基于分岔理论的突触可塑性对神经群动力学特性调控规律研究

夏小飞; 王俊松

doi:10.7498/aps.63.140503

摘要

神经群模型是典型的非线性系统，具有丰富而复杂的动力学行为模式. 神经群兴奋性和抑制性突触具有可塑性，并对神经群动力学特性具有重要调控作用，研究突触可塑性对神经群动力学特性的调控规律具有重要意义. 本文基于分岔理论，通过神经群模型兴奋性和抑制性突触增益的余维一分岔分析，分别给出了神经群运行于单稳、双稳、正常和异常极限环振荡状态的兴奋性和抑制性突触增益的单参数区间；进而通过兴奋性和抑制性突触增益的余维二分岔分析给出了神经群运行于上述多种状态的双参数区域. 上述结果定量剖析了兴奋性与抑制性突触可塑性及二者的相互作用对神经群动力学特性的调控规律，揭示了兴奋性与抑制性的动态平衡在神经电活动调控中所扮演的关键角色，仿真结果验证了分岔分析的正确性. 本文的研究对理解突触可塑性在脑功能的维持及各种神经疾病的诱发机制中所扮演的角色具有重要参考价值.

关键词:

Abstract

Neural mass model is a typical nonlinear system with rich and complex dynamics. Up to now, most bifurcation researches of neural mass model (NMM) have focused on the influence of input or connection parameters between subpopulations on the dynamics of NMM. Actually, the synaptic strength is varied temporally, owing to synaptic plasticity, and plays a crucial role in regulating the dynamics of NMM. However, there are no researches on synaptic strength bifurcation analysis of NMM, and how excitatory and inhibitory synaptic plasticity exerts an influence on the dynamics of NMM is still little known. Motivated by this idea, the bifurcation analysis of excitatory and inhibitory synaptic strength of NMM is conducted in this study. Firstly, codimension-one bifurcation analyses of excitatory and inhibitory synaptic strengths are performed, respectively, through which the parameters regions of stability, bistablility, normal and abnormal oscillation are determined. Secondly, codimension-two bifurcation analysis is conducted, through which we can further gain an insight into the influence of the interaction between excitatory and inhibitory synaptic strengths on the dynamics of NMM. Finally, the bifurcation analysis results is verified by the simulation results. This study of bifurcation reveals two kinds of oscillation mechanisms: limit cycle oscillation mechanism and input-induced transition between two states of the bistability.

Keywords:

作者及机构信息

夏小飞¹,
王俊松^1,2

1.
天津医科大学生物医学工程学院, 天津 300070;

2.
约翰霍普金斯大学神经科学系, 巴尔的摩 21218, 美国

基金项目: 国家自然科学基金重大研究计划（培育项目）（批准号：91132722）和天津医科大学科学研究基金（批准号：088-201201）资助的课题.

Authors and contacts

1.
School of Biomedical Engineering, Tianjin Medical University, Tianjin 300070, China;

2.
Department of Neuroscience and Zanvyl Krieger Mind/Brain Institute, Johns Hopkins University, Baltimore 21218, MD, USA

Funds: Project supported by the Major Research Plan of the National Natural Science Foundation of China (Grant No. 91132722) and the Scientific Research Foundation of Tianjin Medical University, China (Grant No. 088-201201).

