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.     

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.     

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.     

Models for chromatid interference with applications to recombination data

Genetic interference means that the occurrence of one crossover affects the occurrence and/or location of other crossovers in its neighborhood. Of the three components of genetic interference, two are well modeled: the distribution of the number and the locations of chiasmata. For the third component, chromatid interference, there exists only one model. Its application to real data has not yet been published. A further, new model for chromatid interference is presented here. In contrast to the existing model, it is assumed that chromatid interference acts only in the neighborhood of a chiasma. The appropriateness of this model is demonstrated by its application to three sets of recombination data. Both models for chromatid interference increased fit significantly compared to assuming no chromatid interference, at least for parts of the chromosomes. Interference does not necessarily act homogeneously. After extending both models to allow for heterogeneity of chromatid interference, a further improvement in fit was achieved.     

An Analysis of Interference in the Fission Yeast Schizosaccharomyces Pombe

The evaluation of three-point crosses at the tetrad and random spore level leads to the conclusion that both chiasma and chromatid interference are absent in the fission yeast Schizosaccharomyces pombe.     

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.     

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.     

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 search for chromatid interference in the male house mouse

Summary Mouse spermatocyte chiasma frequency observations by Slizynski shew chiasma interference which can be adequately represented by a model due to Mather. Some genetical implications of this model are analysed, assuming various strengths of chromatid interference, and are compared with genetical observations. This indicates that there is little or no chromatid interference in the male mouse, A new map length and recombination frequency conversion table is given, based an the observed chiasma frequencies.

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Zusammenfassung Beobachtungen von Slizynski über Chiasma-Häufigkeit in Maus-Spermatocyten konnten befriedigend ausgedeutet werden auf Grund von Mathers Modell der Chiasma-Interferenz. Die genetischen Folgerungen aus diesem Modell wurden weiterhin untersucht unter Annahme verschiedener Grade von Chromatid-Interferenz. Ein Vergleich mit den genetischen Daten zeigt, daß Chromatid-Interferenz in der Maus gering oder abwesend ist. Unter Zugrundelegung der beobachteten Chiasma-Häufigkeiten wird eine neue Tabelle zur Umwandlung von Rekombinationsdaten in Abständen auf den Chromosomenkarten gegeben.

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With 6 figures in the text.

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Member of the Medical Research Council's scientific staff.     

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.     

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.     

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 relation between pairing preference and chiasma frequency in tetrasomics of rye.

The association pattern of marked tetrasomes of Secale chromosome 1R at meiotic first metaphase was analyzed. Two of the four chromosomes were identical with terminal C-bands at both arms; the other two were also identical but lacked C-bands and were homologous or homeologous with the first two. Four different types of heterozygotes for 1R were studied: (i). autotetraploid hybrids between genetic variants within Secale cereale subsp. cereale, (ii). tetraploid hybrids between subspecies of Secale cereale, (iii). tetraploid hybrids between species of Secale, and (iv). autotetrasomes of S. cereale in a wheat background. Earlier observations that heterozygous associations (banded with unbanded) had consistently higher chiasma frequencies than homozygous associations were extended and confirmed. To analyze this phenomenon more closely, the possible relations between this correlation and several other meiotic phenomena were studied. For this analysis, three genetically different autotetraploid hybrids within S. cereale were selected that differed with respect to the relation between pairing type and chiasma frequency. Special attention was given to different patterns of interference and other meiotic phenomena in the two chromosome arms of chromosome 1R. No relations between such phenomena and the relation between pairing type and chiasma frequency could be established. A hypothesis is formulated assuming that long-distance homologue attraction is concentrated in a limited number of sites and that in different genotypes, different patterns of active sites are present. Moderately weak attraction sites can pair with strong homologous sites under favorable genetic conditions, but two weak sites cannot. Then, heterozygotes have more effective pairing initiation and consequently chiasma formation than homozygotes. Under less favorable conditions, only strong sites are effective, and then, homozygotes pair better, but the chiasma frequency is lower. A model of the forces involved in homologue attraction is presented.     

