Neuronal Dynamics

拟议研究的主要目标是开发数学工具，用于分析生物物理学中的活动模式，基于电导的模型，用于广泛的神经元系统。具体问题的动机模型的活动模式在三个系统。 第一个模型出现在对基底神经节的研究中，基底神经节是大脑的一部分，在运动的产生中起着重要作用。 基底神经节功能障碍与运动障碍如帕金森病和亨廷顿舞蹈病有关。 实验已经证明，基底神经节内的神经元显示出各种动态行为;此外，正常和病理状态之间的活动模式不同。 首席研究员正在开发数学方法来分析这些放电模式的起源和机制。 主要研究者还将考虑昆虫触角叶的模型。 这些神经元表现出复杂的振荡动力学响应气味，然而，单细胞和人口的节奏的机制还没有完全理解。 首席研究员将开发数学模型，以探索昆虫触角叶中气味表征的机制及其学习的修改。 最后，主要研究者正在考虑呼吸节律生成的模型。 哺乳动物的呼吸运动是由下脑干中的神经元网络产生的，这些神经元网络产生神经活动的节律振荡。这个网络的一个有趣的特征是细胞之间明显的高度异质性。 主要研究人员将开发分析工具，以了解异质细胞网络如何表现出同步活动，以及如何随着模型中参数的变化而失去同步。振荡和其他形式的神经元活动出现在整个中枢神经系统。 这些振荡与睡眠节律、癫痫、帕金森氏震颤、感觉处理和学习的产生有关。 振荡行为也出现在呼吸、运动和分泌等生理过程中。 相关神经元网络的模型通常表现出丰富的动态行为结构。 种群节律的例子包括同步振荡、传播波和混沌动力学。 计算模型和数学分析在理解这种复杂动态的机制和预测动态如何随参数变化方面非常有用。 在这个项目中要研究的具体神经元系统包括基底神经节，参与帕金森氏症节律产生的大脑的一部分，昆虫触角叶和前Botzinger复合体，被认为是呼吸节律产生的起源的脑核。

A primary goal of the proposed research is to develop mathematical tools for analyzing activity patterns in biophysical, conductance-based models for a broad class of neuronal systems. Specific issues are motivated by models for activity patterns in three systems. The first model arises in the study of the basal ganglia, a part of the brain that plays an important role in the generation of movements. Dysfunction of the basal ganglia is associated with movement disorders such as Parkinson's disease and Huntington's chorea. Experiments have demonstrated that neurons within the basal ganglia display a variety of dynamic behaviors; moreover, patterns of activity differ between normal and pathological states. The principal investigator is developing mathematical methods for analyzing the origins and mechanisms underlying these firing patterns. The principal investigator will also consider models of the insect antennal lobe. These neurons exhibit complex oscillatory dynamics in response to odors; however, the mechanisms underlying both single-cell and population rhythms are not fully understood. The principal investigator will develop mathematical models to explore mechanisms underlying odor representations in the insect antennal lobe and their modification with learning. Finally, the principal investigator is considering models of respiratory rhythm generation. Breathing movements in mammals are generated by networks of neurons in the lower brain stem that produce rhythmic oscillations of neural activity. One interesting feature of this network is the apparent high degree of heterogeneity among cells. The principal investigator will develop analytic tools to understand how a network of heterogeneous cells can exhibit synchronized activity and how synchronization is lost as parameters in the model are varied. Oscillations and other patterns of neuronal activity arise throughout the central nervous system. These oscillations have been implicated in the generation of sleep rhythms, epilepsy, parkinsonian tremor, sensory processing, and learning. Oscillatory behavior also arises in such physiological processes as respiration, movement, and secretion. Models for the relevant neuronal networks often exhibit a rich structure of dynamic behavior. Examples of population rhythms include synchronized oscillations, propagating waves and chaotic dynamics. Computational models and mathematical analysis can be extremely useful in understanding the mechanisms underlying this complex dynamics and predicting how the dynamics may change with respect to parameters. Specific neuronal systems to be studied in this project include the basal ganglia, a part of the brain implicated in the generation of Parkinsonian rhythms, the insect antennal lobe and the pre-Botzinger complex, a brain nuclei believed to be the origin of respiratory rhythm generation.