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Eavesdropping on the Social Lives of Ca²⁺ Sparks

Leighton T. Izu ^*, Tamás Bányász ^* , C. William Balke ^*  and Ye Chen-Izu ^*

^* Departments of Internal Medicine and Physiology, University of Kentucky College of Medicine, Lexington, Kentucky; and Department of Physiology, Medical and Health Science Center, University of Debrecen, Debrecen, Hungary

Correspondence: Address reprint requests to L. T. Izu, Tel.: 859-323-6882; E-mail: leightonizu{at}uky.edu.

Ca²⁺ sparks arise from the stochastic opening of spatially discrete clusters of ryanodine receptors called a Ca²⁺ release unit (CRU). If the RyR clusters were not spatially separated, then Ca²⁺ released from one RyR would immediately diffuse to its neighbor and lead to uncontrolled, runaway Ca²⁺ release throughout the cell. While physical separation provides some isolation from neighbors, CRUs are not incommunicado. When inter-neighbor interactions become large enough, Ca²⁺ waves spontaneously emerge. A more circumscribed interaction shows up in high-speed two-dimensional confocal images as jumping Ca²⁺ sparks that seem to be sequentially activated along the Z-line and across Z-lines. However, since Ca²⁺ sparks are stochastic events how can we tell whether two sparks occurring close together in space and time are causally related or appeared simply by coincidence? Here we develop a mathematical method to disentangle cause and coincidence in a statistical sense. From our analysis we derive three fundamental properties of Ca²⁺ spark generation: 1), the "intrinsic" spark frequency, the spark frequency one would observe if the CRUs were incommunicado; 2), the coupling strength, which measures how strongly one CRU affects another; and 3), the range over which the communication occurs. These parameters allow us to measure the effect RyR regulators have on the intrinsic activity of CRUs and on the coupling between them.

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