Collaborative Research: Emergent Sequences in Inhibition-Dominated Recurrent Networks

神经活动序列出现在许多大脑区域，包括皮层、海马体和中枢模式产生电路，它们是运动等有节奏行为的基础。此外，当动物在休息或睡眠时，海马体中发生的序列被认为对记忆的处理和巩固至关重要。这些序列是内部生成活动的例子：也就是说，神经活动主要是由神经元之间循环连接的结构形成的。本研究的目的是推进序列生成的数学理论。一个基本的问题是什么类型的网络架构是紧急序列的基础。这项工作将研究具有复杂连接模式和抑制主导动态的循环连接网络中的序列生成机制。然后，该理论将被用于理解和模拟神经序列，重点是海马序列。虽然这项工作是由神经科学推动的，但从单位之间的竞争中出现的顺序活动现象是非常普遍的，因此这里得出的数学结果可能在生物和社会科学的各种更广泛的背景下有用。本研究的主要目标是理解并能够从连接的底层结构中预测循环网络中的神经活动序列集。除了提供关于大脑序列生成的新见解外，本研究还将阐明循环网络中的结构-功能关系，并为分析网络以识别动态相关基序提供工具。本研究将在一个特殊的抑制主导阈值线性网络家族的背景下进行，这是一种常用的循环网络动力学的放电率模型。这些网络自然会产生大量的序列，并且动态与底层连接图紧密相连。此外，它们在数学上易于处理，因此符合序列生成的数学理论。项目1侧重于从方向图构建的网络体系结构，这是一种新型的图，展示了方向动态，而不一定具有前馈体系结构，从而提供了对同步链的重要推广。项目2涉及序列的解剖及其分解为“核心”和“外围”组件，核心是支持顺序吸引子的网络基序，外围由吸引子招募的额外神经元组成。最后，项目3使用在早期项目中发展的理论来分析和模拟在海马序列中观察到的各种现象。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Sequences of neural activity arise in many brain areas, including cortex, hippocampus, and central pattern generator circuits that underlie rhythmic behaviors like locomotion. Moreover, sequences that occur in hippocampus while the animal is at rest or asleep are believed to be critical for memory processing and consolidation. These sequences are examples of internally generated activity: that is, neural activity that is shaped primarily by the structure of recurrent connections between neurons. The goal of this research is to advance the mathematical theory of sequence generation. A fundamental question is what types of network architectures underlie emergent sequences. This work will investigate the mechanisms for sequence generation in recurrently connected networks with complex patterns of connectivity and inhibition-dominated dynamics. The theory will then be used to understand and model neural sequences, with a focus on hippocampal sequences. Although this work is motivated by neuroscience, the phenomenon of sequential activity emerging from competition between units is sufficiently common that the mathematical results derived here are likely to be useful in a variety of broader contexts in the biological and social sciences.The main goal of this research is to understand, and be able to predict, the set of neural activity sequences in a recurrent network from the underlying structure of connectivity. In addition to providing new insights about sequence generation in the brain, this study will elucidate structure-function relationships in recurrent networks and provide tools for analyzing networks to identify dynamically relevant motifs. This research will be carried out in the context of a special family of inhibition-dominated threshold-linear networks, which are a commonly used firing rate model of recurrent network dynamics. These networks naturally give rise to an abundance of sequences, and the dynamics are tightly connected to the underlying connectivity graph. Moreover, they are mathematically tractable and thus amenable to a mathematical theory of sequence generation. Project 1 focuses on network architectures built from directional graphs, a new type of graph exhibiting directional dynamics without necessarily having a feedforward architecture, thus providing an important generalization of synfire chains. Project 2 addresses the anatomy of a sequence and its decomposition into “core” and “peripheral” components, with the core being a network motif that supports a sequential attractor, and the periphery consisting of additional neurons that are recruited by the attractor. Finally, Project 3 uses the theory developed in earlier projects to analyze and model various phenomena observed in hippocampal sequences.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.