This model corresponds to the model presented in Denizot et al, 2019. The model indicates that the frequency of calcium signals crucially depends on the spatial organization of the IP3R channels, including their clustering and co-localization with the other sources of calcium influx to the cytosol. Spontaneous calcium signals generated by the model with realistic PAPs volume and calcium concentration successfully reproduce spontaneous calcium transients that we measured in calcium micro-domains with confocal microscopy. To our knowledge, this model is the first model suited to the investigation of spontaneous calcium dynamics in fine astrocytic processes, a crucial step towards a better understanding of the spatio-temporal integration of astrocyte signals in response to neuronal activity.