Measurement of excitability of tonically firing neurones tested in a variable‐threshold model motoneurone

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Abstract
A new measure of excitability of tonically firing neurones termed the ‘estimated potential’ (EP) was tested on a model motoneurone (MN) with a voltage‐dependent threshold; the threshold followed the noisy membrane potential with an exponential delay. First, the model MN's after‐hyperpolarisation (AHP) was deduced from its interval histogram for tonic firing, using a recently described transform. This provided a ‘distance‐to‐threshold’ measure which underestimated the AHP's absolute size but had the same time course, thereby providing the time constant of the AHP's decay of conductance. The ‘estimated potential’ was then obtained from the classical ‘firing index’ (no. of responses/no. of stimuli) by using the estimated AHP to create a fixed threshold ‘daughter’ model MN to mimic its variable threshold parent and reproduce its input‐output non‐linearities. The EP gave a linear measure of the parent's stimulus‐evoked depolarisation for firing indices up to about 60 %, corresponding to depolarisations of three to four times the noise s.d. The EP was scaled in units of voltage whose absolute value will usually be unknown for real neurones, since it depended upon the details of the parent model. The EP's virtue is that, within its range, combining stimuli gives arithmetical addition and subtraction, thereby improving on the firing index which scales sigmoidally with the input. Moreover, with weak stimuli, the EP for a given input did not change on varying the parent model's firing rate. The estimated ‘distance‐to‐threshold’ AHP did not, however, give an accurate measure of the recovery of excitability following a spike during tonic firing. Excitability then depends upon the ‘survivors’ trajectory’ giving the mean membrane potential, relative to threshold, of those intervals which have ‘survived’ up to the time in question rather than upon the AHP per se; the survivors’ mean is more hyperpolarised because spiking preferentially eliminates trajectories with noise‐induced depolarisation.