Simple Methods for Testing the Molecular Evolutionary Clock Hypothesis

Simple statistical methods for testing the molecular evolutionary clock hypothesis are developed which can be applied to both nucleotide and amino acid sequences. These methods are based on the chi-square test and are applicable even when the pattern of substitution rates is unknown and/or the substitution rate varies among different sites. Furthermore, some of the methods can be applied even when the outgroup is unknown. Using computer simulations, these methods were compared with the likelihood ratio test and the relative rate test. The results indicate that the powers of the present methods are similar to those of the likelihood ratio test and the relative rate test, in spite of the fact that the latter two tests assume that the pattern of substitution rates follows a certain model and that the substitution rate is the same among different sites, while such assumptions are not necessary to apply the present methods. Therefore, the present methods might be useful.     

The Effect of Deleterious Mutations on Neutral Molecular Variation

Selection against deleterious alleles maintained by mutation may cause a reduction in the amount of genetic variability at linked neutral sites. This is because a new neutral variant can only remain in a large population for a long period of time if it is maintained in gametes that are free of deleterious alleles, and hence are not destined for rapid elimination from the population by selection. Approximate formulas are derived for the reduction below classical neutral values resulting from such background selection against deleterious mutations, for the mean times to fixation and loss of new mutations, nucleotide site diversity, and number of segregating sites. These formulas apply to random-mating populations with no genetic recombination, and to populations reproducing exclusively asexually or by self-fertilization. For a given selection regime and mating system, the reduction is an exponential function of the total mutation rate to deleterious mutations for the section of the genome involved. Simulations show that the effect decreases rapidly with increasing recombination frequency or rate of outcrossing. The mean time to loss of new neutral mutations and the total number of segregating neutral sites are less sensitive to background selection than the other statistics, unless the population size is of the order of a hundred thousand or more. The stationary distribution of allele frequencies at the neutral sites is correspondingly skewed in favor of rare alleles, compared with the classical neutral result. Observed reductions in molecular variation in low recombination genomic regions of sufficiently large size, for instance in the centromere-proximal regions of Drosophila autosomes or in highly selfing plant populations, may be partly due to background selection against deleterious mutations.     

Clusters of Identical New Mutations Can Account for the ``overdispersed'''' Molecular Clock

Germ-cell mutations may occur during meiosis, giving rise to independent mutant gametes in a Poisson process, or before meiosis, giving rise to multiple copies of identical mutant gametes at a much higher probability than the Poisson expectation. We report that the occurrence of these early premeiotic clusters of new identical mutant alleles increases the variance-to-mean ratio of mutation rate (R(u) > 1). This leads to an expected variance-to-mean ratio (R(t)) of the molecular clock that is always greater than one and may cover the observed range of R(t) values. Hence, the molecular clock may not be over-dispersed based on this new mutational model that includes clusters. To get a better estimation of R(u) and R(t), one needs measurements of the intrageneration variation of reproductive success (N(i)/N(e(i))), population dynamics (k(i)), and the proportion of new mutations that occur in clusters (r(c)), especially those formed before germ-cell differentiation.     

The Molecular Clock of Neutral Evolution Can Be Accelerated or Slowed by Asymmetric Spatial Structure

Over time, a population acquires neutral genetic substitutions as a consequence of random drift. A famous result in population genetics asserts that the rate, K, at which these substitutions accumulate in the population coincides with the mutation rate, u, at which they arise in individuals: K = u. This identity enables genetic sequence data to be used as a “molecular clock” to estimate the timing of evolutionary events. While the molecular clock is known to be perturbed by selection, it is thought that K = u holds very generally for neutral evolution. Here we show that asymmetric spatial population structure can alter the molecular clock rate for neutral mutations, leading to either K<u or K>u. Our results apply to a general class of haploid, asexually reproducing, spatially structured populations. Deviations from K = u occur because mutations arise unequally at different sites and have different probabilities of fixation depending on where they arise. If birth rates are uniform across sites, then K ≤ u. In general, K can take any value between 0 and Nu. Our model can be applied to a variety of population structures. In one example, we investigate the accumulation of genetic mutations in the small intestine. In another application, we analyze over 900 Twitter networks to study the effect of network topology on the fixation of neutral innovations in social evolution.     

