A multi-base harmonic balance method applied to Hodgkin-Huxley model

Balti, Aymen; Lanza, Valentina; Aziz-Alaoui, M. A.

doi:10.3934/mbe.2018036

Cited by 2 publications

(3 citation statements)

References 37 publications

(82 reference statements)

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“…(Fig. 4, taken from [10] summarizes these facts.) The network model does not incorporate an explicit current injection; however, when in-network, the cells find themselves with contributions to the voltage equation that mimic a current injection in the appropriate range and may undergo some of the bifurcation transitions observed in the single cell.…”

Section: Analysis Of the Hh Equationmentioning

confidence: 82%

“…In the network model, the terms contributing to the voltage equation give rise to effects similar to variation of the injected current I in the single-cell model. It is known, from numerical simulations [10,[34][35][36]45] and references therein, that for an interval of values for I, the system (1.1) exhibits a cascade of bifurcations giving rise to unstable and stable limit cycles, with persistence of the stable stationary point. At a certain critical value within this interval, the stationary point eventually becomes unstable trough a subcritical Hopf bifurcation.…”

Section: Analysis Of the Hh Equationmentioning

confidence: 99%

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Emergent properties in a V1-inspired network of Hodgkin–Huxley neurons

Maama,

Ambrosio,

Aziz-Alaoui

et al. 2024

Math. Model. Nat. Phenom.

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This article is devoted to the analysis of a network of excitatory and inhibitory neurons of Hodgkin-Huxley (HH) type, for which the topology is inspired by that of a layer of visual cortex V1. Our model relies on recent work in this area and thus combines a stochastic drive -- which may be interpreted as an ambient drive for each neuron -- with recurrent inputs resulting from the network activity. After a review of the dynamics of a single HH equation for both the deterministic and the stochastically driven case, we proceed to an analysis of the network. This analysis reveals emergent properties of the system such as partial synchronization and synchronization (defined here as a state of the network for which all the neurons spike within a short interval of time), correlation between excitatory and inhibitory conductances, and oscillations in the Gamma-band frequency. The collective behavior enumerated herein is observed when the input-amplitude parameter $S^{EE}$ measuring excitatory-to-excitatory coupling increases to within a certain range. This article contributes to the understanding of how assemblies of inhibitory and excitatory cells interact together to produce rhythms in the network. It also aims to bring problems from neuroscience to the realm of mathematics.

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Section: Analysis Of the Hh Equationmentioning

confidence: 82%

Section: Analysis Of the Hh Equationmentioning

confidence: 99%

Emergent properties in a V1-inspired network of Hodgkin–Huxley neurons

Maama,

Ambrosio,

Aziz-Alaoui

et al. 2024

Math. Model. Nat. Phenom.

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show abstract

“…Concerning the characterization of neurons, computational modeling is a valuable asset to investigate hypotheses not easily testable through direct experimentation thus allowing to gain biological insights into the working mechanisms of the targeted neurons [55]. Conductance-based models such as the well-known Hodgkin-Huxley model [47,48,49,50,46], as well as those derived from it [30,45], have been widely studied in recent years [17,7,92,27,91,38]. In simple terms, a conductance-based model is a biophysical representation of a neuron in which the ion channels are represented by conductances and the polar membrane by a capacitor.…”

Section: Introductionmentioning

confidence: 99%

On the Modeling of the Three Types of Non-spiking Neurons of the Caenorhabditis elegans

Naudin

Corson

Aziz-Alaoui

et al. 2020

Int. J. Neur. Syst.

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The nematode Caenorhabditis elegans (C. elegans) is a well-known model organism in neuroscience. The relative simplicity of its nervous system, made up of few hundred neurons, shares some essential features with more sophisticated nervous systems, including the human one. If we are able to fully characterize the nervous system of this organism, we will be one step closer to understanding the mechanisms underlying the behavior of living things. Following a recently conducted electrophysiological survey on different C. elegans neurons, this paper aims at modeling the three non-spiking RIM, AIY and AFD neurons (arbitrarily named with three upper case letters by convention). To date, they represent the three possible forms of non-spiking neuronal responses of the C. elegans. To achieve this objective, we propose a conductance-based neuron model adapted to the electrophysiological features of each neuron. These features are based on current biological research and a series of in-silico experiments which use differential evolution to fit the model to experimental data. From the obtained results, we formulate a series of biological hypotheses regarding currents involved in the neuron dynamics. These models reproduce experimental data with a high degree of accuracy while being biologically consistent with state-of-the-art research.

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A multi-base harmonic balance method applied to Hodgkin-Huxley model

Cited by 2 publications

References 37 publications

Emergent properties in a V1-inspired network of Hodgkin–Huxley neurons

Emergent properties in a V1-inspired network of Hodgkin–Huxley neurons

On the Modeling of the Three Types of Non-spiking Neurons of the Caenorhabditis elegans

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