The growing topology of theC. elegansconnectome

Abstract

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 system’s 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 system’s 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-tome’s 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 neuron’s specific birth time and ask if this metric tracks other biological properties of neurons. Our results suggest that the connectome’s 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 organism’s function and its capacity for information processing. Recent work has extended those investigations by focusing on the connectome’s 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 organism’s 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.

Circuit motifs and graph properties of connectome development in C. elegans

“…What biological mechanisms cause such dramatic differences in motif growth-rate? This points to a "preference" for certain structural properties in immature connectomes, and different local structural property preferences in a mature connectome -compatible with parallel observations on topological changes to a connectome during maturation (11). 8), where the probability of connection is equal to the compared graph's density.…”

“…The C. elegans connectome is composed of a dense network with inputs predominantly from sensory neurons and outputs predominantly to The adult connectome has significant variability in loop counts. Previous work (10,11) has suggested that loops and cycles are important for computation in the growing nematode connectome. Here, we use our reproducible graph techniques to quantify this property during development, and show that the total number of loops tends to grow as the animal matures.…”

The neuropeptidergic connectome ofC. elegans

“…For example, the C. elegans connectome, like those of larger nervous systems, exhibits a small-world topology, with relatively high clustering paired with relatively short average path lengths 49,50 . Likewise, the C. elegans nervous system is highly modular, with functionally segregated local clusters of high within-group connectivity [51][52][53][54] . Finally, the worm connectome contains a small number of highly connected hubs, which are interconnected in a core or rich club and facilitate communication between modules 55 ; similar rich club topology has been observed in bigger brains, including the human cortex 56,57 .…”

Topological Data Analysis of C. elegans Locomotion and Behavior

“…Persistence has been successfully used to study high-dimensional time series, especially those that exhibit some quasi-periodic behavior like the undulation of C. elegans ( Tralie, 2016 ; Tralie and Perea, 2018 ). But to the authors’ knowledge, persistent homology has not been previously used to analyze C. elegans behavior, though it and similar techniques have been used to study C. elegans neural data ( Petri et al, 2013 ; Backholm et al, 2015 ; Sizemore et al, 2019 ; Helm et al, 2020 ; Lütgehetmann et al, 2020 ).…”

“…Research into gene expression has used persistent homology to detect patterns or classify whether a signal is periodic ( Dequéant et al, 2008 ; Perea et al, 2015 ). Frequently, persistence has been used to study neural data ( Petri et al, 2013 ; Backholm et al, 2015 ; Stolz et al, 2017 ; Sizemore et al, 2019 ; Helm et al, 2020 ; Lütgehetmann et al, 2020 ), and in many cases neural data from C. elegans , but the analysis tends to rely on clique complexes as the topological space of interest instead of sliding window embeddings.…”