Self-organisation and pattern formation in cellular systems

Protein pattern formation is essential for the spatial organization of many intracellular processes like cell division, flagellum positioning, and chemotaxis. A prominent example of intracellular patterns are the oscillatory pole-to-pole oscillations of Min proteins in E. coli whose biological function is to ensure precise cell division. Cell polarization, a prerequisite for processes such as stem cell differentiation and cell polarity in yeast, is also mediated by a diffusion-reaction process. More generally, these functional modules of cells serve as model systems for self-organization, one of the core principles of life. Under which conditions spatio-temporal patterns emerge, and how these patterns are regulated by biochemical and geometrical factors are major aspects of current research.


In this talk we will present a new theoretical framework to characterize pattern forming systems arbitrarily far from global equilibrium. We will show that reaction-diffusion systems that are driven by locally mass-conserving interactions can be understood in terms of local equilibria of diffusively coupled compartments. Diffusive coupling generically induces lateral redistribution of the globally conserved quantities, and the variable local amounts of these quantities determine the local equilibria in each compartment. We find that, even far from global equilibrium, the system is well characterized by its moving local equilibria. These insight lead to the identification of general design principles of cellular pattern forming systems. We will show how they are implemented for the respective specific biological function in cell division of E. coli and cell polarization in yeast. More broadly, these results reveal conceptually new principles of self-organized pattern-formation that may well govern diverse dynamical systems.