Alternative mechanisms of structuring biomembranes: self-assembly versus self-organization.

We study two mechanisms for the formation of protein patterns near membranes of living cells by mathematical modelling. Self-assembly of protein domains by electrostatic lipid-protein interactions is contrasted with self-organization due to a nonequilibrium biochemical reaction cycle of proteins near the membrane. While both processes lead eventually to quite similar patterns, their evolution occurs on very different length and time scales. Self-assembly produces periodic protein patterns on a spatial scale below 0.1 microm in a few seconds followed by extremely slow coarsening, whereas self-organization results in a pattern wavelength comparable to the typical cell size of 100 microm within a few minutes suggesting different biological functions for the two processes.