Analytical investigation of non-Fickian receptor-mediated endocytosis

The most important process in which viruses and bioparticles can enter the animal cell is receptor mediated endocytosis. The main propellant of this phenomenon is the attraction between receptor molecules floating in the lipid bilayer membrane of the host cell and ligand molecules on the target. In this paper, the aforementioned phenomenon is investigated analytically assuming that the diffusion model of the receptor molecules in the lipid bilayer is non-Fickian. Penetration time of the target molecule in the host cell shows that there is a critical limit for the target molecule size. The molecules larger than this critical size will experience an oscillatory motion without passing the host cell membrane. For instance, it is found that the maximum diameter for a typical target molecule with dimensionless relaxation time of 5 for receptor diffusion into a cell membrane is 0.22 of the membrane length.