Numerical simulation of the stochastic dynamics of inclusions in biomembranes in the presence of surface tension

The stochastic dynamics of inclusions in a randomly fluctuating biomembrane is simulated. These inclusions can represent the embedded proteins and the external particles arriving at a cell membrane. The energetics of the biomembrane is modelled via the Canham-Helfrich Hamiltonian. The contributions of both the bending elastic-curvature energy and the surface tension of the biomembrane are taken into account. The biomembrane is treated as a two-dimensional sheet whose height variations from a reference frame are treated as a stochastic Wiener process. The lateral diffusion parameter associated with this Wiener process coupled with the longitudinal diffusion parameter obtained from the standard Einsteinian diffusion theory completely determines the stochastic motion of the inclusions. It is shown that the presence of surface tension significantly affects the overall dynamics of the inclusions, particularly the rate of capture of the external inclusions, such as drug particles, at the site of the embedded inclusions, such as the embedded proteins.