Multi-scale models of local control of calcium induced calcium release

Calcium-induced-calcium-release in cardiac myocytes is the release of Ca2+Ca2+ from the sarcoplasmic reticulum (SR) triggered by Ca2+Ca2+ entering the cell through L-type Ca2+Ca2+ channels. The Ca2+Ca2+ is released through ryanodine receptors which ‘sense’ local [Ca2+][Ca2+] in the small region (the diadic space) positioned between the t-tubules and the SR. The length-scale of a single diad is of the order of 10 nm and the diffusion time-scale is of order of 1μs with each cell containing approximately 10,000 diadic spaces which act independently. However, typically one is interested in Ca2+Ca2+ currents at the whole cell level and higher. This is a multi-scale problem and cannot be solved by direct computation. In this paper we develop a general framework for deriving approximate solutions of these models.