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The Nonlinear Dynamics of Calcium

  • Vivien Kirk
  • James SneydEmail author
Part of the Frontiers in Applied Dynamical Systems: Reviews and Tutorials book series (FIADS, volume 1)

Abstract

Oscillations and travelling waves in the concentration of free cytosolic calcium are complex dynamical phenomena that play vital roles in cellular function, controlling such processes as contraction, secretion and differentiation. Although, nowadays, these oscillations and waves may be observed experimentally with relative ease, we still lack a rigorous understanding of, firstly, the mechanisms underlying these waves and oscillations in different cell types, and, secondly, the mathematical structures that underlie these complex dynamics. Thus, the study of calcium waves and oscillations is one area in which modellers have, over the years, played a major role. Here, we review our current understanding of the nonlinear dynamics of calcium waves and oscillations, restricting our attention almost wholly to deterministic models.

Keywords

Hopf Bifurcation Bifurcation Diagram Slow Variable Bifurcation Parameter Singular Limit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

This work was supported by the Marsden Fund of the Royal Society of New Zealand and by the National Institutes of Health of the USA (NIDCR R01DE019245).

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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of AucklandAucklandNew Zealand

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