A mathematical model of the tripartite synapse: astrocyte-induced synaptic plasticity.

In this paper, we present a biologically detailed mathematical model of tripartite synapses, where astrocytes modulate short-term synaptic plasticity. The model consists of a pre-synaptic bouton, a post-synaptic dendritic spine-head, a synaptic cleft and a peri-synaptic astrocyte controlling Ca(2 + ) dynamics inside the synaptic bouton. This in turn controls glutamate release dynamics in the cleft. As a consequence of this, glutamate concentration in the cleft has been modeled, in which glutamate reuptake by astrocytes has also been incorporated. Finally, dendritic spine-head dynamics has been modeled. As an application, this model clearly shows synaptic potentiation in the hippocampal region, i.e., astrocyte Ca(2 + ) mediates synaptic plasticity, which is in conformity with the majority of the recent findings (Perea and Araque (Science 317, 1083-1086, 2007); Henneberger et al. (Nature 463, 232-236, 2010); Navarrete et al. (PLoS Biol. 10, e1001259, 2012)).