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Neural Comput. 2019 Apr;31(4):653-680. doi: 10.1162/neco_a_01173. Epub 2019 Feb 14.

Biologically Realistic Mean-Field Models of Conductance-Based Networks of Spiking Neurons with Adaptation.

Author information

1
Unité de Neuroscience, Information et Complexité, CNRS FRE 3693, 91198 Gif sur Yvette, France matteo.divolo@unic.cnrs-gif.fr.
2
Centre de Recherche sur l'inflammation UMR 1149, Inserm-Université Paris Diderot, 75018 Paris, France, and Data Team, Departement d'informatique de l'Ecole normale supérieure, CNRS, PSL Research University, 75005 Paris, France, and European Institute for Theoretical Neuroscience, 75012 Paris, France alberto.romagnoni@ens.fr.
3
European Institute for Theoretical Neuroscience, 75012 Paris, France, and INFN Sezione di Roma, Rome 00185, Italy cristiano0capone@gmail.com.
4
Unité de Neuroscience, Information et Complexité, CNRS FRE 3693, 91198 Gif sur Yvette, France, and European Institute for Theoretical Neuroscience, 75012 Paris, France alain.destexhe@unic.cnrs-gif.fr.

Abstract

Accurate population models are needed to build very large-scale neural models, but their derivation is difficult for realistic networks of neurons, in particular when nonlinear properties are involved, such as conductance-based interactions and spike-frequency adaptation. Here, we consider such models based on networks of adaptive exponential integrate-and-fire excitatory and inhibitory neurons. Using a master equation formalism, we derive a mean-field model of such networks and compare it to the full network dynamics. The mean-field model is capable of correctly predicting the average spontaneous activity levels in asynchronous irregular regimes similar to in vivo activity. It also captures the transient temporal response of the network to complex external inputs. Finally, the mean-field model is also able to quantitatively describe regimes where high- and low-activity states alternate (up-down state dynamics), leading to slow oscillations. We conclude that such mean-field models are biologically realistic in the sense that they can capture both spontaneous and evoked activity, and they naturally appear as candidates to build very large-scale models involving multiple brain areas.

PMID:
30764741
DOI:
10.1162/neco_a_01173
[Indexed for MEDLINE]

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