Stochastic dynamics of neuronal populations with intrinsic and extrinsic noise

具有内在和外在噪声的神经元群体的随机动力学

• 批准号: 1120327
• 负责人: Paul Bressloff
• 金额: $ 35.1万
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-10-01 至 2016-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1120327&HistoricalAwards=false
• 关键词: Stochastic; dynamics; neuronal; populations; intrinsic

In biochemical and gene networks, there is an important distinction between intrinsic and extrinsic noise; extrinsic noise refers to external sources of randomness associated with environmental factors, whereas intrinsic noise refers to random fluctuations arising from the discrete and probabilistic nature of chemical reactions at the molecular level, which are particularly significant when the number of reacting molecules is small. The main goal of this research project is to develop a mathematical theory of intrinsic and extrinsic noise in neuronal population dynamics, adapting analytical methods from the study of chemical master equations such as Langevin approximations, stochastic hybrid systems, and large deviation theory. It is assumed that intrinsic noise at the network level arises from fluctuations about an asynchronous state due to finite size effects, whereas extrinsic noise arises from fluctuating external inputs. The theory is applied to a variety of neurobiological phenomena where noise is thought to play a crucial role, including the stimulus-induced synchronization of neural oscillators during sensory processing, and the generation of oscillations and waves during binocular rivalry. The latter forms the basis for non-invasive studies of human vision.Noise has recently emerged as a key component of many biological systems including the brain. Randomness arises at multiple levels of brain function, ranging from molecular processes such as gene expression and the opening of ion channel proteins to complex networks of brain cells (neurons) that generate behavior. Indeed, the presence of noise has direct behavioral consequences, from setting perceptual and decision thresholds to influencing movement precision. Noise also contributes to the generation of spontaneous activity patterns during resting brain states, which are thought to play an important role in cognition. From one perspective, neuroscientists are interested in how, in spite of significant levels of noise, the brain appears to function reliably, consistent with the idea that it has evolved under the constraints that are imposed by noise. From another perspective, neuroscientists are interested in situations where the presence of noise can either be harmful to or, in certain cases, actually enhance brain function. The main goal of this project is to use mathematical and computational modeling to develop our understanding of how noise that is present at the molecular and cellular levels affects dynamics and information processing at the network level, both in healthy and diseased brains. Numerous behaviors ranging from locomotion to cognitive tasks rely on oscillatory activity generated by networks of neurons in the brain. Despite the predominance and indispensability of brain oscillations, few theoretical tools are available for understanding how such oscillations are generated or controlled. A novel approach is used that combines biological experiments and mathematical analysis to break apart the complex interactions present in network components into simple building blocks. This allows core elements that are important in the generation of oscillations to be extracted and will clarify the role of other existing components in sculpting behavior using mathematical models. The models are tested through experiments that connect real time computer-simulated neurons to small oscillatory network in the crab central nervous systems. This project provides a framework for developing neural-based control systems with potential applications in robotics and bio-inspired computing.

在生化和基因网络中，内在噪声和外在噪声有重要的区别；外在噪声是指与环境因素相关的外部随机性来源，而内在噪声是指由于化学反应在分子水平上的离散性和概率性而产生的随机波动，当反应分子数量较少时，这种波动尤为显著。本研究项目的主要目标是发展神经元种群动力学中内在和外在噪声的数学理论，采用化学主方程研究的分析方法，如朗之万近似、随机混合系统和大偏差理论。假设网络级的固有噪声来自有限尺寸效应引起的异步状态波动，而外在噪声则来自波动的外部输入。该理论被应用于各种神经生物学现象，其中噪声被认为起着至关重要的作用，包括在感觉加工过程中刺激诱导的神经振荡器同步，以及在双目竞争过程中振荡和波的产生。后者构成了非侵入性人类视觉研究的基础。最近，噪音已成为包括大脑在内的许多生物系统的关键组成部分。随机性出现在大脑功能的多个层面，从基因表达和离子通道蛋白打开等分子过程到产生行为的复杂脑细胞（神经元）网络。事实上，噪音的存在有直接的行为后果，从设置感知和决策阈值到影响运动精度。噪音也有助于大脑静息状态下自发活动模式的产生，这被认为在认知中起着重要作用。从一个角度来看，神经科学家感兴趣的是，尽管有大量的噪音，大脑如何表现出可靠的功能，这与大脑在噪音施加的限制下进化的观点是一致的。从另一个角度来看，神经科学家感兴趣的是噪音的存在对大脑有害或在某些情况下实际上增强大脑功能的情况。该项目的主要目标是使用数学和计算建模来发展我们对存在于分子和细胞水平的噪声如何影响健康和患病大脑中网络水平的动态和信息处理的理解。从运动到认知任务的许多行为都依赖于大脑神经元网络产生的振荡活动。尽管大脑振荡占主导地位且不可或缺，但很少有理论工具可用于理解这种振荡是如何产生或控制的。采用一种新颖的方法，将生物实验和数学分析相结合，将网络组件中存在的复杂相互作用分解为简单的构建块。这允许提取在产生振荡中重要的核心元素，并将使用数学模型澄清其他现有组件在雕刻行为中的作用。通过实验将计算机模拟的实时神经元与螃蟹中枢神经系统的小振荡网络连接起来，对模型进行了测试。该项目为开发基于神经的控制系统提供了一个框架，该系统在机器人和生物启发计算方面具有潜在的应用。