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.     

Discrete chiasma formation models and their associated high order interference

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

Simultaneous negative and positive chiasma interference across the break point in interchange heterozygotes

The impossibility to obtain real roots from equations published earlier for estimating chiasma frequencies in the two translocated segments from configuration frequencies in interchange heterozygotes, was shown to be a result of lack of independence of chiasma formation. This is interpreted as negative interference. Similarly, negative interference could be shown to operate between the two interstitial segments. In all cases where a sufficient number of bivalents was formed by the interchange complex, chiasma frequency in the interstitial segments was strikingly higher in bivalents (having no chiasmata in the translocated segments) than in multivalents (with chiasmata in one or both translocated segments). This indicates strong positive interference between the interstitial and translocated segments.Negative interference between opposite-and positive interference between adjacent segments across the break point of the interchange occurred simultaneously in the cell populations. The phenomenon was attributed to complications in effective chromosome pairing at the point of partner exchange which in interchanges is determined by the breakpoint.The material was Secale cereale where five interchanges were analysed in a total of 12000 PMC's from 14 plants.     

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.     

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 interference and centromere co-orientation in a spontaneous translocation heterozygote of Euchorthippus pulvinatus gallicus (Acrididae; Orthoptera)

The meiosis of an individual of the species Euchorthippus pulvinatus gallicus heterozygous for a reciprocal translocation involving chromosomes 3 and 6 has been analysed using the Giemsa C-banding technique. It is concluded that: (i) Chiasma interference in the quadrivalent seems to act only at the arm level. There is no interference across the translocation break point. No interchromosomal chiasma interference could be demonstrated, (ii) The results concerning the co-orientation of the quadrivalent suggest that the length of the chromosomal segments between two adjacent centromeres at metaphase I is related with their orientation behaviour.     

Interchromosome effects on chiasma frequencies in rye

In interchange heterozygotes and interchange trisomics of rye (Secale cereale) correlations between multivalents and bivalents in respect of number of chromosome arm pairs bound at MI, were studied. No significant positive correlations were observed. Significant negative correlations, indicating interchromosome effects, were found only in cell populations that approached anaphase. The effects seem to be generated by non-random loss of chiasmata from chromosome ends. The absence of demonstrable real interchromosome effects on chiasma formation in the material studied may be explained by positive correlations (due to between-cells variation) counteracting possible negative correlations. Another explanation may be found in the fact that intra-chromosome interference, that might be one of the ways through which interchromosome effects act, does not come to expression with the methods of observations used.     

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.     

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.     

Chiasma distribution in Truxaline grasshoppers

Similar patterns of chiasma distribution are found within the individual arms of the chromosome complement in four species of Truxaline grasshopper. There is a linear relationship between chiasma frequency and chromosome arm length although the telocentric elements have a consistently higher mean number of chiasmata per unit of arm length. The positions of successive chiasmata can be defined in terms of residual (r.c. and r.t.) and interference (T) distances which vary in value according to both arm length and chiasma frequency. There is a tendency for one chiasma to lie in a distal position which is accentuated when additional chiasmata form. Supernumerary B chromosomes do not appear to influence the overall control mechanism of chiasma distribution. There is no indication that bivalents within a nucleus compete for chiasmata nor does the chiasma distribution in one arm of the metacentric members influence that in the other. It is suggested that the control of chiasma formation is determined mainly by interference factors.     

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 control of chiasma frequency in Vicia faba L.

Summary InVicia faba two groups of chromosomes can be distinguished and consequently correlations of chiasma frequency can be calculated between the groups and also within the group of small chromosomes. A negative correlation was demonstrated during some analyses while positive ones occurred in others, in fact a wide range of coefficients could be calculated by both methods. It is suggested that negative correlation of chiasma frequency occurs only when reproduction of the chromosomes is precipitated or pairing delayed, so that the degree of pairing may be affected in plants where many chromosomes are present or where the chromosomes are large in size. Such correlations can have no influence on recombination, but rather they are the occasional outcome of the mechanism controlling 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.     

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 formation in the short arm of the nucleolar chromosome of the tomato

Summary A translocation heterozygote in tomato (Lycopersicon esculentum) is shown to have a cyclical type of interchange between the long arms of chromosomes 1, 2 (nucleolar) and 3. A study of chromosome association in this plant at metaphase I has indicated that in 21% of the cells a ring of six chromosomes is present. Since an open ring hexavalent can occur only if there is chiasma formation in all the translocated segments and in all the short arms of the three chromosomes, it is concluded that there is considerable frequency of chiasma formation in the short arm of the nucleolar chromosome. This conclusion contradicts the previous observations that chiasma formation is either absent or very rare in the entirely dark staining chromatic, sometimes referred to as heterochromatic, short arm of the nucleolar chromosome.Part of this investigation was carried out at the Department of Genetics, Agricultural University, Wageningen, when the author was serving a contract between the EURATOM-I.T.A.L. and the Agricultural University.     

The structural organization of the intracerebral giant fiber system of cephalopods

Summary The course of the two intracerebral first-order giant axons of cephalopods at their chiasma, and the fine structure of the contact area between the crossing axons are examined by light and electron microscopy in species of three taxonomic groups (Loligo vulgaris, Sepia officinalis, Illex coindeti). In addition to the well known chiasma of the adult Loligo in which the two axons are fused (Young, 1939), three other chiasma types are described. In each of them there are synapse-like contact areas that suggest a passage of impulses from one axon to the other. (1) The larval Loligo shows a chiasma with crossed axons and contralaterally descending branches; at the apposed membranes in the chiasma there are clusters of electron-transparent vesicles. (2) In the adult Sepia each crossing axon has an ipsi- and a contralaterally descending branch; the apposed membranes of the decussating axons show symmetrical synapse-like areas characterized by a monolayer of electron-transparent vesicles on each side and a regular cleft of 100 Å width. (3) In the adult Illex each axon has only an ipsilaterally descending branch and there are at the point of decussation two crossed collaterals; large masses of electron-transparent vesicles are found on each side of the apposed membranes of the collaterals and the membranes show an increased electron density. It is argued that the four chiasma types serve the same function, i.e., the establishment of functional bilaterality of the giant fiber system. By structural analogy with other, both structurally and functionally known synapses it is suggested that in the decussation of Sepia impulses pass in both ways from one axon to the other. Data of the embryological development of the giant fiber system are summarized.Work supported by the Deutsche Forschungsgemeinschaft (Ma. 259) and by NATO Research Grant No. 273. The collaboration of Dipl. Zool. Elisabeth Braendle from the Zoological Institute of the University Zürich in the examination of the Illex chiasma is gratefully acknowledged.     

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.     

Evidence for separate genetic control of crossing over and chiasma maintenance in maize

The meiotic cytological behavior of chromosomes in maize microsporocytes homozygous for the recessive mutant desynaptic was studied at various stages. It was found that following apparently normal pachytene synapsis there appears to be sporadic precocious desynapsis. By diakinesis bivalents heterozygous for a distal knob have often separated to pairs of univalents, each with a knob-carrying and a knobless chromatid. From the frequency of such events it is inferred that the crossover process is probably not affected by the mutant and that the genetic defect affects instead a distinct function concerned with chiasma maintenance following crossing over. Since precocious separation of dyads to monads at prophase II was also found in the desynaptic material, it is suggested that normal chiasma maintenance until anaphase I and normal dyad integrity maintenance between anaphase I and anaphase II may depend upon the same mechanism; it is also suggested that this may involve a special tendency for cohesiveness of sister chromatids during meiosis, beyond that which is ordinarily found at mitosis.     

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.