Stochastic dynamics of neuronal populations with intrinsic and extrinsic noise

在生物化学和基因网络中，内在噪声和外在噪声之间有一个重要的区别;外在噪声是指与环境因素相关的外部随机性来源，而内在噪声是指分子水平上化学反应的离散性和概率性所产生的随机波动，当反应分子的数量很小时特别重要。本研究项目的主要目标是开发神经元群体动力学中内在和外在噪声的数学理论，适应化学主方程研究的分析方法，如Langevin近似，随机混合系统和大偏差理论。 它是假设在网络级的固有噪声引起的波动有关的异步状态，由于有限的尺寸效应，而外在的噪声引起波动的外部输入。 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，包括刺激诱导的神经振荡器在感觉处理过程中的同步，以及在双眼竞争过程中产生的振荡和波。后者构成了对人类视觉的非侵入性研究的基础。噪声最近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质开放等分子过程到产生行为的脑细胞（神经元）的复杂网络。事实上，噪声的存在具有直接的行为后果，从设置感知和决策阈值到影响运动精度。 噪声还有助于在静息脑状态下产生自发活动模式，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，尽管噪音水平很高，但大脑似乎仍能可靠地发挥作用，这与大脑在噪音限制下进化的观点一致。 从另一个角度来看，神经科学家感兴趣的情况下，噪音的存在可能是有害的，或者在某些情况下，实际上增强了大脑功能。 该项目的主要目标是使用数学和计算建模来发展我们对分子和细胞水平上存在的噪声如何影响健康和患病大脑中网络水平上的动力学和信息处理的理解。 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。 尽管脑振荡的优势和不可或缺，但很少有理论工具可以用来理解这种振荡是如何产生或控制的。 使用一种新的方法，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模块。 这允许提取在产生振荡中重要的核心元素，并将使用数学模型阐明其他现有组件在雕刻行为中的作用。 将计算机模拟的真实的时间神经元与蟹中枢神经系统的振荡网络相连接，对模型进行了验证。 该项目提供了一个框架，开发基于神经的控制系统，在机器人和生物启发计算的潜在应用。

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.