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Proc Natl Acad Sci U S A. 2017 Feb 14;114(7):1456-1461. doi: 10.1073/pnas.1614613114. Epub 2017 Feb 1.

On the dynamical structure of calcium oscillations.

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Department of Mathematics, University of Auckland, Auckland 1142, New Zealand;
Department of Mathematics, University of Auckland, Auckland 1142, New Zealand.
Department of Pharmacology and Physiology, University of Rochester, Rochester, NY 14642.
Department of Microbiology and Physiological Systems, University of Massachusetts Medical School, Worcester, MA 01655.
Department of Pharmacology, School of Dentistry, Health Sciences University of Hokkaido, Ishikari-Tobetsu, Hokkaido 061-0293, Japan.


Oscillations in the concentration of free cytosolic Ca2+ are an important and ubiquitous control mechanism in many cell types. It is thus correspondingly important to understand the mechanisms that underlie the control of these oscillations and how their period is determined. We show that Class I Ca2+ oscillations (i.e., oscillations that can occur at a constant concentration of inositol trisphosphate) have a common dynamical structure, irrespective of the oscillation period. This commonality allows the construction of a simple canonical model that incorporates this underlying dynamical behavior. Predictions from the model are tested, and confirmed, in three different cell types, with oscillation periods ranging over an order of magnitude. The model also predicts that Ca2+ oscillation period can be controlled by modulation of the rate of activation by Ca2+ of the inositol trisphosphate receptor. Preliminary experimental evidence consistent with this hypothesis is presented. Our canonical model has a structure similar to, but not identical to, the classic FitzHugh-Nagumo model. The characterization of variables by speed of evolution, as either fast or slow variables, changes over the course of a typical oscillation, leading to a model without globally defined fast and slow variables.


cytosolic calcium concentration modeling, multiple time scales; inositol trisphosphate receptor; mathematical modeling

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