Structural properties of the Caenorhabditis elegans neuronal network

Biophysical modeling of C. elegans neurons: Single ion currents and whole-cell dynamics of AWCon and RMD

C. elegans neuronal system constitutes the ideal framework for studying simple, yet realistic, neuronal activity, since the whole nervous system is fully characterized with respect to the exact number of neurons and the neuronal connections. Most recent efforts are devoted to investigate and clarify the signal processing and functional connectivity, which are at the basis of sensing mechanisms, signal transmission, and motor control. In this framework, a refined modelof whole neuron dynamics constitutes a key ingredient to describe the electrophysiological processes, both at thecellular and at the network scale. In this work, we present Hodgkin-Huxley-based models of ion channels dynamics black, built on data available both from C. elegans and from other organisms, expressing homologous channels. We combine these channel models to simulate the electrical activity oftwo among the most studied neurons in C. elegans, which display prototypical dynamics of neuronal activation, the chemosensory AWCON and the motor neuron RMD. Our model properly describes the regenerative responses of the two cells. We analyze in detail the role of ion currents, both in wild type and in in silico knockout neurons. Moreover, we specifically investigate the behavior of RMD, identifying a heterogeneous dynamical response which includes bistable regimes and sustained oscillations. We are able to assess the critical role of T-type calcium currents, carried by CCA-1 channels, and leakage currents in the regulation of RMD response. Overall, our results provide new insights in the activity of key C. elegans neurons. The developed mathematical framework constitute a basis for single-cell and neuronal networks analyses, opening new scenarios in the in silico modeling of C. elegans neuronal system.

Nervous-Like Circuits in the Ribosome Facts, Hypotheses and Perspectives

In the past few decades, studies on translation have converged towards the metaphor of a “ribosome nanomachine”; they also revealed intriguing ribosome properties challenging this view. Many studies have shown that to perform an accurate protein synthesis in a fluctuating cellular environment, ribosomes sense, transfer information and even make decisions. This complex “behaviour” that goes far beyond the skills of a simple mechanical machine has suggested that the ribosomal protein networks could play a role equivalent to nervous circuits at a molecular scale to enable information transfer and processing during translation. We analyse here the significance of this analogy and establish a preliminary link between two fields: ribosome structure-function studies and the analysis of information processing systems. This cross-disciplinary analysis opens new perspectives about the mechanisms of information transfer and processing in ribosomes and may provide new conceptual frameworks for the understanding of the behaviours of unicellular organisms.

Connectal coding: discovering the structures linking cognitive phenotypes to individual histories

Cognitive phenotypes characterize our memories, beliefs, skills, and preferences, and arise from our ancestral, developmental, and experiential histories. These histories are written into our brain structure through the building and modification of various brain circuits. Connectal coding, by way of analogy with neural coding, is the art, study, and practice of identifying the network structures that link cognitive phenomena to individual histories. We propose a formal statistical framework for connectal coding and demonstrate its utility in several applications spanning experimental modalities and phylogeny.

The application of degree related clustering coefficient in estimating the link predictability and predicting missing links of networks

Though a lot of valuable algorithms of link prediction have been created, it is still difficult to improve the accuracy of link prediction for some networks. Such difficulties may be due to the intrinsic topological features of these networks. To reveal the correlation between the network topology and the link predictability, we generate a group of artificial networks by keeping some structural features of an initial seed network. Based on these artificial networks and some real networks, we find that five topological measures including clustering coefficient, structural consistency, random walk entropy, network diameter, and average path length significantly show their impact on the link predictability. Then, we define a topological score that combines these important topological features. Specifically, it is an integration of structural consistency with degree-related clustering coefficient defined in this work. This topological score exhibits high correlation with the link predictability. Finally, we propose an algorithm for link prediction based on this topological score. Our experiment on eight real networks verifies good performance of this algorithm in link prediction, which supports the reasonability of the new topological score. This work could be insightful for the study of the link predictability.

Novel Technological Advances in Functional Connectomics in C. elegans

The complete structure and connectivity of the Caenorhabditis elegans nervous system ("mind of a worm") was first published in 1986, representing a critical milestone in the field of connectomics. The reconstruction of the nervous system (connectome) at the level of synapses provided a unique perspective of understanding how behavior can be coded within the nervous system. The following decades have seen the development of technologies that help understand how neural activity patterns are connected to behavior and modulated by sensory input. Investigations on the developmental origins of the connectome highlight the importance of role of neuronal cell lineages in the final connectivity matrix of the nervous system. Computational modeling of neuronal dynamics not only helps reconstruct the biophysical properties of individual neurons but also allows for subsequent reconstruction of whole-organism neuronal network models. Hence, combining experimental datasets with theoretical modeling of neurons generates a better understanding of organismal behavior. This review discusses some recent technological advances used to analyze and perturb whole-organism neuronal function along with developments in computational modeling, which allows for interrogation of both local and global neural circuits, leading to different behaviors. Combining these approaches will shed light into how neural networks process sensory information to generate the appropriate behavioral output, providing a complete understanding of the worm nervous system.

