Pattern formation by electrostatic self-organization of membrane proteins

The electric activity of biological cells and organs such as heart for example is at the origin of various phenomena of pattern formation. The electric membrane potential appears as the order parameter to characterize these spatiotemporal dynamics. A kind of patterns is characterized by a stationary spatial modula- tion of membrane potential along the cell, breaking a symmetry of the system. They are associated to transcellular currents. A mechanism proposed in liter- ature is based on the coupling of the electric current produced by membrane proteins and their electrophoretic mobilities. Beyond its classical linear sta- bility analysis, the numerical and theoretical analysis of this model offers a variety of spatiotemporal dynamics. Firstly, the background in the modeliza- tion of electric phenomena is recalled. Secondly, the analysis is focused on two nonlinear dynamics.