Collaborative Research: The Ever-Changing Network: How Changes in Architecture Shape Neural Computations

我们的大脑一直在变化。经历和记忆会在神经元之间的连接上留下印记。理解这个过程是理解大脑如何工作的基础。虽然这个问题几十年来一直是神经科学的核心问题，但目前研究人员已经做好了取得重大进展的准备——新的记录设备和成像技术正在以前所未有的规模和分辨率揭示大脑网络内的活动和变化。健全的数学模型对于跟上不断增加的数据雪崩至关重要。这个项目的目标是开发数学工具来帮助人们更好地理解神经元网络是如何被经验塑造的。发展这一理论对于理解学习以及相关障碍至关重要。该项目将重点研究学习如何提高大脑的决策能力和存储记忆的能力。参与该项目的研究生和博士后将成为建立的跨学科数学研究社区的一部分。学员将通过在三个机构的综合研究，包括广泛的访问，获得数学神经科学的广阔视野。该研究项目建立在该团队早期成果的基础上，旨在解决生物物理现实神经网络数学分析中的一个核心挑战：大脑活动如何随着时间的推移改变大脑结构。理解神经计算需要描述网络动力学如何与网络架构共同发展。研究小组将通过回答有关神经活动时空模式、网络架构变化以及由此产生的神经计算之间相互作用的具体问题来解决这一挑战。这个项目主要关注两个问题。首先，什么样的数学技术可以描述网络动力学和网络连接向稳定神经元集合的共同进化？为了解决这个问题，本项目将建立一个理论，描述全球网络结构如何在生物物理现实可塑性规则的动态下演变，这些规则在个体尖峰和突触的规模上运作。分析这些模型需要新的多尺度和平均方法。所得方程允许分析网络结构的稳定性及其对刺激驱动的依赖。有了这些结果，第二个问题就可以解决了：网络可塑性是如何创造时空动态来支持神经计算的基本构建模块的？理解可塑性如何形成网络的模型，其动态是对传入刺激的特定操作的基础，将被开发来解决这个问题。长期可塑性重塑网络连通性以编码精确时间序列的机制也将被研究。

Our brains are constantly changing. Experiences and memories leave their imprints on connections between neurons. Understanding this process is fundamental to understanding how the brain works. While this question has been of central importance to neuroscience for decades, at this moment researchers are well positioned to make significant progress -- new recording devices and imaging techniques are revealing the activity and changes within the networks of the brain at unprecedented scale and resolution. Sound mathematical models are essential to keep up with the mounting avalanche of data. The goal of this project is to develop mathematical tools to assist with improving understanding how networks of neurons are shaped by experiences. Developing this theory is crucial for understanding learning, as well as associated disorders. The project will focus on how learning improves the brain's ability to make decisions and store memories. Graduate students and postdocs joining this project will be part of an established, interdisciplinary mathematics research community. Trainees will gain a wide perspective of mathematical neuroscience through integrated research at three institutions, including extensive visits among them. This research project builds on earlier results of this team to address a central challenge in the mathematical analysis of biophysically realistic neuronal networks: How brain activity changes brain structure over time. Understanding neural computation demands a description of how network dynamics co-evolves with network architecture. The research team will address this challenge by answering specific questions about the interplay between spatiotemporal patterns of neural activity, the attendant changes in network architectures, and the resulting neural computations. This project focuses on two main questions. First, what mathematical techniques can describe the co-evolution of network dynamics and network connectivity toward stable assemblies of neurons? To address this question this project will build a theory describing how global network structure evolves under the dynamics of biophysically realistic plasticity rules that operate on the scale of individual spikes and synapses. Analysis of these models requires novel multiscale and averaging methods. The resulting equations allow analysis of the stability of network architectures and their dependence on stimulus drive. With these results, the second question can be addressed: How does network plasticity create spatiotemporal dynamics that support the basic building blocks of neural computation? Models to understand how plasticity forms networks whose dynamics underlie specific operations on incoming stimuli will be developed to address this question. The mechanism by which long-term plasticity can reshape the connectivity of a network to encode a precise temporal sequence of events will also be investigated.