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活动状态与支持它们的潜在神经回路之间的关系。这使得人们对分析神经网络的简化生物模型产生了相当大的兴趣。这些网络模型的大多数分析研究都假定系统在空间上是同质的。然而，最近，主要研究人员已经证明，空间局部化的非均匀输入和神经元之间反复的突触相互作用的综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动产生的细胞和网络机制进行更详细的研究。研究计划将分为三个部分，分别对应于三个不同的神经生物学应用领域：(I)失禁神经组织模型中的癫痫样活动，(Ii)初级视觉皮质模型中刺激诱导的相干振荡，以及(Iii)头部方向系统的两层丘脑网络模型中的局部活动状态。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学相关参数的依赖性。这项工作的数学方面也将适用于其他基于种群的生物系统，其中分子、细胞或生物水平上的基本元素在空间上非局部地相互作用。分析神经组织空间结构活动状态背后的动力学机制对于理解广泛的神经生物学现象至关重要，无论是自然发生的还是病理的。例如，癫痫和偏头痛等神经疾病的特征是电波在大脑表面传播。确定这类疾病发生的各种细胞和网络特性最终可能有助于开发消除这些疾病的临床技术。空间连贯的活动状态也普遍存在于大脑正常的健康功能中，编码视觉和听觉刺激的局部属性，编码头部方向和空间位置，并在短期工作记忆中维持持续的活动状态。

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.