Firing rate equations require a spike synchrony mechanism to correctly describe fast oscillations in inhibitory networks.
Firing rate equations require a spike synchrony mechanism to correctly describe fast oscillations in inhibitory networks.
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DOI：
10.1371/journal.pcbi.1005881
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发表时间：
2017-12
影响因子：
4.3
通讯作者：
Montbrió E
中科院分区：
文献类型：
--
作者：
Devalle F;Roxin A;Montbrió E
抑制性神经元的递归耦合网络在伽马波段中鲁棒地产生振荡。尽管如此，相应的威尔逊-考恩型点火速率方程，这样的抑制人口不产生这样的振荡，没有明确的时间延迟。我们发现，这种差异是由于电压依赖性的尖峰同步机制固有的网络尖峰神经元，这是不是由标准的放电率方程捕获。在这里，我们研究了一个精确的低维描述异构规范1类抑制性神经元网络，其中包括产生同步状态的关键阈值下的动态。在慢突触动力学的限制下，只要外部输入也很慢，尖峰同步机制就被抑制，标准的Wilson-Cowan方程就被正式恢复。然而，即使在这个限制同步尖峰可以引起的输入波动的时间尺度上的膜的时间常数的神经元。因此，我们的平均场方程是标准的Wilson-Cowan方程的扩展，其中尖峰同步也被正确地描述。描述大型神经元系综平均活动的群体模型是研究大型神经元系统协同功能原理的有力数学工具。然而，这些模型没有正确地描述神经元网络中的尖峰同步现象。特别是，它们未能捕捉到抑制性神经元网络中同步振荡的开始。我们发现，这种限制是由于电压依赖的同步机制，这是自然存在于尖峰神经元模型，但没有捕获传统的放电率方程。在这里，我们研究了一组新的宏观方程，其中包括发射率和膜电位动态，并正确地产生快速抑制为基础的同步振荡。在慢突触处理振荡的限制被抑制，和模型减少到一个方程形式上等价于威尔逊-考恩模型。
Recurrently coupled networks of inhibitory neurons robustly generate oscillations in the gamma band. Nonetheless, the corresponding Wilson-Cowan type firing rate equation for such an inhibitory population does not generate such oscillations without an explicit time delay. We show that this discrepancy is due to a voltage-dependent spike-synchronization mechanism inherent in networks of spiking neurons which is not captured by standard firing rate equations. Here we investigate an exact low-dimensional description for a network of heterogeneous canonical Class 1 inhibitory neurons which includes the sub-threshold dynamics crucial for generating synchronous states. In the limit of slow synaptic kinetics the spike-synchrony mechanism is suppressed and the standard Wilson-Cowan equations are formally recovered as long as external inputs are also slow. However, even in this limit synchronous spiking can be elicited by inputs which fluctuate on a time-scale of the membrane time-constant of the neurons. Our meanfield equations therefore represent an extension of the standard Wilson-Cowan equations in which spike synchrony is also correctly described. Population models describing the average activity of large neuronal ensembles are a powerful mathematical tool to investigate the principles underlying cooperative function of large neuronal systems. However, these models do not properly describe the phenomenon of spike synchrony in networks of neurons. In particular, they fail to capture the onset of synchronous oscillations in networks of inhibitory neurons. We show that this limitation is due to a voltage-dependent synchronization mechanism which is naturally present in spiking neuron models but not captured by traditional firing rate equations. Here we investigate a novel set of macroscopic equations which incorporate both firing rate and membrane potential dynamics, and that correctly generate fast inhibition-based synchronous oscillations. In the limit of slow-synaptic processing oscillations are suppressed, and the model reduces to an equation formally equivalent to the Wilson-Cowan model.
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影响因子：
2.9
作者：
Ermentrout, B
通讯作者：
Ermentrout, B
DOI：
10.1098/rstb.2000.0769
发表时间：
2001-03-29
影响因子：
6.3
作者：
Bressloff, PC;Cowan, JD;Wiener, MC
通讯作者：
Wiener, MC
影响因子：
2.9
作者：
Hansel, D;Mato, G
通讯作者：
Mato, G
影响因子：
2.9
作者：
ERMENTROUT, B
通讯作者：
ERMENTROUT, B
影响因子：
2.9
作者：
Chandra, Sarthak;Hathcock, David;Ott, Edward
通讯作者：
Ott, Edward