Diffuso-kinetic membrane budding dynamics

Abstract

A wide range of proteins are known to create shape transformations of biological membranes, where the remodelling is a coupling between the energetic costs from deforming the membrane, the recruitment of proteins that induce a local spontaneous curvature C₀ and the diffusion of proteins along the membrane. We propose a minimal mathematical model that accounts for these processes to describe the diffuso-kinetic dynamics of membrane budding processes. By deploying numerical simulations we map out the membrane shapes, the time for vesicle formation and the vesicle size as a function of the dimensionless kinetic recruitment parameter K₁ and the proteins sensitivity to mean curvature. We derive a time for scission that follows a power law ∼K₁^−2/3, a consequence of the interplay between the spreading of proteins by diffusion and the kinetic-limited increase of the protein density on the membrane. We also find a scaling law for the vesicle size ∼1/(_avC₀), with _av the average protein density in the vesicle, which is confirmed in the numerical simulations. Rescaling all the membrane profiles at the time of vesicle formation highlights that the membrane adopts a self-similar shape.