Population genetic models of duplicated genes

Various population genetic models of duplicated genes are introduced. The problems covered in this review include the fixation process of a duplicated copy, copy number polymorphism, the fates of duplicated genes and single nucleotide polymorphism in duplicated genes. Because of increasing evidence for concerted evolution by gene conversion, this review introduces recently developed gene conversion models. In the first half, models assuming independent evolution of duplicated genes are introduced, and then the effect of gene conversion is considered in the second half.     

Transition between stochastic evolution and deterministic evolution in the presence of selection: general theory and application to virology.

We present here a self-contained analytic review of the role of stochastic factors acting on a virus population. We develop a simple one-locus, two-allele model of a haploid population of constant size including the factors of random drift, purifying selection, and random mutation. We consider different virological experiments: accumulation and reversion of deleterious mutations, competition between mutant and wild-type viruses, gene fixation, mutation frequencies at the steady state, divergence of two populations split from one population, and genetic turnover within a single population. In the first part of the review, we present all principal results in qualitative terms and illustrate them with examples obtained by computer simulation. In the second part, we derive the results formally from a diffusion equation of the Wright-Fisher type and boundary conditions, all derived from the first principles for the virus population model. We show that the leading factors and observable behavior of evolution differ significantly in three broad intervals of population size, N. The "neutral limit" is reached when N is smaller than the inverse selection coefficient. When N is larger than the inverse mutation rate per base, selection dominates and evolution is "almost" deterministic. If the selection coefficient is much larger than the mutation rate, there exists a broad interval of population sizes, in which weakly diverse populations are almost neutral while highly diverse populations are controlled by selection pressure. We discuss in detail the application of our results to human immunodeficiency virus population in vivo, sampling effects, and limitations of the model.     

Transition between Stochastic Evolution and Deterministic Evolution in the Presence of Selection: General Theory and Application to Virology

We present here a self-contained analytic review of the role of stochastic factors acting on a virus population. We develop a simple one-locus, two-allele model of a haploid population of constant size including the factors of random drift, purifying selection, and random mutation. We consider different virological experiments: accumulation and reversion of deleterious mutations, competition between mutant and wild-type viruses, gene fixation, mutation frequencies at the steady state, divergence of two populations split from one population, and genetic turnover within a single population. In the first part of the review, we present all principal results in qualitative terms and illustrate them with examples obtained by computer simulation. In the second part, we derive the results formally from a diffusion equation of the Wright-Fisher type and boundary conditions, all derived from the first principles for the virus population model. We show that the leading factors and observable behavior of evolution differ significantly in three broad intervals of population size, N. The “neutral limit” is reached when N is smaller than the inverse selection coefficient. When N is larger than the inverse mutation rate per base, selection dominates and evolution is “almost” deterministic. If the selection coefficient is much larger than the mutation rate, there exists a broad interval of population sizes, in which weakly diverse populations are almost neutral while highly diverse populations are controlled by selection pressure. We discuss in detail the application of our results to human immunodeficiency virus population in vivo, sampling effects, and limitations of the model.     

Sequence-Dependent Gene Conversion: Can Duplicated Genes Diverge Fast Enough to Escape Conversion?

Conversion between duplicated genes limits their independent evolution. Models in which conversion frequencies decrease as genes diverge are examined to determine conditions under which genes can "escape" further conversion and hence escape from a gene family. A review of results from various recombination systems suggests two classes of sequence-dependence models: (1) the "k-hit" model in which conversion is completely inactivated by a few (k) mutational events, such as the insertion of a mobile element, and (2) more general models where conversion frequency gradually declines as genes diverge through the accumulation of point mutants. Exact analysis of the k-hit model is given and an approximate analysis of a more general sequence-dependent model is developed and verified by computer simulation. If mu is the per nucleotide mutation rate, then neutral duplicated genes diverging through point mutants are likely to escape conversion provided 2 mu/lambda much greater than 0.1, where lambda is the conversion rate between identical genes. If 2 mu/lambda much less than 0.1, the expected number of conversions before escape increases exponentially so that, for biological purposes, the genes never escape conversion. For single mutational events sufficient to block further conversions, occurring at rate nu per copy per generation, many conversions are expected if 2 nu/lambda much less than 1, while the genes essentially evolve independently if 2 nu/lambda much greater than 1. Implications of these results for both models of concerted evolution and the evolution of new gene functions via gene duplication are discussed.     

