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

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