Morphogen prepatterns during mitosis and cytokinesis in flattened cells: three dimensional Turing structures of reaction-diffusion systems in cylindrical coordinates.

Computer simulation of spontaneous morphogen prepattern formation (spatial dissipative structures, Turing structures) is studied during change from a spherical geometry to a flat cylinder (axis ratio 1:5), resembling compression of a spherical cell in metaphase to a flat disc. Abnormal forms of mitosis and cytokinesis have been reported experimentally during this process. The prepatterns obtained numerically account for several of these abnormalities, notably the occurrence of quadripartition in bipolar cells, or the arrest of cytokinesis. The prepatterns recorded may open a route for experimental testing of the prepattern model of mitosis and cytokinesis.