Computations of post‐inductive dynamics in axolotl heart formation

Abstract

This paper reports modelling of heart localization in the axolotl (Ambystoma mexicanum). The region of heart specification in the mesoderm defined by classical induction from the endoderm is larger than the area of final myocardial differentiation. For localizing the area of differentiation within the area of specification, we postulate a reaction-diffusion system that arises within the mesoderm in response to induction from the endoderm. This mechanism generates a spatial pattern for two chemicals, an activator and an inhibitor, corresponding to the area of myocardial differentiation. We postulate a diffusible chemical rescuer, which is absent in the cardiac lethal mutant, and which is a precursor to the reaction-diffusion mechanism. The activator, inhibitor, rescuer, and product of endodermal induction are presented in an enzyme mechanism with rate equations similar to the Gierer-Meinhardt equations. These equations were solved numerically in both one and two spatial dimensions. We have attained quantitative agreement with the experimental data for sizes of tissue regions and for times to heartbeat. Experiments modelled include wild-type heart localization as well as both in vitro and in vivo rescue of cardiac lethal mesoderm with wild-type mesoderm. Based upon the parameters necessary to model heart localization, we make a series of predictions. We predict: a specific profile for the endodermal inducer gradient; the possibility of producing multiple hearts in vivo; and a greater contribution to the heart from the wild-type mesoderm for in vivo transplants with cardiac lethal mesoderm. We make some suggestions as to the possible chemical nature of the substances in the model. We indicate that the inhibitory field and mechanochemical theories are probably not as promising as reaction-diffusion for the mechanism of heart localization.