A two-dimensional compartment model for the reaction-diffusion system of acetylcholine in the synaptic cleft at the neuromuscular junction

A minimal compartment model of the reaction-diffusion system (RD system) of a neurotransmitter in a two-dimensional space of axis-symmetrical disc is proposed to represent the chemical transmission process of a quantum of acetylcholine (ACh) in the synaptic cleft at the neuromuscular junction. The behavior of the RD system for ACh is expressed by a two-dimensional diffusion equation with nonlinear reaction terms due to the rate processes for ACh receptor and acetylcholinesterase. The simulation analysis of the RD system reveals that the radial diffusion process of ACh has more distinctive effects on spontaneous generation of the miniature endplate current (MEPC) than the transverse process. The anisotropic diffusion is effective in the RD system since the diffusion coefficient of ACh in the radial direction is evaluated to be about 1.0×10−6 cm2sec−1 for appropriate characterization of the MEPC, on which the diffusion coefficient in the transverse direction larger than 2.0×10−6 cm2 sec−1 has virtually no effects. The compartment model is thus appropriately constructed to comprise three elements on the transverse coordinate and ten elements on the radial coordinate in the disc with 500 nm of radius and 50 nm of height.