钠离子和钾离子通道噪声扰动对神经网络时空模式的影响

刘少宝; 吴莹; 郝忠文; 李银军; 贾宁

doi:10.7498/aps.61.020503

摘要

研究了钠离子和钾离子通道噪声扰动对Hodgkin-Huxley神经网络放电时空模式的影响. 发现无论钠离子通道噪声还是钾离子通道噪声扰动, 当取定一组温度、噪声强度, 随着耦合强度的增大, 神经网络放电时空斑图总能演化出螺旋波, 而且存在形成螺旋波所需的临界耦合强度. 分析发现钠离子通道噪声有利于神经网络螺旋波的形成, 而钾离子通道噪声不利于螺旋波形成. 结果还表明较低的温度能够使神经网络对噪声更加敏感. 最后, 讨论了特定参数下螺旋波与靶波之间的转化现象.

关键词:

Abstract

Taking into account sodium and potassium ion channel noises, the evolution of the patterns of neuronal networks is investigated. No matter what kind of ion channel noise is working, with coupling coefficient increasing, the spatiotemporal patterns of the neuronal network can be evolved into spiral waves when temperature and noise strength are given, and there is a coupling coefficient threshold for forming a spiral wave. The analysis shows that sodium ion channel noise contributes to the formation of spiral waves in neurons network, while the potassium ion channel noise is not conducive to the formation of spiral waves. In addition, it is found that lower temperature can make the neurons network more sensitive to noise. Finally, the transformation of spiral waves into target waves, in the case of specific parameters is discussed.

Keywords:

作者及机构信息

1.
西安交通大学航天航空学院机械结构强度与振动国家重点实验室, 西安 710049;

2.
西安理工大学理学院工程力学系, 西安 710048

基金项目: 国家自然科学基金(批准号: 10972179, 10872155, 10602003)资助的课题.

Authors and contacts

1.
State key Laboratory for strength and Vibration, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, Chain;

2.
Department of Engineering Mechanics, School of Sciences, Xi’an University of Technology, Xi’an 710048, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 10972179, 10872155, 10602003).

参考文献

[1]	Narahashi T, Anderson C N, MooreWJ 1967 The Journal of General Physiology 50 1413
[2]	Song Y L 2010 Acta Phys. Sin. 59 2334 (in Chinese) [宋艳丽 2010 物理学报 59 2334]
[3]	Armstrong M C, Binstock L 1665 The Journal of General Physiology 48 859
[4]	Steinmetz N P, Manwaniand A, Koch C 2000 Journal of Computational Neuroscience 9 133
[5]	Shou T D 2001 Neurobiology (Beijing: Higher Education Press) p40 (in Chinese) [寿天德 2001 神经生物学 (北京: 高等教育出版社) 第40页]
[6]	Shepherd G M 1998 Neurobiology 2nd ed. (New York: Oxford University Press) p42
[7]	Hodgkin A L, Huxley A F 1952 J. Physiol. 116 449
[8]	Hodgkin A L, Huxley A F 1952 J. Physiol. 117 500
[9]	Correa A M , Bezanilla F, Latorre R 1992 Biophys. J. 61 1332
[10]	Gerhard Schmid, Igor Goychuk 2004 Physica A 344 665
[11]	Armstrong M C, Hille B 1972 The Journal of General Physiology 59 388
[12]	Schmid G, Goychuk I, Hanggi P 2001 Europhys. Lett. 56 22
[13]	Gong Y B, Xie Y H, Xu B and Ma X G 2009 Sci China Ser B 52 20.
[14]	Gong Y B, Xu B, Ma X G, Han J Q, 2008 Sci China Ser B 38 104 (in Chinese) [龚玉兵, 徐舶, 马晓光, 韩吉衢 2008 中国科学 B 38 104]
[15]	Qiao X Y, Li G, Lin L, He B J 2007 Acta Phys. Sin. 56 2448 (in Chinese) [乔晓艳, 李刚, 林凌, 贺秉军物理学报 56 2448]
[16]	Driessche W V 1984 J. Physiol. 356 79
[17]	Martyn P N, Alexander V P 2004 Prog. Biophys. Mol. Bio. 85 501
[18]	Fenton F H, Cherry E M, Hasting H M 2002 Chaos 12 852
[19]	Liu S Q, Lu Q S, Wang Q 1998 Acta. Phys. Sin. 47 1057 (in Chinese) [刘深泉, 陆启韶, 王琪 1998 物理学报 47 1057]
[20]	Zhang G Y, Ma J, Gan Z N, Chen Y 2008 Acta. Phys. Sin. 57 6815 (in Chinese) [张国勇, 马军, 甘正宁, 陈勇 2008 物理学报 57 6815]
[21]	Li Y Y, Zhang H M, Wei C L, Yang M H, Gu H G, Ren W 2009 Journal of Dynamics and Control. 7 230 (in Chinese) [李玉叶, 张慧敏, 魏春玲, 杨明浩, 古华光, 任维 2009 动力学与控制学报 7 230]
[22]	Liu S B, Wu Y, 2010 Journal of Dynamics and Control 8 284 (in Chinese) [刘少宝, 吴莹 2010 动力学与控制学报 8 284]
[23]	Du M M, Wu Y, Pang J Z 2010 The Third International Conference on Dynamics, Vibration and Control (ICDVC-2010)
[24]	Sun X J, Lei J Z, Perc M, Lu Q S, Lv S J 2011 Eur. Phys. J. B 79 61
[25]	Yu G, Ma J, Tang J, Yi M, Jia Y 2008 Int. J. Mod. Phys. B 69 22
[26]	Rappel W J 2001 Chaos 11 71
[27]	Qu Z L, Kil J, Xie F G, Garfinlel A, N.Weiss J 2000 Biophysical Journal 78 2761
[28]	Martyn P N, Alexander V P 2004 Rrog. Biophy. Mol. Bio. 85 501
[29]	Sinha S, Pande A, Pandit R 2001 Phys. Rev. Lett. 86 3678
[30]	Yang J Z, Garfinkel A 2003 Phys. Rev. E 68 066312
[31]	Yang J Z, Xie F G, Qu Z L 2003 Phys. Rev. Lett. 91 148302
[32]	Martin Hall G, Daniel J. Gauthier 2002 Phys. Rev. Lett. 88 198102
[33]	Hu G, Xiao J H, Chua L O, Ladislav Pivka 1998 Phys. Rev. Lett. 80 1884

