Renewal process approach to the theory of genetic linkage: case of no chromatid interference

Models are presented in which the distribution of crossovers at a four-four-strand stage of meiosis results from a renewal process. Probability distributions are obtained for the number of crossover events on a meiotic bivalent and for the number of exchange points in random meiotic products. These distributions are found to fit the observed distribution of these variables reasonably well. Using these distributions and assuming no chromatid interference, relations between map distance and the recombination fraction are obtained. These relations give either better or equivalent fit to data when compared to relations that are designed to account for both chromatid and chiasma interference.     

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.     

Recombination and chiasmata: few but intriguing discrepancies.

The paradigm that meiotic recombination and chiasmata have the same basis has been challenged, primarily for plants. High resolution genetic mapping frequently results in maps with lengths far exceeding those based on chiasma counts. In addition, recombination between specific homoeologous chromosomes derived from interspecific hybrids is sometimes much higher than can be explained by meiotic chiasma frequencies. However, almost the entire discrepancy disappears when proper care is taken of map inflation resulting from the shortcomings of the mapping algorithm and classification errors, the use of dissimilar material, and the difficulty of accurately counting chiasmata. Still, some exchanges, especially of short interstitial segments, cannot readily be explained by normal meiotic behaviour. Aberrant meiotic processes involving segment replacement or insertion can probably be excluded. Some cases of unusual recombination are somatic, possibly premeiotic exchange. For other cases, local relaxation of chiasma interference caused by small interruptions of homology disturbing synaptonemal complex formation is proposed as the cause. It would be accompanied by a preference for compensating exchanges (negative chromatid interference) resulting from asymmetry of the pairing chromatid pairs, so that one side of each pair preferentially participates in pairing. Over longer distances, the pairing face may switch, causing the normal random chromatid participation in double exchanges and the relatively low frequency of short interstitial exchanges. Key words : recombination frequency, map length, chiasmata, discrepancy, chromatid interference.     

Genetics and biology of human ovarian teratomas. II. Molecular analysis of origin of nondisjunction and gene-centromere mapping of chromosome I markers.

Chromosomal heteromorphisms and DNA polymorphisms have been utilized to identify the mechanisms that lead to formation of human ovarian teratomas and to construct a gene-centromere map of chromosome 1 by using those teratomas that arise by meiotic nondisjunction. Of 61 genetically informative ovarian teratomas, 21.3% arose by nondisjunction at meiosis I, and 39.3% arose by meiosis II nondisjunction. Eight polymorphic marker loci on chromosome 1p and one marker on 1q were used to estimate a gene-centromere map. The results show clear linkage of the most proximal 1p marker (NRAS) and the most proximal 1q marker (D1S61) to the centromere at a distance of 14 cM and 20 cM, respectively. Estimated gene-centromere distances suggest that, while recombination occurs normally in ovarian teratomas arising by meiosis II errors, ovarian teratomas arising by meiosis I nondisjunction have altered patterns of recombination. Furthermore, the estimated map demonstrates clear evidence of chiasma interference. Our results suggest that ovarian teratomas can provide a rapid method for mapping genes relative to the centromere.     

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.     

Meiotic parthenogenesis in a root-knot nematode results in rapid genomic homozygosity

Many isolates of the plant-parasitic nematode Meloidogyne hapla reproduce by facultative meiotic parthenogenesis. Sexual crosses can occur, but, in the absence of males, the diploid state appears to be restored by reuniting sister chromosomes of a single meiosis. We have crossed inbred strains of M. hapla that differ in DNA markers and produced hybrids and F(2) lines. Here we show that heterozygous M. hapla females, upon parthenogenetic reproduction, produce progeny that segregate 1:1 for the presence or absence of dominant DNA markers, as would be expected if sister chromosomes are rejoined, rather than the 3:1 ratio typical of a Mendelian cross. Codominant markers also segregate 1:1 and heterozygotes are present at low frequency (<3%). Segregation patterns and recombinant analysis indicate that a homozygous condition is prevalent for markers flanking recombination events, suggesting that recombination occurs preferentially as four-strand exchanges at similar locations between both pairs of non-sister chromatids. With this mechanism, meiotic parthenogenesis would be expected to result in rapid genomic homozygosity. This type of high negative crossover interference coupled with positive chromatid interference has not been observed in fungal or other animal systems in which it is possible to examine the sister products of a single meiosis and may indicate that meiotic recombination in this nematode has novel features.     

