An analytical solution is obtained for the steady-state reaction rate of an intracellular enzyme, recruited to the plasma membrane by active receptors, acting upon a membrane-associated substrate. Influenced by physical and chemical effects, such interactions are encountered in numerous signal-transduction pathways. The generalized modeling framework is the first to combine reaction and diffusion limitations in enzyme action, the finite mean lifetime of receptor-enzyme complexes, reactions in the bulk membrane, and constitutive and receptor-mediated substrate insertion. The theory is compared with other analytical and numerical approaches, and it is used to model two different signaling pathway types. For two-state mechanisms, such as activation of the Ras GTPase, the diffusion-limited activation rate constant increases with enhanced substrate inactivation, dissociation of receptor-enzyme complexes, or crowding of neighboring complexes. The latter effect is only significant when nearly all of the substrate is in the activated state. For regulated supply and turnover pathways, such as phospholipase C-mediated lipid hydrolysis, an additional influence is receptor-mediated substrate delivery. When substrate consumption is rapid, this process significantly enhances the effective enzymatic rate constant, regardless of whether enzyme action is diffusion limited. Under these conditions, however, enhanced substrate delivery can result in a decrease in the average substrate concentration.
Haugh, J. M. (2002). A unified model for signal transduction reactions in cellular membranes. Biophysical Journal, 82(2), 591–604. https://doi.org/10.1016/S0006-3495(02)75424-6