An electrical description of the motoneurone, and its application to the analysis of synaptic potentials

1. The Rall model of the motoneurone, which consists of a lumped resistance and capacitance, representing the soma, in parallel with a distributed resistance—capacitance network of finite length, representing the equivalent dendritic cable, has been used to investigate the effects of varying electrical and geometrical parameters on the time course of transients generated at the model soma. 2. An analytical solution has been obtained for the voltage at the model soma, following a brief current injection at any point on the dendritic cable, in terms of the dendritic to soma conductance ratio, the electrotonic length of the cable, the membrane time constant, and the electrotonic distance between the point of current injection and the soma. This solution has been used to study the response at the soma to currents with a smooth time course, and to brief rectangular current pulses. Computations of these voltage transients are given to illustrate the effect of the above parameters on voltage time course. 3. A method for determining the membrane time constant, the dendritic to soma conductance ratio, and the electrotonic length of the dendritic cable, is described. The method involves measurements from the decay time course of the transient at the soma following a brief current pulse being applied at the soma. 4. A method is described whereby the time course of a synaptic potential, assumed to be generated by synaptic knobs located exclusively at the soma, may be used to determine the motoneurone parameters, and a parameter describing the time course of current injection. 5. A method for estimating the distance between soma and origin of a non-somatic synaptic potential, once the parameters of the motoneurone are known, is described.