A diffusion model for mesoderm induction in amphibian embryos

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.

Morphogen gradients, positional information, and Xenopus: Interplay of theory and experiment

“…Francis Crick, for example, argued that, by making reasonable estimates of the effective diffusion constants and taking into account the known times of patterning events (5-10 hr) and distances over which patterning occurs (less than 1 mm; Wolpert, 1969), a simple model could be constructed to make a gradient with passive diffusion of a small (300 -500 Da) molecule morphogen (Crick, 1970). A more detailed model using passive diffusion has even been made for the specific case of mesodermal patterning in Xenopus embryos (Weyer et al, 1977). In these models, a steady-state gradient is generated by assuming a morphogen source and a distal sink or a distributed decay of the morphogen.…”

Studies on the Formation and State of Determination of the Trunk Organizer in the Newt, Cynops Pyrrhogaster. Ii. Inductive Effect From the Underlying Cranial Archenteron Roof

“…These observations indicate that mesoderm formation in the dorsal marginal zone is not yet complete in the early gastrula stage. As pointed out by HOLTFRETER-BAN (4) and more recently by WEYER et al (30), this primary regional difference in the dorsal marginal zone is still labile and only corresponds partially to the ultimate regional differentiation pattern in the chordamesoderm.…”

Patterning principles of morphogen gradients

“…Due to Laplacian operators in spherical coordinates, a diffusive morphogen emanating from a local source and degraded throughout a spherical surface establish a gradient dependent on the radius of embryo; so does not maintain a scaling for size variations observed between embryos as detailed in Weyer et al . [ 126 ]. This 1977 study modelling Xenopus mesoderm induction proposed either source amplitude to be controlled with embryo sizes, for scale invariance, or sink to be effectively localized to distal end.…”