Eavesdropping on the Social Lives of Ca²⁺ Sparks

¹ University of Kentucky
² University of Kentucky College of Medicine

^* To whom correspondence should be addressed. E-mail: leightonizu{at}uky.edu.

Submitted on May 9, 2007
Revised on June 21, 2007
Accepted on 17 July 2007

	Abstract

Ca²⁺ sparks arise from the stochastic opening of spatially discrete clusters of ryanodine receptors (RyRs) 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 2-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 of RyR regulators have on the intrinsic activity of CRUs and on the coupling between them.

Key Words: calcium sparks, excitation-contraction coupling, modeling