Hidden connectivity structures control collective network dynamics

TL;DR

This paper develops a mathematical framework to understand how eigenmode structures in brain connectivity influence network dynamics, revealing hidden collective structures that control critical phenomena and neural activity patterns.

Contribution

It introduces a novel eigenmode-based approach to characterize connectivity structures and their impact on brain dynamics, uncovering fundamental collective mechanisms beyond traditional motifs.

Findings

Density of nearly-critical eigenvalues controls power-law scaling.

Eigenmode structures enable fine-tuning of neural activity dimensionality.

Hidden collective structures influence brain dynamics beyond local motifs.

Abstract

Many observables of brain dynamics appear to be optimized for computation. Which connectivity structures underlie this fine-tuning? We propose that many of these structures are naturally encoded in the space that more directly relates to network dynamics - the space of the connectivity eigenmodes. We develop a mathematical theory to impose eigenmode structures on connectivity, systematically characterizing their effect on network dynamics. We find the density of nearly-critical eigenvalues to be a particularly fundamental structure. It flexibly controls the power-law scaling of dynamical observables, in analogy with the system's spatial dimension in classical critical phenomena. This mechanism provides control over observables which are found to be fine-tuned in brain networks, but remained so far unexplained by traditionally studied structures, such as connectivity motifs. Specifically, the slope of the principal component spectrum of neural activity can be fine-tuned, as observed in primary visual cortex of mice. Furthermore, a novel transition between high and low dimensional activity allows for a wide and flexible tuning of dimensionality, as observed throughout cortex. The here discovered structures thus largely complement motifs. In fact, they are of a different, collective nature: they are not reflected by any local motif configuration. This result shows that many functionally relevant structures can remain hidden within the apparent randomness of highly heterogeneous cortical circuits. Our methods enable revealing these structures and investigate their effect on network dynamics.