Multilocus half-tetrad analysis and centromere mapping in citrus: evidence of SDR mechanism for 2n megagametophyte production and partial chiasma interference in mandarin cv 'Fortune'

The genetic structure of 2n gametes and, particularly, the parental heterozygosity restitution at each locus depends on the meiotic process by which they originated, with first-division restitution and second-division restitution (SDR) being the two major mechanisms. The origin of 2n gametes in citrus is still controversial, although sexual polyploidisation is widely used for triploid seedless cultivar development. In this study, we report the analysis of 2n gametes of mandarin cv 'Fortune' by genotyping 171 triploid hybrids with 35 simple sequence repeat markers. The microsatellite DNA allele counting-peak ratios method for allele-dosage evaluation proved highly efficient in segregating triploid progenies and allowed half-tetrad analysis (HTA) by inferring the 2n gamete allelic configuration. All 2n gametes arose from the female genitor. The observed maternal heterozygosity restitution varied between 10 and 82%, depending on the locus, thus SDR appears to be the mechanism underlying 2n gamete production in mandarin cv 'Fortune'. A new method to locate the centromere, based on the best fit between observed heterozygosity restitution within a linkage group and theoretical functions under either partial or no chiasmata interference hypotheses was successfully applied to linkage group II. The maximum value of heterozygosity restitution and the pattern of restitution along this linkage group would suggest there is partial chiasma interference. The implications of such a restitution mechanism for citrus breeding are discussed.     

Modeling Interference in Genetic Recombination

In analyzing genetic linkage data it is common to assume that the locations of crossovers along a chromosome follow a Poisson process, whereas it has long been known that this assumption does not fit the data. In many organisms it appears that the presence of a crossover inhibits the formation of another nearby, a phenomenon known as ``interference.' We discuss several point process models for recombination that incorporate position interference but assume no chromatid interference. Using stochastic simulation, we are able to fit the models to a multilocus Drosophila dataset by the method of maximum likelihood. We find that some biologically inspired point process models incorporating one or two additional parameters provide a dramatically better fit to the data than the usual ``no-interference' Poisson model.     

Configurations resulting from iso-chromatid and iso-subchromatid unions after meiotic and mitotic prophase irradiation

Summary By making use of the chromosomes of Trillium erectum as a model, potential and actual configurations arising from presumed iso-chromatid and iso-subchromatid unions after irradiation of meiotic or mitotic prophase have been studied and analyzed. Diagrams and photographs of various recognizable types of chromatid or subchromatid rearrangements are presented. A minimum of two iso-chromatid unions within an arm of a single chromosome in meiotic prophase, if separated by a single chiasma, can give rise to a monocentric chromosome with a triplicated segment, the middle portion of which is an inversion. A minimum of two iso-subchromatid breaks within an arm at either meiotic or mitotic prophase also can result in the production of a monocentric chromosome containing a triplicated segment. The stage of appearance of dicentrics or bridges arising from chromatid or subchromatid unions in meiotic prophase is influenced by chiasma number and pattern and by the number of strands per chromosome or chromatid. Some of the rearrangements described may have genetic and evolutionary implication of considerable potential importance which has not been recognized previously.Research carried out at Brookhaven National Laboratory under the auspices of the U.S. Atomic Energy Commission.     

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.     

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     

Chiasma-based models of multilocus recombination: increased power for exclusion mapping and gene ordering

Cytological evidence indicates that the number of chiasmata which can occur on any given chromosome arm is limited. In this paper a Monte-Carlo simulation study is used to compare the power of a model of multilocus recombination parameterized in terms of chromosome-specific chiasma distributions with the traditional model parameterized by recombination fractions in adjacent intervals. Two specific gene mapping problems are considered: excluding a test locus from a given chromosome map and ordering a test locus with respect to a fixed map of syntenic marker loci. We show that the chiasma-based models require significantly fewer observations to exclude or order a test locus and that they are quite robust to errors in specifying the underlying true chiasma distribution.     

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.