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

## TL;DR

This paper derives a simple formula for the permeability of a ring of immobile membrane particles, providing insights into lipid transport in crowded membranes and validating results with numerical simulations.

## Contribution

It introduces an analytical expression for ring permeability that is robust and applicable to various particle arrangements, advancing understanding of membrane transport.

## Key findings

- Analytical permeability formula matches numerical results.
- Permeability depends on particle line fraction.
- Implications for lipid diffusion in crowded membranes.

## Abstract

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.