Mathematical Analysis of Networks of Neurons with Multiple Time Scales

科佩尔9706694研究员和她的同事们研究神经元网络的动力学，特别是其输出是有节奏的网络。这项研究使用动力学系统的方法来了解细胞水平上的属性(固有的膜动力学)和细胞之间的相互连接(突触属性)如何影响网络行为。本研究主要围绕两类问题展开。第一个问题涉及网络同步或部分同步的机制。这些问题主要涉及大脑皮层网络，其中有大量相似的细胞。另一类主要由较小的无脊椎动物网络推动，涉及网络频率和网络中细胞之间的相对相位的确定和调节。在这两类问题中，这项工作都是由特定的神经元网络推动的，但技术足够广泛，可以在激励例子之外对结果进行推广。将要使用和开发的动力系统方法利用了与细胞的内在和突触动力学过程相关的许多不同的时间尺度。一个目标是了解网络行为是如何通过改变参数来调节的，这些参数改变了动态过程的哪个子集在产生网络输出中最重要。在控制运动控制、感觉处理以及睡眠和清醒状态的神经系统中，都发现了产生节律输出的神经元网络。神经系统的节律性活动也可以在病理状态下看到，比如癫痫和帕金森氏症。尽管有很多关于参与细胞的生理学的详细信息，但人们还不知道如何利用动态复杂的组件来构建网络来执行其适当的任务。本研究旨在确定节奏网络输出的一致性、频率和相位关系的调节机制。这种识别可能会让科学家更深入地了解神经系统如何使用节奏来产生适当的行为，以及移除产生病理状态(包括震颤)的节奏活动的技术。

Kopell 9706694 The investigator and her colleagues study the dynamics of networks of neurons, especially networks whose output is rhythmic. The research uses methods of dynamical systems to understand how properties at the cellular level (intrinsic membrane dynamics) and the interconnections among the cells (synaptic properties) affect the network behavior. The research focuses on two kinds of problems. The first concerns the mechanisms by which networks synchronize or partially synchronize. These problems mainly concern cortical networks in which there are large numbers of similar cells. The other class, motivated mainly by smaller invertebrate networks, is concerned with the determination and regulation of network frequency and relative phases among cells in the network. In both classes of problems, the work is motivated by specific networks of neurons, but the techniques are broad enough to allow generalization of the results beyond the motivating examples. The dynamical systems methods to be used and developed exploit the many different times scales associated with the intrinsic and synaptic dynamical processes of the cells. One goal is to understand how network behavior is modulated by changing parameters that alter which subset of dynamical processes is most important in producing the network output. Networks of neurons producing rhythmic output are found in neural systems governing motor control, sensory processing, and in both sleeping and awake states. Rhythmic activity in the nervous system is also seen in pathological states, such as epilepsy and Parkinson's disease. Though there is much detailed information about the physiology of participating cells, it is not understood how networks that make use of dynamically complicated components are constructed to carry out their appropriate tasks. This research aims to identify mechanisms by which coherence, frequency and phase relationships of the rhythmic network output are regulated. Such identification can potentially allow scientists a deeper understanding of how the nervous sytem uses rhythms to produce appropriate behavior, as well as techniques for removing rhythmic activity that produces pathological states, including tremor.