A diversity of localized timescales in network activity.
Neurons show diverse timescales, so that different parts of a network respond with disparate temporal dynamics. Such diversity is observed both when comparing timescales across brain areas and among cells within local populations; the underlying circuit mechanism remains unknown. We examine conditions under which spatially local connectivity can produce such diverse temporal behavior. In a linear network, timescales are segregated if the eigenvectors of the connectivity matrix are localized to different parts of the network. We develop a framework to predict the shapes of localized eigenvectors. Notably, local connectivity alone is insufficient for separate timescales. However, localization of timescales can be realized by heterogeneity in the connectivity profile, and we demonstrate two classes of network architecture that allow such localization. Our results suggest a framework to relate structural heterogeneity to functional diversity and, beyond neural dynamics, are generally applicable to the relationship between structure and dynamics in biological networks. DOI: http://dx.doi.org/10.7554/eLife.01239.001.
Department of Applied Mathematics, Yale University, New Haven, United States.
Rishidev
R
Chaudhuri
Alberto
A
Bernacchia
Xiao-Jing
XJ
Wang
D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D009474:Neurons / Q000502:physiology*; D062211:Spatio-Temporal Analysis; D013997:Time Factors
network dynamics; neural networks; timescales