Structural properties of the Caenorhabditis elegans neuronal network

Tyraminergic corollary discharge filters reafferent perception in a chemosensory neuron

Interpreting sensory information requires its integration with the current behavior of the animal. However, how motor-related circuits influence sensory information processing is incompletely understood. Here, we report that current locomotor state directly modulates the activity of BAG CO₂ sensory neurons in Caenorhabditis elegans. By recording neuronal activity in animals freely navigating CO₂ landscapes, we found that during reverse crawling states, BAG activity is suppressed by tyraminergic corollary discharge signaling. We provide genetic evidence that tyramine released from the RIM reversal interneurons extrasynaptically activates the inhibitory chloride channel LGC-55 in BAG. Disrupting this pathway genetically leads to excessive behavioral responses to CO₂ stimuli. Moreover, we find that LGC-55 signaling cancels out perception of self-produced CO₂ and O₂ stimuli when animals reverse into their own gas plume in ethologically relevant aqueous environments. Our results show that sensorimotor integration involves corollary discharge signals directly modulating chemosensory neurons.

Geometric framework to predict structure from function in neural networks

Neural computation in biological and artificial networks relies on the nonlinear summation of many inputs. The structural connectivity matrix of synaptic weights between neurons is a critical determinant of overall network function, but quantitative links between neural network structure and function are complex and subtle. For example, many networks can give rise to similar functional responses, and the same network can function differently depending on context. Whether certain patterns of synaptic connectivity are required to generate specific network-level computations is largely unknown. Here we introduce a geometric framework for identifying synaptic connections required by steady-state responses in recurrent networks of threshold-linear neurons. Assuming that the number of specified response patterns does not exceed the number of input synapses, we analytically calculate the solution space of all feedforward and recurrent connectivity matrices that can generate the specified responses from the network inputs. A generalization accounting for noise further reveals that the solution space geometry can undergo topological transitions as the allowed error increases, which could provide insight into both neuroscience and machine learning. We ultimately use this geometric characterization to derive certainty conditions guaranteeing a nonzero synapse between neurons. Our theoretical framework could thus be applied to neural activity data to make rigorous anatomical predictions that follow generally from the model architecture.

Social cognitive network neuroscience

Over the past three decades, research from the field of social neuroscience has identified a constellation of brain regions that relate to social cognition. Although these studies have provided important insights into the specific neural regions underlying social behavior, they may overlook the broader neural context in which those regions and the interactions between them are embedded. Network neuroscience is an emerging discipline that focuses on modeling and analyzing brain networks-collections of interacting neural elements. Because human cognition requires integrating information across multiple brain regions and systems, we argue that a novel social cognitive network neuroscience approach-which leverages methods from the field of network neuroscience and graph theory-can advance our understanding of how brain systems give rise to social behavior. This review provides an overview of the field of network neuroscience, discusses studies that have leveraged this approach to advance social neuroscience research, highlights the potential contributions of social cognitive network neuroscience to understanding social behavior and provides suggested tools and resources for conducting network neuroscience research.

Two pathways are required for ultrasound-evoked behavioral changes in Caenorhabditis elegans

Ultrasound has been shown to affect the function of both neurons and non-neuronal cells, but, the underlying molecular machinery has been poorly understood. Here, we show that at least two mechanosensitive proteins act together to generate C. elegans behavioral responses to ultrasound stimuli. We first show that these animals generate reversals in response to a single 10 msec pulse from a 2.25 MHz ultrasound transducer. Next, we show that the pore-forming subunit of the mechanosensitive channel TRP-4, and a DEG/ENaC/ASIC ion channel MEC-4, are both required for this ultrasound-evoked reversal response. Further, the trp-4;mec-4 double mutant shows a stronger behavioral deficit compared to either single mutant. Finally, overexpressing TRP-4 in specific chemosensory neurons can rescue the ultrasound-triggered behavioral deficit in the mec-4 null mutant, suggesting that both TRP-4 and MEC-4 act together in affecting behavior. Together, we demonstrate that multiple mechanosensitive proteins likely cooperate to transform ultrasound stimuli into behavioral changes.

Computational Inference of Synaptic Polarities in Neuronal Networks

Synaptic polarity, that is, whether synapses are inhibitory (-) or excitatory (+), is challenging to map, despite being a key to understand brain function. Here, synaptic polarity is inferred computationally considering three experimental scenarios, depending on the nature of available input data, using the Caenorhabditis elegans connectome as an example. First, the inputs consist of detailed neurotransmitter (NT) and receptor (R) gene expression, integrated through the connectome model (CM). The CM formulates the problem through a wiring rule network that summarizes how NT-R pairs govern synaptic polarity, and resolves 356 synaptic polarities in addition to the 1752 known polarities. Second, known synaptic polarities are considered as an input, in addition to the NT and R gene expression data, but without wiring rules. These data train the spatial connectome model, which infers the polarity of 81% of the CM-resolved connections at > 95 $>95$ % precision, while also inferring 147 of the remaining unknown polarities. Last, without known expression or wiring rules, polarities are inferred through a network sign prediction problem. As an illustration of high performance in this case, the generalized CM is introduced. These results address imminent challenges in unveiling large-scale synaptic polarities, an essential step toward more realistic brain models.

