C-L processes involving higher order positive (negative) interference for any two collections of disjoint chromosomal regions

Interference is said to take place whenever crossover events fail to occur at random along the chromosome. The nature of higher order interference (positive or negative) is introduced. It is shown how interference is determined by the chiasma formation process operating along the chromosome and especially by the count-location (C-L) chiasma formation process. We discuss a simple mechanism among C-L processes that can generate prescribed higher order positive interference or prescribed higher order negative interference between any two collections of disjoint genomic regions.Supported in part by NIH grant GM 28016     

Pch2 Links Chromosome Axis Remodeling at Future Crossover Sites and Crossover Distribution during Yeast Meiosis

Segregation of homologous chromosomes during meiosis I depends on appropriately positioned crossovers/chiasmata. Crossover assurance ensures at least one crossover per homolog pair, while interference reduces double crossovers. Here, we have investigated the interplay between chromosome axis morphogenesis and non-random crossover placement. We demonstrate that chromosome axes are structurally modified at future crossover sites as indicated by correspondence between crossover designation marker Zip3 and domains enriched for axis ensemble Hop1/Red1. This association is first detected at the zygotene stage, persists until double Holliday junction resolution, and is controlled by the conserved AAA+ ATPase Pch2. Pch2 further mediates crossover interference, although it is dispensable for crossover formation at normal levels. Thus, interference appears to be superimposed on underlying mechanisms of crossover formation. When recombination-initiating DSBs are reduced, Pch2 is also required for viable spore formation, consistent with further functions in chiasma formation. pch2Δ mutant defects in crossover interference and spore viability at reduced DSB levels are oppositely modulated by temperature, suggesting contributions of two separable pathways to crossover control. Roles of Pch2 in controlling both chromosome axis morphogenesis and crossover placement suggest linkage between these processes. Pch2 is proposed to reorganize chromosome axes into a tiling array of long-range crossover control modules, resulting in chiasma formation at minimum levels and with maximum spacing.     

Multipoint Genetic Mapping with Trisomy Data

Trisomy is the most common genetic abnormality in humans and is the leading cause of mental retardation. Although molecular studies that use a large number of highly polymorphic markers have been undertaken to understand the recombination patterns for chromosome abnormalities, there is a lack of multilocus approaches to incorporating crossover interference in the analysis of human trisomy data. In the present article, we develop two statistical methods that simultaneously use all genetic information in trisomy data. The first approach relies on a general relationship between multilocus trisomy probabilities and multilocus ordered-tetrad probabilities. Under the assumption that no more than one chiasma exists in each marker interval, we describe how to use the expectation-maximization algorithm to examine the probability distribution of the recombination events underlying meioses that lead to trisomy. One limitation of the first approach is that the amount of computation increases exponentially with the number of markers. The second approach models the crossover process as a chi(2) model. We describe how to use hidden Markov models to evaluate multilocus trisomy probabilities. Our methods are applicable when both parents are available or when only the nondisjoining parent is available. For both methods, genetic distances among a set of markers can be estimated and the pattern of overall chiasma distribution can be inspected for differences in recombination between meioses exhibiting trisomy and normal meioses. We illustrate the proposed approaches through their application to a set of trisomy 21 data.     

Crossover interference in the mouse

We present an analysis of crossover interference in the mouse genome, on the basis of high-density genotype data from two reciprocal interspecific backcrosses, comprising 188 meioses. Overwhelming evidence was found for strong positive crossover interference with average strength greater than that implied by the Carter-Falconer map function. There was some evidence for interchromosomal variation in the level of interference, with smaller chromosomes exhibiting stronger interference. We further compared the observed numbers of crossovers to previous cytological observations on the numbers of chiasmata and evaluated evidence for the obligate chiasma hypothesis.     

Broad-Scale Recombination Patterns Underlying Proper Disjunction in Humans

Although recombination is essential to the successful completion of human meiosis, it remains unclear how tightly the process is regulated and over what scale. To assess the nature and stringency of constraints on human recombination, we examined crossover patterns in transmissions to viable, non-trisomic offspring, using dense genotyping data collected in a large set of pedigrees. Our analysis supports a requirement for one chiasma per chromosome rather than per arm to ensure proper disjunction, with additional chiasmata occurring in proportion to physical length. The requirement is not absolute, however, as chromosome 21 seems to be frequently transmitted properly in the absence of a chiasma in females, a finding that raises the possibility of a back-up mechanism aiding in its correct segregation. We also found a set of double crossovers in surprisingly close proximity, as expected from a second pathway that is not subject to crossover interference. These findings point to multiple mechanisms that shape the distribution of crossovers, influencing proper disjunction in humans.     

