Cooperative engulfment of nanoparticles by membranes and vesicles

Cellular uptake and expulsion of nanoparticles and viruses often involves a substantial particle concentration at the cell membrane. These particles, many of which are distributed across the cell at relatively large distances, cooperate to enter or exit the cell, highlighting the importance of engulfment cooperativity. Here, we explore the cooperative entry and exit of two and multiple distant nanoparticles to and from curved vesicles, representing cellular endocytosis and exocytosis, respectively. We discover indirect engulfment cooperativity between distant nanoparticles wrapped by vesicles, driven by vesicle curvature, which is absent for particles engulfed by a flat bilayer. For the cooperative entry of two identical particles into the vesicle, we identify a counter-intuitive symmetry-breaking in which one fully-engulfed and one non-engulfed particle is more likely than two fully-engulfed or two non-engulfed particles. As a result, with a high concentration of closely-sized external particles, only half of the particles are expected to be successfully internalized by the vesicle, while the remaining half remains unwrapped, and partially engulfed particles are unlikely. In contrast, the cooperative exit of internal particles from the vesicle is characterized by the simultaneous partial engulfment of the particles that are continuously wrapped by the vesicle. This explains how evolution has harnessed membrane curvature for the simultaneous budding of multiple viral particles, a crucial step in viral infection. Our findings for the cooperative entry of multiple particles have significant implication for achieving efficient drug concentration in drug delivery applications.