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A Computational Model of Interactions Between A Computational Model of Interactions Between Neuronal and Astrocytic Networks: The Role of Astrocytes in the Stability of the Neuronal Firing Rate Kerstin Lenk, Eero Satuvuori, Jules Lallouette, Antonio Ladrón-De-Guevara, Hugues Berry, Jari Hyttinen To cite this version: Kerstin Lenk, Eero Satuvuori, Jules Lallouette, Antonio Ladrón-De-Guevara, Hugues Berry, et al.. A Computational Model of Interactions Between Neuronal and Astrocytic Networks: The Role of Astrocytes in the Stability of the Neuronal Firing Rate. Frontiers in Computational Neuroscience, Frontiers, 2020, 13, pp.1-19. 10.3389/fncom.2019.00092. hal-02453587 HAL Id: hal-02453587 https://hal.archives-ouvertes.fr/hal-02453587 Submitted on 23 Jan 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. ORIGINAL RESEARCH published: 22 January 2020 doi: 10.3389/fncom.2019.00092 A Computational Model of Interactions Between Neuronal and Astrocytic Networks: The Role of Astrocytes in the Stability of the Neuronal Firing Rate Kerstin Lenk 1*†, Eero Satuvuori 1,2,3,4†, Jules Lallouette 5,6, Antonio Ladrón-de-Guevara 1, Hugues Berry 5,6 and Jari A. K. Hyttinen 1 1 BioMediTech, Faculty of Medicine and Health Technology, Tampere University, Tampere, Finland, 2 Institute for Complex Systems (ISC), National Research Council (CNR), Sesto Fiorentino, Italy, 3 Department of Physics and Astronomy, University of Florence, Sesto Fiorentino, Italy, 4 Department of Human Movement Sciences, MOVE Research Institute Amsterdam, Vrije Universiteit Amsterdam, Amsterdam, Netherlands, 5 INRIA, Villeurbanne, France, 6 LIRIS UMR5205, University of Lyon, Villeurbanne, France Edited by: Yu-Guo Yu, Fudan University, China Recent research in neuroscience indicates the importance of tripartite synapses and Reviewed by: gliotransmission mediated by astrocytes in neuronal system modulation. Although Maurizio De Pittà, the astrocyte and neuronal network functions are interrelated, they are fundamentally Basque Center for Applied Mathematics, Spain different in their signaling patterns and, possibly, the time scales at which they Xiaojuan Sun, operate. However, the exact nature of gliotransmission and the effect of the tripartite Beijing University of Posts and synapse function at the network level are currently elusive. In this paper, we propose Telecommunications (BUPT), China a computational model of interactions between an astrocyte network and a neuron *Correspondence: Kerstin Lenk network, starting from tripartite synapses and spanning to a joint network level. Our [email protected] model focuses on a two-dimensional setup emulating a mixed in vitro neuron-astrocyte †These authors have contributed cell culture. The model depicts astrocyte-released gliotransmitters exerting opposing equally to this work 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 Received: 24 June 2019 Accepted: 20 December 2019 networks with various levels of astrocyte contributions and neuronal activity levels. Our Published: 22 January 2020 results indicate that astrocytes prolong the burst duration of neurons, while restricting Citation: hyperactivity. Thus, in our model, the effect of astrocytes is homeostatic; the firing rate Lenk K, Satuvuori E, Lallouette J, of the network stabilizes to an intermediate level independently of neuronal base activity. Ladrón-de-Guevara A, Berry H and Hyttinen JAK (2020) A Computational Our computational model highlights the plausible roles of astrocytes in interconnected Model of Interactions Between astrocytic and neuronal networks. Our simulations support recent findings in neurons and Neuronal and Astrocytic Networks: The Role of Astrocytes in the Stability astrocytes in vivo and in vitro suggesting that astrocytic networks provide a modulatory of the Neuronal Firing Rate. role in the bursting of the neuronal network. Front. Comput. Neurosci. 