Modeling the Reaction Transport of Synaptic Acetylcholine Released at High Frequency in Weakly Electric Fish

Abstract

Studying the synaptic transmission in the neuromuscular junction (NMJ) is central to the understanding of firing electrical signals at high frequencies. In this work, we present the processes involving acetylcholine and its receptors in the synaptic transmission across the cleft.

A one-dimensional diffusion model is proposed to explain the behavior of the reaction -diffusion system with nonlinear reaction terms monitoring the interaction of acetylcholine with the enzyme and the receptors. A proper numerical method is applied to solve the one-dimensional diffusion equation along the symmetry axis of the cylindrically shaped cleft with Neumann boundary condition on the postsynaptic end.

We assumed a periodic release of ACh in the frequency range of 200Hz to 500Hz. The kinetics of receptors (particularly the open receptors) during the release of acetylcholine to changes in selected parameters are investigated. We chose typical values for the concentration of ACh, the flux of ACh, and the surface concentration of receptors. The effects of the varying parameters, enzyme concentration, input flux, and the receptor concentration on the emission of acetylcholine in the synaptic cleft and the subsequent impact on the dynamics of the receptors are studied and discussed.

As the firing rate is increased, the enzyme concentration also has to be increased to ensure that the ACh receptors (AChR) close in between two releases of ACh. Our study revealed that the enzyme reaction limits our model. The concentration of ACh reaching the receptors falls close to a threshold and the receptors do not close completely during firing at a high frequency, such as 500 Hz. Our model can be used to describe the neuronal transmission across the synaptic up to about 500Hz. This being close to the physiological limit of Eigenmannia, it suggests that the mechanism described in this thesis reflects reality.