Physiology, morphology and detailed passive models of cerebellar Purkinje cells

1. Purkinje cells (PCs) from guinea-pig cerebellar slices were physiologically characterized using intracellular techniques. Extracellular caesium ions were used to linearize the membrane properties of PCs near the resting potential. Under these conditions the average input resistance, RN, was 29 M omega, the average system time constant, tau 0, was 82 ms and the average cable length, LN, was 0.59. 2. Three PCs were fully reconstructed following physiological measurements and staining with horseradish peroxidase. Assuming that each spine has an area of 1 micron 2 and that the spine density over the spiny dendrites is ten spines per micrometre length, the total membrane area of each PC is approximately 150,000 microns 2, of which approximately 100,000 microns 2 is in the spines. 3. Detailed passive cable and compartmental models were built for each of the three reconstructed PCs. Computational methods were devised to incorporate globally the huge number of spines into these models. In all three cells the models predict that the specific membrane resistivity, Rm, of the soma is much lower than the dendritic Rm (approximately 500 and approximately 100,000 omega cm2 respectively). The specific membrane capacitance, Cm, is estimated to be 1.5-2 muF cm-2 and the specific cytoplasm resistivity, Ri, is 250 omega cm. 4. The average cable length of the dendrites according to the model is 0.13 lambda, suggesting that under caesium conditions PCs are electrically very compact. Brief somatic spikes, however, are expected to attenuate 30-fold when spreading passively into the dendritic terminals. A simulated 200 Hz train of fast, 90 mV somatic spikes produced a smooth 12 mV steady depolarization at the dendritic terminals. 5. A transient synaptic conductance increase, with a 1 nS peak at 0.5 ms and a driving force of 60 mV, is expected to produce approximately 20 mV peak depolarization at the spine head membrane. This EPSP then attenuates between 200- and 900-fold into the soma. Approximately 800 randomly distributed and synchronously activated spiny inputs are required to fire the soma. 6. The passive model of the PC predicts a poor resolution of the spatio-temporal pattern of the parallel fibre input. An equally sized, randomly distributed group of approximately 1% of the parallel fibres, activated within a time window of a few milliseconds, would result in approximately the same composite EPSP at the soma.

Authors: Rapp M, Segev I, Yarom Y.
Year of publication: 1994
Journal: J Physiol. 1994 Jan 1;474(1):101-18.

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