Spontaneous Biological Pattern Formation in the Three-Dimensional Sphere. Prepatterns in Mitosis and Cytokinesis

Abstract

Spontaneous pattern formation may arise in (bio) chemical networks coupled to diffusion, i.e. an initial homogeneous distribution of certain chemical species may become unstable by changing variables such as enzyme activity or simply the size (radius) of the sphere. Hereby a new inhomogeneous, yet stable, concentration distribution is set up within the sphere, without any outside control imposing the geometry of the pattern, which is created spontaneously. Such spatial dissipative structures, or Turing structures, give rise to gradient- formation, i.e. high concentration at one (spontaneously created) pole and low at the opposite pole, a phenomenon of particular interest in the context of prepattern formation in blastulas. They also give rise to a bipolar concentration pattern, which should be an ideal prepattern for spindleformation and chromosome distribution in the process of mitosis (cell division).