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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
41/2010

Quantitative aspects of L-type Ca$^{2+}$ currents

Henry Tuckwell

Abstract

$\rm Ca^{2+}$ currents in neurons and muscle cells have been classified as being one of 5 types of which four, L, N, P/Q and R were said to be high threshold and one, T, was designated low threshold. This review focuses on quantitative aspects of L-type currents. L-type channels are now distinguished according to their structure as one of four main subtypes $\rm Ca_v1.1 - \rm Ca_v1.4$. L-type calcium currents play many fundamental roles in cellular dynamical processes including pacemaking in neurons and cardiac cells, the activation of transcription factors involved in synaptic plasticity and in immune cells.

The half-activation potentials of L-type currents $\rm I_{CaL}$ have been ascribed values as low as -50 mV and as high as near 0 mV. The inactivation of $\rm I_{CaL}$ has been found to be both voltage (VDI) and calcium-dependent (CDI) and the latter component may involve calcium-induced calcium release. CDI is often an important aspect of dynamical models of cell electrophysiology.

We describe the basic components in modeling $\rm I_{CaL}$ including activation and both voltage and calcium dependent inactivation and the two main approaches to determining the current. We review, by means of tables of values from over 65 representative studies, the various details of the dynamical properties associated with $\rm I_{CaL}$ that have been found experimentally or employed in the last 25 years in deterministic modeling in various nervous system and cardiac cells. Distributions and statistics of several parameters related to activation and inactivation are obtained. There are few reliable experimental data on L-type calcium current kinetics for cells at physiological calcium ion concentrations. Neurons are divided approximately into two groups with experimental half-activation potentials that are high, $\approx$ -18.3 mV, or low, $\approx$ -36.4 mV, which correspond closely with those for $\rm Ca_v1.2$ and $\rm Ca_v1.3$ channels in physiological solutions. There are very few experimental data on time constants of activation, those available suggesting values around 0.5 to 1 ms. In modeling, a wide range of time constants has been employed. A major problem for quantitative studies due to lack of experimental data has been the use of kinetic parameters from one cell type for others. Inactivation time constants for VDI have been found experimentally with average 65 ms.

Examples of calculations of $\rm I_{CaL}$ are made for linear and constant field methods and the effects of CDI are illustrated for single and double pulse protocols and the results compared with experiment. The review ends with a discussion and analysis of experimental subtype ($\rm Ca_v1.1 - \rm Ca_v1.4$) properties and their roles in normal, including pacemaker activity, and many pathological states.

Received:
Aug 3, 2010
Published:
Aug 9, 2010
Keywords:
L-type, Calcium, Neuronal models

Related publications

inJournal
2012 Repository Open Access
Henry C. Tuckwell

Quantitative aspects of L-type \(Ca^{2+}\) currents

In: Progress in neurobiology, 96 (2012) 1, pp. 1-31