Bulletin of Mathematical Biology (2009) 71: 1543–1579 DOI 10.1007/s11538-009-9413-y ORIGINAL ARTICLE A Computational Analysis of Localized Ca 2+ -Dynamics Generated by Heterogeneous Release Sites Zachary Cooper, Michael Greenwood, Borbala Mazzag ∗ Department of Mathematics, Humboldt State University, Arcata, CA 95521, USA Received: 13 August 2007 / Accepted: 10 February 2009 / Published online: 14 May 2009 © Society for Mathematical Biology 2009 Abstract We investigate the role of heterogeneous expression of IP 3 R and RyR in gen- erating diverse elementary Ca 2+ signals. It has been shown empirically (Wojcikiewicz and Luo in Mol. Pharmacol. 53(4):656–662, 1998; Newton et al. in J. Biol. Chem. 269(46):28613–28619, 1994; Smedt et al. in Biochem. J. 322(Pt. 2):575–583, 1997) that tissues express various proportions of IP 3 and RyR isoforms and this expression is dynamically regulated (Parrington et al. in Dev. Biol. 203(2):451–461, 1998; Fissore et al. in Biol. Reprod. 60(1):49–57, 1999; Tovey et al. in J. Cell Sci. 114(Pt. 22):3979– 3989, 2001). Although many previous theoretical studies have investigated the dynam- ics of localized calcium release sites (Swillens et al. in Proc. Natl. Acad. Sci. U.S.A. 96(24):13750–13755, 1999; Shuai and Jung in Proc. Natl. Acad. Sci. U.S.A. 100(2):506– 510, 2003a; Shuai and Jung in Phys. Rev. E, Stat. Nonlinear Soft Matter Phys. 67(3 Pt. 1):031905, 2003b; Thul and Falcke in Biophys. J. 86(5):2660–2673, 2004; DeRemi- gio and Smith in Cell Calcium 38(2):73–86, 2005; Nguyen et al. in Bull. Math. Biol. 67(3):393–432, 2005), so far all such studies focused on release sites consisting of iden- tical channel types. We have extended an existing mathematical model (Nguyen et al. in Bull. Math. Biol. 67(3):393–432, 2005) to release sites with two (or more) receptor types, each with its distinct channel kinetics. Mathematically, the release site is represented by a transition probability matrix for a collection of nonidentical stochastically gating channels coupled through a shared Ca 2+ domain. We demonstrate that under certain conditions a previously defined mean-field approximation of the coupling strength does not accurately reproduce the release site dynamics. We develop a novel approximation and establish that its performance in these instances is superior. We use this mathematical framework to study the effect of heterogeneity in the Ca 2+ -regulation of two colocalized channel types on the release site dynamics. We consider release sites consisting of channels with both Ca 2+ -activation and inactivation (“four-state channels”) and channels with Ca 2+ - activation only (“two-state channels”) and show that for the appropriate parameter values, synchronous channel openings within a release site with any proportion of two-state to four-state channels are possible, however, the larger the proportion of two-state channels, ∗ Corresponding author. E-mail address: borim@humboldt.edu (Borbala Mazzag). url: http://www.humboldt.edu/~bcm9. The first two authors contributed equally to the manuscript.