FUNCTIONAL IDENTIFICATION OF THE INPUT-OUTPUT TRANSFORMS OF MOTONEURONS IN THE RAT AND CAT

1. We studied the responses of rat hypoglossal and cat lumbar motoneur ones to a variety of excitatory and inhibitory injected current transi ents during repetitive discharge. The amplitudes and time courses of t he transients were comparable to those of the synaptic currents underl ying unitary and small compound postsynaptic potentials (PSPs) recorde d in these cells. Poisson trains of ten of these excitatory and ten in hibitory current transients were combined with an additional independe nt, high-frequency random waveform to approximate band limited white n oise. The white noise waveform was then superimposed on long duration (39 a) suprathreshold current steps. 2. We measured the effects of eac h of the current transients on motoneurone discharge by compiling peri stimulus time histograms (PSTHs) between the times of occurrence of in dividual current transients and motoneurone discharges. We estimated t he changes in membrane potential associated with each current transien t by approximating the passive response of the motoneurone with a simp le resistance-capacitance circuit. The relations between the features of these simulated PSPs and those of the PSTHs were similar to those r eported previously for red PSPs: the short-latency PSTH peak (or troug h) was generally longer than the initial phase of the PSP derivative, but shorter than the time course of the PSP itself. Linear models of t he PSP to PSTH transform based on the PSP time course, the time deriva tive of the PSP, or a linear combination of the two parameters could n ot reproduce the full range of PSTH profiles observed. 3. We also used the responses of the motoneurones to the white noise stimulus to deri ve zero-, first-and second-order Wiener kernels, which provide a quant itative description of the relation between injected current and disch arge probability. The convolution integral computed for an injected cu rrent waveform and the first-order Wiener kernel should provide the be st linear prediction of the associated PSTH. This linear model provide d good matches to the PSTHs associated with a wide range of current tr ansients. However, for the largest amplitude current transients, a sig nificant improvement in the PSTH match was often achieved by expanding the model to include the convolution of the second-order Wiener kerne l with the input. 4. The overall transformation of current inputs into firing rate could be approximated by a second-order Wiener model, i.e . a cascade of a dynamic, linear filter follow ed by a static nonlinea rity. At a given mean firing rate, the non-linear component of the res ponse of the motoneurone could be described by the square of the linea r component multiplied by a constant coefficient. The amplitude of the response of the linear component increased with the average firing ra te, whereas the value of the multiplicative coefficient in the non-lin ear component decreased. As a result, the overall transform could be p redicted from the mean firing rate and the linear impulse response, yi elding a relatively simple, general description of the motoneurone inp ut-output function.