A bidomain threshold model of propagating calcium waves

Thul, Ruediger; Smith, G.D.; Coombes, Stephen

Abstract

We present a bidomain fire-diffuse-fire model that facilitates mathematical analysis of propagating waves of elevated intracellular calcium (Ca) in living cells. Modelling Ca release as a threshold process allows the explicit construction of travelling wave solutions to probe the dependence of Ca wave speed on physiologically important parameters such as the threshold for Ca release from the endoplasmic reticulum (ER) to the cytosol, the rate of Ca resequestration from the cytosol to the ER, and the total [Ca] (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 Ca 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 Ca wave speed on the total [Ca].


The original publication is available at www.springerlink.com (Journal of Mathematical Biology)

Citation

Thul, R., Smith, G., & Coombes, S. (2008). A bidomain threshold model of propagating calcium waves. Journal of Mathematical Biology, 56(4), https://doi.org/10.1007/s00285-007-0123-5

• Journal Article Type: Article
• Online Publication Date: Sep 5, 2007
• Publication Date: Apr 1, 2008
• Deposit Date: Oct 22, 2007
• Publicly Available Date: Oct 22, 2007
• Journal: Journal of Mathematical Biology
• Print ISSN: 0303-6812
• Electronic ISSN: 1432-1416
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 56
• Issue: 4
• DOI: https://doi.org/10.1007/s00285-007-0123-5
• Keywords: Bidomain models, Calcium waves, Stability, Wave bifurcation
• Public URL: https://nottingham-repository.worktribe.com/output/1015329
• Publisher URL: http://dx.doi.org/10.1007/s00285-007-0123-5
• Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/s00285-007-0123-5