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Alexandersen CG, Duprat C, Ezzati A, Houzelstein P, Ledoux A, Liu Y, Saghir S, Destexhe A, Tesler F, Depannemaecker D. A Mean Field to Capture Asynchronous Irregular Dynamics of Conductance-Based Networks of Adaptive Quadratic Integrate-and-Fire Neuron Models. Neural Comput 2024; 36:1433-1448. [PMID: 38776953 DOI: 10.1162/neco_a_01670] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2023] [Accepted: 02/01/2024] [Indexed: 05/25/2024]
Abstract
Mean-field models are a class of models used in computational neuroscience to study the behavior of large populations of neurons. These models are based on the idea of representing the activity of a large number of neurons as the average behavior of mean-field variables. This abstraction allows the study of large-scale neural dynamics in a computationally efficient and mathematically tractable manner. One of these methods, based on a semianalytical approach, has previously been applied to different types of single-neuron models, but never to models based on a quadratic form. In this work, we adapted this method to quadratic integrate-and-fire neuron models with adaptation and conductance-based synaptic interactions. We validated the mean-field model by comparing it to the spiking network model. This mean-field model should be useful to model large-scale activity based on quadratic neurons interacting with conductance-based synapses.
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Affiliation(s)
| | - Chloé Duprat
- Paris-Saclay University, Institute of Neuroscience, CNRS, 91400 Saclay, France
- Institut de Neurosciences des Systèmes, Aix-Marseille University, INSERM, 13005 Marseille, France
| | - Aitakin Ezzati
- Institut de Neurosciences des Systèmes, Aix-Marseille University, INSERM, 13005 Marseille, France
| | - Pierre Houzelstein
- Group for Neural Theory, LNC2, INSERM U960, DEC, École Normale Supérieure-PSL University, 75005 Paris, France
| | - Ambre Ledoux
- Paris-Saclay University, Institute of Neuroscience, CNRS, 91400 Saclay, France
| | - Yuhong Liu
- Institute of Physiological Chemistry, Johannes Gutenberg University of Mainz, 55128 Mainz, Germany
- Institute of Experimental Epileptology and Cognition Research, University of Bonn Medical Center, 53127 Bonn, Germany
| | - Sandra Saghir
- Department of Software Engineering and Theoretical Computer Science, Technische Universität Berlin, 10623 Berlin, Germany
| | - Alain Destexhe
- Paris-Saclay University, Institute of Neuroscience, CNRS, 91400 Saclay, France
| | - Federico Tesler
- Paris-Saclay University, Institute of Neuroscience, CNRS, 91400 Saclay, France
| | - Damien Depannemaecker
- Institut de Neurosciences des Systèmes, Aix-Marseille University, INSERM, 13005 Marseille, France
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Spaeth A, Haussler D, Teodorescu M. Model-Agnostic Neural Mean Field With The Refractory SoftPlus Transfer Function. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.02.05.579047. [PMID: 38370695 PMCID: PMC10871173 DOI: 10.1101/2024.02.05.579047] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/20/2024]
Abstract
Due to the complexity of neuronal networks and the nonlinear dynamics of individual neurons, it is challenging to develop a systems-level model which is accurate enough to be useful yet tractable enough to apply. Mean-field models which extrapolate from single-neuron descriptions to large-scale models can be derived from the neuron's transfer function, which gives its firing rate as a function of its synaptic input. However, analytically derived transfer functions are applicable only to the neurons and noise models from which they were originally derived. In recent work, approximate transfer functions have been empirically derived by fitting a sigmoidal curve, which imposes a maximum firing rate and applies only in the diffusion limit, restricting applications. In this paper, we propose an approximate transfer function called Refractory SoftPlus, which is simple yet applicable to a broad variety of neuron types. Refractory SoftPlus activation functions allow the derivation of simple empirically approximated mean-field models using simulation results, which enables prediction of the response of a network of randomly connected neurons to a time-varying external stimulus with a high degree of accuracy. These models also support an accurate approximate bifurcation analysis as a function of the level of recurrent input. Finally, the model works without assuming large presynaptic rates or small postsynaptic potential size, allowing mean-field models to be developed even for populations with large interaction terms.
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Affiliation(s)
- Alex Spaeth
- Electrical and Computer Engineering Department, University of California, Santa Cruz, Santa Cruz, CA, United States
- Genomics Institute, University of California, Santa Cruz, Santa Cruz, CA, United States
| | - David Haussler
- Genomics Institute, University of California, Santa Cruz, Santa Cruz, CA, United States
- Biomolecular Engineering Department, University of California, Santa Cruz, Santa Cruz, CA, United States
| | - Mircea Teodorescu
- Electrical and Computer Engineering Department, University of California, Santa Cruz, Santa Cruz, CA, United States
- Genomics Institute, University of California, Santa Cruz, Santa Cruz, CA, United States
- Biomolecular Engineering Department, University of California, Santa Cruz, Santa Cruz, CA, United States
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