A Mathematical Model of 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 Ca2+ 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 Ca2+ mediates synaptic plasticity, which is in conformity with the majority of the recent findings (Perea & Araque, 2007; Henneberger et al., 2010; Navarrete et al., 2012). 
Shivendra Tewari and Kaushik Majumdar
q-bio.NC math.DS q-bio.CB q-bio.SC