Mutation and recombination with tight linkage

An exact solution of the mutation-recombination equation in continuous time is presented, with linear ordering of the sites and at most one mutation or crossover event taking place at every instant of time. The differential equation may be obtained from a mutation-recombination model with discrete generations, in the limit of short generations, or weak mutation and recombination. The solution relies on the multilinear structure of the dynamical system, and on the commuting properties of the mutation and recombination operators. It is obtained through diagonalization of the mutation term, followed by a transformation to certain measures of linkage disequilibrium that simultaneously linearize and diagonalize the recombination dynamics. The collection of linkage disequilibria, as well as their decay rates, are given in closed form. Received: 26 January 1999 / Revised version: 20 October 2000 / Published online: 10 April 2001     

Quasispecies and recombination

Recombination is introduced into Eigen's theory of quasispecies evolution. Comparing numerical simulations of the rate equations in the non-recombining and recombining cases show that recombination has a strong effect on the error threshold and, for a wide range of mutation rates, gives rise to two stable fixed points in the dynamics. This bi-stability results in the existence of two error thresholds. However, we prove that, for low mutation rates the bi-stability breaks down and the unique equilibrium distribution is concentrated around the sequence with highest fitness.     

In vivo recombination and the production of hybrid genes

In vivo recombination between homologous genes is increasingly being favoured as a means of generating proteins with altered and novel specificities. The typical procedure requires the cloning of two related genes on a single replicative plasmid of Escherichia coli and the selection or screening of recombinants. Up to now the recombination process between the cloned genes was generally thought to involve the recA function and the availability of free ends in the DNA molecule to be recombined. Our results show that neither is necessary. Recombinants are obtained by simply growing the bacteria that host the plasmid carrying the two cloned genes.     

Time to fixation in the presence of recombination

We study the evolutionary dynamics of a haploid population of infinite size recombining with a probability r in a two locus model. Starting from a low fitness locus, the population is evolved under mutation, selection and recombination until a finite fraction of the population reaches the fittest locus. An analytical method is developed to calculate the fixation time T to the fittest locus for various choices of epistasis. We find that: (1) for negative epistasis, T decreases slowly for small r but decays fast at larger r; (2) for positive epistasis, T increases linearly for small r and mildly for large r; (3) for compensatory mutation, T diverges as a power law with logarithmic corrections as the recombination fraction approaches a critical value. Our calculations are seen to be in good agreement with the exact numerical results.     

On the minimum number of recombination events in the evolutionary history of DNA sequences

In representing the evolutionary history of a set of binary DNA sequences by a connected graph, a set theoretical approach is introduced for studying recombination events. We show that set theoretical constraints have direct implications on the number of recombination events. We define a new lower bound on the number of recombination events and demonstrate the usefulness of our new approach through several explicit examples.     

RadB acts in homologous recombination in the archaeon Haloferax volcanii,consistent with a role as recombination mediator

Homologous recombination plays a central role in the repair of double-strand DNA breaks, the restart of stalled replication forks and the generation of genetic diversity. Regulation of recombination is essential since defects can lead to genome instability and chromosomal rearrangements. Strand exchange is a key step of recombination – it is catalysed by RecA in bacteria, Rad51/Dmc1 in eukaryotes and RadA in archaea. RadB, a paralogue of RadA, is present in many archaeal species. RadB has previously been proposed to function as a recombination mediator, assisting in RadA-mediated strand exchange. In this study, we use the archaeon Haloferax volcanii to provide evidence to support this hypothesis. We show that RadB is required for efficient recombination and survival following treatment with DNA-damaging agents, and we identify two point mutations in radA that suppress the ΔradB phenotype. Analysis of these point mutations leads us to propose that the role of RadB is to act as a recombination mediator, which it does by inducing a conformational change in RadA and thereby promoting its polymerisation on DNA.     

