It is argued that Brownian motion makes a less significant contributio
n to the movements of molecules and particles inside cells than is com
monly believed, and that the numbers of similar molecules and particle
s within any near-homogeneous subcompartment of the cell internum are
insufficient to justify the statistical assumptions implicit in the de
rivation of the diffusion equation. For these reasons, it is contended
that, contrary to accepted opinion, diffusion theory cannot provide a
n explanation for intracellular transport at the molecular level. Alth
ough attempts have been made to adapt diffusion theory to complex medi
a, the conclusion is that none satisfactorily overcomes the problem of
applying the theory to cell biology. However, the heuristic influence
of the theory on cellular biophysics and physiology is noted, and pos
sible alternative frameworks for interpreting the valuable experimenta
l data obtained from such studies are outlined. (C) 1995 Academic Pres
s Limited