The effective size of mixed sexually and asexually reproducing populations

Using the transition matrix of inbreeding and coancestry coefficients, the inbreeding (N(eI)), variance (N(eV)), and asymptotic (N(e lambda)) effective sizes of mixed sexual and asexual populations are formulated in terms of asexuality rate (delta), variance of asexual (C) and sexual (K) reproductive contributions of individuals, correlation between asexual and sexual contributions (rho(ck)), selfing rate (beta), and census population size (N). The trajectory of N(eI) toward N(e lambda) changes crucially depending on delta, N, and beta, whereas that of N(eV) is rather consistent. With increasing asexuality, N(e lambda) either increases or decreases depending on C, K, and rho(ck). The parameter space in which a partially asexual population has a larger N(e lambda) than a fully sexual population is delineated. This structure is destroyed when N(1 - delta) < 1 or delta > 1 - 1/N. With such a high asexuality, tremendously many generations are required for the asymptotic size N(e lambda) to be established, and N(e lambda) is extremely large with any value of C, K, and rho(ck) because the population is dominated eventually by individuals of the same genotype and the allelic diversity within the individuals decays quite slowly. In reality, the asymptotic state would occur only occasionally, and instantaneous rather than asymptotic effective sizes should be practical when predicting evolutionary dynamics of highly asexual populations.     

The coalescent with selection on copy number variants

We develop a coalescent-based simulation tool to generate patterns of single nucleotide polymorphisms (SNPs) in a wide region encompassing both the original and duplicated genes. Selection on the new duplicated copy and interlocus gene conversion between the two copies are incorporated. This simulation enables us to explore how selection on duplicated copies affects the pattern of SNPs. The fixation of an advantageous duplicated copy causes a strong reduction in polymorphism not only in the duplicated copy but also in its flanking regions, which is a typical signature of a selective sweep by positive selection. After fixation, polymorphism gradually increases by accumulating neutral mutations and eventually reaches the equilibrium value if there is no gene conversion. When gene conversion is active, the number of SNPs in the duplicated copy quickly increases by transferring SNPs from the original copy; therefore, the time when we can recognize the signature of selection is decreased. Because this effect of gene conversion is restricted only to the duplicated region, more power to detect selection is expected if a flanking region to the duplicated copy is used.     

Nucleotide sequence of the O gene and of the origin of replication in bacteriophage lambda DNA.

The nucleotide sequence of the O gene in bacteriophage lambda DNA is presented. According to two possible initiator codons, the primary structure of the O protein deduced from the DNA sequence consists of 278 or 299 amino acid residues. Structure and function of the O protein--one of the two phage initiator proteins for lambda DNA replication--are discussed in the light of a secondary structure model for the O protein. The central part of the O gene contains a cluster of symmetrical sequences extending over 160 base pairs. The point mutation of the cis-dominant replication mutant ti12 is located in this region.     

Fixation probability and time in subdivided populations

New alleles arising in a population by mutation ultimately are either fixed or lost. Either is possible, for both beneficial and deleterious alleles, because of stochastic changes in allele frequency due to genetic drift. Spatially structured populations differ from unstructured populations in the probability of fixation and the time that this fixation takes. Previous results have generally made many assumptions: that all demes contribute to the next generation in exact proportion to their current sizes, that new mutations are beneficial, and that new alleles have additive effects. In this article these assumptions are relaxed, allowing for an arbitrary distribution among demes of reproductive success, both beneficial and deleterious effects, and arbitrary dominance. The effects of population structure can be expressed with two summary statistics: the effective population size and a variant of Wright's F(ST). In general, the probability of fixation is strongly affected by population structure, as is the expected time to fixation or loss. Population structure changes the effective size of the species, often strongly downward; smaller effective size increases the probability of fixing deleterious alleles and decreases the probability of fixing beneficial alleles. On the other hand, population structure causes an increase in the homozygosity of alleles, which increases the probability of fixing beneficial alleles but somewhat decreases the probability of fixing deleterious alleles. The probability of fixing new beneficial alleles can be simply described by 2hs(1 - F(ST))N(e)/N(tot), where hs is the change in fitness of heterozygotes relative to the ancestral homozygote, F(ST) is a weighted version of Wright's measure of population subdivision, and N(e) and N(tot) are the effective and census sizes, respectively. These results are verified by simulation for a broad range of population structures, including the island model, the stepping-stone model, and a model with extinction and recolonization.     

