Mechanisms of frequency preference in neurons and networks: biophysics and dynamics

神经系统中普遍存在特定频段的节律性振荡。它们来自参与神经元的合作活动和网络突触连接。了解神经元的内在生物物理特性如何与振荡输入电流和突触电导相互作用，对于理解在振荡神经元网络中选择首选频率的机制是至关重要的。共振是指神经元对振荡输入表现出较好的频率响应的能力。现有的关于谐振的数学研究主要集中在线性模型或基于电导的线性化模型上。用数值模拟研究了非线性效应。神经元模型中的共振的一般理论是缺乏的，也缺乏适当的数学工具来回答关键的生物物理和动力学问题。这个项目的目的是开发在神经元系统中产生优先频率响应的一般理论原理，其中包括非线性和时间尺度的多样性的影响，并以允许研究潜在机制的方式扩展现有的动力系统工具。该项目有三个具体目标：(I)确定在幅度和相位上产生对振荡输入的首选频率反应的神经元阈值下机制，(Ii)确定阈值下共振从阈值下传递到峰区的机制，以及(Iii)评估共振和突触电流如何相互作用以在神经元网络中产生对振荡输入的首选频率响应。此项目中的模型有两个级别的描述。生物物理模型被用来理解参与电流对网络动力学的影响，并做出可通过实验验证的预测。最小模型用于使用动态系统工具进行数学分析。将开发的数学工具将为研究具有更高描述水平的模型中的首选频率响应提供理论框架。在大脑的不同区域观察到了特定频段的节律性振荡，并与健康和疾病的认知和运动行为有关。网络振荡来自参与神经元的协作活动，但这些神经元如何相互作用以在大脑中产生连贯的活动才刚刚开始被理解。这个项目涉及神经元对振荡输入的反应，以及如何利用这些反应来理解神经元网络的动力学。作为测试案例，我们主要关注海马体和内嗅觉皮质的神经元。大脑这些区域的节律振荡与包括学习、记忆和导航在内的各种认知过程有关。这些区域的神经元网络也是癫痫和阿尔茨海默病等神经系统疾病的焦点。这个项目的目的是了解在神经元和神经元网络中产生对振荡输入的首选频率响应的生物物理和动力学机制，并开发适当的数学工具来回答关键的机械问题。这项工作将在与实验神经学家持续合作的背景下进行，旨在实现我们的建模和理论工作与各种合作者的实验努力之间的紧密结合，以便一方的发现将为另一方提供信息。参与该项目的学生将在NJIT/罗格斯大学校园内成熟的跨学科环境中接受数学和神经科学之间的接口培训，并将为加入数学和生物医学科学的科学工作组做好准备。

Rhythmic oscillations at characteristic frequency bands are ubiquitous in the nervous systems. They emerge from the cooperative activity of the participating neurons and network synaptic connectivity. Understanding how the intrinsic biophysical properties of neurons interact with oscillatory input currents and synaptic conductances is essential to understand the mechanisms by which preferred frequencies are selected in oscillatory neuronal networks. Resonance refers to the ability of a neuron to exhibit a preferred frequency response to oscillatory inputs. Existing mathematical studies on resonance have focused primarily on linear models or linearized conductance-based models. Nonlinear effects have been examined using numerical simulations. A general theory of resonance in neuronal models is lacking, as are appropriate mathematical tools to answer key biophysical and dynamic questions. The aim of this project is to develop general theoretical principles for the generation of preferred frequency responses in neuronal systems that incorporate the effects of nonlinearities and the diversity of time scales, and to expand existing dynamical systems tools in ways that allow for the investigation of the underlying mechanisms. This project has three specific aims: (i) to identify the neuronal subthreshold mechanisms of generation of preferred frequency responses in both amplitude and phase to oscillatory inputs, (ii) to identify the mechanisms by which subthreshold resonances are communicated from the subthreshold to the spiking regimes, and (iii) to evaluate how resonance and synaptic currents interact to generate preferred frequency responses to oscillatory inputs in networks of neurons. The models in this project have two levels of description. Biophysical models are used to understand the effect of the participating currents on the network dynamics and to make experimentally verifiable predictions. Minimal models are used for mathematical analysis using dynamical systems tools. The mathematical tools to be developed will provide a theoretical framework for the investigation of preferred frequency responses in models with higher levels of descriptions. Rhythmic oscillations at characteristic frequency bands have been observed in various areas of the brain and have been implicated in cognition and motor behavior in both health and disease. Network oscillations result from the cooperative activity of the participating neurons, but how these neurons interact to produce coherent activity in the brain is only beginning to be understood. This project deals with the responses of neurons to oscillatory inputs, and how these responses can be used to understand the dynamics of neuronal networks. As test cases, we focus primarily on neurons of the hippocampus and the entorhinal cortex. Rhythmic oscillations in these areas of the brain have been implicated in various cognitive processes including learning, memory and navigation. Neuronal networks in these areas are also the focus of diseases of the nervous systems such as epilepsy and Alzheimer's disease. The purpose of this project is to understand the biophysical and dynamic mechanisms that underlie the generation of preferred frequency responses to oscillatory inputs in neurons and neuronal networks, and to develop the appropriate mathematical tools to answer key mechanistic questions. This work will be carried out in the context of ongoing collaborations with experimental neuroscientists, and is designed to achieve a close integration between our modeling and theoretical efforts and the experimental efforts of various collaborators so that findings from one side will inform the other. Students participating in this project will be trained at the interface between Mathematics and Neuroscience in the well-established interdisciplinary environment at the NJIT/Rutgers campus, and will be prepared to join the scientific task force in the mathematical and biomedical sciences.