient between the two. The expected correlation coefficient can be obtained under the neutral theory using these estimated values of the variances. The expected coefficient is found to often be one-half to two-thirds of the observed value. Possible causes for the disagreement were discussed, such as correlated selective constraints on the two types of substitutions and excess doublet mutations. The variance of mutation rate and that of selective constraint were also estimated. The results show that the coefficient of variation of the former is 0.2–0.3, whereas that of the latter is 0.7–0.9. Correspondence to: T. Ohta     

Association between nonsynonymous mutations of starch synthase IIa and starch quality in rice (Oryza sativa)

Starch quality is one of the most important agronomic traits in Asian rice, Oryza sativa. Starch synthase IIa (SsIIa) is a major candidate gene for starch quality variation. Within SsIIa, three nonsynonymous mutations in exon 8 have been shown to affect enzyme activity when expressed in Escherichia coli. To search for the variation in SsIIa that is responsible for starch quality variation in rice, we sequenced the SsIIa exon 8 region and measured starch quality as starch disintegration in alkali for 289 accessions of cultivated rice and 57 accessions of its wild ancestor, Oryza rufipogon. A general linear model and nested clade analysis were used to identify the associations between the three nonsynonymous single nucleotide polymorphisms (SNPs) and starch quality. Among the three nonsynonymous SNPs, we found strong evidence of association at one nucleotide site ('SNP 3'), corresponding to a Leu/Phe replacement at codon 781. A second SNP, corresponding to a Val/Met replacement at codon 737, could potentially show an association with increased sample sizes. Variation in SsIIa enzyme activity is associated with the cohesiveness of rice grains when cooked, and our findings are consistent with selection for more cohesive grains during the domestication of tropical japonica rice.     

Synonymous and nonsynonymous rate variation in nuclear genes of mammals

A maximum likelihood approach was used to estimate the synonymous and nonsynonymous substitution rates in 48 nuclear genes from primates, artiodactyls, and rodents. A codon-substitution model was assumed, which accounts for the genetic code structure, transition/transversion bias, and base frequency biases at codon positions. Likelihood ratio tests were applied to test the constancy of nonsynonymous to synonymous rate ratios among branches (evolutionary lineages). It is found that at 22 of the 48 nuclear loci examined, the nonsynonymous/synonymous rate ratio varies significantly across branches of the tree. The result provides strong evidence against a strictly neutral model of molecular evolution. Our likelihood estimates of synonymous and nonsynonymous rates differ considerably from previous results obtained from approximate pairwise sequence comparisons. The differences between the methods are explored by detailed analyses of data from several genes. Transition/transversion rate bias and codon frequency biases are found to have significant effects on the estimation of synonymous and nonsynonymous rates, and approximate methods do not adequately account for those factors. The likelihood approach is preferable, even for pairwise sequence comparison, because more-realistic models about the mutation and substitution processes can be incorporated in the analysis. Received: 17 May 1997 / Accepted: 28 September 1997     

X-linked adrenomyeloneuropathy associated with 14 novel ALD-gene mutations: no correlation between type of mutation and age of onset

Adrenomyeloneuropathy (AMN) represents a milder form of X-linked adrenoleukodystrophy (ALD), the most frequent peroxisomal disorder. The disease is characterised by an abnormal accumulation of saturated, very long chain, fatty acids, because of altered peroxisomal ?-oxidation that concomitantly leads to demyelination in the central and peripheral nervous systems. ALD shows a highly variable phenotypic expression and extensive mutation analysis in ALD patients has failed to establish a genotype-phenotype correlation, even in the presence of the same ALD-gene defect. Therefore, we have looked for a relationship between the molecular lesion and the age of onset in 19 patients with a well-classified clinical course of AMN. The nearly complete novel spectrum of ALD gene mutations identified has revealed no obvious correlation between the type of mutation and age of AMN onset in this small series. However, intrafamiliar concordance could be observed with respect to the occurrence of adrenocortical insufficiency. This supports the idea of one (or more) additional gene(s) contributing to the phenotypic expression of ALD. Electronic Publication     

Spatial covariation of mutation and nonsynonymous substitution rates in vertebrate mitochondrial genomes

Mitochondrial genomes encode fundamental subunits of the basic energy producing machinery of eukaryotic cells that are under strong functional constraint. Paradoxically, these genes evolve rapidly in general, and there is substantial variation in evolutionary rates among genes within genomes. In order to investigate spatial variation in selection intensity, we conducted tests of neutrality using ratios of synonymous to nonsynonymous substitutions (dN/dS = omega) on numerous protein gene segments from fishes and mammals. Values of omega were very low for nearly all genomic regions. However, values of both omega and dN varied in a clinal pattern with increasing distance from the light-strand origin of replication. Spatial heterogeneity of nonsynonymous substitution rates exhibits a significantly positive correlation with variation in mutation rates that are related to the mode of mitochondrial DNA replication. The finding that nonsynonymous substitution rates are proportional to mutation rates is expected if a majority of substitutions are selectively neutral or slightly deleterious. Spatial patterns of among-gene variation in nonsynonymous rates were highly similar between fishes and mammals, suggesting that forces governing mitochondrial gene evolution have remained relatively constant over 450 Myr of vertebrate evolution. Conservation of substitution patterns despite major shifts in thermal habit and metabolic demands among taxa implicates a conserved replication mechanism controlling relative mutation rates as a major determinant of mitochondrial protein evolution.     

