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在电位耦合条件下，利用Morris-Lecar神经元模型构造环链神经元网络，研究了离子通道分布不均匀情形下神经元网络群体电活动的演化和转变问题. 在数值研究中通过改变局部区域的离子通道电导值模拟离子通道的非均匀分布，并对其可能的机制进行了分析. 还研究了网络中局部区域的钙离子电导的差异性和钾离子电导的差异性如何逐渐激发周边神经元，以及诱发的行波如何依赖于神经元之间的耦合强度. 研究发现，增大钙离子电导到一定程度或减小钾离子电导到一定程度可以诱发周围神经元产生兴奋并产生稳定的行波；相反，减小钙离子电导或增大钾离子电导则会减缓或阻断行波的传递. 在同时改变钙离子电导和钾离子电导的情况下，行波的诱发和传播完全依赖于钙离子电导的增量和钾离子电导的减量.
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关键词:
- Morris-Lecar神经元 /
- 离子通道的非均匀分布 /
- 环链网络
In this paper, we investigate the evolution and transition of collective electric activities of neurons in a ring network, induced by inhomogeneous distribution of ion channels. The local kinetics is measured by Morris-Lecar under voltage coupling type. In the numerical studies, the effect of inhomogeneous distribution of ion channels is simulated by changing the conductance in ion channels embedded in the membrane, and the potential mechanism is discussed. The effect of diversity of conductance between calcium and potassium ions on the activating of the adjacent neurons, and the dependence of developed travelling wave on the coupling intensity, are investigated in detail. The activating and waking up the nonexcitable or quiescent neurons with type I and type II excitability, are investigated, respectively. The numerical results confirm that the adjacent neurons are activated and the stable travelling wave is developed in the ring network of neurons when the conductance of calcium ions is increased beyond a certain threshold or the conductance of potassium ions is reduced below another threshold; while the propagation of the travelling wave could be slowed down or suppressed when the conductance of calcium ions is reduced or the conductance of potassium ion is increased. The development or emergence of travelling wave and propagation are greatly dependent on the increase of conductance of calcium ions and the decrease of potassium conductance.[1] Song Y L 2010 Acta Phys. Sin. 59 2334 (in Chinese) [宋艳丽2010 物理学报 59 2334]
[2] Touboul J, Brette R 2009 SIAM J. Appl. Dyn. Syst. 8 1462
[3] Kashima K, Kawamura Y, Imura J 2011 Automatica 47 1249
[4] Coombes S, Thul R, Wedgwood K C A 2012 Physica D 241 2042
[5] Chen J, Li C G 2011 Acta Phys. Sin. 60 020502 (in Chinese) [陈军, 李春光 2011 物理学报 60 020502]
[6] Rech P C 2012 Chin. Phys. Lett. 29 60506
[7] Lin K K, Shea-Brown E, Young L S 2009 J. Comput. Neurosci. 27 135
[8] Liu Y, Xie Y 2010 Acta Phys. Sin. 59 2147 (in Chinese) [刘勇, 谢勇 2010 物理学报 59 2147]
[9] Ma Q Y, Haider M R, Shrestha V L, Massoud Y 2012 Analog. Integr. Circ. Sig. Proc. 73 329
[10] Hindmarsh J L, Rose R M A 1984 Proc. R. Soc. London B 221 87
