A variable-threshold motoneuron model that incorporates time- and voltage-dependent potassium and calcium conductances

Abstract

1. A "threshold-crossing" motoneuron model was developed to relate recently described biophysical features of cat alpha-motoneurons to motoneuron discharge behavior. This model incorporated three features not included in precedent models: 1) a low-threshold, persistent calcium current; 2) realistic voltage dependencies of the major ionic conductances; and 3) a variable spike threshold. The effects of these additional biophysical features on model behavior were investigated by successively adding them to a fixed threshold model with a single potassium conductance. 2. Fixed-threshold models with either one or two potassium conductances could not produce appropriate discharge behavior. Steady-state frequency-current (F-I) relations were characterized by a continuously increasing slope, unlike the piecewise linear relations observed in real motoneurons. These models also produced unrealistically high discharge rates at the highest levels of "injected" current. 3. The addition of a variable spike threshold, which was made to increase linearly with the magnitude of injected current, could limit maximum discharge rates to more realistic levels. However, steady-state F-I relations still did not exhibit the appropriate shape. 4. The incorporation of a low-threshold calcium current led to a good quantitative agreement between the steady-state F-I relations produced by the model and those obtained in real motoneurons. In addition, the steady-state relation between total membrane current and membrane voltage (I-V relation) of the model was very similar to those measured in real motoneurons. The model's I-V and F-I relations were both very sensitive to the exact form of the steady-state relation between the magnitude of the calcium conductance and membrane voltage. 5. Additional modifications, which included a second calcium conductance and a factor relating spike threshold to membrane voltage, helped to produce more realistic afterhyperpolarizations and first-interval F-I relations. 6. Bistable discharge behavior could be produced by reducing the slow potassium conductance and increasing the time constants governing the activation and deactivation of the low-threshold calcium conductance. 7. The final model thus reproduces a wide range of motoneuron behaviors including subthreshold rectification, piecewise linear first interval and steady-state F-I relations, and, with appropriate modifications, bistable discharge behavior. Nonetheless, by simplifying the representation of fast spike conductances as well as the kinetics of the other ionic conductances, the model remains simple enough to be incorporated into a larger neural network.