Theoretical analyses of chiasmata using a novel chiasma graph method applied to Chinese hamsters, mice, and dog.

Some basic concepts of chiasma (including chiasma distribution, chiasma frequency, interstitial and terminal chiasmata, and chiasma interference) are reexamined theoretically in the light of gene shuffling, and a new method for chiasma analysis termed the chiasma graph is proposed. Chiasma graphs are developed for three mammals with greatly different chromosome numbers: Chinese hamster (with n = 11), mice (n = 20), and a dog (n = 39). The results demonstrate that interstitial chiasmata can contribute both to gene shuffling and to the binding of bivalents, but that so-called terminal chiasmata are in fact mostly achiasmatic terminal associations, the main function of which is to bind bivalents. For this reason, terminal chiasmata should be excluded when chiasma frequency is estimated. It is also demonstrated that interstitial chiasmata distribute on bivalents randomly and uniformly, except at the centromere and telomere. Interference distance fluctuates almost randomly above a minimum value equivalent to about 1.8% of total bivalent length at diakinesis. These results indicate that chiasma formation in mammals is principally a random event. The demonstrated minimum interference distance seems consistent with the polymerization model for chiasma formation. Some cytological aspects of crossing-over are discussed with reference to the minimum interaction theory for eukaryotic chromosome evolution.