Symmetry group factorization reveals the structure-function relation in the neural connectome of Caenorhabditis elegans

TL;DR

This paper uncovers how symmetry group factorization in the C. elegans connectome reveals the relationship between neural structure and function, identifying functional sectors and hierarchical processing structures.

Contribution

It introduces a novel symmetry-based framework to analyze the connectome, revealing structural-functional links and predicting new neural subnetwork architectures.

Findings

Symmetries in the connectome correspond to functional categories.

Normal subgroup actions partition neurons into functional sectors.

Hierarchical block-circulant structures relate to neural processing filters.

Abstract

The neural connectome of the nematode Caenorhabditis elegans has been completely mapped, yet in spite of being one of the smallest connectomes (302 neurons), the design principles that explain how the connectome structure determines its function remain unknown. Here, we find symmetries in the locomotion neural circuit of C. elegans, each characterized by its own symmetry group which can be factorized into the direct product of normal subgroups. The action of these normal subgroups partitions the connectome into sectors of neurons that match broad functional categories. Furthermore, symmetry principles predict the existence of novel finer structures inside these normal subgroups forming feedforward and recurrent networks made of blocks of imprimitivity. These blocks constitute structures made of circulant matrices nested in a hierarchy of block-circulant matrices, whose functionality is understood in terms of neural processing filters responsible for fast processing of information.