Neuroscience Needs Network Science.

The brain is a complex system comprising a myriad of interacting neurons, posing significant challenges in understanding its structure, function, and dynamics. Network science has emerged as a powerful tool for studying such interconnected systems, offering a framework for integrating multiscale data and complexity. To date, network methods have significantly advanced functional imaging studies of the human brain and have facilitated the development of control theory-based applications for directing brain activity. Here, we discuss emerging frontiers for network neuroscience in the brain atlas era, addressing the challenges and opportunities in integrating multiple data streams for understanding the neural transitions from development to healthy function to disease. We underscore the importance of fostering interdisciplinary opportunities through workshops, conferences, and funding initiatives, such as supporting students and postdoctoral fellows with interests in both disciplines. By bringing together the network science and neuroscience communities, we can develop novel network-based methods tailored to neural circuits, paving the way toward a deeper understanding of the brain and its functions, as well as offering new challenges for network science.

Dissecting the functional organization of the C. elegans serotonergic system at whole-brain scale.

Serotonin influences many aspects of animal behavior. But how serotonin acts on its diverse receptors across the brain to modulate global activity and behavior is unknown. Here, we examine how serotonin release in C. elegans alters brain-wide activity to induce foraging behaviors, like slow locomotion and increased feeding. Comprehensive genetic analyses identify three core serotonin receptors (MOD-1, SER-4, and LGC-50) that induce slow locomotion upon serotonin release and others (SER-1, SER-5, and SER-7) that interact with them to modulate this behavior. SER-4 induces behavioral responses to sudden increases in serotonin release, whereas MOD-1 induces responses to persistent release. Whole-brain imaging reveals widespread serotonin-associated brain dynamics, spanning many behavioral networks. We map all sites of serotonin receptor expression in the connectome, which, together with synaptic connectivity, helps predict which neurons show serotonin-associated activity. These results reveal how serotonin acts at defined sites across a connectome to modulate brain-wide activity and behavior.

Neuroscience needs Network Science.

The brain is a complex system comprising a myriad of interacting elements, posing significant challenges in understanding its structure, function, and dynamics. Network science has emerged as a powerful tool for studying such intricate systems, offering a framework for integrating multiscale data and complexity. Here, we discuss the application of network science in the study of the brain, addressing topics such as network models and metrics, the connectome, and the role of dynamics in neural networks. We explore the challenges and opportunities in integrating multiple data streams for understanding the neural transitions from development to healthy function to disease, and discuss the potential for collaboration between network science and neuroscience communities. We underscore the importance of fostering interdisciplinary opportunities through funding initiatives, workshops, and conferences, as well as supporting students and postdoctoral fellows with interests in both disciplines. By uniting the network science and neuroscience communities, we can develop novel network-based methods tailored to neural circuits, paving the way towards a deeper understanding of the brain and its functions.

Dissecting the Functional Organization of the C. elegans Serotonergic System at Whole-Brain Scale.

Serotonin controls many aspects of animal behavior and cognition. But how serotonin acts on its diverse receptor types in neurons across the brain to modulate global activity and behavior is unknown. Here, we examine how serotonin release from a feeding-responsive neuron in C. elegans alters brain-wide activity to induce foraging behaviors, like slow locomotion and increased feeding. A comprehensive genetic analysis identifies three core serotonin receptors that collectively induce slow locomotion upon serotonin release and three others that interact with them to further modulate this behavior. The core receptors have different functional roles: some induce behavioral responses to sudden increases in serotonin release, whereas others induce responses to persistent release. Whole-brain calcium imaging reveals widespread serotonin-associated brain dynamics, impacting different behavioral networks in different ways. We map out all sites of serotonin receptor expression in the connectome, which, together with synaptic connectivity, helps predict serotonin-associated brain-wide activity changes. These results provide a global view of how serotonin acts at defined sites across a connectome to modulate brain-wide activity and behavior.

Maximizing brain networks engagement via individualized connectome-wide target search.

BACKGROUND: In recent years, the possibility to noninvasively interact with the human brain has led to unprecedented diagnostic and therapeutic opportunities. However, the vast majority of approved interventions and approaches still rely on anatomical landmarks and rarely on the individual structure of networks in the brain, drastically reducing the potential efficacy of neuromodulation. OBJECTIVE: Here we implemented a target search algorithm leveraging on mathematical tools from Network Control Theory (NCT) and whole brain connectomics analysis. By means of computational simulations, we aimed to identify the optimal stimulation target(s)- at the individual brain level- capable of reaching maximal engagement of the stimulated networks' nodes. RESULTS: At the model level, in silico predictions suggest that stimulation of NCT-derived cerebral sites might induce significantly higher network engagement, compared to traditionally employed neuromodulation sites, demonstrating NCT to be a useful tool in guiding brain stimulation. Indeed, NCT allows us to computationally model different stimulation scenarios tailored on the individual structural connectivity profiles and initial brain states. CONCLUSIONS: The use of NCT to computationally predict TMS pulse propagation suggests that individualized targeting is crucial for more successful network engagement. Future studies will be needed to verify such prediction in real stimulation scenarios.

