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Ion channels in the membrane of neuron can be blocked by some toxic chemicals. Blocking ion channels will reduce the conductivity and the number of activated channels, and affect the electrical activity of neurons. And then the spatiotemporal patterns of neuronal network would be changed. In this paper, the nearest-neighbor coupled Hodgkin-Huxley neuronal network with periodic boundary is adapted to the investigation of the evolution of spatiotemporal patterns of neuronal network when the sodium and potassium ion channels are blocked randomly, by using numerical method. The results indicate that sodium ion and potassium ion channel random blockage could lead to the breakup of spiral wave. Furthermore, we analyze the firing probability of neuronal network and find that sodium ion channel random blockage reduces the excitability of neuronal network, which is sensitive to noise; but potassium ion channel random blockage enhances the excitability of neuronal network. Compared with uniform blockage of ion channels, the random blockage of ion channels makes neuronal network have rich dynamics phenomena. Finally, the no-flux boundary condition is applied and the results are similar to the above ones.
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Keywords:
- neuronal network /
- ion channel /
- random blockage /
- spatiotemporal dynamics
[1] Izhikevich E M 2000 Int. J. Bifurcat. Chaos 6 1171
[2] Armstrong M C, Binstock L 1965 J. Gen. Physiol. 48 859
[3] Li Y 1999 Mod. Diagn. Treat. 10 122 (in Chinese) [李泱 1999 现代诊断与治疗 10 122]
[4] Yang L, Huang Y Z 2003 Chin. J. Cardiac Pacing Electrophysiol. 17 81 (in Chinese) [杨琳, 黄诒焯 2003 中国心脏起搏与心电生理杂志 17 81]
[5] Hodgkin A L, Huxley A F 1952 J. Physiol. 117 500
[6] Huang X Y, Troy W C, Yang Q, Ma H T, Laing C R, Schiff S J, Wu J Y 2004 J. Neurosci. 24 9897
[7] Schiff S J, Huang X Y, Wu J Y 2007 Phys. Rev. Lett. 98 178102
[8] Huang X Y, Xu W F, Liang J M, Takagaki K, Gao X, Wu J Y 2010 Neuron 68 978
[9] Gray R A, Pertsow A M, Jalife J 1998 Nature 392 75
[10] Karma A 1993 Phys. Rev. Lett. 71 1103
[11] Beaumont J, Davidenko N, Davidenko J M, Jalife J 1998 Biophys. J. 75 1
[12] Zhang H J, Wang P Y, Zhao Y Y 2005 Chin. Phys. Lett. 22 287
[13] Aslanidia Q V, Bailey A, Biktashev V N, Clayton R H, Holden A V 2002 Chaos 12 843
[14] Zhao L, Yang J P, Zheng Y H 2013 Acta Phys. Sin. 62 028701 (in Chinese) [赵龙, 杨继平, 郑艳红 2013 62 028701]
[15] He D H, Hu G, Zhan M, Ren W, Gao Z 2002 Phys. Rev. E 65 1
[16] Ma J, Wu Y, Ying H P, Jia Y 2011 Chin. Sci. Bull. 56 151
[17] Qian Y 2012 Chin. Phys. B 21 088201
[18] Osipov G V, Shulgin B V, Collins J J 1998 Phys. Rev. E 58 6955
[19] Li Y Y, Zhang H M, Wei C L, Yang M H, Gu H G, Ren W 2009 Chin. Phys. Lett. 26 030504
[20] Ma J, Tang J, Zhang A H, Jia Y 2010 Sci. China: Phys. Mech. Astron. 53 672
[21] Liu S B, Wu Y, Hao Z W, Li Y J, Jia N 2012 Acta Phys. Sin. 61 020503 (in Chinese) [刘少宝, 吴莹, 郝忠文, 李银军, 贾宁 2012 61 020503]
[22] Li Y Y, Jia B, Gu H G 2012 Acta Phys. Sin. 61 070504 (in Chinese) [李玉叶, 贾冰, 古华光 2012 61 070504]
[23] Ma J, Jia Y, Tang J, Yang L J 2008 Chin. Phys. Lett. 25 4325
[24] Tang Z, Li Y Y, Xi L, Jia B, Gu H G 2012 Commun. Theor. Phys. 57 61
