Understanding the role of astrocytes in brain computation is a nascent challenge, promising immense rewards, in terms of new neurobiological knowledge that can be translated into artificial intelligence. In our ongoing effort to identify principles endowing the astrocyte with unique functions in brain computation, and translate them into neural-astrocytic networks (NANs), we propose a biophysically realistic model of an astrocyte that preserves the experimentally observed spatial allocation of its distinct subcellular compartments. We show how our model may encode, and modulate, the extent of synchronous neural activity via calcium waves that propagate intracellularly across the astrocytic compartments. This relationship between neural activity and astrocytic calcium waves has long been speculated but it is still lacking a mechanistic explanation. Our model suggests an astrocytic "calcium cascade" mechanism for neuronal synchronization, which may empower NANs by imposing periodic neural modulation known to reduce coding errors. By expanding our notions of information processing in astrocytes, our work aims to solidify a computational role for non-neuronal cells and incorporate them into artificial networks.