Gene Duplicability-Connectivity-Complexity across Organisms and a Neutral Evolutionary Explanation

Gene duplication has long been acknowledged by biologists as a major evolutionary force shaping genomic architectures and characteristics across the Tree of Life. Major research has been conducting on elucidating the fate of duplicated genes in a variety of organisms, as well as factors that affect a gene’s duplicability–that is, the tendency of certain genes to retain more duplicates than others. In particular, two studies have looked at the correlation between gene duplicability and its degree in a protein-protein interaction network in yeast, mouse, and human, and another has looked at the correlation between gene duplicability and its complexity (length, number of domains, etc.) in yeast. In this paper, we extend these studies to six species, and two trends emerge. There is an increase in the duplicability-connectivity correlation that agrees with the increase in the genome size as well as the phylogenetic relationship of the species. Further, the duplicability-complexity correlation seems to be constant across the species. We argue that the observed correlations can be explained by neutral evolutionary forces acting on the genomic regions containing the genes. For the duplicability-connectivity correlation, we show through simulations that an increasing trend can be obtained by adjusting parameters to approximate genomic characteristics of the respective species. Our results call for more research into factors, adaptive and non-adaptive alike, that determine a gene’s duplicability.     

The Evolutionary Potential of Phenotypic Mutations

Errors in protein synthesis, so-called phenotypic mutations, are orders-of-magnitude more frequent than genetic mutations. Here, we provide direct evidence that alternative protein forms and phenotypic variability derived from translational errors paved the path to genetic, evolutionary adaptations via gene duplication. We explored the evolutionary origins of Saccharomyces cerevisiae IDP3 - an NADP-dependent isocitrate dehydrogenase mediating fatty acids ß-oxidation in the peroxisome. Following the yeast whole genome duplication, IDP3 diverged from a cytosolic ancestral gene by acquisition of a C-terminal peroxisomal targeting signal. We discovered that the pre-duplicated cytosolic IDPs are partially localized to the peroxisome owing to +1 translational frameshifts that bypass the stop codon and unveil cryptic peroxisomal targeting signals within the 3’-UTR. Exploring putative cryptic signals in all 3’-UTRs of yeast genomes, we found that other enzymes related to NADPH production such as pyruvate carboxylase 1 (PYC1) might be prone to peroxisomal localization via cryptic signals. Using laboratory evolution we found that these translational frameshifts are rapidly imprinted via genetic single base deletions occurring within the very same gene location. Further, as exemplified here, the sequences that promote translational frameshifts are also more prone to genetic deletions. Thus, genotypes conferring higher phenotypic variability not only meet immediate challenges by unveiling cryptic 3’-UTR sequences, but also boost the potential for future genetic adaptations.     

Circadian Rhythms in NEUROSPORA CRASSA: Interactions between Clock Mutations

Mutations at four loci in Neurospora crassa that alter the period of the circadian rhythm have been used to construct a series of double mutant strains in order to detect interactions between these mutations. Strains carrying mutations at three of these loci have altered periods on minimal media: prd-1, several alleles at the olir (oligomycin resistance) locus and four alleles at the frq locus. A mutation at the fourth locus, cel, which results in a defect in fatty acid synthesis, also leads to lengthening of the period when the medium is supplemented with linoleic acid (18:2). The cel mutation was crossed into strains carrying the frq, prd-1 and olir mutations, and the periods of the double mutant strains with and without 18:2 supplementation were determined. In addition, data from the literature for other combinations of loci and/or chemical effects on the period have been reanalyzed.--It was found that both prd-1 and olir are epistatic to the effects of 18:2 on cel; in the series of cel frq double mutant strains, the period-lengthening effect of 18:2 is inversely proportional to the period of the frq parent, indicating an interaction between frq and cel; period effects reported in the literature can be described as changes by a fixed ratio or percentage of the period rather than by a fixed number of hours, and the data, therefore, can support a multiplicative as well as an additive model.--Several biochemical interpretations of these interactions are discussed, based on simple chemical kinetics, enzyme inhibition kinetics and the control of flux through metabolic pathways.     

