对Hodgkin-Huxley神经元网络的theta嵌套的gamma节律的数值研究
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摘要
人和动物在进行学习、记忆等高级认知的过程中,大脑的很多区域会产生不同频率范围的节律。这些节律一方面可以独立地发挥自己的作用,另一方面也可以相互作用、相互调节。一般低频率节律的相位会对高频率节律的振幅进行调节,使两者耦合起来产生嵌套的节律,从而生成更为复杂的大脑活动。经研究,这些嵌套的节律对于记忆的编码和再现有着至关重要的作用。
通过数值模拟,我们发现在HH神经元网络中能产生两种频率范围的节律：theta节律(4-8Hz)和gamma节律(30-100Hz)。如果低频率的theta节律的相位对高频率的gamma节律的振幅进行适当地调节,那么将会产生theta嵌套的gamma节律。然而这种调节需要抑制性慢的神经元和抑制性快的神经元同时与兴奋性神经元之间存在突触连接,并且还需要足够强的外加刺激电流的刺激,缺少任何一种条件都将无法产生theta嵌套的gamma节律,即突触连接的电导系数gGAse、gGAfe和外加刺激电流Iapp不能为0。我们发现电导系数gGAse的增大会使theta节律的能量变大,从而使theta节律的相位和gamma节律的振幅的耦合(CFC:cross-frequency coupling)强度增大,而且在此过程中,各个兴奋性神经元之间的theta节律的相位同步性增加。然而随着电导系数ggGAfe的增大,产生的现象却完全相反。
学习是大脑的一个重要功能,而由NMDA受体介导的电流与学习记忆密切相关。然而我们发现在一定条件下,如果只加强由NMDA受体介导的电流的电导系数gNMee,反而不会产生学习的效果。只有同时加强gNMes和由GABAA类受体介导的电流的电导系数gGAse,才会产生学习的效果。换言之,要产生学习这种现象需要NMDA受体和GABAA类受体的相互协调。在学习过程中,theta节律的能量增强,CFC强度增大,各个兴奋性神经元之间的theta节律的相位同步性增加。
Multiple brain regions can generate rhythm in different frequency bands when animals, including humans, are undergoing cognitive tasks, such as learning, memory tasks and so on. These rhythms can occur simultaneously and work respectively, they can also interact with each other and much more complex brain activities can take place when nested rhythms generate as the amplitude of the high frequency rhythm is modulated by the phase of the low one. Resent research have indicated that these nested rhythms play an important role in memory coding and recalling.
According to our computational simulation, we find that the HH neuronal net-work can generate both theta(4-8Hz) and gamma (30-100Hz)rhythm. And the theta-nested gamma rhythm occurs when the amplitude of high frequency gamma rhythm is modulated by the phase of low frequency theta rhythm. However, this modulating needs the synaptic connection from inhibitory fast neurons to excitatory neurons and the connection from inhibitory slow neurons to excitatory neurons, accompanied by the appropriate applied current. It is found that nested rhythm can't generate if any one of these three terms is not available, namely the applied current Iapp, the synaptic conductances gGAse and gGAfe which can't be zero. We find that the power of theta rhythm increases when the conductance gGAse increases, it leads to the increasing of the magnitude of phase-amplitude cross-frequency coupling(CFC) between theta and gamma rhythm, and the phase synchronization of theta rhythm among excited neurons increases in this process. However, a completely opposite result takes place when the conductance gGAfe increases.
An important function of brain is to take charge of learning, and the current me-diated by NMDA receptor can facilitate learning. However, if we only increase the conductance gNMee, the learning activity can't be aroused. Only when the conduc-tances gGAse and gNMes, as well as gNMee increase simultaneously, will the learning activity occur. In other words, the cooperation between NMDA receptor and GABAA receptor is the key for generating the learning effect. The power of theta rhythm in-crease during learning, and the magnitude of the phase-amplitude CFC also increases, but the phase synchronization of theta rhythm among excited neurons increases.
