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兴奋性作用诱发神经簇放电个数不增反降的分岔机制

曹奔 关利南 古华光

兴奋性作用诱发神经簇放电个数不增反降的分岔机制

曹奔, 关利南, 古华光
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  • 非线性动力学在识别神经放电的复杂现象、机制和功能方面发挥了重要作用.不同于传统观念,本文提出了兴奋性作用可以降低而不是增加簇内放电个数的新观点.在簇放电模式休止期的适合相位施加强度合适的脉冲或自突触电流,能诱发簇内放电个数降低;电流的施加相位越早,所需的强度阈值越大,簇内放电个数越少.进一步,利用快慢变量分离获得的簇放电的动力学性质进行了理论解释.簇放电模式表现出低电位的休止期和高电位的放电的交替,存在于快子系统的鞍结分岔点和同宿轨分岔点之间;放电起始于鞍结分岔、结束于同宿轨分岔;越靠近同宿轨分岔从休止期跨越到放电所需的电流强度越大.因此,电流在休止期上的作用相位越早,就越靠近同宿轨分岔,因而从休止期跨越到放电需要的电流强度阈值越大,放电起始相位到同宿轨分岔之间的区间变小导致放电个数变少.研究结果丰富了非线性现象及机制,对兴奋性作用提出了新看法,给出了调控簇放电模式的新途径.
    • 基金项目: 国家自然科学基金(批准号:11872276,11572225,11372224)资助的课题.
    [1]

    Glass L 2001 Nature 410 277

    [2]

    Izhikevich E M 2000 Int. J. Bifurcation Chaos 10 1171

    [3]

    Braun H A, Wissing H, Schäfer K, Hirsch M C 1994 Nature 367 270

    [4]

    Braun H A, Schwabedal J, Dewald M, Finke C, Postnova S, Huber M T, Wollweber B, Schneider H, Hirsch M C, Voigt K, Feudel U, Moss F 2011 Chaos 21 047509

    [5]

    Gu H G, Pan B B 2015 Nonlinear Dyn. 81 2107

    [6]

    Jia B, Gu H G 2017 Int. J. Bifurcation Chaos 27 1750113

    [7]

    Wang X J, Rinzel J 1992 Neural Comput. 4 84

    [8]

    Wang X J, Rinzel J 1993 Neuroscience 53 899

    [9]

    van V C, Abbott L F, Bard E G 1994 J. Comput. Neurosci. 1 313

    [10]

    Cobb S R, Buhl E H, Halasy K, Paulsen O, Somogyi P 1995 Nature 378 75

    [11]

    Bose A, Kunec S 2001 Neurocomputing 38 505

    [12]

    Elson R C, Selverston A I, Abarbanel H D I, Rabinovich M 2002 J. Neurophysiol. 88 1166

    [13]

    Belykh I, Shilnikov A 2008 Phys. Rev. Lett. 101 078102

    [14]

    Gu H G, Zhao Z G 2015 PloS One 10 e0138593

    [15]

    Jia B, Wu Y C, He D, Guo B H, Xue L 2018 Nonlinear Dyn. 93 1599

    [16]

    Zhao Z G, Jia B, Gu H G 2016 Nonlinear Dyn. 86 1549

    [17]

    Jia B 2018 Int. J. Bifurcation Chaos 28 1850030

    [18]

    Tamas G, Buhl E H, Somogyi P 1997 J. Neurosci. 17 6352

    [19]

    Bacci A, Huguenard J R, Prince D A 2003 J. Neurosci. 23 859

    [20]

    Bacci A, Huguenard J R, Prince D A 2005 Trends Neurosci. 28 602

    [21]

    Bacci A, Huguenard J R 2006 Neuron 49 119

    [22]

    Saada R, Miller N, Hurwitz I, Susswein A J 2009 Curr. Biol. 19 479

    [23]

    Deleuze C, Pazienti A, Bacci A 2014 Curr. Opin. Neurobiol. 26 64

    [24]

    Straiker A, Dvorakova M, Zimmowitch A, Mackie K 2018 Mol. Pharmacol. 94 743

    [25]

    Qin H X, Ma J, Wang C N, Wu Y 2014 PloS One 9 e100849

    [26]

    Qin H X, Ma J, Wang C N, Chu R T 2014 Sci. China Phys. Mech. Astron. 57 1918

    [27]

    Wang H T, Ma J, Chen Y L, Chen Y 2014 Commun. Nonlinear Sci. Numer. Simul. 19 3242

    [28]

