Simulation analysis of the effects of the simultaneous release of quanta of acetylcholine on the endplate current at the neuromuscular junction

Arrival of an action potential to a nerve terminal at the neuromuscular junction induces the release of a few hundred quanta of acetylcholine (ACh) into the synaptic cleft, resulting in depolarization of the muscle cell which is observed as the endplate current (EPC). The release of each quantum of ACh invokes the miniature endplate current (MEPC), so that an EPC could be generated by summation of the MEPCs both in time during evolution of the EPC and in space for a certain area of the post-synaptic membrane. In this study, a mathematical model for EPC generation is developed as a reaction–diffusion system (RD system) which represents the dynamic behavior of ACh in the chemical transmission process with the simultaneous quantum release of ACh. The RD system for ACh is mathematically expressed by a two-dimensional diffusion equation with nonlinear reaction terms due to the rate processes for acetylcholinesterase (AChE) and ACh receptor (AChR). Numerical solution of the governing equation with the method of lines and the Gear method yields temporal changes in relative concentrations of the open channel form of AChR which is assumed to be equivalent to the EPC. Analysis of the behavior of the RD system with respect to the various distances between the release sites of ACh on the pre-synaptic membrane demonstrates that the amplitude of EPC is quite sensitive to the distances around 0.5μm, but independent of the values of the diffusion coefficient of ACh in the synaptic cleft.