Termination of Cardiac Ca2+ Sparks: An Investigative Mathematical Model of Calcium-Induced Calcium Release

Model Status

This is the original unchecked version of the model imported from the previous CellML model repository, 24-Jan-2006.

Model Structure

The activation of Ca²⁺ sparks is an essential step in cardiac excitation-contraction coupling. A Ca²⁺ spark arises when voltage-gated, L-type Ca²⁺ channels in the sarcolemmal (SL) membrane open. Ca²⁺ diffuses into the cell, causing the concentration of intracellular calcium [Ca²⁺]_i to rise, especially in the region close to the channel in the sub-space between the sarcolemmal and the sarcoplasmic reticulum (SR) membranes (see the figure below). This local increase in [Ca²⁺]_i triggers the opening of SR Ca²⁺-release channels (ryanodine receptors, or RyRs) located in the sub-space. Ca²⁺ from the intracellular SR store is released, causing a large further increase in [Ca²⁺]_i, which is recognised as a Ca²⁺ spark. Ca²⁺ spark activation displays both high gain - a small amount of trigger Ca²⁺ activates a large amount of released Ca²⁺ - and positive feedback - release of Ca²⁺ raises [Ca²⁺]_i and tends to trigger more Ca²⁺ release.

Despite the extensive knowledge outlined above, there is still uncertainty about the mechanisms underlying the termination of Ca²⁺ sparks. In their 2002 paper, Eric A. Sobie, Keith W. Dilly, Jader dos Santos Cruz, W. Jonathan Lederer, and M. Saleet Jafri propose a new hypothesis called sticky cluster, to describe the behaviour of Ca²⁺ sparks in the heart. Their mathematical model focuses on how Ca²⁺ sparks are terminated, and how the variable number of RyRs in a cluster may influence spark behaviour. They suggest that spark termination is dependent on two factors: the effect of [Ca²⁺]_lumen on RyR gating, and and coupled gating between RyRs in a cluster.

The complete original paper reference is cited below:

Termination of Cardiac Ca²⁺ Sparks: An Investigative Mathematical Model of Calcium-Induced Calcium Release, Eric A. Sobie, Keith W. Dilly, Jader dos Santos Cruz, W. Jonathan Lederer, and M. Saleet Jafri, 2002, Biophysical Journal , 83, 59-78. (Full text and PDF versions of the article are available to subscribers on the Biophysical Journal website.) PubMed ID: 12080100

Layout of the model elements.

The model is separated out into two main components: 1) Mathematical description of SR Ca²⁺ release through an RyR cluster at the extracellular-sarcolemmal junction. 2) Mathematical description of the Ca²⁺ spark produced by the Ca²⁺ efflux. This component of the model is largely based on a previously published model of Ca²⁺ diffusion, buffering and imaging processes that produce the Ca²⁺ spark (Smith et al., 1998).