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A diffusion model for mesoderm induction in amphibian embryos.

C J Weyer·P D Nieuwkoop·A Lindenmayer
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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 x 10(-5)/sec and for the diffusion constant to be 0.24 x 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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AmphibiansAnimalsDiffusionEmbryo, NonmammalianMathematicsModels, BiologicalJournal Article

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C J Weyer, P D Nieuwkoop, A Lindenmayer. 1977. A diffusion model for mesoderm induction in amphibian embryos.. https://doi.org/10.1007/bf00048425

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