Calcium Current (I-CaHVA) and Ca2+ Dynamics

A single species of voltage-gated calcium channel, the N-type high voltage-activated neuronal subtype (CaHVA), was used in the model. The current mediated by this channel was previously described in rat cerebellar granule cells in situ by Rossi et al. (1994). Voltage-gated calcium channels that contribute to the propagation of action potentials in neurons are typically classified by voltage dependence and gating kinetics. Two major subtypes are those that activate at low depolarization, usually below or at threshold for NaF, and inactivate quickly, and those that, like the CaHVA included in this model, activate at depolarizations closer to 0mV and inactivate slowly.

Aside from initiating a variety of intracellular signalling pathways, the I-CaHVA inward current contributes both to membrane depolarization during the action potential and to the activation of voltage and calcium gated potassium channels. Although calcium currents have been shown to support several mechanistically distinct types of bursting activity, such as plateau depolarization and calcium spiking as seen in cardiac tissue, and KCa / CaHVA bursting wherein calcium accumulation in a thin shell beneath the interior membrane surface during a fast spike train activates hyperpolarizing KCa channels to such a degree that repetive firing is eventually shut off, the role of I-CaHVA in this model is more to tune spike width, attenuation, and threshold sensitivity (via interactions with I-KCa) than to act as a driving factor in repetetive firing and/or bursting.

Modeling of intracellular Ca2+ dynamics, taken from D’Angelo et al. (2001), was necessary for computation of I-CaHVA inactivation and I-KCa gating. The following equation was used to determine intracellular Ca2+ concentration:

d [Ca2+]/d t = -Ica/(2F Ad) — (b Ca([Ca2+] — [Ca2+]o)) (7)

where F is Faraday’s constant (9.649 x 104 coulombs per mole) is the depth of the shell adjacent to the internal membrane surface of area A, b Ca is a constant describing the rate of Ca2+ buffering via various intracellular fluxes, diffusion, and Ca2+ proteins, and [Ca2+]o indicates extracellular Ca+ concentration at rest. As in D’Angelo et al. (2001), Ca2+ dynamics were set to produce Ca2+ transients on the order of 1m M, Ca0 was taken from measurements of rat cerebellar granule cells in culture (Irving et al., 1992), and the following parameters were used in equation (7) above: d = 200nm, b Ca = 1.5, and [Ca2+]o = 100nM.

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