Mean-field approximation of network of biophysical neurons driven by conductance-based ion exchange

Bandyopadhyay, Abhirup; Rabuffo, Giovanni; Calabrese, Carmela; Gudibanda, Kashyap; Depannemaecker, Damien; Ivanov, Anton; Bernard, Christophe; Jirsa, Viktor K.; Petkoski, Spase

doi:10.1101/2021.10.29.466427

Cited by 10 publications

(7 citation statements)

References 102 publications

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“…Many different approaches are possible to capture brain dynamics at the mesoscopic scale [Bandyopadhyay et al, 2021, Brunel and Hakim, 2015, Cakan and Obermayer, 2021, El Boustani and Destexhe, 2009, Huang and Lin, 2018, Montbrió et al, 2015, Nykamp and Tranchina, 2000, Schmutz et al, 2020, Schwalger and Chizhov, 2019, Wilson and Cowan, 1972], and each of these approaches is relevant to capture specific features of the dynamics of spiking networks. Some specificities of the mean-field methods studied here are the possibility of considering the sparse connectivity, conductance-based interactions and the finite size of the populations.…”

Section: Discussionmentioning

confidence: 99%

Dynamics and bifurcation structure of a mean-field model of adaptive exponential integrate-and-fire networks

Kusch,

Depannemaecker,

Destexhe

et al. 2023

Preprint

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The study of brain activity spans diverse scales and levels of description, and requires the development of computational models alongside experimental investigations to explore integrations across scales. The high dimensionality of spiking networks presents challenges for understanding their dynamics. To tackle this, a mean-field formulation offers a potential approach for dimensionality reduction while retaining essential elements. Here, we focus on a previously developed mean-field model of Adaptive Exponential (AdEx) networks, utilized in various research works. We provide a systematic investigation of its properties and bifurcation structure, which was not available for this model. We show that this provides a comprehensive description and characterization of the model to assist future users in interpreting their results. The methodology includes model construction, stability analysis, and numerical simulations. Finally, we offer an overview of dynamical properties and methods to characterize the mean-field model, which should be useful for for other models.

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Section: Discussionmentioning

confidence: 99%

Dynamics and bifurcation structure of a mean-field model of adaptive exponential integrate-and-fire networks

Kusch,

Depannemaecker,

Destexhe

et al. 2023

Preprint

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“…Other adiabatic approaches in this field are appearing, e.g. to consider slow variables modeling conductance-based ion exchange [2].…”

Section: Discussionmentioning

confidence: 99%

Exact reduction methods for networks of neurons with complex dynamic phenotypes

Guerreiro¹,

Volo²,

Gutkin³

2022

Preprint

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Collective dynamics of spiking networks of neurons has been of central interest to both computation neuroscience and network science. Over the past years a new generation of neural population models based on exact reductions (ER) of spiking networks have been developed. However, most of these efforts have been limited to networks of neurons with simple dynamics (e.g. the quadratic integrate and fire models). Here, we present an extension of ER to conductance-based networks of two-dimensional Izhikevich neuron models. We employ an adiabatic approximation, which allows us to analytically solve the continuity equation describing the evolution of the state of the neural population and thus to reduce model dimensionality. We validate our results by showing that the reduced mean-field description we derived can qualitatively and quantitatively describe the macroscopic behaviour of populations of two-dimensional QIF neurons with different electrophysiological profiles (regular firing, adapting, resonator and type III excitable). Most notably, we apply this technique to develop an ER for networks of neurons with bursting dynamics.

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“…Recently, Bandyopadhyay et al [57] have derived a mean-field model for the network of the Hodgkin-Huxley neurons including the effect of ion-exchange between intracellular and extracellular environment. They use quasi-steady state assumptions and numerical fitting to approximate the Hodgkin-Huxley model by a piecewise-defined QIF model and then apply the Montbrió approach.…”

Section: W|ηmentioning

confidence: 99%

Exact mean-field models for spiking neural networks with adaptation

Chen¹,

Campbell²

2022

Preprint

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Networks of spiking neurons with adaption have been shown to be able to reproduce a wide range of neural activities, including the emergent population bursting and spike synchrony that underpin brain disorders and normal function. Exact mean-field models derived from spiking neural networks are extremely valuable, as such models can be used to determine how individual neuron and network parameters interact to produce macroscopic network behaviour. In the paper, we derive and analyze a set of exact mean-field equations for the neural network with spike frequency adaptation. Specifically, our model is a network of Izhikevich neurons, where each neuron is modeled by a two dimensional system consisting of a quadratic integrate and fire equation plus an equation which implements spike frequency adaptation. Previous work deriving a meanfield model for this type of network, relied on the assumption of sufficiently slow dynamics of the adaptation variable. However, this approximation did not succeeded in establishing an exact correspondence between the macroscopic description and the realistic neural network, especially when the adaptation time constant was not large. The challenge lies in how to achieve a closed set of mean-field equations with the inclusion of the mean-field expression of the adaptation variable. We address this challenge by using a Lorentzian ansatz combined with the moment closure approach to arrive at the mean-field system in the thermodynamic limit.The resulting macroscopic description is capable of qualitatively and quantitatively describing the collective dynamics of the neural network, including transition between tonic firing and bursting. We extend the approach to a network of two populations of neurons and discuss the accuracy and efficacy of our mean-field approximations by examining all assumptions that are imposed during the derivation. Numerical bifurcation analysis of our mean-field models reveal bifurcations not previously observed in the models, including a novel mechanism for emergence of bursting in the network. We anticipate our results will provide a tractable and reliable tool to investigate the underlying mechanism of brain function and dysfunction from the perspective of theoretical neuroscience.

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Mean-field approximation of network of biophysical neurons driven by conductance-based ion exchange

Cited by 10 publications

References 102 publications

Dynamics and bifurcation structure of a mean-field model of adaptive exponential integrate-and-fire networks

Dynamics and bifurcation structure of a mean-field model of adaptive exponential integrate-and-fire networks

Exact reduction methods for networks of neurons with complex dynamic phenotypes

Exact mean-field models for spiking neural networks with adaptation

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