Using reaction-diffusion modeling to probe high-frequency cholinergic transmission

Abstract

The vertebrate skeletal muscle fiber's endplate current is well-modeled by scaling up the spontaneous miniature endplate currents (mepcs) of voltage-clamped neuromuscular junctions (NMJ). Mepc characteristics couple tightly to binding of pre-synaptically-released acetylcholine (ACh) at post-synaptic receptors plus elimination of ACh by synaptic-cleft acetylcholinesterase (AChE). The question we address: Could the same “cholinergic machinery” muscles use for intermittent, relatively low-frequency endplate currents be redeployed to trigger the continual high-Hz output underlying electric organ discharge (EOD) in gymnotid electric fish like the glass knifefish, Eigenmannia? This question arises a) because, following a whole-genome duplication ∼¼ billion years ago, gymnotids (Amazon-Basin teleosts encompassing both Eigenmannia and their close relatives, the electric eels, Electrophorus) evolved non-contractile electric organs from the duplicate “muscle excitability-genome,” b) because Eigenmannia sustains EODs night-and-day at 200-600 Hz, and c) because supplying pre-synaptic ACh is high-cost relative to firing post-synaptic action potentials, efficient ACh-use is biologically non-trivial and motivates a need to model high-Hz cholinergic transmission. Here, via one-dimensional reaction-diffusion modeling plus a lateral escape mechanism for ACh, we simulate the events between ACh-release (singly, 200 Hz, 500 Hz) and ACh-binding to post-synaptic receptors in the presence of synaptic-cleft AChE. Using open AChRs (not channel current) as our metric, we first show that our model accords with published accounts of mepc time courses (single ACh-releases). Here, we show how the ACh-release time course, synaptic gap width, ACh-diffusion coefficient, and the density and cleft-distribution of AChE affect open-AChR(time). ACh-release at 200Hz and 500Hz is then examined. To address efficiency, the fraction of released-AChs yielding open AChRs is monitored as the quantity of ACh/release is varied. We find standard “NMJ machinery” to be operative at upper gymnotid frequencies, and thus wonder if the NMJ pre-synaptic ACh-supply machinery is, likewise, “over-engineered.”