A diffusion model for mesoderm induction in amphibian embryos

Acta Biotheoretica 26 (3) (1977)
Abstract
In this paper we try to answer the question whether diffusion is a possible mechanism to explain mesoderm induction in Amphibians. First the embryological data are discussed and a hypothesis for mesoderm formation is set forth. The blastula being essentially a hollow sphere, we assume that the induction mechanism in an embryo at the blastula stage can be simulated by diffusion-reaction processes on spherical surfaces. A model is constructed for the simple case when the source is held constant with respect to time, the decay proportional to the concentration and the diffusion coefficient a constant, From simulation we find a (best) value for the decay constant to be 6 × 10–5/sec and for the diffusion constant to be 0.24 × 10– 6 cm2/sec. The relation between the parameters is derived from an analytic solution for the diffusion process on a spherical surface with a continuously producing point source and the concentration proportional to the decay. The form and regulative properties of the steady concentration gradient are discussed.
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