Mathematical Relationships between Spinal Motoneuron Properties

Abstract

AbstractOur understanding of the behaviour of spinal alpha-motoneurons (MNs) in mammals partly relies on our knowledge of the relationships between MN membrane properties, such as MN size, resistance, rheobase, capacitance, time constant, axonal conduction velocity and afterhyperpolarization period. Qualitative relations between some of these properties are often assumed based on scattered but converging evidence from experimental studies and review papers.We reprocessed the data from 40 experimental studies in adult cat, rat and mouse MN preparations in vivo to empirically derive precise mathematical relationships between MN electrophysiological and anatomical properties. This validated mathematical framework, which demonstrates that the MN membrane properties are all related to each other, expands our knowledge in neural electrophysiology beyond available literature data. For example, it extends the Henneman’s size principle by the association between MN size and all other MN properties.The derived mathematical relationships provide a convenient tool for neuroscientists and experimenters to estimate non-measurable MN properties, to explore relationships between pairs of MN properties never concurrently observed in previous experiments, to support future experimental investigations, or to investigate inter-mammalian-species variations in MN membrane properties. Using this mathematical framework, which supports the classic description of a MN as a membrane equivalent electrical circuit, modelers can build profiles of inter-consistent MN-specific properties to scale advanced models of MNs, with consequences on our understanding of the neural control of movement.