Molecular Clock of Neutral Mutations in a Fitness-Increasing Evolutionary Process

The molecular clock of neutral mutations, which represents linear mutation fixation over generations, is theoretically explained by genetic drift in fitness-steady evolution or hitchhiking in adaptive evolution. The present study is the first experimental demonstration for the molecular clock of neutral mutations in a fitness-increasing evolutionary process. The dynamics of genome mutation fixation in the thermal adaptive evolution of Escherichia coli were evaluated in a prolonged evolution experiment in duplicated lineages. The cells from the continuously fitness-increasing evolutionary process were subjected to genome sequencing and analyzed at both the population and single-colony levels. Although the dynamics of genome mutation fixation were complicated by the combination of the stochastic appearance of adaptive mutations and clonal interference, the mutation fixation in the population was simply linear over generations. Each genome in the population accumulated 1.6 synonymous and 3.1 non-synonymous neutral mutations, on average, by the spontaneous mutation accumulation rate, while only a single genome in the population occasionally acquired an adaptive mutation. The neutral mutations that preexisted on the single genome hitchhiked on the domination of the adaptive mutation. The successive fixation processes of the 128 mutations demonstrated that hitchhiking and not genetic drift were responsible for the coincidence of the spontaneous mutation accumulation rate in the genome with the fixation rate of neutral mutations in the population. The molecular clock of neutral mutations to the fitness-increasing evolution suggests that the numerous neutral mutations observed in molecular phylogenetic trees may not always have been fixed in fitness-steady evolution but in adaptive evolution.     

Backbone 1H, 13C, and 15N resonance assignments for lysozyme from bacteriophage lambda

Lysozyme from lambda bacteriophage (λ lysozyme) is an 18 kDa globular protein displaying some of the structural features common to all lysozymes; in particular, λ lysozyme consists of two structural domains connected by a helix, and has its catalytic residues located at the interface between these two domains. An interesting feature of λ lysozyme, when compared to the well-characterised hen egg-white lysozyme, is its lack of disulfide bridges; this makes λ lysozyme an interesting system for studies of protein folding. A comparison of the folding properties of λ lysozyme and hen lysozyme will provide important insights into the role that disulfide bonds play in the refolding pathway of the latter protein. Here we report the ¹H, ¹³C and ¹⁵N backbone resonance assignments for λ lysozyme by heteronuclear multidimensional NMR spectroscopy. These assignments provide the starting point for detailed investigation of the refolding pathway using pulse-labelling hydrogen/deuterium exchange experiments monitored by NMR.     

THE DISTINCTIVE FOOTPRINTS OF LOCAL HITCHHIKING IN A VARIED ENVIRONMENT AND GLOBAL HITCHHIKING IN A SUBDIVIDED POPULATION

Loci with higher levels of population differentiation than the neutral expectation are traditionally interpreted as evidence of ongoing selection that varies in space. This article emphasizes an alternative explanation that has been largely overlooked to date: in species subdivided into large subpopulations, enhanced differentiation can also be the signature left by the fixation of an unconditionally favorable mutation on its chromosomal neighborhood. This is because the hitchhiking effect is expected to diminish as the favorable mutation spreads from the deme in which it originated to other demes. To discriminate among the two alternative scenarios one needs to investigate how genetic structure varies along the chromosomal region of the locus. Local hitchhiking is shown to generate a single sharp peak of differentiation centered on the adaptive polymorphism and the standard signature of a selective sweep only in those subpopulations in which the allele is favored. Global hitchhiking produces two domes of differentiation on either side of the fixed advantageous mutation and signatures of a selective sweep in every subpopulation, albeit of different magnitude. Investigating population differentiation around a locus that strongly differentiates two otherwise genetically similar populations of the marine mussel Mytilus edulis, plausible evidence for the global hitchhiking hypothesis has been obtained. Global hitchhiking is a neglected phenomenon that might prove to be important in species with large population sizes such as many marine invertebrates.     

Cloning, nucleotide sequence, and mutagenesis of a gene (irpA) involved in iron-deficient growth of the cyanobacterium Synechococcus sp. strain PCC7942.

We describe the cloning and sequencing of a gene from the cyanobacterium Synechococcus sp. strain PCC7942, designated irpA (iron-regulated protein A), that encodes for a protein involved in iron acquisition or storage. Polyclonal antibodies raised against proteins which accumulate during iron-deficient growth were used as probes to isolate immunopositive clones from a lambda gt11 genomic expression library. The clone, designated lambda gtAN26, carried a 1.7-kilobase (kb) chromosomal DNA insert and was detected by cross-reactivity with antibody against a 36-kilodalton protein. It was possible to map a 20-kb portion of the chromosome with various DNA probes from lambda gt11 and lambda EMBL-3 clones, and Southern blot analysis revealed that the irpA gene was present in a single copy and localized within a 1.7-kb PstI fragment. DNA sequencing revealed an open reading frame of 1,068 nucleotides capable of encoding 356 amino acids which yields a protein with a molecular weight of 38,584. The hydropathy profile of the polypeptide indicated a putative N-terminal signal sequence of 44 amino acid residues. IrpA is a cytoplasmic membrane protein as determined by biochemistry and electron microscopy immunocytochemistry. The upstream region of the irpA gene contained a consensus sequence similar to the aerobactin operator in Escherichia coli. This fact, plus a mutant with a mutation in irpA that is unable to grow under iron-deficient conditions, led us to suggest that irpA is regulated by iron and that the gene product is involved in iron acquisition or storage.     