The Impact of Neutral Mutations on Genome Evolvability

Beneficial mutations are rare and deleterious mutations are purged by natural selection. As a result, the vast majority of mutations that accumulate in genomes belong to the class of neutral mutations. Over the last two decades, neutral mutations, despite their null effect on fitness, have been shown to affect evolvability by providing access to new phenotypes through subsequent mutations that would not have been available otherwise. Here we propose that in addition, many mutations — independent of their selective effects — can affect the mutability of neighboring DNA sequences and modulate the efficacy of homologous recombination. Such mutations do not change the spectrum of accessible phenotypes, but rather the rate at which new phenotypes will be produced. Therefore, neutral mutations that accumulate in genomes have an important long-term impact on the evolutionary fate of genomes.     

On the Overdispersed Molecular Clock

Rates of molecular evolution at some loci are more irregular than described by simple Poisson processes. Three situations under which molecular evolution would not follow simple Poisson processes are reevaluated from the viewpoint of the neutrality hypothesis: concomitant or multiple substitutions in a gene, fluctuating substitution rates in time caused by coupled effects of deleterious mutations and bottlenecks, and changes in the degree of selective constraints against a gene (neutral space) caused by successive substitutions. The common underlying assumption that these causes are lineage nonspecific excludes the case where mutation rates themselves change systematically among lineages or taxonomic groups, and severely limits the extent of variation in the number of substitutions among lineages. Even under this stringent condition, however, the third hypothesis, the fluctuating neutral space model, can generate fairly large variation. This is described by a time-dependent renewal process, which does not exhibit any episodic nature of molecular evolution. It is argued that the observed elevated variances in the number of nucleotide or amino acid substitutions do not immediately call for positive Darwinian selection in molecular evolution.     

Molecular Evolution in a Multisite Nearly Neutral Mutation Model

A simple nearly neutral mutation model of protein evolution was studied using computer simulation assuming a constant population size. In this model, a gene consists of a finite number of codons and there is no recombination within a gene. Each codon has two replacement and one silent sites. The fitness of a gene was determined multiplicatively by amino acids specified by codons (the independent multicodon model). Nucleotide diversity at replacement sites decreases as selection becomes stronger. A reduction of nucleotide diversity at silent sites also occurs as selection intensifies but the magnitude of the reduction is not a monotone function of the intensity of selection. The dispersion index is close to one. The average value of Tajima's and Fu and Li's statistics are negative and their absolute values increases as selection intensifies. However, their powers of detecting selection under the present model were not high unless the number of sites is large or mutation rate is high. The MK test was shown to detect intermediate selection fairly well. For comparison, the house-of-cards model was also investigated and its behavior was shown to be more sensitive to changes of population size than that of the independent multicodon model. The relevance of the present model for explaining protein evolution was discussed comparing its prediction and recent DNA data. Received: 24 May 1999 / Accepted: 17 August 1999     

Genealogy of Neutral Genes and Spreading of Selected Mutations in a Geographically Structured Population

In a geographically structured population, the interplay among gene migration, genetic drift and natural selection raises intriguing evolutionary problems, but the rigorous mathematical treatment is often very difficult. Therefore several approximate formulas were developed concerning the coalescence process of neutral genes and the fixation process of selected mutations in an island model, and their accuracy was examined by computer simulation. When migration is limited, the coalescence (or divergence) time for sampled neutral genes can be described by the convolution of exponential functions, as in a panmictic population, but it is determined mainly by migration rate and the number of demes from which the sample is taken. This time can be much longer than that in a panmictic population with the same number of breeding individuals. For a selected mutation, the spreading over the entire population was formulated as a birth and death process, in which the fixation probability within a deme plays a key role. With limited amounts of migration, even advantageous mutations take a large number of generations to spread. Furthermore, it is likely that these mutations which are temporarily fixed in some demes may be swamped out again by non-mutant immigrants from other demes unless selection is strong enough. These results are potentially useful for testing quantitatively various hypotheses that have been proposed for the origin of modern human populations.     

