Self-Organized Molecular Sorting on Fluid Membranes

Molecular sorting is a fundamental process responsible for the organization of matter in eukaryotic cells. It allows cells to counteract the homogenizing effect of diffusion, and to maintain different functional properties in appropriated membrane subregions. A recent phenomenological theory proposes that this process could emerge from two main physical phenomena, (a) phase separation induced by molecular self-aggregation and (b) vesicle nucleation due to a coupling between particle presence and membrane spontaneous curvature. To further explore this theory preceding works introduced a minimal lattice gas model, in which the membrane is described as a flat two dimensional surface, and investigated its stationary state numerically. In this work the model is extended to take place on a fluid membrane. This allows to introduce an interaction between the presence of particles and the surface spontaneous curvature, which couples the molecular sorting process with surface fluctuations. The membrane is described using the Helfrich Hamiltonian, which allows to do some theoretical predictions, and simulated employing a Dynamically Triangulated Monte Carlo (DTMC) model. The latter is used to simulate both thermal fluctuations and diffusion of the surface, onto which particles behaving accordingly to a Markov process of insertion, domain aggregation and extraction are insterted and coupled with curvature. Various properties of both the membrane and the distillation process are investigated at different values of the particle curvature coupling and the elastic constant.