Pattern formation mechanisms of self-organizing reaction-diffusion systems.

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.

Morphogenesis in robot swarms.

Morphogenesis allows millions of cells to self-organize into intricate structures with a wide variety of functional shapes during embryonic development. This process emerges from local interactions of cells under the control of gene circuits that are identical in every cell, robust to intrinsic noise, and adaptable to changing environments. Constructing human technology with these properties presents an important opportunity in swarm robotic applications ranging from construction to exploration.

High-throughput mathematical analysis identifies Turing networks for patterning with equally diffusing signals.

The Turing reaction-diffusion model explains how identical cells can self-organize to form spatial patterns. It has been suggested that extracellular signaling molecules with different diffusion coefficients underlie this model, but the contribution of cell-autonomous signaling components is largely unknown. We developed an automated mathematical analysis to derive a catalog of realistic Turing networks.