Calculation of diffusion-limited kinetics for the reactions in collision coupling and receptor cross-linking

Both enzyme (e.g., G-protein) activation via a collision coupling model and the formation of cross-linked receptors by a multivalent ligand involve reactions between two molecules diffusing in the plasma membrane. The diffusion of these molecules is thought to play a critical role in these two early signal transduction events. In reduced dimensions, however, diffusion is not an effective mixing mechanism; consequently, zones in which the concentration of particular molecules (e.g., enzymes, receptors) becomes depleted or enriched may form. To examine the formation of these depletion/ accumulation zones and their effect on reaction rates and ultimately the cellular response, Monte Carlo techniques are used to simulate the reaction and diffusion of molecules in the plasma membrane. The effective reaction rate at steady state is determined in terms of the physical properties of the tissue and ligand for both enzyme activation via collision coupling and the generation of cross-linked receptors. The diffusion-limited reaction rate constant is shown to scale with the mean square displacement of a receptor-ligand complex. The rate constants determined in the simulation are compared with other theoretical predictions as well as experimental data.