Abstract

Experimental studies of protein-pattern formation (both in vivo and in vitro) have stimulated new interest in the dynamics of reaction–diffusion systems. Much of the past theoretical work on pattern formation has focused on idealized two-component models in one spatial dimension. In contrast, biological systems comprise many different components with complex kinetic interactions that play out in three-dimensional geometries. I will present three case studies—each combining experiments and theory—which demonstrate that biological systems generically exhibit several distinct and coexisting pattern-forming mechanisms. The theoretical analysis is based on local equilibria theory which describes the dynamics of mass-conserving reaction–diffusion systems terms of mass-redistribution and moving local equilibria. Based on this physical foundation, I will show how coexisting mechanisms can emerge from (i) different interaction domains on a single protein species (MinDE system of E. coli), (ii) different submodules within a network of many protein species (Cdc42 system of budding yeast), and (iii) due to different bulk-volume to surface-area ratios (MinDE system of E. coli). This third study highlights the essential role of spatial geometry for systems with bulk-surface coupling.