Network of Neuronal Oscillators

研究者和他的同事们开发了数学工具来分析神经网络生物物理模型的种群节律。这些模型表现出丰富的振荡行为结构。即使是单个细胞的动力学也可能相当复杂；例如，它可以触发周期性的尖峰或动作电位的爆发，然后是一个接近静止行为的沉默阶段。群体节律的例子包括同步行为，即网络中的每个细胞同时放电，以及集群行为，即整个细胞群体分解成组；单个组内的细胞同步发射，不同组之间相互不同步。活动可能以波状的方式在网络中传播。网络的种群节律是由三个独立组件之间的相互作用产生的：神经元的内在特性，神经元之间耦合的突触特性，以及耦合的结构。这些组件中的每一个都可能包括许多参数和多个时间尺度。研究者开发的数学技术可以帮助确定这些组成部分在形成突发网络行为中的作用。这可能会导致对给定网络中可能出现的节律进行分类，并有助于确定为了显示某些观察到的动态，模型必须有多复杂。研究者研究的节律类型贯穿于整个中枢神经系统。以丘脑网络为例：这些网络与睡眠节律、某些形式的癫痫和帕金森震颤的产生有关。研究者研究了同一组神经元如何在不同的睡眠阶段表现出截然不同的节律，以及在从一个睡眠阶段过渡到另一个睡眠阶段时，神经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神经节神经元表现出截然不同的种群节律。研究者开发并分析了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.