Matter exchange as a physical mechanism for pattern formation in membranes

Heterogeneous lipid composition in cell membranes is key to biological function, acting as one of the main mechanisms to exchange information between cells or between a cell and its environment. The underlying mechanisms controlling pattern formation are still under debate. In this work, we consider a theoretical phase-field model to describe the composition of a two-dimensional membrane exchanging matter with a reservoir. The model includes matter absorption and desorption in the membrane with different rates. By only assuming matter conservation in the system membrane-reservoir, we show with extensive numerical simulations that, depending on these rates, a complex patterned composition distribution emerges in the membrane. The pattern emergence is due to Spatio-temporal memory effects. With a semi-analytical argument, we compute the typical size of domains as a function of the absorption and desorption rates. We find scaling relations that are in excellent agreement with our numerical simulations. Our results show that the causes of heterogeneous lipid composition may be justified in simple physical terms.