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.     

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.     

Intrachromosomal Recombination in Saccharomyces cerevisiae : Reciprocal Exchange in an Inverted Repeat and Associated Gene Conversion

Intrachromosomal gene conversion has not shown a strong association with reciprocal exchanges. However, reciprocal exchanges do occur between intrachromosomal repeats. To understand the relationship between reciprocal exchange and gene conversion in repeated sequences the recombination behavior of an inverted repeat was studied. We have found that in one orientation a single copy of the kanr gene of the bacterial transposon Tn903 flanked by part of the inverted repeats IS903 does not give G418 resistance in Saccharomyces cerevisiae. A reciprocal exchange in the IS903 repeats inverts the kanr gene, which then gives G418 resistance in a single copy. Using this as a selection for intrachromosomal reciprocal exchange we have introduced multiple restriction site heterologies into the IS903 repeats and examined the crossover products for associated gene conversions. Approximately 50% of crossovers, both in mitosis and meiosis, were associated with a gene conversion. This suggests that these crossovers result from an intermediate that gives a gene conversion in 50% of the events, that is, both reciprocal exchange and gene conversion between repeated sequences have a common origin. The data are most consistent with a heteroduplex mismatch repair mechanism.     

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 Effects of Insertions on Mammalian Intrachromosomal Recombination

We examined the effects of insertion mutations on intrachromosomal recombination. A series of mouse L cell lines carrying mutant herpes simplex virus thymidine kinase (tk) heteroalleles was generated; these lines differed in the nature of their insertion mutations. In direct repeat lines with different large insertions in each gene, there was a 20-fold drop in gene conversion rate and only a five-fold drop in crossover rate relative to the analogous rates in lines with small insertions in each gene. Surprisingly, in direct repeat lines carrying the same large insertion in each gene, there was a larger drop in both types of recombination. When intrachromosomal recombination between inverted repeat tk genes with different large insertions was examined, we found that the rate of gene conversion dropped five-fold relative to small insertions, while the rate of crossing over was unaffected. The differential effects on conversion and crossing over imply that gene conversion is more sensitive to insertion mutation size. Finally, the fraction of gene conversions associated with a crossover increased from 2% for inverted repeats with small insertions to 18% for inverted repeats with large insertions. One interpretation of this finding is that during intrachromosomal recombination in mouse cells long conversion tracts are more often associated with crossing over.     

Biased intrachromosomal gene conversion in a chromosome lineage

A model for the evolution of a family of tandemly repeated genes in a single chromosome lineage under intrachromosomal gene conversion [43] is analyzed further and extended. Direct and diffusion approximations are derived for the exact fixation probabilities, mean time to fixation or loss, and mean conditional fixation time of Nagylaki and Petes [43]. The distribution of the number of variant repeats under the joint action of gene conversion and reversible mutation is investigated; exact and approximate expressions are derived for the stationary distribution. It is shown that conversional bias greatly increases the amount of sequence homogeneity at equilibrium. The diffusion processes studied here also apply to selection and mutation in a finite population, and some new results are established for that classical problem.Supported by National Science Foundation Grant DEB81-03530. This paper is dedicated to the memory of Charles C. Conley (1933–1984), who greatly influenced and generously helped and taught the author.     

Substrate length requirements for efficient mitotic recombination in Saccharomyces cerevisiae.

An ectopic recombination system using ura3 heteroalleles varying in size from 80 to 960 bp has been used to examine the effect of substrate length on spontaneous mitotic recombination. The ura3 heteroalleles were positioned either on nonhomologous chromosomes (heterochromosomal repeats) or as direct or inverted repeats on the same chromosome (intrachromosomal repeats). While the intrachromosomal events occur at rates at least 2 orders of magnitude greater than the corresponding heterochromosomal events, the recombination rate for each type of repeat considered separately exhibits a linear dependence on substrate length. The linear relationships allow estimation of the corresponding minimal efficient processing segments, which are approximately 250 bp regardless of the relative positions of the repeats in the yeast genome. An examination of the distribution of recombination events into simple gene conversion versus crossover events indicates that reciprocal exchange is more sensitive to substrate size than is gene conversion.     

