Fibration symmetries and cluster synchronization in the Caenorhabditis elegans connectome

TL;DR

This paper investigates how fiber symmetries in the Caenorhabditis elegans connectome can predict neuron synchronization, using graph symmetries and differential equation simulations to validate the predictions.

Contribution

It introduces the use of fibration symmetries to analyze connectome structure and predict neuronal synchronization, extending previous symmetry approaches.

Findings

Fiber symmetries accurately predict neuron synchronization.

Fibration symmetries decompose the connectome into fundamental units.

Predictions hold under realistic, non-ideal connectivity conditions.

Abstract

Capturing how the Caenorhabditis elegans connectome structure gives rise to its neuron functionality remains unclear. It is through fiber symmetries found in its neuronal connectivity that synchronization of a group of neurons can be determined. To understand these we investigate graph symmetries and search for such in the symmetrized versions of the forward and backward locomotive sub-networks of the Caenorhabditi elegans worm neuron network. The use of ordinarily differential equations simulations admissible to these graphs are used to validate the predictions of these fiber symmetries and are compared to the more restrictive orbit symmetries. Additionally fibration symmetries are used to decompose these graphs into their fundamental building blocks which reveal units formed by nested loops or multilayered fibers. It is found that fiber symmetries of the connectome can accurately predict neuronal synchronization even under not idealized connectivity as long as the dynamics are within stable regimes of simulations.