Reaction–Diffusion and Diffusion-Driven Fronts in Reversible Redox Autocatalytic Networks

Abstract

Autocatalysis plays a critical role in the self-organization of chemical and biological systems, influencing phenomena such as bistability and reaction–diffusion front formation. In the rhizosphere, the regulation of reactive oxygen species (ROS) is mediated by intricate networks of reversible autocatalytic reactions, yet the mechanisms governing their spatiotemporal dynamics remain unclear. Here, we perform comprehensive numerical simulations of a reaction–diffusion model for ROS dynamics incorporating redox couples, sodium borohydride, and oxygen. We identify oxidation-driven autocatalysis as the primary mechanism responsible for the emergence of stable reaction–diffusion fronts that propagate with constant velocity and shape, whereas reduction fronts display diffusive broadening attenuated by the local oxygen concentration. Furthermore, we demonstrate that reversible quadratic autocatalytic cycles coupled to a simple autocatalyst removal and diffusion are sufficient to reproduce these characteristic front behaviors. These results also provide insights that are transferable to a wide range of autocatalytic networks exhibiting spatiotemporal pattern formation.