Network of Neuronal Oscillators

研究人员特曼9802339和他的同事们开发了数学工具，用于分析神经元网络生物物理模型的种群节律。这些模型展示了丰富的振荡行为结构。即使是单个细胞的动力学也可能是相当复杂的；例如，它可能会激发周期性的尖峰或动作电位的爆发，随后是近乎静止的静默阶段。群体节奏的例子包括同步行为和集群，在同步行为中，网络中的每个细胞同时激发，在集群中，整个细胞群体分解成组；单个组中的细胞同步激发，不同的组彼此不同步。活动可以通过网络以波浪式的方式传播。一个网络的种群节奏是由三个独立成分之间的相互作用产生的：神经元的内在属性，神经元之间耦合的突触属性，以及耦合的体系结构。这些组件中的每一个可以包括许多参数和多个时间尺度。研究人员开发的数学技术可以帮助确定这些组件中的每个组件在形成紧急网络行为中所起的作用。这可能导致对给定网络可能出现的节律进行分类，并有助于确定模型必须有多复杂才能显示某些观察到的动态。研究人员研究的节律类型在整个中枢神经系统中出现。例如，考虑丘脑网络：它们与睡眠节律、某些形式的癫痫和帕金森震颤的产生有关。研究人员研究了同一组神经元如何表现出在不同睡眠阶段发生的非常不同的节奏，以及在从一个睡眠阶段过渡到另一个阶段期间，网络必须发生什么变化。最近的实验表明，正常动物和帕金森病动物的基底节神经元呈现出截然不同的种群节律。研究人员开发和分析这些网络的生物物理模型，以确定导致这些节律产生的因素。

Terman 9802339 The investigator and his colleagues develop mathematical tools for analyzing the population rhythms of biophysical models for neuronal networks. These models exhibit a rich structure of oscillatory behavior. The dynamics of even a single cell can be quite complicated; it may, for example, fire either periodic spikes or bursts of action potentials that are followed by a silent phase of near quiescent behavior. Examples of population rhythms include synchronous behavior, in which every cell in the network fires at the same time, and clustering, in which the entire population of cells breaks up into groups; cells within a single group fire synchronously and different groups are desynchronized from each other. Activity may propagate through the network in a wave-like manner. A network's population rhythm results from interactions between three separate components: the intrinsic properties of neurons, the synaptic properties of coupling between neurons, and the architecture of coupling. Each of these components may include numerous parameters and multiple time scales. The mathematical techniques that are developed by the investigator can help determine the role each of these components plays in shaping the emergent network behavior. This may lead to a classification of the possible rhythms that can emerge from a given network and help determine how complicated a model must be in order to display some observed dynamics. The types of rhythms that the investigator studies arise throughout the central nervous system. Consider, for example, thalamic networks: these have been implicated in the generation of sleep rhythms, certain forms of epilepsy, and Parkinson tremor. The investigator studies how the same set of neurons can exhibit the very different rhythms that take place during different stages of sleep and what changes must occur in the networks during the transition from one stage of sleep to another. Recent experiments have demons trated that neurons in the basal ganglia exhibit quite different population rhythms in normal and parkinsonian animals. The investigator develops and analyzes biophysical models for these networks in order to determine factors responsible for the generation of these rhythms.