A common structure in recurrent networks supports neural sequence generation locally and in downstream neurons

Neural sequences, characterized by neurons or groups of neurons that fire one after the other, have been observed in multiple brain regions, across species, and are known to underlie a diversity of brain functions. To flexibly support behaviour and cognition, neural sequences exhibit much variability in properties like their temporal width, baseline, and peak firing rate. Despite this variability and the central role that sequences play in supporting brain function, a framework that explains how flexible sequences are generated and dynamically maintained within a circuit is still missing. Here we go beyond traditional approaches that investigate a one-to-one relationship between network connectivity and specific sequential dynamics. Instead, we train recurrent neural network models to generate a repertoire of sequential dynamics and characterize the obtained connectivity matrices. We found that different connectivity matrices can generate the same neural sequence, yet all connectivity matrices that generate a specific sequence share a common connectivity profile, defined here as the average weight between pairs of neurons as a function of their distance in the sequence ordering. It is the connectivity profile, as opposed to the connectivity matrix, that serves as a fingerprint of the sequential dynamics and shapes the network response to perturbations of the neural activity. Our model predictions were consistent with results obtained from experimental data recorded across brain regions and across species. Finally, we demonstrated that neural sequences can facilitate and constrain the formation of a large repertoire of sequences in downstream brain regions, with the potential of acting as scaffolds for a wide range of computations. Altogether, our results explain how network connectivity can generate a diversity of neural sequences across circuits and how those sequences can be flexibly adapted. Our framework reveals sequences as a common algorithm to support brain function across brain regions and species.