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Computation in a single neuron: Hodgkin and Huxley revisited [article]

Blaise Aguera y Arcas, Adrienne L. Fairhall, William Bialek
2002 arXiv   pre-print
Our analysis provides a new understanding of the computational properties of the Hodgkin--Huxley model.  ...  A spiking neuron "computes" by transforming a complex dynamical input into a train of action potentials, or spikes.  ...  Brenner for discussions at the start of this work, and M. Berry for comments on the manuscript.  ... 
arXiv:physics/0212113v2 fatcat:6dld3pgmrjfv5aprcg4eoeau3u

Computation in a Single Neuron: Hodgkin and Huxley Revisited

Blaise Agüera y Arcas, Adrienne L. Fairhall, William Bialek
2003 Neural Computation  
A spiking neuron "computes" by transforming a complex dynamical input into a train of action potentials, or spikes.  ...  We apply these methods to analyze the simplest biophysically realistic model neuron, the Hodgkin-Huxley (HH) model, using this system to illustrate the general methodological issues.  ...  Brenner for discussions at the start of this work, and M. Berry for comments on the manuscript.  ... 
doi:10.1162/08997660360675017 pmid:14511510 fatcat:5hiyy7d2avftrlfeamikj6gx2m

Revisiting the Hodgkin-Huxley and Fitzhugh-Nagumo models of action potential propagation

2019 Letters in Applied NanoBioScience  
The influence of neuron mechanical deformation on the generation and propagation of the action potential is studied by revisiting the Hodgkin-Huxley (H-H) and the Fitzhugh-Nagumo (F-N) models within a  ...  The electromechanical consideration of the generation and propagation of the action potential is a very promising field with important clinical implications and wide perspectives for further understanding  ...  Revisiting the Hodgkin-Huxley and Fitzhugh-Nagumo models of action potential propagation Page | 607 Therefore, the equilibrium is asymptotically stable and its attraction domain extends to the whole  ... 
doi:10.33263/lianbs83.604612 fatcat:uab77mtoazabnbggkc64q7tu2u

Correlation susceptibility and single neuron computation

Sungho Hong, Erik De Schutter
2008 BMC Neuroscience  
Hodgkin-Huxley (HH) which is relatively sensi-  ...  This result revisited the question of how rate and correlation based coding would work in a neural population.  ...  Hodgkin-Huxley (HH) which is relatively sensi-tive to the mean (integrator), and the other one is a Hodgkin-Huxley neuron with low sodium conductance (HHLS) which show higher sensitivity to the stimulus  ... 
doi:10.1186/1471-2202-9-s1-p141 fatcat:bu3fyoz22zgc7d4pvg6hfjaeue

Neuronal behaviors: A control perspective

Guillaume Drion, Timothy O'Leary, Julie Dethier, Alessio Franci, Rodolphe Sepulchre
2015 2015 54th IEEE Conference on Decision and Control (CDC)  
The purpose of this tutorial is to introduce and analyze models of neurons from a control perspective and to show how recently developed analytical tools help to address important biological questions.  ...  We use this insight to shed light on a key problem in experimental neurophysiology, the challenge of understanding the sensitivity of neuronal behaviors to underlying parameters in empiricallyderived models  ...  Values are computed using the Goldman-Hodgkin-Katz (GHK) equation, considering K + and N a + ions only. Ion concentrations are as in A.  ... 
doi:10.1109/cdc.2015.7402491 dblp:conf/cdc/DrionODFS15 fatcat:t6kr7ismjfbp7nxvrc5hanfu2a

Computing with Spiking Neuron Networks [chapter]

Hélène Paugam-Moisy, Sander Bohte
2012 Handbook of Natural Computing  
Highly inspired from natural computing in the brain and recent advances in neurosciences, they derive their strength and interest from an accurate modeling of synaptic interactions between neurons, taking  ...  This chapter relates the history of the "spiking neuron" in Section 1 and summarizes the most currently-in-use models of neurons and synaptic plasticity in Section 2.  ...  Fig. 7 7 Electrical model of "spiking" neuron as defined by Hodgkin and Huxley.  ... 
doi:10.1007/978-3-540-92910-9_10 fatcat:uixmvc27zjgirg5oobqaqwccpe

A Novel Phase Portrait for Neuronal Excitability

Guillaume Drion, Alessio Franci, Vincent Seutin, Rodolphe Sepulchre, Vladimir Brezina
2012 PLoS ONE  
Introduction Rooted in the seminal work of Hodgkin and Huxley [1] , conductance-based models have become a central paradigm to describe the electrical behavior of neurons.  ...  Results Planar Reduction of Hodgkin-Huxley Model Revisited in the Light of Calcium Channels Calcium channels participate in the spiking pattern by providing, together with sodium channels, a source of  ... 
doi:10.1371/journal.pone.0041806 pmid:22905107 pmcid:PMC3414513 fatcat:c7ark6zd5zfo5jvd5ebtygc2ri

A Novel Phase Portrait to Understand Neuronal Excitability [article]

