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De Schutter: Purkinje Cell Model

Estimates of Model Parameters

The Hodgkin-Huxley equations employed by this model require detailed information on channel kinetics and peak conductances. In principle, all of these data should be obtained from the cell being simulated. However, all the necessary data are rarely available for any particular neuron. For this reason it is usually necessary to obtain kinetic information from a variety of sources.

Estimating channel conductances

Constructing an accurate representation of an ionic channel also requires an estimate of the channel . However, channel conductance values measured in voltage-clamp experiments are often quite variable [8] and are only indicative. For this reason, channel s in the model were not based on experimental measurements [1, 2].

Estimating channel densities

Having established and parameterized the equations governing the voltage-dependent behavior of the ionic conductances in this cell, it was necessary to determine the channel densities in the model. Because precise information on channel densities is not technically obtainable, channel densities, usually expressed as , are largely a free parameter in detailed single-cell models [1, 4, 7, 10].

Estimates of other parameters for ionic channels

Constructing an accurate representation of an ionic channel also requires an estimate of the channel . However, channel conductance values measured in voltage-clamp experiments are often quite variable [8] and are only indicative. For this reason, channel s in the model were not based on experimental measurements [1, 2].

Temperature dependence of channel kinetics

Temperature is a well-known critical parameter for channel kinetics [3]. In the current simulations the in vivo and in vitro data used to tune the model were collected at 37 ^∘ C whereas all of the published voltage-clamp data were obtained at room temperature. Assuming a Q 10 factor of 3 [5] all rate constants were multiplied by a factor of 5.

Modeling calcium concentrations

In the present model realistic simulation of Ca²⁺ concentrations was not attempted. However, computation of Ca²⁺ concentrations was required to activate the KC and K2 channels. Because these channels are assumed to be sensitive to the quickly changing, high Ca²⁺ concentrations just below the membrane surface [6], Ca²⁺ concentrations were computed in a thin submembrane shell [9]. These shells integrated the full Ca²⁺ inflow through the CaP and CaT channels. Their volume and decay time constants were initially free parameters in the model. The model tuning resulted in shells 0.2 μm deep with a decay time of 0.1 ms. The basal internal Ca²⁺ concentration was 0.040 μM; the outside concentration was constant at 2.4 mM. These concentrations were also used to compute Nernst potentials [3] for the CaP and CaT currents.

References