title: Effects of maximal sodium and potassium conductance on the stability of Hodgkin-Huxley model.
abstract: Hodgkin-Huxley (HH) equation is the first cell computing model in the world and pioneered the use of model to study electrophysiological problems. The model consists of four differential equations which are based on the experimental data of ion channels. Maximal conductance is an important characteristic of different channels. In this study, mathematical method is used to investigate the importance of maximal sodium conductance gNA and maximal potassium conductance gK. Applying stability theory, and taking gNA and gK as variables, we analyze the stability and bifurcations of the model. Bifurcations are found when the variables change, and bifurcation points and boundary are also calculated. There is only one bifurcation point when gNA is the variable, while there are two points when gK is variable. The (gNA,  gK) plane is partitioned into two regions and the upper bifurcation boundary is similar to a line when both gNA and gK are variables. Numerical simulations illustrate the validity of the analysis. The results obtained could be helpful in studying relevant diseases caused by maximal conductance anomaly.
authors.affiliation: Biocomputing Research Center, School of Computer Science and Technology, Harbin Institute of Technology, Harbin 150001, China.
authors.forename: Yue
authors.identifier: 0000-0002-4515-8931
authors.initials: Y
authors.lastname: Zhang
authors.affiliation: Biocomputing Research Center, School of Computer Science and Technology, Harbin Institute of Technology, Harbin 150001, China.
authors.forename: Kuanquan
authors.initials: K
authors.lastname: Wang
authors.affiliation: Biocomputing Research Center, School of Computer Science and Technology, Harbin Institute of Technology, Harbin 150001, China.
authors.forename: Yongfeng
authors.initials: Y
authors.lastname: Yuan
authors.affiliation: Biocomputing Research Center, School of Computer Science and Technology, Harbin Institute of Technology, Harbin 150001, China.
authors.forename: Dong
authors.identifier: 0000-0002-7887-2111
authors.initials: D
authors.lastname: Sui
authors.affiliation: Biocomputing Research Center, School of Computer Science and Technology, Harbin Institute of Technology, Harbin 150001, China ; School of Physics & Astronomy, University of Manchester, Manchester, UK.
authors.forename: Henggui
authors.initials: H
authors.lastname: Zhang
mesh_terms: D000465:Algorithms; D000818:Animals; D003198:Computer Simulation; D004594:Electrophysiology / Q000379:methods*; D006801:Humans; D017136:Ion Transport; D008564:Membrane Potentials / Q000502:physiology; D008959:Models, Neurological; D008962:Models, Theoretical; D009474:Neurons / Q000502:physiology; D015221:Potassium Channels / Q000737:chemistry; D015222:Sodium Channels / Q000737:chemistry; D012984:Software
chemical_list: D015221:Potassium Channels; D015222:Sodium Channels
references.citation: Gen Physiol Biophys. 1986 Apr;5(2):135-52
references.pmid: 3792818
references.citation: Am J Physiol Heart Circ Physiol. 2000 Jul;279(1):H397-421
references.pmid: 10899081
references.citation: Biol Cybern. 1992;66(5):413-8
references.pmid: 1314101
references.citation: Biol Cybern. 2000 Mar;82(3):215-22
references.pmid: 10664108
references.citation: Circ Res. 2011 Jun 24;109(1):71-9
references.pmid: 21566216
references.citation: Exp Physiol. 2009 May;94(5):496-508
references.pmid: 19139064
references.citation: J Physiol. 1952 Apr;116(4):497-506
references.pmid: 14946715
references.citation: Biophys J. 2008 Jan 15;94(2):392-410
references.pmid: 18160660
references.citation: Biophys J. 1983 Jan;41(1):87-9
references.pmid: 6824756
references.citation: Nature. 1960 Nov 5;188:495-7
references.pmid: 13729365
references.citation: Am J Physiol Heart Circ Physiol. 2002 Apr;282(4):H1437-51
references.pmid: 11893581
references.citation: PLoS Comput Biol. 2011 May;7(5):e1002061
references.pmid: 21637795
references.citation: J Physiol. 1952 Apr;116(4):473-96
references.pmid: 14946714
references.citation: Biomed Res Int. 2013;2013:872454
references.pmid: 23936852
references.citation: Biol Cybern. 1995 Jul;73(2):149-54
references.pmid: 7545012
references.citation: Int J Clin Pract. 2006 Feb;60(2):222-8
references.pmid: 16451297
references.citation: Circulation. 2008 May 13;117(19):2449-57
references.pmid: 18458165
references.citation: Curr Biol. 2005 Nov 22;15(22):2069-72
references.pmid: 16303569
references.citation: Math Biosci Eng. 2013 Aug;10(4):979-96
references.pmid: 23906199
references.citation: J Theor Biol. 1978 Apr 6;71(3):401-20
references.pmid: 642538
references.citation: J Physiol. 1952 Aug;117(4):500-44
references.pmid: 12991237
references.citation: Interface Focus. 2013 Apr 6;3(2):20120067
references.pmid: 24427521