Molecular motion in cell membranes: analytic study of fence-hindered random walks

TL;DR

This paper provides an analytic model for the confined motion of molecules in cell membranes, deriving explicit formulas for diffusion behavior and applying them to experimental data on receptor and lipid diffusion.

Contribution

It introduces a new analytic approach based on Master equations to describe fence-hindered molecular diffusion in cell membranes, with explicit solutions and practical applications.

Findings

Derived explicit formulas for mean square displacement and diffusion constants.

Extracted compartment sizes from experimental single particle tracking data.

Validated analytical results against observed diffusion of receptors and lipids.

Abstract

A theoretical calculation is presented to describe the confined motion of transmembrane molecules in cell membranes. The study is analytic, based on Master equations for the probability of the molecules moving as random walkers, and leads to explicit usable solutions including expressions for the molecular mean square displacement and effective diffusion constants. One outcome is a detailed understanding of the dependence of the time variation of the mean square displacement on the initial placement of the molecule within the confined region. How to use the calculations is illustrated by extracting (confinement) compartment sizes from experimentally reported published observations from single particle tracking experiments on the diffusion of gold-tagged G-protein coupled mu-opioid receptors in the normal rat kidney cell membrane, and by further comparing the analytical results to observations on the diffusion of phospholipids, also in normal rat kidney cells.