Multistability and hysteresis-based mechanism of pattern formation in biology

Abstract

Multistability plays an important role in cell signalling. Coupled with the diffusion process, it may give rise to spatial patterns in chemical and biological systems. Such processes lead to nonlinear dynamical models with multiple steady states, which differ from the usual reaction-diffusion systems. To investigate mechanism of pattern formation based on these concepts we propose a model consisting of a reaction-diffusion equation coupled with an ordinary differential equation. The test organism for mathematical modelling is a fresh-water polyp Hydra. The model considered here is a minimal version of the receptor-based model with multistability proposed by Marciniak-Czochra (Math Biosci 199:97-119, 2006). It describes the dynamics of nonlinear intracellular signalling coupled to cell-to-cell communication via diffusive molecules and shows how bistability and hysteresis in the kinetic system may result in spatial patterning. In particular, it is shown that multistability without the hysteresis effect is not enough for creation of stable patterns. Biologically, this model explains results of experiments such as grafting which are not easily explicable by the pure reaction-diffusion (Turing type) patterning. © Springer-Verlag Berlin Heidelberg 2013.