Relation between shapes of post‐synaptic potentials and changes in firing probability of cat motoneurones

The shapes of post-synaptic potentials (p.s.p.s) in cat motoneurones were compared with the time course of changes in firing probability during repetitive firing. Excitatory and inhibitory post-synaptic potentials (e.p.s.p.s and i.p.s.p.s) were evoked by electrical stimulation of peripheral nerve filaments. With the motoneurone quiescent, the shape of each p.s.p. was obtained by compiling post-stimulus averages of the membrane potential. Depolarizing current was then injected to evoke repetitive firing, and the post-stimulus time histogram of motoneurone spikes was obtained; this histogram reveals the primary features (peak and/or trough) of the cross-correlogram between stimulus and spike trains. The time course of the correlogram features produced by each p.s.p. was compared with the p.s.p. shape and its temporal derivative.2. E.p.s.p.s of different sizes (0.15-3.1 mV, mean 0.75 mV) and shapes were investigated. The primary correlogram peak began, on the average, 0.48 msec after onset of the e.p.s.p., and reached a maximum 0.29 msec before the summit of the e.p.s.p; in many cases the correlogram peak was followed by a trough, in which firing rate fell below base-line rate. The height of the correlogram peak with respect to base-line firing rate increased in proportion to both the amplitude of the e.p.s.p.s and the magnitude of their rising slope (in these data, amplitude and rising slope also covaried).3. The mean half-width of the correlogram peaks (0.65+/-0.28 msec (S.D.)) agreed better with the average half-width of the e.p.s.p. derivatives (0.55+/-0.33 msec) than with the half-width of the e.p.s.p.s (4.31+/-1.50 msec). The shape of the primary correlogram peak produced by simple e.p.s.p.s often resembled the temporal derivative of the e.p.s.p. rise. For larger e.p.s.p.s, the shape of the correlogram peak closely matched the e.p.s.p. derivative, while smaller e.p.s.p.s in appreciable synaptic noise often generated correlogram peaks somewhat wider than their derivatives. On the other hand, the match between the correlogram trough that followed the peak and the negative slope of the e.p.s.p. was better for the small e.p.s.p.s than for the large e.p.s.p.s; for large e.p.s.p.s the drop in firing rate during the trough was typically limited at zero. These relations were tested further by comparing the integral of the correlogram with the time course of the e.p.s.p. For large e.p.s.p.s, the correlogram integral matched the rising phase of the e.p.s.p. quite well, although it underestimated the rate of decline of the e.p.s.p.4. Complex e.p.s.p.s with distinct components during their rising phase often produced correlogram peaks that did not accurately reflect the features in their temporal derivative. Temporal summation of large e.p.s.p.s and summation of their derivatives was linear, but the resulting correlogram peaks did not add linearly; the second correlogram peak was often smaller than the first. However, when small e.p.s.p.s were summed, the correlogram peaks more closely matched the e.p.s.p. derivatives.5. Compound i.p.s.p.s produced primary correlogram troughs followed by a shallow compensatory peak. The width of the trough extended through the peak of the i.p.s.p., well into the falling phase of the i.p.s.p. During the trough the firing rate usually dropped to zero. Thus, the primary correlogram features produced by large i.p.s.p.s did not resemble any linear combination of the shape of the i.p.s.p. and/or its temporal derivative. Moreover, the integral of the correlogram did not resemble the i.p.s.p.6. The major observations are consistent with a motoneurone model in which a membrane potential ramp approaches a voltage threshold for spike initiation. Near threshold, e.p.s.p.s superimposed on the ramp advance the occurrence of spikes to their rising phase, producing a correlogram peak resembling their temporal derivative. Synaptic noise would increase the probability of sampling the peak of the e.p.s.p., leading to wider correlogram peaks. I.p.s.p.s would delay the occurrence of spikes to their falling phase.