A circuit basis for morphogenesis

Abstract

Morphogenesis is the generation of structural patterns through a dynamic process. The mathematical basis of morphogenesis has long been studied with the key initial work by Alan Turing. This paper explores the consequences of a circuit basis for reaction-diffusion systems on morphogenesis, including the reachability of patterns and the logical basis of pattern stability. We consider how morphological patterns can arise through iterative computation and produce robust forms. Through an exhaustive analysis of reaction-diffusion dynamics in a minimal model of morphogenesis, we show how the stability and reachability of morphologies are influenced by their circuit basis. We show that this model exhibits similar behavior to the recently experimentally observed dynamics not accounted for by Turing's original model. We conclude by presenting an additional class of metastable patterns exhibited in this model.