Thul R., Smith G.D., Coombes S. — A bidomain threshold model of propagating calcium waves :: Электронная библиотека попечительского совета мехмата МГУ

We present a bidomain fire-diffuse-fire model that facilitates mathematical analysis of propagating waves of elevated intracellular calcium ( $Ca^{2+}$ ) in living cells. Modeling $Ca^{2+}$ release as a threshold process allows the explicit construction of traveling wave solutions to probe the dependence of $Ca^{2+}$ wave speed on physiologically important parameters such as the threshold for $Ca^{2+}$ release from the endoplasmic reticulum (ER) to the cytosol, the rate of $Ca^{2+}$ resequestration from the cytosol to the ER, and the total [ $Ca^{2+}$ ] (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 $Ca^{2+}$ 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 $Ca^{2+}$ wave speed on the total [ $Ca^{2+}$ ].