[11] Duan L X, Lu Q S 2005 Chin. Phys. Lett. 22 1325
[12] Wang P, Zhang J Q, Ren H L 2010 Chin. J. Chem. Phys. 23 23
[13] Ma J, Huang L, Xie Z B, Wang C N 2012 Commun. Nonlinear Sci. Numer. Sim. 17 2659
[14] Izhikevich 2004 IEEE Trans. Neural Networ. 15 1063
[15] Sanger T D 1989 Neural Networks 2 459
[16] Kawato M, Furukawa K, Suzuki R 1987 Biol. Cybern. 57 169
[17] Richard M D, Lippmann R P 1991 Neural Comput. 3 484
[18] Yu H T, Wang J, Liu C, Che Y Q, Deng B, Wei X L 2012 Acta Phys. Sin. 61 068702 (in Chinese) [于海涛, 王江, 刘晨, 车艳秋, 邓斌, 魏熙乐 2012 物理学报 61 068702]
[19] Li H, Zhang Y X, Polaskova P, Havel J 2002 Acta Chem. Sin. 60 1264 (in Chinese) [李华, 张雅雄, Polaskova P, Havel J 2002 化学学报 60 1264]
[20] Zhang P J, Du L, Li Y L 2011 J. Syst. Sim. 23 2552 (in Chinese) [张平健, 杜雷, 李运龙 2011 系统仿真学报 23 2552]
[21] Shao Y F 2012 Neurocomputing 93 1
[22] Vreeswijk C, Sompolinsky H 1996 Science 274 1724
[23] Marichal R L, González E J, Marichal G N 2012 Neural Networks 36 51
[24] Wang Q Y, Perc M, Duan Z S 2010 Int. J. Mod. Phys. B 24 1201
[25] 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 物理学报 61 070504]
[26] Hu B L, Ma J, Li F, Pu Z S 2013 Acta Phys. Sin. 62 058701 (in Chinese) [胡柏林, 马军, 李凡, 蒲忠胜 2013 物理学报 62 058701]
[27] 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 物理学报 62 028701]
[28] Liang X B, Liu X S, Liu A Z, Wang B L 2009 Acta Phys. Sin. 58 5065 (in Chinese) [梁晓冰, 刘希顺, 刘安芝, 王博亮 2009 物理学报 58 5065]
[29] Wang H T, Wang L F, Yu L C, Chen Y 2011 Phys. Rev. E 83 021915
[30] Lim S 2010 J. Comput. Neurosci. 28 1
[31] Gong Y B, Lin X, Hao Y H, Ma X G 2011 Fluct. Noise Lett. 10 1
[32] Grau-Moya J, Pons A J, Garcia-Ojalvo J 2012 Int. J. Bifur. Chaos 22 1250175
[33] Gröschel M, Götze R, Ernst A, Basta D 2010 J. Neurotraum. 27 1499
[34] Medvedev G S, Zhuravytska S 2012 J. Nonlinear Sci. 22 689
[35] Morris C, Lecar H 1981 Biophys. J. 35 193
[36] Gu H G, Jia B, Li Y Y, Chen G R 2013 Physica A 392 1361
[37] Ma J, Xie Z B, Chen J X 2012 Acta Phys. Sin. 61 038701 (in Chinese) [马军, 谢振博, 陈江星 2012 物理学报 61 038701]
[38] Wu X Y, Ma J 2013 Plos One 18 55403
[39] Wu X Y, Ma J, Li F, Jia Y 2013 Commun. Nonlinear Sci. Numer. Sim. 18 3350
[40] Xue M, Wang J, Deng B, Wei X L, Chen Y Y 2013 Acta Phys. Sin. 62 098701 (in Chinese) [薛明, 王江, 邓斌, 魏熙乐, 陈颖源 2013 物理学报 62 098701]
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[1] Song Y L 2010 Acta Phys. Sin. 59 2334 (in Chinese) [宋艳丽2010 物理学报 59 2334]
[2] Touboul J, Brette R 2009 SIAM J. Appl. Dyn. Syst. 8 1462
[3] Kashima K, Kawamura Y, Imura J 2011 Automatica 47 1249
[4] Coombes S, Thul R, Wedgwood K C A 2012 Physica D 241 2042
[5] Chen J, Li C G 2011 Acta Phys. Sin. 60 020502 (in Chinese) [陈军, 李春光 2011 物理学报 60 020502]
