Budding of an Adhesive Elastic Particle out of a Lipid Vesicle

The problem of particle budding out of a lipid vesicle is of fundamental importance to our understanding of the biophysical mechanisms involved in viral budding and exocytosis. Here, we present a theoretical study on the outward budding of an adhesive elastic particle out of a lipid vesicle of different spontaneous curvatures. It is shown that a discontinuous shape transformation can occur for budding out of a vesicle with positive spontaneous curvature but not for a vesicle with zero or negative spontaneous curvature, and that softer particles require stronger adhesion energy to achieve full release from the vesicle. Calculations also indicate that the adhesion energy required for full release increases as the spontaneous curvature of the vesicle decreases. A rich variety of budding phase diagrams accounting for the stable or metastable states of no budding, partial budding, and full release are determined. Endocytosis, exocytosis, intracellular budding of elastic particles and related biological implications are discussed. Our results provide physical insights into the biophysical mechanisms of viral budding and exocytosis, and may also provide rational design guidelines for controlled drug delivery systems.