生物钟的分子机制研究进展

RecentDevelopmentsinMolecularMechanismsofBiologicalClockHouBingkai(DepartmentofBiology,ShandongUniversity,Jinan250100)YuHuimin(DepartmentofBiochemistry,ShandongEducationCollege,Jinan250013)生物的昼夜节奏表现,从单细胞生物到多细胞生物,从原校生物到真核生物都曾被描述过。由于这种现象在生物界广泛存在,关于它的特征、意义和机理的研究日益受到人们重视。其中最重要和最吸引人的方面是它的测时系统—一生物钟（biologicalclock）,也称生物振荡器（oscillators）。近年来,人们从分子水平对生物钟的研究比较活…     

Evolutionary Invasion and Escape in the Presence of Deleterious Mutations

Replicators such as parasites invading a new host species, species invading a new ecological niche, or cancer cells invading a new tissue often must mutate to adapt to a new environment. It is often argued that a higher mutation rate will favor evolutionary invasion and escape from extinction. However, most mutations are deleterious, and even lethal. We study the probability that the lineage will survive and invade successfully as a function of the mutation rate when both the initial strain and an adaptive mutant strain are threatened by lethal mutations. We show that mutations are beneficial, i.e. a non-zero mutation rate increases survival compared to the limit of no mutations, if in the no-mutation limit the survival probability of the initial strain is smaller than the average survival probability of the strains which are one mutation away. The mutation rate that maximizes survival depends on the characteristics of both the initial strain and the adaptive mutant, but if one strain is closer to the threshold governing survival then its properties will have greater influence. These conclusions are robust for more realistic or mechanistic depictions of the fitness landscapes such as a more detailed viral life history, or non-lethal deleterious mutations.     

蓝藻生物钟分子机理的研究进展

蓝藻是具有内源性生物钟的简单生物.虽然蓝藻生物钟具有跟真核生物同样的基础特征,但其相关基因和蛋白质与真核生物没有同源性.蓝藻生物钟的核心是kai基因簇及其编码的蛋白KaiA,KaiB和KaiC.这三种Kai蛋白相互作用调节KaiC的磷酸化状态,从而产生昼夜节律信息.KaiC的磷酸化循环是昼夜节律的起博器,调控包括kai基因在内的相关基因的节律性表达.组氨酸蛋白激酶的磷酸化传递可将环境信息输入和将节律信息输出生物钟核心.     

Probing Evolutionary Repeatability: Neutral and Double Changes and the Predictability of Evolutionary Adaptation

Background

The question of how organisms adapt is among the most fundamental in evolutionary biology. Two recent studies investigated the evolution of Escherichia coli in response to challenge with the antibiotic cefotaxime. Studying five mutations in the β-lactamase gene that together confer significant antibiotic resistance, the authors showed a complex fitness landscape that greatly constrained the identity and order of intermediates leading from the initial wildtype genotype to the final resistant genotype. Out of 18 billion possible orders of single mutations leading from non-resistant to fully-resistant form, they found that only 27 (1.5×10⁻⁷%) pathways were characterized by consistently increasing resistance, thus only a tiny fraction of possible paths are accessible by positive selection. I further explore these data in several ways.

Principal Findings

Allowing neutral changes (those that do not affect resistance) increases the number of accessible pathways considerably, from 27 to 629. Allowing multiple simultaneous mutations also greatly increases the number of accessible pathways. Allowing a single case of double mutation to occur along a pathway increases the number of pathways from 27 to 259, and allowing arbitrarily many pairs of simultaneous changes increases the number of possible pathways by more than 100 fold, to 4800. I introduce the metric ‘repeatability,’ the probability that two random trials will proceed via the exact same pathway. In general, I find that while the total number of accessible pathways is dramatically affected by allowing neutral or double mutations, the overall evolutionary repeatability is generally much less affected.

Conclusions

These results probe the conceivable pathways available to evolution. Even when many of the assumptions of the analysis of Weinreich et al. (2006) are relaxed, I find that evolution to more highly cefotaxime resistant β-lactamase proteins is still highly repeatable.     

Understanding Neutral Genomic Molecular Clocks

The molecular clock hypothesis is a central concept in molecular evolution and has inspired much research into why evolutionary rates vary between and within genomes. In the age of modern comparative genomics, understanding the neutral genomic molecular clock occupies a critical place. It has been demonstrated that molecular clocks run differently between closely related species, and generation time is an important determinant of lineage specific molecular clocks. Moreover, it has been repeatedly shown that regional molecular clocks vary even within a genome, which should be taken into account when measuring evolutionary constraint of specific genomic regions. With the availability of a large amount of genomic sequence data, new insights into the patterns and causes of variation in molecular clocks are emerging. In particular, factors such as nucleotide composition, molecular origins of mutations, weak selection and recombination rates are important determinants of neutral genomic molecular clocks.