The Worm Connectome: Back to the Future

Large-scale efforts are underway to map the neuronal connectomes of various animal species. In 1986 White et al. reported the first complete reconstruction of the nervous system connectome of an animal. Largely through manual reconstruction of serial electron micrographs, the authors characterized the morphology of each of the 302 neurons of the adult nematode C. elegans, and mapped the chemical and electrical synapses that connect them. This wiring diagram has profoundly influenced behavioral neurobiology and network science, and it continues to offer a guide for the impact of connectomics on neurobiology.

The development of brain network hubs

Some brain regions have a central role in supporting integrated brain function, marking them as network hubs. Given the functional importance of hubs, it is natural to ask how they emerge during development and to consider how they shape the function of the maturing brain. Here, we review evidence examining how brain network hubs, both in structural and functional connectivity networks, develop over the prenatal, neonate, childhood, and adolescent periods. The available evidence suggests that structural hubs of the brain arise in the prenatal period and show a consistent spatial topography through development, but undergo a protracted period of consolidation that extends into late adolescence. In contrast, the hubs of brain functional networks show a more variable topography, being predominantly located in primary cortical areas in early development, before moving to association areas by late childhood. These findings suggest that while the basic anatomical infrastructure of hubs may be established early, the functional viability and integrative capacity of these areas undergoes extensive postnatal maturation. Not all findings are consistent with this view however. We consider methodological factors that might drive these inconsistencies, and which should be addressed to promote a more rigorous investigation of brain network development.

Glia-Neuron Interactions in Caenorhabditis elegans

Glia are abundant components of animal nervous systems. Recognized 170 years ago, concerted attempts to understand these cells began only recently. From these investigations glia, once considered passive filler material in the brain, have emerged as active players in neuron development and activity. Glia are essential for nervous system function, and their disruption leads to disease. The nematode Caenorhabditis elegans possesses glial types similar to vertebrate glia, based on molecular, morphological, and functional criteria, and has become a powerful model in which to study glia and their neuronal interactions. Facile genetic and transgenic methods in this animal allow the discovery of genes required for glial functions, and effects of glia at single synapses can be monitored by tracking neuron shape, physiology, or animal behavior. Here, we review recent progress in understanding glia-neuron interactions in C. elegans. We highlight similarities with glia in other animals, and suggest conserved emerging principles of glial function.

Neural Interactome: Interactive Simulation of a Neuronal System

Connectivity and biophysical processes determine the functionality of neuronal networks. We, therefore, developed a real-time framework, called Neural Interactome^,, to simultaneously visualize and interact with the structure and dynamics of such networks. Neural Interactome is a cross-platform framework, which combines graph visualization with the simulation of neural dynamics, or experimentally recorded multi neural time series, to allow application of stimuli to neurons to examine network responses. In addition, Neural Interactome supports structural changes, such as disconnection of neurons from the network (ablation feature). Neural dynamics can be explored on a single neuron level (using a zoom feature), back in time (using a review feature), and recorded (using presets feature). The development of the Neural Interactome was guided by generic concepts to be applicable to neuronal networks with different neural connectivity and dynamics. We implement the framework using a model of the nervous system of Caenorhabditis elegans (C. elegans) nematode, a model organism with resolved connectome and neural dynamics. We show that Neural Interactome assists in studying neural response patterns associated with locomotion and other stimuli. In particular, we demonstrate how stimulation and ablation help in identifying neurons that shape particular dynamics. We examine scenarios that were experimentally studied, such as touch response circuit, and explore new scenarios that did not undergo elaborate experimental studies.

Computational methods for identifying the critical nodes in biological networks

A biological network is complex. A group of critical nodes determines the quality and state of such a network. Increasing studies have shown that diseases and biological networks are closely and mutually related and that certain diseases are often caused by errors occurring in certain nodes in biological networks. Thus, studying biological networks and identifying critical nodes can help determine the key targets in treating diseases. The problem is how to find the critical nodes in a network efficiently and with low cost. Existing experimental methods in identifying critical nodes generally require much time, manpower and money. Accordingly, many scientists are attempting to solve this problem by researching efficient and low-cost computing methods. To facilitate calculations, biological networks are often modeled as several common networks. In this review, we classify biological networks according to the network types used by several kinds of common computational methods and introduce the computational methods used by each type of network.