通过数值模拟,我们发现在HH神经元网络中能产生两种频率范围的节律：theta节律(4-8Hz)和gamma节律(30-100Hz)。如果低频率的theta节律的相位对高频率的gamma节律的振幅进行适当地调节,那么将会产生theta嵌套的gamma节律。然而这种调节需要抑制性慢的神经元和抑制性快的神经元同时与兴奋性神经元之间存在突触连接,并且还需要足够强的外加刺激电流的刺激,缺少任何一种条件都将无法产生theta嵌套的gamma节律,即突触连接的电导系数gGAse、gGAfe和外加刺激电流Iapp不能为0。我们发现电导系数gGAse的增大会使theta节律的能量变大,从而使theta节律的相位和gamma节律的振幅的耦合(CFC:cross-frequency coupling)强度增大,而且在此过程中,各个兴奋性神经元之间的theta节律的相位同步性增加。然而随着电导系数ggGAfe的增大,产生的现象却完全相反。
学习是大脑的一个重要功能,而由NMDA受体介导的电流与学习记忆密切相关。然而我们发现在一定条件下,如果只加强由NMDA受体介导的电流的电导系数gNMee,反而不会产生学习的效果。只有同时加强gNMes和由GABAA类受体介导的电流的电导系数gGAse,才会产生学习的效果。换言之,要产生学习这种现象需要NMDA受体和GABAA类受体的相互协调。在学习过程中,theta节律的能量增强,CFC强度增大,各个兴奋性神经元之间的theta节律的相位同步性增加。
Multiple brain regions can generate rhythm in different frequency bands when animals, including humans, are undergoing cognitive tasks, such as learning, memory tasks and so on. These rhythms can occur simultaneously and work respectively, they can also interact with each other and much more complex brain activities can take place when nested rhythms generate as the amplitude of the high frequency rhythm is modulated by the phase of the low one. Resent research have indicated that these nested rhythms play an important role in memory coding and recalling.
According to our computational simulation, we find that the HH neuronal net-work can generate both theta(4-8Hz) and gamma (30-100Hz)rhythm. And the theta-nested gamma rhythm occurs when the amplitude of high frequency gamma rhythm is modulated by the phase of low frequency theta rhythm. However, this modulating needs the synaptic connection from inhibitory fast neurons to excitatory neurons and the connection from inhibitory slow neurons to excitatory neurons, accompanied by the appropriate applied current. It is found that nested rhythm can't generate if any one of these three terms is not available, namely the applied current Iapp, the synaptic conductances gGAse and gGAfe which can't be zero. We find that the power of theta rhythm increases when the conductance gGAse increases, it leads to the increasing of the magnitude of phase-amplitude cross-frequency coupling(CFC) between theta and gamma rhythm, and the phase synchronization of theta rhythm among excited neurons increases in this process. However, a completely opposite result takes place when the conductance gGAfe increases.
An important function of brain is to take charge of learning, and the current me-diated by NMDA receptor can facilitate learning. However, if we only increase the conductance gNMee, the learning activity can't be aroused. Only when the conduc-tances gGAse and gNMes, as well as gNMee increase simultaneously, will the learning activity occur. In other words, the cooperation between NMDA receptor and GABAA receptor is the key for generating the learning effect. The power of theta rhythm in-crease during learning, and the magnitude of the phase-amplitude CFC also increases, but the phase synchronization of theta rhythm among excited neurons increases.
引文
[1]Buzsaki. G, Draguhn. A, Neuronal oscillations in cortical networks [J]. Science. 2004.304:1926-1929.
[2]Osipova. D, Hermes. D, Jensen.O, Gamma power is phase-locked to posterior alpha activity [J]. PLoS ONE.2008.3(12):e3990.
[3]Buzsaki. G, Theta oscillations in the Hippocampus [J]. Neuron.2002,33:1-20.
[4]Osipova. D, Takashima. A, Oostenveld. R, et al, Theta and gamma oscilla-tions predict encoding and retrieval of declarative memory [J]. J Neurosci.2006. 26(28):7523-7531.
