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Purkinje Cell Model–De Schutter

Maximum conductances

Table 1: ˉg for the voltage and Ca2+-dependent channels in 2 different versions of the Purkinje cell model.
PM9 Model
PM10 Model
NameSomaMain DendriteRest of DendriteSomaMain DendriteRest of Dendrite
NaF 7,500 0.0 0.0 7,500 0.0 0.0
NaP 1.0 0.0 0.0 1.0 0.0 0.0
CaP 0.0 4.5 4.5 0.0 4.0 4.5
CaT 0.5 0.5 0.5 0.5 0.5 0.5
Kh 0.3 0.0 0.0 0.3 0.0 0.0
Kdr 600.0 60.0 0.0 900.0 90.0 0.0
KM 0.040 0.010 0.013 0.140 0.040 0.013
KA 15.0 2.0 0.0 15.0 2.0 0.0
KC 0.0 80.0 80.0 0.0 80.0 80.0
K2 0.0 0.39 0.39 0.0 0.39 0.39
Extent of the main dendrite is shown in Figure 1.
ˉg : maximum conductance mS/cm2. For other abbreviations, see Table 1.

Channel Densities

In the present model, simulations were started using initial guesses for the ˉg of the different channels in four zones of the cell, i.e. the soma, the main dendrite, the smooth dendrites, and the spiny dendrites (see Fig. 1). ˉg s were then altered until the model could reproduce the characteristic firing behavior of Purkinje cells during current injection in vitro [32], as described in Figs. 3–7. During this optimization process it was not necessary to distinguish between the smooth and spiny dendrites. In addition, optimal performance required that the Kdr and A currents be present in the main dendrite as well as in the soma.

Also, several combinations of ˉg were found that could account for the responses of Purkinje cells to current injection. For contrast, versions PM9 and PM10 are presented, where PM10 represents a Purkinje cell with higher K+ channel densities, i.e., a leakier cell.

Robustness to Changes in Channel Densities

The principle parameters used to tune this model to the current injection data were the distribution and density of specific ion channels. Although Table described the final distribution for this model, it was also important to determine how sensitive the modeling results were to these particular density values.

A full search of the 10,000 dimensional parameter space for this model would have been computationally prohibitive (see [1]). Accordingly, the approach we have taken involved examining the effect of changing the density of a single-channel type on the physiological responses to current injection in the soma. The results showed, perhaps not surprisingly, that small-amplitude currents like NaP and CaT currents, KA, or KM could be completely removed with little effect, except for small changes in firing frequency. The same was true for increasing KA or KM by a factor of 2 or 3. Similar increases in NaP or CaT currents, however, caused fast spiking in the soma to saturate (as in Fig. 3D) at lower current amplitudes and could turn the cell into a spontaneously firing or bursting neuron.

The model was more sensitive to changes of the conductances involved in spike generation and repolarization. Small changes resulted in a shift of the f -I curve and of the current amplitude at which dendritic spiking started. Changes in the dendritic currents involved in spiking could suppress all dendritic spiking (reducing CaP current by 220 %, increasing Kdr by > 40 %, KC by 25 %, or K2 by 10 % ) or make dendritic bursting the unique mode of firing of the cell (reducing NaF current by 50 %, increasing CaP current by 50 %, or decreasing Kdr by 20 % or KC or K2 by 10 %). NaF current could be reduced by 70 % before NaF spikes disappeared.

The model was thus sensitive to small changes in density of CaP, KC, and K2 currents; in other words, the region of parameter space that generated correct model responses was not very large for these currents. Note, however, that larger changes could be applied to these channel densities if one of the other current densities was changed in the opposite direction. The model was less sensitive to changes in the other currents, like for example the densities of voltage-dependent K+ currents (cf. Table [?]).

Channel Distributions

The density and distribution of channels in the model were the main uncontrolled variables in these simulations. Experimental techniques do not yet exist to give detailed distribution and density information for all ionic channels in a given cell. Accordingly, by searching parameter space, detailed single cell models can make predictions concerning this critical information [1]. In the current case, the initial channel distributions were primarily based on the speculations of [32]. The results of the model largely confirm these predictions with a few modifications.


[1]   US Bhalla and JM Bower. Exploring parameter space in detailed single neuron models: Simulations of the mitral and granule cells of the olfactory bulb. Journal of Neurophysiology, 6:1948–1965, 1993.

[2]   RR Llinás and M Sugimori. Electrophysiological properties of in vitro Purkinje cell dendrites in mammalian cerebellar slices. Journal of Physiology (Lond.), 305:197–213, 1980.

[3]   RR Llinás and M Sugimori. Electrophysiological properties of in vitro Purkinje cell somata in mammalian cerebellar slices. Journal of Physiology (Lond.), 305:171–195, 1980.