A Mathematical Model of Tripartite Synapse: Astrocyte Induced Synaptic Plasticity

Shivendra Tewari† shivendra.tewari@gmail.com
Systems Science and Informatics Unit Indian Statistical Institute 8th Mile, Mysore Road Bangalore 560059, India

Kaushik Majumdar kmajumdar@isibang.ac.in Systems Science and Informatics Unit Indian Statistical Institute 8th Mile, Mysore Road Bangalore 560059, India

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). 1 Introduction One of the most significant challenges in neuroscience is to identify the cellular and molecular processes that underlie learning and memory formation (Lynch, 2004). Cajal originally hypothesized that information storage relies on changes in strength of synaptic connections between neurons that are active (Cajal, 1913). Hebb supported this hypothesis and proposed that if two neurons are active at the same time, the synaptic efficiency of the appropriate synapse will be strengthened (Hebb, 1949). Synaptic transmission is a dynamic process. Post-synaptic responses wax and wane as pre-synaptic activity evolves. Forms of synaptic enhancement, such as facilitation, augmentation, and post-tetanic potentiation, are usually attributed to effects of a

† Shivendra Tewari’s present address is Biotechnology & Bioengineering Center and Department of Physiology, Medical College of Wisconsin, 8701 Watertown Plank Road, Milwaukee, WI 53226, USA.

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residual elevation in pre-synaptic Ca2+ concentration ([Ca2+]), acting on one or more molecular targets that appear to be distinct from the secretory trigger responsible for fast exocytosis and phasic release of transmitter to single action potential (Zucker & Regehr, 2002). It is now well established that the astrocytic mGluR detects synaptic activity and responds via activation of the calcium-induced calcium release pathway, leading to elevated Ca2+ levels. The spread of these levels within micro-domain of one cell can coordinate the activity of disparate synapses that are associated with the same micro-domain (Perea & Araque, 2002). The notion of tripartite synapse consisting of pre-synaptic neuron, post-synaptic neuron and astrocyte has taken a firm root in experimental (Araque, et al., 1999; Newman, 2003; Perea & Araque, 2007) as well as theoretical neuroscience (Nadkarni & Jung, 2003; Volman et al., 2007; Nadkarni, et al., 2008). Astrocytes play crucial roles in the control of Hebbian plasticity (Fellin, 2009). There is a recent report, that at least in the hippocampus, astrocyte Ca2+ signaling does not modulate short-term or long-term synaptic plasticity (Agulhon, et al., 2010). However evidences of astrocytic modulation of synaptic plasticity are more abundant including in hippocampus (Vernadakis, 1996; Haydon, 2001; Yang et al., 2003; Andersson, 2010; Henneberger, et al., 2010). Neuronal activities can trigger Ca2+ elevations in astrocytes (Porter & McCarthy, 1996; Fellin, 2009) leading to concentration increase in adjacent glial cells including astrocytes, which expresses a variety of receptors (Newman, 2003). These activated receptors increase astrocyte [Ca2+], and release transmitters, including glutamate, D-serine, ATP (Parpura et al., 1994; Henneberger et al., 2010) etc. The released gliotransmitters feed-back onto the pre-synaptic terminal either to enhance or to depress further release of neurotransmitter (Newman, 2003; Navarrete & Araque, 2010) including glutamate, which is mediated by Ca2+ concentration in the pre-synaptic terminal. It is worthy to note that Ca2+ elevations are both necessary and sufficient to evoke glutamate release from astrocytes (Haydon, 2001). On the other hand short-term synaptic depression is caused by depletion of the releasable vesicle pool due to recent release in response to pre-synaptic action potential (Wu & Borst, 1999). This entire chain of Ca2+ mediated pre-synaptic activity consisting of both short-term enhancement (STE) and short-term depression (STD) can be called short-term synaptic plasticity or simply short-term plastici