Mathematical properties of the r2 measure of linkage disequilibrium

Statistics for linkage disequilibrium (LD), the non-random association of alleles at two loci, depend on the frequencies of the alleles at the loci under consideration. Here, we examine the r(2) measure of LD and its mathematical relationship to allele frequencies, quantifying the constraints on its maximum value. Assuming independent uniform distributions for the allele frequencies of two biallelic loci, we find that the mean maximum value of r(2) is approximately 0.43051, and that r(2) can exceed a threshold of 4/5 in only approximately 14.232% of the allele frequency space. If one locus is assumed to have known allele frequencies--the situation in an association study in which LD between a known marker locus and an unknown trait locus is of interest--we find that the mean maximum value of r(2) is greatest when the known locus has a minor allele frequency of approximately 0.30131. We find that in 1/4 of the space of allowed values of minor allele frequencies and haplotype frequencies at a pair of loci, the unconstrained maximum r(2) allowing for the possibility of recombination between the loci exceeds the constrained maximum assuming that no recombination has occurred. Finally, we use r(max)(2) to examine the connection between r(2) and the D(') measure of linkage disequilibrium, finding that r(2)/r(max)(2)=D('2) for approximately 72.683% of the space of allowed values of (p(a),p(b),p(ab)). Our results concerning the properties of r(2) have the potential to inform the interpretation of unusual LD behavior and to assist in the design of LD-based association-mapping studies.     

Multi-site adaptation in the presence of infrequent recombination

The adverse effect of co-inheritance linkage of a large number of sites on adaptation has been studied extensively for asexual populations. However, it is insufficiently understood for multi-site populations in the presence of recombination. In the present work, motivated by our studies of HIV evolution in infected patients, we consider a model of haploid populations with infrequent recombination. We assume that small quantities of beneficial alleles preexist at a large number of sites and neglect new mutation. Using a generalized form of the traveling wave method, we show that the effectiveness of recombination is impeded and the adaptation rate is decreased by inter-sequence correlations, arising due to the fact that some pairs of homologous sites have common ancestors existing after the onset of adaptation. As the recombination rate per individual becomes smaller, site pairs with common ancestors become more frequent, making recombination even less effective. In addition, an increasing number of sites become identical by descent across large samples of sequences, causing reversion of the direction of evolution and the loss of beneficial alleles at these sites. As a result, within a 10-fold range of the recombination rate, the average adaptation rate falls from 90% of the infinite-recombination value down to 10%. The entire transition from almost maximum to almost zero may occur at very small recombination rates. Interestingly, the strong effect of linkage on the adaptation rate is predicted in the absence of average linkage disequilibrium (Lewontin’s measure).     

Perturbation analysis of a two-locus model with directional selection and recombination

A population genetic two-locus model with additive, directional selection and recombination is considered. It is assumed that recombination is weaker than selection; i.e., the recombination parameter r is smaller than the selection coefficients. This assumption is appropriate for describing the effects of two-locus selection at the molecular level. The model is formulated in terms of ordinary differential equations (ODES) for the gamete frequencies x = (x ₁, x ₂, x ₃, x ₄), defined on the simplex S ₄. The ODEs are analyzed using first a regular pertubation technique. However, this approach yields satisfactory results only if r is very small relative to the selection coefficients and if the initial values x(0) are in the interior part of S ₄. To cope with this problem, a novel two-scale perturbation method is proposed which rests on the theory of averaging of vectorfields. It is demonstrated that the zeroth-order solution of this two-scale approach approximates the numerical solution of the model well, even if recombination rate is on the order of the selection coefficients.     

细菌重组系统及其应用研究进展

利用重组酶和辅助蛋白共同作用于DNA片段上,使不同基因重新组合以完成基因重组的现象在细菌中广泛存在,基因重组对于细菌的遗传多样性、进化等具有重要意义。目前,细菌基因重组主要分为同源重组、位点特异性重组和转座重组3种类型。本文主要对细菌重组系统重组酶的种类、作用机制及其在细菌遗传操作中的应用策略进行阐述。     

Interplay between modifications of chromatin and meiotic recombination hotspots

Meiotic recombination lies at the heart of sexual reproduction. It is essential for producing viable gametes with a normal haploid genomic content and its dysfunctions can be at the source of aneuploidies, such as the Down syndrome, or many genetic disorders. Meiotic recombination also generates genetic diversity that is transmitted to progeny by shuffling maternal and paternal alleles along chromosomes. Recombination takes place at non-random chromosomal sites called 'hotspots'. Recent evidence has shown that their location is influenced by properties of chromatin. In addition, many studies in somatic cells have highlighted the need for changes in chromatin dynamics to allow the process of recombination. In this review, we discuss how changes in the chromatin landscape may influence the recombination map, and reciprocally, how recombination events may lead to epigenetic modifications at sites of recombination, which could be transmitted to progeny.     

