A mathematical analysis of the generation and termination of calcium sparks

Calcium sparks are local regenerative releases of Ca(2+) from a cluster of ryanodine receptors on the sarcoplasmic reticulum. During excitation-contraction coupling in cardiac cells, Ca(2+) sparks are triggered by Ca(2+) entering the cell via the T-tubules (Ca(2+)-induced Ca(2+) release). However under conditions of calcium overload, Ca(2+) sparks can be triggered spontaneously. The exact process by which Ca(2+) sparks terminate is still an open question, although both deterministic and stochastic processes are likely to be important. In this article, asymptotic methods are used to analyze a single Ca(2+) spark model, which includes both deterministic and stochastic biophysical mechanisms. The analysis calculates both spark frequencies and spark duration distributions, and shows under what circumstances stochastic transitions are important. Additionally, a model of the coupling of the release channels via the FK-binding protein is analyzed.