Phase synchronization and intermittent behavior in healthy and Alzheimer-affected human-brain-based neural network

We study the dynamical proprieties of phase synchronization and intermittent behavior of neural systems using a network of networks structure based on an experimentally obtained human connectome for healthy and Alzheimer-affected brains. We consider a network composed of 78 neural subareas (subnetworks) coupled with a mean-field potential scheme. Each subnetwork is characterized by a small-world topology, composed of 250 bursting neurons simulated through a Rulkov model. Using the Kuramoto order parameter we demonstrate that healthy and Alzheimer-affected brains display distinct phase synchronization and intermittence properties as a function of internal and external coupling strengths. In general, for the healthy case, each subnetwork develops a substantial level of internal synchronization before a global stable phase-synchronization state has been established. For the unhealthy case, despite the similar internal subnetwork synchronization levels, we identify higher levels of global phase synchronization occurring even for relatively small internal and external coupling. Using recurrence quantification analysis, namely the determinism of the mean-field potential, we identify regions where the healthy and unhealthy networks depict nonstationary behavior, but the results denounce the presence of a larger region or intermittent dynamics for the case of Alzheimer-affected networks. A possible theoretical explanation based on two locally stable but globally unstable states is discussed.

Neuronal cell types in the fly: single-cell anatomy meets single-cell genomics

At around 150 000 neurons, the adult Drosophila melanogaster central nervous system is one of the largest species, for which a complete cellular catalogue is imminent. While numerically much simpler than mammalian brains, its complexity is still difficult to parse without grouping neurons into consistent types, which can number 1-1000 cells per hemisphere. We review how neuroanatomical and gene expression data are being used to discover neuronal types at scale. The correlation among multiple co-varying neuronal properties, including lineage, gene expression, morphology, connectivity, response properties and shared behavioral significance is essential to the definition of neuronal cell type. Initial studies comparing morphological and transcriptomic definitions of neuronal type suggest that these are highly consistent, but there is much to do to match these approaches brain-wide. Matched single-cell transcriptomic and morphological data provide an effective reference point to integrate other data types, including connectomics data. This will significantly enhance our ability to make functional predictions from brain wiring diagrams as well facilitating molecular genetic manipulation of neuronal types.

Plasticity of the Electrical Connectome of C. elegans

The specific patterns and functional properties of electrical synapses of a nervous system are defined by the neuron-specific complement of electrical synapse constituents. We systematically examined the molecular composition of the electrical connectome of the nematode C. elegans through a genome- and nervous-system-wide analysis of the expression patterns of the invertebrate electrical synapse constituents, the innexins. We observe highly complex combinatorial expression patterns throughout the nervous system and found that these patterns change in a strikingly neuron-type-specific manner throughout the nervous system when animals enter an insulin-controlled diapause arrest stage under harsh environmental conditions, the dauer stage. By analyzing several individual synapses, we demonstrate that dauer-specific electrical synapse remodeling is responsible for specific aspects of the altered locomotory and chemosensory behavior of dauers. We describe an intersectional gene regulatory mechanism involving terminal selector and FoxO transcription factors mediating dynamic innexin expression plasticity in a neuron-type- and environment-specific manner.

Solitary states in multiplex networks owing to competing interactions

Recent researches in network science demonstrate the coexistence of different types of interactions among the individuals within the same system. A wide range of situations appear in ecological and neuronal systems that incorporate positive and negative interactions. Also, there are numerous examples of systems that are best represented by the multiplex configuration. The present article investigates a possible scenario for the emergence of a newly observed remarkable phenomenon named as solitary state in coupled dynamical units in which one or a few units split off and behave differently from the other units. For this, we consider dynamical systems connected through a multiplex architecture in the presence of both positive and negative couplings. We explore our findings through analysis of the paradigmatic FitzHugh-Nagumo system in both equilibrium and periodic regimes on the top of a multiplex network having positive inter-layer and negative intra-layer interactions. We further substantiate our proposition using a periodic Lorenz system with the same scheme and show that an opposite scheme of competitive interactions may also work for the Lorenz system in the chaotic regime.

Genetically engineered animal models of Parkinson's disease: From worm to rodent

Parkinson's disease (PD) is a progressive neurological disorder characterised by aberrant accumulation of insoluble proteins, including alpha-synuclein, and a loss of dopaminergic neurons in the substantia nigra. The extended neurodegeneration leads to a drop of striatal dopamine levels responsible for disabling motor and non-motor impairments. Although the causes of the disease remain unclear, it is well accepted among the scientific community that the disorder may also have a genetic component. For that reason, the number of genetically engineered animal models has greatly increased over the past two decades, ranging from invertebrates to more complex organisms such as mice and rats. This trend is growing as new genetic variants associated with the disease are discovered. The EU Joint Programme - Neurodegenerative Disease Research (JPND) has promoted the creation of an online database aiming at summarising the different features of experimental models of Parkinson's disease. This review discusses available genetic models of PD and the extent to which they adequately mirror the human pathology and reflects on future development and uses of genetically engineered experimental models for the study of PD.