[6] Rech P C 2012 Chin. Phys. Lett. 29 60506
[7] Lin K K, Shea-Brown E, Young L S 2009 J. Comput. Neurosci. 27 135
[8] Liu Y, Xie Y 2010 Acta Phys. Sin. 59 2147 (in Chinese) [刘勇, 谢勇 2010 物理学报 59 2147]
[9] Ma Q Y, Haider M R, Shrestha V L, Massoud Y 2012 Analog. Integr. Circ. Sig. Proc. 73 329
[10] Hindmarsh J L, Rose R M A 1984 Proc. R. Soc. London B 221 87
[11] Duan L X, Lu Q S 2005 Chin. Phys. Lett. 22 1325
[12] Wang P, Zhang J Q, Ren H L 2010 Chin. J. Chem. Phys. 23 23
[13] Ma J, Huang L, Xie Z B, Wang C N 2012 Commun. Nonlinear Sci. Numer. Sim. 17 2659
[14] Izhikevich 2004 IEEE Trans. Neural Networ. 15 1063
[15] Sanger T D 1989 Neural Networks 2 459
[16] Kawato M, Furukawa K, Suzuki R 1987 Biol. Cybern. 57 169
[17] Richard M D, Lippmann R P 1991 Neural Comput. 3 484
[18] Yu H T, Wang J, Liu C, Che Y Q, Deng B, Wei X L 2012 Acta Phys. Sin. 61 068702 (in Chinese) [于海涛, 王江, 刘晨, 车艳秋, 邓斌, 魏熙乐 2012 物理学报 61 068702]
[19] Li H, Zhang Y X, Polaskova P, Havel J 2002 Acta Chem. Sin. 60 1264 (in Chinese) [李华, 张雅雄, Polaskova P, Havel J 2002 化学学报 60 1264]
[20] Zhang P J, Du L, Li Y L 2011 J. Syst. Sim. 23 2552 (in Chinese) [张平健, 杜雷, 李运龙 2011 系统仿真学报 23 2552]
[21] Shao Y F 2012 Neurocomputing 93 1
[22] Vreeswijk C, Sompolinsky H 1996 Science 274 1724
[23] Marichal R L, González E J, Marichal G N 2012 Neural Networks 36 51
[24] Wang Q Y, Perc M, Duan Z S 2010 Int. J. Mod. Phys. B 24 1201
[25] 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 物理学报 61 070504]
[26] Hu B L, Ma J, Li F, Pu Z S 2013 Acta Phys. Sin. 62 058701 (in Chinese) [胡柏林, 马军, 李凡, 蒲忠胜 2013 物理学报 62 058701]
[27] 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 物理学报 62 028701]
[28] Liang X B, Liu X S, Liu A Z, Wang B L 2009 Acta Phys. Sin. 58 5065 (in Chinese) [梁晓冰, 刘希顺, 刘安芝, 王博亮 2009 物理学报 58 5065]
[29] Wang H T, Wang L F, Yu L C, Chen Y 2011 Phys. Rev. E 83 021915
[30] Lim S 2010 J. Comput. Neurosci. 28 1
[31] Gong Y B, Lin X, Hao Y H, Ma X G 2011 Fluct. Noise Lett. 10 1
[32] Grau-Moya J, Pons A J, Garcia-Ojalvo J 2012 Int. J. Bifur. Chaos 22 1250175
[33] Gröschel M, Götze R, Ernst A, Basta D 2010 J. Neurotraum. 27 1499
[34] Medvedev G S, Zhuravytska S 2012 J. Nonlinear Sci. 22 689
[35] Morris C, Lecar H 1981 Biophys. J. 35 193
[36] Gu H G, Jia B, Li Y Y, Chen G R 2013 Physica A 392 1361
[37] Ma J, Xie Z B, Chen J X 2012 Acta Phys. Sin. 61 038701 (in Chinese) [马军, 谢振博, 陈江星 2012 物理学报 61 038701]
[38] Wu X Y, Ma J 2013 Plos One 18 55403
[39] Wu X Y, Ma J, Li F, Jia Y 2013 Commun. Nonlinear Sci. Numer. Sim. 18 3350
[40] Xue M, Wang J, Deng B, Wei X L, Chen Y Y 2013 Acta Phys. Sin. 62 098701 (in Chinese) [薛明, 王江, 邓斌, 魏熙乐, 陈颖源 2013 物理学报 62 098701]
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