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A bidomain threshold model of propagating calcium waves

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Abstract

We present a bidomain fire-diffuse-fire model that facilitates mathematical analysis of propagating waves of elevated intracellular calcium (Ca2+) in living cells. Modeling Ca2+ release as a threshold process allows the explicit construction of traveling wave solutions to probe the dependence of Ca2+ wave speed on physiologically important parameters such as the threshold for Ca2+ release from the endoplasmic reticulum (ER) to the cytosol, the rate of Ca2+ resequestration from the cytosol to the ER, and the total [Ca2+] (cytosolic plus ER). Interestingly, linear stability analysis of the bidomain fire-diffuse-fire model predicts the onset of dynamic wave instabilities leading to the emergence of Ca2+ waves that propagate in a back-and-forth manner. Numerical simulations are used to confirm the presence of these so-called ‘tango waves’ and the dependence of Ca2+ wave speed on the total [Ca2+].

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK

    R. Thul & S. Coombes

  2. Department of Applied Science, The College of William and Mary, Williamsburg, VA, 23187, USA

    G. D. Smith

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  1. R. Thul
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Thul, R., Smith, G.D. & Coombes, S. A bidomain threshold model of propagating calcium waves. J. Math. Biol. 56, 435–463 (2008). https://doi.org/10.1007/s00285-007-0123-5

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  • DOI: https://doi.org/10.1007/s00285-007-0123-5

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