Gene Conversion, Linkage, and the Evolution of Multigene Families

The evolution of the probabilities of genetic identity within and between the loci of a multigene family is investigated. Unbiased gene conversion, equal crossing over, random genetic drift, and mutation to new alleles are incorporated. Generations are discrete and nonoverlapping; the diploid, monoecious population mates at random. The linkage map is arbitrary, and the location dependence of the probabilities of identity is formulated exactly. The greatest of the rates of gene conversion, random drift, and mutation is epsilon much less than 1. For interchromosomal conversion, the equilibrium probabilities of identity are within order epsilon [i.e., O(epsilon)] of those in a simple model that has no location dependence and, at equilibrium, no linkage disequilibrium. At equilibrium, the linkage disequilibria are of O(epsilon); they are evaluated explicitly with an error of O(epsilon 2); they may be negative if symmetric heteroduplexes occur. The ultimate rate and pattern of convergence to equilibrium are within O(epsilon 2) and O(epsilon), respectively, of that of the same simple model. If linkage is loose (i.e., all the crossover rates greatly exceed epsilon, though they may still be much less than 1/2), the linkage disequilibria are reduced to O(epsilon) in a time of O(-ln epsilon). If intrachromosomal conversion is incorporated, the same results hold for loose linkage, except that, if the crossover rates are much less than 1/2, then the linkage disequilibria generally exceed those for pure interchromosomal conversion.     

On the divergence of genes in multigene families

Statistical properties of the amount of divergence of genes in multigene families are studied. The model considered is an infinite-site neutral model with unbiased intrachromosomal conversion, unbiased interchromosomal conversion, and recombination. By considering the time back to the most recent common ancestor of two genes, both the probability of identity and the moments of S, the number of sites that differ between two sampled genes, are obtained. We find that if recombination rates are large or conversion is always interchromosomal, then the expectation of S is 4N mu n where N is the population size, mu is the rate of mutation per generation per gene and n is the number of genes in the gene family, as the conversion rates approach zero, the moments of divergence do not approach the moments of divergence with conversion rates equal to zero, and it is possible for a decrease in the rate of intrachromosomal conversion to result in a higher probability of identity, but a greater mean divergence of the two genes.     

A method for estimating the mutation,gene conversion and recombination parameters in small multigene families

A simple two-locus gene conversion model is considered to investigate the amounts of DNA variation and linkage disequilibrium in small multigene families. The exact solutions for the expectations and variances of the amounts of variation within and between two loci are obtained. It is shown that gene conversion increases the amount of variation within each locus and decreases the amount of variation between two loci. The expectation and variance of the amount of linkage disequilibrium are also obtained. Gene conversion generates positive linkage disequilibrium and the degree of linkage disequilibrium decreases as the recombination rate is increased. Using the theoretical results, a method for estimating the mutation, gene conversion, and recombination parameters is developed and applied to the data of the Amy multigene family in Drosophila melanogaster. The gene conversion rate is estimated to be approximately 60-165 times higher than the mutation rate for synonymous sites.     

DIFFERENTIATION OF A MULTIGENE FAMILY BETWEEN POPULATIONS

Differentiation of a multigene family between populations is investigated under the forces of intrachromosomal unbiased gene conversion, neutral mutation, recombination, and random drift. The infinite-site model without recombination within the gene is employed, and the average numbers of the different sites between pairs of genes at the same locus and at different loci from two populations that divided some time ago are calculated as functions of time. Since differentiation is a relative concept in which differences between populations are expressed in comparison with those within a population and since there is most likely a reduction in population size after the division of populations, the time-dependent behavior of the corresponding quantities within a population is also investigated using approximate and numerical methods. It is found that intrachromosomal unbiased gene conversion promotes differentiation at the same locus but promotes or retards that between different loci, depending on the parameters in a recently divided population.     

