Hysteresis-driven Structure Formation in Biochemical Networks

A mechanism of structure formation, based on hysteresis behaviour is presented. A bisubstrate kinetic system with substrate inhibition, discussed previously in the context of Turing structure formation, may show hysteresis behaviour, when embedded in a metabolic network: the system may possess multiple steady states and may be switched from one stable fixpoint to the other. When cells containing this type of system are diffusively coupled, under certain conditions patterns result, which, as is demonstrated, are not of the Turing type. The main difference to diffusion-driven (Turing) structures is the fact that the hysteresis-driven patterns emerge under diffusive conditions, under which both the homogeneous and the asymmetrical steady state is stable. The resulting special properties and biological implications are discussed.