Invited review: Unearthing the mechanisms of age-related neurodegenerative disease using Caenorhabditis elegans

As human life expectancy increases, neurodegenerative diseases present a growing public health threat, for which there are currently few effective treatments. There is an urgent need to understand the molecular and genetic underpinnings of these disorders so new therapeutic targets can be identified. Here we present the argument that the simple nematode worm Caenorhabditis elegans is a powerful tool to rapidly study neurodegenerative disorders due to their short lifespan and vast array of genetic tools, which can be combined with characterization of conserved neuronal processes and behavior orthologous to those disrupted in human disease. We review how pre-existing C. elegans models provide insight into human neurological disease as well as an overview of current tools available to study neurodegenerative diseases in the worm, with an emphasis on genetics and behavior. We also discuss open questions that C. elegans may be particularly well suited for in future studies and how worms will be a valuable preclinical model to better understand these devastating neurological disorders.

A Graph Network Model for Neural Connection Prediction and Connection Strength Estimation

Objective. Reconstruction of connectomes at the cellular scale is a prerequisite for understanding the principles of neural circuits. However, due to methodological limits, scientists have reconstructed the connectomes of only a few organisms such as C. elegans, and estimated synaptic strength indirectly according to their size and number. Approach. Here, we propose a graph network model to predict synaptic connections and estimate synaptic strength by using the calcium activity data from C. elegans. Main results. The results show that this model can reliably predict synaptic connections in the neural circuits of C. elegans, and estimate their synaptic strength, which is an intricate and comprehensive reflection of multiple factors such as synaptic type and size, neurotransmitter and receptor type, and even activity dependence. In addition, the excitability or inhibition of synapses can be identified by this model. We also found that chemical synaptic strength is almost linearly positively correlated to electrical synaptic strength, and the influence of one neuron on another is non-linearly correlated with the number between them. This reflects the intrinsic interaction between electrical and chemical synapses. Significance. Our model is expected to provide a more accessible quantitative and data-driven approach for the reconstruction of connectomes in more complex nervous systems, as well as a promising method for accurately estimating synaptic strength.

Blind demixing methods for recovering dense neuronal morphology from barcode imaging data

Cellular barcoding methods offer the exciting possibility of 'infinite-pseudocolor' anatomical reconstruction-i.e., assigning each neuron its own random unique barcoded 'pseudocolor,' and then using these pseudocolors to trace the microanatomy of each neuron. Here we use simulations, based on densely-reconstructed electron microscopy microanatomy, with signal structure matched to real barcoding data, to quantify the feasibility of this procedure. We develop a new blind demixing approach to recover the barcodes that label each neuron, and validate this method on real data with known barcodes. We also develop a neural network which uses the recovered barcodes to reconstruct the neuronal morphology from the observed fluorescence imaging data, 'connecting the dots' between discontiguous barcode amplicon signals. We find that accurate recovery should be feasible, provided that the barcode signal density is sufficiently high. This study suggests the possibility of mapping the morphology and projection pattern of many individual neurons simultaneously, at high resolution and at large scale, via conventional light microscopy.

Revealing directed effective connectivity of cortical neuronal networks from measurements

In the study of biological networks, one of the major challenges is to understand the relationships between network structure and dynamics. In this paper, we model in vitro cortical neuronal cultures as stochastic dynamical systems and apply a method that reconstructs directed networks from dynamics [Ching and Tam, Phys. Rev. E 95, 010301(R) (2017)2470-004510.1103/PhysRevE.95.010301] to reveal directed effective connectivity, namely, the directed links and synaptic weights, of the neuronal cultures from voltage measurements recorded by a multielectrode array. The effective connectivity so obtained reproduces several features of cortical regions in rats and monkeys and has similar network properties as the synaptic network of the nematode Caenorhabditis elegans, whose entire nervous system has been mapped out. The distribution of the incoming degree is bimodal and the distributions of the average incoming and outgoing synaptic strength are non-Gaussian with long tails. The effective connectivity captures different information from the commonly studied functional connectivity, estimated using statistical correlation between spiking activities. The average synaptic strengths of excitatory incoming and outgoing links are found to increase with the spiking activity in the estimated effective connectivity but not in the functional connectivity estimated using the same sets of voltage measurements. These results thus demonstrate that the reconstructed effective connectivity can capture the general properties of synaptic connections and better reveal relationships between network structure and dynamics.

Dynamic functional connectivity in the static connectome of Caenorhabditis elegans

A hallmark of adaptive behavior is the ability to flexibly respond to sensory cues. To understand how neural circuits implement this flexibility, it is critical to resolve how a static anatomical connectome can be modulated such that functional connectivity in the network can be dynamically regulated. Here, we review recent work in the roundworm Caenorhabditis elegans on this topic. EM studies have mapped anatomical connectomes of many C. elegans animals, highlighting the level of stereotypy in the anatomical network. Brain-wide calcium imaging and studies of specified neural circuits have uncovered striking flexibility in the functional coupling of neurons. The coupling between neurons is controlled by neuromodulators that act over long timescales. This gives rise to persistent behavioral states that animals switch between, allowing them to generate adaptive behavioral responses across environmental conditions. Thus, the dynamic coupling of neurons enables multiple behavioral states to be encoded in a physically stereotyped connectome.

Reconstruction of neocortex: Organelles, compartments, cells, circuits, and activity

We assembled a semi-automated reconstruction of L2/3 mouse primary visual cortex from ∼250 × 140 × 90 μm3 of electron microscopic images, including pyramidal and non-pyramidal neurons, astrocytes, microglia, oligodendrocytes and precursors, pericytes, vasculature, nuclei, mitochondria, and synapses. Visual responses of a subset of pyramidal cells are included. The data are publicly available, along with tools for programmatic and three-dimensional interactive access. Brief vignettes illustrate the breadth of potential applications relating structure to function in cortical circuits and neuronal cell biology. Mitochondria and synapse organization are characterized as a function of path length from the soma. Pyramidal connectivity motif frequencies are predicted accurately using a configuration model of random graphs. Pyramidal cells receiving more connections from nearby cells exhibit stronger and more reliable visual responses. Sample code shows data access and analysis.

