Cellular signalling and excitable media
Calcium signalling has been a recurring theme in my work on excitable systems. I am particularly interested in how discrete calcium-release events give rise to travelling waves, and how intracellular geometry and calcium stores shape propagation.
Calcium release and wave propagation
Calcium-induced calcium release provides a positive feedback mechanism: calcium entering the cytosol can trigger further release from intracellular stores. Spatial coupling through diffusion allows local events to recruit neighbouring release sites, generating sparks, waves or oscillations.
My early work with Yulia Timofeeva and Robert Hinch developed fire-diffuse-fire descriptions of this process. Release sites are treated as discrete events coupled by diffusion, making it possible to analyse wave speeds, initiation, propagation failure and the role of stochastic release without resolving every molecular detail.
Geometry, stores and propagation
A central mathematical issue is the interaction between local release rules and the geometry of the cell. Work with Rüdiger Thul and collaborators developed bidomain threshold models in which calcium moves between cytosol and intracellular stores. These models allow the effects of store dynamics and sensitisation to be studied alongside spatial propagation.
In subsequent work with Martin Bootman and colleagues, we investigated calcium organisation in atrial myocytes. Whole-cell three-dimensional models show how the distribution of release sites and intracellular structures can influence the persistence and shape of calcium waves. These questions matter because abnormal propagation can be associated with pro-arrhythmic activity.
Selected publications
- R. Thul, K. Rietdorf, M. D. Bootman and S. Coombes (2015), Unifying principles of calcium wave propagation — insights from a three-dimensional model for atrial myocytes, Biochimica et Biophysica Acta — Molecular Cell Research 1853, 2131–2143.
- R. Thul, S. Coombes, H. L. Roderick and M. D. Bootman (2012), Subcellular calcium dynamics in a whole cell model of an atrial myocyte, Proceedings of the National Academy of Sciences 109, 2150–2155.
- R. Thul, S. Coombes and G. D. Smith (2009), Sensitisation of waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics, Physica D 238, 2142–2152.
- R. Thul, G. D. Smith and S. Coombes (2008), A bidomain threshold model of propagating calcium waves, Journal of Mathematical Biology 56, 435–463.
- S. Coombes, R. Hinch and Y. Timofeeva (2004), Receptors, sparks and waves in a fire-diffuse-fire framework for calcium release, Progress in Biophysics and Molecular Biology 85, 197–216.
- S. Coombes and Y. Timofeeva (2003), Sparks and waves in a stochastic fire-diffuse-fire model of calcium release, Physical Review E 68, 021915.
- Y. Timofeeva and S. Coombes (2003), Wave bifurcation and propagation failure in a model of calcium release, Journal of Mathematical Biology 47, 249–269.
- S. Coombes (2001), The effect of ion pumps on the speed of travelling waves in the fire-diffuse-fire model of Ca²⁺ release, Bulletin of Mathematical Biology 63, 1–20.