Revisiting the role of spike afterhyperpolarization and spike threshold in motoneuron current-frequency gain

The relationship between synaptic or injecting input level and firing rate is an important metric to characterize neuron input-output dynamics. In this study, we examine two long-held, but never validated, assumptions in the "algebraic summation of afterhyperpolarization" theory, which explains how firing rate varies with input (typically referred to as input current-frequency modulation or "F-I gain"). In the theory, the afterhyperpolarizations themselves, along with spike threshold, were assumed constant. That is, whereas they were central concepts in the theory, they were not included in any feedback loops, wherein they could both affect and be affected by firing rate. We performed intracellular recordings from spinal motoneurons in the adult cat to determine whether F-I gain correlates with the afterhyperpolarization and/or spike threshold. We observe that the afterhyperpolarization does indeed appear to be out of the F-I gain mechanism loop, and thus that original assumption holds. However, the presented experimental evidence indicates that the spike threshold appears to be in the loop. That is, spike threshold variation associated with input correlates with F-I gain. We present an extension to the original theory, which explains the F-I gain experimental correlations.