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 ona 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 crossoversin 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 regulationof recombination observedin both genetic andcytological experiments. While the model was quantitativelycompared to data from only Drosophila and Saccharomyces,the regulation observedin these species is qualitatively similarto the regulation of recombination observedin other organisms. N 1916 MULLERreported that a crossover in one and Saccharomyces gene conversions with a genetic I region of a Drosophila chromosome changes the crossover show chiasma interference but gene conver- probability of a crossover in an adjacentregion sions without exchange of flanking markers do not (MULLER19 16). Subsequent work in other eukaryotes interfere with other gene conversions, either with or revealed in general a distance-dependent reductionin without associated crossovers (STADLER1959; MOR- the probability of a second crossover, known as posi- TIMER and FOCEL1974). Chromatid interference, a tive chiasma interference. Interference is expressed deviation from the 1 :2:1 distribution of 2-, 3-, and 4- in terms of coincidence, which is the ratioof observed strand double crossovers, is not detected via tetrad to expected coincident crossovers in two linked re- analysisin Saccharomyces (MORTIMER and FOGEL gions. Interference has beenobserved atboth the 1974) or in crosses of Drosophila with attached X cytological and genetic levels. Forexample, coinci- chromosomes (EMERSONand BEADLE1933). dence as a function of distance has been measured Electron microscopic studies of pachytene synapto- genetically in Drosophilamelanogaster (WEINSTEIN nemal complexes resulted in the discovery of recom- 19 18) and in Saccharomyces cerevisiae (MORTIMERand bination nodules (SCHRANTZ1970; GILLIES1972) (for FOCEL 1974). Inboth organisms, interference is reviews, see VON WETTSTEIN, RASSMUSSENand HOLM strong for closely linked regions and falls off with 1984; CARPENTER1989). Two types of recombination increasing separation. Cytologically, interference has nodules have been observed.Based on their temporal been examined in terms of coincidence of chiasmata, appearance in meiotic nuclei they have been termed the cross-shaped associations betweenhomologous early and laterecombination nodules (CARPENTER chromosomes seen in diakinesis and considered to be 1989); however, it has not been established that late an outcomeof genetic exchanges (forreview SeeJONES recombination nodules arise from early recombina- 1984). Forexample, on thelong arm of the L3 tion nodules. The demonstration that late recombi- bivalent of Chorthzppusbrunneus complete interfer- nation nodules parallel chiasmata in frequency and ence is observed over distances of 25-30% of the distribution has led to the proposal that late recom- length of the bivalent arm (LAURIE 1980), and no bination nodules are directly involved in meiotic re- interference is observed for regions longer than 60% combination (CARPENTER1975). The distributions of of the length of the bivalent arm. late recombination nodules,chiasmata, and crossovers Geneticexperiments have provided clues tothe are comparable in terms of number per chromosome relationship between recombination and interference. and positions on chromosome arms. Late recombina- In S. cerevisiae and in D. malanogaster, roughly one- tion nodules have been associated with sites of local- half of all gene conversions are associated with recip- ized DNA synthesis (CARPENTER1981), which is be- rocal recombination (HURST, FOCELand MORTIMER lieved to occur during recombination. (For models of 1972; HILLIKER andCHOVNICK 198 1). In Neurospora recombination see MESSELSON and RADDINC1975; (knrtics 126: 1127-1 138 (December, 1990) 1128 J. S. King and R. K. Mortimer TABLE 1 Comparison of genome sizes and recombination levels for several organisms Organism DNAco/Mb MbMb/chr chi/biv N co/biv cM/gen SC wn/biv Schizosaccharomyces pombe 14 3 1,895 12.6 n.d. 4.7 2.7 n.d. Saccharomyces cerevisiae 14 16 4,300 5.4 n.d. 0.88 6.14 1.56 Neurospora crassaNeurospora 7 47 1,000 2.9 n.d. 6.71 0.43 8.29 Drosophila melanogasterDrosophila 1.9 285180 3 n.d. 6015.33 0.032 Caenorhabditiselegans 100 6 300 1.o n.d. 16.7 0.06 5.8 Bombyx mori 500 28 2,900 2.1 n.d.0.12 17.8 9.21 Homo sapiens Homo 3,500 23 3,000 3.0 n.d. 130 0.023 10.26 Mus musculus Mus 3,000 20 1,630 1.6 n.d. 150 0.1 1 n.d. Zea mays 8,000 10 1,300 2.632.5 1.70.0033 800 Lilium long9orumLilium 12180,000 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 andcrossovers 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 ROTHSTEIN198 1 .) thy because a growing body of evidence suggests that For thesereasons it is believed that late recombination some DNA sites havemuch higher recombination nodules, chiasmata and genetic crossovers are all man- rates than other sites. Stochastic models can also be ifestations of the same event: reciprocal meiotic re- based on a limited supply of a necessary component. combination. Criticisms of stochastic models stem from their inabil- Regulation of recombination events is apparent at ity to account for interference without additional as- several levels. The number of crossovers per chro- sumptions. Stochastic models based on a small number mosome arm was shown to be nonrandom (HALDANE of sites are not supportedby the fact that in Drosoph- 1931; WEINSTEIN1936) since, compared to a Poisson ila some chromosomal sequences thatare moved distribution with the same average, the number of adopt the exchange distribution characteristic of the Drosophila X chromosomes with no crossovers was new location (BAKERand CARPENTER 1972). Further- underrepresented and the number with one or two more, in Saccharomyces the allelic recombination rate crossovers was overrepresented. The distributions of of a DNA sequence varies significantly, depending on late nodules, chiasmata, and crossovers are nonuni- its location in the genome (LICHTEN,BORTS and HA- form in terms of position along chromosomes and BER 1987).It is also clear from fine-scale genetic nonrandom in terms of distances between them. The analysis that there are many sites at which recombi- positions of crossovers along the telocentric X chro- nation may occur along a chromosome. However, in mosome of Drosophila tend to be centrally located in any one meiosis, recombination occurs at only a few single crossover tetrads and tend to have one cross- of these sites. over near the centromere and the other crossover Other models are based on pairing, in whichcertain near the distal telomere in double crossover tetrads chromosomal regions are assumed to pair first and (CHARLES 1938). are therefore more likely to undergo recombination. Several models have been proposed to account for However,without additional assumptions this does either interference or the distributions of chiasmata not account foreither interferenceor for theobserved alongchromosomes (for review see JONES 1984). distribution of crossovers between chromosomes. Still Some of the models address interference but fail to other models are steric, i.e. the molecules that catalyze account for the observed distributions of chiasmata recombination eventsphysically blockadjacent events. between chromosomes. Others models only address It is difficult to account for the nonrandom distribu- the distributions of chiasmata and donot account for tion of events betweenchromosomes with these interference. A model of particular interest was pro- models, and based on electron micrographs, it is dif- posed by EGELin 1978. EGEL’Smodel is based on ficult to explain how a few nodules that are small possibilities of exchanges that are established before relative to the length of the synaptonemal complex synapsis and serve as initiation centers ofsynapsis. could have such a strongeffect on each other. Another Synapsis is then followed by formation of synaptone- criticism is that the source of the steric interference mal complex, which prevents