Five voltage-gated potassium channels previously shown to be expressed in rat cerebellar granule cells (D’Angelo et al., 2001), all conducting an outward hyperpolarizing current, were included in the model. Gating kinetics, activation, and inactivation parameters were taken from D’Angelo et al. (2001), and channel densities on the membrane were adjusted to optimally fit target ELL granular cell voltage outputs as a function of input stimulus conductances.

The first group of potassium channels, I-KV, I-KA, and I-KCa, contribute to the hyperpolarizing downstoke of the action potential spike. I-KV is a typical delayed rectifier, Hodgkin-Huxley (1952) type channel that provides the main rapid, hyperpolarizing current to counteract I-NaF during the spike. I-KV activates rapidly following strong depolarization, and does not inactivate but rather exhibits a rapid exponential decay with time after opening. I-KA, the afterhyperpolarizing current, is also fast activating but differs from I-KV in that it inactivates as a function of voltage and tends to exert its hyperpolarizing effects slightly later in the action potential downstroke and also more prominently in the spike-initiating neighborhood of the I-NaF threshold than I-KV. I-KCa, also known as the "big-K channel" for its large single channel hyperpolarizing conductance, exhibits dual activation dependence on depolarizing voltage and intracellular Ca²⁺ concentration. The functional significance of this for the spike train or bursting event is progressive spike attenuation due to Ca²⁺ accumulation, as local Ca²⁺ concentrations near the membrane can rise dramatically during repetitive spiking.

The second group of K⁺ channels included in the model tend to be active at membrane potentials hyperpolarized from threshold for I-NaF; in other words, they exert more influence on the dynamics of integrating synaptic inputs and setting subthreshold oscillations, preferential input frequencies (resonance), and overall excitability from resting potential. I-KIR is an inwardly rectifying channel, which means that it activates at membrane potentials close to resting (between –80 and –65mV) and inactivates during a spike or bursting event. The overall effect of I-KIR on the model is similar to that of the leak currents, in that its two main roles are indiscriminately dampening excitatory inputs and aiding in membrane potential return to resting following the cessation of depolarizing events such as repetetive firing and bursting. Although I-KIR exerts a direct effect on dampening initial excitability, it acts primarily to complete the final return to resting and not to actually cause the depolarizing event to end.

The final K⁺ channel included in the model, I-KM, is responsible for the slow-activating, non-inactivating, muscarinic sensitive, TEA insensitive K⁺ current described recently by D’Angelo et al. (2001) to be necessary for intrinsic bursting and resonance in rat cerebellar granule cells. Typically, this current will activate with the first depolarizing upstroke and continue to increase slowly during a burst until it eventually prevents initiation of a subsequent spike. Although the current does not increase between spikes, it also does not decrease significantly until a considerable amount of time has passed at hyperpolarized membrane potentials (on the order of 30-40 ms, several times longer than the average interspike interval (ISI) of 5-12ms seen in this model).

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