[5]Jensen. O, Kaiser. J, Lachaux. J. P, Human gamma-frequency oscillations associ-ated with attention and memory [J]. Trends in Neurosciences.2007.30(7):317-324.
[6]Jensen. O, Colgin. L. L, Cross-frequency coupling between neuronal oscillations [J]. Trends Cogn Sci.2007.11(7):267-269.
[7]Canolty. R. T, Edwards. E, Dalal. S. S, et al, High gamma power is phase-locked to theta oscillations in human neocortex [J]. Science.2006.313:1626-1628.
[8]Lisman. J. E, Idiart. M. A. P, Storage of 7±2 short term memories in oscillatory subcycles [J]. Science.1995.267:1512-1515.
[9]Lisman. J. E, The theta/gamma discrete phase code occurring during the hip-pocampal phase precession may be a more general brain coding scheme [J]. Hip-pocampus.2005.15:913-922.
[10]Tort. A. B. L, Komorowski. R, Manns. J, et al, Theta-gamma coupling increases during the learning of item-context associations [J]. Proc Natl Acad Sci USA. 2009.106:20942-20947.
[11]Kendrick. K. M., et al, Learning facilitated theta-nested gamma in inferotemporal cortex. Nature Precedings [J].2009. hdl:/10101/npre.2009.3151.1.
[12]Tort. A. B. L, Kramer. M. A, Thorn. C, et al, Dynamic cross-frequency couplings of local field potential oscillations in rat striatum and hippocampus during perfor-mance of a t-maze task [J]. Proc Natl Acad Sci USA.2008.105:20517-20522.
[13]Cohen. M. X, Axmacher. N, Lenartz. D, et al, Good vibrations:cross-frequency coupling in the human nucleus accumbens during reward processing [J]. J Cogn Neurosci.2009a.21:875-889.
[14]Cohen. M. X, Elger. C. E, Fell. J, Oscillatory activity and phaseamplitude cou-pling in the human medial frontal cortex during decision making [J]. J Cogn Ncu-rosci.2009b.21:390-402.
[15]Schroeder. C. E, Lakatos. P, Low-frequency neuronal oscillations as instruments of sensory selection [J]. TRENDS NEUROSCI.2009.32(1):9-18.
[16]Young. C. K, Eggermont. J, Coupling of mesoscopic brain oscillations:recent advances in analytical and theoretical perspectives. [J]. Progress in Neurobiology. 2009.89(1):61-78.
[17]Handel. B, Haarmeier. T, Cross-frequency coupling of brain oscillations indicates the success in visual motion discrimination [J]. Neuroimage.2009.45:1040-1046.
[18]Wulff. P, et al, Hippocampal theta rhythm and its coupling with gamma oscilla-tions require fast inhibition onto parvalbumin-positive interneurons [J]. Proc Natl Acad Sci USA.2009.106:3561-3566.
[19]Axmacher. N, et al, Cross-frequency coupling supports multi-item working mem-ory in the human hippocampus [J]. Pro Natl Acad Sci USA.2010.107:3228-3233.
[20]Soltesz. I, Deschenes. M, Low-and high-frequency membrane potential oscil-lations during theta activity in CA1 and CA3 pyramidal neurons of the rat hip-pocampus under ketamine-xylazine anesthesia [J]. J Neurophysiol.1993.70:97-116.
[21]Bragin. A, et al, Gamma (40-100 Hz) oscillation in the hippocampus of the be-having rat [J]. J Neurosci.1995.15:47-60.
[22]White. J. A, Banks. M, Pearce. R, Kopell. N, Networks of interneurons with fast and slow CABAA kinetics provide substrate for mixed gamma-theta rhythm [J]. Proc Natl Acad Sci USA.2000.97:8128-8133.
[23]Tyagarajan. S. K, Fritschy. J. M, GABAA receptors, gephyrin and homeostatic synaptic plasticity [J]. J Physiol.2010.588:101-106.
