Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics

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

Abstract

We present a bidomain threshold model of intracellular calcium (Ca²⁺) dynamics in which, as suggested by recent experiments, the cytosolic threshold for Ca²⁺ liberation is modulated by the Ca²⁺ concentration in the releasing compartment. We explicitly construct stationary fronts and determine their stability using an Evans function approach. Our results show that a biologically motivated choice of a dynamic threshold, as opposed to a constant threshold, can pin stationary fronts that would otherwise be unstable. This illustrates a novel mechanism to stabilise pinned interfaces in continuous excitable systems. Our framework also allows us to compute travelling pulse solutions in closed form and systematically probe the wave speed as a function of physiologically important parameters. We find that the existence of travelling wave solutions depends on the time scale of the threshold dynamics, and that facilitating release by lowering the cytosolic threshold increases the wave speed. The construction of the Evans function for a travelling pulse shows that of the co-existing fast and slow solutions the slow one is always unstable.

Citation

Thul, R., Coombes, S., & Smith, G. (2009). Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics. Physica D: Nonlinear Phenomena, 238, https://doi.org/10.1016/j.physd.2009.08.011

• Journal Article Type: Article
• Publication Date: Jan 1, 2009
• Deposit Date: Sep 2, 2009
• Publicly Available Date: Sep 2, 2009
• Journal: Physica D
• Print ISSN: 0167-2789
• Electronic ISSN: 1872-8022
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 238
• DOI: https://doi.org/10.1016/j.physd.2009.08.011
• Public URL: https://nottingham-repository.worktribe.com/output/1014927
• Publisher URL: http://www.elsevier.com/wps/find/journaldescription.cws_home/505714/description#description