方波电流对混合簇放电的影响及其动力学分析
Influence of Square Wave Current on Mixed Bursting and Its Dynamic Analysis
摘要: Pre-Bötzinger复合体(简称pre-BötC)是新生哺乳动物产生正常呼吸节律的关键部位。当神经元受到外部刺激时，其放电模式会发生改变。方波电流是最简单且易实现的一种电流形式。本文通过调控方波电流的三个变量，来研究方波电流对神经元放电模式的影响。并通过时间序列和单参数分岔分析以及双参数分岔分析的方法，探究放电模式产生及转迁的动力学机制。结果表明方波电流可以诱导神经元产生混合簇放电。本文的研究结果为进一步理解神经系统中混合簇放电的产生机制提供了有益的参考。
Abstract: Pre-Bötzinger complex (referred to as pre-BötC) is a key site in the generation of normal respiratory rhythm in newborn mammals. When neurons are subjected to external stimuli, their firing patterns change. Square wave current is one of the simplest and easily achievable forms of current. In this paper, we investigate the effects of square current on the firing pattern of neurons by regulating three variables of square current. By time series, single-parameter bifurcation analysis and two-parameter bifurcation analysis, the dynamic mechanism of generation and transition of bursting pattern is explored. The results show that square current can induce neurons to generate mixed bursting. The findings of this paper can provide some reference for further understanding the generation mechanism of mixed bursting in the nervous system.
文章引用：蒋亚璐, 陈雪丽. 方波电流对混合簇放电的影响及其动力学分析[J]. 力学研究, 2023, 12(1): 56-67. https://doi.org/10.12677/IJM.2023.121006

参考文献

[1] Pace, R.W., Mackay, D.D., Feldman, J.L., et al. (2007) Inspiratory Bursts in the Pre-Bötzinger Complex Depend on a Calcium-Activated Non-Specific Cation Current Linked to Glutamate Receptors in Neonatal Mice. The Journal of Physiology, 582, 113-125. [Google Scholar] [CrossRef] [PubMed]
[2] Izhikevich, E.M. (2000) Neural Excitability, Spiking and Bursting. International Journal of Bifurcation and Chaos, 10, 1171-1266. [Google Scholar] [CrossRef] 
[3] Stojilkovic, S.S., Zemkova, H. and Van Goor, F. (2005) Biophysical Basis of Pituitary Cell Type-Specific 〖ca〗^(2+)Signaling-Secretion Coupling. Trends in Endocrinology & Metabolism, 16, 152-159. [Google Scholar] [CrossRef] [PubMed]
[4] Smith, J.C., Ellenberger, H.H., Ballanyi, K., Richter, D.W. and Feldman, J.L. (1991) Pre-Bötzinger Complex: A Brainstem Region That May Generate Respiratory Rhythm in Mammals. Science, 254, 726-729. [Google Scholar] [CrossRef] [PubMed]
[5] Lieske, S.P., Thoby-Brisson, M., Telgkamp, P., et al. (2000) Reconfiguration of the Neural Network Controlling Multiple Breathing Patterns: Eupnea, Sighs and Gasps. Nature Neuroscience, 3, 600-607. [Google Scholar] [CrossRef] [PubMed]
[6] Ding, X. and Li, Y. (2016) Period-Adding Bifurcation of Neural Firings Induced by Inhibitory Autapses with Time-Delay. Acta Physica Sinica, 65, 210502.
[7] Butera, R.J., Rinzel, J. and Smith, J.C. (1999) Models of Respiratory Rhythm Generation in the Pre-Bötzinger Complex. I. Bursting Pacemaker Neurons. Journal of Neurophysiology, 82, 382-397. [Google Scholar] [CrossRef] [PubMed]
[8] Butera, R.J., John, R. and Smith, J.C. (1999) Models of Respiratory Rhythm Generation in the Pre-Bötzinger Complex. II. Populations of Coupled Pacemaker Neurons. Journal of Neurophysiology, 82, 398-415. [Google Scholar] [CrossRef] [PubMed]
[9] Rubin, J.E., Hayes, J.A., Mendenhall, J.L., et al. (2009) Calcium-Activated Nonspecific Cation Current and Synaptic Depression Promote Network-Dependent Burst Oscillations. Proceedings of the National Academy of Sciences, 106, 2939-2944. [Google Scholar] [CrossRef] [PubMed]
[10] Lü, Z., Liu, M. and Duan, L. (2021) Dynamical Analysis of Dendritic Mixed Bursting within the Pre-Bötzinger Complex. Nonlinear Dynamics, 103, 897-912. [Google Scholar] [CrossRef] 
[11] Wang, Y.Y. and Rubin, J.E. (2017) Timescales and Mechanisms of Sigh-Like Bursting and Spiking in Models of Rhythmic Respiratory Neurons. The Journal of Mathematical Neuroscience, 7, Article No. 3. [Google Scholar] [CrossRef] [PubMed]
[12] Ji, W., Liu, M. and Duan, L. (2021) Influence of Electric Current and Magnetic Flow on Firing Patterns of Pre-Bötzinger Complex Model. Neural Plasticity, 2021, Article ID: 6655933. [Google Scholar] [CrossRef] [PubMed]
[13] Duan, L., Liang, T., Zhao, Y. and Xi, H. (2021) Multi-Time Scale Dynamics of Mixed Depolarization Block Bursting. Nonlinear Dynamics, 103, 1043-1053. [Google Scholar] [CrossRef] 
[14] Wang, Y. and Rubin, J.E. (2016) Multiple Timescale Mixed Bursting Dynamics in a Respiratory Neuron Model. Journal of Computational Neuroscience, 41, 245-268. [Google Scholar] [CrossRef] [PubMed]
[15] Lü, Z., Chen, L. and Duan, L. (2019) Bifurcation Analysis of Mixed Bursting in the Pre-Bötzinger Complex. Applied Mathematical Modelling, 67, 234-251.
[16] Park, C. and Rubin, J.E. (2013) Cooperation of Intrinsic Bursting and Calcium Oscillations Underlying Activity Patterns of Model Pre-Bötzinger Complex Neurons. Journal of Computational Neuroscience, 34, 345-366. [Google Scholar] [CrossRef] [PubMed]

为你推荐