Gene Conversion, Linkage, and the Evolution of Repeated Genes Dispersed among Multiple Chromosomes

The evolution of the probabilities of genetic identity within and between the loci of a multigene family dispersed among multiple chromosomes is investigated. Unbiased gene conversion, equal crossing over, random genetic drift, and mutation to new alleles are incorporated. Generations are discrete and nonoverlapping; the diploid, monoecious population mates at random. The linkage map is arbitrary, but the same for every chromosome; the dependence of the probabilities of identity on the location on each chromosome is formulated exactly. The greatest of the rates of gene conversion, random drift, and mutation is epsilon much less than 1. Under the assumption of loose linkage (i.e., all the crossover rates greatly exceed epsilon, though they may still be much less than 1/2), explicit approximations are obtained for the equilibrium values of the probabilities of identity and of the linkage of disequilibria. The probabilities of identity are of order one [i.e., O(1)] and do not depend on location; the linkage disequilibria are of O(epsilon) and, within each chromosome, depend on location through the crossover rates. It is demonstrated also that the ultimate rate and pattern of convergence to equilibrium are close to that of a much simpler, location-independent model. If intrachromosomal conversion is absent, the above results hold even without the assumption of loose linkage. In all cases, the relative errors are of O(epsilon). Even if the conversion rate between genes on nonhomologous chromosomes is considerably less than between genes on the same chromosome or homologous chromosomes, the probabilities of identity between the former genes are still almost as high as those between the latter, and the rate of convergence is still not much less than with equal conversion rates. If the crossover rates are much less than 1/2, then most of the linkage disequilibrium is due to intrachromosomal conversion. If linkage is loose, the reduction of the linkage disequilibria to O(epsilon) requires only O(-ln epsilon) generations.     

The Evolution of Multigene Families under Intrachromosomal Gene Conversion

A model for the evolution of the probabilities of genetic identity within and between loci of a multigene family in a finite population is formulated and investigated. Unbiased intrachromosomal gene conversion, equal crossing over between tandemly repeated genes, random genetic drift and mutation to new alleles are incorporated. Generations are discrete and nonoverlapping; the diploid, monoecious population mates at random. Formulas for the equilibrium values of the probabilities of identity and a cubic equation for the rate of convergence are deduced. Numerical examples indicate the following. The amount of homology at equilibrium generally decreases as the mutation rate, the population size and the number of repeats increase; it may increase or decrease with increasing crossover rate. The intralocus homology has an intermediate minimum, whereas the interlocus homology increases, as the rate of gene conversion increases. The intralocus homology decreases, whereas the interlocus homology increases, as the proportion of symmetric heteroduplexes increases. The characteristic convergence time can be sufficiently short to imply that intrachromosomal gene conversion may be an important mechanism for maintaining sequence homogeneity among repeated genes. The convergence time decreases as the conversion rate and the proportion of symmetric heteroduplexes increase; although exceptions occur, it generally increases as the population size and the number of repeats increase; it may increase or decrease with increasing crossover rate.     

The evolutionary rate of duplicated genes under concerted evolution

The effect of directional selection on the fixation process of a single mutation that spreads in a multigene family by gene conversion is investigated. A simple two-locus model with two alleles, A and a, is first considered in a random-mating diploid population with size N. There are four haplotypes, AA, Aa, aA, and aa, and selection works on the number of alleles A in a diplod (i = 0, 1, 2, 3, 4). Because gene conversion is allowed between the two loci, when the mutation rate is very low, either AA or aa will fix in the population eventually. We consider a situation where a single mutant, A, arises in one locus when a is fixed in both loci. Then, we derive the fixation probability analytically, and the fixation time is investigated by simulations. It is found that gene conversion has an effect to increase the "effective" population size, so that weak selection works more efficiently in a multigene family. With these results, we discuss the effect of gene conversion on the rate of molecular evolution in a multigene family undergoing concerted evolution. We also argue about the applicability of the theoretical results to models of multigene families with more than two loci.     

Theoretical population genetics of repeated genes forming a multigene family

The evolution of repeated genes forming a multigene family in a finite population is studied with special reference to the probability of gene identity, i.e., the identity probability of two gene units chosen from the gene family. This quantity is called clonality and is defined as the sum of squares of the frequencies of gene lineages in the family. The multigene family is undergoing continuous unequal somatic crossing over, ordinary interchromosomal crossing over, mutation and random frequency drift. Two measures of clonality are used: clonality within one chromosome and that between two different chromosomes. The equilibrium properties of the means, the variances and the covariance of the two measures of clonality are investigated by using the diffusion equation method under the assumption of constant number of gene units in the multigene family. Some models of natural selection based on clonality are considered. The possible significance of the variance and covariance of clonality among the chromosomes on the adaptive differentiation of gene families such as those producing antibodies is discussed.     