Use of a Chromosomal Inverted Repeat to Demonstrate That the Rad51 and Rad52 Genes of Saccharomyces Cerevisiae Have Different Roles in Mitotic Recombination

An intrachromosomal recombination assay that monitors events between alleles of the ade2 gene oriented as inverted repeats was developed. Recombination to adenine prototrophy occurred at a rate of 9.3 X 10(-5)/cell/generation. Of the total recombinants, 50% occurred by gene conversion without crossing over, 35% by crossover and 15% by crossover associated with conversion. The rate of recombination was reduced 3,000-fold in a rad52 mutant, but the distribution of residual recombination events remained similar to that seen in the wild type strain. In rad51 mutants the rate of recombination was reduced only 4-fold. In this case, gene conversion events unassociated with a crossover were reduced 18-fold, whereas crossover events were reduced only 2.5-fold. A rad51 rad52 double mutant strain showed the same reduction in the rate of recombination as the rad52 mutant, but the distribution of events resembled that seen in rad51. From these observations it is concluded that (i) RAD52 is required for high levels of both gene conversions and reciprocal crossovers, (ii) that RAD51 is not required for intrachromosomal crossovers, and (iii) that RAD51 and RAD52 have different functions, or that RAD52 had functions in addition to those of the Rad51/Rad52 protein complex.     

Assessing the pathogenic potential of the V(D)J recombinase by interlocus immunoglobulin light-chain gene rearrangement.

Chromosomal translocations involving antigen receptor genes and oncogenes have been observed in several forms of lymphoid malignancy. Observations of their lymphocyte-restricted occurrence and a molecular analysis of some translocation breakpoints have suggested that some of these rearrangements are generated by V(D)J recombinase activity. However, a direct correlation between this activity and the generation of such rearrangements has never been established. In addition, because these aberrant rearrangements are usually detected only after a tumor has been formed, the frequency with which the recombinase machinery generates translocations has never been assessed directly. To approach these issues, immunoglobulin light-chain gene rearrangements were induced in pre-B cells transformed by temperature-sensitive mutants of Abelson murine leukemia virus and PCR was used to identify interlocus recombinants. Vlambda Jkappa and Vkappa Jlambda rearrangements as well as signal joints resulting from the recombination of Vlambda and Jkappa coding elements were recovered and were found to be similar in structure to conventional intrachromosomal joints. Because these products were detected only when the cells were undergoing active intralocus rearrangement, they provide direct evidence that translocations can be generated by the V(D)J recombinase machinery. Dilution analyses revealed that interlocus rearrangements occur about 1,000 times less frequently than conventional intralocus rearrangements. Considering the large numbers of lymphocytes generated throughout life, aberrant rearrangements generated by the V(D)J recombinase may be relatively common.     

Genetic and Molecular Analysis of Recombination Events in Saccharomyces Cerevisiae Occurring in the Presence of the Hyper-Recombination Mutation Hpr1

The hyper-recombination mutation hpr1 specifically increases mitotic intrachromatid crossovers, with no effect on other mitotic recombination events such as unequal sister chromatid exchange and plasmid-chromosome recombination, and no effect on meiotic recombination and a lesser effect on intrachromosomal gene conversion. The excision repair RAD1 gene is partially required for the expression on the hpr1 phenotype. The simplest hypothesis to account for some of the hpr1 stimulated recombination events is that a heteroduplex DNA intermediate and localized gene conversion are involved. hpr1 stimulated crossover events are independent of intrachromosomal gene conversion events stimulated by the hyper-gene conversion mutation hpr5. This result suggests that different intrachromosomal recombination processes are affected in each mutant strain. We propose that HPR1 may function to inhibit intrachromatid crossovers.     

Direct-repeat analysis of chromatid interactions during intrachromosomal recombination in mouse cells.

Homologous intrachromosomal recombination between linked genes can involve interactions that are either intramolecular (intrachromatid) or intermolecular (sister chromatid). To assess the relative proportions of chromatid interactions, we report studies of intrachromosomal recombination in mouse L cells containing herpes simplex virus thymidine kinase genes in two alternative configurations of direct repeats. By comparing products of reciprocal exchanges between these two configurations, we conclude that the majority of interactions that give rise to crossover products involve unequally paired sister chromatids after DNA replication. Analyses of an additional class of crossover products that involve discontinuous associated gene conversion suggest that these recombination events involve a heteroduplex DNA intermediate.     

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.     

Gene repeat expansion and contraction by spontaneous intrachromosomal homologous recombination in mammalian cells

Homologous recombination (HR) is important in repairing errors of replication and other forms of DNA damage. In mammalian cells, potential templates include the homologous chromosome, and after DNA replication, the sister chromatid. Previous work has shown that the mammalian recombination machinery is organized to suppress interchromosomal recombination while preserving intrachromosomal HR. In the present study, we investigated spontaneous intrachromosomal HR in mouse hybridoma cell lines in which variously numbered tandem repeats of the µ heavy chain constant (Cµ) region reside at the haploid, chromosomal immunoglobulin µ heavy chain locus. This organization provides the opportunity to investigate recombination between homologous gene repeats in a well-defined chromosomal locus under conditions in which recombinants are conveniently recovered. This system revealed several features about the mammalian intrachromosomal HR process: (i) the frequency of HR was high (recombinants represented as much as several percent of the total of recombinants and non-recombinants); (ii) the recombination process appeared to be predominantly non-reciprocal, consistent with the possibility of gene conversion; (iii) putative gene conversion tracts were long (up to 13.4 kb); (iv) the recombination process occurred with precision, initiating and terminating within regions of shared homology. The results are discussed with respect to mammalian intrachromosomal HR involving interactions both within and between sister chromatids.     