Statistical Perspective on Functional and Causal Neural Connectomics: A Comparative Study

Representation of brain network interactions is fundamental to the translation of neural structure to brain function. As such, methodologies for mapping neural interactions into structural models, i.e., inference of functional connectome from neural recordings, are key for the study of brain networks. While multiple approaches have been proposed for functional connectomics based on statistical associations between neural activity, association does not necessarily incorporate causation. Additional approaches have been proposed to incorporate aspects of causality to turn functional connectomes into causal functional connectomes, however, these methodologies typically focus on specific aspects of causality. This warrants a systematic statistical framework for causal functional connectomics that defines the foundations of common aspects of causality. Such a framework can assist in contrasting existing approaches and to guide development of further causal methodologies. In this work, we develop such a statistical guide. In particular, we consolidate the notions of associations and representations of neural interaction, i.e., types of neural connectomics, and then describe causal modeling in the statistics literature. We particularly focus on the introduction of directed Markov graphical models as a framework through which we define the Directed Markov Property—an essential criterion for examining the causality of proposed functional connectomes. We demonstrate how based on these notions, a comparative study of several existing approaches for finding causal functional connectivity from neural activity can be conducted. We proceed by providing an outlook ahead regarding the additional properties that future approaches could include to thoroughly address causality.

Autonomous inference of complex network dynamics from incomplete and noisy data

The availability of empirical data that capture the structure and behaviour of complex networked systems has been greatly increased in recent years; however, a versatile computational toolbox for unveiling a complex system's nodal and interaction dynamics from data remains elusive. Here we develop a two-phase approach for the autonomous inference of complex network dynamics, and its effectiveness is demonstrated by the tests of inferring neuronal, genetic, social and coupled oscillator dynamics on various synthetic and real networks. Importantly, the approach is robust to incompleteness and noises, including low resolution, observational and dynamical noises, missing and spurious links, and dynamical heterogeneity. We apply the two-phase approach to infer the early spreading dynamics of influenza A flu on the worldwide airline network, and the inferred dynamical equation can also capture the spread of severe acute respiratory syndrome and coronavirus disease 2019. These findings together offer an avenue to discover the hidden microscopic mechanisms of a broad array of real networked systems.

Neuropeptidergic regulation of compulsive ethanol seeking in C. elegans

Despite the catastrophic consequences of alcohol abuse, alcohol use disorders (AUD) and comorbidities continue to strain the healthcare system, largely due to the effects of alcohol-seeking behavior. An improved understanding of the molecular basis of alcohol seeking will lead to enriched treatments for these disorders. Compulsive alcohol seeking is characterized by an imbalance between the superior drive to consume alcohol and the disruption or erosion in control of alcohol use. To model the development of compulsive engagement in alcohol seeking, we simultaneously exploited two distinct and conflicting Caenorhabditis elegans behavioral programs, ethanol preference and avoidance of aversive stimulus. We demonstrate that the C. elegans model recapitulated the pivotal features of compulsive alcohol seeking in mammals, specifically repeated attempts, endurance, and finally aversion-resistant alcohol seeking. We found that neuropeptide signaling via SEB-3, a CRF receptor-like GPCR, facilitates the development of ethanol preference and compels animals to seek ethanol compulsively. Furthermore, our functional genomic approach and behavioral elucidation suggest that the SEB-3 regulates another neuropeptidergic signaling, the neurokinin receptor orthologue TKR-1, to facilitate compulsive ethanol-seeking behavior.

Cortical Representation of Touch in Silico

With its six layers and ~ 12,000 neurons, a cortical column is a complex network whose function is plausibly greater than the sum of its constituents'. Functional characterization of its network components will require going beyond the brute-force modulation of the neural activity of a small group of neurons. Here we introduce an open-source, biologically inspired, computationally efficient network model of the somatosensory cortex's granular and supragranular layers after reconstructing the barrel cortex in soma resolution. Comparisons of the network activity to empirical observations showed that the in silico network replicates the known properties of touch representations and whisker deprivation-induced changes in synaptic strength induced in vivo. Simulations show that the history of the membrane potential acts as a spatial filter that determines the presynaptic population of neurons contributing to a post-synaptic action potential; this spatial filtering might be critical for synaptic integration of top-down and bottom-up information.

Modelling learning in C. elegans chemosensory and locomotive circuitry for T-maze navigation

Recently, a new type of Caenorhabditis elegans associative learning was reported, where nematodes learn to reach a target arm in an empty T‐maze, after they have successfully located reward (food) in the same side arm of a similar, baited, training maze. Here, we present a simplified mathematical model of C. elegans chemosensory and locomotive circuitry that replicates C. elegans navigation in a T‐maze and predicts the underlying mechanisms generating maze learning. Based on known neural circuitry, the model circuit responds to food‐released chemical cues by modulating motor neuron activity that drives simulated locomotion. We show that, through modulation of interneuron activity, such a circuit can mediate maze learning by acquiring a turning bias, even after a single training session. Simulated nematode maze navigation during training conditions in food‐baited mazes and during testing conditions in empty mazes is validated by comparing simulated behaviour with new experimental video data, extracted through the implementation of a custom‐made maze tracking algorithm. Our work provides a mathematical framework for investigating the neural mechanisms underlying this novel learning behaviour in C. elegans. Model results predict neuronal components involved in maze and spatial learning and identify target neurons and potential neural mechanisms for future experimental investigations into this learning behaviour.

