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

在特征频带的节律振荡在神经系统中是普遍存在的。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，对于了解振荡神经元网络中选择首选频率的机制至关重要。共振是指神经元对振荡输入表现出优选频率响应的能力。现有的谐振数学研究主要集中在线性模型或线性化的电导模型。非线性效应已被检查使用数值模拟。神经元模型中的共振的一般理论是缺乏的，因为是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一般的理论原则，用于生成首选的频率响应的神经元系统，将非线性和时间尺度的多样性的影响，并扩大现有的动力系统工具的方式，允许调查的基本机制。该项目有三个具体目标：（i）识别产生对振荡输入的振幅和相位的优选频率响应的神经元亚阈值机制，（ii）识别亚阈值共振从亚阈值传递到尖峰机制的机制，以及（iii）评估共振和突触电流如何相互作用以产生对神经元网络中的振荡输入的优选频率响应。本项目中的模型有两个描述级别。生物物理模型被用来理解参与电流对网络动态的影响，并进行实验验证的预测。最小模型用于使用动态系统工具的数学分析。要开发的数学工具将提供一个理论框架的调查首选的频率响应模型与更高层次的描述。在大脑的各个区域都观察到了特征频带的节律振荡，并且与健康和疾病中的认知和运动行为有关。网络振荡是由参与的神经元的合作活动引起的，但是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，我们主要关注海马和内嗅皮层的神经元。大脑这些区域的节律振荡与各种认知过程有关，包括学习、记忆和导航。这些区域的神经元网络也是神经系统疾病的焦点，如癫痫和阿尔茨海默病。该项目的目的是了解生物物理和动力学机制，这些机制是神经元和神经元网络对振荡输入产生首选频率响应的基础，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科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工作之间的紧密结合，以便一方的发现将告知另一方。参加该项目的学生将在NJIT/Rutgers校园完善的跨学科环境中接受数学和神经科学之间的接口培训，并准备加入数学和生物医学科学的科学工作队。

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.