Matveev Victor, Bose Amitabha, Nadim Farzan
Department of Mathematical Sciences, New Jersey Institute of Technology, Cullimore Hall, University Heights, Newark, NJ 07102-1982, USA
J Comput Neurosci. 2007 Oct;23(2):169-87. doi: 10.1007/s10827-007-0026-x. Epub 2007 Apr 18.
Out-of-phase bursting is a functionally important behavior displayed by central pattern generators and other neural circuits. Understanding this complex activity requires the knowledge of the interplay between the intrinsic cell properties and the properties of synaptic coupling between the cells. Here we describe a simple method that allows us to investigate the existence and stability of anti-phase bursting solutions in a network of two spiking neurons, each possessing a T-type calcium current and coupled by reciprocal inhibition. We derive a one-dimensional map which fully characterizes the genesis and regulation of anti-phase bursting arising from the interaction of the T-current properties with the properties of synaptic inhibition. This map is the burst length return map formed as the composition of two distinct one-dimensional maps that are each regulated by a different set of model parameters. Although each map is constructed using the properties of a single isolated model neuron, the composition of the two maps accurately captures the behavior of the full network. We analyze the parameter sensitivity of these maps to determine the influence of both the intrinsic cell properties and the synaptic properties on the burst length, and to find the conditions under which multistability of several bursting solutions is achieved. Although the derivation of the map relies on a number of simplifying assumptions, we discuss how the principle features of this dimensional reduction method could be extended to more realistic model networks.
异相爆发是中枢模式发生器和其他神经回路所表现出的一种功能上重要的行为。理解这种复杂的活动需要了解细胞内在特性与细胞间突触耦合特性之间的相互作用。在这里，我们描述了一种简单的方法，该方法使我们能够研究由两个发放脉冲的神经元组成的网络中反相爆发解的存在性和稳定性，每个神经元都具有T型钙电流并通过相互抑制进行耦合。我们推导了一个一维映射，它全面地描述了由T电流特性与突触抑制特性相互作用产生的反相爆发的产生和调节。这个映射是爆发长度返回映射，它由两个不同的一维映射组成，每个一维映射由不同的一组模型参数调节。虽然每个映射都是使用单个孤立模型神经元的特性构建的，但这两个映射的组合准确地捕捉了整个网络的行为。我们分析这些映射的参数敏感性，以确定细胞内在特性和突触特性对爆发长度的影响，并找到实现几种爆发解多重稳定性的条件。尽管映射的推导依赖于一些简化假设，但我们讨论了这种降维方法的主要特征如何能够扩展到更现实的模型网络。