[24]White. J. A, Synchronization and oscillatory dynamics in heterogeneous, mutually inhibited neurons [J]. Journal of Computational Neuroscience.1998.5:5-16.
[25]Penny. W. D, Duzel. E, Miller. K. J, Ojemann. J. G, Testing for nested oscillation [J]. J Neurosci Methods.2008.174(1):50-61.
[26]Torrence. C, Compo. G. P, A practical guide to wavelet analysis[J]. Bull of the American Meteorological Society.1998.79:61-78.
[27]Tort. A. B. L, Komorowski. R, Kopell. N. J, Eichenbum. H, Measuring phase-amplitude coupling between neuronal oscillations of different frequencies [J]. J Neurophysiol.2010.104:1195-1210.
[28]DeCoteau. W. E, et al, Learning-related coordination of striatal and hippocampal theta rhythms during acquisition of a procedural maze task [J]. Proc Natl Acad Sci USA.2007.104:5644-5649.
[29]Montgomery. S. M, Betancur. M. I, Buzsaki. G, Behavior-dependent coordi-nation of multiple theta dipoles in the hippocampus. J Neurosci [J].2009. 29:1381-1394.
[30]Lakatos. P, et al, An oscillation hierarchy controlling neuronal excitability and stimulus processing in the auditory cortex [J]. J Neurophysiol.2005.94:1904-1911.
[31]Buzsaki. G, et al, Hippocampal network patterns of activity in the mouse [J]. Neuroscience.2003.116:201-211.
[32]Hentschke. H, Perkins. M. G, Pearce. R. A, et al, Muscarinic blockade weakens interaction of gamma with theta rhythms in mouse hippocampus [J]. Eur J Neu-rosci.2007.26:1642-1656.
[33]阮迪云.神经生物学[M].合肥：中国科学技术大学出版社.2008：110-136.
[2]Osipova. D, Hermes. D, Jensen.O, Gamma power is phase-locked to posterior alpha activity [J]. PLoS ONE.2008.3(12):e3990.
[3]Buzsaki. G, Theta oscillations in the Hippocampus [J]. Neuron.2002,33:1-20.
[4]Osipova. D, Takashima. A, Oostenveld. R, et al, Theta and gamma oscilla-tions predict encoding and retrieval of declarative memory [J]. J Neurosci.2006. 26(28):7523-7531.
[5]Jensen. O, Kaiser. J, Lachaux. J. P, Human gamma-frequency oscillations associ-ated with attention and memory [J]. Trends in Neurosciences.2007.30(7):317-324.
[6]Jensen. O, Colgin. L. L, Cross-frequency coupling between neuronal oscillations [J]. Trends Cogn Sci.2007.11(7):267-269.
[7]Canolty. R. T, Edwards. E, Dalal. S. S, et al, High gamma power is phase-locked to theta oscillations in human neocortex [J]. Science.2006.313:1626-1628.
[8]Lisman. J. E, Idiart. M. A. P, Storage of 7±2 short term memories in oscillatory subcycles [J]. Science.1995.267:1512-1515.
[9]Lisman. J. E, The theta/gamma discrete phase code occurring during the hip-pocampal phase precession may be a more general brain coding scheme [J]. Hip-pocampus.2005.15:913-922.
[10]Tort. A. B. L, Komorowski. R, Manns. J, et al, Theta-gamma coupling increases during the learning of item-context associations [J]. Proc Natl Acad Sci USA. 2009.106:20942-20947.
[11]Kendrick. K. M., et al, Learning facilitated theta-nested gamma in inferotemporal cortex. Nature Precedings [J].2009. hdl:/10101/npre.2009.3151.1.
[12]Tort. A. B. L, Kramer. M. A, Thorn. C, et al, Dynamic cross-frequency couplings of local field potential oscillations in rat striatum and hippocampus during perfor-mance of a t-maze task [J]. Proc Natl Acad Sci USA.2008.105:20517-20522.
[13]Cohen. M. X, Axmacher. N, Lenartz. D, et al, Good vibrations:cross-frequency coupling in the human nucleus accumbens during reward processing [J]. J Cogn Neurosci.2009a.21:875-889.
