Quantitative Modelling applied to Aspects of Neuromuscular Function

Abstract

A quantitative mathematical model is proposed which defines synthesis, storage and release of the neurotransmitter, acetylcholine, at the nerve ending. The approach has been to gather a wide spectrum of information and to formulate a concensus which best describes neuromuscular function. On the basis of this factual evidence (i.e. both quantitative and qualitative), a lumped parameter, quasi time independent model has been conceived, which considers some 50 parameters and variables which appear to define or contribute to aspects of acetylcholine release. The model seeks to provide an overall picture of neuromuscular function and is used to simulate several aspects of nerve behaviour when evoked in normal, raised calcium, or raised magnesium solutions. An explanation is offered concerning oscillating stores of free acetylcholine (not obvious by electrophysiological experiment) in terms of the general movement of quanta within the nerve ending. The translocation of quanta into three distinct stores is a fundamental feature of the model, and is examined in detail against wider aspects of neuromuscular function. The theoretical results obtained from the model are compared with experimental findings from several sources, and critically discussed. Necessary refinements are suggested and implemented and it is concluded that the model is adequate in describing acetylcholine release. Areas of further development work are detailed so that the model may be extended to more fully simulate general neuromuscular function.