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.     

A demonstration of a 1:1 correspondence between chiasma frequency and recombination using a Lolium perenne/Festuca pratensis substitution

A single chromosome of the grass species Festuca pratensis has been introgressed into Lolium perenne to produce a diploid monosomic substitution line 2n = 2x = 14. The chromatin of F. pratensis and L. perenne can be distinguished by genomic in situ hybridization (GISH), and it is therefore possible to visualize the substituted F. pratensis chromosome in the L. perenne background and to study chiasma formation in a single marked bivalent. Recombination occurs freely in the F. pratensis/L. perenne bivalent, and chiasma frequency counts give a predicted map length for this bivalent of 76 cM. The substituted F. pratensis chromosome was also mapped with 104 EcoRI/Tru91 and HindIII/Tru91 amplified fragment length polymorphisms (AFLPs), generating a marker map of 81 cM. This map length is almost identical to the map length of 76 cM predicted from the chiasma frequency data. The work demonstrates a 1:1 correspondence between chiasma frequency and recombination and, in addition, the absence of chromatid interference across the Festuca and Lolium centromeres.     

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.     

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).     

The relationship between genetic and cytogenetic maps of pea. I. Standard and translocation karyotypes.

A detailed cytogenetical study of inbred lines of pea and their F1 hybrids has been undertaken to study the relationship between the cytogenetic map and the molecular linkage map. The mitotic karyotypes of a standard pea line, JI15, a translocation line, JI61, and line JI281, a line used in the production of a mapping population, are given. A chromosome rearrangement detected by cytogenetic analysis of mitotic chromosomes has been further defined by synaptonemal complex (SC) analysis and the study of metaphase I chromosome behaviour. This meiotic analysis has allowed a comparison of SC physical lengths, observed chiasma frequencies, and recombination frequencies, as estimated from the genetic map, as a means of comparing physical and genetic distances.     

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.     

Investigation of Homologous Crossing over and Sister Chromatid Exchange in the Wheat Nor-B2 Locus Coding for Rrna and Gli-B2 Locus Coding for Gliadins

Recombination was investigated within the Nor-B2 locus of wheat chromosome 6B that contains several thousand of the 18S-5.8S-26S rRNA (rDNA) repeated units. Additionally, recombination was assessed for several chromosome regions, in arm 6Bq between the centromere and the B2 locus (awn suppressor) and in arm 6Bp between the centromere and Nor-B2, between Nor-B2 and a distal C-band and between Nor-B2 and Gli-B2 coding for gliadins. The experimental design permitted the distinction between crossing over between homologous chromosomes and exchange between sister chromatids. No homologous crossing over within the Nor-B2 locus was found in a sample of 446 chromosomes, but one exchange with the attributes of unequal sister chromatid exchange was identified. The molecular characteristics of this presumed sister chromatid exchange indicate that the spacer variants present in the Nor-B2 locus are clustered. No homologous recombination was detected within the distal Gli-B2 locus containing repeated genes coding for gliadin seed-storage proteins. Both arms of chromosome 6B showed low crossing-over frequency in the proximal regions. The distance from the centromere to Nor-B2 was only from 0.3 to 2.2 cM although it accounts for about two-thirds of the metaphase chromosome arm, which shows a great distortion of the metaphase map of the arm. The level of homologous recombination within the Nor-B2 locus is lower than in the chromosome region immediately distal to it. Whether it is comparable to that in the chromosome region proximal to it could not be determined. Recombination frequencies of different pairs of chromosome 6B in all but one interval paralleled the frequencies of their metaphase I pairing: Lower pairing at metaphase I was paralleled by lower crossing-over frequency. This relationship indicated that reduced metaphase I pairing between 6B chromosomes from different populations is due to impaired crossing-over and not due to precocious chiasma terminalization.     

Genetic mapping: X chromosome

Starting with the male chiasma distribution for chromosome 2, a significantly better fit is obtained to lod scores for the X chromosome if terminalization of distal chiasmata is assumed. The linkage data are not consistent with a uniform distribution of chiasmata, absence of terminalization, or restriction of terminalization to the distal band. As information about the genetic map of the X chromosome increases, the map will be freed from assumptions about chiasma distribution. At present, however, even fragmentary data on the male are useful to construct a genetic map that, by converting physical assignments to equivalent genetic recombinations, has no inconsistencies between genetic and physical map orders.     