Terror in the dirt: Sensory determinants of host seeking in soil-transmitted mammalian-parasitic nematodes

Infection with gastrointestinal parasitic nematodes is a major cause of chronic morbidity and economic burden around the world, particularly in low-resource settings. Some parasitic nematode species, including the human-parasitic threadworm Strongyloides stercoralis and human-parasitic hookworms in the genera Ancylostoma and Necator, feature a soil-dwelling infective larval stage that seeks out hosts for infection using a variety of host-emitted sensory cues. Here, we review our current understanding of the behavioral responses of soil-dwelling infective larvae to host-emitted sensory cues, and the molecular and cellular mechanisms that mediate these responses. We also discuss the development of methods for transgenesis and CRISPR/Cas9-mediated targeted mutagenesis in Strongyloides stercoralis and the closely related rat parasite Strongyloides ratti. These methods have established S. stercoralis and S. ratti as genetic model systems for gastrointestinal parasitic nematodes and are enabling more detailed investigations into the neural mechanisms that underlie the sensory-driven behaviors of this medically and economically important class of parasites.

A Pipeline for Volume Electron Microscopy of the Caenorhabditis elegans Nervous System

The “connectome,” a comprehensive wiring diagram of synaptic connectivity, is achieved through volume electron microscopy (vEM) analysis of an entire nervous system and all associated non-neuronal tissues. White et al. (1986) pioneered the fully manual reconstruction of a connectome using Caenorhabditis elegans. Recent advances in vEM allow mapping new C. elegans connectomes with increased throughput, and reduced subjectivity. Current vEM studies aim to not only fill the remaining gaps in the original connectome, but also address fundamental questions including how the connectome changes during development, the nature of individuality, sexual dimorphism, and how genetic and environmental factors regulate connectivity. Here we describe our current vEM pipeline and projected improvements for the study of the C. elegans nervous system and beyond.

Web-Based Interfaces for Virtual C. elegans Neuron Model Definition, Network Configuration, Behavioral Experiment Definition and Experiment Results Visualization

The Si elegans platform targets the complete virtualization of the nematode Caenorhabditis elegans, and its environment. This paper presents a suite of unified web-based Graphical User Interfaces (GUIs) as the main user interaction point, and discusses their underlying technologies and methods. The user-friendly features of this tool suite enable users to graphically create neuron and network models, and behavioral experiments, without requiring knowledge of domain-specific computer-science tools. The framework furthermore allows the graphical visualization of all simulation results using a worm locomotion and neural activity viewer. Models, experiment definitions and results can be exported in a machine-readable format, thereby facilitating reproducible and cross-platform execution of in silico C. elegans experiments in other simulation environments. This is made possible by a novel XML-based behavioral experiment definition encoding format, a NeuroML XML-based model generation and network configuration description language, and their associated GUIs. User survey data confirms the platform usability and functionality, and provides insights into future directions for web-based simulation GUIs of C. elegans and other living organisms. The tool suite is available online to the scientific community and its source code has been made available.

Synaptic noise facilitates the emergence of self-organized criticality in the Caenorhabditis elegans neuronal network

Avalanches with power-law distributed size parameters have been observed in neuronal networks. This observation might be a manifestation of self-organized criticality (SOC). Yet, the physiological mechanisms of this behaviour are currently unknown. Describing synaptic noise as transmission failures mainly originating from the probabilistic nature of neurotransmitter release, this study investigates the potential of this noise as a mechanism for driving the functional architecture of the neuronal networks towards SOC. To this end, a simple finite state neuron model, with activity dependent and synapse specific failure probabilities, was built based on the known anatomical connectivity data of the nematode Ceanorhabditis elegans. Beginning from random values, it was observed that synaptic noise levels picked out a set of synapses and consequently an active subnetwork that generates power-law distributed neuronal avalanches. The findings of this study bring up the possibility that synaptic failures might be a component of physiological processes underlying SOC in neuronal networks.

VAST (Volume Annotation and Segmentation Tool): Efficient Manual and Semi-Automatic Labeling of Large 3D Image Stacks

Recent developments in serial-section electron microscopy allow the efficient generation of very large image data sets but analyzing such data poses challenges for software tools. Here we introduce Volume Annotation and Segmentation Tool (VAST), a freely available utility program for generating and editing annotations and segmentations of large volumetric image (voxel) data sets. It provides a simple yet powerful user interface for real-time exploration and analysis of large data sets even in the Petabyte range.

Theoretical Principles of Multiscale Spatiotemporal Control of Neuronal Networks: A Complex Systems Perspective

Success in the fine control of the nervous system depends on a deeper understanding of how neural circuits control behavior. There is, however, a wide gap between the components of neural circuits and behavior. We advance the idea that a suitable approach for narrowing this gap has to be based on a multiscale information-theoretic description of the system. We evaluate the possibility that brain-wide complex neural computations can be dissected into a hierarchy of computational motifs that rely on smaller circuit modules interacting at multiple scales. In doing so, we draw attention to the importance of formalizing the goals of stimulation in terms of neural computations so that the possible implementations are matched in scale to the underlying circuit modules.