A model for the correlation of mutation rate with GC content and the origin of GC-rich isochores

Based on the biochemical kinetics of DNA replication and mutagenesis, including misincorporation and correction, a model has been developed for studying the relationships among the mutation rate (u), the G + C content of the sequence (f), and the G + C proportion in the nucleotide precursor pool (N). Also a measure for the next-nucleotide effect, called the maximum capacity of the next-nucleotide effect (MC), has been proposed. Under the normal physiological conditions of mammalian germ cells, our results indicate: (1) the equilibrium G + C content in a sequence is approximately equal to the G + C proportion in the nucleotide precursor pool, i.e., f ≈ N, which is independent of the next-nucleotide effect; (2) an inverted-V-shaped distribution of mutation rates with respect to G + C contents is predicted, when the next-nucleotide effect is week, i.e., MC ≈ 1; (3) the distribution becomes flatter (i.e., inverted-U-shaped) as MC increases, but the peak at 50% GC is still observed when MC < 2; and (4) the peak disappears when MC > 2.8, that is, when the next-nucleotide effect becomes strong. Our results suggest that changes in the relative concentrations of nucleotide precursors can cause variations among genes both in mutation rate and in G + C content and that compositional isochores (DNA segments with a homogeneous G + C content) can arise in a genome due to differences in replication times of DNA segments. Correspondence to: W.-H. Li     

Patterns of intra- and interhost nonsynonymous variation reveal strong purifying selection in dengue virus

Considerable uncertainty surrounds the evolutionary rates of and selection pressures acting on arthropod-borne RNA viruses (arboviruses). In particular, it is unclear why arboviruses such as dengue virus show substantial genetic variation within individual humans and mosquitoes yet low long-term rates of amino acid substitution. To address this question, I compared patterns of nonsynonymous variation in populations of dengue virus sampled at different levels of evolutionary divergence. Although nonsynonymous variation was abundant in viral populations within individual humans, there was a marked reduction in the frequency of nonsynonymous mutations in interhost comparisons. Moreover, intrahost genetic variation corresponded to a random pattern of mutation, and most of the sites that exhibited nonsynonymous variation within hosts were invariant at deeper phylogenetic levels. This loss of long-term nonsynonymous variation is the signature of extensive purifying selection such that more than 90% of all nonsynonymous mutations are deleterious. Consequently, although arboviruses are able to successfully adapt to diverse cell types, they are characterized by a high rate of deleterious mutation.     

The problem of counting sites in the estimation of the synonymous and nonsynonymous substitution rates: implications for the correlation between the synonymous substitution rate and codon usage bias

Most methods for estimating the rate of synonymous and nonsynonymous substitution per site define a site as a mutational opportunity: the proportion of sites that are synonymous is equal to the proportion of mutations that would be synonymous under the model of evolution being considered. Here we demonstrate that this definition of a site can give misleading results and that a physical definition of site should be used in some circumstances. We illustrate our point by reexamining the relationship between codon usage bias and the synonymous substitution rate. It has recently been shown that the rate of synonymous substitution, calculated using the Goldman-Yang method, which encapsulates the mutational-opportunity definition of a site at a high level of sophistication, is either positively correlated or uncorrelated to synonymous codon bias in Drosophila. Using other methods, which account for synonymous codon bias but define a site physically, we show that there is a negative correlation between the synonymous substitution rate and codon bias and that the lack of a negative correlation using the Goldman-Yang method is due to the way in which the number of synonymous sites is counted. We also show that there is a positive correlation between the synonymous substitution rate and third position GC content in mammals, but that the relationship is considerably weaker than that obtained using the Goldman-Yang method. We argue that the Goldman-Yang method is misleading in this context and conclude that methods that rely on a mutational-opportunity definition of a site should be used with caution.     

Nonsense and missense mutations in hemophilia A: estimate of the relative mutation rate at CG dinucleotides.

Hemophilia A is an X-linked disease of coagulation caused by deficiency of factor VIII. Using cloned cDNA and synthetic oligonucleotide probes, we have now screened 240 patients and found CG-to-TG transitions in an exon in nine. We have previously reported four of these patients; and here we report the remaining five, all of whom were severely affected. In one patient a TaqI site was lost in exon 23, and in the other four it was lost in exon 24. The novel exon 23 mutation is a CG-to-TG substitution at the codon for amino acid residue 2166, producing a nonsense codon in place of the normal codon for arginine. Similarly, the exon 24 mutations are also generated by CG-to-TG transitions, either on the sense strand producing nonsense mutations or on the antisense strand producing missense mutations (Arg to Gln) at position 2228. The novel missense mutations are the first such mutations observed in association with severe hemophilia A. These results provide further evidence that recurrent mutations are not uncommon in hemophilia A, and they also allow us to estimate that the extent of hypermutability of CG dinucleotides is 10-20 times greater than the average mutation rate for hemophilia A.     