施引文献

[1]	Narahashi T, Anderson C N, MooreWJ 1967 The Journal of General Physiology 50 1413
[2]	Song Y L 2010 Acta Phys. Sin. 59 2334 (in Chinese) [宋艳丽 2010 物理学报 59 2334]
[3]	Armstrong M C, Binstock L 1665 The Journal of General Physiology 48 859
[4]	Steinmetz N P, Manwaniand A, Koch C 2000 Journal of Computational Neuroscience 9 133
[5]	Shou T D 2001 Neurobiology (Beijing: Higher Education Press) p40 (in Chinese) [寿天德 2001 神经生物学 (北京: 高等教育出版社) 第40页]
[6]	Shepherd G M 1998 Neurobiology 2nd ed. (New York: Oxford University Press) p42
[7]	Hodgkin A L, Huxley A F 1952 J. Physiol. 116 449
[8]	Hodgkin A L, Huxley A F 1952 J. Physiol. 117 500
[9]	Correa A M , Bezanilla F, Latorre R 1992 Biophys. J. 61 1332
[10]	Gerhard Schmid, Igor Goychuk 2004 Physica A 344 665
[11]	Armstrong M C, Hille B 1972 The Journal of General Physiology 59 388
[12]	Schmid G, Goychuk I, Hanggi P 2001 Europhys. Lett. 56 22
[13]	Gong Y B, Xie Y H, Xu B and Ma X G 2009 Sci China Ser B 52 20.
[14]	Gong Y B, Xu B, Ma X G, Han J Q, 2008 Sci China Ser B 38 104 (in Chinese) [龚玉兵, 徐舶, 马晓光, 韩吉衢 2008 中国科学 B 38 104]
[15]	Qiao X Y, Li G, Lin L, He B J 2007 Acta Phys. Sin. 56 2448 (in Chinese) [乔晓艳, 李刚, 林凌, 贺秉军物理学报 56 2448]
[16]	Driessche W V 1984 J. Physiol. 356 79
[17]	Martyn P N, Alexander V P 2004 Prog. Biophys. Mol. Bio. 85 501
[18]	Fenton F H, Cherry E M, Hasting H M 2002 Chaos 12 852
[19]	Liu S Q, Lu Q S, Wang Q 1998 Acta. Phys. Sin. 47 1057 (in Chinese) [刘深泉, 陆启韶, 王琪 1998 物理学报 47 1057]
[20]	Zhang G Y, Ma J, Gan Z N, Chen Y 2008 Acta. Phys. Sin. 57 6815 (in Chinese) [张国勇, 马军, 甘正宁, 陈勇 2008 物理学报 57 6815]
[21]	Li Y Y, Zhang H M, Wei C L, Yang M H, Gu H G, Ren W 2009 Journal of Dynamics and Control. 7 230 (in Chinese) [李玉叶, 张慧敏, 魏春玲, 杨明浩, 古华光, 任维 2009 动力学与控制学报 7 230]
[22]	Liu S B, Wu Y, 2010 Journal of Dynamics and Control 8 284 (in Chinese) [刘少宝, 吴莹 2010 动力学与控制学报 8 284]
[23]	Du M M, Wu Y, Pang J Z 2010 The Third International Conference on Dynamics, Vibration and Control (ICDVC-2010)
[24]	Sun X J, Lei J Z, Perc M, Lu Q S, Lv S J 2011 Eur. Phys. J. B 79 61
[25]	Yu G, Ma J, Tang J, Yi M, Jia Y 2008 Int. J. Mod. Phys. B 69 22
[26]	Rappel W J 2001 Chaos 11 71
[27]	Qu Z L, Kil J, Xie F G, Garfinlel A, N.Weiss J 2000 Biophysical Journal 78 2761
[28]	Martyn P N, Alexander V P 2004 Rrog. Biophy. Mol. Bio. 85 501
[29]	Sinha S, Pande A, Pandit R 2001 Phys. Rev. Lett. 86 3678
[30]	Yang J Z, Garfinkel A 2003 Phys. Rev. E 68 066312
[31]	Yang J Z, Xie F G, Qu Z L 2003 Phys. Rev. Lett. 91 148302
[32]	Martin Hall G, Daniel J. Gauthier 2002 Phys. Rev. Lett. 88 198102
[33]	Hu G, Xiao J H, Chua L O, Ladislav Pivka 1998 Phys. Rev. Lett. 80 1884

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