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Action Potential Initiation in the Hodgkin-Huxley Model

Lucy J. Colwell, Michael P. Brenner, Karl J. Friston
2009 PLoS Computational Biology  
Citation: Colwell LJ, Brenner MP (2009) Action Potential Initiation in the Hodgkin-Huxley Model. PLoS Comput Biol 5(1): e1000265.  ...  Due to this antagonism, it is argued that Hodgkin-Huxley-type models are unable to explain action potential initiation observed in cortical neurons in vivo or in vitro.  ...  Acknowledgments The writing of the paper was done in part at the Kavli Institute for Theoretical Physics.  ... 
doi:10.1371/journal.pcbi.1000265 pmid:19148265 pmcid:PMC2607014 fatcat:of3uhhvncbgghdkygmfaq5enum

Chaos in the Hodgkin--Huxley Model

John Guckenheimer, Ricardo A. Oliva
2002 SIAM Journal on Applied Dynamical Systems  
The Hodgkin-Huxley model was developed to characterize the action potential of a squid axon. It has served as an archetype for compartmental models of the electrophysiology of biological membranes.  ...  This note demonstrates previously unobserved dynamics in the Hodgkin-Huxley model, namely, the existence of chaotic solutions in the model with its original parameters.  ...  Recall that the Hodgkin-Huxley convention for membrane potential reverses the sign from modern conventions, and so the voltage spikes of action potentials are negative in the Hodgkin-Huxley model.  ... 
doi:10.1137/s1111111101394040 fatcat:lniomhkey5es7mrbydx4bouwei

On a nonlinear electromechanical model of nerve [article]

Alain M. Dikande
2021 arXiv   pre-print
In the dynamical regime, numerical simulations of the modified Hodgkin-Huxley equation lead to a variety of typical figures for the transmembrane voltage, reminiscent of action potentials observed in real  ...  The generation of action potential brings into play specific mechanosensory stimuli manifest in the variation of membrane capacitance, resulting from the selective membrane permeability to ions exchanges  ...  In sec. 4, numerical simulations of the modified Hodgkin-Huxley equation are carried out assuming the three stationary solutions as initial profiles of the action potential.  ... 
arXiv:2102.10400v1 fatcat:evjcnqruczfddde3bu6eb37pym

Analysis of the Optimal Channel Density of the Squid Giant Axon Using a Reparameterized Hodgkin–Huxley Model

Thomas D. Sangrey, W. Otto Friesen, William B Levy
2004 Journal of Neurophysiology  
A reparameterized Hodgkin-Huxley-type model is developed that improves the 1952 model's fit to the biological action potential.  ...  Analysis of the optimal channel density of the squid giant axon using a reparameterized Hodgkin-Huxley model. J Neurophysiol 91: 2541-2550, 2004; 10.1152/jn.00646.2003.  ...  The gating current initially counteracts the Na ϩ current at the foot of the action potential, causing the initial depolarization to be retarded relative to the standard Hodgkin-Huxley model, which does  ... 
doi:10.1152/jn.00646.2003 pmid:14749318 fatcat:7shvqwt2v5atjktfu7edzabeb4

The Hodgkin—Huxley Model [chapter]

Mark Nelson, John Rinzel
1998 The Book of GENESIS  
Alan Lloyd Hodgkin and Andrew Huxley authored a succession of five papers describing the nonlinear ordinary differential equations that model how action potentials can be initiated and propagated through  ...  for the initiation and propagation of an action potential in a neuron was named after its creators in 1952.  ...  The Hodgkin-Huxley model can be summarized neatly into four separate ordinary differential equations with some supporting functions.  ... 
doi:10.1007/978-1-4612-1634-6_4 fatcat:ww3akp2ssjhhxmwnw5n7fby4wa

Page 260 of Journal of Science Education and Technology Vol. 1, Issue 4 [page]

1992 Journal of Science Education and Technology  
Hodgkin-Huxley Model Background An electrically excitable cell, such as a neuron or a muscle cell, produces a change in the potential across its membrane called the action potential.  ...  However, during an action potential the membrane potential is not constrained by an external source, and the Hodgkin-Huxley model consists of a set of four coupled, nonlinear equations for which analytical  ... 

Thermal block of action potentials is primarily due to voltage-dependent potassium currents: A modeling study

Mohit Ganguly, Michael W Jenkins, E Duco Jansen, Hillel J Chiel
2019 Journal of Neural Engineering  
Thermal block of action potential conduction using infrared lasers is a new modality for manipulating neural activity.  ...  It could be used for analysis of the nervous system and for therapeutic applications. We sought to understand the mechanisms of thermal block.  ...  Acknowledgments We thank Dr Kendrick M Shaw (Massachusetts General Hospital), Dr Ted Carnevale (Yale University), and Alex Williams (Stanford University) for initial guidance in setting up the simulations  ... 
doi:10.1088/1741-2552/ab131b pmid:30909171 fatcat:wk2j5rgagrg6vfatw6kmpkocey

Semi Analytic Solution of Hodgkin-Huxley Model by Homotopy Perturbation Method

Khairunnisa Khan, Hisham bin Zubair Syed
2021 Punjab University journal of mathematics  
Hodgkin-Huxley model is a system of four non-linear coupled differential equations which describes and explains the threshold and action potential by a stimulus arising in a single neuron.  ...  Further, this analytic solution can describe many key properties such as the threshold potential, the action potential and the refractory period. MATLAB software is used to simulate the solution.  ...  This research was funded in full through a research grant by IBA-Karachi, for which we would like to thank them.  ... 
doi:10.52280/pujm.2021.531105 fatcat:a3q2nllscjelhm6j53zzkkengm

