Analysis of Spark Versus Non-Spark Mediated SR Calcium Leak using a Langevin Description of Stochastic Calcium Release

Abstract

Markov chain models of the coupled gating of intracellular calcium channels are used to study the stochastic dynamics of SR calcium release and whole cell calcium homeostasis [see e.g., Hartman et al. AJP Heart Circ Physiol 299(6):H1996-2008, 2010]. However, the large number of channels per release site (100-250) results in a combinatorial state space explosion that causes whole cell models that enumerate the Markov chain state space to be computationally intensive. We present an alternative Langevin formulation, i.e., a system of stochastic ordinary differential equations, for the stochastic dynamics of calcium release sites composed of many identical channels. The Langevin formulation accurately reproduces the stationary distribution for the fraction of open channels determined from the corresponding Markov chain model and over a wide range of parameters yields similar spark properties (e.g., the distribution of spark amplitude and duration). We present a whole cell model of calcium homeostasis that incorporates the Langevin description of stochastic calcium release by coupling the associated Fokker-Planck equation to concentration balance equations for bulk myoplasmic and network SR calcium under the assumption of rapid equilibration of diadic subspace and junctional SR calcium. We found that myoplasmic and SR calcium increased both spark and non-spark mediated SR calcium leak, consistent with a recent experimental study [Bovo et al. J Physiol 589(24) 6039-6050, 2011]. Future work will investigate SR calcium leak during intracellular calcium transients and extensions of this modeling approach.