A coalescence approach to gene conversion

In this paper we develop a coalescent model with intralocus gene conversion. Such models are of increasing importance in the analysis of intralocus variability and linkage disequilibrium. We derive the distribution of the waiting time until a gene conversion event occurs in a sample in terms of the distribution of the length of the transferred segment, zeta. We do not assume any specific form of the distribution of zeta. Further, given that a gene conversion event occurs we find the distribution of (sigma, tau), the end points of the transferred segment and derive results on correlations between local trees in positions chi(1) and chi(2). Among other results we show that the correlation between the branch lengths of two local trees in the coalescent with gene conversion (and no recombination) decreases toward a nonzero constant when the distance between chi(1) and chi(2) increases. Finally, we show that a model including both recombination and gene conversion might account for the lack of intralocus associations found in, e.g., Drosophila melanogaster.     

Enhancement of somatic intrachromosomal homologous recombination in Arabidopsis by the HO endonuclease.

The HO endonuclease promotes gene conversion between mating-type alleles in yeast by a DNA double-strand break at the site of conversion (the MAT-Y/Z site). As a first step toward understanding the molecular basis of homologous recombination in higher plants, we demonstrate that expression of HO in Arabidopsis enhances intrachromosomal recombination between inverted repeats of two defective beta-glucuronidase (gus) genes (GUS- test construct). One of these genes has the Y/Z site. The two genes share 2.5 kb of DNA sequence homology around the HO cut site. Somatic recombination between the two repeats was determined by using a histochemical assay of GUS activity. The frequency of Gus+ sectors in leaves of F1 plants from a cross between parents homozygous for the GUS- test construct and HO, respectively, was 10-fold higher than in F1 plants from a cross between the same plant containing the GUS- test construct and a wild-type parent. Polymerase chain reaction analysis showed restoration of the 5' end of the GUS gene in recombinant sectors. The induction of intrachromosomal gene conversion in Arabidopsis by HO reveals the general utility of site-specific DNA endonucleases in producing targeted homologous recombination in plant genomes.     

On the Pattern of Polymorphisms at Major Histocompatibility Complex Loci

The pattern of polymorphisms at major histocompatibility complex loci was studied by computer simulations and by DNA sequence analysis. Two types of selection, overdominance plus short-term selection and maternal–fetal incompatibility, were simulated for a gene family with intra- and interlocus gene conversion. Both types of selection were found to be consistent with the observed patterns of polymorphisms. It was also found that the more interlocus conversion occurs, the higher the divergence becomes at both nonsynonymous and synonymous sites. The ratio of nonsynonymous-to-synonymous divergence among alleles decreases as the interlocus conversion rate increases. These results agree with the interpretation that the rate of interlocus conversion is lower in human genes than in genes of other nonprimate mammals. This is because, in the latter, synonymous divergence at the ARS (antigen recognition site) is often higher than that at the non-ARS, whereas in the former, this is not so. Also, the ratio of nonsynonymous to synonymous substitutions at the ARS tends to be higher in human genes than in other mammalian genes. The main difference between overdominance plus short-term selection and maternal–fetal interaction is that the number of alleles and heterozygosity per locus are higher in the latter than in the former under the presumed selection intensities. However, the average divergence among alleles tends to be lower in the latter than in the former under similar conditions. Received: 30 September 1997 / Accepted: 15 December 1997     

Conservative Intrachromosomal Recombination between Inverted Repeats in Mouse Cells: Association between Reciprocal Exchange and Gene Conversion

