Transport models of the neurotransmitter-receptor interaction

Recently, in membrane transport studies, we have observed the duality of ligand-binding site interactions in a structural protein membrane. Separately, the role of membrane anisotropy in the transport/catalytic behavior of an enzyme-membrane was investigated and modeled by the present authors. In this work, we are combining the ideas of duality and anisotropy in a diffusional analysis of the phenomenon of migration of the neurotransmitter species acetylcholine (ACh) in the post-synaptic region of the neuromuscular junction. Employing the principle of mass conservation, a transient diffusion equation was formulated for ACh migration in this region; it was solved by numerical computation for the appropriate boundary conditions. Concentration profiles were generated and, with the aid of a simple linear coupling expressing regulation of the ion channel function by the ACh species bound to receptor sites in the active conformation, successful simulations of the nerve-muscle end-plate potential were obtained. Two subcases were considered: (a) static unilayer diffusional zone or "membrane." (b) moving active layer (multilayer or envelope membrane). Both models are capable of closely matching the normalized concentration profiles of the actively bound neurotransmitter species to the profile of normalized end-plate potential in reduced scale. A transport basis for the familiar two-state receptor-transmitter interaction is demonstrated and a plausible explanation of the role of geometry of the synaptic cleft and the function of junctional cholinesterases is provided. Arguments utilizing results from the literature, together with our simulation results, are employed in critical reexamination of the key concepts (diffusion, duality, anisotropy) and their validity is strengthened.