## A deterministic model predicts the properties of stochastic calcium oscillations in airway smooth muscle cells.

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##### Author

Cao, P; Tan, X; Donovan, G; Sanderson, MJ; Sneyd, J##### Date

2014-08##### Source Title

PLoS Computational Biology##### Publisher

Public Library of Science (PLoS)##### University of Melbourne Author/s

Cao, Pengxing##### Affiliation

School of Mathematics and Statistics##### Metadata

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Journal Article##### Citations

Cao, P., Tan, X., Donovan, G., Sanderson, M. J. & Sneyd, J. (2014). A deterministic model predicts the properties of stochastic calcium oscillations in airway smooth muscle cells.. PLoS Comput Biol, 10 (8), pp.e1003783-. https://doi.org/10.1371/journal.pcbi.1003783.##### Access Status

**Open Access**

##### Open Access at PMC

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4133161##### 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.

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