Collaborative Research: Emergent Sequences in Inhibition-Dominated Recurrent Networks

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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.