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De Schutter: Purkinje Cell Model


The primary parameters searched in this model involved the locations and densities of the different channels. Although the complexity of the current model has not allowed us to undertake a full parameter search, as has been done in some other recent modeling studies [1], we have explored in detail variations on key parameters to examine the overall robustness of the results. As can be expected from a model that shows so much response variability, it was found to be quite robust to changes in channel densities.

Results were most sensitive to changes in the densities of the CaP, KC, and K2 channels. However, these three channels are actually tied together, i.e., modifying the density of one of them will change the activation of the other two during the dendritic spiking cycle. They are also linked through our simple representation of Ca2+ concentration, which drives activation of the KC and K2 channels. For this reason, robustness of the model could be maintained over a wider range of channel densities for even these conductances, provided more than one channel density was changed at once. In fact, the initial process of model tuning primarily involved manually changing the densities of these three channels in an effort to obtain correct levels of dendritic excitability.

Robustness of modeling results

Having tuned the model to replicate in vitro responses to current injection, we ran several simulations to test the robustness of the basic model. These tests helped to build confidence that the model has biological validity.


Initial modeling experiments were based on the anatomic reconstruction of one particular Purkinje cell. Accordingly, it was important to determine the sensitivity of the results to this particular morphology. To do this, identical channel equations and densities (PM 9) were placed into two additional Purkinje cells, reconstructed by [?]; the results are shown in Fig. 8.

In both cells the response properties of the model fell well within the normal variation seen in Purkinje cell recordings. Simulations of current injections in the soma produced the same typical pattern as in our model of Purkinje cell1 (Fig. 3), i.e., at low intensities steady firing of fast somatic spikes superimposed on an increasing plateau potential and at higher intensities the presence of dendritic Ca2+ spikes. The details of these firing patterns were, however, quite different for the three cells. Cell2 is smaller than cell1 (Fig. 1) and thus had a larger RN [?]. As a consequence, the Na+ currents caused a more pronounced plateau potential and the somatic spikes were less well repolarized. This resulted in a progressive attenuation of spike amplitude because of incomplete removal of inactivation of NaF current. Note, however, that despite this buildup of inactivation, spiking did not saturate at a depolarized level during the 1.5 nA current injection, whereas it did in cell3 (not shown). The firing pattern of cell3 is more similar to that of cell1, but with a shift in the f - I curve. This can be explained by the small soma and short, thin main dendrite, which caused a smaller total Kdr and KM conductances in the model of this cell (Table 2).


[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.