Bilateral Symmetry and Asymmetry in the C. elegans Connectome: A Graph-Theoretic Analysis based on Redundancy Measures

Understanding the balance between symmetry and asymmetry in animal nervous systems is crucial for unraveling the complexities of neural architectures and their functions. Previous studies have primarily focused on morphological symmetry, such as neuron placement, leaving the symmetry in the functional architecture largely unexplored. The current study investigates this aspect within the Caenorhabditis elegans connectomes by introducing a graph-theoretic approach. By defining a mirror-symmetry index, we quantitatively assess the symmetry in these connectomes, revealing a significant level of bilateral symmetry alongside notable asymmetry. Our approach also incorporates measures including connectivity similarity, motif-fingerprint differences, and path-compensation index to evaluate the networks functional redundancy and its capacity to compensate for unilateral disturbances. Here we show the C. elegans connectomes robust bilateral symmetry, which not only facilitates similar functions across neuron pairs but also ensures resilience against disruptions. This redundancy is not confined to symmetrical connections; it also includes asymmetric ones, adding to the neural networks complexity. An in-depth analysis into different neuron types shows varied redundancy levels: high in interneurons, moderate in motor neurons, and low in sensory neurons. This pattern suggests a strategic neural design where diverse inputs from sensory neurons, coupled with the stable integration by interneurons, lead to coordinated actions through motor neurons. This study advances our understanding of neural connectomes, offering insights into the intricate balance of symmetry and asymmetry in neural systems and their implications for complex, adaptive behaviors.