For cellular functions like cell division and polarization, protein pattern formation driven by NTPase cycles is a key spatial control strategy. Analyzing the robustness of cell-division control in E. coli by pole-to-pole oscillations of the Min protein system, one is driven to ask how the structure of highly nonlinear reaction–diffusion patterns can be predicted from the underlying reaction networks. We show that a central concept from equilibrium physics—interfacial tension—arises in an effective manner from distinct underlying physics in intracellular protein patterns: The cyclic, NTPase-driven attachment and detachment of proteins at pattern interfaces. We introduce “Turing mixtures” and “foams” by developing generalized Neumann and Plateau laws for interface junctions and foam vertices. Our theory describes central features of the stationary patterns formed by the Min system in vitro. In contrast to liquid foams, we demonstrate that interfacial-tension-driven coarsening can be interrupted, and an intrinsic pattern wavelength selected. Our approach offers a new understanding of self-organization in non-equilibrium systems governed by a conservation law.
Hosts: Michael Abbott, Isabella Graf, and Mason Rouches