参考文献

[1]	Hashemi M, Valizadeh A, Azizi Y 2012 Phys. Rev. E 85 021917
[2]	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]
[3]	Yang Z Q 2010 Acta Phys. Sin. 59 5319 (in Chinese) [杨卓琴 2010 59 5319]
[4]	Gu H G, Hui L, Jia B 2012 Acta Phys. Sin. 61 080504 (in Chinese) [古华光, 惠磊, 贾冰 2012 61 080504]
[5]	Lopes da Silva F H, Hoeks A, Smits H, Zetterberg L H 1974 Kybernetik 15 27
[6]	Jansen B H, Rit V G 1995 Biol. Cybern. 73 357
[7]	Liu X, Ma B W, Liu H J 2013 Acta Phys. Sin. 62 020202 (in Chinese) [刘仙, 马百旺, 刘会军 2013 62 020202]
[8]	Zheng Y, Luo J J, Harris S, Kennerley A, Berwick J, Billings S A, Mayhew J 2012 NeuroImage 63 81
[9]	Wang J S, Xu Y 2014 Acta Phys. Sin. 63 068701 (in Chinese) [王俊松, 徐瑶 2014 63 068701]
[10]	Stephan K E, Kasper L, Harrison L M, Daunizeau J, den Ouden H E, Breakspear M, Friston K J 2008 NeuroImage 42 649
[11]	David O, Friston K J 2003 NeuroImage 20 1743
[12]	Deco G, Jirsa V K, Robinson P A, Breakspear M, Friston K 2008 PLoS. Comput. Biol. 4 e1000092
[13]	Destexhe A, Sejnowski T J 2009 Biol. Cybern. 101 1
[14]	Cui D, Li X L, Ji X Q, Liu L X 2011 Sci. China: Infom. Sci. 54 1283 (in Chinese) [崔冬, 李小俚, 吉学青, 刘兰祥 2011 中国科学: 信息科学 54 1283]
[15]	Uhlhaas P J, Singer W 2010 Nat. Rev. Neurosci. 11 100
[16]	Schnitzler A, Gross J 2005 Nat. Rev. Neurosci. 6 285
[17]	Paulo C, Rech 2012 Chin. Phys. Lett. 29 060506
[18]	Liu X, Gao Q, Li X L 2014 Chin. Phys. B 23 010202
[19]	Wang H X, He C 2003 Chin. Phys. B 12 259
[20]	Grimbert F, Faugeras O 2006 Neural Comput. 18 3052
[21]	Touboul J, Wendling F, Chauvel P, Faugeras O 2011 Neural Comput. 23 3232
[22]	Spiegler A, Kiebel S J, Atay F M, Knösche T R 2010 NeuroImage 52 1041
[23]	Goodfellow M, Schindler K, Baier G 2011 NeuroImage 55 920
[24]	Goodfellow M, Schindler K, Baier G 2012 NeuroImage 59 2644
[25]	Coombes S 2010 NeuroImage 52 731
[26]	Abbott L F, Nelson S B 2000 Nat. Neurosci. 3 1178
[27]	Citri A, Malenka R C 2007 Neuropsychopharmacology 33 18
[28]	Žiburkus J, Cressman J R, Schiff S J 2013 J. Neurophysiol. 109 1296
[29]	Dhooge A, Govaerts W, Kuznetsov Y A 2003 ACM Trans. Math. Softw. 29 141

施引文献

[1]	Hashemi M, Valizadeh A, Azizi Y 2012 Phys. Rev. E 85 021917
[2]	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]
[3]	Yang Z Q 2010 Acta Phys. Sin. 59 5319 (in Chinese) [杨卓琴 2010 59 5319]
[4]	Gu H G, Hui L, Jia B 2012 Acta Phys. Sin. 61 080504 (in Chinese) [古华光, 惠磊, 贾冰 2012 61 080504]
[5]	Lopes da Silva F H, Hoeks A, Smits H, Zetterberg L H 1974 Kybernetik 15 27
[6]	Jansen B H, Rit V G 1995 Biol. Cybern. 73 357
[7]	Liu X, Ma B W, Liu H J 2013 Acta Phys. Sin. 62 020202 (in Chinese) [刘仙, 马百旺, 刘会军 2013 62 020202]
[8]	Zheng Y, Luo J J, Harris S, Kennerley A, Berwick J, Billings S A, Mayhew J 2012 NeuroImage 63 81
[9]	Wang J S, Xu Y 2014 Acta Phys. Sin. 63 068701 (in Chinese) [王俊松, 徐瑶 2014 63 068701]
[10]	Stephan K E, Kasper L, Harrison L M, Daunizeau J, den Ouden H E, Breakspear M, Friston K J 2008 NeuroImage 42 649
[11]	David O, Friston K J 2003 NeuroImage 20 1743
[12]	Deco G, Jirsa V K, Robinson P A, Breakspear M, Friston K 2008 PLoS. Comput. Biol. 4 e1000092
[13]	Destexhe A, Sejnowski T J 2009 Biol. Cybern. 101 1
[14]	Cui D, Li X L, Ji X Q, Liu L X 2011 Sci. China: Infom. Sci. 54 1283 (in Chinese) [崔冬, 李小俚, 吉学青, 刘兰祥 2011 中国科学: 信息科学 54 1283]
[15]	Uhlhaas P J, Singer W 2010 Nat. Rev. Neurosci. 11 100
[16]	Schnitzler A, Gross J 2005 Nat. Rev. Neurosci. 6 285
[17]	Paulo C, Rech 2012 Chin. Phys. Lett. 29 060506
[18]	Liu X, Gao Q, Li X L 2014 Chin. Phys. B 23 010202
[19]	Wang H X, He C 2003 Chin. Phys. B 12 259
[20]	Grimbert F, Faugeras O 2006 Neural Comput. 18 3052
[21]	Touboul J, Wendling F, Chauvel P, Faugeras O 2011 Neural Comput. 23 3232
[22]	Spiegler A, Kiebel S J, Atay F M, Knösche T R 2010 NeuroImage 52 1041
[23]	Goodfellow M, Schindler K, Baier G 2011 NeuroImage 55 920
[24]	Goodfellow M, Schindler K, Baier G 2012 NeuroImage 59 2644
[25]	Coombes S 2010 NeuroImage 52 731
[26]	Abbott L F, Nelson S B 2000 Nat. Neurosci. 3 1178
[27]	Citri A, Malenka R C 2007 Neuropsychopharmacology 33 18
[28]	Žiburkus J, Cressman J R, Schiff S J 2013 J. Neurophysiol. 109 1296
[29]	Dhooge A, Govaerts W, Kuznetsov Y A 2003 ACM Trans. Math. Softw. 29 141