    Wang H T, Chen Y 2015 Chin. Phys. B 24 128709

    [29]

    Guo D Q, Chen M M, Perc M, Wu S D, Xia C, Zhang Y S, Xu P, Xia Y, Yao D Z 2016 Europhys. Lett. 114 30001

    [30]

    Guo D Q, Wu S D, Chen M M, Perc M, Zhang Y S, Ma J L, Cui Y, Xu P, Xia Y, Yao D Z 2016 Sci. Rep. 6 14

    [31]

    Ma J, Xu Y, Wang C N, Jin W Y 2016 Physica A 461 586

    [32]

    Yilmaz E, Baysal V, Ozer M, Perc M 2016 Physica A 444 538

    [33]

    Gong Y, Wang B, Xie H 2016 Biosystems 150 132

    [34]

    Yang X, Yu Y, Sun Z 2017 Chaos 27 083117

    [35]

    Lisman J E 1997 Trends Neurosci. 20 38

    [36]

    Izhikevich E M, Desai N S, Walcott E C, Hoppensteadt F C 2003 Trends Neurosci. 26 161

    [37]

    Rulkov N F 2002 Phys. Rev. E 65 041922

    [38]

    Rulkov N F 2001 Phys. Rev. Lett. 86 183

    [39]

    Rinzel J 1987 Lecture Notes in Biomathematics (Berlin: Springer-Verlag) p267

    [40]

    Buschle L R, Kurz F T, Kampf T, Wagner W L, Dueer J, Stiller W, Konietzke P, Wünnemann F, Mall M A, Wielpütz M O, Schlemmer H P, Ziener C H 2017 Phys. Rev. E 95 022415

    [41]

    Tsutome H, Yuichi H, Takao O, Masahiro T 2009 Phys. Rev. E 80 051921

    [42]

    Guo D Q 2011 Cogn. Neurodyn. 5 293

    [43]

    Chen F, Xia L, Li C G 2012 Chin. Phys. Lett. 29 070501

    [44]

    Guo D Q, Wang Q Y, Perc M 2012 Phys. Rev. E 85 061905

    [45]

    Wang Q Y, Murks A, Perc M, Lu Q S 2011 Chin. Phys. B 20 040504

  • [1]

    Glass L 2001 Nature 410 277

    [2]

    Izhikevich E M 2000 Int. J. Bifurcation Chaos 10 1171

    [3]

    Braun H A, Wissing H, Schäfer K, Hirsch M C 1994 Nature 367 270

    [4]

    Braun H A, Schwabedal J, Dewald M, Finke C, Postnova S, Huber M T, Wollweber B, Schneider H, Hirsch M C, Voigt K, Feudel U, Moss F 2011 Chaos 21 047509

    [5]

    Gu H G, Pan B B 2015 Nonlinear Dyn. 81 2107

    [6]

    Jia B, Gu H G 2017 Int. J. Bifurcation Chaos 27 1750113

    [7]

    Wang X J, Rinzel J 1992 Neural Comput. 4 84

    [8]

    Wang X J, Rinzel J 1993 Neuroscience 53 899

    [9]

    van V C, Abbott L F, Bard E G 1994 J. Comput. Neurosci. 1 313

    [10]

    Cobb S R, Buhl E H, Halasy K, Paulsen O, Somogyi P 1995 Nature 378 75

    [11]

    Bose A, Kunec S 2001 Neurocomputing 38 505

    [12]

    Elson R C, Selverston A I, Abarbanel H D I, Rabinovich M 2002 J. Neurophysiol. 88 1166

    [13]

    Belykh I, Shilnikov A 2008 Phys. Rev. Lett. 101 078102

    [14]

    Gu H G, Zhao Z G 2015 PloS One 10 e0138593

    [15]

    Jia B, Wu Y C, He D, Guo B H, Xue L 2018 Nonlinear Dyn. 93 1599

    [16]

    Zhao Z G, Jia B, Gu H G 2016 Nonlinear Dyn. 86 1549

    [17]

    Jia B 2018 Int. J. Bifurcation Chaos 28 1850030

    [18]

    Tamas G, Buhl E H, Somogyi P 1997 J. Neurosci. 17 6352

    [19]

    Bacci A, Huguenard J R, Prince D A 2003 J. Neurosci. 23 859

    [20]

    Bacci A, Huguenard J R, Prince D A 2005 Trends Neurosci. 28 602

    [21]

    Bacci A, Huguenard J R 2006 Neuron 49 119

    [22]

