Starting from the experimental data on ATP evoked calcium responses in astrocytes, a biophysical model describing these phenomena was built. The simulations showed, in agreement with the experimental findings, that the intracellular calcium fluxes mediated by the P2X and P2Y purinoreceptors are responsible for the biphasic ATP evoked calcium response in astrocytes. Then, the modulation effects on the neural dynamics arising from the release of glutamate from astrocyte are also investigated. By using a minimal network model describing a neuron coupled to the astrocyte, we demonstrated that the calcium extrusion rate through the astrocyte membrane is critically involved in the generation of different firing patterns of the neuron.