Variation in recombination rate across the genome: evidence and implications

Recent data from humans and other species provide convincing evidence of variation in recombination rate in different genomic regions. Comparison of physical and genetic maps reveals variation on a scale of megabases, with substantial differences between sexes. Recombination is often suppressed near centromeres and elevated near telomeres, but neither of these observations is true for all chromosomes. In humans, patterns of linkage disequilibrium and experimental measures of recombination from sperm-typing reveal dramatic hotspots of recombination on a scale of kilobases. Genome-wide variation in the amount of crossing-over may be due to variation in the density of hotspots, the intensity of hotspots, or both. Theoretical models of selection and linkage predict that genetic variation will be reduced in regions of low recombination, and this prediction is supported by data from several species. Heterogeneity in rates of crossing-over provides both an opportunity and a challenge for identifying disease genes: as associations occur in blocks, genomic regions containing disease loci may be identified with relatively few markers, yet identifying the causal mutations is unlikely to be achieved through associations alone.     

Frequency and character of alternative somatic recombination fates of paralogous genes during T-DNA integration

A synthetic RBCSB gene cluster was transformed into Arabidopsis in order to simultaneously evaluate the frequency and character of somatic illegitimate recombination, homologous recombination, and targeted gene replacement events associated with T-DNA-mediated transformation. The most frequent type of recombination event observed was illegitimate integration of the T-DNA without activation of the silent ΔRBCS1B: LUC transgene. Sixteen luc⁺ (firefly luciferase positive) T1 plants were isolated. Six of these were due to illegitimate recombination events resulting in a gene trapping effect. Nine resulted from homologous recombination between paralogous RBCSB sequences associated with T-DNA integration. The frequency of somatic homologous recombination associated with T-DNA integration was almost 200 times higher than previously reported rates of meiotic homologous recombination with the same genes. The distribution of (somatic homologous) recombination resolution sites generally fits a fractional interval length model. However, a small region adjacent to an indel showed a significant over-representation of resolution sites, suggesting that DNA mismatch recognition may also play an important role in the positioning of somatic resolution sites. The frequency of somatic resolution within exon-2 was significantly different from that previously observed during meiotic recombination. Electronic Supplementary Material Supplementary material is available for this article at     

Function of cloned T4 recombination genes, uvsX and uvsY, in cells of Escherichia coli

Summary Genes uvsX and uvsY of bacteriophage T4 both control genetic recombination and repair of damaged DNA, and their mutant phenotypes bear a striking resemblance to each other. It has been shown recently that the uvsX gene product is analogous to the recA gene product of Escherichia coli (Yonesaki et al. 1985; Yonesaki and Minagawa 1985; Formosa and Alberts 1986), but the function of the uvsY gene is unknown. To obtain further insight into the function of these genes we introduced plasmid-borne copies of the two genes separately or together into E. coli. The uvsX gene rendered recA ^- cells more resistant to UV and raised the recombination frequency of phage and E. coli, but hampered induction of the prophage and the SOS function of E. coli. The uvsY gene had no detectable function when introduced alone into E. coli but significantly enhanced the function of the uvsX gene when the two plasmid-borne genes were introduced together.     

The effect of recombination on the neutral evolution of genetic robustness

Conventional population genetics considers the evolution of a limited number of genotypes corresponding to phenotypes with different fitness. As model phenotypes, in particular RNA secondary structure, have become computationally tractable, however, it has become apparent that the context dependent effect of mutations and the many-to-one nature inherent in these genotype-phenotype maps can have fundamental evolutionary consequences. It has previously been demonstrated that populations of genotypes evolving on the neutral networks corresponding to all genotypes with the same secondary structure only through neutral mutations can evolve mutational robustness [E. van Nimwegen, J.P. Crutchfield, M. Huynen, Neutral evolution of mutational robustness, Proc. Natl. Acad. Sci. USA 96(17), 9716-9720 (1999)], by concentrating the population on regions of high neutrality. Introducing recombination we demonstrate, through numerically calculating the stationary distribution of an infinite population on ensembles of random neutral networks that mutational robustness is significantly enhanced and further that the magnitude of this enhancement is sensitive to details of the neutral network topology. Through the simulation of finite populations of genotypes evolving on random neutral networks and a scaled down microRNA neutral network, we show that even in finite populations recombination will still act to focus the population on regions of locally high neutrality.     

