EXPERIMENTAL EVALUATION OF INPUT-OUTPUT MODELS OF MOTONEURON DISCHARGE

1. We measured the modulation of the background firing rate of cat spi nal motoneurons produced by simulated, repetitive excitatory postsynap tic potentials (EPSPs) to test the accuracy of several proposed motone uron input-output functions. Rhythmic discharge was elicited in the mo toneurons by injecting suprathreshold current steps 1-1.5 a in duratio n. On alternate trials, trains of short (0.5-5 ms) current pulses were superimposed on the current steps to simulate the effects of trains o f individual EPSPs. The increase in firing rate (Delta F) due to the a ddition of the pulses was calculated as the difference in motoneuron d ischarge rate between trials with and without the superimposed pulse t rains. 2. In the same motoneurons, we were able to study the effects o f changes in pulse frequency, duration, and amplitude, as well as chan ges in the background discharge rate. A sublinear relationship between pulse rate and Delta F was observed, with Delta F rising relatively s teeply with increasing pulse frequency at low pulse rates and saturati ng at high pulse rates. A similarly shaped relation was observed betwe en Delta F and pulse duration. In contrast, Delta F generally increase d in a greater than linear fashion with increasing pulse amplitude. 3. In previous studies we demonstrated that when a relatively constant s ynaptic input is produced by high-frequency synaptic activity, Delta F is approximately equal to the product of the net synaptic current rea ching the soma and the slope of the motoneuron's steady-state frequenc y-current (f-1) relation. In the present study, this input-output func tion consistently underestimated the observed Delta F, particularly fo r low input rates, indicating that the transient current pulses are mo re effective in modulating motoneuron discharge than an equivalent amo unt of constant current. 4. Other investigators have proposed input-ou tput functions derived from the relation between synaptic potential am plitude and the magnitude of the peak of a cross correlogram compiled from the discharge of the pre- and postsynaptic neurons. These functio ns consistently overestimated the observed Delta F, particularly for h igh pulse rates. This overestimation may result in part from the fact that the effects of a synaptic potential (or current pulse) on postsyn aptic discharge probability also include a period of decreased firing probability. Moreover, the cross correlation function may depend on th e arrival rate of synaptic potentials (or current pulses). 5. Another proposed input-output function based on a simple threshold-crossing mo del of the motoneuron with a fixed spike threshold predicts firing rat es that were often close to the observed Delta F. However, the model d id not reproduce the observed relations between Delta F and input puls e rate or pulse duration. 6. The deficiencies of the basic threshold-c rossing model may arise from the fact that it does not incorporate var iations in membrane conductance and firing threshold that occur in rea l motoneurons. A more complete motoneuron model that incorporates both of these features was able to replicate the observed Delta Fs associa ted with changes in input pulse frequency and duration.