Automated classification of synaptic vesicles in electron tomograms of C. elegans using machine learning

Synaptic vesicles (SVs) are a key component of neuronal signaling and fulfil different roles depending on their composition. In electron micrograms of neurites, two types of vesicles can be distinguished by morphological criteria, the classical “clear core” vesicles (CCV) and the typically larger “dense core” vesicles (DCV), with differences in electron density due to their diverse cargos. Compared to CCVs, the precise function of DCVs is less defined. DCVs are known to store neuropeptides, which function as neuronal messengers and modulators [1]. In C. elegans, they play a role in locomotion, dauer formation, egg-laying, and mechano- and chemosensation [2]. Another type of DCVs, also referred to as granulated vesicles, are known to transport Bassoon, Piccolo and further constituents of the presynaptic density in the center of the active zone (AZ), and therefore are important for synaptogenesis [3].

To better understand the role of different types of SVs, we present here a new automated approach to classify vesicles. We combine machine learning with an extension of our previously developed vesicle segmentation workflow, the ImageJ macro 3D ART VeSElecT. With that we reliably distinguish CCVs and DCVs in electron tomograms of C. elegans NMJs using image-based features. Analysis of the underlying ground truth data shows an increased fraction of DCVs as well as a higher mean distance between DCVs and AZs in dauer larvae compared to young adult hermaphrodites. Our machine learning based tools are adaptable and can be applied to study properties of different synaptic vesicle pools in electron tomograms of diverse model organisms.

Neuron dynamics variability and anomalous phase synchronization of neural networks

Anomalous phase synchronization describes a synchronization phenomenon occurring even for the weakly coupled network and characterized by a non-monotonous dependence of the synchronization strength on the coupling strength. Its existence may support a theoretical framework to some neurological diseases, such as Parkinson's and some episodes of seizure behavior generated by epilepsy. Despite the success of controlling or suppressing the anomalous phase synchronization in neural networks applying external perturbations or inducing ambient changes, the origin of the anomalous phase synchronization as well as the mechanisms behind the suppression is not completely known. Here, we consider networks composed of N = 2000 coupled neurons in a small-world topology for two well known neuron models, namely, the Hodgkin-Huxley-like and the Hindmarsh-Rose models, both displaying the anomalous phase synchronization regime. We show that the anomalous phase synchronization may be related to the individual behavior of the coupled neurons; particularly, we identify a strong correlation between the behavior of the inter-bursting-intervals of the neurons, what we call neuron variability, to the ability of the network to depict anomalous phase synchronization. We corroborate the ideas showing that external perturbations or ambient parameter changes that eliminate anomalous phase synchronization and at the same time promote small changes in the individual dynamics of the neurons, such that an increasing individual variability of neurons implies a decrease of anomalous phase synchronization. Finally, we demonstrate that this effect can be quantified using a well known recurrence quantifier, the "determinism." Moreover, the results obtained by the determinism are based on only the mean field potential of the network, turning these measures more suitable to be used in experimental situations.

Functionally asymmetric motor neurons contribute to coordinating locomotion of Caenorhabditis elegans

Locomotion circuits developed in simple animals, and circuit motifs further evolved in higher animals. To understand locomotion circuit motifs, they must be characterized in many models. The nematode Caenorhabditis elegans possesses one of the best-studied circuits for undulatory movement. Yet, for 1/6^th of the cholinergic motor neurons (MNs), the AS MNs, functional information is unavailable. Ventral nerve cord (VNC) MNs coordinate undulations, in small circuits of complementary neurons innervating opposing muscles. AS MNs differ, as they innervate muscles and other MNs asymmetrically, without complementary partners. We characterized AS MNs by optogenetic, behavioral and imaging analyses. They generate asymmetric muscle activation, enabling navigation, and contribute to coordination of dorso-ventral undulation as well as anterio-posterior bending wave propagation. AS MN activity correlated with forward and backward locomotion, and they functionally connect to premotor interneurons (PINs) for both locomotion regimes. Electrical feedback from AS MNs via gap junctions may affect only backward PINs.

From head to tail: a neuromechanical model of forward locomotion in Caenorhabditis elegans

With 302 neurons and a near-complete reconstruction of the neural and muscle anatomy at the cellular level, Caenorhabditis elegans is an ideal candidate organism to study the neuromechanical basis of behaviour. Yet despite the breadth of knowledge about the neurobiology, anatomy and physics of C. elegans, there are still a number of unanswered questions about one of its most basic and fundamental behaviours: forward locomotion. How the rhythmic pattern is generated and propagated along the body is not yet well understood. We report on the development and analysis of a model of forward locomotion that integrates the neuroanatomy, neurophysiology and body mechanics of the worm. Our model is motivated by experimental analysis of the structure of the ventral cord circuitry and the effect of local body curvature on nearby motoneurons. We developed a neuroanatomically grounded model of the head motoneuron circuit and the ventral nerve cord circuit. We integrated the neural model with an existing biomechanical model of the worm's body, with updated musculature and stretch receptors. Unknown parameters were evolved using an evolutionary algorithm to match the speed of the worm on agar. We performed 100 evolutionary runs and consistently found electrophysiological configurations that reproduced realistic control of forward movement. The ensemble of successful solutions reproduced key experimental observations that they were not designed to fit, including the wavelength and frequency of the propagating wave. Analysis of the ensemble revealed that head motoneurons SMD and RMD are sufficient to drive dorsoventral undulations in the head and neck and that short-range posteriorly directed proprioceptive feedback is sufficient to propagate the wave along the rest of the body.This article is part of a discussion meeting issue 'Connectome to behaviour: modelling C. elegans at cellular resolution'.

