AN ACTIVE MEMBRANE MODEL OF THE CEREBELLAR PURKINJE-CELL .1. SIMULATION OF CURRENT CLAMPS IN SLICE

1. A detailed compartmental model of a cerebellar Purkinje cell with a ctive dendritic membrane was constructed. The model was based on anato mic reconstructions of single Purkinje cells and included 10 different types of voltage-dependent channels described by Hodgkin-Huxley equat ions, derived from Purkinje cell-specific voltage-clamp data where ava ilable. These channels included a fast and persistent Na+ channel, thr ee voltage-dependent K+ channels, T-type and P-type Ca2+ channels, and two types of Ca2+-activated K+ channels. 2. The ionic channels were d istributed differentially over three zones of the model, with Na+ chan nels in the soma, fast K+ channels in the soma and main dendrite, and Ca2+ channels and Ca2+-activated K+ channels in the entire dendrite. C hannel densities in the model were varied until it could reproduce Pur kinje 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 som atic spikes were caused by Na+ channels and repolarized by the delayed rectifier. When higher-amplitude current injections were given, sodiu m spiking increased in frequency until the model generated large dendr itic Ca2+ spikes. Analysis of membrane currents underlying this behavi or showed that these Ca2+ spikes were caused by the P-type Ca2+ channe l and repolarized by the BK-type Ca2+-activated K+ channel. As in phar macological blocking experiments, removal of Na+ channels abolished th e fast spikes and removal of Ca2+ channels removed Ca2+ spiking. 4. In addition to spiking behavior, the model also produced slow plateau po tentials in both the dendrite and soma. These longer-duration potentia ls occurred in response to both short and prolonged current steps. Ana lysis of the model demonstrated that the plateau potentials in the som a were caused by the window current component of the fast Na+ current, which was much larger than the current through the persistent Na+ cha nnels. Plateau potentials in the dendrite were carried by the same P-t ype 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 Ca2+-activated K+ channel, which dynamically ch anged 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 a ll of the ionic channels. For most of the channels, modifying their de nsities by factors of greater than or equal to 2 resulted only in left or right shifts of the frequency-current curve. However, changes of > 20% to the amount of P-type Ca2+ channels or of one of the Ca2+-activa ted K+ channels in the model either suppressed dendritic spikes or cau sed the model to always fire Ca2+ spikes. Modeling results were also r obust to variations in Purkinje cell morphology. We simulated models o f two other anatomically reconstructed Purkinje cells with the same ch annel distributions and got similar responses to current injections. 6 . The model was used to compare the electrotonic length of the Purkinj e cell in the presence and absence of active dendritic conductances. T he electrotonic distance from soma to the tip of the most distal dendr ite increased from 0 57 lambda in a passive model to 0.95 lambda in a quiet model with active membrane. During a dendritic spike generated b y current injection the distance increased even more, to 1.57 lambda. 7. Finally, the model was used to study the probable accuracy of exper imental voltage-clamp data. Whole-cell patch-clamp conditions were sim ulated by blocking most of the K+ currents in the model. The increased electrotonic length due to the active dendritic membrane caused space clamp to fail, resulting in membrane potentials in proximal and dista l dendrites that differed critically from the holding potential in the soma.