An Extension of a Model for the Evolution of Multigene Families by Unequal Crossing over

Evolution of a multigene family is studied from the standpoint of population genetics. It is assumed that the multigene family is undergoing continuous interchromosomal unequal crossing over, mutation and random frequency drift. The equilibrium properties of the probability of gene identity (clonality) are investigated, using two measures: identity probability within and between chromosomes. The measures represent homogeneity of genes within a family in one chromosome and similarity of gene families between two homologous chromosomes. The means, the variances and the covariance of these two measures of identity probability are obtained by using the diffusion equation method. It is shown that the means and the variances are generally smaller than those predicted in the previous model assuming intrachromosomal (sister chromatid) unequal crossing over (Ohta 1978a,b).     

Inferring outcrossing in the homothallic fungus Sclerotinia sclerotiorum using linkage disequilibrium decay

The occurrence and frequency of outcrossing in homothallic fungal species in nature is an unresolved question. Here we report detection of frequent outcrossing in the homothallic fungus Sclerotinia sclerotiorum. In using multilocus linkage disequilibrium (LD) to infer recombination among microsatellite alleles, high mutation rates confound the estimates of recombination. To distinguish high mutation rates from recombination to infer outcrossing, 8 population samples comprising 268 S. sclerotiorum isolates from widely distributed agricultural fields were genotyped for 12 microsatellite markers, resulting in multiple polymorphic markers on three chromosomes. Each isolate was homokaryotic for the 12 loci. Pairwise LD was estimated using three methods: Fisher''s exact test, index of association (I_A) and Hedrick''s D′. For most of the populations, pairwise LD decayed with increasing physical distance between loci in two of the three chromosomes. Therefore, the observed recombination of alleles cannot be simply attributed to mutation alone. Different recombination rates in various DNA regions (recombination hot/cold spots) and different evolutionary histories of the populations could explain the observed differences in rates of LD decay among the chromosomes and among populations. The majority of the isolates exhibited mycelial incompatibility, minimizing the possibility of heterokaryon formation and mitotic recombination. Thus, the observed high intrachromosomal recombination is due to meiotic recombination, suggesting frequent outcrossing in these populations, supporting the view that homothallism favors universal compatibility of gametes instead of traditionally believed haploid selfing in S. sclerotiorum. Frequent outcrossing facilitates emergence and spread of new traits such as fungicide resistance, increasing difficulties in managing Sclerotinia diseases.     

Genetic Control of Intrachromosomal Recombination in Saccharomyces Cerevisiae. I. Isolation and Genetic Characterization of Hyper-Recombination Mutations

Eight complementation groups have been defined for recessive mutations conferring an increased mitotic intrachromosomal recombination phenotype (hpr genes) in Saccharomyces cerevisiae. Some of the mutations preferentially increase intrachromosomal gene conversion (hpr4, hpr5 and hpr8) between repeated sequences, some increase loss of a marker between duplicated genes (hpr1 and hpr6), and some increase both types of events (hpr2, hpr3 and hpr7). New alleles of the CDC2 and CDC17 genes were recovered among these mutants. The mutants were also characterized for sensitivity to DNA damaging agents and for mutator activity. Among the more interesting mutants are hpr5, which shows a biased gene conversion in a leu2-112::URA3::leu2-k duplication; and hpr1, which has a much weaker effect on interchromosomal mitotic recombination than on intrachromosomal mitotic recombination. These analyses suggest that gene conversion and reciprocal exchange can be separated mutationally. Further studies are required to show whether different recombination pathways or different outcomes of the same recombination pathway are controlled by the genes identified in this study.     