Neural architectures in the light of comparative connectomics

Since the Cambrian, animals diversified from a few body forms or bauplans, into many extinct and all extant species. A characteristic neural architecture serves each bauplan. How the connectome of each animal differs from that of closely related species or whether it converged into an optimal architecture shared with more distant ones is unknown. Recent technological innovations in molecular biology, microscopy, digital data storage and processing, and computational neuroscience have lowered the barriers for whole-brain connectomics. Comparative connectomics of suitable, relatively small, representative species across the phylogenetic tree can infer the archetypal neural architecture of each bauplan and identify any circuits that possibly converged onto a shared and potentially optimal, structure.

Where the genome meets the connectome: Understanding how genes shape human brain connectivity

The integration of modern neuroimaging methods with genetically informative designs and data can shed light on the molecular mechanisms underlying the structural and functional organization of the human connectome. Here, we review studies that have investigated the genetic basis of human brain network structure and function through three complementary frameworks: (1) the quantification of phenotypic heritability through classical twin designs; (2) the identification of specific DNA variants linked to phenotypic variation through association and related studies; and (3) the analysis of correlations between spatial variations in imaging phenotypes and gene expression profiles through the integration of neuroimaging and transcriptional atlas data. We consider the basic foundations, strengths, limitations, and discoveries associated with each approach. We present converging evidence to indicate that anatomical connectivity is under stronger genetic influence than functional connectivity and that genetic influences are not uniformly distributed throughout the brain, with phenotypic variation in certain regions and connections being under stronger genetic control than others. We also consider how the combination of imaging and genetics can be used to understand the ways in which genes may drive brain dysfunction in different clinical disorders.

Black-box model reduction of the C. Elegans nervous system. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2021;2021:4174-4179. [PMID: 34892144 DOI: 10.1109/embc46164.2021.9630241]

In recent years, modeling neurons and neuronal collections with high accuracy have become central issues of neuroscience. The development of efficient algorithms for their simulation as well as the increase in computational power and parallelization need to keep up with the quantity and complexity of novel recordings and reconstructions reported by the experimental neuroscientists. The extraction of low-order equivalents that capture the essential aspects of the high-accuracy models is an essential part of the simulation process. The complexity of these models require the use of black-box data-oriented reduction approaches. We create a detailed model of the nervous system of a very known organism, C. Elegans, and show that it can be reduced using a modified data-driven model reduction method up to the order of 4 with very little loss in accuracy. The reduced model is able to predict the behaviour of the original for time ranges beyond the data used for the reduction.

A weighted network analysis framework for the hourglass effect-And its application in the C. elegans connectome

Understanding hierarchy and modularity in natural as well as technological networks is of utmost importance. A major aspect of such analysis involves identifying the nodes that are crucial to the overall processing structure of the network. More recently, the approach of hourglass analysis has been developed for the purpose of quantitatively analyzing whether only a few intermediate nodes mediate the information processing between a large number of inputs and outputs of a network. We develop a new framework for hourglass analysis that takes network weights into account while identifying the core nodes and the extent of hourglass effect in a given weighted network. We use this framework to study the structural connectome of the C. elegans and identify intermediate neurons that form the core of sensori-motor pathways in the organism. Our results show that the neurons forming the core of the connectome show significant differences across the male and hermaphrodite sexes, with most core nodes in the male concentrated in sex-organs while they are located in the head for the hermaphrodite. Our work demonstrates that taking weights into account for network analysis framework leads to emergence of different network patterns in terms of identification of core nodes and hourglass structure in the network, which otherwise would be missed by unweighted approaches.

Small brains for big science

As the study of the human brain is complicated by its sheer scale, complexity, and impracticality of invasive experiments, neuroscience research has long relied on model organisms. The brains of macaque, mouse, zebrafish, fruit fly, nematode, and others have yielded many secrets that advanced our understanding of the human brain. Here, we propose that adding miniature insects to this collection would reduce the costs and accelerate brain research. The smallest insects occupy a special place among miniature animals: despite their body sizes, comparable to unicellular organisms, they retain complex brains that include thousands of neurons. Their brains possess the advantages of those in insects, such as neuronal identifiability and the connectome stereotypy, yet are smaller and hence easier to map and understand. Finally, the brains of miniature insects offer insights into the evolution of brain design.

Sensory perception of environmental cues as a modulator of aging and neurodegeneration: Insights from Caenorhabditis elegans

Environmental stimuli such as temperature, food, and smell significantly influence the physiology and behavior of animals. Animals are differentially adapted to maintain their internal body functions in response to varied environmental conditions. These external cues are sensed by specialized neurons which are a part of the chemosensory and thermosensory systems. The inability to respond correctly to varied environmental conditions may result in compromised bodily functions and reduced longevity. For example, the ability to sense food is derived from the integrated action of olfactory and gustatory systems. The damage to the olfactory system will affect our decision of palatable food items which in turn can affect the response of the gustatory system, ultimately causing abnormal feeding habits. Recent studies have provided evidence that aging is regulated by sensory perception of environment. Aging is one of the most common causes of various neurodegenerative diseases and the perception of environmental cues is also found to regulate the development of neurodegenerative phenotype in several animal models. However, specific molecular signaling pathways involved in the process are not completely understood. The research conducted on one of the best-studied animal models of aging, Caenorhabditis elegans, has demonstrated multiple examples of gene-environment interaction at the neuronal level which affects life span. The findings may be useful to identify the key neuronal regulators of aging and age-related diseases in humans owing to conserved core metabolic and aging pathways from worms to humans.