Amplified fragment length polymorphism analysis to assess crossover interference and homozygosity in gynogenetic diploid Pacific abalone (Haliotis discus hannai)

Recombination analysis in gynogenetic diploids is a powerful tool for assessing the degree of inbreeding, investigating crossover events and understanding chiasma interference during meiosis. To estimate the marker–centromere recombination rate, the inheritance pattern of 654 amplified fragment length polymorphism (AFLP) markers was examined in the 72‐h veliger larvae of two meiogynogenetic diploid families in the Pacific abalone (Haliotis discus hannai). The second‐division segregation frequency (y) of the AFLP loci ranged from 0.00 to 0.96, with 23.9% of loci showing y‐values higher than 0.67, evidencing the existence of interference. The average recombination frequency across the 654 AFLP loci was 0.45, allowing estimation of the fixation index of 0.55, indicating that meiotic gynogenesis could provide an effective means of rapid inbreeding in the Pacific abalone. The AFLP loci have a small proportion (4.4%) of y‐values greater than 0.90, suggesting that a relatively low or intermediate degree of chiasma interference occurred in the abalone chromosomes. The information obtained in this study will enhance our understanding of the abalone genome and will be useful for genetic studies in the species.     

Cost-benefit analysis of recombination and its application for understanding of chiasma interference.

A cost-benefit analysis of recombination was undertaken. The beneficial effects of crossing-over are proportional to the frequency of recombinant offspring, while its harmful effects (errors of crossing-over leading to mutations) are proportional to the number of crossover exchanges. An equilibrium point should exist where the beneficial effects of crossing-over are balanced by its harmful effects. It is suggested that natural selection sustains a number of crossover exchanges per meiosis at the level that provides highest benefit-cost difference. Chiasma interference prevents the arising of closely located exchanges which are less effective in the production of recombinants than exchanges separated by some "interference distance". Computer simulation shows that chiasma interference increases the recombination effectiveness of the multiple crossover exchanges as compared to the case without interference.     

On chiasma formation point processes having the count location property

The count-location (C-L) chiasma formation schemes introduced by Karlin and Liberman (1979b) encompass a broad class of map functions involving positive, negative or no chiasma interference. The C-L schemes do not explictly assume a specific mechanism of crossover formation, but rather a statistical property of the process. If viewed as a stochastic point process along the chromosome, it is shown that a crossing over mechanism having the C-L property is actually a rescaled mixture of Poisson processes. Surprisingly it turns out that these C-L point processes involve negative interference throughout the entire genome.Research supported in part by NIH grants GM 28016 and GM 10452     

Discrete chiasma formation models and their associated high order interference

. We introduce some special chiasma formation processes. First a family of discrete chiasma formation processes is introduced and we determine the nature of higher order interference associated with those processes. Secondly we consider a two-stage chiasma formation process, where the associated recombination frequency between two markers depends not only on their map distance but also on their location along the chromosomes. We characterise under this process, in some cases, the nature of interference between two segments. Received: 22 January 1996 / Revised version: 17 September 1997     

Proposed genetic nomenclature rules for Tetrahymena thermophila,Paramecium primaurelia and Paramecium tetraurelia. The Seventh International Meeting on Ciliate Molecular Biology Genetics Nomenclature.

Ordered tetrad data yield information on chromatid interference, chiasma interference, and centromere locations. In this article, we show that the assumption of no chromatid interference imposes certain constraints on multilocus ordered tetrad probabilities. Assuming no chromatid interference, these constraints can be used to order markers under general chiasma processes. We also derive multilocus tetrad probabilities under a class of chiasma interference models, the chi-square models. Finally, we compare centromere map functions under the chi-square models with map functions proposed in the literature. Results in this article can be applied to order genetic markers and map centromeres using multilocus ordered tetrad data.     