Intrachromosomal gene conversion, linkage, and the evolution of multigene families

The evolution of the probabilities of genetic identity within and between tandemly repeated loci of a multigene family is investigated analytically and numerically. Unbiased intrachromosomal gene conversion, equal crossing over, random genetic drift, and mutation to new alleles are incorporated. Generations are discrete and nonoverlapping; the diploid, monoecious population mates at random. Under the restriction that there is at most one crossover in the multigene family per individual per generation, the dependence on location of the probabilities of identity is treated exactly. In the "homogeneous" approximation to this "exact" model, end effects are disregarded; in the "exchangeable" approximation, to which all previous work was confined, all position dependence is neglected. Numerical results indicate that the exchangeable and homogeneous models are both qualitatively correct, the exchangeable model is sometimes too inaccurate for quantitative conclusions, and the homogeneous model is always more accurate than the exchangeable one and is always sufficiently accurate for quantitative conclusions.     

The Saccharomyces cerevisiae recombination enhancer biases recombination during interchromosomal mating-type switching but not in interchromosomal homologous recombination

Haploid Saccharomyces can change mating type through HO-endonuclease cleavage of an expressor locus, MAT, followed by gene conversion using one of two repository loci, HML or HMR, as donor. The mating type of a cell dictates which repository locus is used as donor, with a cells using HML and alpha cells using HMR. This preference is established in part by RE, a locus on the left arm of chromosome III that activates the surrounding region, including HML, for recombination in a cells, an activity suppressed by alpha 2 protein in alpha cells. We have examined the ability of RE to stimulate different forms of interchromosomal recombination. We found that RE exerted an effect on interchromosomal mating-type switching and on intrachromosomal homologous recombination but not on interchromosomal homologous recombination. Also, even in the absence of RE, MAT alpha still influenced donor preference in interchromosomal mating-type switching, supporting a role of alpha 2 in donor preference independent of RE. These results suggest a model in which RE affects competition between productive and nonproductive recombination outcomes. In interchromosome gene conversion, RE enhances both productive and nonproductive pathways, whereas in intrachromosomal gene conversion and mating-type switching, RE enhances only the productive pathway.     

The mutational load of a multigene family with uniform members

The mutational load of a multigene family with uniform members was studied by computer simulations. Two models of selection, truncation and exponential fitness, were examined, by using a simple model of gene conversion. It was found that the load is much smaller than the Haldane-Muller prediction under the truncation selection, and that it becomes approximately equal to the value calculated by the formula, nv(1-q)/(m-nq), where n is the copy number, v is the rate of detrimental mutation per gene copy, m is the truncation point in terms of the number of detrimental genes eliminated, and q is the equilibrium frequency of detrimental mutation. However the equilibrium frequency cannot be analytically obtained. For the exponential fitness model, the load is close to the Haldane-Muller value. When there is no gene conversion, the load becomes larger than the cases with conversion both for the truncation and the exponential fitness models. Thus, gene conversion or other mechanisms that are responsible for contraction-expansion of mutants on chromosomes helps eliminating deleterious mutations occurring in multigene families.     

De novo rearrangements found in 2% of index patients with spinal muscular atrophy: mutational mechanisms, parental origin, mutation rate, and implications for genetic counseling.

Spinal muscular atrophy (SMA) is a relatively common autosomal recessive neuromuscular disorder. We have identified de novo rearrangements in 7 (approximately 2%) index patients from 340 informative SMA families. In each, the rearrangements resulted in the absence of the telomeric copy of the survival motor neuron (SMN) gene (telSMN), in two cases accompanied by the loss of the neuronal apoptosis-inhibitory protein gene . Haplotype analysis revealed unequal recombination in four cases, with loss of markers Ag1-CA and C212, which are near the 5' ends of the SMN genes. In one case, an interchromosomal rearrangement involving both the SMN genes and a regrouping of Ag1-CA and C212 alleles must have occurred, suggesting either interchromosomal gene conversion or double recombination. In two cases, no such rearrangement was observed, but loss of telSMN plus Ag1-CA and C212 alleles in one case suggested intrachromosomal deletion or gene conversion. In six of the seven cases, the de novo rearrangement had occurred during paternal meiosis. Direct detection of de novo SMA mutations by molecular genetic means has allowed us to estimate for the first time the mutation rate for a recessive disorder in humans. The sex-averaged rate of 1.1 x 10(-4), arrived at in a proband-based approach, compares well with the rate of 0.9 x 10(-4) expected under a mutation-selection equilibrium for SMA. These findings have important implications for genetic counseling and prenatal diagnosis in that they emphasize the relevance of indirect genotype analysis in combination with direct SMN-gene deletion testing in SMA families.     

