  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 micron 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
micron within a few minutes suggesting different biological functions for the
two processes.