Synthetic ablations in the C. elegans nervous system.

Synthetic lethality, the finding that the simultaneous knockout of two or more individually nonessential genes leads to cell or organism death, has offered a systematic framework to explore cellular function, and also offered therapeutic applications. Yet the concept lacks its parallel in neuroscience-a systematic knowledge base on the role of double or higher order ablations in the functioning of a neural system. Here, we use the framework of network control to systematically predict the effects of ablating neuron pairs and triplets on the gentle touch response. We find that surprisingly small sets of 58 pairs and 46 triplets can reduce muscle controllability in this context, and that these sets are localized in the nervous system in distinct groups. Further, they lead to highly specific experimentally testable predictions about mechanisms of loss of control, and which muscle cells are expected to experience this loss.

Multi-subject Stochastic Blockmodels for adaptive analysis of individual differences in human brain network cluster structure.

There is considerable interest in elucidating the cluster structure of brain networks in terms of modules, blocks or clusters of similar nodes. However, it is currently challenging to handle data on multiple subjects since most of the existing methods are applicable only on a subject-by-subject basis or for analysis of an average group network. The main limitation of per-subject models is that there is no obvious way to combine the results for group comparisons, and of group-averaged models that they do not reflect the variability between subjects. Here, we propose two new extensions of the classical Stochastic Blockmodel (SBM) that use a mixture model to estimate blocks or clusters of connected nodes, combined with a regression model to capture the effects of subject-level covariates on individual differences in cluster structure. The proposed Multi-Subject Stochastic Blockmodels (MS-SBMs) can flexibly account for between-subject variability in terms of homogeneous or heterogeneous covariate effects on connectivity using subject demographics such as age or diagnostic status. Using synthetic data, representing a range of block sizes and cluster structures, we investigate the accuracy of the estimated MS-SBM parameters as well as the validity of inference procedures based on the Wald, likelihood ratio and permutation tests. We show that the proposed multi-subject SBMs recover the true cluster structure of synthetic networks more accurately and adaptively than standard methods for modular decomposition (i.e. the Fast Louvain and Newman Spectral algorithms). Permutation tests of MS-SBM parameters were more robustly valid for statistical inference and Type I error control than tests based on standard asymptotic assumptions. Applied to analysis of multi-subject resting-state fMRI networks (13 healthy volunteers; 12 people with schizophrenia; n=268 brain regions), we show that Heterogeneous Stochastic Blockmodel (Het-SBM) identifies a range of network topologies simultaneously, including modular and core structures.

Brain Networks Reveal the Effects of Antipsychotic Drugs on Schizophrenia Patients and Controls.

The study of brain networks, including those derived from functional neuroimaging data, attracts a broad interest and represents a rapidly growing interdisciplinary field. Comparing networks of healthy volunteers with those of patients can potentially offer new, quantitative diagnostic methods and a framework for better understanding brain and mind disorders. We explore resting state functional Magnetic Resonance Imaging (fMRI) data through network measures. We construct networks representing 15 healthy individuals and 12 schizophrenia patients (males and females), all of whom are administered three drug treatments: i) a placebo; and two antipsychotic medications ii) aripiprazole and iii) sulpiride. We compare these resting state networks to a performance at an "N-back" working memory task. We demonstrate that not only is there a distinctive network architecture in the healthy brain that is disrupted in schizophrenia but also that both networks respond to antipsychotic medication. We first reproduce the established finding that brain networks of schizophrenia patients exhibit increased efficiency and reduced clustering compared with controls. Our data then reveal that the antipsychotic medications mitigate this effect, shifting the metrics toward those observed in healthy volunteers, with a marked difference in efficacy between the two drugs. Additionally, we find that aripiprazole considerably alters the network statistics of healthy controls. Examining the "N-back" working memory task, we establish that aripiprazole also adversely affects their performance. This suggests that changes to macroscopic brain network architecture result in measurable behavioral differences. This is one of the first studies to directly compare different medications using a whole-brain graph theoretical analysis with accompanying behavioral data. The small sample size is an inherent limitation and means a degree of caution is warranted in interpreting the findings. Our results lay the groundwork for an objective methodology with which to calculate and compare the efficacy of different treatments of mind and brain disorders.

Editorial: Bridging Scales and Levels.

Network neuroscience strives to understand the networks of the brain on all spatiotemporal scales and levels of observation. Current experimental and theoretical capabilities are beginning to facilitate a more holistic perspective, uniting these networks. This focus feature, "Bridging Scales and Levels," aims to document current research and looks to future progress towards this vision.

