title: A deterministic model predicts the properties of stochastic calcium oscillations in airway smooth muscle cells.
abstract: The inositol trisphosphate receptor ([Formula: see text]) is one of the most important cellular components responsible for oscillations in the cytoplasmic calcium concentration. Over the past decade, two major questions about the [Formula: see text] have arisen. Firstly, how best should the [Formula: see text] be modeled? In other words, what fundamental properties of the [Formula: see text] allow it to perform its function, and what are their quantitative properties? Secondly, although calcium oscillations are caused by the stochastic opening and closing of small numbers of [Formula: see text], is it possible for a deterministic model to be a reliable predictor of calcium behavior? Here, we answer these two questions, using airway smooth muscle cells (ASMC) as a specific example. Firstly, we show that periodic calcium waves in ASMC, as well as the statistics of calcium puffs in other cell types, can be quantitatively reproduced by a two-state model of the [Formula: see text], and thus the behavior of the [Formula: see text] is essentially determined by its modal structure. The structure within each mode is irrelevant for function. Secondly, we show that, although calcium waves in ASMC are generated by a stochastic mechanism, [Formula: see text] stochasticity is not essential for a qualitative prediction of how oscillation frequency depends on model parameters, and thus deterministic [Formula: see text] models demonstrate the same level of predictive capability as do stochastic models. We conclude that, firstly, calcium dynamics can be accurately modeled using simplified [Formula: see text] models, and, secondly, to obtain qualitative predictions of how oscillation frequency depends on parameters it is sufficient to use a deterministic model.
authors.affiliation: Department of Mathematics, University of Auckland, Auckland, New Zealand.
authors.forename: Pengxing
authors.initials: P
authors.lastname: Cao
authors.affiliation: Department of Microbiology and Physiological Systems, University of Massachusetts Medical School, Worcester, Massachusetts, United States of America.
authors.forename: Xiahui
authors.initials: X
authors.lastname: Tan
authors.affiliation: Department of Mathematics, University of Auckland, Auckland, New Zealand.
authors.forename: Graham
authors.initials: G
authors.lastname: Donovan
authors.affiliation: Department of Microbiology and Physiological Systems, University of Massachusetts Medical School, Worcester, Massachusetts, United States of America.
authors.forename: Michael J
authors.initials: MJ
authors.lastname: Sanderson
authors.affiliation: Department of Mathematics, University of Auckland, Auckland, New Zealand.
authors.forename: James
authors.initials: J
authors.lastname: Sneyd
mesh_terms: D000818:Animals; D002118:Calcium / Q000378:metabolism*; D020013:Calcium Signaling / Q000502:physiology*; D053496:Inositol 1,4,5-Trisphosphate Receptors / Q000378:metabolism*; D016014:Linear Models; D008168:Lung / Q000737:chemistry / Q000166:cytology* / Q000378:metabolism; D051379:Mice; D008807:Mice, Inbred BALB C; D008954:Models, Biological; D032389:Myocytes, Smooth Muscle / Q000166:cytology / Q000378:metabolism / Q000502:physiology*; D013269:Stochastic Processes
chemical_list: D053496:Inositol 1,4,5-Trisphosphate Receptors; D002118:Calcium