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Carlu M, Chehab O, Dalla Porta L, Depannemaecker D, Héricé C, Jedynak M, Köksal Ersöz E, Muratore P, Souihel S, Capone C, Zerlaut Y, Destexhe A, di Volo M. A mean-field approach to the dynamics of networks of complex neurons, from nonlinear Integrate-and-Fire to Hodgkin-Huxley models. J Neurophysiol 2020; 123:1042-1051. [PMID: 31851573 PMCID: PMC7099478 DOI: 10.1152/jn.00399.2019] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2019] [Revised: 12/05/2019] [Accepted: 12/09/2019] [Indexed: 11/22/2022] Open
Abstract
We present a mean-field formalism able to predict the collective dynamics of large networks of conductance-based interacting spiking neurons. We apply this formalism to several neuronal models, from the simplest Adaptive Exponential Integrate-and-Fire model to the more complex Hodgkin-Huxley and Morris-Lecar models. We show that the resulting mean-field models are capable of predicting the correct spontaneous activity of both excitatory and inhibitory neurons in asynchronous irregular regimes, typical of cortical dynamics. Moreover, it is possible to quantitatively predict the population response to external stimuli in the form of external spike trains. This mean-field formalism therefore provides a paradigm to bridge the scale between population dynamics and the microscopic complexity of the individual cells physiology.NEW & NOTEWORTHY Population models are a powerful mathematical tool to study the dynamics of neuronal networks and to simulate the brain at macroscopic scales. We present a mean-field model capable of quantitatively predicting the temporal dynamics of a network of complex spiking neuronal models, from Integrate-and-Fire to Hodgkin-Huxley, thus linking population models to neurons electrophysiology. This opens a perspective on generating biologically realistic mean-field models from electrophysiological recordings.
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Affiliation(s)
- M. Carlu
- Department of Integrative and Computational Neuroscience, Paris-Saclay Institute of Neuroscience, Centre National de la Recherche Scientifique, Gif sur Yvette, France
| | - O. Chehab
- Ecole Normale Superieure Paris-Saclay, France
| | - L. Dalla Porta
- Institut d’Investigacions Biomèdiques August Pi i Sunyer, Barcelona, Spain
| | - D. Depannemaecker
- Department of Integrative and Computational Neuroscience, Paris-Saclay Institute of Neuroscience, Centre National de la Recherche Scientifique, Gif sur Yvette, France
| | - C. Héricé
- Strathclyde Institute of Pharmacy and Biomedical Sciences, Glasgow, Scotland, United Kingdom
| | - M. Jedynak
- Université Grenoble Alpes, Grenoble Institut des Neurosciences and Institut National de la Santé et de la Recherche Médicale (INSERM), U1216, France
| | - E. Köksal Ersöz
- INSERM, U1099, Rennes, France
- MathNeuro Team, Inria Sophia Antipolis Méditerranée, Sophia Antipolis, France
| | - P. Muratore
- Physics Department, Sapienza University, Rome, Italy
| | - S. Souihel
- Université Côte d’Azur, Inria Sophia Antipolis Méditerranée, France
| | - C. Capone
- Department of Integrative and Computational Neuroscience, Paris-Saclay Institute of Neuroscience, Centre National de la Recherche Scientifique, Gif sur Yvette, France
| | - Y. Zerlaut
- Department of Integrative and Computational Neuroscience, Paris-Saclay Institute of Neuroscience, Centre National de la Recherche Scientifique, Gif sur Yvette, France
| | - A. Destexhe
- Department of Integrative and Computational Neuroscience, Paris-Saclay Institute of Neuroscience, Centre National de la Recherche Scientifique, Gif sur Yvette, France
| | - M. di Volo
- Department of Integrative and Computational Neuroscience, Paris-Saclay Institute of Neuroscience, Centre National de la Recherche Scientifique, Gif sur Yvette, France
- Laboratoire de Physique Théorique et Modelisation, Université de Cergy-Pontoise, Cergy-Pontoise, France
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