Permeability of immobile rings of membrane inclusions to in-plane flow

We study the flow of membranal fluid through a ring of immobile particles mimicking, for example, a fence around a membrane corral. We obtain a simple closed-form expression for the permeability coefficient of the ring as a function of the particles’ line fraction. The analytical results agree with those of numerical calculations and are found to be robust against changes in particle number and corral shape. From the permeability results, we infer the collective diffusion coefficient of lipids through the ring and discuss possible implications for collective lipid transport in a crowded membrane.