A two-component model for phase separation driven molecular sorting

Molecular sorting is a highly complex process taking place in eukaryotic cells, in which specific cargo molecules are collected in vesicles and dispatched to appropriate destinations. The first fundamental step of sorting, vesicle formation, is possible through the aggregation, on the membrane, of cargo molecules and a number of different endocytic proteins. The formation of such aggregate promotes membrane bending, leading to the budding and the extraction of a vesicle enriched with the engulfed molecular components. Recently, a theoretical model of this process was proposed, where the following events are described: proteins arrive on a membrane region, diffuse and aggregate into localized enriched domains, that are ultimately extracted after reaching a characteristic size. Under appropriate conditions, the system self-organizes into a driven non-equilibrium stationary state, that is characterized by the coexistence of phase-separated sorting domains with a gas of freely diffusing molecules. In that prototypical model the aggregation of proteins of a single type was considered, however this is far from the actual biological process. To take more into account the complexity of the phenomenon, here we propose a two-component model, in which sorting domains are formed by the aggregation of two species: cargo and auxiliary molecules. Cargo can only diffuse laterally once inserted into the membrane, implying that its concentration field is locally conserved. Auxiliary molecules are present in a fixed number and are recycled after each extraction event. Differently from the cargo, auxiliaries are able to shuttle between membrane and cytosol, where their diffusivity is much faster then on the membrane. This fast redistribution mechanism implies that the concentration field of the auxiliaries is approximately globally - but not locally - conserved on the membrane. By extensive numerical investigation we show that our model is characterized by a rich phenomenology, where the stability of low density stationary states changes as a function of the number of auxiliaries and of the aggregation parameter. This results in a new, sharp transition between a parameter region where sorting occurs under optimal conditions and neighboring regions where sorting is disfavoured. Simulations also show the appearance of a parameter region where peculiar cascade effects in the extraction events are observed. Finally, we observed that faster shuttling of the auxiliary molecules can increase the efficiency of the sorting process.