Sensorimotor integration in Caenorhabditis elegans: a reappraisal towards dynamic and distributed computations

The nematode Caenorhabditis elegans is a tractable model system to study locomotion, sensory navigation and decision-making. In its natural habitat, it is thought to navigate complex multisensory environments in order to find food and mating partners, while avoiding threats like predators or toxic environments. While research in past decades has shed much light on the functions and mechanisms of selected sensory neurons, we are just at the brink of understanding how sensory information is integrated by interneuron circuits for action selection in the worm. Recent technological advances have enabled whole-brain Ca2+ imaging and Ca2+ imaging of neuronal activity in freely moving worms. A common principle emerging across multiple studies is that most interneuron activities are tightly coupled to the worm's instantaneous behaviour; notably, these observations encompass neurons receiving direct sensory neuron inputs. The new findings suggest that in the C. elegans brain, sensory and motor representations are integrated already at the uppermost sensory processing layers. Moreover, these results challenge a perhaps more intuitive view of sequential feed-forward sensory pathways that converge onto premotor interneurons and motor neurons. We propose that sensorimotor integration occurs rather in a distributed dynamical fashion. In this perspective article, we will explore this view, discuss the challenges and implications of these discoveries on the interpretation and design of neural activity experiments, and discuss possible functions. Furthermore, we will discuss the broader context of similar findings in fruit flies and rodents, which suggest generalizable principles that can be learnt from this amenable nematode model organism.This article is part of a discussion meeting issue 'Connectome to behaviour: modelling C. elegans at cellular resolution'.

c302: a multiscale framework for modelling the nervous system of Caenorhabditis elegans

The OpenWorm project has the ambitious goal of producing a highly detailed in silico model of the nematode Caenorhabditis elegans. A crucial part of this work will be a model of the nervous system encompassing all known cell types and connections. The appropriate level of biophysical detail required in the neuronal model to reproduce observed high-level behaviours in the worm has yet to be determined. For this reason, we have developed a framework, c302, that allows different instances of neuronal networks to be generated incorporating varying levels of anatomical and physiological detail, which can be investigated and refined independently or linked to other tools developed in the OpenWorm modelling toolchain.

This article is part of a discussion meeting issue ‘Connectome to behaviour: modelling C. elegans at cellular resolution’.

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'.

Functional connectomics from neural dynamics: probabilistic graphical models for neuronal network of Caenorhabditis elegans

We propose an approach to represent neuronal network dynamics as a probabilistic graphical model (PGM). To construct the PGM, we collect time series of neuronal responses produced by the neuronal network and use singular value decomposition to obtain a low-dimensional projection of the time-series data. We then extract dominant patterns from the projections to get pairwise dependency information and create a graphical model for the full network. The outcome model is a functional connectome that captures how stimuli propagate through the network and thus represents causal dependencies between neurons and stimuli. We apply our methodology to a model of the Caenorhabditis elegans somatic nervous system to validate and show an example of our approach. The structure and dynamics of the C. elegans nervous system are well studied and a model that generates neuronal responses is available. The resulting PGM enables us to obtain and verify underlying neuronal pathways for known behavioural scenarios and detect possible pathways for novel scenarios.This article is part of a discussion meeting issue 'Connectome to behaviour: modelling C. elegans at cellular resolution'.

On the nature and use of models in network neuroscience

Network theory provides an intuitively appealing framework for studying relationships among interconnected brain mechanisms and their relevance to behaviour. As the space of its applications grows, so does the diversity of meanings of the term network model. This diversity can cause confusion, complicate efforts to assess model validity and efficacy, and hamper interdisciplinary collaboration. In this Review, we examine the field of network neuroscience, focusing on organizing principles that can help overcome these challenges. First, we describe the fundamental goals in constructing network models. Second, we review the most common forms of network models, which can be described parsimoniously along the following three primary dimensions: from data representations to first-principles theory; from biophysical realism to functional phenomenology; and from elementary descriptions to coarse-grained approximations. Third, we draw on biology, philosophy and other disciplines to establish validation principles for these models. We close with a discussion of opportunities to bridge model types and point to exciting frontiers for future pursuits.

