Pattern Formation at Cellular Membranes by Phosphorylation and Dephosphorylation of Proteins

We consider a classical model on activation of proteins, based in two reciprocal enzymatic biochemical reactions. The combination of phosphorylation and dephosphorylation reactions of proteins is a well established mechanism for protein activation in cell signalling. We introduce different affinity of the two versions of the proteins to the membrane and to the cytoplasm. The difference in the diffusion coefficient at the membrane and in the cytoplasm together with the high density of proteins at the membrane which reduces the accessible area produces domain formation of protein concentration at the membrane. We differentiate two mechanisms responsible for the pattern formation inside of living cells and discuss the consequences of these models for cell biology.