A phase plane analysis of neuron–astrocyte interactions

Abstract

Intensive experimental studies have shown that astrocytes are active partners in modulation of synaptic transmission. In the present research, we study neuron–astrocyte signaling using a biologically inspired model of one neuron synapsing one astrocyte. In this model, the firing dynamics of the neuron is described by the Morris–Lecar model and the Ca2+ dynamics of a single astrocyte explained by a functional model introduced by Postnov and colleagues. Using the coupled neuron–astrocyte model and based on the results of the phase plane analyses, it is demonstrated that the astrocyte is able to activate the silent neuron or change the neuron spiking frequency through bidirectional communication. This suggests that astrocyte feedback signaling is capable of modulating spike transmission frequency by changing neuron spiking frequency. This effect is described by a saddle–node on invariant circle bifurcation in the coupled neuron–astrocyte model. In this way, our results suggest that the neuron–astrocyte crosstalk has a fundamental role in producing diverse neuronal activities and therefore enhances the information processing capabilities of the brain.