Potential role of a ventral nerve cord central pattern generator in forward and backward locomotion in Caenorhabditis elegans

C. elegans locomotes in an undulatory fashion, generating thrust by propagating dorsoventral bends along its body. Although central pattern generators (CPGs) are typically involved in animal locomotion, their presence in C. elegans has been questioned, mainly because there has been no evident circuit that supports intrinsic network oscillations. With a fully reconstructed connectome, the question of whether it is possible to have a CPG in the ventral nerve cord (VNC) of C. elegans can be answered through computational models. We modeled a repeating neural unit based on segmentation analysis of the connectome. We then used an evolutionary algorithm to determine the unknown physiological parameters of each neuron so as to match the features of the neural traces of the worm during forward and backward locomotion. We performed 1,000 evolutionary runs and consistently found configurations of the neural circuit that produced oscillations matching the main characteristic observed in experimental recordings. In addition to providing an existence proof for the possibility of a CPG in the VNC, we suggest a series of testable hypotheses about its operation. More generally, we show the feasibility and fruitfulness of a methodology to study behavior based on a connectome, in the absence of complete neurophysiological details.

Evidence of Rentian Scaling of Functional Modules in Diverse Biological Networks

Biological networks have long been known to be modular, containing sets of nodes that are highly connected internally. Less emphasis, however, has been placed on understanding how intermodule connections are distributed within a network. Here, we borrow ideas from engineered circuit design and study Rentian scaling, which states that the number of external connections between nodes in different modules is related to the number of nodes inside the modules by a power-law relationship. We tested this property in a broad class of molecular networks, including protein interaction networks for six species and gene regulatory networks for 41 human and 25 mouse cell types. Using evolutionarily defined modules corresponding to known biological processes in the cell, we found that all networks displayed Rentian scaling with a broad range of exponents. We also found evidence for Rentian scaling in functional modules in the Caenorhabditis elegans neural network, but, interestingly, not in three different social networks, suggesting that this property does not inevitably emerge. To understand how such scaling may have arisen evolutionarily, we derived a new graph model that can generate Rentian networks given a target Rent exponent and a module decomposition as inputs. Overall, our work uncovers a new principle shared by engineered circuits and biological networks.

Higher-order clustering in networks

A fundamental property of complex networks is the tendency for edges to cluster. The extent of the clustering is typically quantified by the clustering coefficient, which is the probability that a length-2 path is closed, i.e., induces a triangle in the network. However, higher-order cliques beyond triangles are crucial to understanding complex networks, and the clustering behavior with respect to such higher-order network structures is not well understood. Here we introduce higher-order clustering coefficients that measure the closure probability of higher-order network cliques and provide a more comprehensive view of how the edges of complex networks cluster. Our higher-order clustering coefficients are a natural generalization of the traditional clustering coefficient. We derive several properties about higher-order clustering coefficients and analyze them under common random graph models. Finally, we use higher-order clustering coefficients to gain new insights into the structure of real-world networks from several domains.

Cellomics approach for high-throughput functional annotation of Caenorhabditis elegans neural network

In Caenorhabditis elegans, which has only 302 neurons, relationships between behaviors and neural networks are not easily elucidated. In this study, we proposed a novel cellomics approach enabling high-throughput and comprehensive exploration of the functions of a single neuron or a subset of neurons in a complex neural network on a particular behavior. To realize this, we combined optogenetics and Brainbow technologies. Using these technologies, we established a C. elegans library where opsin is labeled in a randomized pattern. Behavioral analysis on this library under light illumination enabled high-throughput annotation of neurons affecting target behaviors. We applied this approach to the egg-laying behavior of C. elegans and succeeded in high-throughput confirmation that hermaphrodite-specific neurons play an important role in the egg-laying behavior. This cellomics approach will lead to the accumulation of neurophysiological and behavioral data of the C. elegans neural network, which is necessary for constructing neuroanatomically grounded models of behavior.

Morphological Diversity Strongly Constrains Synaptic Connectivity and Plasticity

Synaptic connectivity between neurons is naturally constrained by the anatomical overlap of neuronal arbors, the space on the axon available for synapses, and by physiological mechanisms that form synapses at a subset of potential synapse locations. What is not known is how these constraints impact emergent connectivity in a circuit with diverse morphologies. We investigated the role of morphological diversity within and across neuronal types on emergent connectivity in a model of neocortical microcircuitry. We found that the average overlap between the dendritic and axonal arbors of different types of neurons determines neuron-type specific patterns of distance-dependent connectivity, severely constraining the space of possible connectomes. However, higher order connectivity motifs depend on the diverse branching patterns of individual arbors of neurons belonging to the same type. Morphological diversity across neuronal types, therefore, imposes a specific structure on first order connectivity, and morphological diversity within neuronal types imposes a higher order structure of connectivity. We estimate that the morphological constraints resulting from diversity within and across neuron types together lead to a 10-fold reduction of the entropy of possible connectivity configurations, revealing an upper bound on the space explored by structural plasticity.

Estimating the impact of structural directionality: How reliable are undirected connectomes?