13:92. doi: 10.3389/fncom.2019.00092 Keywords: simulation, neuron, astrocyte, network, calcium signaling, gliotransmission Frontiers in Computational Neuroscience | www.frontiersin.org 1 January 2020 | Volume 13 | Article 92 Lenk et al. Neural Network Model INTRODUCTION Dedicated computational models of the cross-talk between neuron networks and astrocytes have been successfully employed Neuroscience research has focused for long on neurons and to explore specific issues related to neuron-astrocyte interactions their interacting networks. However, the brain also consists of (for a review, see Oschmann et al., 2018). For example, Amiri a large number of other different cell types, among which glial et al. (2013) combined two coupled Morris-Lecar neuron models cells represent roughly 50% of the brain cells (Kettenmann and the dynamic astrocyte model of Postnov et al. (2009). and Verkhratsky, 2008; Azevedo et al., 2009). Among glial They simulated 50 pyramidal neurons, 50 interneurons, and 50 cells, astrocytes offer metabolic support to neurons, regulate astrocytes, connected in a chain-like manner, with each astrocyte the extracellular ions like potassium and calcium released connected to one pyramidal cell, one interneuron, and one upon neuronal activity (Dallérac et al., 2013; Hertz et al., neighboring astrocyte via gap junctions. This study suggested 2015) and uptake neurotransmitters (Bezzi et al., 1998; Araque that increasing the influence of the astrocytes toward the neurons et al., 2001; Perea and Araque, 2007; Volterra et al., 2014). leads to a reduction of the synchronized neuronal oscillations. Indeed, some of the synapses of the central nervous system are Valenza et al. (2013) developed a transistor-like description of contacted by astrocytes that wrap around them, thus forming the tripartite synapse and also included short-term synaptic a structural ensemble called the tripartite synapse: presynaptic plasticity for excitatory synapses. They simulated a network neuron, post-synaptic neuron and the ensheathing astrocyte containing 1,000 neurons and 1,500 astrocytes where at least one (Araque et al., 1999). astrocyte was linked to each neuron. This model was able to 2+ Intracellular calcium (Ca ) transients are a prominent produce spontaneous polychronous activity—i.e., reproducible readout signal of astrocyte activity, and happens at different time-locked but not synchronous firing—in neural groups. time scales (Kastanenka et al., 2019). They may be triggered More recently, Aleksin et al. (2017) presented neural network by neuronal activity (Di Castro et al., 2011; Dallérac et al., simulation software called ARACHNE, which is partially based 2013). At glutamatergic synapses, inositol 1,4,5-trisphosphate on the NEURON environment. This model includes a chain-like (IP3) is released in the astrocyte cytoplasm after some of structure in ring form, basic equations for the internal astrocytic the presynaptically released glutamate binds to metabotropic dynamics and extracellular diffusion of gliotransmitters (volume glutamate receptors in the astrocytic plasma membrane. The transmission). Additionally, Stimberg et al. (2019) recently 2+ 2+ released IP3 binds to IP3- and Ca -gated Ca channels in presented how the Brian 2 simulator can be used to model the membrane of the endoplasmic reticulum, thus leading to networks of interacting neurons and astrocytes. The authors 2+ a Ca elevation in the astrocyte cytosol. In return, these notably showed how, after a period of high external stimulation 2+ transient changes in the level of free cytoplasmic Ca lead of the neurons, gliotransmission can maintain a high level of 2+ to the opening of further IP3 channels in a Ca -induced neuronal activity and firing synchrony for several seconds after 2+ 2+ Ca release (CICR) mechanism that further amplifies Ca the end of the external stimulation. Although those modeling release from the endoplasmic reticulum. The internal calcium studies clearly advanced our understanding of the interaction pathways may also be linked to the release by the astrocyte of between neuron networks and astrocyte networks, few of them so-called gliotransmitters—like glutamate, D-serine, adenosine included all three of the following significant ingredients of triphosphate (ATP), and GABA (γ-aminobutyric acid)—that astrocyte networks: (i) Astrocytes form gap junction-based influence the activity of the contacted neurons (Pasti et al., 2001; networks that convey calcium-based signals as waves (Charles Henneberger et al., 2010; Zorec et al., 2012; Araque et al., 2014; et al., 1996; Fellin, 2009); (ii) each astrocyte contacts a large Sahlender et al., 2014). number of synapses, estimated to be up to 100,000 synapses Neuron-astrocyte interactions are thought to occur— per astrocyte in rat hippocampus (Bushong et al., 2002); and or be initiated—at the thinnest astrocytic processes/branchlets (iii) astrocytes can release distinct types of gliotransmitters (Bazargani and Attwell, 2016; Bindocci et al., 2017). Furthermore, (Di Castro et al., 2011; Sahlender et al., 2014; Schwarz et al.,
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