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A Mathematical Analysis of the Generation and Termination of Calcium Sparks

University Laboratory of Physiology and Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford, United Kingdom

Correspondence: Address reprint requests to Dr. Robert Hinch, E-mail: hinch{at}maths.ox.ac.uk.

Calcium sparks are local regenerative releases of Ca²⁺ from a cluster of ryanodine receptors on the sarcoplasmic reticulum. During excitation-contraction coupling in cardiac cells, Ca²⁺ sparks are triggered by Ca²⁺ entering the cell via the T-tubules (Ca²⁺-induced Ca²⁺ release). However under conditions of calcium overload, Ca²⁺ sparks can be triggered spontaneously. The exact process by which Ca²⁺ 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 Ca²⁺ 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.

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