Genetic Positioning of Centromeres through Half-Tetrad Analysis in Gynogenetic Diploid Families of the Zhikong Scallop (Chlamys farreri)

Centromere mapping is a powerful tool for improving linkage maps, investigating crossover events, and understanding chiasma interference during meiosis. Ninety microsatellite markers selected across all linkage groups (LGs) from a previous Chlamys farreri genetic map were studied in three artificially induced meiogynogenetic families for centromere mapping by half-tetrad analysis. Inheritance analyses showed that all 90 microsatellite loci conformed to Mendelian inheritance in the control crosses, while 4.4 % of the microsatellite loci showed segregation departures from an expected 1:1 ratio of two homozygote classes in meiogynogenetic progeny. The second division segregation frequency (y) of the microsatellites ranged from 0.033 to 0.778 with a mean of 0.332, confirming the occurrence of partial chiasma interference in this species. Heterogeneity of y is observed in one of 42 cases in which markers were typed in more than one family, suggesting variation in gene–centromere recombination among families. Centromere location was mostly in accordance with the C. farreri karyotype, but differences in marker order between linkage and centromere maps occurred. Overall, this study makes the genetic linkage map a more complete and informative tool for genomic studies and it will also facilitate future research of the structure and function of the scallop centromeres.     

Maximal power tests for detecting defects in meiotic recombination

We have determined the marker separations (genetic distances) that maximize the probability, or power, of detecting meiotic recombination deficiency when only a limited number of meiotic progeny can be assayed. We find that the optimal marker separation is as large as 30-100 cM in many cases. Provided the appropriate marker separation is used, small reductions in recombination potential (as little as 50%) can be detected by assaying a single interval in as few as 100 progeny. If recombination is uniformly altered across the genomic region of interest, the same sensitivity can be obtained by assaying multiple independent intervals in correspondingly fewer progeny. A reduction or abolition of crossover interference, with or without a reduction of recombination proficiency, can be detected with similar sensitivity. We present a set of graphs that display the optimal marker separation and the number of meiotic progeny that must be assayed to detect a given recombination deficiency in the presence of various levels of crossover interference. These results will aid the optimal design of experiments to detect meiotic recombination deficiency in any organism.     

Statistical Analysis of Chromatid Interference

The nonrandom occurrence of crossovers along a single strand during meiosis can be caused by either chromatid interference, crossover interference or both. Although crossover interference has been consistently observed in almost all organisms since the time of the first linkage studies, chromatid interference has not been as thoroughly discussed in the literature, and the evidence provided for it is inconsistent. In this paper with virtually no restrictions on the nature of crossover interference, we describe the constraints that follow from the assumption of no chromatid interference for single spore data. These constraints are necessary consequences of the assumption of no chromatid interference, but their satisfaction is not sufficient to guarantee no chromatid interference. Models can be constructed in which chromatid interference clearly exists but is not detectable with single spore data. We then extend our analysis to cover tetrad data, which permits more powerful tests of no chromatid interference. We note that the traditional test of no chromatid interference based on tetrad data does not make full use of the information provided by the data, and we offer a statistical procedure for testing the no chromatid interference constraints that does make full use of the data. The procedure is then applied to data from several organisms. Although no strong evidence of chromatid interference is found, we do observe an excess of two-strand double recombinations, i.e., negative chromatid interference.     

Chiasma-based genetic map of the mouse X chromosome

The X chromosome pair was identified in diakinesis/metaphase I stage mouse oocytes using a repeat sequence DNA probe and fluorescence in situ hybridisation. Chiasma positions along the X bivalent were measured in 57 oocytes from 4 females. Overall, our observations showed that while there were no obvious hotspots for chiasma formation along the X chromosome, there was a tendency to favour the distal end. Minimum inter-chiasma distances were substantial indicating the occurrence of strong genetic interference. Estimates of both genetic distances and recombination fractions for any interval along the chromosome can be calculated from the chiasma data. The average chiasma frequency for the X bivalent was 1.37 giving an estimated total genetic map length of 68.5 cM. In general, the pattern of chiasma distribution along the X chromosome resembled that anticipated from recombination distances in published consensus linkage maps. There were, however, some intriguing differences between the two approaches. The reason for these discrepancies are unknown but may be related to lack of precision in cytogenetic mapping of loci, inter-strain and/or interspecies differences in the genetic controls over the distribution of crossover events. One advantage of the chiasma analysis approach is its suitability for investigating these problems.     

Characterization of human crossover interference

We present an analysis of crossover interference over the entire human genome, on the basis of genotype data from more than 8,000 polymorphisms in eight CEPH families. Overwhelming evidence was found for strong positive crossover interference, with average strength lying between the levels of interference implied by the Kosambi and Carter-Falconer map functions. Five mathematical models of interference were evaluated: the gamma model and four versions of the count-location model. The gamma model fit the data far better than did any of the other four models. Analysis of intercrossover distances was greatly superior to the analysis of crossover counts, in both demonstrating interference and distinguishing between the five models. In contrast to earlier suggestions, interference was found to continue uninterrupted across the centromeres. No convincing differences in the levels of interference were found between the sexes or among chromosomes; however, we did detect possible individual variation in interference among the eight mothers. Finally, we present an equation that provides the probability of the occurrence of a double crossover between two nonrecombinant, informative polymorphisms.     

