The growing topology of the C. elegans connectome

Probing the developing neural circuitry in Caenorhabditis elegans has enhanced our understanding of nervous systems. The C. elegans connectome, like those of other species, is characterized by a rich club of densely connected neurons embedded within a small-world architecture. This organization of neuronal connections, captured by quantitative network statistics, provides insight into the systems capacity to perform integrative computations. Yet these network measures are limited in their ability to detect weakly connected motifs, such as topological cavities, that may support the systems capacity to perform segregated computations. We address this limitation by using persistent homology to track the evolution of topological cavities in the growing C. elegans connectome throughout neural development, and assess the degree to which the growing connec-tomes topology is resistant to biological noise. We show that the developing connectome topology is both relatively robust to changes in neuron birth times and not captured by similar growth models. Additionally, we quantify the consequence of a neurons specific birth time and ask if this metric tracks other biological properties of neurons. Our results suggest that the connectomes growing topology is a robust feature of the developing con-nectome that is distinct from other network properties, and that the growing topology is particularly sensitive to the exact birth times of a small set of predominantly motor neurons. By utilizing novel measurements that track biological features, we anticipate that our study will be helpful in the construction of more accurate models of neuronal development in C. elegans. Author SummaryNetwork analyses have identified several local and global properties of the C. elegans connectome that are relevant to the organisms function and its capacity for information processing. Recent work has extended those investigations by focusing on the connectomes growth, in an effort to uncover potential drivers of connectome formation. Here we investigate connectome growth from the perspective of applied algebraic topology, by tracking both changing and persistent homology. In doing so, we are able to measure the resilience of the growth process to perturbations, and assess spatial variations in that resilience throughout the organisms body. Our findings provide new insights regarding the development of this simple natural connectome, as we have determined the existence of a robust and topologically simple network feature that is unexplained by the presence of other notable features of the connectome.