[25] Ma J, Huang L, Wang C N, Pu Z S 2013 Commun. Theor. Phys. 59 233
[26] Gong Y B, Xu B, Ma X G, Han J Q 2008 Sci. China B 38 104 (in Chinese) [龚玉兵, 徐舶, 马晓光, 韩吉衢 2008 中国科B辑 38 104]
[27] Gong Y B, Hao Y H, Xie Y H 2010 Physica A 389 349
[28] Ozer M, Perc M, Uzuntarla M 2009 Epl-Europhys. Lett. 86 1
[29] Schmid G, Goychuk I, Hanggi P 2004 Phys. Biol. 1 61
[30] Ma J, Huang L, Tang J, Ying H P, Jin W Y 2012 Commun. Nonlinear Sci. Numer. Simul. 17 4281
[31] Liu S B, Wu Y, Li J J, Xie Y, Tan N 2013 Nonlinear Dynam. 73 1055
[32] Wu X Y, Ma J, Li F, Jia Y 2013 Commun. Nonlinear Sci. Numer. Simul. 18 3350
[33] Ma J, Huang L, Ying H P, Pu Z S 2012 Chin. Sci. Bull. 57 2094
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[1] Izhikevich E M 2000 Int. J. Bifurcat. Chaos 6 1171
[2] Armstrong M C, Binstock L 1965 J. Gen. Physiol. 48 859
[3] Li Y 1999 Mod. Diagn. Treat. 10 122 (in Chinese) [李泱 1999 现代诊断与治疗 10 122]
[4] Yang L, Huang Y Z 2003 Chin. J. Cardiac Pacing Electrophysiol. 17 81 (in Chinese) [杨琳, 黄诒焯 2003 中国心脏起搏与心电生理杂志 17 81]
[5] Hodgkin A L, Huxley A F 1952 J. Physiol. 117 500
[6] Huang X Y, Troy W C, Yang Q, Ma H T, Laing C R, Schiff S J, Wu J Y 2004 J. Neurosci. 24 9897
[7] Schiff S J, Huang X Y, Wu J Y 2007 Phys. Rev. Lett. 98 178102
[8] Huang X Y, Xu W F, Liang J M, Takagaki K, Gao X, Wu J Y 2010 Neuron 68 978
[9] Gray R A, Pertsow A M, Jalife J 1998 Nature 392 75
[10] Karma A 1993 Phys. Rev. Lett. 71 1103
[11] Beaumont J, Davidenko N, Davidenko J M, Jalife J 1998 Biophys. J. 75 1
[12] Zhang H J, Wang P Y, Zhao Y Y 2005 Chin. Phys. Lett. 22 287
[13] Aslanidia Q V, Bailey A, Biktashev V N, Clayton R H, Holden A V 2002 Chaos 12 843
[14] Zhao L, Yang J P, Zheng Y H 2013 Acta Phys. Sin. 62 028701 (in Chinese) [赵龙, 杨继平, 郑艳红 2013 62 028701]
[15] He D H, Hu G, Zhan M, Ren W, Gao Z 2002 Phys. Rev. E 65 1
[16] Ma J, Wu Y, Ying H P, Jia Y 2011 Chin. Sci. Bull. 56 151
[17] Qian Y 2012 Chin. Phys. B 21 088201
[18] Osipov G V, Shulgin B V, Collins J J 1998 Phys. Rev. E 58 6955
[19] Li Y Y, Zhang H M, Wei C L, Yang M H, Gu H G, Ren W 2009 Chin. Phys. Lett. 26 030504
[20] Ma J, Tang J, Zhang A H, Jia Y 2010 Sci. China: Phys. Mech. Astron. 53 672
[21] Liu S B, Wu Y, Hao Z W, Li Y J, Jia N 2012 Acta Phys. Sin. 61 020503 (in Chinese) [刘少宝, 吴莹, 郝忠文, 李银军, 贾宁 2012 61 020503]
[22] Li Y Y, Jia B, Gu H G 2012 Acta Phys. Sin. 61 070504 (in Chinese) [李玉叶, 贾冰, 古华光 2012 61 070504]
[23] Ma J, Jia Y, Tang J, Yang L J 2008 Chin. Phys. Lett. 25 4325
[24] Tang Z, Li Y Y, Xi L, Jia B, Gu H G 2012 Commun. Theor. Phys. 57 61
[25] Ma J, Huang L, Wang C N, Pu Z S 2013 Commun. Theor. Phys. 59 233
[26] Gong Y B, Xu B, Ma X G, Han J Q 2008 Sci. China B 38 104 (in Chinese) [龚玉兵, 徐舶, 马晓光, 韩吉衢 2008 中国科B辑 38 104]
[27] Gong Y B, Hao Y H, Xie Y H 2010 Physica A 389 349
[28] Ozer M, Perc M, Uzuntarla M 2009 Epl-Europhys. Lett. 86 1
[29] Schmid G, Goychuk I, Hanggi P 2004 Phys. Biol. 1 61
[30] Ma J, Huang L, Tang J, Ying H P, Jin W Y 2012 Commun. Nonlinear Sci. Numer. Simul. 17 4281
[31] Liu S B, Wu Y, Li J J, Xie Y, Tan N 2013 Nonlinear Dynam. 73 1055
[32] Wu X Y, Ma J, Li F, Jia Y 2013 Commun. Nonlinear Sci. Numer. Simul. 18 3350
[33] Ma J, Huang L, Ying H P, Pu Z S 2012 Chin. Sci. Bull. 57 2094
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