Theoretical evidence that more microtubules reach the cortex at the pole than at the equator during anaphase in sea urchin eggs

Astral microtubules are rapidly elongated during anaphase and telophase in sea urchin eggs. The number of microtubules extending to the cell surface was calculated with a computer. For the calculations, microtubules were assumed to radiate from the astral center uniformly over angles. Although microtubules from two asters freely overlapped around the equator, the number per the unit area, i.e. the surface density, was larger in the polar region than in the equatorial region. The ratio of the theoretically calculated numbers in the two regions was close to the ratio obtained from the ultrastructural observations by Asnes and Schroeder in 1979. When counted in the longitudinal section including two astral centers, the microtubule number was a little larger in the equatorial region than in the polar region. However, the numbers do not represent the surface density because the two-dimensional section contains only a small portion of all the microtubules spreading in the three-dimensional space. The fluorescence image for tubulin, in most cases, provides the microtubule distribution in the longitudinal section. Therefore, from such an image, we cannot judge whether the surface density of astral microtubules is larger at the pole or at the equator.