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Mathematical Medicine and Biology Advance Access originally published online on March 21, 2008
Mathematical Medicine and Biology 2008 25(1):65-85; doi:10.1093/imammb/dqn004
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Calcium release site ultrastructure and the dynamics of puffs and sparks

Hilary DeRemigio and Jeffrey R. Groff

Department of Applied Science, The College of William and Mary, Williamsburg, VA 23187, USA

Gregory D. Smith{dagger}

Department of Applied Science, McGlothlin-Street Hall, Room 305, The College of William and Mary, Williamsburg, VA 23187, USA and Mathematical, Biosciences Institute, Ohio State University, Columbus, OH 43210, USA

{dagger} Email: greg{at}as.wm.edu

Received on August 13, 2007. Revised on January 18, 2008. Accepted on January 29, 2008.

When Markov chain models of intracellular Ca2+-regulated Ca2+ channels are coupled via a mathematical representation of a Ca2+ microdomain, simulated Ca2+ release sites may exhibit the phenomenon of ‘stochastic Ca2+ excitability’ reminiscent of Ca2+ puffs and sparks. Interestingly, some single-channel models that include Ca2+ inactivation are not particularly sensitive to channel density, so long as the requirement for inter-channel communication is satisfied, while other single-channel models that do not include Ca2+ inactivation open and close synchronously only when the channel density is in a prescribed range. This observation led us to hypothesize that single-channel models with Ca2+ inactivation would be less sensitive to the details of release site ultrastructure than models that lack a slow Ca2+ inactivation process. To determine if this was the case, we simulated Ca2+ release sites composed of instantaneously coupled Ca2+-regulated Ca2+ channels whose random spatial locations were chosen from a uniform distribution on a disc of specified radius and compared the resulting release site dynamics to simulations with channels arranged on hexagonal lattices. Analysis of puff/spark statistics confirmed our hypothesis that puffs and sparks are less sensitive to the spatial organization of release sites when the single-channel model includes a slow inactivation process. We also investigated the validity of several different mean-field reductions that do not explicitly account for the details of release site ultrastructure. The most successful approximation maintains a distinction between each channel's substantial influence on its own stochastic gating and the collective contribution of elevated [Ca2+] from neighbouring channels.

Keywords: puff; spark; ultrastructure; calcium


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