Best Janet, Park Choongseok, Terman David, Wilson Charles
Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA.
J Comput Neurosci. 2007 Oct;23(2):217-35. doi: 10.1007/s10827-007-0029-7. Epub 2007 May 16.
Changes in firing patterns are an important hallmark of the functional status of neuronal networks. We apply dynamical systems methods to understand transitions between irregular and rhythmic firing in an excitatory-inhibitory neuronal network model. Using the geometric theory of singular perturbations, we systematically reduce the full model to a simpler set of equations, one that can be studied analytically. The analytic tools are used to understand how an excitatory-inhibitory network with a fixed architecture can generate both activity patterns for possibly different values of the intrinsic and synaptic parameters. These results are applied to a recently developed model for the subthalamopallidal network of the basal ganglia. The results suggest that an increase in correlated activity, corresponding to a pathological state, may be due to an increased level of inhibition from the striatum to the inhibitory GPe cells along with an increased ability of the excitatory STN neurons to generate rebound bursts.
放电模式的变化是神经网络功能状态的一个重要标志。我们应用动力系统方法来理解兴奋性 - 抑制性神经网络模型中不规则放电和节律性放电之间的转变。利用奇异摄动的几何理论，我们系统地将完整模型简化为一组更简单的方程，一组可以进行解析研究的方程。这些解析工具用于理解具有固定结构的兴奋性 - 抑制性网络如何能够为内在和突触参数的可能不同值生成两种活动模式。这些结果被应用于最近开发的基底神经节丘脑底核 - 苍白球网络模型。结果表明，与病理状态相对应的相关活动增加可能是由于从纹状体到抑制性苍白球外部（GPe）细胞的抑制水平增加，以及兴奋性丘脑底核（STN）神经元产生反弹爆发的能力增强。
