Exact theoretical study of diffusion of nanoparticles around cell-membranes

Abstract

The aim of this work is a theoretical study of normal and anomalous diffusion laws of nanoparticles moving freely around an interacting cell-membrane. Using generalized Langevin and Smoluchowski equations theories which are equivalent, we determined the time variation of mean square displacement, time diffusion coefficient and variance of position. The essential conclusion is that, at large times, the diffusion of the target nanoparticle is faster, in intermediate times, the movement is slow, and in large times, the movement is blocked in the perpendicular direction to the cell-membrane. Finally, the cage effect was also discussed.