Guan Linan, Gu Huaguang, Zhang Xinjing
School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou, China.
School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, China.
Front Comput Neurosci. 2024 Feb 9;18:1303925. doi: 10.3389/fncom.2024.1303925. eCollection 2024.
Antiphase bursting related to the rhythmic motor behavior exhibits complex dynamics modulated by the inhibitory synaptic current (), especially in the presence of the hyperpolarization-activated cation current (). In the present paper, the dynamics of antiphase bursting modulated by the and is studied in three aspects with a theoretical model. Firstly, the and the slow with strong strength are the identified to be the necessary conditions for the antiphase bursting. The dependence of the antiphase bursting on the two currents is different for low (escape mode) and high (release mode) threshold voltages () of the inhibitory synapse. Secondly, more detailed co-regulations of the two currents to induce opposite changes of the bursting period are obtained. For the escape mode, increase of the induces elevated membrane potential of the silence inhibited by a strong and shortened silence duration to go beyond , resulting in reduced bursting period. For the release mode, increase of the induces elevated tough value of the former part of the burst modulated by a nearly zero and lengthen burst duration to fall below , resulting in prolonged bursting period. Finally, the fast-slow dynamics of the antiphase bursting are acquired. Using one-and two-parameter bifurcations of the fast subsystem of a single neuron, the burst of the antiphase bursting is related to the stable limit cycle, and the silence modulated by a strong to the stable equilibrium to a certain extent. The mainly modulates the dynamics within the burst and quiescent state. Furthermore, with the fast subsystem of the coupled neurons, the silence is associated with the unstable equilibrium point. The results present theoretical explanations to the changes in the bursting period and fast-slow dynamics of the antiphase bursting modulated by the and , which is helpful for understanding the antiphase bursting and modulating rhythmic motor patterns.
与节律性运动行为相关的反相爆发表现出由抑制性突触电流（）调制的复杂动力学，特别是在存在超极化激活阳离子电流（）的情况下。在本文中，利用理论模型从三个方面研究了由和调制的反相爆发的动力学。首先，确定和具有强强度的慢是反相爆发的必要条件。对于抑制性突触的低（逃逸模式）和高（释放模式）阈值电压（），反相爆发对这两种电流的依赖性不同。其次，获得了两种电流更详细的共同调节以诱导爆发周期的相反变化。对于逃逸模式，的增加会导致被强抑制的静息膜电位升高，静息持续时间缩短至超过，从而导致爆发周期缩短。对于释放模式，的增加会导致由几乎为零的调制的爆发前半部分的阈值升高，爆发持续时间延长至低于，从而导致爆发周期延长。最后，获得了反相爆发的快-慢动力学。利用单个神经元快速子系统的单参数和双参数分岔，反相爆发的爆发与稳定极限环有关，而被强调制的静息在一定程度上与稳定平衡点有关。主要调制爆发和静止状态内的动力学。此外，对于耦合神经元的快速子系统，静息与不稳定平衡点相关。结果为和调制的反相爆发的爆发周期和快-慢动力学变化提供了理论解释，这有助于理解反相爆发和调节节律性运动模式。
