An allometric relationship between mitotic spindle width, spindle length, and ploidy in Caenorhabditis elegans embryos

The mitotic spindle is a diamond-shaped molecular apparatus crucial for chromosomal segregation. The regulation of spindle length is well studied, but little is known about spindle width. Previous studies suggested that the spindle can self-organize to maintain a constant aspect ratio between its length and width against physical perturbations. Here we determine the widths of metaphase spindles of various sizes observed during embryogenesis in Caenorhabditis elegans, including small spindles obtained by knocking down the tpxl-1 or spd-2 gene. The spindle width correlates well with the spindle length, but the aspect ratio between the spindle length and spindle width is not constant, indicating an allometric relationship between these parameters. We characterize how DNA quantity (ploidy) affects spindle shape by using haploid and polyploid embryos. We find that the length of the hypotenuse, which corresponds to the distance from the apex of the metaphase plate to the spindle pole, remains constant in each cell stage, regardless of ploidy. On the basis of the quantitative data, we deduce an allometric equation that describes the spindle width as a function of the length of the hypotenuse and ploidy. On the basis of this equation, we propose a force-balance model to determine the spindle width.