Reduction of a Hodgkin-Huxley-type model for a mammalian neuron at body temperature

Hodgkin-Huxley-type models mimick the electrical behavior of excitable membranes quite realistically. However, inclusion of many different ionic channels into such a model yields a highly complex set of differential equations. In this paper a reduction of a full Hodgkin-Huxley-type model based on voltage-clamp data from small rat neurons in the supraoptic nucleus area is introduced. It was found that two of the ionic channel gating variables of the full model preserved a rather close relationship during simulations. This allowed to express one of these gating variables in terms of the other one thus reducing the number of differential equations the model is based on. The behavior of the reduced model was very similar to that of the full model. In particular, important physiological features as spike shape and constant-input-to-interspike-interval relationship were (almost) identical in the full and the reduced model.