Department of Mathematics, Tufts University, Medford, Massachusetts, United States of America.
PLoS Comput Biol. 2012 Feb;8(2):e1002362. doi: 10.1371/journal.pcbi.1002362. Epub 2012 Feb 9.
In networks of excitatory and inhibitory neurons with mutual synaptic coupling, specific drive to sub-ensembles of cells often leads to gamma-frequency (25-100 Hz) oscillations. When the number of driven cells is too small, however, the synaptic interactions may not be strong or homogeneous enough to support the mechanism underlying the rhythm. Using a combination of computational simulation and mathematical analysis, we study the breakdown of gamma rhythms as the driven ensembles become too small, or the synaptic interactions become too weak and heterogeneous. Heterogeneities in drives or synaptic strengths play an important role in the breakdown of the rhythms; nonetheless, we find that the analysis of homogeneous networks yields insight into the breakdown of rhythms in heterogeneous networks. In particular, if parameter values are such that in a homogeneous network, it takes several gamma cycles to converge to synchrony, then in a similar, but realistically heterogeneous network, synchrony breaks down altogether. This leads to the surprising conclusion that in a network with realistic heterogeneity, gamma rhythms based on the interaction of excitatory and inhibitory cell populations must arise either rapidly, or not at all. For given synaptic strengths and heterogeneities, there is a (soft) lower bound on the possible number of cells in an ensemble oscillating at gamma frequency, based simply on the requirement that synaptic interactions between the two cell populations be strong enough. This observation suggests explanations for recent experimental results concerning the modulation of gamma oscillations in macaque primary visual cortex by varying spatial stimulus size or attention level, and for our own experimental results, reported here, concerning the optogenetic modulation of gamma oscillations in kainate-activated hippocampal slices. We make specific predictions about the behavior of pyramidal cells and fast-spiking interneurons in these experiments.
在具有相互突触耦合的兴奋性和抑制性神经元网络中，特定的驱动亚细胞集通常会导致γ频率（25-100 Hz）振荡。然而，当被驱动的细胞数量太少时，突触相互作用可能不够强或不够均匀，无法支持产生节律的机制。我们使用计算模拟和数学分析的组合，研究了随着被驱动的集合变得太小，或者突触相互作用变得太弱和不均匀，γ节律的破坏。驱动或突触强度的异质性在节律的破坏中起着重要作用；尽管如此，我们发现对均匀网络的分析为不均匀网络中节律的破坏提供了一些见解。特别是，如果参数值使得在均匀网络中，需要几个γ周期才能达到同步，那么在类似但现实的不均匀网络中，同步会完全崩溃。这导致了一个令人惊讶的结论，即在具有现实异质性的网络中，基于兴奋性和抑制性细胞群体相互作用的γ节律必须要么快速产生，要么根本不产生。对于给定的突触强度和异质性，基于两个细胞群体之间的突触相互作用足够强的要求，在一个以γ频率振荡的集合中可能存在的细胞数量存在一个（软）下限。这一观察结果为最近关于猴初级视觉皮层中γ振荡通过改变空间刺激大小或注意力水平进行调制的实验结果以及我们这里报告的关于在海人酸激活的海马切片中光遗传调制γ振荡的实验结果提供了一些解释。我们对这些实验中锥体细胞和快速放电中间神经元的行为做出了具体的预测。
