Physical interactions promote Turing patterns

TL;DR

This paper demonstrates that physical interactions between species significantly influence Turing pattern formation, reducing the need for large diffusion differences and linking pattern formation to phase separation phenomena.

Contribution

It introduces a model incorporating direct physical interactions into reaction-diffusion systems, revealing their impact on Turing patterns and connecting them to phase separation.

Findings

Weak repulsion lowers the diffusion and reaction requirements for patterns.

Strong interactions can cause phase separation with characteristic length scales.

Physical interactions must be considered for realistic modeling of pattern formation.

Abstract

Turing's mechanism is often invoked to explain periodic patterns in nature, although direct experimental support is scarce. Turing patterns form in reaction-diffusion systems when the activating species diffuse much slower than the inhibiting species, and the involved reactions are highly non-linear. Such reactions can originate from co-operativity, whose physical interactions should also affect diffusion. We here take direct interactions into account and show that they strongly affect Turing patterns. We find that weak repulsion between the activator and inhibitor can substantially lower the required differential diffusivity and reaction non-linearity. In contrast, strong interactions can induce phase separation, but the resulting length scale is still typically governed by the fundamental reaction-diffusion length scale. Taken together, our theory connects traditional Turing patterns with chemically active phase separation, thus describing a wider range of systems. Moreover, we demonstrate that even weak interactions affect patterns substantially, so they should be incorporated when modeling realistic systems.