    Saada R, Miller N, Hurwitz I, Susswein A J 2009 Curr. Biol. 19 479

    [23]

    Deleuze C, Pazienti A, Bacci A 2014 Curr. Opin. Neurobiol. 26 64

    [24]

    Straiker A, Dvorakova M, Zimmowitch A, Mackie K 2018 Mol. Pharmacol. 94 743

    [25]

    Qin H X, Ma J, Wang C N, Wu Y 2014 PloS One 9 e100849

    [26]

    Qin H X, Ma J, Wang C N, Chu R T 2014 Sci. China Phys. Mech. Astron. 57 1918

    [27]

    Wang H T, Ma J, Chen Y L, Chen Y 2014 Commun. Nonlinear Sci. Numer. Simul. 19 3242

    [28]

    Wang H T, Chen Y 2015 Chin. Phys. B 24 128709

    [29]

    Guo D Q, Chen M M, Perc M, Wu S D, Xia C, Zhang Y S, Xu P, Xia Y, Yao D Z 2016 Europhys. Lett. 114 30001

    [30]

    Guo D Q, Wu S D, Chen M M, Perc M, Zhang Y S, Ma J L, Cui Y, Xu P, Xia Y, Yao D Z 2016 Sci. Rep. 6 14

    [31]

    Ma J, Xu Y, Wang C N, Jin W Y 2016 Physica A 461 586

    [32]

    Yilmaz E, Baysal V, Ozer M, Perc M 2016 Physica A 444 538

    [33]

    Gong Y, Wang B, Xie H 2016 Biosystems 150 132

    [34]

    Yang X, Yu Y, Sun Z 2017 Chaos 27 083117

    [35]

    Lisman J E 1997 Trends Neurosci. 20 38

    [36]

    Izhikevich E M, Desai N S, Walcott E C, Hoppensteadt F C 2003 Trends Neurosci. 26 161

    [37]

    Rulkov N F 2002 Phys. Rev. E 65 041922

    [38]

    Rulkov N F 2001 Phys. Rev. Lett. 86 183

    [39]

    Rinzel J 1987 Lecture Notes in Biomathematics (Berlin: Springer-Verlag) p267

    [40]

    Buschle L R, Kurz F T, Kampf T, Wagner W L, Dueer J, Stiller W, Konietzke P, Wünnemann F, Mall M A, Wielpütz M O, Schlemmer H P, Ziener C H 2017 Phys. Rev. E 95 022415

    [41]

    Tsutome H, Yuichi H, Takao O, Masahiro T 2009 Phys. Rev. E 80 051921

    [42]

    Guo D Q 2011 Cogn. Neurodyn. 5 293

    [43]

    Chen F, Xia L, Li C G 2012 Chin. Phys. Lett. 29 070501

    [44]

    Guo D Q, Wang Q Y, Perc M 2012 Phys. Rev. E 85 061905

    [45]

    Wang Q Y, Murks A, Perc M, Lu Q S 2011 Chin. Phys. B 20 040504

  • 引用本文:
    Citation:
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出版历程
  • 收稿日期:  2018-09-08
  • 修回日期:  2018-11-12
  • 刊出日期:  2019-12-20

兴奋性作用诱发神经簇放电个数不增反降的分岔机制

  • 同济大学航空航天与力学学院, 上海 200092
    基金项目: 

    国家自然科学基金(批准号:11872276,11572225,11372224)资助的课题.

摘要: 非线性动力学在识别神经放电的复杂现象、机制和功能方面发挥了重要作用.不同于传统观念,本文提出了兴奋性作用可以降低而不是增加簇内放电个数的新观点.在簇放电模式休止期的适合相位施加强度合适的脉冲或自突触电流,能诱发簇内放电个数降低;电流的施加相位越早,所需的强度阈值越大,簇内放电个数越少.进一步,利用快慢变量分离获得的簇放电的动力学性质进行了理论解释.簇放电模式表现出低电位的休止期和高电位的放电的交替,存在于快子系统的鞍结分岔点和同宿轨分岔点之间;放电起始于鞍结分岔、结束于同宿轨分岔;越靠近同宿轨分岔从休止期跨越到放电所需的电流强度越大.因此,电流在休止期上的作用相位越早,就越靠近同宿轨分岔,因而从休止期跨越到放电需要的电流强度阈值越大,放电起始相位到同宿轨分岔之间的区间变小导致放电个数变少.研究结果丰富了非线性现象及机制,对兴奋性作用提出了新看法,给出了调控簇放电模式的新途径.

English Abstract

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