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It is now widely accepted that glia cells and gamma-aminobutyric acidergic (GABA) interneurons dynamically regulate synaptic transmission and neuronal activity in time and space. This paper presents a biophysical model that captures the interaction between an astrocyte cell, a GABA interneuron and pre/postsynaptic neurons. Specifically, GABA released from a GABA interneuron triggers in astrocytes the release of calcium (Ca2+) from the endoplasmic reticulum via the inositol 1, 4, 5-trisphosphate (IP3) pathway. This results in gliotransmission which elevates the presynaptic transmission probability rate (PR) causing weight potentiation and a gradual increase in postsynaptic neuronal firing, that eventually stabilizes. However, by capturing the complex interactions between IP3, generated from both GABA and the 2-arachidonyl glycerol (2-AG) pathway, and PR, this paper shows that this interaction not only gives rise to an initial weight potentiation phase but also this phase is followed by postsynaptic bursting behavior. Moreover, the model will show that there is a presynaptic frequency range over which burst firing can occur. The proposed model offers a novel cellular level mechanism that may underpin both seizure-like activity and neuronal synchrony across different brain regions.