Repetitive firing of a model motoneuron: inhibitory effect of a Ca2+ -activated potassium conductance on the slope of the frequency-current relationship.

We developed a novel motoneuron model to examine the role of voltage-independent, Ca(2+)-activated potassium conductance (AHP conductance, or gAHP) in regulating repetitive firing. In addition to gAHP, the model also includes five voltage-gated conductances and a system that can reproduce Ca(2+) dynamics in the cytoplasm. Conductance kinetics were based on empirical data, and the model reproduced the piecewise linear, steady-state frequency-current relationship (f-I curve). The model revealed that gAHP has a "braking effect" that suppresses spike generation and thereby reduces firing frequency; the magnitude of the reduction in firing frequency is proportional to the temporal average of gAHP activation; and the level of activation depends on the magnitude of the injected current. Moreover, plotting the activation level as a function of injected current produced a bell-shaped curve, and this relationship was essential to the transition of the f-I curve. In conclusion, our study confirms the importance of gAHP to repetitive firing and presents a novel explanation for the piecewise linear f-I curve of motoneurons.