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     

Casares’ map function: no need for a ‘corrected’ Haldane’s map function

A genetic map function M(d) = RF provides a mapping from the additive genetic distance d to the non-additive recombination fraction RF between a given pair of loci, where the recombination fraction is the proportion of gametes that are recombinant between the two loci. Genetic map functions are needed because in most experiments all we can directly observe are the recombination events. However, since a recombination event is only observed if there are an odd number of crossovers between the two loci, recombination fractions are not additive. One of the most widely used map functions is Haldane’s map function, which is derived under the assumptions of no chiasma and no chromatid interference, and has been in widespread use since 1919. However, Casares recently proposed a ‘corrected’ Haldane’s map function – we show here that this ‘corrected’ map function is not correct due to faulty assumptions and mistakes in its derivation.     

Molecular studies of linkage group XIX of Chlamydomonas reinhardtii: evidence against a basal body location

Linkage group XIX (also known as the UNI linkage group) in the green alga, Chlamydomonas reinhardtii, exhibits a number of unusual properties that have lead to the suggestion that it represents a basal body-associated chromosome. To begin a molecular analysis of this linkage group, we have identified DNA sequences from it and used them to determine the copy number of linkage group XIX within the cell. We find that linkage group XIX is present in the same copy number per cell as nuclear linkage groups in both haploid and diploid strains. We also find that the copy number of linkage group XIX is unchanged in mutants lacking basal bodies. We conclude that there is no convincing evidence that linkage group XIX localizes to the basal bodies of Chlamydomonas reinhardtii cells.     

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.     

Methods for studying recombination on chromosomes that undergo nondisjunction

A lod score method is provided for mapping genes relative to the centromere using family data from autosomal trisomies. Such gene-centromere mapping can be performed whenever two or more members of a meiotic tetrad can be recovered. The critical mapping parameter is not the recombination value theta or the map distance omega, but the probability of nonreduction in a heterozygous host, the probability of heterozygosity (nonreduction) is 1-gamma/2 for a meiosis I error and gamma for a meiosis II error. Under various assumptions regarding chiasma interference, gamma can be related to theta and omega. We provide specific methods for estimating gamma and theta from trisomy data using maximum likelihood, so that recombination may be studied on chromosomes that underwent nondisjunction.     

Construction of a 10,000-marker ultradense genetic recombination map of potato: providing a framework for accelerated gene isolation and a genomewide physical map

An ultradense genetic linkage map with >10,000 AFLP loci was constructed from a heterozygous diploid potato population. To our knowledge, this is the densest meiotic recombination map ever constructed. A fast marker-ordering algorithm was used, based on the minimization of the total number of recombination events within a given marker order in combination with genotyping error-detection software. This resulted in "skeleton bin maps," which can be viewed as the most parsimonious marker order. The unit of distance is not expressed in centimorgans but in "bins." A bin is a position on the genetic map with a unique segregation pattern that is separated from adjacent bins by a single recombination event. Putative centromeres were identified by a strong clustering of markers, probably due to cold spots for recombination. Conversely, recombination hot spots resulted in large intervals of up to 15 cM without markers. The current level of marker saturation suggests that marker density is proportional to physical distance and independent of recombination frequency. Most chromatids (92%) recombined once or never, suggesting strong chiasma interference. Absolute chiasma interference within a chromosome arm could not be demonstrated. Two examples of contig construction and map-based cloning have demonstrated that the marker spacing was in accordance with the expected physical distance: approximately one marker per BAC length. Currently, the markers are used for genetic anchoring of a physical map of potato to deliver a sequence-ready minimal tiling path of BAC contigs of specific chromosomal regions for the potato genome sequencing consortium (http://www.potatogenome.net).     

Sex-specific recombination rates in zebrafish (Danio rerio)

In many organisms, the rate of genetic recombination is not uniform along the length of chromosomes or between sexes. To compare the relative recombination rates during meiosis in male and female zebrafish, we constructed a genetic map based on male meiosis. We developed a meiotic mapping panel of 94 androgenetic haploid embryos that were scored for genetic polymorphisms. The resulting male map was compared to female and sex-average maps. We found that the recombination rate in male meiosis is dramatically suppressed relative to that of female meiosis, especially near the centromere. These findings have practical applications for experimental design. The use of exclusively female meiosis in a positional cloning project maximizes the ratio of genetic map distance to physical distance. Alternatively, the use of exclusively male meiosis to localize a mutation initially to a linkage group or to maintain relationships of linked alleles minimizes recombination, thereby facilitating some types of analysis.     

Basal body/centriolar DNA: molecular genetic studies in Chlamydomonas

In Chlamydomonas reinhardtii, mutations on an unusual linkage group, the uni linkage group (ULG), affect structure and function of basal bodies. The ULG shows Mendelian segregation, but its genetic map is circular. Molecular cloning of fragments of the ULG was accomplished by taking advantage of restriction fragment length polymorphisms generated by crosses to Chlamydomonas smithii. These clones were used as probes to determine the size and form of the ULG chromosome; it is a 6-9 megabase linear molecule. Use of the probes for in situ DNA hybridization in cells localized the ULG chromosome to basal bodies.     