Mutations at the human minisatellite MS32 integrated in yeast occur with high frequency in meiosis and involve complex recombination events

Minisatellites are composed of tandem repetitive DNA sequences and are present at many positions in the human genome. They frequently mutate to new length alleles in the germline, by complex and incompletely understood recombination mechanisms which may operate during meiosis. In several minisatellites the mutation events are restricted to one end of the repeat array, indicating a possible association with elements that act in cis. Mutant alleles do not show exchange of flanking regions. To construct a model system suitable for further investigations of the mutation process, we have integrated the human minisatellite MS32, flanked by synthetic markers, in the vicinity of a meiotic recombination hot spot upstream of the LEU2 locus in the yeast Saccharomyces cerevisiae. Here we provide direct evidence for a meiotic origin of MS32 mutations. Mutation events were polarised towards both ends of the minisatellite and varied from simple duplications and deletions to complex intra- and interallelic events. Interallelic events were frequently accompanied by exchange of regions flanking the minisatellite. The results also support the notion that cis-acting elements are involved in the mutational process. The fact that MS32 mutant structures are similar in yeast and human shows that meiotic recombination plays a crucial role in both organisms and emphasises the usefulness of yeast strains harbouring minisatellites as a model system for the study of minisatellite mutation. Received: 1 March 1997 / Accepted: 16 May 1997     

Consistency of estimators of the population-scaled recombination rate

We consider (approximate) likelihood methods for estimating the population-scaled recombination rate from population genetic data. We show that the dependence between the data from two regions of a chromosome decays inversely with the amount of recombination between the two regions. We use this result to show that the maximum likelihood estimator (mle) for the recombination rate, based on the composite likelihood of Fearnhead and Donnelly, is consistent. We also consider inference based on the pairwise likelihood of Hudson. We consider two approximations to this likelihood, and prove that the mle based on one of these approximations is consistent, while the mle based on the other approximation (which is used by McVean, Awadalla and Fearnhead) is not.     

A heuristic method to reconstruct the history of sequences subject to recombination

Summary Sequences subject to recombination and gene conversion defy phylogenetic analysis by traditional methods since their evolutionary history cannot be adequately summarized by a tree. This study investigates ways to describe their evolutionary history and proposes a method giving a partial reconstruction of this history. Multigene families, viruses, and alleles from within populations experience recombinations/gene conversions, so the questions studied here are relevant for a large body of data and the suggested solutions should be very practical. The method employed was implemented in a program, RecPars, written in C and was used to analyze nine retroviruses.     

Genetic control of sex-dependent meiotic recombination in the major histocompatibility complex of the mouse.

Meiotic recombination within the proximal region of the major histocompatibility complex (MHC) of the mouse is not random but occurs in clusters at certain restricted sites, so-called recombinational hotspots. The wm7 haplotype of the MHC, derived from the wild mouse, enhances recombination specifically during female meiosis within a fragment of 1.3 kb of DNA located between the A beta 3 and A beta 2 genes in genetic crosses with laboratory haplotypes. Previous studies revealed no significant strain differences in nucleotide sequences around the hotspot, irrespective of the ability of the strain to enhance the recombination. It appeared that a distant genetic element might, therefore, control the rate of recombination. In the present study, original recombinants whose breakpoints were defined by direct sequencing of PCR-amplified DNAs were tested for the rate of secondary recombination in the crosses with laboratory strains in order to determine the location of such a genetic element. The results clearly demonstrated that the chromosomal segment proximal to the hotspot is essential for enhancement of recombination. Moreover, the male recombination is suppressed by a segment distal to the hotspot.