A Polymerization Model of Chiasma Interference and Corresponding Computer Simulation

A model of chiasma interference is proposed and simulated on a computer. The model uses random events and a polymerization reaction to regulate meiotic recombination between and along chromosomes. A computer simulation of the model generates distributions of crossovers per chromosome arm, position of events along the chromosome arm, distance between crossovers in two-event tetrads, and coincidence as a function of distance. Outputs from the simulation are compared to data from Saccharomyces cerevisiae and the X chromosome of Drosophila melanogaster. The simulation demonstrates that the proposed model can produce the regulation of recombination observed in both genetic and cytological experiments. While the model was quantitatively compared to data from only Drosophila and Saccharomyces, the regulation observed in these species is qualitatively similar to the regulation of recombination observed in other organisms.     

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.     

RFLP maps of potato and their alignment with the homoeologous tomato genome

Summary An RFLP linkage map of the potato is presented which comprises 304 loci derived from 230 DNA probes and one morphological marker (tuber skin color). The self-incompatibility locus of potato was mapped to chromosome I, which is homoeologous to tomato chromosome I. By mapping chromosome-specific tomato RFLP markers in potato and, vice versa, potato markers in tomato, the different potato and tomato RFLP maps were aligned to each other and the similarity of the potato and tomato genome was confirmed. The numbers given to the 12 potato chromosomes are now in accordance with the established tomato nomenclature. Comparisons between potato RFLP maps derived from different genetic backgrounds revealed conservation of marker order but differences in chromosome and total map length. In particular, significant reduction of map length was observed in interspecific compared to intraspecific crosses. The distribution of regions with distorted segregation ratios in the genome was analyzed for four potato parents. The most prominent distortion of recombination was found to be caused by the self-incompatibility locus.     

Chromosomal control of chiasma distribution in house mice. Analysis of chiasma distribution in homo- and heterozygotes by inversion in chromosome 1

Examination of chiasma distribution in the chromosome 1 in male mice homo- and heterozygous for distal inversion In(1)12Rk and in normal mice was carried out. No differences in chiasma distribution was found between homozygotes for the inversion and homozygotes for normal chromosome 1. A drastic change in this trait was revealed in heterozygous animals. In heterozygotes, the telomeric segments of SC were asynapsed and unavailable for recombination. This leads to significant decrease in the frequency of bivalents bearing chiasmata in pretelomeric region. In turn, it produced chiasma redistribution in proximal noninverted portion of the bivalent 1. These results could be interpreted as evidence for chromosomal control of chiasma distribution pattern: the distance of certain part of the chromosome from telomere and interference (which also operates at the chromosomal level) are more important for determination of the chiasmata frequency in the given region, than its genetic content.     

Linkage mapping of a polymorphic plumage locus associated with intermorph incompatibility in the Gouldian finch (Erythrura gouldiae)

Colour polymorphism is known to facilitate speciation but the genetic basis of animal pigmentation and how colour polymorphisms contribute to speciation is poorly understood. Restricted recombination may promote linkage disequilibrium between the colour locus and incompatibility genes. Genomic rearrangement and the position of relevant loci within a chromosome are important factors that influence the frequency of recombination. Therefore, it is important to know the position of the colour locus, gene order and recombination landscape of the chromosome to understand the mechanism that generates incompatibilities between morphs. Recent studies showed remarkable pre- and postzygotic incompatibilities between sympatric colour morphs of the Gouldian finch (Erythrura gouldiae), in which head feather colour is genetically determined by a single sex-linked locus, Red. We constructed a genetic map for the Z chromosome of the Gouldian finch (male-specific map distance=131 cM), using 618 captive-bred birds and 34 microsatellite markers, to investigate the extent of inter- and intraspecific genomic rearrangements and variation in recombination rate within the Z chromosome. We refined the location of the Red locus to a ~7.2-cM interval in a region with a moderate recombination rate but outside the least-recombining, putative centromeric region. There was no evidence of chromosome-wide genomic rearrangements between the chromosomes carrying the red or black alleles with the current marker resolution. This work will contribute to identifying the causal gene, which will in turn enable alternative explanations for the association between incompatibility and colouration, such as fine-scale linkage disequilibrium, genomic rearrangements and pleiotropy, to be tested.     

