Hunding A
J Math Biol. 1984;19(3):249-63. doi: 10.1007/BF00277098.
Spontaneous pattern formation may arise in biological systems as primary and secondary bifurcations to nonlinear parabolic partial differential equations describing chemical reaction-diffusion systems. Bipolarity in mitosis and cleavage planes in cytokinesis may be related to this formation of prepatterns. Three dimensional prepatterns are investigated, as they emerge in flattened spheres (i.e. oblate spheroids). Pattern sequences and selection rules are established numerically. The results confirm previously recorded results of the spherical and prolate regions, upon which a prepattern theory of mitosis and cytokinesis is based. Especially, the phenomenon of 90 degree axis tilting and the formation of a highly symmetrical saddle shaped pattern, crucial for the prepattern theory of mitosis and cytokinesis, is examined. Present results show, that these phenomena are stabilized in oblate spheroids. The bipolar "mitosis" prepattern is found as well, although the polar axis may appear with an angle toward the axis of the oblate spheroid. These results are thus further support for the prepattern theory of mitosis and cytokinesis.
自发模式形成可能在生物系统中作为描述化学反应 - 扩散系统的非线性抛物型偏微分方程的一级和二级分岔而出现。有丝分裂中的双极性和胞质分裂中的分裂平面可能与此预模式的形成有关。研究了三维预模式，因为它们出现在扁平球体（即扁球体）中。通过数值方法建立了模式序列和选择规则。结果证实了之前关于球形和长球形区域的记录结果，有丝分裂和胞质分裂的预模式理论就是基于这些结果。特别是，研究了对于有丝分裂和胞质分裂的预模式理论至关重要的90度轴倾斜现象和高度对称的鞍形模式的形成。目前的结果表明，这些现象在扁球体中是稳定的。尽管极轴可能相对于扁球体的轴以一定角度出现，但也发现了双极“有丝分裂”预模式。因此，这些结果进一步支持了有丝分裂和胞质分裂的预模式理论。