Characterization of the Brain Functional Architecture of Psychostimulant Withdrawal Using Single-Cell Whole-Brain Imaging

Numerous brain regions have been identified as contributing to withdrawal behaviors, but it is unclear the way in which these brain regions as a whole lead to withdrawal. The search for a final common brain pathway that is involved in withdrawal remains elusive. To address this question, we implanted osmotic minipumps containing either saline, nicotine (24 mg/kg/d), cocaine (60 mg/kg/d), or methamphetamine (4 mg/kg/d) for one week in male C57BL/6J mice. After one week, the minipumps were removed and brains collected 8 h (saline, nicotine, and cocaine) or 12 h (methamphetamine) after removal. We then performed single-cell whole-brain imaging of neural activity during the withdrawal period when brains were collected. We used hierarchical clustering and graph theory to identify similarities and differences in brain functional architecture. Although methamphetamine and cocaine shared some network similarities, the main common neuroadaptation between these psychostimulant drugs was a dramatic decrease in modularity, with a shift from a cortical-driven to subcortical-driven network, including a decrease in total hub brain regions. These results demonstrate that psychostimulant withdrawal produces the drug-dependent remodeling of functional architecture of the brain and suggest that the decreased modularity of brain functional networks and not a specific set of brain regions may represent the final common pathway associated with withdrawal.

An asymmetric mechanical code ciphers curvature-dependent proprioceptor activity

A repetitive gait cycle is an archetypical component within the behavioral repertoire of many animals including humans. It originates from mechanical feedback within proprioceptors to adjust the motor program during locomotion and thus leads to a periodic orbit in a low-dimensional space. Here, we investigate the mechanics, molecules, and neurons responsible for proprioception in Caenorhabditis elegans to gain insight into how mechanosensation shapes the orbital trajectory to a well-defined limit cycle. We used genome editing, force spectroscopy, and multiscale modeling and found that alternating tension and compression with the spectrin network of a single proprioceptor encodes body posture and informs TRP-4/NOMPC and TWK-16/TREK2 homologs of mechanosensitive ion channels during locomotion. In contrast to a widely accepted model of proprioceptive “stretch” reception, we found that proprioceptors activated locally under compressive stresses in-vivo and in-vitro and propose that this property leads to compartmentalized activity within long axons delimited by curvature-dependent mechanical stresses.

C. elegans-based chemosensation strategy for the early detection of cancer metabolites in urine samples

Chemosensory receptors play a crucial role in distinguishing the wide range of volatile/soluble molecules by binding them with high accuracy. Chemosensation is the main sensory modality in organisms lacking long-range sensory mechanisms like vision/hearing. Despite its low number of sensory neurons, the nematode Caenorhabditis elegans possesses several chemosensory receptors, allowing it to detect about as many odorants as mammals. Here, we show that C. elegans displays attraction towards urine samples of women with breast cancer, avoiding control ones. Behavioral assays on animals lacking AWC sensory neurons demonstrate the relevance of these neurons in sensing cancer odorants: calcium imaging on AWC increases the accuracy of the discrimination (97.22%). Also, chemotaxis assays on animals lacking GPCRs expressed in AWC allow to identify receptors involved in binding cancer metabolites, suggesting that an alteration of a few metabolites is sufficient for the cancer discriminating behavior of C. elegans, which may help identify a fundamental fingerprint of breast cancer.

Connectomes across development reveal principles of brain maturation

An animal's nervous system changes as its body grows from birth to adulthood and its behaviours mature^1-8. The form and extent of circuit remodelling across the connectome is unknown^3,9-15. Here we used serial-section electron microscopy to reconstruct the full brain of eight isogenic Caenorhabditis elegans individuals across postnatal stages to investigate how it changes with age. The overall geometry of the brain is preserved from birth to adulthood, but substantial changes in chemical synaptic connectivity emerge on this consistent scaffold. Comparing connectomes between individuals reveals substantial differences in connectivity that make each brain partly unique. Comparing connectomes across maturation reveals consistent wiring changes between different neurons. These changes alter the strength of existing connections and create new connections. Collective changes in the network alter information processing. During development, the central decision-making circuitry is maintained, whereas sensory and motor pathways substantially remodel. With age, the brain becomes progressively more feedforward and discernibly modular. Thus developmental connectomics reveals principles that underlie brain maturation.

Bio-instantiated recurrent neural networks: Integrating neurobiology-based network topology in artificial networks

Biological neuronal networks (BNNs) are a source of inspiration and analogy making for researchers that focus on artificial neuronal networks (ANNs). Moreover, neuroscientists increasingly use ANNs as a model for the brain. Despite certain similarities between these two types of networks, important differences can be discerned. First, biological neural networks are sculpted by evolution and the constraints that it entails, whereas artificial neural networks are engineered to solve particular tasks. Second, the network topology of these systems, apart from some analogies that can be drawn, exhibits pronounced differences. Here, we examine strategies to construct recurrent neural networks (RNNs) that instantiate the network topology of brains of different species. We refer to such RNNs as bio-instantiated. We investigate the performance of bio-instantiated RNNs in terms of: (i) the prediction performance itself, that is, the capacity of the network to minimize the cost function at hand in test data, and (ii) speed of training, that is, how fast during training the network reaches its optimal performance. We examine bio-instantiated RNNs in working memory tasks where task-relevant information must be tracked as a sequence of events unfolds in time. We highlight the strategies that can be used to construct RNNs with the network topology found in BNNs, without sacrificing performance. Despite that we observe no enhancement of performance when compared to randomly wired RNNs, our approach demonstrates how empirical neural network data can be used for constructing RNNs, thus, facilitating further experimentation with biologically realistic network topologies, in contexts where such aspect is desired.

