Evaluation of reaction rate enhancement by reduction in dimensionality

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.