Dynamical Complexity in the C.elegans Neural Network

TL;DR

This study models the C.elegans neural network using Hindmarsh-Rose equations, analyzing its dynamical complexity and information integration, revealing how synchronization patterns relate to information content and chaos.

Contribution

It introduces a novel application of the $ ext{Φ}_{ ext{AR}}$ measure to the C.elegans network, linking dynamical complexity with information integration and synchronization states.

Findings

C.elegans brain generates more information than its parts.

Higher integrated information occurs with specific synchronization patterns.

Low chaos correlates with high information integration.

Abstract

We model the neuronal circuit of the C.elegans soil worm in terms of Hindmarsh-Rose systems of ordinary differential equations, dividing its circuit into six communities pointed out by the walktrap and Louvain methods. Using the numerical solution of these equations, we analyze important measures of dynamical complexity, namely synchronicity, the largest Lyapunov exponent, and the $\Phi_{\mbox{AR}}$ auto-regressive integrated information theory measure, which has been suggested to reflect different levels of consciousness. We show that $\Phi_{\mbox{AR}}$ provides a useful measure of the information contained in the C.elegans brain dynamic network. Our analysis reveals that the C.elegans brain dynamic network generates more information than the sum of its constituent parts, and that attains higher levels of integrated information for couplings for which either all its communities are highly synchronized, or there is a mixed state of highly synchronized and desynchronized communities. Both situations are characterized by relatively low chaotic behavior.