Methods for analyzing neuronal structure and activity in Caenorhabditis elegans

The model research animal Caenorhabditis elegans has unique properties making it particularly advantageous for studies of the nervous system. The nervous system is composed of a stereotyped complement of neurons connected in a consistent manner. Here, we describe methods for studying nervous system structure and function. The transparency of the animal makes it possible to visualize and identify neurons in living animals with fluorescent probes. These methods have been recently enhanced for the efficient use of neuron-specific reporter genes. Because of its simple structure, for a number of years, C. elegans has been at the forefront of connectomic studies defining synaptic connectivity by electron microscopy. This field is burgeoning with new, more powerful techniques, and recommended up-to-date methods are here described that encourage the possibility of new work in C. elegans. Fluorescent probes for single synapses and synaptic connections have allowed verification of the EM reconstructions and for experimental approaches to synapse formation. Advances in microscopy and in fluorescent reporters sensitive to Ca2+ levels have opened the way to observing activity within single neurons across the entire nervous system.

Maximum Entropy Principle Underlies Wiring Length Distribution in Brain Networks

A brain network comprises a substantial amount of short-range connections with an admixture of long-range connections. The portion of long-range connections in brain networks is observed to be quantitatively dissimilar across species. It is hypothesized that the length of connections is constrained by the spatial embedding of brain networks, yet fundamental principles that underlie the wiring length distribution remain unclear. By quantifying the structural diversity of a brain network using Shannon's entropy, here we show that the wiring length distribution across multiple species-including Drosophila, mouse, macaque, human, and C. elegans-follows the maximum entropy principle (MAP) under the constraints of limited wiring material and the spatial locations of brain areas or neurons. In addition, by considering stochastic axonal growth, we propose a network formation process capable of reproducing wiring length distributions of the 5 species, thereby implementing MAP in a biologically plausible manner. We further develop a generative model incorporating MAP, and show that, for the 5 species, the generated network exhibits high similarity to the real network. Our work indicates that the brain connectivity evolves to be structurally diversified by maximizing entropy to support efficient interareal communication, providing a potential organizational principle of brain networks.

Cellular connectomes as arbiters of local circuit models in the cerebral cortex

With the availability of cellular-resolution connectivity maps, connectomes, from the mammalian nervous system, it is in question how informative such massive connectomic data can be for the distinction of local circuit models in the mammalian cerebral cortex. Here, we investigated whether cellular-resolution connectomic data can in principle allow model discrimination for local circuit modules in layer 4 of mouse primary somatosensory cortex. We used approximate Bayesian model selection based on a set of simple connectome statistics to compute the posterior probability over proposed models given a to-be-measured connectome. We find that the distinction of the investigated local cortical models is faithfully possible based on purely structural connectomic data with an accuracy of more than 90%, and that such distinction is stable against substantial errors in the connectome measurement. Furthermore, mapping a fraction of only 10% of the local connectome is sufficient for connectome-based model distinction under realistic experimental constraints. Together, these results show for a concrete local circuit example that connectomic data allows model selection in the cerebral cortex and define the experimental strategy for obtaining such connectomic data.

Caenorhabditis elegans learning in a structured maze is a multisensory behavior

We show that C. elegans nematodes learn to associate food with a combination of proprioceptive cues and information on the structure of their surroundings (maze), perceived through mechanosensation. By using the custom-made Worm-Maze platform, we demonstrate that C. elegans young adults can locate food in T-shaped mazes and, following that experience, learn to reach a specific maze arm. C. elegans learning inside the maze is possible after a single training session, it resembles working memory, and it prevails over conflicting environmental cues. We provide evidence that the observed learning is a food-triggered multisensory behavior, which requires mechanosensory and proprioceptive input, and utilizes cues about the structural features of nematodes' environment and their body actions. The CREB-like transcription factor and dopamine signaling are also involved in maze performance. Lastly, we show that the observed aging-driven decline of C. elegans learning ability in the maze can be reversed by starvation.

Controlling network ensembles

The field of optimal control typically requires the assumption of perfect knowledge of the system one desires to control, which is an unrealistic assumption for biological systems, or networks, typically affected by high levels of uncertainty. Here, we investigate the minimum energy control of network ensembles, which may take one of a number of possible realizations. We ensure the controller derived can perform the desired control with a tunable amount of accuracy and we study how the control energy and the overall control cost scale with the number of possible realizations. Our focus is in characterizing the solution of the optimal control problem in the limit in which the systems are drawn from a continuous distribution, and in particular, how to properly pose the weighting terms in the objective function. We verify the theory in three examples of interest: a unidirectional chain network with uncertain edge weights and self-loop weights, a network where each edge weight is drawn from a given distribution, and the Jacobian of the dynamics corresponding to the cell signaling network of autophagy in the presence of uncertain parameters.

Application of the control usually requires complete knowledge of the system, which is rare for biological networks characterized by uncertainty. Klickstein et al. propose an optimal control for uncertain systems represented by network ensembles where only weight distributions for edges are known.