Genetic and physical analyses of sister chromatid exchange in yeast meiosis.

We have used nonessential circular minichromosomes to monitor sister chromatid exchange during yeast meiosis. Genetic analysis shows that a 64-kb circular minichromosome undergoes sister chromatid exchange during 40% of meioses. This frequency is not reduced by the presence of a homologous linear minichromosome. Furthermore, sister chromatid exchange can be stimulated by the presence of a 12-kb ARG4 DNA fragment, which contains initiation sites for meiotic gene conversion. Using physical analysis, we have directly identified a product of sister chromatid exchange: a head-to-tail dimer form of a circular minichromosome. This dimer form is absent in a rad50S mutant strain, which is deficient in processing of the ends of meiosis-specific double-stranded breaks into single-stranded DNA tails. Our studies suggest that meiotic sister chromatid exchange is stimulated by the same mechanism as meiotic homolog exchange.     

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.     

Genetic circularity of the Proteus mirabilis linkage map.

The T incompatibility group plasmid R394 can mobilize the chromosome of Proteus mirabilis strain PM5006. It transferred relatively large segments, corresponding to at least 20 min on the D plasmid chromosomal map of the organism. The frequency of recombination for a large number of selected markers was nearly constant at 5 X 10(-6) per donor cell and it is concluded that mobilization takes place from a number of chromosomal sites. All recombinants were R+ and displayed all properties of the plasmid. By analysing crosses for co-inheritance frequencies of unselected markers, a number of chromosomal loci were assembled in linear array. Linkage between markers at the ends of this linkage group was established to markers at the respective termini of the existing D plasmid linkage group. This established a composite circular linkage map of genes of the P. mirabilis strain PM5006 chromosome.     

Cohesin SMC1 beta is required for meiotic chromosome dynamics, sister chromatid cohesion and DNA recombination

Sister chromatid cohesion ensures the faithful segregation of chromosomes in mitosis and in both meiotic divisions. Meiosis-specific components of the cohesin complex, including the recently described SMC1 isoform SMC1 beta, were suggested to be required for meiotic sister chromatid cohesion and DNA recombination. Here we show that SMC1 beta-deficient mice of both sexes are sterile. Male meiosis is blocked in pachytene; female meiosis is highly error-prone but continues until metaphase II. Prophase axial elements (AEs) are markedly shortened, chromatin extends further from the AEs, chromosome synapsis is incomplete, and sister chromatid cohesion in chromosome arms and at centromeres is lost prematurely. In addition, crossover-associated recombination foci are absent or reduced, and meiosis-specific perinuclear telomere arrangements are impaired. Thus, SMC1 beta has a key role in meiotic cohesion, the assembly of AEs, synapsis, recombination, and chromosome movements.     

Comments on lack of interference in the four strand model of crossing over

Summary Assuming a four strand model and no chromatid interference, lack of chiasma interference is known to be equivalent to the assumption that the formation of chiasmata follows a Poisson process. We prove that lack of chiasma interference is also equivalent to the assumption that a random gamete shows recombination on any given interval of a chromosome independently of recombination on all disjoint intervals. Both assumptions are sufficient, but not necessary, for Haldane's formula relating recombination to map distance to be true, as we demonstrate by specific counterexamples. These issues are discussed in the context of the theory of stochastic point processes.Research supported by: University of California at Los Angeles, NIH Special Resources Grant RR-3, and USPHS Predoctoral Traineeship GM 7104.     

Recombination patterns reveal information about centromere location on linkage maps

Linkage mapping is often used to identify genes associated with phenotypic traits and for aiding genome assemblies. Still, many emerging maps do not locate centromeres – an essential component of the genomic landscape. Here, we demonstrate that for genomes with strong chiasma interference, approximate centromere placement is possible by phasing the same data used to generate linkage maps. Assuming one obligate crossover per chromosome arm, information about centromere location can be revealed by tracking the accumulated recombination frequency along linkage groups, similar to half‐tetrad analyses. We validate the method on a linkage map for sockeye salmon (Oncorhynchus nerka) with known centromeric regions. Further tests suggest that the method will work well in other salmonids and other eukaryotes. However, the method performed weakly when applied to a male linkage map (rainbow trout; O. mykiss) characterized by low and unevenly distributed recombination – a general feature of male meiosis in many species. Further, a high frequency of double crossovers along chromosome arms in barley reduced resolution for locating centromeric regions on most linkage groups. Despite these limitations, our method should work well for high‐density maps in species with strong recombination interference and will enrich many existing and future mapping resources.