Zheng Tianyi, Kotani Kiyoshi, Jimbo Yasuhiko
Graduate School of Engineering, The University of Tokyo, Tokyo, 113-8656, Japan.
Research Center for Advanced Science and Technology, The University of Tokyo, Tokyo, 153-8904, Japan.
Sci Rep. 2021 Jun 21;11(1):12960. doi: 10.1038/s41598-021-91389-8.
Gamma oscillation is crucial in brain functions such as attentional selection, and is inextricably linked to both heterogeneity and noise (or so-called stochastic fluctuation) in neuronal networks. However, under coexistence of these factors, it has not been clarified how the synaptic reversal potential modulates the entraining of gamma oscillation. Here we show distinct effects of heterogeneity and noise in a population of modified theta neurons randomly coupled via GABAergic synapses. By introducing the Fokker-Planck equation and circular cumulants, we derive a set of two-cumulant macroscopic equations. In bifurcation analyses, we find a stabilizing effect of heterogeneity and a nontrivial effect of noise that results in promoting, diminishing, and shifting the oscillatory region, and is largely dependent on the reversal potential of GABAergic synapses. These findings are verified by numerical simulations of a finite-size neuronal network. Our results reveal that slight changes in reversal potential and magnitude of stochastic fluctuations can lead to immediate control of gamma oscillation, which would results in complex spatio-temporal dynamics for attentional selection and recognition.
γ振荡在诸如注意力选择等大脑功能中至关重要，并且与神经网络中的异质性和噪声（或所谓的随机波动）有着千丝万缕的联系。然而，在这些因素共存的情况下，尚不清楚突触反转电位如何调节γ振荡的同步。在这里，我们展示了通过GABA能突触随机耦合的一群经过修改的θ神经元中异质性和噪声的不同影响。通过引入福克 - 普朗克方程和循环累积量，我们推导出了一组双累积量宏观方程。在分岔分析中，我们发现异质性具有稳定作用，而噪声具有非平凡的作用，导致振荡区域的促进、减弱和移动，并且在很大程度上取决于GABA能突触的反转电位。这些发现通过有限大小神经网络的数值模拟得到了验证。我们的结果表明，反转电位和随机波动幅度的微小变化可导致对γ振荡的即时控制，这将导致注意力选择和识别的复杂时空动态。
