A bidomain threshold model of propagating calcium waves

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⁺].