title: Markov chain models of coupled intracellular calcium channels: Kronecker structured representations and benchmark stationary distribution calculations.
abstract: Mathematical models of calcium release sites derived from Markov chain models 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 distribution calculations using numerical iterative solution techniques that leverage this structure. In this context we find multi-level methods and certain preconditioned projection methods superior to simple Gauss-Seidel type iterations. Response measures such as the number of channels in a particular state converge more quickly using these numerical iterative methods than occupation measures calculated via Monte Carlo simulation.
authors.affiliation: Department of Applied Science, The College of William and Mary, Williamsburg, VA 23187, USA.
authors.forename: Hilary
authors.initials: H
authors.lastname: Deremigio
authors.forename: Peter
authors.initials: P
authors.lastname: Kemper
authors.forename: M Drew
authors.initials: MD
authors.lastname: Lamar
authors.forename: Gregory D
authors.initials: GD
authors.lastname: Smith
mesh_terms: D000465:Algorithms; D015220:Calcium Channels / Q000737:chemistry* / Q000378:metabolism*; D020013:Calcium Signaling; D019295:Computational Biology; D003198:Computer Simulation; D015640:Ion Channel Gating; D007700:Kinetics; D008390:Markov Chains; D008954:Models, Biological
chemical_list: D015220:Calcium Channels