The Reduced Model of Astrocyte Calcium Dynamics in GABAeric Tripartite Synapse

Reduced macroscopic scale models of neuronal dynamics allow to perform large scale multiple neuron simulation in real time. The detailed biophysical model of tripartite gamma-aminobutyric acid (GABA) synapse is well studied and its reduction to a macroscale model allow to account an astrocyte influence on short and long term synaptic plasticity. In the work the detailed model of the astrocyte calcium dynamics is reproduced and the reduced model is presented. The detailed model reproduce a typical calcium concentration waves in astrocyte cytosol during presynaptic neuron stimulation in GABAeric synapse. The reduced model that can reproduce calcium waves is presented as a two-dimensional dynamical system. The functions of two system’s variables evolution and time constants were evaluated from the detailed model trajectory in phase plane. It have been shown that the trajectory of the reduced system on phase plane can reflect astrocyte calcium dynamics on the basis of a series of presynaptic neuron action potential times. The astrocyte calcium concentration function reproduced by the reduced model determine extrasynaptic slow currents for presynaptic and postsynaptic neuron and can be further applied for direct computation of inhibitory postsynaptic potential of GABA synapse.