Unraveling the interplay between connectivity and spatio-temporal dynamics in
neuronal networks is a key step to advance our understanding of neuronal
information processing. Here we investigate how particular features of network
connectivity underpin the propensity of neural networks to generate
slow-switching assembly (SSA) dynamics, i.e., sustained epochs of increased
firing within assemblies of neurons which transition slowly between different
assemblies throughout the network. We show that the emergence of SSA activity
is linked to spectral properties of the asymmetric synaptic weight matrix. In
particular, the leading eigenvalues that dictate the slow dynamics exhibit a
gap with respect to the bulk of the spectrum, and the associated Schur vectors
exhibit a measure of block-localization on groups of neurons, thus resulting in
coherent dynamical activity on those groups. Through simple rate models, we
gain analytical understanding of the origin and importance of the spectral gap,
and use these insights to develop new network topologies with alternative
connectivity paradigms which also display SSA activity. Specifically, SSA
dynamics involving excitatory and inhibitory neurons can be achieved by
modifying the connectivity patterns between both types of neurons. We also show
that SSA activity can occur at multiple timescales reflecting a hierarchy in
the connectivity, and demonstrate the emergence of SSA in small-world like
networks. Our work provides a step towards understanding how network structure
(uncovered through advancements in neuroanatomy and connectomics) can impact on
spatio-temporal neural activity and constrain the resulting dynamics.Comment: The first two authors contributed equally -- 18 pages, including
supplementary material, 10 Figures + 2 SI Figure