The mechanics of crossing-over

Abstract

A theoretical treatment of the frequency distribution of chiasmata along a chromosome is developed, based on Darlington’s postulate of relating crossing-over to chromosome coiling. Each chromatid is assumed to be an elastic thread subject to torsion and longitudinal stress, which is liable to break (but not yield) at a definite breaking load. It is supposed further that when an interchange occurs after a break, the consequential relief of torsional strain is confined to a small region round the location of the break, resulting in a lowering of the probability of a further break. The assumption about the effect of a break is formulated in a suitable way and an expression for the distribution function is thence derived. It is shown that in the limit of no interference this distribution goes over to the Poisson type, in conformity with Haldane’s conclusions. Expressions are calculated for the mean and the standard deviation of the distribution; the former gives the relation between the mean chiasma frequency and chromosome-length.