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The morphology of the models was based on a detailed light microscopic reconstruction of horseradish peroxidase-filled guinea pig Purkinje cells by M. Rapp of the Hebrew University of Jerusalem, Israel [7, ?]. All simulations were performed with a model using the morphology of cell I of Rapp et al. [?] unless otherwise noted. We applied the same shrinkage factor of 10 % as did Rapp.
The final model described here contained 1,600 compartments. As is standard for compartmental modeling [5, 6], this number was determined by the morphology of the cell and by simulation requirements for numerical accuracy. In particular, when active channels are used, it has been previously shown that the electrotonic length of compartments should be < 0.05 λ[1].
In our model, the passive electrotonic length of single compartments ranged from 0.009 to 0.05 λ. Because these electrotonic lengths were short, we were able to use more computationally efficient asymmetric compartments (this GENESIS object corresponds to a three-element segment, as described by [8]. Simulations done with and without asymmetric compartments confirmed that the difference in input resistance (RN) and system time constant (τ0) for a passive membrane model was < 1 %.
A rat Purkinje cell is known to have ~ 150,000 dendritic spines [3]. However, because the morphological data used to build the current model were obtained with light microscopic techniques, the location and shapes of dendritic spines for the reconstructed cell were not known. Accordingly, spines were not simulated. Instead, membrane surface was added to the spiny dendritic compartments (defined as dendrites with a diameter ~ 3.17 μm) to compensate for missing spines [4, 7]. On the basis of published electron microscopic (EM) reconstructions of rat Purkinje cell spines [2] we assumed a density of 13 spines per 1 μm dendritic length, with a membrane surface for a spine of 1.33 μm2 [2].
[1] JW Cooley and FA Jr Dodge. Digital computer solutions for excitation and propagation of the nerve impulse. Biophysical Journal, 6:583–599, 1966.
[2] KM Harris and JK Stevens. Dendritic spine of rat cerebellar purkinje cells: Serial electron microscopy with reference to their biophysical characteristics. Journal of Neuroscience, 8:4455–4469, 1988.
[3] RJ Harvey and RM Napper. Quantitative studies of the mammalian cerebellum. Progress in Neurobiology, 36:437–463, 1991.
[4] WR Holmes and CD Woody. Effects of uniform and non-uniform synaptic ‘activation-distributions’ on cable properties of modeled cortical pyramidal neurons. Brain Research, 505:12–22, 1989.
[5] W Rall. Theory of physiological properties of dendrites. Annals of the New York Academy of Sciences, 96:1071–1092, 1962.
[6] W Rall. Theoretical significance of dendritic trees for neuronal input-output relations. In RF Reiss, editor, Neuronal Theory and Modeling, pages 73–97. Stanford CA: Stanford University Press, 1964.
[7] M Rapp, Y Yarom, and I Segev. The impact of parallel fiber background activity on the cable properties of cerebellar Purkinje cells. Neural Computation, 4:518–533, 1992.
[8] I Segev, JW Fleshman, JP Miller, and B Bunow. Modeling the electrical behavior of anatomically complex neurons using a network analysis program: Passive membrane. Biological Cybernetics, 53:27–40, 1985.