Simulation Study of a Multigene Family, with Special Reference to the Evolution of Compensatory Advantageous Mutations

We investigate the evolution of a multigene family incorporating the forces of drift, mutation, gene conversion, unequal crossing over and selection. The use of simulation studies is required due to the complexity of the model. Selection is modeled in two modes: positive selection as a function of the number of different beneficial alleles and negative selection against deleterious alleles. We assume that gene conversion is unbiased, and that all mutations are initially deleterious. Compensation between mutants creates beneficial and neutral alleles, and allowances are made for compensatory mutations either within or between the members of a multigene family. We find that gene conversion can enhance the rate of acquisition of compensatory advantageous mutations when genes are redundant.     

Recombination disequilibrium in ideal and natural populations

Following Hardy-Weinberg disequilibrium (HWD) occurring at a single locus and linkage disequilibrium (LD) between two loci in generations, we here proposed the third genetic disequilibrium in a population: recombination disequilibrium (RD). RD is a measurement of crossover interference among multiple loci in a random mating population. In natural populations besides recombination interference, RD may also be due to selection, mutation, gene conversion, drift and/or migration. Therefore, similarly to LD, RD will also reflect the history of natural selection and mutation. In breeding populations, RD purely results from recombination interference and hence can be used to build or evaluate and correct a linkage map. Practical examples from F₂, testcross and human populations indeed demonstrate that RD is useful for measuring recombination interference between two short intervals and evaluating linkage maps. As with LD, RD will be important for studying genetic mapping, association of haplotypes with disease, plant breading and population history.     

Recombination,selection, and the evolution of tandem gene arrays

Multigene families—immunity genes or sensory receptors, for instance—are often subject to diversifying selection. Allelic diversity may be favored not only through balancing or frequency-dependent selection at individual loci but also by associating different alleles in multicopy gene families. Using a combination of analytical calculations and simulations, we explored a population genetic model of epistatic selection and unequal recombination, where a trade-off exists between the benefit of allelic diversity and the cost of copy abundance. Starting from the neutral case, where we showed that gene copy number is Gamma distributed at equilibrium, we derived also the mean and shape of the limiting distribution under selection. Considering a more general model, which includes variable population size and population substructure, we explored by simulations mean fitness and some summary statistics of the copy number distribution. We determined the relative effects of selection, recombination, and demographic parameters in maintaining allelic diversity and shaping the mean fitness of a population. One way to control the variance of copy number is by lowering the rate of unequal recombination. Indeed, when encoding recombination by a rate modifier locus, we observe exactly this prediction. Finally, we analyzed the empirical copy number distribution of 3 genes in human and estimated recombination and selection parameters of our model.     

Saccharomyces Cerevisiae Rad52 Alleles Temperature-Sensitive for the Repair of DNA Double-Strand Breaks

We have screened for mutations of the Saccharomyces cerevisiae RAD52 gene which confer a temperature-sensitive (ts) phenotype with respect to either the repair of DNA lesions caused by methyl methanesulfonate (MMS) or the recombination of an intrachromosomal recombination reporter. We were readily able to isolate alleles ts for the repair of lesions caused by MMS but were unable to find alleles with a severe ts deficiency in intrachromosomal recombination. We extensively characterized four strains conferring ts growth on MMS agar. These strains also exhibit ts survival when exposed to γ-radiation or when the HO endonuclease is constitutively expressed. Although none of the four alleles confers a severe ts defect in intrachromosomal recombination, two confer significant defects in tests of mitotic, interchromosomal recombination carried out in diploid strains. The mutant diploids sporulate, but the two strains with defects in interchromosomal recombination have reduced spore viability. Meiotic recombination is not depressed in the two diploids with reduced spore viability. Thus, in the two strains with reduced spore viability, defects in mitotic and meiotic recombination do not correlate. Sequence analysis revealed that in three of the four ts alleles the causative mutations are in the first one-third of the open reading frame while the fourth is in the C-terminal third.