Author(s)： Hiroshi Yoshida

J. Math-for-Ind. 3B (2011) 93-98.

• File： JMI2011B-1.pdf (143KB)

Abstract
Regeneration phenomena in cricket legs and Planarians have recently been studied at the single cellular level. Within a cell, Dachsous and Fat molecules, and between cells, Dachsous-Fat heterodimers, are considered related to regeneration phenomena. Inspired by recent studies on Dachsous and Fat, we modeled a cell chain with heterodimers and analyzed it. We parameterized redistribution of heterodimers during cell division, which is poorly understood. We then derived equations in parameters to regenerate the heterodimeric pattern even if part of the cell chain is excised. This excision model contained eight parameters, and hence we used a few algebraic methods to suit models that are described by a set of polynomials. A number of biological phenomena have recently been analyzed through algebraic methods; thereby, we can directly derive equations in parameters. The derived equations show that some specific relation between the redistribution ratio of heterodimers allows a cell chain to regenerate its heterodimeric pattern.

Keyword(s).　 Dachsous-Fat system, regeneration, algebraic methods, developmental biology