Absence of interference in association with gene conversion in Sordaria fimicola, and presence of interference in association with ordinary recombination

From the analysis of large samples of gene conversion asci in the g locus of Sordaria fimicola, it was found that neither the conversion event itself nor conversion-associated recombination of flanking markers cause either chiasma or chromatid interference with crossing over in a neighboring interval. The presence of more than one kind of crossover event, one causing interference the other not, is considered. The existence of two kinds of gene loci, one of single-cistron composition and the other of multiple-cistron composition, is discussed in relation to reciprocal recombination within a locus.     

Dominant enhancer effect of the meiotic mei4 mutant on recombination frequencies restricted to linkage group VI in Podospora anserina.

Summary A mutant which increases second division segregation (SDS) frequency of locus 110 (linkage group VI) was isolated. It was called mei4 because of its meiotic deficiency. The present paper deals with its effect on meiotic recombination when heterozygous. mei4 then only acts on linkage group VI. The SDS frequencies were increased for all markers used, except locus 5 located very close to the centromere. This quasi general enhancement results exclusively in an enlargement of map distance on linkage group VI's proximal part. Crosses involving three mutant genes allowed to check that the distances on the distal part were constant. This is due to a real lack of crossover frequency modification in this region and not to a change of chiasma interference. Among the seven linkage groups of Podospora anserina, group VI exhibits several other particularities concerning meiotic recombination, especially a lower positive chiasma interference and a more regular crossover distribution, suggesting a particular recombination regulation.Laboratoire associé n⁰ 86 du Centre National de la Recherche Scientifique     

Statistical analysis of half-tetrads.

Half-tetrads, where two meiotic products from a single meiosis are recovered together, arise in different forms in a variety of organisms. Closely related to ordered tetrads, half-tetrads yield information on chromatid interference, chiasma interference, and centromere positions. In this article, for different half-tetrad types and different marker configurations, we derive the relations between multilocus half-tetrad probabilities and multilocus ordered tetrad probabilities. These relations are used to obtain equality and inequality constraints among multilocus half-tetrad probabilities that are imposed by the assumption of no chromatid interference. We illustrate how to apply these results to study chiasma interference and to map centromeres using multilocus half-tetrad data.     

The effect of a deficiency and a deletion on recombination in chromosome 1BL in wheat

To test two models of chiasma allocation and the distribution of crossing-over in chromosomes, genetic mapping was performed in normal, deletion and deficiency chromosome arms 1BL of wheat, Triticum aestivum L. Shortening of the chromosome arm, either by a deletion of the proximal half of the arm or by a deficiency of the terminal quarter of the arm's length, significantly reduced the frequency of multiple crossovers but did not affect the distribution of the distal, presumably the first, crossover in the arm. In the deficiency chromosome, the recombination rate in the terminal segment was much higher than that in the same segment of the complete arm. This suggests that recombination frequency is not an inherent characteristic of a segment but depends on the segment's position on the centromere-telomere axis. These observations support the classical model of chiasma distribution along the chromosome based on the point of pairing initiation, chromosome length and the positive chiasma interference. The study also demonstrates that the distribution and frequency of recombination in a chromosome segment can be manipulated. Therefore, even the segments with very low recombination frequencies could be saturated with large numbers of crossover events to produce high-density genetic maps.     

Evidence for non-random spatial distribution of meiotic exchanges in Podospora anserina: comparison between linkage groups 1 and 6.

Summary In Podospora anserina, positive and very efficient chiasma interference is observed. However, its modalities are different for the two linkage groups 1 (LG1) and 6 (LG6) studied here.In the right arm of LG1, two zones exist in which always occurs only one crossing-over. They are formed independently each other. Moreover, the genetic map consists of clusters of genes located near the centromere and at the limit between the two interference zones. It is postulated that this structure of the map results from the localization of crossing-over in the middle of each zone. We suppose that the type of chiasma interference, in Podospora, is a typical one as it is in Drosophila. It seems that both these phenomena are under common genetical control.In the LG6, we observe a weaker positive chiasma interference without crossing-over localization.Laboratoire associé au C.N.R.S.n^o 086