A Computational Model of Interactions Between Neuronal and Astrocytic Networks: The Role of Astrocytes in the Stability of the Neuronal Firing Rate

Abstract

Recent research in neuroscience indicates the importance of tripartite synapses and gliotransmission mediated by astrocytes in neuronal system modulation. Although the astrocyte and neuronal network functions are interrelated, they are fundamentally different in their signaling patterns and, possibly, the time scales at which they operate. However, the exact nature of gliotransmission and the effect of the tripartite synapse function at the network level are currently elusive. In this paper, we propose a computational model of interactions between an astrocyte network and a neuron network, starting from tripartite synapses and spanning to a joint network level. Our model focuses on a two-dimensional setup emulating a mixed in vitro neuron-astrocyte cell culture. The model depicts astrocyte-released gliotransmitters exerting opposing effects on the neurons: increasing the release probability of the presynaptic neuron while hyperpolarizing the post-synaptic one at a longer time scale. We simulated the joint networks with various levels of astrocyte contributions and neuronal activity levels. Our results indicate that astrocytes prolong the burst duration of neurons, while restricting hyperactivity. Thus, in our model, the effect of astrocytes is homeostatic; the firing rate of the network stabilizes to an intermediate level independently of neuronal base activity. Our computational model highlights the plausible roles of astrocytes in interconnected astrocytic and neuronal networks. Our simulations support recent findings in neurons and astrocytes in vivo and in vitro suggesting that astrocytic networks provide a modulatory role in the bursting of the neuronal network.

Larger Connection Radius Increases Hub Astrocyte Number in a 3-D Neuron–Astrocyte Network Model

“…In the discrete-time model INEXA [13], the neuronal firing rate λ i of a postsynaptic neuron i is calculated for each time slice t k of 5 ms as follows:…”

“…We extended the INEXA model [13] with the following modifications: To change from a planar to a 3D topology, we kept a similar volume as described in the paper (Figure 1). The network space from planar dimensions (750x750x10 µm 3 , which resembles the culture area of a planar MEA) was altered to 180x180x180 µm 3 in 3D.…”

“…Recently, we implemented a combined neuron-astrocyte network model called INEXA [13], [14]. Therewith, we investigated the astrocyte's influence on the neuronal network stability.…”

“…The simulations resembled in vitro experiments with planar multielectrode arrays (MEAs). In the INEXA model, the astrocytes and neurons communicated through the tripartite synapse by exchanging activating and depressing transmitters [13]. In the model, each astrocyte was connected to several hundreds of synapses.…”

“…Since network nodes with higher degrees exist, an astrocyte connected to more than 75% of its neighbors is defined as a hub astrocyte, which presents the strongest influence in the overall network activity [9], [10]. First, we create planar and 3D neuron-astrocyte networks using the previously-mentioned INEXA model [13] and compare their characteristics. Second, we vary the distance range within which two astrocytes are coupled to each other in the 3D network.…”