Molecular sorting on a fluctuating membrane

Molecular sorting is a fundamental ordering process taking place in eukaryotic cells, whereby proteins and other biomolecules are sorted and distilled into lipid vesicles. This process aims at countering the homoge- nizing effect of diffusion. Molecules attach to lipid membranes and later- ally diffuse, then due to a variety of direct and indirect interactions, these molecules tend to aggregate in domains characterized by specific chemical compositions. In their turn, such may promote membrane bending and fission, and are ultimately packed into lipid vesicles, that are then deliv- ered to appropriate intracellular destinations with the aid of molecular motors. This vesicles distillation phenomenon can be investigated from a physics perspective. The process of molecules attaching and sorting on the membrane and then being extracted as aggregates can be seen as a system driven out of its thermodynamic equilibrium which eventually reaches a stationary state. In previous studies this phenomenon was in- vestigated without accounting for the effect of membrane fluctuations and molecules coupling to the membrane. However the presence of biomolec- ular inclusions on the membrane perturbs locally some of its properties (e.g. bending rigidity or local spontaneous curvature) and gives rise to membrane-mediated interactions between inclusions. This kind of inter- actions have been widely studied since the 90s. Seems thus reasonable to ask what is the role of these fluctuation-induced interactions in the process of distillation taking place on lipid membranes. These long-range membrane-mediated interactions are not pairwise additive, thus their ef- fect on the process of molecular sorting, where the membrane is rich of inclusions, is non-trivial. In this work this phenomenon is investigated numerically, with particular interest on the efficiency of the sorting pro- cess.