Collateral damage: Spread of repeat-induced point mutation from a duplicated DNA sequence into an adjoining single-copy gene inNeurospora crassa

Repeat-induced point mutation (RIP) is an unusual genome defense mechanism that was discovered inNeurospora crassa. RIP occurs during a sexual cross and induces numerous G : C to A : T mutations in duplicated DNA sequences and also methylates many of the remaining cytosine residues. We measured the susceptibility of theerg-3 gene, present in single copy, to the spread of RIP from duplications of adjoining sequences. Genomic segments of defined length (1, 1.5 or 2 kb) and located at defined distances (0, 0.5, 1 or 2 kb) upstream or downstream of theerg-3 open reading frame (ORF) were amplified by polymerase chain reaction (PCR), and the duplications were created by transformation of the amplified DNA. Crosses were made with the duplication strains and the frequency oferg-3 mutant progeny provided a measure of the spread of RIP from the duplicated segments into theerg-3 gene. Our results suggest that ordinarily RIP-spread does not occur. However, occasionally the mechanism that confines RIP to the duplicated segment seems to fail (frequency 0.1–0.8%) and then RIP can spread across as much as 1 kb of unduplicated DNA. Additionally, the bacterialhph gene appeared to be very susceptible to the spread of RIP-associated cytosine methylation.     

Interplay between Pleiotropy and Secondary Selection Determines Rise and Fall of Mutators in Stress Response

Mutators are clones whose mutation rate is about two to three orders of magnitude higher than the rate of wild-type clones and their roles in adaptive evolution of asexual populations have been controversial. Here we address this problem by using an ab initio microscopic model of living cells, which combines population genetics with a physically realistic presentation of protein stability and protein-protein interactions. The genome of model organisms encodes replication controlling genes (RCGs) and genes modeling the mismatch repair (MMR) complexes. The genotype-phenotype relationship posits that the replication rate of an organism is proportional to protein copy numbers of RCGs in their functional form and there is a production cost penalty for protein overexpression. The mutation rate depends linearly on the concentration of homodimers of MMR proteins. By simulating multiple runs of evolution of populations under various environmental stresses—stationary phase, starvation or temperature-jump—we find that adaptation most often occurs through transient fixation of a mutator phenotype, regardless of the nature of stress. By contrast, the fixation mechanism does depend on the nature of stress. In temperature jump stress, mutators take over the population due to loss of stability of MMR complexes. In contrast, in starvation and stationary phase stresses, a small number of mutators are supplied to the population via epigenetic stochastic noise in production of MMR proteins (a pleiotropic effect), and their net supply is higher due to reduced genetic drift in slowly growing populations under stressful environments. Subsequently, mutators in stationary phase or starvation hitchhike to fixation with a beneficial mutation in the RCGs, (second order selection) and finally a mutation stabilizing the MMR complex arrives, returning the population to a non-mutator phenotype. Our results provide microscopic insights into the rise and fall of mutators in adapting finite asexual populations.     

Environmental Fluctuations and Level of Density-Compensation Strongly Affects the Probability of Fixation and Fixation Times

The probability of, and time to, fixation of a mutation in a population has traditionally been studied by the classic Wright–Fisher model where population size is constant. Recent theoretical expansions have covered fluctuating populations in various ways but have not incorporated models of how the environment fluctuates in combination with different levels of density-compensation affecting fecundity. We tested the hypothesis that the probability of, and time to, fixation of neutral, advantageous and deleterious mutations is dependent on how the environment fluctuates over time, and on the level of density-compensation. We found that fixation probabilities and times were dependent on the pattern of autocorrelation of carrying capacity over time and interacted with density-compensation. The pattern found was most pronounced at small population sizes. The patterns differed greatly depending on whether the mutation was neutral, advantageous, or disadvantageous. The results indicate that the degree of mismatch between carrying capacity and population size is a key factor, rather than population size per se, and that effective population sizes can be very low also when the census population size is far above the carrying capacity. This study highlights the need for explicit population dynamic models and models for environmental fluctuations for the understanding of the dynamics of genes in populations.     

Population-genetic models of the fates of duplicate genes

The ultimate fate of a duplicated gene is that it either silenced through inactivating mutations or both copies are maintained by selection. This later fate can occur via neofunctionalization wherein one copy acquires a new function or by subfunctionalization wherein the original function of the gene is partitioned across both copies. The relative probabilities of these three different fates involve often very subtle iterations between of population size, mutation rate, and selection. All three of these fates are critical to the expansion and diversification of gene families.