Pattern formation mechanisms of self-organizing reaction-diffusion systems

Abstract

Embryonic development is a largely self-organizing process, in which the adult body plan arises from a ball of cells with initially nearly equal potency. The reaction-diffusion theory first proposed by Alan Turing states that the initial symmetry in embryos can be broken by the interplay between two diffusible molecules, whose interactions lead to the formation of patterns. The reaction-diffusion theory provides a valuable framework for self-organized pattern formation, but it has been difficult to relate simple two-component models to real biological systems with multiple interacting molecular species. Recent studies have addressed this shortcoming and extended the reaction-diffusion theory to realistic multi-component networks. These efforts have challenged the generality of previous central tenets derived from the analysis of simplified systems and guide the way to a new understanding of self-organizing processes. Here, we discuss the challenges in modeling multi-component reaction-diffusion systems and how these have recently been addressed. We present a synthesis of new pattern formation mechanisms derived from these analyses, and we highlight the significance of reaction-diffusion principles for developmental and synthetic pattern formation.

Highlights

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  The reaction-diffusion theory has been proposed to explain self-organized pattern formation during development.

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  Recent mathematical analyses of realistic reaction-diffusion systems challenge central previous tenets in the field.

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  The novel theoretical insights can drive advances in developmental and synthetic biology.