Canavier Carmen C
Department of Cell Biology and Anatomy, Louisiana State University Health Sciences Center New Orleans, New Orleans, Louisiana, United States.
J Neurophysiol. 2025 Jun 1;133(6):1630-1640. doi: 10.1152/jn.00045.2025. Epub 2025 Apr 29.
A mean field method for pulse-coupled oscillators with delays used a self-connected oscillator to represent a synchronous cluster of - 1 oscillators and a single oscillator assumed to be perturbed from the cluster. A periodic train of biexponential conductance input was divided into a tonic and a phasic component representing the mean field input. A single cycle of the phasic conductance from the cluster was applied to the single oscillator embedded in the tonic component at different phases to measure the change in the cycle length in which the perturbation was initiated, that is, the first-order phase response curve (PRC), and the second-order PRC in the following cycle. A homogeneous network of 100 biophysically calibrated inhibitory interneurons with either shunting or hyperpolarizing inhibition tested the predictive power of the method. A self-consistency criterion predicted the oscillation frequency of the network from the PRCs as a function of the synaptic delay. The major determinant of the stability of synchrony was the sign of the slope of the first-order PRC of the single oscillator in response to an input from the self-connected cluster at a phase corresponding to the delay value. For most short delays, first-order PRCs correctly predicted the frequency and stability of simulated network activity. However, considering the second-order PRC improved the frequency prediction and resolved an incorrect prediction of stability of global synchrony at delays close to the free running period of single neurons in which a discontinuity in the PRC precluded existence of 1:1 self-locking. A mean field theory for synchrony in neural networks in which neurons are generally above threshold in the mean-driven regime is developed to extend and complement mean field theory previously developed by others for neurons that are generally below threshold in the fluctuation-driven regime. This work extends phase response curve theory as applied to high-frequency oscillations in networks with synaptic inputs that are not short with respect to the network period.
一种用于带延迟的脉冲耦合振荡器的平均场方法，使用一个自连接振荡器来表示(N - 1)个振荡器的同步簇，并假设单个振荡器受到该簇的扰动。周期性的双指数电导输入序列被分为一个稳态分量和一个相位分量，分别代表平均场输入。将来自簇的相位电导的单个周期在不同相位应用于嵌入在稳态分量中的单个振荡器，以测量在其中启动扰动的周期长度的变化，即一阶相位响应曲线（PRC），以及随后周期中的二阶PRC。一个由100个经过生物物理校准的抑制性中间神经元组成的均匀网络，具有分流或超极化抑制，测试了该方法的预测能力。一个自洽标准根据PRC预测网络的振荡频率，该频率是突触延迟的函数。同步稳定性的主要决定因素是单个振荡器在对应于延迟值的相位处响应来自自连接簇的输入时一阶PRC的斜率符号。对于大多数短延迟，一阶PRC正确地预测了模拟网络活动的频率和稳定性。然而，考虑二阶PRC改善了频率预测，并解决了在接近单个神经元自由运行周期的延迟处对全局同步稳定性的错误预测，在该延迟处PRC中的不连续性排除了1:1自锁的存在。发展了一种用于神经网络同步的平均场理论，其中神经元在平均驱动状态下通常高于阈值，以扩展和补充先前由其他人针对在波动驱动状态下通常低于阈值的神经元所发展的平均场理论。这项工作扩展了相位响应曲线理论，该理论适用于具有相对于网络周期而言不短的突触输入的网络中的高频振荡。