Circumventing neural damage in a C. elegans chemosensory circuit using genetically engineered synapses

Neuronal loss can considerably diminish neural circuit function, impairing normal behavior by disrupting information flow in the circuit. Here, we use genetically engineered electrical synapses to reroute the flow of information in a C. elegans damaged chemosensory circuit in order to restore organism behavior. We impaired chemotaxis by removing one pair of interneurons from the circuit then artificially coupled two other adjacent neuron pairs by ectopically expressing the gap junction protein, connexin, in them. This restored chemotaxis in the animals. We expected to observe linear and direct information flow between the connexin-coupled neurons in the recovered circuit but also revealed the formation of new potent left-right lateral electrical connections within the connexin-expressing neuron pairs. Our analysis suggests that these additional electrical synapses help restore circuit function by amplifying weakened neuronal signals in the damaged circuit in addition to emulating the wild-type circuit. A record of this paper's transparent peer review process is included in the Supplemental Information.

Computing Temporal Sequences Associated With Dynamic Patterns on the C. elegans Connectome

Understanding how the structural connectivity and spatial geometry of a network constrains the dynamics it is able to support is an active and open area of research. We simulated the plausible dynamics resulting from the known C. elegans connectome using a recent model and theoretical analysis that computes the dynamics of neurobiological networks by focusing on how local interactions among connected neurons give rise to the global dynamics in an emergent way. We studied the dynamics which resulted from stimulating a chemosensory neuron (ASEL) in a known feeding circuit, both in isolation and embedded in the full connectome. We show that contralateral motorneuron activations in ventral (VB) and dorsal (DB) classes of motorneurons emerged from the simulations, which are qualitatively similar to rhythmic motorneuron firing pattern associated with locomotion of the worm. One interpretation of these results is that there is an inherent-and we propose-purposeful structural wiring to the C. elegans connectome that has evolved to serve specific behavioral functions. To study network signaling pathways responsible for the dynamics we developed an analytic framework that constructs Temporal Sequences (TSeq), time-ordered walks of signals on graphs. We found that only 5% of TSeq are preserved between the isolated feeding network relative to its embedded counterpart. The remaining 95% of signaling pathways computed in the isolated network are not present in the embedded network. This suggests a cautionary note for computational studies of isolated neurobiological circuits and networks.

Structural and developmental principles of neuropil assembly in C. elegans

Neuropil is a fundamental form of tissue organization within the brain¹, in which densely packed neurons synaptically interconnect into precise circuit architecture^2,3. However, the structural and developmental principles that govern this nanoscale precision remain largely unknown^4,5. Here we use an iterative data coarse-graining algorithm termed 'diffusion condensation'⁶ to identify nested circuit structures within the Caenorhabditis elegans neuropil, which is known as the nerve ring. We show that the nerve ring neuropil is largely organized into four strata that are composed of related behavioural circuits. The stratified architecture of the neuropil is a geometrical representation of the functional segregation of sensory information and motor outputs, with specific sensory organs and muscle quadrants mapping onto particular neuropil strata. We identify groups of neurons with unique morphologies that integrate information across strata and that create neural structures that cage the strata within the nerve ring. We use high resolution light-sheet microscopy^7,8 coupled with lineage-tracing and cell-tracking algorithms^9,10 to resolve the developmental sequence and reveal principles of cell position, migration and outgrowth that guide stratified neuropil organization. Our results uncover conserved structural design principles that underlie the architecture and function of the nerve ring neuropil, and reveal a temporal progression of outgrowth-based on pioneer neurons-that guides the hierarchical development of the layered neuropil. Our findings provide a systematic blueprint for using structural and developmental approaches to understand neuropil organization within the brain.

A multi-scale brain map derived from whole-brain volumetric reconstructions

Animal nervous system organization is crucial for all body functions and its disruption can lead to severe cognitive and behavioural impairment1. This organization relies on features across scales-from the localization of synapses at the nanoscale, through neurons, which possess intricate neuronal morphologies that underpin circuit organization, to stereotyped connections between different regions of the brain2. The sheer complexity of this organ means that the feat of reconstructing and modelling the structure of a complete nervous system that is integrated across all of these scales has yet to be achieved. Here we present a complete structure-function model of the main neuropil in the nematode Caenorhabditis elegans-the nerve ring-which we derive by integrating the volumetric reconstructions from two animals with corresponding3 synaptic and gap-junctional connectomes. Whereas previously the nerve ring was considered to be a densely packed tract of neural processes, we uncover internal organization and show how local neighbourhoods spatially constrain and support the synaptic connectome. We find that the C. elegans connectome is not invariant, but that a precisely wired core circuit is embedded in a background of variable connectivity, and identify a candidate reference connectome for the core circuit. Using this reference, we propose a modular network architecture of the C. elegans brain that supports sensory computation and integration, sensorimotor convergence and brain-wide coordination. These findings reveal scalable and robust features of brain organization that may be universal across phyla.

Generalizable Machine Learning in Neuroscience Using Graph Neural Networks

Although a number of studies have explored deep learning in neuroscience, the application of these algorithms to neural systems on a microscopic scale, i.e. parameters relevant to lower scales of organization, remains relatively novel. Motivated by advances in whole-brain imaging, we examined the performance of deep learning models on microscopic neural dynamics and resulting emergent behaviors using calcium imaging data from the nematode C. elegans. As one of the only species for which neuron-level dynamics can be recorded, C. elegans serves as the ideal organism for designing and testing models bridging recent advances in deep learning and established concepts in neuroscience. We show that neural networks perform remarkably well on both neuron-level dynamics prediction and behavioral state classification. In addition, we compared the performance of structure agnostic neural networks and graph neural networks to investigate if graph structure can be exploited as a favourable inductive bias. To perform this experiment, we designed a graph neural network which explicitly infers relations between neurons from neural activity and leverages the inferred graph structure during computations. In our experiments, we found that graph neural networks generally outperformed structure agnostic models and excel in generalization on unseen organisms, implying a potential path to generalizable machine learning in neuroscience.