[14]Cohen. M. X, Elger. C. E, Fell. J, Oscillatory activity and phaseamplitude cou-pling in the human medial frontal cortex during decision making [J]. J Cogn Ncu-rosci.2009b.21:390-402.
[15]Schroeder. C. E, Lakatos. P, Low-frequency neuronal oscillations as instruments of sensory selection [J]. TRENDS NEUROSCI.2009.32(1):9-18.
[16]Young. C. K, Eggermont. J, Coupling of mesoscopic brain oscillations:recent advances in analytical and theoretical perspectives. [J]. Progress in Neurobiology. 2009.89(1):61-78.
[17]Handel. B, Haarmeier. T, Cross-frequency coupling of brain oscillations indicates the success in visual motion discrimination [J]. Neuroimage.2009.45:1040-1046.
[18]Wulff. P, et al, Hippocampal theta rhythm and its coupling with gamma oscilla-tions require fast inhibition onto parvalbumin-positive interneurons [J]. Proc Natl Acad Sci USA.2009.106:3561-3566.
[19]Axmacher. N, et al, Cross-frequency coupling supports multi-item working mem-ory in the human hippocampus [J]. Pro Natl Acad Sci USA.2010.107:3228-3233.
[20]Soltesz. I, Deschenes. M, Low-and high-frequency membrane potential oscil-lations during theta activity in CA1 and CA3 pyramidal neurons of the rat hip-pocampus under ketamine-xylazine anesthesia [J]. J Neurophysiol.1993.70:97-116.
[21]Bragin. A, et al, Gamma (40-100 Hz) oscillation in the hippocampus of the be-having rat [J]. J Neurosci.1995.15:47-60.
[22]White. J. A, Banks. M, Pearce. R, Kopell. N, Networks of interneurons with fast and slow CABAA kinetics provide substrate for mixed gamma-theta rhythm [J]. Proc Natl Acad Sci USA.2000.97:8128-8133.
[23]Tyagarajan. S. K, Fritschy. J. M, GABAA receptors, gephyrin and homeostatic synaptic plasticity [J]. J Physiol.2010.588:101-106.
[24]White. J. A, Synchronization and oscillatory dynamics in heterogeneous, mutually inhibited neurons [J]. Journal of Computational Neuroscience.1998.5:5-16.
[25]Penny. W. D, Duzel. E, Miller. K. J, Ojemann. J. G, Testing for nested oscillation [J]. J Neurosci Methods.2008.174(1):50-61.
[26]Torrence. C, Compo. G. P, A practical guide to wavelet analysis[J]. Bull of the American Meteorological Society.1998.79:61-78.
[27]Tort. A. B. L, Komorowski. R, Kopell. N. J, Eichenbum. H, Measuring phase-amplitude coupling between neuronal oscillations of different frequencies [J]. J Neurophysiol.2010.104:1195-1210.
[28]DeCoteau. W. E, et al, Learning-related coordination of striatal and hippocampal theta rhythms during acquisition of a procedural maze task [J]. Proc Natl Acad Sci USA.2007.104:5644-5649.
[29]Montgomery. S. M, Betancur. M. I, Buzsaki. G, Behavior-dependent coordi-nation of multiple theta dipoles in the hippocampus. J Neurosci [J].2009. 29:1381-1394.
[30]Lakatos. P, et al, An oscillation hierarchy controlling neuronal excitability and stimulus processing in the auditory cortex [J]. J Neurophysiol.2005.94:1904-1911.
[31]Buzsaki. G, et al, Hippocampal network patterns of activity in the mouse [J]. Neuroscience.2003.116:201-211.
[32]Hentschke. H, Perkins. M. G, Pearce. R. A, et al, Muscarinic blockade weakens interaction of gamma with theta rhythms in mouse hippocampus [J]. Eur J Neu-rosci.2007.26:1642-1656.
[33]阮迪云.神经生物学[M].合肥：中国科学技术大学出版社.2008：110-136.