Differentiation between wheat chromosomes 4B and 4D.

A linkage map based on homoeologous recombination, induced by the absence of the Ph1 locus, between chromosome 4D of Triticum aestivum L. (genomes AABBDD) and chromosome 4B of T. turgidum L. (genomes AABB) was compared with a linkage map of chromosome 4Am of T. monococcum L. and a consensus map of chromosomes 4B and 4D of T. aestivum based on homologous recombination. The 4D/4B homoeologous map was only one-third the length of the homologous maps and all intervals were reduced relative to the 4B-4D consensus map. After the homoeologous map was corrected for this overall reduction in recombination, the distribution of recombination in the short arm was similar in both types of maps. In the long arm, homoeologous recombination declined disproportionally in the distal to proximal direction. This gradient was shown to be largely caused by severe segregation distortion reflecting selection against 4D genetic material. The segregation distortion had a maximum that coincided with the centromere and likely had a polygenic cause. Chromosomes 4D and 4B were colinear and recombination between them occurred in almost all intervals where homologous recombination occurred. These findings suggest that these chromosomes are not differentiated structurally and that the differentiation is not segmental. In the presence of Ph1, metaphase I chromosome pairing between chromosomes composed of homologous and differentiated regions correlated with the lengths of the homologous regions. No compensatory allocation of crossovers into the homologous regions was detected. In this respect, the present results are in dramatic contrast with the crossover allocation into the pseudoautosomal region in the mammalian male meiosis.     

Recombination map of the common shrew, Sorex araneus (Eulipotyphla, Mammalia)

The Eurasian common shrew (Sorex araneus L.) is characterized by spectacular chromosomal variation, both autosomal variation of the Robertsonian type and an XX/XY(1)Y(2) system of sex determination. It is an important mammalian model of chromosomal and genome evolution as it is one of the few species with a complete genome sequence. Here we generate a high-precision cytological recombination map for the species, the third such map produced in mammals, following those for humans and house mice. We prepared synaptonemal complex (SC) spreads of meiotic chromosomes from 638 spermatocytes of 22 males of nine different Robertsonian karyotypes, identifying each autosome arm by differential DAPI staining. Altogether we mapped 13,983 recombination sites along 7095 individual autosomes, using immunolocalization of MLH1, a mismatch repair protein marking recombination sites. We estimated the total recombination length of the shrew genome as 1145 cM. The majority of bivalents showed a high recombination frequency near the telomeres and a low frequency near the centromeres. The distances between MLH1 foci were consistent with crossover interference both within chromosome arms and across the centromere in metacentric bivalents. The pattern of recombination along a chromosome arm was a function of its length, interference, and centromere and telomere effects. The specific DNA sequence must also be important because chromosome arms of the same length differed substantially in their recombination pattern. These features of recombination show great similarity with humans and mice and suggest generality among mammals. However, contrary to a widespread perception, the metacentric bivalent tu usually lacked an MLH1 focus on one of its chromosome arms, arguing against a minimum requirement of one chiasma per chromosome arm for correct segregation. With regard to autosomal chromosomal variation, the chromosomes showing Robertsonian polymorphism display MLH1 foci that become increasingly distal when comparing acrocentric homozygotes, heterozygotes, and metacentric homozygotes. Within the sex trivalent XY(1)Y(2), the autosomal part of the complex behaves similarly to other autosomes.     

Spatiotemporal Asymmetry of the Meiotic Program Underlies the Predominantly Distal Distribution of Meiotic Crossovers in Barley

