  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 is 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 determine 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.
