Several laboratories have measured lateral diffusion of single particl
es on the cell surface, and these measurements may reveal an otherwise
inaccessible level of submicroscopic organization of cell membranes.
Pitfalls in the interpretation of these experiments are analyzed. Rand
om walks in unobstructed systems show structure that could be interpre
ted as free diffusion, obstructed diffusion, directed motion, or trapp
ing in finite domains. To interpret observed trajectories correctly, o
ne must consider not only the trajectories themselves but also the pro
babilities of occurrence of various trajectories. Measures of the asym
metry of obstructed and unobstructed random walks are calculated, and
probabilities are evaluated for random trajectories that resemble eith
er directed motion or diffusion in a bounded region.