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     

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.     

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     

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.     

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.     

The relationship between count-location and stationary renewal models for the chiasma process

It is often convenient to define models for the process of chiasma formation at meiosis as stationary renewal models. However, count-location models are also useful, particularly to capture the biological requirement of at least one chiasma per chromosome. The Sturt model and truncated Poisson model are both count-location models with this feature. We show that the truncated Poisson model can also be expressed as a stationary renewal model, while the Sturt model cannot. More generally, we show that there is only one family of count-location models for the chiasma process that can also be expressed as stationary renewal models. The models in this family can exhibit either positive or negative interference.     

Cytogenetics of the mealybug Planococcus citri (Risso) (Homoptera: Coccoidea): genetic markers,lethals, and chromosome rearrangements

Conventional types of cytogenetic studies with the mealybug, Planococcus citri (Risso), are possible with the use of genetic markers and meiotic analysis in the female. The loci of an eye-color mutant, salmon, and a wing-shape mutant, banjo, are linked with about 22 per cent recombination. These markers have been used in the identification and maintenance of lethals and rearrangements. All the cytologically identifiable rearrangements have proved to be reciprocal translocations, some symmetric, others, grossly asymmetric or otherwise complicated. No simple breakage products have been recovered. On the basis of their effects on crossing over, some of the lethals are believed to be associated with small rearrangements. The bivalents normally have one chiasma; only 1.2 per cent have two. Interference is decidedly decreased in chiasma formation in translocation heterozygotes, and in genetic recombination with suspected small rearrangements associated with lethals; it is also decreased, but less markedly, in genetic recombination with lethals in translocations. These various results are discussed in relationship to the holokinetic nature of the coccid chromosome, and natural increases in coccid chromosome number, as well as in regard to the effect of rearrangements on interference.Supported by grants from the National Science Foundation, currently GB 8196, and by a professorship (1968–69) for the senior author in the Miller Institute for Basic Research in Science.Dedicated to Dr. Sally Hughes-Schrader on the occasion of her seventy-fifth birthday.     

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.     

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     

Linkage Group Xix of Chlamydomonas Reinhardtii Has a Linear Map

Linkage group XIX (or the UNI linkage group) of Chlamydomonas reinhardtii has been reported to show a circular meiotic recombination map. A circular map predicts the existence of strong chiasma and chromatid interference, which would lead to an excess number of two-strand double crossovers during meiosis. We have tested this prediction in multipoint crosses. Our results are consistent with a linear linkage group that shows positive chiasma interference and no chromatid interference. Chiasma interference occurs both within arms and across the centromere. Of the original loci that contributed to the circular map, we find that two map to other linkage groups and a third cannot be retested because the mutant strain that defined it has been lost. A second reported unusual property for linkage group XIX was the increase in meiotic recombination with increases in temperature during a period that precedes the onset of meiosis. Although we observed changes in recombination frequencies in some intervals on linkage group XIX in crosses to CC-1952, and in strains heterozygous for the mutation ger1 at 16°, we also show that our strains do not exhibit the previously observed patterns of temperature-sensitive recombination for two different pairs of loci on linkage group XIX. We conclude that linkage group XIX has a linear genetic map that is not significantly different from other Chlamydomonas linkage groups.     

Detection of Genetic Interference: Simulation Studies and Mouse Data

Genetic chiasma interference occurs when the occurrence of one crossover (or chiasma) influences the probability of another crossover occurring nearby. We investigated, by simulation studies, the power of three statistical methods to detect interference. Neither the traditional three-locus method nor a multiplicative model approach are very powerful, while a multilocus-feasible map function approach is more powerful, particularly as the number of loci increases. We show that the power to detect interference is quite sensitive to the underlying type of interference. When we tested for interference in two mouse data sets (from chromosomes 1 and 12), we found significant evidence of positive interference.     

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.     

Comparative chiasma analysis using a computerised optical digitiser

A new computerised technique has been devised for measuring the distribution of chiasmata along diplotene bivalents. The method involves the introduction into the field of view of the microscope, of a fine light spot which can be accurately manipulated along the chromosomes of each bivalent. The data recorded include (a) the positions of the chiasmata along the bivalent in terms of their relative distances from the centromere and (b) the individual bivalent and cellular chiasma frequencies. — The method has been applied to the analysis of chiasma distribution patterns in the two known species of the genus Caledia, C. species nova 1 and C. captiva and in two chromosomal races of the latter. Statistical tests indicate that within bivalents at least 40% of the comparative distribution patterns of chiasmata between races and species are significantly different. Similar comparisons between populations within races reveal only 18% significant differences. — The observed distribution patterns of chiasmata in this genus suggest that chiasma formation is sequential from centromere to telomere. — The variation in the frequency and distribution of chiasmata between races and species suggests that the interference distances between successive chiasmata are, at least partially, independent of chiasma frequency and position. — The interracial and interspecific differences in chromosome structure are correlated with changes in chiasma pattern.     

