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Reseach Article

Dynamics of HH Model for Excitable Neuron with Added Voltage Gated Calcium Channel

Published on September 2014 by D K Sharma, Akhil Ranjan Garg
National Conference on Advances in Technology and Applied Sciences
Foundation of Computer Science USA
NCATAS - Number 2
September 2014
Authors: D K Sharma, Akhil Ranjan Garg
34eeb614-bdef-4466-9dee-007baa1c0d9d

D K Sharma, Akhil Ranjan Garg . Dynamics of HH Model for Excitable Neuron with Added Voltage Gated Calcium Channel. National Conference on Advances in Technology and Applied Sciences. NCATAS, 2 (September 2014), 19-24.

@article{
author = { D K Sharma, Akhil Ranjan Garg },
title = { Dynamics of HH Model for Excitable Neuron with Added Voltage Gated Calcium Channel },
journal = { National Conference on Advances in Technology and Applied Sciences },
issue_date = { September 2014 },
volume = { NCATAS },
number = { 2 },
month = { September },
year = { 2014 },
issn = 0975-8887,
pages = { 19-24 },
numpages = 6,
url = { /proceedings/ncatas/number2/17953-1614/ },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Proceeding Article
%1 National Conference on Advances in Technology and Applied Sciences
%A D K Sharma
%A Akhil Ranjan Garg
%T Dynamics of HH Model for Excitable Neuron with Added Voltage Gated Calcium Channel
%J National Conference on Advances in Technology and Applied Sciences
%@ 0975-8887
%V NCATAS
%N 2
%P 19-24
%D 2014
%I International Journal of Computer Applications
Abstract

Hodgkin and Huxley conducted Voltage Clamped experiments to study mechanism for generation of action potential in giant Axon of Squid and proposed a simple mathematical model. Their model remains basis for understanding electrical activities in excitable neurons even today. Looking back at their work after six decades certain inadequacies are observed in the proposed model. One of limitation was that whole mechanism was expressed using only Na and K ions, role of other ions like Ca, Mg and Cl were not considered. Calcium is the most common ion available in all most all cells, behaviour of which was not understood by then. However with information available now we proposed a simple extended model which includes calcium current in HH model. The extended model is used to study affects of calcium current on action potential and at the same time also to prove that HH model remains stable and can generate self-sustaining regenerative action potential spikes even with added Ca current.

References
  1. A. L. Hodgkin and A. F. Huxley, "A quantitative description of membrane current and its application to conduction and excitation in nerve", J. Physiol. 1952; 117; 500-544.
  2. Claym Armstrong, "Voltage - Dependent Ion Channels and Their Gating", Physiological Reviews Vol. 72, No. 4 (Suppl. ), October 1992 U. S. A.
  3. D. Sterratt, B. Graham, A. Gillies and D. Willshaw, "Principles of computational modelling in neuroscience", Cambridge University Press, New York, 2011.
  4. E. W. Mccleskey, A. P. Fox, D. Feldmani and R. W. Tsien,"Different type of Calcium channels," J. exp. Biol. 124, 177-190 (1986) 177.
  5. C. F. Stevens, "Hodgkin-Huxley Analysis", The Salk Institute for Biological Studies, San Diego, CA, USA 2007.
  6. Liang Sun, Jing Song Fan, John W. Clark and Philip T. Palade, "A model of the L type Ca channel in rat ventricular myocytes: ion selectivity and inactivation mechanisms", Journal of Physiology (2000), 529. 1, pp. 139—158
  7. Mathew B. M C Farlane andWilliam F. Gilly Yt Proc," Spatial localization of calcium channels in giant fiber lobe neurons of the squid (Loligo opalescens)" Natl. Acad. Sci. USA Vol. 93, May 1996 pp. 5067-5071.
  8. Michelangelo Paci1, Laura Sartiani, Martina Del Lungo, Marisa Jaconi, Alessandro Mugelli, Elisabetta Cerbai, Stefano Severi1, Michelangelo Paci1, Laura Sartiani, Martina Del Lungo, Marisa Jaconi, Alessandro Mugelli, Elisabetta Cerbai, and Stefano Severi1," Mathematical modelling of the action potential of human embryonic stem cell derived cardiomyocytes, Neurobiology, Paci et al. BioMedical Engineering OnLine 2012, 11:61.
  9. P. G. Kostyuk, 0. A. Kristhal and V. I. Pidoplichko, "Calcium inward current and related charge movement in the membrane of snail neurones", J. Physiol (1981), 310, pp. 403-421 403.
  10. Pascal Wallisch, Michacl Lusignan, Marc Benayoun, Tanya I Baker, Adam S Dickey, Nicholas G Hatsopoulos, Matlab for Neuroscientists (An introduction to scientific Computig in Matlab),Academic Press USA, 2009.
  11. Idam Seger, Chiristof Koch, "Method in Neuronal Modeling (From ion to Network)", MIT Press, Landon, 1998.
Index Terms

Computer Science
Information Sciences

Keywords

Voltage Clamp Axon Action Potential Mathematical Model Calcium Current