Membrane fluidity and the probability of complement fixation

We develop a mathematical theory of the role of membrane fluidity in the initiation of the IgG mediated complement cascade. The basic assumption is that C1q must be at least doubly bound to activate C1r, but that once C1q is doubly bound, C1r still requires some mean finite time tau to become enzymatically active. If C1q dissociates during this time interval, C1r cannot be activated. We consider the consequences of the simplest model of fluidity--one in which the difference between "fluid phase" lipids and "non-fluid phase" lipids is to allow protein mobility, but not a change in protein conformation. We show that under these conditions fluidity will effect C1r activation only if the rate of formation of multiply bound C1q is limited by diffusion in the membrane. If diffusion in the membrane is not rate-limiting, then, within the framework of this model, fluidity has no effect whatsoever on C1r activation. Thus, an experimental determination that C1q binding is not rate-limited by diffusion in the surface, but that fluidity does effect activation, would suggest a protein conformational change resulting perhaps from altered lipid composition. If diffusion in the surface does rate limit multiple C1q binding, we predict the possibility of an optimum diffusion coefficient for activation. For suitably chosen and reasonable parameter values this optimum will occur in the range (10(-11) less than or equal to D less than or equal to 10(-8) cm2/sec. We predict further, under these circumstances, a precipitous drop in the probability of activation above the optimum. The abrupt switch from a high probability of activation to essentially no probability of activation suggests the possibility of a very sensitive control mechanism exploitable by relatively small changes in membrane lipid composition.     

Spontaneous mutation rate changes in Saccharomyces cerevisiae at combinations of hsm3 and hsm6 mutations with rad52 mutation

Long-term storage at +4°C and cultivation at +30°C changes the spontaneous mutation rate of the yeast Saccharomyces cerevisiae double mutants rad52hsm3Δ and rad52hsm6-1. Combinations of hsm3 and hsm6 mutations with rad52 mutation lead to a decrease of the spontaneous mutation rate mediated by DNA repair synthesis in multiply replanted strains in comparison with the same strains investigated right after RAD52 gene decay. Combinations of hsm3 and hsm6 mutations with mutations in other genes of the RAD52 epistatic group did not provide a spontaneous mutation rate decrease.     

E-cadherin mutations and cell motility: A genotype-phenotype correlation

E-cadherin has a determinant role in tumour progression, acting as an invasion and metastasis suppressor. Germline mutations of E-cadherin gene (CDH1) occur in 30% of families with Hereditary Diffuse Gastric Cancer (HDGC); of these 23% are missense mutations. The CDH1 missense mutations described to date span the entire gene and some lead to significant functional consequences. In this study, we explored the hypothesis that mutations affecting different E-cadherin protein domains have distinct effects on cell motility. To accomplish our objective we characterized the effect of eleven HDGC CDH1 germline missense mutations (T118R, L214P, G239R, A298T, T340A, P373L, R749W, E757K, E781D, P799R and V832M) on cell motility. Further, we studied their effect on the activation of signalling pathways known to be relevant for cell motility such as the EGFR, Src kinase and MAPKs. CDH1 mutations localized on the extracellular and juxtamembrane domains, both affecting the integrity of the extracellular domain, led to increased cell motility accompanied by increased EGFR activation. Moreover, we observed that cells expressing extracellular mutants exhibit increased activation of Src kinase and p38 MAPK. Our results allowed the identification of the E-cadherin domains pivotal for cell motility, further demonstrated a genotype-phenotype correlation, and defined a subset of HDGC cases which may benefit from EGFR inhibitors.     

Estimation of the upper limit of the mutation rate and mean heterozygous effect of deleterious mutations

Deng et al. have recently proposed that estimates of an upper limit to the rate of spontaneous mutations and their average heterozygous effect can be obtained from the mean and variance of a given fitness trait in naturally segregating populations, provided that allele frequencies are maintained at the balance between mutation and selection. Using simulations they show that this estimation method generally has little bias and is very robust to violations of the mutation-selection balance assumption. Here I show that the particular parameters and models used in these simulations generally reduce the amount of bias that can occur with this estimation method. In particular, the assumption of a large mutation rate in the simulations always implies a low bias of estimates. In addition, the specific model of overdominance used to check the violation of the mutation-selection balance assumption is such that there is not a dramatic decline in mean fitness from overdominant mutations, again implying a low bias of estimates. The assumption of lower mutation rates and/or other models of balancing selection may imply considerably larger biases of the estimates, making the reliability of the proposed method highly questionable.