Emergence of Slow-Switching Assemblies in Structured Neuronal Networks
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.
© 2015 Schaub et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Received: October 29, 2014; Accepted: February 16, 2015; Published: July 15, 2015. MTS acknowledges support from the Studienstiftung des deutschen Volkes and a Santander Mobility Award. MTS and MB acknowledge support through a grant to MB from the Engineering and Physical Sciences Research Council (EPSRC, grant EP/I017267/1) of the UK under the Mathematics underpinning the Digital Economy program. YNB, CAA, and CK thank the G. Harold & Leila Y. Mathers Foundation. CAA acknowledges support from the Swiss National Science Foundation (SNSF, grant PA00P3-131470). Author Contributions: Conceived and designed the experiments: MTS YNB CAA MB. Performed the experiments: MTS YNB. Analyzed the data: MTS YNB. Wrote the paper: MTS YNB CAA CK MB.
Supplemental Material - S1_Fig.pdf
Supplemental Material - S2_Fig.pdf
Published - journal.pcbi.1004196.pdf
Erratum - pcbi.1005288.pdf
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