On the structural connectivity of large-scale models of brain networks at cellular level

The brain’s structural connectivity plays a fundamental role in determining how neuron networks generate, process, and transfer information within and between brain regions. The underlying mechanisms are extremely difficult to study experimentally and, in many cases, large-scale model networks are of great help. However, the implementation of these models relies on experimental findings that are often sparse and limited. Their predicting power ultimately depends on how closely a model’s connectivity represents the real system. Here we argue that the data-driven probabilistic rules, widely used to build neuronal network models, may not be appropriate to represent the dynamics of the corresponding biological system. To solve this problem, we propose to use a new mathematical framework able to use sparse and limited experimental data to quantitatively reproduce the structural connectivity of biological brain networks at cellular level.

A Neuromechanical Model of Multiple Network Rhythmic Pattern Generators for Forward Locomotion in C. elegans

Multiple mechanisms contribute to the generation, propagation, and coordination of the rhythmic patterns necessary for locomotion in Caenorhabditis elegans. Current experiments have focused on two possibilities: pacemaker neurons and stretch-receptor feedback. Here, we focus on whether it is possible that a chain of multiple network rhythmic pattern generators in the ventral nerve cord also contribute to locomotion. We use a simulation model to search for parameters of the anatomically constrained ventral nerve cord circuit that, when embodied and situated, can drive forward locomotion on agar, in the absence of pacemaker neurons or stretch-receptor feedback. Systematic exploration of the space of possible solutions reveals that there are multiple configurations that result in locomotion that is consistent with certain aspects of the kinematics of worm locomotion on agar. Analysis of the best solutions reveals that gap junctions between different classes of motorneurons in the ventral nerve cord can play key roles in coordinating the multiple rhythmic pattern generators.

Comprehensive Perspectives on Experimental Models for Parkinson's Disease

Parkinson’s disease (PD) ranks second among the most common neurodegenerative diseases, characterized by progressive and selective loss of dopaminergic neurons. Various cross-species preclinical models, including cellular models and animal models, have been established through the decades to study the etiology and mechanism of the disease from cell lines to nonhuman primates. These models are aimed at developing effective therapeutic strategies for the disease. None of the current models can replicate all major pathological and clinical phenotypes of PD. Selection of the model for PD largely relies on our interest of study. In this review, we systemically summarized experimental PD models, including cellular and animal models used in preclinical studies, to understand the pathogenesis of PD. This review is intended to provide current knowledge about the application of these different PD models, with focus on their strengths and limitations with respect to their contributions to the assessment of the molecular pathobiology of PD and identification of the therapeutic strategies for the disease.

Searching for Errors in Models of Complex Dynamic Systems

Mathematical modeling is seen as a key step to understand, predict, and control the temporal dynamics of interacting systems in such diverse areas like physics, biology, medicine, and economics. However, for large and complex systems we usually have only partial knowledge about the network, the coupling functions, and the interactions with the environment governing the dynamic behavior. This incomplete knowledge induces structural model errors which can in turn be the cause of erroneous model predictions or misguided interpretations. Uncovering the location of such structural model errors in large networks can be a daunting task for a modeler. Here, we present a data driven method to search for structural model errors and to confine their position in large and complex dynamic networks. We introduce a coherence measure for pairs of network nodes, which indicates, how difficult it is to distinguish these nodes as sources of an error. By clustering network nodes into coherence groups and inferring the cluster inputs we can decide, which cluster is affected by an error. We demonstrate the utility of our method for the C. elegans neural network, for a signal transduction model for UV-B light induced morphogenesis and for synthetic examples.

Test of robustness of pharyngeal neural networks in Caenorhabditis elegans

The nematode worm Caenorhabditis elegans is a model for deciphering the neural circuitry that transmits information from sensory organ to muscle tissue. It is also studied for disentangling the characteristics of the network, the efficiency of its design, and for testing theoretical models on how information is encoded. For this study, the efficiency of the synaptic connections was studied by testing the robustness of the neural network. A randomization test of robustness was applied to previously computed neural modules of the pharynx of C. elegans. The results support robustness as a reason for the observed over connectiveness across the pharyngeal system. In addition, rare events of single-neuron loss may expectedly lead to loss of function in a neural system.

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.

On the Modeling of the Three Types of Non-spiking Neurons of the Caenorhabditis elegans

The nematode Caenorhabditis elegans (C. elegans) is a well-known model organism in neuroscience. The relative simplicity of its nervous system, made up of few hundred neurons, shares some essential features with more sophisticated nervous systems, including the human one. If we are able to fully characterize the nervous system of this organism, we will be one step closer to understanding the mechanisms underlying the behavior of living things. Following a recently conducted electrophysiological survey on different C. elegans neurons, this paper aims at modeling the three non-spiking RIM, AIY and AFD neurons (arbitrarily named with three upper case letters by convention). To date, they represent the three possible forms of non-spiking neuronal responses of the C. elegans. To achieve this objective, we propose a conductance-based neuron model adapted to the electrophysiological features of each neuron. These features are based on current biological research and a series of in-silico experiments which use differential evolution to fit the model to experimental data. From the obtained results, we formulate a series of biological hypotheses regarding currents involved in the neuron dynamics. These models reproduce experimental data with a high degree of accuracy while being biologically consistent with state-of-the-art research.