Meiosis involves reciprocal exchange of genetic information between homologous chromosomes to generate new allelic combinations. In cereals, the distribution of genetic crossovers, cytologically visible as chiasmata, is skewed toward the distal regions of the chromosomes. However, many genes are known to lie within interstitial/proximal regions of low recombination, creating a limitation for breeders. We investigated the factors underlying the pattern of chiasma formation in barley (Hordeum vulgare) and show that chiasma distribution reflects polarization in the spatiotemporal initiation of recombination, chromosome pairing, and synapsis. Consequently, meiotic progression in distal chromosomal regions occurs in coordination with the chromatin cycles that are a conserved feature of the meiotic program. Recombination initiation in interstitial and proximal regions occurs later than distal events, is not coordinated with the cycles, and rarely progresses to form chiasmata. Early recombination initiation is spatially associated with early replicating, euchromatic DNA, which is predominately found in distal regions. We demonstrate that a modest temperature shift is sufficient to alter meiotic progression in relation to the chromosome cycles. The polarization of the meiotic processes is reduced and is accompanied by a shift in chiasma distribution with an increase in interstitial and proximal chiasmata, suggesting a potential route to modify recombination in cereals.     

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     

Recombinational error and deletion formation in Neisseria gonorrhoeae: a role for RecJ in the production of pilE L deletions

Genetic linkage within Neisseria gonorrhoeae populations is in equilibrium, yet the physical linkage map indicates a relatively stable chromosome structure, despite an apparently vast potential for mispairing between repeated sequences (e.g. between the multiple pil or opa alleles, or through mispairing of any of the numerous small repeated sequences that are liberally scattered throughout the chromosome). Therefore, the stability of the physical linkage map suggests that aberrant recombination between repeated sequences is a rare event. This study was undertaken to explore some of the parameters that may govern deletion events between short direct oligonucleotide repeats, using a chromosomal locus that appears to be especially prone to deletions (the pilin expression locus; pilE). In this report, we demonstrate that deletion formation at pilE occurs primarily through recombinational error following a pilE/pilS interaction; illegitimate (i.e. RecA-independent) events can occur, but they are infrequent. In contrast, when genetically engineered opa deletion substrates were constructed and placed in the chromosome, deletions at the opa loci were infrequent even under rec(+) conditions. A model is presented in which the gonococcal RecA and RecJ proteins promote pilE deletions through a recombination event that is templated or stabilised by a pilE/pilS interaction.     

Unexpected behavior of an inverted rye chromosome arm in wheat

Distal location of chiasmata in chromosome arms is thought to be a consequence of the distal initiation of synapsis. Observations of meiotic behavior of a rye chromosome with an inverted arm show that patterns of chiasma distribution and frequency are also inverted; therefore, the patterns of synapsis and chiasma distribution are independent, and recombination frequency along a chromosome is position-independent and segment-specific. Since cases of random distribution of chiasmata and recombination are known in rye, a genetic mechanism must be present that licenses specific chromosome regions for recombination. Large differences in the metaphase I pairing of the inversion in various combinations of two armed and telocentric chromosomes confirm the major role of the telomere bouquet in early homologue recognition. However, occasional synapsis and chiasmate pairing of the distal regions of normal arms with the proximal regions of the inversion suggest that an alternative mechanism for juxtaposing of homologues must also be present. Synapsis in inversion heterozygotes was mostly complete but in the antiparallel orientation, hence defying homology, but non-homologues never synapsed. Instances of synapsis strictly limited to the chiasma-capable segments of the arm suggest that, in rye, both recombination-dependent and recombination-independent mechanisms for homologue recognition must be present.     

Variation in chiasma frequency among eight accessions of Arabidopsis thaliana

Natural variation in meiotic recombination frequency in Arabidopsis thaliana has been assessed by analyzing chiasma frequency variation among a range of geographically and ecologically diverse accessions. Fifty pollen mother cells at metaphase I of meiosis were analyzed from each of eight accessions and fluorescence in situ hybridization was applied to enable identification of all 10 chromosome arms. There was no significant variation in mean chiasma frequency between plants within accessions, but there was significant variation between accessions. Further analysis confirmed this finding and identified two particular accessions, Cvi and Ler, as having chiasma frequencies significantly lower than those of the other accessions. The analysis also revealed that the pattern of chiasma distribution between arms and among chromosomes is not consistent over accessions. Further detailed analyses were conducted on each individual chromosome (1-5) in turn, revealing that chromosome 4, one of the acrocentric chromosomes, is the least variable while the other acrocentric chromosome (2) is the most variable. These findings indicate the existence of recombination regulatory elements in Arabidopsis and we conclude that it may be possible in the future to identify these elements and determine their mode of action. The practical implications of such developments are considerable.