A mechanistic model for morphogenesis and regeneration of limbs and imaginal discs.

When an amphibian limb, cockroach leg or Drosophila imaginal disc is subjected to a surgical operation, it is capable of regenerating or duplicating certain parts. Although the structure of the regenerated tissue varies depending on the location and mass of the amputated or transplanted part, it can be predicted from a set of formal rules, called the polar coordinate model [French et al., (1976) Science 193, 969-983; Bryant et al., (1981) Science 212, 993-1002]. In the polar coordinate model, it is assumed (and experimentally proven) that the juxtaposition of normally non-adjacent cells stimulates cell proliferation locally, which implies that the underlying mechanism which gives positional values to each cell, is also responsible for the control of cell growth. Because locally activated proliferation alters the shape and size of the developmental field, the question of how to control the cell growth is the central problem in the regeneration of the limbs and imaginal discs. In this paper, I propose a possible underlying mechanism for the 'polar coordinate rules', and show how this mechanistic model explains the experimental results using computer simulation. The proposed mechanism is an extension of Turing's model (1952). In addition to the reaction-diffusion of the molecules, cell proliferation is taken into consideration. With appropriate initial conditions, the computer simulation shows that a small mass of cells grows up to form a mature limb, and that the mature limb is able to respond to surgical operations as predicted by the polar coordinate model.