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De Schutter: Purkinje Cell Model


Figure 1: Activation and inactivation properties of the A current (KA, —) in the model. Seady-state activation and inactivation vs. voltage are plotted at the left, the time constants of activation and inactivation(τm and τh) vs. voltage in the middle (Note: Semilogarithmic scale), and a simulation of representative voltage-clamp currents at the right, obtained from a spherical cell and assuming a complete block of all other channels. The voltage clamps simulate steps from a holding potential of -110 to -70 mV up to 0 mV in 10 mV increments. The voltage-clamp current amplitude has been scaled arbitrarily because we mainly wanted to demonstrate the current kinetics.

The A Current (KA)

The presence of a conductance like an A current (KA) in the Purkinje cell was shown by [6]. We derived our equations for KA from the original reports on A currents [23] modified to fit the data in the two reports on Purkinje cell A currents that were available at that time. The whole cell voltage-clamp study of cultured Purkinje cells by [5] (their Fig. 9) provided data about the activation and inactivation time constants and the steady-state inactivation, and a single-electrode voltage-clamp study in slice by [7] supplied steady-state activation data.

Recently [9] published a more complete report on a single-electrode voltage-clamp study of the Purkinje cell. The average threshold for activation they report is lower than the value used in our model, but there seems to be a large natural variability in the activation curves (compare their Fig. 1 with their Table 1). The steady-state inactivation curve of [9] is similar to ours and to the kinetics of A currents in other systems [28] but they report a much slower inactivation time constant than [5].

One point of contention in the literature about the distribution of ionic channels involves the presence or absence of an A current in the distal dendrites [16]. One argument for a more extensive distribution is that a depolarizing bias current, which would inactivate A currents, also causes the dendrite to fire spikes more easily. However, a similar result would be expected if the depolarization also activated a plateau current, as shown in Fig. 11. Moreover, in contrast to the expected 4-aminopyridine (4-AP) sensitivity of A currents [8], the outward current described by [6] was not blocked by 4-AP. In addition, voltage-clamp data [9] do not support a distal dendritic location of the A current. Patch-clamp studies of cultured Purkinje cells [4] have shown the A current to be present in both somatic and dendritic membrane, but it is likely that patches were obtained from smooth dendrites only. In the current model an A current was present in the soma and main dendrite. However, dendritic spiking was more influenced by the K2 Ca2+ -activated K+ current, which allowed a finer control of dendritic excitability than the A current, which inactivated quickly during long current injections.


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[8]   MA Rogawski. The A-current: How ubiquitous a feature of excitable cells is it? Trends in Neurosciences, 8:214–219, 1985.

[9]   Y Wang, JC Strahlendorf, and HK Strahlendorf. A transient voltage-dependent outward potassium current in mammalian cerebellar purkinje cells. Brain Research, 567:153–158, 1991.