The chiasma-inducing pheromone of locusts

To the two quantitative criteria for phase transformation of locusts, viz. nymphal colour and adult morphometric ratios, the change in chiasma frequencies during meiosis in the male can now be added: gregarization or swarming induces an increase in chiasma formation. The atmosphere around crowded locusts contains a pheromone which is absorbed and causes a reactive haemolymph in locust hoppers. This haemolymph may be injected into solitarious hoppers or nymphs to induce increased chiasma formation. Certain solvents like risella oil and dimethyl sulphoxide will extract the pheromone from such an atmosphere, and bio-assays with these extracts have been demonstrated to be chiasma-inducing. Such extracts are, however, not chiasma-inducing in the albino mutant, but the haemolymph from crowded normal-coloured hoppers is reactive in the albino hopper. In addition the albino mutant is solitaria-like in both morphometric ratios and chiasma frequencies. These data indicate a relationship between the melanization cycle and chiasma induction: the previously postulated melanin-inducing pheromone and this chiasma-inducing pheromone are probably identical. On the other hand, this pheromone of nymphs and the sex-maturation pheromone of adults are not identical, although the latter may be a modified form of the other. The effect of the nymphal pheromone on adult morphometric ratios is not clear although some correlation has been shown to exist between raised chiasma frequencies in treated solitaries and advances towards gregaria ratios. It may be that in this pheromone we have, what may be called, a gregarizing principle.     

Alteration of the sex determining system resulting from structural change of the sex chromosomes in the frog Rana rugosa

Rana rugosa in Japan is divided into four geographical races on the basis of the karyotype of the sex chromosomes: one in which heteromorphic sex chromosomes occur in the female sex (ZW/ZZ-system), another in which they are present in males (XX/XY-system), and the remaining two in which no heteromorphism is seen in either sex. The last two inherit the XX/XY sex determining system. Y and Z chromosomes in the former two are of the same karyotype as the no. 7 chromosomes seen in one of the latter two, whereas X and W are caused by two inversions that occurred in the original Xs (no. 7). In this study, we first attempted to detect the structural difference between the resulting X and W by examining their chiasma formation. The chiasma distribution between X and W was closely similar to that between two Xs, suggesting that the W and X are identical in structure. Regarding the change from XX/XY- to ZW/ZZ-system, the simplest explanation is that the putative female-determining gene(s) on the W grew functionally stronger by inversions. Next, we examined the sex of triploids having two Xs and one Z. The data showed that the triploids with two original Xs and a Z were all male, whereas most of those with two resulting Xs and a Z developed into females as expected. We speculated that the female-determining gene(s) on the resulting X grew mildly stronger functionally by position effect, whereas those on the W grew much stronger for some other reason (e.g., duplication). J. Exp. Zool. 286:313-319, 2000.     

Chiasma distribution in asynaptic Locusta migratoria

The formation of chiasmata in six full sib male partially asynaptic individuals of Locusta migratoria has been studied. The mean chiasma frequency per cell was 2.3 both at diplotene and metaphase I. Chiasmata tended to be distributed evenly among the bivalents. The frequency and distribution of the chiasmata in each type of bivalent (L, M, or S) depended on the level of asynapsis and on interference between the bivalents. Short bivalents were the most affected by interference, while M bivalents associated independently of L and S bivalent behaviour.     

Chiasma patterns in a translocation derived duplication heterozygote of rye

Relative multivalent and bivalent configuration frequencies at first meiotic metaphase of a translocation derived duplication heterozygote of rye have been used to study recombination (chiasma) patterns. After multivalent pairing chiasma frequency is greatly reduced in the segments proximal to the duplication even when no chiasma is formed. There is positive interference after multivalent pairing between the duplication and the two adjacent segments, possibly especially the interstitial segment of the donor chromosome. A variegated type of across-centromere interference is inferred for both chromosomes. The duplication can in principle be applied in a hybrid variety using chromosomal male sterility genes. The restriction of recombination is not as effective as claimed for some other systems working with excess chromosomal material.     

Chiasma frequency effects of structural chromosome change

Three structural chromosome changes in the plant Hypochoeris radicata 2n = 8 have been tested for their effects on chiasma formation: (1) centric fission of chromosome 1, (2) a whole arm exchange between chromosomes 1 and 3, and (3) an interchange between the long arm of chromosome 1 and the short arm of 2 which gives an effectively three-armed pachytene multiple. Mean chiasma frequencies were compared between full-sibs in families segregating for the rearrangements. In each family the chiasma frequency was higher in heterozygotes than basic homozygotes. The size of the chiasma increase is dependant on the number of additional potentially-paired segments in the complement at pachytene. Fission heterozygotes and 1/2 interchange heterozygotes, with one extra pairing region, both form about 0.45 more chiasmata per PMC than full-sib basic homozygotes. The 1/3 exchange, with two additional pairing regions, increases chiasma frequency by twice this, about 0.85 per PMC. Individuals homozygous for the centric fission maintain the raised chiasma level. The chiasma increase appears limited to the chromosome(s) affected by structural change with no detectable interchromosomal effect.     

Spontaneous chromosome mutations in Truxaline grasshoppers

Three distinct mutant conditions are described in single male individuals from three species of short horn grasshopper. Of these, one is an entire germ line mutant of Myrmeleotettix maculatus, heterozygous for a centric fusion between single M₄ and M₅ telocentric chromosomes. In contrast, the remaining two mutants are present in mosaic form. One is heterozygous for an L₁-M₄ interchange in Omocestus viridulus, the other tetrasomic for the M₄ chromosome in Chorthippus parallelus which in addition is characterised by the inclusion of a supernumerary heterochromatic segment on one S₈ homologue. Centric fusion in Myrmehotettix maculatus has neither disturbed the chiasma potential of the elements constituting the fusion multiple nor, has it apparently influenced the production of balanced gametes. The pattern of chiasma formation in the L₁-M₄ interchange multiple lends support to the contention that the process of chiasma formation originates near the distal end of chromosome arms in Omocestus viridulus. There is no interaction between the two mutant conditions of tetrasomy and the presence of supernumerary segments in Chorthippus parallelus. Moreover, because of the precocious nature of two of the four M₄ homologues there is little tendency to form multivalents. The two M₄ bivalents share a similar mean chiasma frequency.     

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.