A Computational Analysis of Localized Ca2 -Dynamics Generated by Heterogeneous Release Sites

作者：Cooper Zachary; Greenwood Michael; Mazzag Borbala^*

来源：Bulletin of Mathematical Biology, 2009, 71(7): 1543-1579.

DOI：10.1007/s11538-009-9413-y

• Heterogeneous release site
• Stochastic gating
• Synchronous channel activity
• Puff
• Spark
• Puff/spark termination
• Ryanodine and IP3 receptor subtypes
• Coexpression of ryanodine receptors and IP3 receptors

We investigate the role of heterogeneous expression of IP3R and RyR in generating diverse elementary Ca2 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 IP3 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 dynamics 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; DeRemigio 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 identical 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 Ca2 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 Ca2 -regulation of two colocalized channel types on the release site dynamics. We consider release sites consisting of channels with both Ca2 -activation and inactivation ("four-state channels") and channels with Ca2 -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, the more sensitive the dynamics are to the exact spatial positioning of the channels and the distance between channels. Specifically, the clustering of even a small number of two-state channels interferes with puff/spark termination and increases puff durations or leads to a tonic response.

• 出版日期2009-10