Travelling lipid domains in a dynamic model for protein-induced pattern formation in biomembranes.

Cell membranes are composed of a mixture of lipids. Many biological processes require the formation of spatial domains in the lipid distribution of the plasma membrane. We have developed a mathematical model that describes the dynamic spatial distribution of acidic lipids in response to the presence of GMC proteins and regulating enzymes. The model encompasses diffusion of lipids and GMC proteins, electrostatic attraction between acidic lipids and GMC proteins as well as the kinetics of membrane attachment/detachment of GMC proteins. If the lipid-protein interaction is strong enough, phase separation occurs in the membrane as a result of free energy minimization and protein/lipid domains are formed. The picture is changed if a constant activity of enzymes is included into the model. We chose the myristoyl-electrostatic switch as a regulatory module. It consists of a protein kinase C that phosphorylates and removes the GMC proteins from the membrane and a phosphatase that dephosphorylates the proteins and enables them to rebind to the membrane. For sufficiently high enzymatic activity, the phase separation is replaced by travelling domains of acidic lipids and proteins. The latter active process is typical for nonequilibrium systems. It allows for a faster restructuring and polarization of the membrane since it acts on a larger length scale than the passive phase separation. The travelling domains can be pinned by spatial gradients in the activity; thus the membrane is able to detect spatial clues and can adapt its polarity dynamically to changes in the environment.