Spiking Neural P Systems with Astrocytes Producing Calcium

The astrocytes are cells which play an essential role in the functioning and interaction of neurons by feeding the respective neurons with calcium ions. Drawing inspiration from this two-way relationship in which the astrocytes influence and are influenced by the neurons by means of calcium ions, in this paper, we define and study spiking neural P systems with astrocytes producing calcium. Distinct from the usual firing rules in spiking neural P systems, the firing condition not only depends on the spikes collected in a neuron but also on the calcium units received from astrocytes. From the perspective of topological structure, the new variant is shown as a directed graph in which synapses link either astrocytes or neurons, as well as astrocytes to neurons and conversely. The computational power of spiking neural P systems with astrocytes producing calcium is investigated; it is proved that these systems using a limited number of rules are Turing universal as both number generating and number accepting devices. It is also presented how to obtain normal forms by removing forgetting rules and delays while preserving the computational power.