Uncovering the genetic blueprint of the C. elegans nervous system

Despite rapid advances in connectome mapping and neuronal genetics, we lack theoretical and computational tools to unveil, in an experimentally testable fashion, the genetic mechanisms that govern neuronal wiring. Here we introduce a computational framework to link the adjacency matrix of a connectome to the expression patterns of its neurons, helping us uncover a set of genetic rules that govern the interactions between neurons in contact. The method incorporates the biological realities of the system, accounting for noise from data collection limitations, as well as spatial restrictions. The resulting methodology allows us to infer a network of 19 innexin interactions that govern the formation of gap junctions in Caenorhabditis elegans, five of which are already supported by experimental data. As advances in single-cell gene expression profiling increase the accuracy and the coverage of the data, the developed framework will allow researchers to systematically infer experimentally testable connection rules, offering mechanistic predictions for synapse and gap junction formation.

There is ample Please confirm or correct postal code added to each affiliation.experimental evidence that the connectome, capturing the neuron-level wiring of a brain, is at least partially genetically encoded. Indeed, while neurons are clustered into broad classes based on their morphology and function, these observed differences between cells are known to be rooted in the differential expression patterns of their genes and proteins (1–10). Consequently, perturbations that alter the genetic identity of individual neurons can induce significant changes in wiring (11, 12). Furthermore, developmental neuroscience has unveiled multiple genetic factors contributing to the formation of neuronal circuits. For example, the connectomes of Caenorhabditis elegans and higher organisms rely on a combination of body and wiring localization (13–18), and cell–cell recognition specificity, for both synaptic (19) and gap junction (GJ) connections (11, 20, 21). In the mouse retina, proteins, like connexin-36, play a known role in coupling rods and cones through GJs (22), and, in D. melanogaster, neurons expressing the same olfactory receptor converge onto the same set of projection neurons (23). While these studies offer strong experimental support for the genetic roots of neuronal wiring, we continue to lack a general framework to identify the genetic mechanisms that determine the presence or the absence of specific neuronal connections (12, 21, 24).These advances have prompted the development of statistical approaches designed to identify genes involved in neuronal connectivity. At coarser spatial scales, where collections of spatially proximal neurons are profiled together, data availability has led to the development of correlative and predictive approaches that connect regional gene expression and connectivity in the mouse brain (25, 26). At the neuronal scale, Kaufman et al. (27) demonstrated a correlation between gene expression and neuronal connectivity, and Varadan et al. (28) identified a genetic rule for chemical synapses through an entropy minimization approach. Despite these important advances, existing frameworks fail to incorporate spatial constraints for synapse formation. Indeed, past work in mice, macaque, and C. elegans suggests that connection probability decays with spatial distance between soma (17, 29). Strictly speaking, synapses can only exist between neurons in physical contact along their surface. This limitation was recognized by Baruch et al. (30) in their inference of genetic rules, estimating neuronal contact information from neuronal connectivity itself. Here we can take advantage of recent high-resolution efforts to map a neuronal “contactome” in C. elegans, that also offer an accurate consideration of spatial and contact information (31). Notwithstanding these promising advances, progress toward unveiling the genetic rules of synapse formation is remarkably slow compared to the tremendous experimental progress focusing on mapping the connectome and the gene expression patterns of individual neurons (32–34).The gap between experimental and computational progress raises a fundamental question: Is it computationally feasible to infer the genetic rules that govern synapse formation from the available experimental data? For instance, in C. elegans, we wish to describe the genetic rules that govern the wiring of neurons of a relatively sparse connectome of N≈300 neurons (32) using as input the combinatorial expression patterns of m≈20,000 genes (34). Even if we reduce the genetic complexity to the binary expression of individual genes, m genes can encode a very large number (N=2m) of neuronal identities. Hence, as we try to infer the list of genes whose expression pattern can encode the observed connectome, we are faced with a heavily underdetermined problem: In C. elegans, the combinatorial expression of m=log2(N)<9 genes is sufficient to fully describe the observed connectome. Although humans have N≈86 billion neurons (35), and m≈20,000 genes, the number of neurons is dwarfed by the combinatorial gene expression space of size 2m, where the expression pattern of m genes determines whether two neurons can synapse. Indeed, if only the binary expression of three genes contributes to synapse formation in each neuron, they allow for 1/6×m3=1.3×1012 combinations, an order of magnitude larger than the number of neurons in a human brain, leading again to serious overfitting. We are therefore faced with an astronomical search space, and the challenge to extract meaningful genetic rules in a heavily ill-conditioned problem of finding them from inherently limited experimental data.To overcome these difficulties, here we develop a theoretical framework to systematically infer the genetic rules that contribute to the formation and maintenance of synapses and GJs between neurons in contact. We show that these genetic rules can be systematically extracted from three datasets: 1) a comprehensive map of the connectome, 2) a protein expression atlas of the individual neurons, and 3) a list of neurons in physical contact. Finally, we apply our modeling framework to the roundworm C. elegans. We do so because the C. elegans connectome is believed to be largely identical across individuals (33, 36, 37), and hence predetermined by the genetic markers that label each neuron (5, 20). Yet, the genetic mechanisms that determine which neurons can synapse with each other remain largely unknown even in this simple and well-studied organism (21). We show that we can overcome overfitting by restricting our analysis to genes known to be involved in GJ formation, and developing a spatial connectome model (SCM) to properly account for physical restrictions for wiring. We demonstrate the utility of the proposed modeling framework by predicting 19 interactions between innexin proteins responsible for GJ formation, finding that 5 of them are supported by previous experimental data.