Neural Oscillations and Waves Induced by Local Network Inhomogeneities

理论神经生物学中的一个重要挑战是理解大脑中空间结构化活动状态与支持它们的底层神经回路之间的关系。这导致了相当大的兴趣，在分析减少生物模型的神经网络。这些网络模型的大多数分析研究假设系统是空间均匀的。然而，最近，主要研究者已经表明，空间局部化的非均匀输入和神经元之间的经常性突触相互作用的组合效应可以导致非平凡形式的相干振荡和波。这激发了目前的研究项目，该项目将对这些振荡和波的产生背后的细胞和网络机制进行更详细的研究。该研究计划将分为三个部分，对应于三个不同的神经生物学应用领域：（I）癫痫样活动的模型中的去抑制神经组织，（II）刺激诱导的相干振荡的模型中的初级视觉皮层，和（III）本地化的活动状态，在一个双层丘脑网络模型的头部方向系统。在每一种情况下，将分析相干活动状态的存在和稳定性，并确定它们对各种生物相关参数的依赖性。数学方面的工作也将适用于其他人口为基础的生物系统，其中的基本要素在分子，细胞或有机体水平上相互作用nonlocally在space.Analysis的动力学机制的基础上的空间结构的活动状态在神经组织是至关重要的了解范围广泛的神经生物学现象，自然发生的和病理。例如，癫痫和偏头痛等神经系统疾病的特征在于波在大脑表面传播。确定这些疾病发病背后的各种细胞和网络特性最终可能有助于开发消除它们的临床技术。空间相干活动状态在大脑的正常健康功能期间也很普遍，编码视觉和听觉刺激的局部特性，编码头部方向和空间位置，并在短期工作记忆中保持持续的活动状态。

One of the important challenges in theoretical neurobiology is understanding the relationship between spatially structured activity states in the brain and the underlying neural circuitry that supports them. This has led to considerable interest in analyzing reduced biological models of neuronal networks. Most analytical studies of these network models assume that the system is spatially homogeneous. Recently, however, the principal investigator has shown that the combined effect of a spatially localized inhomogeneous input and recurrent synaptic interactions between neurons can result in nontrivial forms of coherent oscillations and waves. This motivates the current research project, which will carry out a more detailed study of the cellular and network mechanisms underlying the generation of these oscillations and waves. The research program will be divided into three parts corresponding to three distinct neurobiological application areas: (I) epileptiform activity in a model of disinhibited neural tissue, (II) stimulus-induced coherent oscillations in a model of primary visual cortex, and (III) localized activity states in a two-layer thalamic network model of the head direction system. In each of these cases the existence and stability of coherent activity states will be analyzed, and their dependence on various biologically relevant parameters will be determined. The mathematical aspects of the work will also be applicable to other population-based biological systems, in which the basic elements at the molecular, cellular or organismal level interact nonlocally in space.Analysis of the dynamical mechanisms underlying spatially structured activity states in neural tissue is crucially important for understanding a wide range of neurobiological phenomena, both naturally occurring and pathological. For example, neurological disorders such as epilepsy and migraine are characterized by waves propagating across the surface of the brain. Determining the various cellular and network properties underlying the onset of such disorders could ultimately help in developing clinical techniques for eliminating them. Spatially coherent activity states are also prevalent during the normal healthy functioning of the brain, encoding local properties of visual and auditory stimuli, encoding head direction and spatial location, and maintaining persistent activity states in short-term working memory.