A Polymerization Model of Chiasma Interference and ... A model of chiasma interference is proposed and

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  • Copyright 0 1990 by the Genetics Society of America

    A Polymerization Model of Chiasma Interference and Corresponding Computer Simulation

    Jeff S. King* and Robert K. Mortimert?* *Graduate Group in Biophysics, University of California, Berkeley, California 94720, tDepartment of Molecular and Cell Biology,

    Division of Genetics, University of California, Berkeley, Calfornia 94720, and $Division of Cellular and Molecular Biology, Lawrence Berkeley Laboratory, Berkeley, California 94720

    Manuscript received April 16, 1990 Accepted for publication August 29, 1990

    ABSTRACT 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 chromo- somes. 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 demon- strates 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.

    I N 1916 MULLER reported that a crossover in one region of a Drosophila chromosome changes the probability of a crossover in an adjacent region (MULLER 19 16). Subsequent work in other eukaryotes revealed in general a distance-dependent reduction in the probability of a second crossover, known as posi- tive chiasma interference. Interference is expressed in terms of coincidence, which is the ratio of observed to expected coincident crossovers in two linked re- gions. Interference has been observed at both the cytological and genetic levels. For example, coinci- dence as a function of distance has been measured genetically in Drosophila melanogaster (WEINSTEIN 19 18) and in Saccharomyces cerevisiae (MORTIMER and FOCEL 1974). In both organisms, interference is strong for closely linked regions and falls off with increasing separation. Cytologically, interference has been examined in terms of coincidence of chiasmata, the cross-shaped associations between homologous chromosomes seen in diakinesis and considered to be an outcome of genetic exchanges (for review SeeJONES 1984). For example, on the long arm of the L3 bivalent of Chorthzppus brunneus complete interfer- ence is observed over distances of 25-30% of the length of the bivalent arm (LAURIE 1980), and no interference is observed for regions longer than 60% of the length of the bivalent arm.

    Genetic experiments have provided clues to the relationship between recombination and interference. In S. cerevisiae and in D. malanogaster, roughly one- half of all gene conversions are associated with recip- rocal recombination (HURST, FOCEL and MORTIMER 1972; HILLIKER and CHOVNICK 198 1) . In Neurospora

    (knrtics 126: 1127-1 138 (December, 1990)

    and Saccharomyces gene conversions with a genetic crossover show chiasma interference but gene conver- sions without exchange of flanking markers do not interfere with other gene conversions, either with or without associated crossovers (STADLER 1959; MOR- TIMER and FOCEL 1974). Chromatid interference, a deviation from the 1 :2: 1 distribution of 2-, 3-, and 4- strand double crossovers, is not detected via tetrad analysis in Saccharomyces (MORTIMER and FOGEL 1974) or in crosses of Drosophila with attached X chromosomes (EMERSON and BEADLE 1933).

    Electron microscopic studies of pachytene synapto- nemal complexes resulted in the discovery of recom- bination nodules (SCHRANTZ 1970; GILLIES 1972) (for reviews, see VON WETTSTEIN, RASSMUSSEN and HOLM 1984; CARPENTER 1989). Two types of recombination nodules have been observed. Based on their temporal appearance in meiotic nuclei they have been termed early and late recombination nodules (CARPENTER 1989); however, it has not been established that late recombination nodules arise from early recombina- tion nodules. The demonstration that late recombi- nation nodules parallel chiasmata in frequency and distribution has led to the proposal that late recom- bination nodules are directly involved in meiotic re- combination (CARPENTER 1975). The distributions of late recombination nodules, chiasmata, and crossovers are comparable in terms of number per chromosome and positions on chromosome arms. Late recombina- tion nodules have been associated with sites of local- ized DNA synthesis (CARPENTER 1981), which is be- lieved to occur during recombination. (For models of recombination see MESSELSON and RADDINC 1975;

  • 1128 J. S. King and R. K. Mortimer

    TABLE 1

    Comparison of genome sizes and recombination levels for several organisms

    Organism DNA Mb N cM/gen co/biv chi/biv Mb/chr co/Mb SC wn/biv

    Schizosaccharomyces pombe 14 3 1,895 12.6 n.d. 4.7 2.7 14 16 4,300 Saccharomyces cerevisiae 5.4 n.d. 0.88 6.14 1.56