Neuronal Synchronization of Electrical Activity, Using the Hodgkin-Huxley Model and RCLSJ Circuit
Neuronal Synchronization of Electrical Activity, using the Hodgkin-Huxley Model and RCLSJ Circuit

Jose A. Díaz M., Oscar Téquita, Fernando Naranjo
2016 Ingeniería y Ciencia  
using the Hodgkin-Huxley Model and RCLSJ Circuit.  ...  These HH model make possible simulate the main neuronal dynamics characteristics such as action potentials, firing threshold and refractory period.  ...  Mathematical model The model of Hodgkin-Huxley contains four nonlinear ordinary differential equations that describe the generation and propagation of action potentials.  ... 
doi:10.17230/ingciencia.12.23.5 fatcat:fztmr7wtu5hdpcvz3o6sz35w54

The Hodgkin Huxley Model: Analysis of Dynamic Behavior of the Action Potential in the Giant Squid Axon

S Suresh, V Bhavani, K Gopala Krishna, Ch Bhaskar Sri Sai, D U V V Siva Kumar, Raghu Institute of Technology
2020 International Journal of Engineering Research and  
To generate action potential, different methods should be implemented. To improve the propagation of action potential, we use an accurate and efficient method i.e. Hodgkin-Huxley model.  ...  HODGKIN HUXLEY MODEL The Hodgkin-Huxley model is one among the biological models (Abbott & Kepler, 1990), utilizes four differential equations to live the potential of the membrane.  ... 
doi:10.17577/ijertv9is050731 fatcat:4b3nxepb7jd35arxkozrh2bviu

All-Or-None Principle And Weakness Of Hodgkin-Huxley Mathematical Model

S. A. Sadegh Zadeh, C. Kambhampati
2017 Zenodo  
The results clearly showed that the mathematical model of Hodgkin-Huxley does not observe this fundamental law in neurophysiology to generating action potentials.  ...  This study shows that further mathematical studies on the Hodgkin-Huxley model are needed in order to create a model without this weakness.  ...  The Hodgkin-Huxley model is a four-dimensional mathematical model. This model presents current flow via ionselective channels in the membrane of the neuron.  ... 
doi:10.5281/zenodo.1314591 fatcat:3cmbafiibngmvlzwnotj5e67dy

All-Or-None Principle And Weakness Of Hodgkin-Huxley Mathematical Model

S. A. Sadegh Zadeh, C. Kambhampati
2017 Zenodo  
The results clearly showed that the mathematical model of Hodgkin-Huxley does not observe this fundamental law in neurophysiology to generating action potentials.  ...  This study shows that further mathematical studies on the Hodgkin-Huxley model are needed in order to create a model without this weakness.  ...  The Hodgkin-Huxley model is a four-dimensional mathematical model. This model presents current flow via ionselective channels in the membrane of the neuron.  ... 
doi:10.5281/zenodo.1132916 fatcat:i4vitnwft5cofcb2r4zxgov34q

A Novel Approach to Simulate Hodgkin-Huxley-like Excitation With COMSOL Multiphysics

Johannes Martinek, Yvonne Stickler, Martin Reichel, Winfried Mayr, Frank Rattay
2008 Artificial Organs  
Most simulations concerning electrical activation of human muscles are based on the modeling approach of Hodgkin and Huxley.  ...  Knowledge of the potential distributions in both domains is necessary for calculating the development and the propagation of action potentials along the fiber.  ...  The coupled value is inserted as V e in Equ. 6 and therefore in the Hodgkin-Huxley model.  ... 
doi:10.1111/j.1525-1594.2008.00611.x pmid:18782131 fatcat:lnxspquvfvbb3no5i5w5ls3ln4

The Effect of Membrane Parameters on the Properties of the Nerve Impulse

N.H. Sabah, K.N. Leibovic
1972 Biophysical Journal  
ABSIRACT The effect of varying membrane capacitance, conductance, and rate constants on the properties of the nerve impulse is considered in terms of the degree of regeneration in the Hodgkin-Huxley model  ...  It is shown through computer simulation that reducing regeneration generally increases the duration of the action potential and decreases its amplitude, rate of rise, and conduction velocity.  ...  and duration (dash-dotted line) with 13 for an action potential propagating steadily along an infinite Hodgkin-Huxley cable model for the squid giant axon.  ... 
doi:10.1016/s0006-3495(72)86150-2 pmid:4341459 pmcid:PMC1484131 fatcat:w5bwtf2yzvdpbblisb2xqlf52i

Sir Andrew Huxley: 1917–2012

Robert Simmons
2012 Current Biology  
Huxley again calculated action potentials based on what are now known as the Hodgkin-Huxley equations. The work was finally published in 1952.  ...  At this time, Hodgkin favored carrier models -invoking membrane-bound molecules that would carry ions from one side of the axon membrane to the other -and Huxley calculated action potentials based on kinetic  ... 
doi:10.1016/j.cub.2012.06.016 pmid:23012738 fatcat:sjtiblou7jbplps742mn4rshoy
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