تجزیه و تحلیل شبیه سازی اثرات انتشار همزمان کوانتوم استیل کولین اندپلییت کنونی در محل اتصال عصبی عضلانی

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 0.5 μm, but independent of the values of the diffusion coefficient of ACh in the synaptic cleft.

A two-dimensional compartment model for the dynamic behavior of acetylcholine (ACh), a typical neurotransmitter, in spontaneous generation of the miniature endplate current (MEPC) at the neuromuscular junction has been proposed [8] to analyze the transient process of the synaptic transmission. The model is formulated in a polar coordinate system of the radial and transverse axes to express the respective diffusion process of ACh in the axis-symmetrical disc which represents a certain effective space in the synaptic cleft for the generation of MEPC. It is revealed from the analysis with this model that the radial diffusion process of ACh has more distinctive effects on spontaneous generation of the MEPC than the transverse diffusion process, so that even the homogeneous state is apparently allowed in the transverse direction. This model is also applied to examine the functional significance of the specific structures of the junctional folds [5] and of the synaptic vesicles [7] at the neuromuscular junction. The neurotransmitter release mechanism is further analyzed with the model through evaluation of the characteristic parameters of MEPC [6]. In this study, the compartment model is modified to delineate the process for the generation of the endplate current (EPC) comprised of a number of MEPCs in response to the respective quantal release of ACh. Instead of the polar coordinate system, the Cartesian coordinate system with the two orthogonal axes in a square plate of the synaptic cleft is employed to represent the dynamic behavior of multiple MEPCs. Diffusion of ACh takes place in the longitudinal directions and the homogeneous concentration of ACh is assumed in the transverse direction. The effects of the density of the quantal release of ACh on generation of the EPC are analyzed with the model, revealing that the change in the distance between the release sites of ACh on the pre-synaptic membrane has significant effects on the amplitude of EPC regardless of the values of the diffusion coefficient of ACh in the synaptic cleft.

The simulation analysis with the two-dimensional compartment model is performed for characterization of EPC generated at the neuromuscular junction with respect to the various distances between the quantal release sites of ACh on the pre-synaptic membrane. It is demonstrated that the amplitude of EPC is quite sensitive to the distances around 0.5 μm, i.e. under this condition slight change in the number of the ACh packets could have significant effects on the amplitude of EPC.