Reaction-Diffusion Modeling to Assess what Limits Effective Acetylcholine Fluctuations at High Frequency Cholinergic Electroplaques

Abstract

In the weakly electric fish Eigenmannia (glass knifefish), high frequency (200-550Hz) electric organ discharge (EOD) is driven by high frequency cholinergic synaptic input onto the electrocytes at their electroplaques. Evolutionarily, this system derives from skeletal muscle endplate synapses. We are interested in what, physically, limits the rapidity with which acetylcholine (ACh) concentrations can oscillate to successfully activate post-synaptic ACh receptors (AChR) and thereby trigger EODs at the oscillating frequency. Assuming periodic release of ACh into a 50nm wide cylindrical synaptic gap, we solve numerically a one dimensional reaction-diffusion model at 200Hz and 500Hz. The model included the diffusion of ACh and its interactions with AChesterase (AChE) and AChRs. For ACh released periodically at the two frequencies, we vary the ratio of ACh input to the AChE concentration. The biochemical/biophysical characteristics of AChE/ACh and AChR/ACh are those typical of neuromuscular junctions. The AChR can be in four states: closed (AR), with one or two bound ACh molecules (AR1 and AR2) and finally open state (AR2open). At 500Hz a higher AChE/ACh ratio is needed to remove ACh from the cleft between consecutive ACh releases. Only a small fraction of the ACh molecules reaches the AChRs, and there are residual amounts of ACh molecules from the preceding release. Previous computational studies showed that the persistently present ACh should not impede high frequency electrocyte firing, provided the cholinergic current is subthreshold for triggering firing. In our simulations, the fast AChE-ACh reactions (not AChR-ACh kinetics) limit the upper frequency for triggering electrocyte action potentials. We suggest, therefore, that carry-over (persistent) activation of AChRs could account for the observed upper limit for EOD frequency in Eigenmannia individuals.