Directionality is a fundamental feature of network connections. Most structural brain networks are intrinsically directed because of the nature of chemical synapses, which comprise most neuronal connections. Because of the limitations of noninvasive imaging techniques, the directionality of connections between structurally connected regions of the human brain cannot be confirmed. Hence, connections are represented as undirected, and it is still unknown how this lack of directionality affects brain network topology. Using six directed brain networks from different species and parcellations (cat, mouse, C. elegans, and three macaque networks), we estimate the inaccuracies in network measures (degree, betweenness, clustering coefficient, path length, global efficiency, participation index, and small-worldness) associated with the removal of the directionality of connections. We employ three different methods to render directed brain networks undirected: (a) remove unidirectional connections, (b) add reciprocal connections, and (c) combine equal numbers of removed and added unidirectional connections. We quantify the extent of inaccuracy in network measures introduced through neglecting connection directionality for individual nodes and across the network. We find that the coarse division between core and peripheral nodes remains accurate for undirected networks. However, hub nodes differ considerably when directionality is neglected. Comparing the different methods to generate undirected networks from directed ones, we generally find that the addition of reciprocal connections (false positives) causes larger errors in graph-theoretic measures than the removal of the same number of directed connections (false negatives). These findings suggest that directionality plays an essential role in shaping brain networks and highlight some limitations of undirected connectomes.

Multimodal sensory processing in Caenorhabditis elegans

Multisensory integration is a mechanism that allows organisms to simultaneously sense and understand external stimuli from different modalities. These distinct signals are transduced into neuronal signals that converge into decision-making neuronal entities. Such decision-making centres receive information through neuromodulators regarding the organism's physiological state and accordingly trigger behavioural responses. Despite the importance of multisensory integration for efficient functioning of the nervous system, and also the implication of dysfunctional multisensory integration in the aetiology of neuropsychiatric disease, little is known about the relative molecular mechanisms. Caenorhabditis elegans is an appropriate model system to study such mechanisms and elucidate the molecular ways through which organisms understand external environments in an accurate and coherent fashion.

Mesoscale connectomics

Brain cells communicate with one another via local and long-range synaptic connections. Structural connectivity is the foundation for neural function. Brain-wide connectivity can be described at macroscopic, mesoscopic and microscopic levels. The mesoscale connectome represents connections between neuronal types across different brain regions. Building a mesoscale connectome requires a detailed understanding of the cell type composition of different brain regions and the patterns of inputs and outputs that each of these cell types receives and forms, respectively. In this review, I discuss historical and contemporary tracing techniques in both anterograde and retrograde directions to map the input and output connections at population and individual cell levels, as well as imaging and network analysis approaches to build mesoscale connectomes for mammalian brains.

The control structure of the nematode Caenorhabditis elegans: Neuro-sensory integration and proprioceptive feedback

We develop a biophysically realistic model of the nematode C. elegans that includes: (i) its muscle structure and activation, (ii) key connectomic activation circuitry, and (iii) a weighted and time-dynamic proprioception. In combination, we show that these model components can reproduce the complex waveforms exhibited in C. elegans locomotive behaviors, chiefly omega turns. This is achieved via weighted, time-dependent suppression of the proprioceptive signal. Though speculative, such dynamics are biologically plausible due to the presence of neuromodulators which have recently been experimentally implicated in the escape response, which includes an omega turn. This is the first integrated neuromechanical model to reveal a mechanism capable of generating the complex waveforms observed in the behavior of C. elegans, thus contributing to a mathematical framework for understanding how control decisions can be executed at the connectome level in order to produce the full repertoire of observed behaviors.

Community Detection in Complex Networks via Clique Conductance

Network science plays a central role in understanding and modeling complex systems in many areas including physics, sociology, biology, computer science, economics, politics, and neuroscience. One of the most important features of networks is community structure, i.e., clustering of nodes that are locally densely interconnected. Communities reveal the hierarchical organization of nodes, and detecting communities is of great importance in the study of complex systems. Most existing community-detection methods consider low-order connection patterns at the level of individual links. But high-order connection patterns, at the level of small subnetworks, are generally not considered. In this paper, we develop a novel community-detection method based on cliques, i.e., local complete subnetworks. The proposed method overcomes the deficiencies of previous similar community-detection methods by considering the mathematical properties of cliques. We apply the proposed method to computer-generated graphs and real-world network datasets. When applied to networks with known community structure, the proposed method detects the structure with high fidelity and sensitivity. When applied to networks with no a priori information regarding community structure, the proposed method yields insightful results revealing the organization of these complex networks. We also show that the proposed method is guaranteed to detect near-optimal clusters in the bipartition case.

Structural and functional properties of a probabilistic model of neuronal connectivity in a simple locomotor network

Although, in most animals, brain connectivity varies between individuals, behaviour is often similar across a species. What fundamental structural properties are shared across individual networks that define this behaviour? We describe a probabilistic model of connectivity in the hatchling Xenopus tadpole spinal cord which, when combined with a spiking model, reliably produces rhythmic activity corresponding to swimming. The probabilistic model allows calculation of structural characteristics that reflect common network properties, independent of individual network realisations. We use the structural characteristics to study examples of neuronal dynamics, in the complete network and various sub-networks, and this allows us to explain the basis for key experimental findings, and make predictions for experiments. We also study how structural and functional features differ between detailed anatomical connectomes and those generated by our new, simpler, model (meta-model).