    Neurospora crassa 47 7 1,000 2.9 n.d. 6.71 0.43 8.29 Drosophila melanogaster 180 3 285 1.9 n.d. 60 0.032 15.33 Caenorhabditis elegans 100 6 300 1 .o n.d. 16.7 0.06 5.8 Bombyx mori 500 28 2,900 2.1 n.d. 17.8 0.12 9.21 Homo sapiens 3,000 23 3,500 3.0 n.d. 130 0.023 10.26 Mus musculus 3,000 20 1,630 1.6 n.d. 150 0.1 1 n.d. Zea mays 8,000 10 1,300 2.6 1.7 800 0.0033 32.5 Lilium long9orum 180,000 12 n.d. n.d. 2.4 15,000 0.0000 16 308.3


    Amount of DNA in base pairs, number of chromosomes, size of genetic map, and size of synaptonemal complexes. While the organisms listed have radically different amounts of DNA, they are similar in terms of cM per genome and crossovers per bivalent. Data are from: VON WETTSTEIN, RASSMUSSEN and HOLM (1984), FASMAN (1976), O’BRIEN (1987) and WHITE (1977). Abbreviations: Mb = megabase-pairs, cM = centimorgans, gen = genome, co = crossovers, biv = bivalent, chi = chiasmata, chr = chromosome, SC = synaptonemal complex, N = the haploid number of chromosomes, n.d. = no data.

    and ORR-WEAVER, SZOSTAK and ROTHSTEIN 198 1 .) For these reasons it is believed that late recombination nodules, chiasmata and genetic crossovers are all man- ifestations of the same event: reciprocal meiotic re- combination.

    Regulation of recombination events is apparent at several levels. The number of crossovers per chro- mosome arm was shown to be nonrandom (HALDANE 1931; WEINSTEIN 1936) since, compared to a Poisson distribution with the same average, the number of Drosophila X chromosomes with no crossovers was underrepresented and the number with one or two crossovers was overrepresented. The distributions of late nodules, chiasmata, and crossovers are nonuni- form in terms of position along chromosomes and nonrandom in terms of distances between them. The positions of crossovers along the telocentric X chro- mosome of Drosophila tend to be centrally located in single crossover tetrads and tend to have one cross- over near the centromere and the other crossover near the distal telomere in double crossover tetrads (CHARLES 1938).

    Several models have been proposed to account for either interference or the distributions of chiasmata along chromosomes (for review see JONES 1984). Some of the models address interference but fail to account for the observed distributions of chiasmata between chromosomes. Others models only address the distributions of chiasmata and do not account for interference. A model of particular interest was pro- posed by EGEL in 1978. EGEL’S model is based on possibilities of exchanges that are established before synapsis and serve as initiation centers of synapsis. Synapsis is then followed by formation of synaptone- mal complex, which prevents the establishment of further possibilities of exchange. This results in posi- tive interference.

    Stochastic models, based on recombination sites with individual crossover probabilities, are notewor-

    thy because a growing body of evidence suggests that some DNA sites have much higher recombination rates than other sites. Stochastic models can also be based on a limited supply of a necessary component. Criticisms of stochastic models stem from their inabil- ity to account for interference without additional as- sumptions. Stochastic models based on a small number of sites are not supported by the fact that in Drosoph- ila some chromosomal sequences that are moved adopt the exchange distribution characteristic of the new location (BAKER and CARPENTER 1972). Further- more, in Saccharomyces the allelic recombination rate of a DNA sequence varies significantly, depending on its location in the genome (LICHTEN, BORTS and HA- BER 1987). It is also clear from fine-scale genetic analysis that there are many sites at which recombi- nation may occur along a chromosome. However, in any one meiosis, recombination occurs at only a few of these sites.

    Other models are based on pairing, in which certain chromosomal regions are assumed to pair first and are therefore more likely to undergo recombination. However, without additional assumptions this does not account for either interference or for th