Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics
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...
| Main Authors: | , , |
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| Format: | Article |
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Elsevier
2009
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| Online Access: | https://eprints.nottingham.ac.uk/1120/ |
| _version_ | 1848790540833783808 |
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| author | Thul, Ruediger Coombes, Stephen Smith, G.D. |
| author_facet | Thul, Ruediger Coombes, Stephen Smith, G.D. |
| author_sort | Thul, Ruediger |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T18:14:15Z |
| format | Article |
| id | nottingham-1120 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:14:15Z |
| publishDate | 2009 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-11202020-05-04T20:27:05Z https://eprints.nottingham.ac.uk/1120/ Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics Thul, Ruediger Coombes, Stephen Smith, G.D. 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. Elsevier 2009 Article PeerReviewed Thul, Ruediger, Coombes, Stephen and Smith, G.D. (2009) Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics. Physica D, 238 . pp. 2142-2152. ISSN 0167-2789 http://www.elsevier.com/wps/find/journaldescription.cws_home/505714/description#description doi:10.1016/j.physd.2009.08.011 doi:10.1016/j.physd.2009.08.011 |
| spellingShingle | Thul, Ruediger Coombes, Stephen Smith, G.D. Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics |
| title | Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics |
| title_full | Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics |
| title_fullStr | Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics |
| title_full_unstemmed | Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics |
| title_short | Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics |
| title_sort | sensitisation waves in a bidomain fire-diffuse-fire model of intracellular ca²⁺ dynamics |
| url | https://eprints.nottingham.ac.uk/1120/ https://eprints.nottingham.ac.uk/1120/ https://eprints.nottingham.ac.uk/1120/ |