Estimates of EPSP amplitude based on changes in motoneuron discharge rate and probability

When motor units are discharging tonically, transient excitatory synaptic inputs produce an increase in the probability of spike occurrence and also increase the instantaneous discharge rate. Several researchers have proposed that these induced changes in discharge rate and probability can be used to estimate the amplitude of the underlying excitatory post-synaptic potential (EPSP). We tested two different methods of estimating EPSP amplitude by comparing the amplitude of simulated EPSPs with their effects on the discharge of rat hypoglossal motoneurons recorded in an in vitro brainstem slice preparation. The first estimation method (simplified-trajectory method) is based on the assumptions that the membrane potential trajectory between spikes can be approximated by a 10 mV post-spike hyperpolarization followed by a linear rise to the next spike and that EPSPs sum linearly with this trajectory. We hypothesized that this estimation method would not be accurate due to interspike variations in membrane conductance and firing threshold that are not included in the model and that an alternative method based on estimating the effective distance to threshold would provide more accurate estimates of EPSP amplitude. This second method (distance-to-threshold method) uses interspike interval statistics to estimate the effective distance to threshold throughout the interspike interval and incorporates this distance-to-threshold trajectory into a threshold-crossing model. We found that the first method systematically overestimated the amplitude of small (<5 mV) EPSPs and underestimated the amplitude of large (>5 mV EPSPs). For large EPSPs, the degree of underestimation increased with increasing background discharge rate. Estimates based on the second method were more accurate for small EPSPs than those based on the first model, but estimation errors were still large for large EPSPs. These errors were likely due to two factors: (1) the distance to threshold can only be directly estimated over a limited portion of the interspike interval and (2) the distance to threshold can be affected by the EPSP itself. Both methods provide the most accurate EPSP estimates for EPSP amplitudes less than 5 mV and moderate background discharge rates (~15 imp/s).