[1]	刘贺, 杨亚晶, 唐玉凝, 魏衍举. 声致液滴失稳动力学研究. , 2024, 73(20): 204204. doi: 10.7498/aps.73.20240965
[2]	陈雪丽, 夏露源, 王智慧, 段利霞. 电磁感应驱动下闭环呼吸控制系统中的混合节律及其动力学分析. , 2024, 73(18): 180502. doi: 10.7498/aps.73.20240847
[3]	李瑞, 徐邦林, 周建芳, 姜恩华, 汪秉宏, 袁五届. 一种突触可塑性导致的觉醒-睡眠周期中突触强度变化和神经动力学转变. , 2023, 72(24): 248706. doi: 10.7498/aps.72.20231037
[4]	高艺雯, 王影, 田文得, 陈康. 空间调制的驱动外场下活性聚合物的动力学行为. , 2022, 71(24): 240501. doi: 10.7498/aps.71.20221367
[5]	郭科鑫, 于海洋, 韩弘, 卫欢欢, 龚江东, 刘璐, 黄茜, 高清运, 徐文涛. 基于水热法制备三氧化钼纳米片的人工突触器件. , 2020, 69(23): 238501. doi: 10.7498/aps.69.20200928
[6]	陈义豪, 徐威, 王钰琪, 万相, 李岳峰, 梁定康, 陆立群, 刘鑫伟, 连晓娟, 胡二涛, 郭宇锋, 许剑光, 童祎, 肖建. 基于二维材料MXene的仿神经突触忆阻器的制备和长/短时程突触可塑性的实现. , 2019, 68(9): 098501. doi: 10.7498/aps.68.20182306
[7]	牛帅, 帅建伟, 祁宏. Bcl-2蛋白抑制钙信号的建模与全局动力学分析. , 2017, 66(23): 238701. doi: 10.7498/aps.66.238701
[8]	孟凡一, 段书凯, 王丽丹, 胡小方, 董哲康. 一种改进的WOx忆阻器模型及其突触特性分析. , 2015, 64(14): 148501. doi: 10.7498/aps.64.148501
[9]	徐志成, 钟伟荣. C60轰击石墨烯的瞬间动力学. , 2014, 63(8): 083401. doi: 10.7498/aps.63.083401
[10]	包伯成, 王春丽, 武花干, 乔晓华. 忆阻电路降维建模与特性分析. , 2014, 63(2): 020504. doi: 10.7498/aps.63.020504
[11]	王俊松, 徐瑶. 基于描述函数方法的神经群自激振荡特性分析. , 2014, 63(6): 068701. doi: 10.7498/aps.63.068701
[12]	贾红艳, 陈增强, 薛薇. 分数阶Lorenz系统的分析及电路实现. , 2013, 62(14): 140503. doi: 10.7498/aps.62.140503
[13]	刘仙, 马百旺, 刘会军. 神经群模型中癫痫状棘波的闭环控制性能研究. , 2013, 62(2): 020202. doi: 10.7498/aps.62.020202
[14]	陈军, 李春光. 禁忌学习神经元模型的电路设计及其动力学研究. , 2011, 60(2): 020502. doi: 10.7498/aps.60.020502
[15]	张青, 王杰智, 陈增强, 袁著祉. 共轭Chen混沌系统的分岔分析及基于该系统的超混沌生成研究. , 2008, 57(4): 2092-2099. doi: 10.7498/aps.57.2092
[16]	罗宇峰, 钟澄, 张莉, 严学俭, 李劲, 蒋益明. 方块电阻法原位表征Cu薄膜氧化反应动力学规律. , 2007, 56(11): 6722-6726. doi: 10.7498/aps.56.6722
[17]	张维, 周淑华, 任勇, 山秀明. Turbo译码算法的分岔与控制. , 2006, 55(2): 622-627. doi: 10.7498/aps.55.622
[18]	付文玉, 侯锡苗, 贺丽霞, 郑志刚. 少体硬球系统的动力学与统计研究. , 2005, 54(6): 2552-2556. doi: 10.7498/aps.54.2552
[19]	李剑锋, 张红东, 邱枫, 杨玉良. 模拟囊泡形变动力学的新方法离散空间变分法. , 2005, 54(9): 4000-4005. doi: 10.7498/aps.54.4000
[20]	王宏霞, 何晨. 细胞神经网络的动力学行为. , 2003, 52(10): 2409-2414. doi: 10.7498/aps.52.2409

计量

文章访问数: 6708
PDF下载量: 564
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板