AJP - Regulatory, Integrative and Comparative Physiology, Vol 243, Issue 5 475-R479, Copyright © 1982 by American Physiological Society
Evaluation of reaction rate enhancement by reduction in dimensionality
F. W. Wiegel and C. DeLisi
The paths followed by ligands as they react with or dissociate from cell
surface receptors may include weak association with nonreceptor portions of
the surface followed by lateral diffusion in the plane of the membrane to a
receptor. The change in dimensionality of the diffusion process by
utilization of these nonspecific paths has been invoked by a number of
investigators as a mechanism for enhancing reaction rate in biological
systems. This paper extends our previous work on the calculation of
diffusive rate constants for ligand-receptor paths. We find that they have
little effect on rate constants unless the number of free receptors per
cell has been reduced to less than or equal to 10(2). This number
represents better than 90% occupancy for most eukaryotes, suggesting that
the dimensional change mechanism is of limited consequence. We show further
that when the free receptor number is low enough for rate enhancement, then
the primary parameter of consequence is D'K*/D, where D' and D are the two-
and three-dimensional diffusion coefficients, respectively, and K* the
nonspecific affinity. A 10-fold rate enhancement with 100 free receptors
requires that this parameter be of order 10(-3). This value is barely
within the lower limit imposed by currently available experimental
information, casting doubt on the relevance of nonspecific paths in
cellular systems.
