Mechanics of receptor-mediated endocytosis

Abstract

Most viruses and bioparticles endocytosed by cells have characteristic sizes in the range of tens to hundreds of nanometers. The process of viruses entering and leaving animal cells is mediated by the binding interaction between ligand molecules on the viral capid and their receptor molecules on the cell membrane. How does the size of a bioparticle affect receptor-mediated endocytosis? Here, we study how a cell membrane containing diffusive mobile receptors wraps around a ligand-coated cylindrical or spherical particle. It is shown that particles in the size range of tens to hundreds of nanometers can enter or exit cells via wrapping even in the absence of clathrin or caveolin coats, and an optimal particles size exists for the smallest wrapping time. This model can also be extended to include the effect of clathrin coat. The results seem to show broad agreement with experimental observations.

Fig. 1.

The life cycle of an animal virus. (a) Adsorption or docking with the host receptor protein. (b) Entry into the host cytoplasm. (c) Biosynthesis of viral components. (d) Assembly of viral components into complete viral units. (e) Budding from the host cell.

Fig. 2.

Schematic illustration of the problem. (a) An initially flat membrane containing diffusive receptor molecules wraps around a ligand-coated particle. (b) The receptor density distribution in the membrane becomes nonuniform upon ligand-receptor binding; the receptor density is depleted in the near vicinity of the binding area and induces diffusion of receptors toward the binding site.

Fig. 3.

The normalized minimum wrapping radius versus the receptor density ratio for uptake of a cylindrical particle (solid curve) and a spherical particle (dashed curve) into a membranes of infinite size.

Fig. 4.

The normalized wrapping time t_w/(B/ξ_LD) versus the normalized particles radius with and e_RL = 15 for uptake of a particle into an infinite membrane (dashed curve) and a finite membrane (solid curve). In the case of a finite membrane, B = 20, ξ_L = 5 × 10³/μm², and L = 10 μm. (a) Cylindrical particle with normalized minimum and maximum wrapping radii of 0.21 and 0.5. (b) Spherical particle with normalized minimum and maximum wrapping radii of 0.42 and 7.9.

Fig. 5.

The normalized optimal radius and the normalized optimal wrapping time t^*/(B/ξ_LD) versus the receptor density ratio for uptake of a cylindrical particle (solid curve) and a spherical particle (dashed curve) into a membrane of infinite size. Here, we have taken e_RL = 15 with the critical receptor density ratio . (a) Optimal radius. (b) Optimal wrapping time.