  The effect of disorder in the energetic heights and in the physical locations
of fence barriers encountered by transmembrane molecules such as proteins and
lipids in their motion in cell membranes is studied theoretically. The
investigation takes as its starting point a recent analysis of a periodic
system with constant distances between barriers and constant values of barrier
heights, and employs effective medium theory to treat the disorder. The
calculations make possible, in principle, the extraction of confinement
parameters such as mean compartment sizes and mean intercompartmental
transition rates from experimentally reported published observations. The
analysis should be helpful both as an unusual application of effective medium
theory and as an investigation of observed molecular movements in cell
membranes.
