Correlated dynamics of inclusions in a supported membrane

TL;DR

This paper extends the hydrodynamic theory of supported membranes to include substrate effects, deriving how membrane inclusions influence diffusion and response at various distances, with implications for membrane biophysics.

Contribution

It provides new analytical expressions for coupling diffusion coefficients of inclusions in supported membranes, accounting for substrate proximity and inclusion concentration effects.

Findings

Coupling coefficients decay as 1/r^2 at large distances.

Inclusions modify membrane response at short distances, resembling a 2D suspension.

Large-distance response remains unaffected by inclusions.

Abstract

The hydrodynamic theory of heterogeneous fluid membranes is extended to the case of a membrane adjacent to a solid substrate. We derive the coupling diffusion coefficients of pairs of membrane inclusions in the limit of large separation compared to the inclusion size. Two-dimensional compressive stresses in the membrane make the coupling coefficients decay asymptotically as $1/r^2$ with interparticle distance $r$. For the common case, where the distance to the substrate is of sub-micron scale, we present expressions for the coupling between distant disklike inclusions, which are valid for arbitrary inclusion size. We calculate the effect of inclusions on the response of the membrane and the associated corrections to the coupling diffusion coefficients to leading order in the concentration of inclusions. While at short distances the response is modified as if the membrane were a two-dimensional suspension, the large-distance response is not renormalized by the inclusions.