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A Simplified Local Control Model of Calcium-Induced Calcium Release in Cardiac Ventricular Myocytes

R. Hinch ^*, J. L. Greenstein , A. J. Tanskanen , L. Xu  and R. L. Winslow 

^* Mathematical Institute, University of Oxford, Oxford, United Kingdom; and The Center for Cardiovascular Bioinformatics and Modeling and The Whitaker Biomedical Engineering Institute, The Johns Hopkins University Whiting School of Engineering and School of Medicine, Baltimore, Maryland

Correspondence: Address reprint requests to Dr. Robert Hinch, Oxford University, Mathematical Institute, 24–29 St. Giles, Oxford OX1 3LB UK. Tel.: 44-1-865-280-614; E-mail: hinch{at}maths.ox.ac.uk.

Calcium (Ca²⁺)-induced Ca²⁺ release (CICR) in cardiac myocytes exhibits high gain and is graded. These properties result from local control of Ca²⁺ release. Existing local control models of Ca²⁺ release in which interactions between L-Type Ca²⁺ channels (LCCs) and ryanodine-sensitive Ca²⁺ release channels (RyRs) are simulated stochastically are able to reconstruct these properties, but only at high computational cost. Here we present a general analytical approach for deriving simplified models of local control of CICR, consisting of low-dimensional systems of coupled ordinary differential equations, from these more complex local control models in which LCC-RyR interactions are simulated stochastically. The resulting model, referred to as the coupled LCC-RyR gating model, successfully reproduces a range of experimental data, including L-Type Ca²⁺ current in response to voltage-clamp stimuli, inactivation of LCC current with and without Ca²⁺ release from the sarcoplasmic reticulum, voltage-dependence of excitation-contraction coupling gain, graded release, and the force-frequency relationship. The model does so with low computational cost.

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