Recombination in mammalian cells is thought to involve both reciprocal and nonreciprocal modes of exchange, although rigorous proof is lacking due to the inability to recover all products of an exchange. To investigate further the relationship between these modes of exchange, we have analyzed intrachromosomal recombination between duplicated herpes simplex virus thymidine kinase (HSV tk) mutant alleles arranged as inverted repeats in cultured mouse L cells. In crosses between inverted repeats, a single intrachromatid reciprocal exchange leads to inversion of the sequence between the crossover sites and recovery of both genes involved in the event. The majority of recombinant products do not display such inversion and are thus consistent with a nonreciprocal mode of recombination (gene conversion). The remaining products display the sequence inversion predicted for intrachromatid reciprocal exchange. In light of the fact that intrachromatid exchanges occur, the rarity of intrachromatid double reciprocal exchanges strengthens the interpretation that the majority of events in this and previous investigations involve gene conversion. Furthermore, in accord with prediction, one-third of the reciprocal recombinants (inversions) display associated gene conversion. This association suggests that reciprocal and nonreciprocal modes of exchange are mechanistically related in mammalian cells. Finally, the occurrence of inversion recombinants suggests that intrachromosomal recombination can be a conservative (nondestructive) process.     

The evolution of MHC diversity: evidence of intralocus gene conversion and recombination in a single-locus system

Gene conversion, the unidirectional exchange of genetic material between homologous sequences, is thought to strongly influence patterns of genetic diversity. The high diversity of major histocompatibility complex (MHC) genes in many species is thought to reflect a long history of gene conversion events both within and among loci. Theoretical work suggests that intra- and interlocus gene conversion leave characteristic signatures of nucleotide diversity, but empirical studies of MHC variation have rarely been able to analyze the effects of conversion events in isolation, due to the presence of multiple gene copies in most species. The potbellied seahorse (Hippocampus abdominalis), a species with a single copy of the MH class II beta-chain gene (MHIIb), provides an ideal system in which to explore predictions on the effects of intralocus gene conversion on patterns of genetic diversity. The genetic diversity of the MHIIb peptide binding region (PBR) is high in the seahorse, similar to other vertebrate species. In contrast, the remainder of the gene shows a total absence of synonymous variation and low levels of intronic sequence diversity, concentrated in 3 short repetitive regions and 1-12 SNPs per intron. The distribution of substitutions across the gene results in a patchwork pattern of shared polymorphism between otherwise divergent sequences. The pattern of nucleotide diversity observed in the seahorse MHIIb gene is congruent with theoretical expectations for intralocus gene conversion, indicating that this evolutionary mechanism has played an important role in MHC gene evolution, contributing to both the high diversity in the PBR and the low diversity outside this region. Neutral variation at this locus may be further reduced due to biases in nucleotide composition and functional constraints.     

Association of reciprocal exchange with gene conversion between the repeated segments of 2-micron circle

The occurrence of reciprocal exchange of flanking DNA during gene conversion between the repeated segments of the yeast plasmid, 2-micron circle has been examined. The conversion event is induced by making a double-stranded gap within one of the repeats in vitro and allowing the gap to be repaired in vivo. The repair takes place with frequent recombination of flanking markers. Neither the topology of the plasmid substrates (linear or circular) nor the relative orientation of the repeats affects the association rule significantly. These events are reminiscent of meiotic gene conversion between homologous chromosomes but contrast sharply with mitotic or meiotic intrachromosomal gene conversion. It would appear that the difference between the outcomes of intramolecular gene conversion on a chromosome and on a plasmid gapped in vitro does not result from the different physical states of intracellular versus transformed DNA. A gene conversion event in a 2-micron circle : : Tn5 plasmid mediated by the 2-micron circle recombinase (FLP) in vivo, which is formally analogous to the yeast mating type interconversion, often results in recombination of flanking markers. The reaction can be mimicked, in the absence of FLP, by gapping the plasmid within one of the 2-micron circle repeats in vitro and carrying out gap repair in vivo.     

Analysis of intrachromosomal duplications in yeast Saccharomyces cerevisiae: a possible model for their origin

The complete genome of the yeast Saccharomyces cerevisiae was investigated for intrachromosomal duplications at the level of nucleotide sequences. The analysis was performed by looking for long approximate repeats (from 30 to 3,885 bp) present on each of the chromosomes. We show that direct and inverted repeats exhibit very different characteristics: the two copies of direct repeats are more similar and longer than those of inverted repeats. Furthermore, contrary to the inverted repeats, a large majority of direct repeats appear to be closely spaced. The distance (delta) between the two copies is generally smaller than 1 kb. Further analysis of these "close direct repeats" shows a negative correlation between delta and the percentage of identity between the two copies, and a positive correlation between delta and repeat length. Moreover, contrary to the other categories of repeats, close direct repeats are mostly located within coding sequences (CDSs). We propose two hypotheses in order to interpret these observations: first, the deletion/conversion rate is negatively correlated with delta; second, there exists an active duplication mechanism which continuously creates close direct repeats, the other intrachromosomal repeats being the result, by chromosomal rearrangements of these "primary repeats."