Caenorhabditis elegans and the network control framework-FAQs.

Control is essential to the functioning of any neural system. Indeed, under healthy conditions the brain must be able to continuously maintain a tight functional control between the system's inputs and outputs. One may therefore hypothesize that the brain's wiring is predetermined by the need to maintain control across multiple scales, maintaining the stability of key internal variables, and producing behaviour in response to environmental cues. Recent advances in network control have offered a powerful mathematical framework to explore the structure-function relationship in complex biological, social and technological networks, and are beginning to yield important and precise insights on neuronal systems. The network control paradigm promises a predictive, quantitative framework to unite the distinct datasets necessary to fully describe a nervous system, and provide mechanistic explanations for the observed structure and function relationships. Here, we provide a thorough review of the network control framework as applied to Caenorhabditis elegans (Yan et al. 2017 Nature550, 519-523. (doi:10.1038/nature24056)), in the style of Frequently Asked Questions. We present the theoretical, computational and experimental aspects of network control, and discuss its current capabilities and limitations, together with the next likely advances and improvements. We further present the Python code to enable exploration of control principles in a manner specific to this prototypical organism.This article is part of a discussion meeting issue 'Connectome to behaviour: modelling C. elegans at cellular resolution'.

Recordings of Caenorhabditis elegans locomotor behaviour following targeted ablation of single motorneurons.

Lesioning studies have provided important insight into the functions of brain regions in humans and other animals. In the nematode Caenorhabditis elegans, with a small nervous system of 302 identified neurons, it is possible to generate lesions with single cell resolution and infer the roles of individual neurons in behaviour. Here we present a dataset of ~300 video recordings representing the locomotor behaviour of animals carrying single-cell ablations of 5 different motorneurons. Each file includes a raw video of approximately 27,000 frames; each frame has also been segmented to yield the position, contour, and body curvature of the tracked animal. These recordings can be further analysed using publicly-available software to extract features relevant to behavioural phenotypes. This dataset therefore represents a useful resource for probing the neural basis of behaviour in C. elegans, a resource we hope to augment in the future with ablation recordings for additional neurons.

Network control principles predict neuron function in the Caenorhabditis elegans connectome.

Recent studies on the controllability of complex systems offer a powerful mathematical framework to systematically explore the structure-function relationship in biological, social, and technological networks. Despite theoretical advances, we lack direct experimental proof of the validity of these widely used control principles. Here we fill this gap by applying a control framework to the connectome of the nematode Caenorhabditis elegans, allowing us to predict the involvement of each C. elegans neuron in locomotor behaviours. We predict that control of the muscles or motor neurons requires 12 neuronal classes, which include neuronal groups previously implicated in locomotion by laser ablation, as well as one previously uncharacterized neuron, PDB. We validate this prediction experimentally, finding that the ablation of PDB leads to a significant loss of dorsoventral polarity in large body bends. Importantly, control principles also allow us to investigate the involvement of individual neurons within each neuronal class. For example, we predict that, within the class of DD motor neurons, only three (DD04, DD05, or DD06) should affect locomotion when ablated individually. This prediction is also confirmed; single cell ablations of DD04 or DD05 specifically affect posterior body movements, whereas ablations of DD02 or DD03 do not. Our predictions are robust to deletions of weak connections, missing connections, and rewired connections in the current connectome, indicating the potential applicability of this analytical framework to larger and less well-characterized connectomes.

The rich club of the C. elegans neuronal connectome.

There is increasing interest in topological analysis of brain networks as complex systems, with researchers often using neuroimaging to represent the large-scale organization of nervous systems without precise cellular resolution. Here we used graph theory to investigate the neuronal connectome of the nematode worm Caenorhabditis elegans, which is defined anatomically at a cellular scale as 2287 synaptic connections between 279 neurons. We identified a small number of highly connected neurons as a rich club (N = 11) interconnected with high efficiency and high connection distance. Rich club neurons comprise almost exclusively the interneurons of the locomotor circuits, with known functional importance for coordinated movement. The rich club neurons are connector hubs, with high betweenness centrality, and many intermodular connections to nodes in different modules. On identifying the shortest topological paths (motifs) between pairs of peripheral neurons, the motifs that are found most frequently traverse the rich club. The rich club neurons are born early in development, before visible movement of the animal and before the main phase of developmental elongation of its body. We conclude that the high wiring cost of the globally integrative rich club of neurons in the C. elegans connectome is justified by the adaptive value of coordinated movement of the animal. The economical trade-off between physical cost and behavioral value of rich club organization in a cellular connectome confirms theoretical expectations and recapitulates comparable results from human neuroimaging on much larger scale networks, suggesting that this may be a general and scale-invariant principle of brain network organization.