Models of metaphase I quadrivalent positioning in Allium triquetrum

Abstract

Diagrammatic and trigonometric models are described for the positioning of the 4/6 interchange quadrivalent at metaphase I in Allium triquetrum. The models predict a series of distributions for quadrivalent position in lateral squashes of metaphase I chromosomes and establish the theoretical restrictions for quadrivalent positioning on the metaphase plate. The models are also used to investigate the effect of the squash on chromosome position. The models assume that components of the quadrivalents take up positions on the metaphase plate in arrangements similar to those of normal bivalents; that all pollen mother cells have an equal chance of being squashed through any plane; and that bivalents and quadrivalents are affected equally, and are projected in parallel during the squash procedure. Polar view drawings of A. triquetrum metaphase I pollen mother cells provide the empirical base for the modelling procedures. To model the random placement of quadrivalents on the metaphase plate, theoretical quadrivalent placements are assigned to neighbouring pairs of positions normally held by bivalents in the polar view drawings. The polar view positions are projected onto a linear array to simulate the squashing procedure in actual cells. Polar view quadrivalent placements are translated into positions along this array and the positions of the placements are recorded using the notation employed by Rickards (1984, 1985). This modelling procedure was carried out on 100 polar views each with a single plane of projection (Single Angle Projection Squash model) and on a single stylised polar view with multiple planes of projection (Multiple Angle Projection Squash model). The model data was compared with four sets of observed data from Rickards (1984, 1985) to test whether the latter conform to a random or non-random positional distribution. The original forms of the models predict only one of the observed set distributions (alternate medium), but with modification of the acceptance criteria for quadrivalent placements, the models predict the distributions for a further two observed sets (alternate low, alternate high). The remaining observed set distribution (adjacent) can be predicted only if the model assumption that all cells have an equal chance of being squashed through any plane is rejected. The model results provide corroborative evidence of the non-random positioning of the 4/6 quadrivalent at metaphase I. Model results also indicate that some forms of non-random chromosome positioning can be detected using the squash procedure even if the planes of squash employed are random.