Shape and energy of a membrane bud induced by protein coats or viral protein assembly

Intracellular transport vesicles and enveloped virus production is mediated by the polymerization of proteins that form bi-dimensional curved and rigid structures, or "coats", on a membrane. Using the classical framework of fluid membrane elasticity, we compute numerically the shape and the mechanical energy of the membrane deformation induced by a coat at different stage of growth. We furthermore derive analytical approximate expressions for the membrane shape and energy. They are found to be very accurate when compared to numerical calculations. These analytical expressions should be useful when building a relevant model of coat polymerization kinetics. We also discuss some consequences of the membrane energy features on the coat assembly process, showing that at high tension a kinetically arrested state of incomplete assembly could exist.