Modifying the models of calcium dynamics in astrocytes by ryanodine release

The influence of ryanodine channels on the cytosole Ca$^{2+}$ dynamics was studied. We added the equations for ryanodine receptors and voltage-gated calcium channels into the original De Pitta et al. model of Ca$^{2+}$. The derived model was shown to have significantly wider range of predictions: we derived the frequency of cytosole calcium spontaneous oscillations (which are absent in the original De Pitta et al. model) for various existing models of Ca$^{2+}$ signalling in astrocytes. Particularly, the initial De Pitta et al. results can be converted to either Lavrentovich and Hemkin model or in the Dupont et al model predictions. The absence of the Ca$^{2+}$ oscillations in astrocytes with the active ryanodine channels only was recently reported. This behaviour can be achieved in our model predictions for the certain values of parameters, which are supposedly responsible for the bifurcation landscape between the oscillatory and non-oscillatory dynamics of cytosol Ca$^{2+}$ in astrocytes. We also investigated the interplay between the spontaneous and glutamate-triggered oscillations.