Modelling meso-scale diffusion processes in stochastic fluid bio-membranes

The space-time dynamics of rigid inhomogeneities (inclusions) free to move in a randomly fluctuating fluid biomembrane is derived and numerically simu lated as a function of the membrane shape changes. Both vertically placed ( embedded) inclusions and horizontally placed (surface) inclusions are consi dered. The energetics of the membrane, as a two-dimensional (2D) meso-scale continuum sheet, is described by the Canham-Helfrich Hamiltonian, with the membrane height function treated as a stochastic process. The diffusion pa rameter of this process acts as the link coupling the membrane shape fluctu ations to the kinematics of the inclusions. The latter is described via Ito stochastic differential equation. In addition to stochastic forces? the in clusions also experience membrane-induced deterministic forces. Our aim is to simulate the diffusion-driven aggregation of inclusions and show how the external inclusions arrive at the sites of the embedded inclusions. The mo del has potential use in such emerging fields as designing a targeted drug delivery system. (C) 1999 Elsevier Science B.V. All rights reserved.