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De Schutter: Purkinje Cell Model


In slice preparations, different Purkinje cells often have quite different firing patterns, especially as concerns the pattern of interacting somatic and dendritic spikes (Fig. 11 in [4]) and the slope of the f -I curve. However, a compartmental model is deterministic, i.e., always producing the same output for a given input. Variability in response properties comes about only as a result of varying parameters in the model.

In the case of the current model, we found that all of the reported variations in firing patterns could be obtained by simply changing the density of K+ conductances in the soma and the main dendrite of the model. Figures 3 and 4 compare the firing of a model with low K+ conductance (PM9) with a model with high K+ conductance (PM 10). Although these models were similar in all responses described so far, they showed richly different patterns of somatic firing that encompassed most of the observed ones. Compare, for example, the somatic responses toward the end of the current injections in Figs. 3B and C, and 4D and after the current step in Fig. 3D. The higher K+ channel densities in model PM 10 made the soma also less excitable, resulting in a shallower f - I curve (Fig. 6A).


Although any particular set of parameters in the model generated an identical (deterministic) output, we have also found that slight variations in parameters could produce the kinds of subtle variations seen in Purkinje cell recordings. Thus different levels of current injection, small changes in the densities of outward currents (PM9 versus PM10), or slight changes in morphology generated subtle changes in model output. Under these conditions the Purkinje cell model responded generally in the same way but also showed small variations in the details of its responses (e.g., in the sequence of action potentials). We believe this variability in the model is important, because the specific objective of this effort was to represent the entire population of Purkinje cells rather than just one individual cell [1].

One of the variable aspects of Purkinje cells that has been previously described involves the details of the f - I curve [4]. Further, this curve can change during long recordings of the same cell (D. Jaeger, personal communication). It is interesting that changes in the density of the delayed rectifier and noninactivating K+ channels in the model alone could cause a lot of this variability, as can be seen by comparing Fig. 3 with Fig. 4 and in the f - I curves of Fig. 6A. The results from patch-clamp recordings demonstrating that Purkinje cell Kdr channels are under metabolic control by protein kinase C, which attenuates Kdr current [3] could provide one mechanism for short term changes inf-1 relationships. Further, our finding that somatic action potentials only repolarized completely when Kdr channels were added to the main dendrite showed that the Kdr channel also controls the coupling between the soma and more distal dendrite that may influence thesef-I relationships. This distribution of Kdr channels matches data obtained with voltage-sensitive dye imaging, where a decoupling between the soma and the more distal dendrite could be removed by blocking K+ channels [2].


[1]   JM Bower and C Koch. Experimentalists and modelers: Can we all just get along? Trends in Neurosciences, 15:458–461, 1992.

[2]   T Knöpfel, C Staub, and BH Gähwiler. Spatial spread of voltage transients in cerebellar Purkinje cells. Society for Neuroscience Abstracts, 16:636, 1990.

[3]   DJ Linden, M Smeye, and SC Sun. An electrophysiological correlate of protein kinase C isozyme distribution in cultured cerebellar neurons. Journal of Neuroscience, 12:3601–3608, 1992.

[4]   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.