Alessio Franci, Guillaume Drion, Vincent Seutin, Rodolphe Sepulchre
2011 arXiv   pre-print
Fifty years ago, Fitzugh introduced a phase portrait that became famous for a twofold reason: it captured in a physiological way the qualitative behavior of Hodgkin-Huxley model and it revealed the power  ...  We show that including this extra current in Hodgkin-Huxley dynamics leads to a revision of Fitzugh-Nagumo phase portrait that affects in a fundamental way the reduced modeling of neural excitability.  ...  Introduction Rooted in the seminal work of Hodgkin and Huxley [12] , conductance-based models have become a central paradigm to describe the electrical behavior of neurons.  ... 
arXiv:1112.2588v1 fatcat:mxa3kuopmve37pjnzpbmsbhyhe

Modulation and Robustness of Endogenous Neuronal Spiking [article]

Guillaume Drion, Alessio Franci, Vincent Seutin, Rodolphe Sepulchre
2013 arXiv   pre-print
Neuronal spiking exhibits an exquisite combination of modulation and robustness properties, rarely matched in artificial systems.  ...  Plugging those equivalent feedback gains in a minimal abstract model recovers many experimental modulation scenarii as modulatory paths in elementary two-parameter charts.  ...  -FNRS (VS) and by two grants from the Belgian Science Policy (IAP7/10 (VS) and IAP7/19 (RS)). The authors gratefully acknowledge several constructive discussions with Dr.  ... 
arXiv:1311.2200v1 fatcat:ee334u4t5jckxhjp5yyyw7ei7i

Course 2 Understanding neuronal dynamics by geometrical dissection of minimal models [chapter]

A. Borisyuk, J. Rinzel
2005 Les Houches  
Functions τx(V ) (in A) and x∞(V ) (in B) in Hodgkin-Huxley equations 2.1 for m (dotted), n(solid) and h (dashed).  ...  Modes of neuronal activity. A-B: Excitability in response to a brief current pulse (Hodgkin-Huxley model, same as in section 2, pulse duration 1 msec).  ... 
doi:10.1016/s0924-8099(05)80008-3 fatcat:mrcdc55gbbgbrdgiu44hwkjcgm

Dynamic Spatiotemporal Synaptic Integration in Cortical Neurons: Neuronal Gain, Revisited

Rony Azouz
2005 Journal of Neurophysiology  
Dynamic spatiotemporal synaptic integration in cortical neurons: neuronal gain, revisited.  ...  The prevailing view is that this modulation reflects a change in the relationship between mean input and output firing rate brought about by variation in neuronal membrane characteristics.  ...  Voltage-gated Na ϩ and K ϩ conductances were implemented using the Hodgkin-Huxley equations (Hodgkin and Huxley 1952a,b; Noble 1966) .  ... 
doi:10.1152/jn.00542.2005 pmid:15987760 fatcat:wyuezved7zallkult553dzdrta

Are biological neurons that vicious ? Or only their models ? [article]

T. Vieville, B. Cessac
2010 arXiv   pre-print
Its main conclusions have been published in "On dynamics of integrate-and-fi re neural networks with conductance based synapses", arXiv:0709.4370 and  ...  Hodgkin-Huxley) would include a non-linear conductance and an adaptive current depending on V and some other dynamical variable.  ...  It is a perspective of this work, to revisit section 3 and propose a more realistic neuron simulation.  ... 
arXiv:0709.4367v4 fatcat:onhmdj2jj5glxkrzh4xjx3rfyi

Emergent Properties in a V1-Inspired Network of Hodgkin-Huxley Neurons [article]

M. Maama, B. Ambrosio, M.A. Aziz-Alaoui, S.M. Mintchev
2021 arXiv   pre-print
This article is devoted to the theoretical and numerical analysis of a network of excitatory and inhibitory neurons of Hodgkin-Huxley (HH) type, for which the topology is inspired by that of a single local  ...  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.  ...  Introduction Background and motivation This paper deals with the analysis of the dynamics of a Network of Hodgkin-Huxley (HH) Ordinary Differential Equations (ODEs).  ... 
arXiv:2004.10656v2 fatcat:s36vu6wkdvdzlge2dwkvtyxpty

Coupling-induced population synchronization in an excitatory population of subthreshold Izhikevich neurons

Sang-Yoon Kim, Woochang Lim
2013 Cognitive Neurodynamics  
As a final step, the coupling induces oscillator death (quenching of noise-induced spikings) because each neuron is attracted to a noisy equilibrium state.  ...  Transitions between population synchronization and incoherence are well described in terms of an order parameter O.  ...  as the Hodgkin-Huxley model (Hodgkin and Huxley 1952) , yet as computationally efficient as the integrate-and-fire model (Lapicque 1907; Abbott 1999) .  ... 
doi:10.1007/s11571-013-9256-y pmid:24427222 pmcid:PMC3825146 fatcat:xp4ex2lnbvcpnm76xdm5cg3kqu

Neuronal Networks with Gap Junctions: A Study of Piecewise Linear Planar Neuron Models

S. Coombes
2008 SIAM Journal on Applied Dynamical Systems  
Here we analyze a class of exactly soluble single neuron models, capable of producing realistic action potential shapes, that can be used as the basis for understanding dynamics at the network level.  ...  Under constant current injection the periodic response and phase response curve (PRC) is calculated in closed form.  ...  I would like to thank Bard Ermentrout and three anonymous referees for useful comments that have improved the presentation of the work in this paper.  ... 
doi:10.1137/070707579 fatcat:62vjjmjatbbbplsdvsilm742b4
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