An active membrane model of the cerebellar Purkinje cell. I. Simulation of current clamps in slice

Abstract

1. A detailed compartmental model of a cerebellar Purkinje cell with active dendritic membrane was constructed. The model was based on anatomic reconstructions of single Purkinje cells and included 10 different types of voltage-dependent channels described by Hodgkin-Huxley equations, derived from Purkinje cell-specific voltage-clamp data where available. These channels included a fast and persistent Na+ channel, three voltage-dependent K+ channels, T-type and P-type Ca2+ channels, and two types of Ca(2+)-activated K+ channels. 2. The ionic channels were distributed differentially over three zones of the model, with Na+ channels in the soma, fast K+ channels in the soma and main dendrite, and Ca2+ channels and Ca(2+)-activated K+ channels in the entire dendrite. Channel densities in the model were varied until it could reproduce Purkinje cell responses to current injections in the soma or dendrite, as observed in slice recordings. 3. As in real Purkinje cells, the model generated two types of spiking behavior. In response to small current injections the model fired exclusively fast somatic spikes. These somatic spikes were caused by Na+ channels and repolarized by the delayed rectifier. When higher-amplitude current injections were given, sodium spiking increased in frequency until the model generated large dendritic Ca2+ spikes. Analysis of membrane currents underlying this behavior showed that these Ca2+ spikes were caused by the P-type Ca2+ channel and repolarized by the BK-type Ca(2+)-activated K+ channel. As in pharmacological blocking experiments, removal of Na+ channels abolished the fast spikes and removal of Ca2+ channels removed Ca2+ spiking. 4. In addition to spiking behavior, the model also produced slow plateau potentials in both the dendrite and soma. These longer-duration potentials occurred in response to both short and prolonged current steps. Analysis of the model demonstrated that the plateau potentials in the soma were caused by the window current component of the fast Na+ current, which was much larger than the current through the persistent Na+ channels. Plateau potentials in the dendrite were carried by the same P-type Ca2+ channel that was also responsible for Ca2+ spike generation. The P channel could participate in both model functions because of the low-threshold K2-type Ca(2+)-activated K+ channel, which dynamically changed the threshold for dendritic spike generation through a negative feedback loop with the activation kinetics of the P-type Ca2+ channel. 5. These model responses were robust to changes in the densities of all of the ionic channels.(ABSTRACT TRUNCATED AT 400 WORDS)