Effects of membrane curvature on molecular sorting

Molecular sorting is the main biological mechanism, which allows eucaryotic cells to organize chemical factors in specific membrane regions, in order to maintain their functions. A recent phenomenological theory has proposed that this process could occur by combining two physical phenomena: molecular self-aggregation and vesicle nucleation. To further investigate molecular sorting, these previous works introduced a minimal lattice-gas model and described the lipid membrane as a two-dimensional flat surface. Here, we develop the model, considering various aspects of molecular sorting on different surfaces, which describe the lipid membrane, in order to analyse the possible effects due to curvature. Based on previous studies, our goal is to show that nucleation and domain extraction occur more in regions with high curvature. For this purpose, we study the phenomenon of molecular sorting on three fixed surfaces: a flat surface, with zero curvature, a spherical surface, with constant curvature and an ellipsoidal surface, with variable curvature. Furthermore, we also investigate various properties of nucleation and statistical correlation between domains. The membrane is simulated with a Gillespie algorithm, used to reproduce phenomena of insertion, diffusion, domain aggregation and extraction.