Abstract

Mathematical models of calcium release sites derived from Markov chain mod- els of intracellular calcium channels exhibit collective gating reminiscent of the experimentally observed phenomenon of stochastic calcium excitability (i.e., calcium puffs and sparks). We present a Kronecker structured representation for calcium release site models and perform benchmark stationary distribu- tion calculations using numerical iterative solution techniques that leverage this structure. In this context we find multi-level methods and certain pre- conditioned projection methods superior to simple Gauss-Seidel type iterations. Response measures such as the number of channels in a particular state con- verge more quickly using these numerical iterative methods than occupation measures calculated via Monte Carlo simulation.