Relationship between the mechanisms of gamma rhythm generation and the magnitude of the macroscopic phase response function in a population of excitatory and inhibitory modified quadratic integrate-and-fire neurons
Relationship between the mechanisms of gamma rhythm generation and the magnitude of the macroscopic phase response function in a population of excitatory and inhibitory modified quadratic integrate-and-fire neurons
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DOI：
10.1103/physreve.97.012209
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发表时间：
2018-01-16
影响因子：
2.4
通讯作者：
Kotani, Kiyoshi
中科院分区：
文献类型：
--
作者：
Akao, Akihiko;Ogawa, Yutaro;Kotani, Kiyoshi
伽马振荡被认为在大脑功能中发挥着重要作用。中间神经元伽马（ING）和锥体中间神经元伽马（PING）机制已被提议作为这些振荡的产生机制。然而，伽马振荡的产生机制和动力学特性之间的关系仍不清楚。在伽玛振荡的动态特性中，相位响应函数 (PRF) 很重要，因为它编码振荡对输入的响应。最近，通过应用于模型相关 Fokker-Planck 方程 (FPE) 的伴随方法计算了产生 ING 节律的修饰 θ 神经元抑制群的 PRF。修改后的 theta 模型结合了基于电导的突触以及电压和电流动态。在这里，我们通过使用修改的 theta 模型创建兴奋-抑制 (E-I) 网络来扩展之前的工作，并使用相应的 FPE 描述群体动态。我们对 FPE 进行了分叉分析，以找到产生伽马振荡的参数区域。为了通过振荡参数区域的生成机制来标记振荡参数区域，我们根据抑制群体的驱动因素以数学上合理的方式定义了 ING 和 PING 型伽玛振荡。我们通过这些生成机制标记了振荡参数区域，并通过 FPE 上的伴随方法导出 PRF，以研究每种振荡类型对输入的响应的差异。导出并比较了 PING 和 ING 机制的 PRF。我们发现 PING 情况下兴奋群体的 PRF 幅度大于 ING 情况。最后，修改后的 theta 神经元的 E-I 群体使我们能够分析 PING 型伽马振荡的 PRF 以及 E 和 I 群体的夹带能力。我们发现了一个参数区域，其中 E 和 I 的 PRF 在 PING 振荡的情况下均为纯正值。将由各自 PRF 控制的 E 和 I 刺激的不同夹带能力与有限模型神经元群的直接模拟进行比较。我们发现，通过刺激抑制性群体比通过刺激兴奋性群体更容易引入伽马节律，正如实验发现的那样。
Gamma oscillations are thought to play an important role in brain function. Interneuron gamma (ING) and pyramidal interneuron gamma (PING) mechanisms have been proposed as generation mechanisms for these oscillations. However, the relation between the generationmechanisms and the dynamical properties of the gamma oscillation are still unclear. Among the dynamical properties of the gamma oscillation, the phase response function (PRF) is important because it encodes the response of the oscillation to inputs. Recently, the PRF for an inhibitory population of modified theta neurons that generate an ING rhythm was computed by the adjoint method applied to the associated Fokker-Planck equation (FPE) for the model. The modified theta model incorporates conductancebased synapses as well as the voltage and current dynamics. Here, we extended this previous work by creating an excitatory-inhibitory (E-I) network using the modified theta model and described the population dynamics with the corresponding FPE. We conducted a bifurcation analysis of the FPE to find parameter regions which generate gamma oscillations. In order to label the oscillatory parameter regions by their generation mechanisms, we defined ING-and PING-type gamma oscillation in a mathematically plausible way based on the driver of the inhibitory population. We labeled the oscillatory parameter regions by these generation mechanisms and derived PRFs via the adjoint method on the FPE in order to investigate the differences in the responses of each type of oscillation to inputs. PRFs for PING and ING mechanisms are derived and compared. We found the amplitude of the PRF for the excitatory population is larger in the PING case than in the ING case. Finally, the E-I population of the modified theta neuron enabled us to analyze the PRFs of PING-type gamma oscillation and the entrainment ability of E and I populations. We found a parameter region in which PRFs of E and I are both purely positive in the case of PING oscillations. The different entrainment abilities of E and I stimulation as governed by the respective PRFs was compared to direct simulations of finite populations of model neurons. We find that it is easier to entrain the gamma rhythm by stimulating the inhibitory population than by stimulating the excitatory population as has been found experimentally.