Signed motif analysis of the Caenorhabditis elegans neuronal network reveals positive feedforward and negative feedback loops

BMC Biology https://doi.org/10.1186/s12915-026-02641-4 Article in Press Signed motif analysis of the Caenorhabditis elegans neuronal network reveals positive feedforward and negative feedback loops Gabor Szilagyi, Attila Gulyas, Zsolt Vassy, Peter Csermely & Bank Fenyves Received: 28 Oct 2025 Accepted: 14 May 2026 Cite this article as: Szilagyi, G., Gulyas, A., Vassy, Z. et al. Signed motif analysis of the Caenorhabditis elegans neuronal network reveals positive feedforward and negative feedback loops. BMC Biol (2026). https://doi.org/10.1186/s1291 5-026-02641-4 A E R P S S We are providing an unedited version of this manuscript to give early access to its findings. Before final publication, the manuscript will undergo further editing. Please note there may be errors present which affect the content, and all legal disclaimers apply. IN If this paper is publishing under a Transparent Peer Review model then Peer Review reports will publish with the final article. I T R E L C ©The Author(s) 2026. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ ACCEPTED ARTICLEMANUSCRIPT IN PRESS Signed motif analysis of the Caenorhabditis elegans neuronal network reveals positive feedforward and negative feedback loops Gabor S. Szilagyi1,2, Attila Gulyas1, Zsolt Vassy1, Peter Csermely1, Bank G. Fenyves1,3 Affiliations: 1. Department of Molecular Biology, Semmelweis University, Budapest, Hungary S S 3. Department of Emergency Medicine, Semmelweis University, Budapest, Hungary E PR IN Corresponding author: Bank G. Fenyves E L Mail address: Ulloi ut 26, BudapestC 1085, Hungary I T Email: R A 2. Department of Orthopedics, Semmelweis University, Budapest, Hungary ACCEPTED ARTICLEMANUSCRIPT IN PRESS Abstract Background: Nervous systems are complex biological networks with largely unknown structural and functional characteristics. Motif analysis is a robust tool that can reveal the unique aspects of connectivity in a complex network. An ideal candidate for motif analysis is the connectome of the nematode Caenorhabditis elegans, which is the first fully reconstructed nervous system. Results: We performed, for the first time, edge-polarity based signed motif analysis on the C. elegans connectome using recent data on the connection signs of this network and a novel structure-preserving randomization method. We identified 56 significantly over- and 1 underrepresented three-node signed motifs and revealed that certain motifs (e.g., positive S S E distinguished nodes by their are overabundant in the C. elegans connectome. We further R P corresponding neuron modalities (e.g., sensory vs. motor neurons), and found that each N I significant feedforward and feedback loop has a characteristic neuronal layout. E L C the importance and potential of signed motif analysis Conclusions: Our findings demonstrate I T in understanding biological networks. The motif enumeration tool and definition system we R A feedforward, negative feedback, disinhibitory feedback, and incoherent feedforward loops) developed can be used to analyze signed motifs in other complex networks. KEYWORDS: connectome, feedforward excitation, feedback inhibition, feedback disinhibition, incoherent feedforward loop, biological switches, topology preserving randomization ACCEPTED ARTICLEMANUSCRIPT IN PRESS Background Nervous systems are complex biological networks that generate behavior through neural activity mediated by synaptic connectivity. Biological networks share common global (e.g., small-worldness, cost-efficient wiring) and local (e.g., clustering, modularization) properties that allow optimal information processing [1–4]. Importantly, detailed structural characteristics can be revealed by investigating a network’s composition from smaller building blocks, called motifs (Fig. 1A). Motifs are frequently occurring subgraphs that correspond to different biological functions [3]. A subgraph is a graph whose nodes and edges are subsets of another graph, with two main types: induced and partial [5]. A subgraph is induced when it consists of a subset of nodes from a network and all the edges that connect S S chosen nodes (Fig. 1B). The classical concept is that ifE a specific subgraph occurs in a R P network more frequently than expected, that subgraph might play a crucial role in the N I network; hence, it is called a motif. Motifs have been examined in a variety of real-world E L C [3, 4, 6]. Like the networks themselves, motifs are and, more importantly, brain networks I T characterized primarily byR their nodes and edges. A them. On the other hand, partial subgraphs contain only some of the edges connecting the ACCEPTED ARTICLEMANUSCRIPT IN PRESS E L C IN S S E R P I T AR Fig. 1. Overview of motif definitions. A) Three-node motif structures with directed edges. B) Induced and partial motifs. Partial motifs are subgraphs of their corresponding induced motif. For example, the induced motif E contains five different partial motifs. A similar concept is discussed in McDonnell et al. (2014) and Sporns & Kötter (2004). C) Definition of signed motifs by coloring the edges (of motif G in the example). An edge can be either excitatory or inhibitory. ACCEPTED ARTICLEMANUSCRIPT IN PRESS Particularly in brain networks, edges can be labelled (colored) by the polarity of the connection they represent, i.e., excitatory or inhibitory (Fig. 1C). This is important, as structurally identical motifs with different polarity patterns can have completely different biological functions. However, edge polarity-labeled (i.e., signed) motif analysis is rarely performed on neuronal networks, since large-scale polarity data are lacking in most species. Even though there are now multiple known connectomes [7, 8], the neuronal network of the nematode Caenorhabditis elegans was the first completely reconstructed cell-level representation of a living organism’s nervous system [9, 10], consisting of 302 neurons and ~5000 connections in a hermaphrodite. In previous work on truncated and partial worm S S 10–14]. At the same time, changes in motif occurrences during the animal's development E R have also been observed [13]. Motif analy (...truncated)