Despite recent interest in reconstructing neuronal networks, complete wiring diagrams on the level of individual synapses remain scarce and the insights into function they can provide remain unclear. Even for Caenorhabditis elegans, whose neuronal network is relatively small and stereotypical from animal to animal, published wiring diagrams are neither accurate nor complete and self-consistent. Using materials from White et al. and new electron micrographs we assemble whole, self-consistent gap junction and chemical synapse networks of hermaphrodite C. elegans. We propose a method to visualize the wiring diagram, which reflects network signal flow. We calculate statistical and topological properties of the network, such as degree distributions, synaptic multiplicities, and small-world properties, that help in understanding network signal propagation. We identify neurons that may play central roles in information processing and network motifs that could serve as functional modules of the network. We explore propagation of neuronal activity in response to sensory or artificial stimulation using linear systems theory and find several activity patterns that could serve as substrates of previously described behaviors. Finally, we analyze the interaction between the gap junction and the chemical synapse networks. Since several statistical properties of the C. elegans network, such as multiplicity and motif distributions are similar to those found in mammalian neocortex, they likely point to general principles of neuronal networks. The wiring diagram reported here can help in understanding the mechanistic basis of behavior by generating predictions about future experiments involving genetic perturbations, laser ablations, or monitoring propagation of neuronal activity in response to stimulation.
Avalanches with power-law distributed size parameters have been observed in neuronal networks. This observation might be a manifestation of the self-organized criticality (SOC). Yet, the physiological mechanicsm of this behavior is 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 an…
We develop a biophysical model of neuro-sensory integration in the model organism Caenorhabditis elegans. Building on recent experimental findings of the neuron conductances and their resolved connectome, we posit the first full dynamic model of the neural voltage excitations that allows for a characterization of input stimuli to behavioral responses. Thus a clear connection between receptory cell inputs to downstream motor-responses is illustrated, showing that robust, low-dimensional bifurcation structures dominate neural pathways of activity. The underlying bifurcation structures discovered…
Recordings of whole brain activity with single neuron resolution are now feasible in simple organisms. Yet, it is still challenging to appropriately simplify such complex, noisy, and multivariate data in order to reveal general principles of nervous system function. Here, we develop a method that allows us to extract global brain dynamics from pan-neuronal imaging. Success of this method is rooted in a surprising mathematical connection between dimensionality reduction and a general class of thermodynamic systems. Application of this theoretical framework to the nervous system of C. elegans re…
Despite the relative simplicity of C. elegans, its locomotion machinery is not yet well understood. We focus on the generation of dorsoventral body bends. While central pattern generators are commonly involved in animal locomotion, their presence in C. elegans has been questioned due to a lack of an evident neural circuit to support it. We developed a computational model grounded in the available neuroanatomy and neurophysiology and we used an evolutionary algorithm to explore the space of possible configurations of the circuit that matched the neural traces observed during forward and backwar…
A central problem of neuroscience involves uncovering the principles governing the organization of nervous systems which ensure robustness in brain development. The nematode Caenorhabditis elegans provides us with a model organism for studying this question. In this paper, we focus on the invariant connection structure and spatial arrangement of the neurons comprising the somatic neuronal network of this organism to understand the key developmental constraints underlying its design. We observe that neurons with certain shared characteristics - such as, neural process lengths, birth time cohort…
Connectomics has focused primarily on the mapping of synaptic links in the brain; yet it is well established that extrasynaptic volume transmission, especially via monoamines and neuropeptides, is also critical to brain function. Here we present a draft monoamine connectome, along with a partial neuropeptide connectome, for the nematode C. elegans, based on new and published expression data for biosynthetic genes and receptors. Thus, the neuronal connectome can be represented as a multiplex network, with synaptic, gap junction, and neuromodulatory layers representing alternative modes of inter…
The pharynx of the nematode Caenorhabditis elegans is a neuromuscular pump that exhibits two typical motions: pumping and peristalsis. While the dynamics of these motions are well characterized, the underlying mechanisms generating most of them are not known. In this paper, we propose comprehensive and detailed mechanisms that can explain the various observed dynamics of the different pharyngeal areas: the dynamics of the pumping muscles - corpus, anterior isthmus, and terminal bulb - and the peristalsis dynamics of the posterior isthmus muscles. While the suggested mechanisms are consistent w…
{\it Caenorhabditis elegans} nematode worms are the only animals with the known detailed neural connectivity diagram, well characterized genomics, and relatively simple quantifiable behavioral output. With this in mind, many researchers view this animal as the best candidate for a systems biology approach, where one can integrate molecular and cellular knowledge to gain global understanding of worm's behavior. This work reviews some research in this direction, emphasizing computational perspective, and points out some successes and challenges to meet this lofty goal.
A Benchmark Analysis of Graph and Non-Graph Methods for Caenorhabditis Elegans Neuron Classification
Department of Computer Science, Emory University, USA（计算机科学系，埃默里大学，美国）；Department of Biomedical Informatics, Emory University, USA（生物医学信息学系，埃默里大学，美国）；College of AI, Tsinghua University, China（人工智能学院，清华大学，中国）
Graph theoretical analyses of nervous systems usually omit the aspect of connection polarity, due to data insufficiency. The chemical synapse network of Caenorhabditis elegans is a well-reconstructed directed network, but the signs of its connections are yet to be elucidated. Here, we present the gene expression-based sign prediction of the ionotropic chemical synapse connectome of C. elegans (3,638 connections and 20,589 synapses total), incorporating available presynaptic neurotransmitter and postsynaptic receptor gene expression data for three major neurotransmitter systems. We made predict…
We introduce SIM-CE, an advanced, user-friendly modeling and simulation environment in Simulink for performing multi-scale behavioral analysis of the nervous system of Caenorhabditis elegans (C. elegans). SIM-CE contains an implementation of the mathematical models of C. elegans's neurons and synapses, in Simulink, which can be easily extended and particularized by the user. The Simulink model is able to capture both complex dynamics of ion channels and additional biophysical detail such as intracellular calcium concentration. We demonstrate the performance of SIM-CE by carrying out neuronal, …
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 hypothesise 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…
Caenorhabditis elegans (C. elegans) illustrated remarkable behavioral plasticities including complex non-associative and associative learning representations. Understanding the principles of such mechanisms presumably leads to constructive inspirations for the design of efficient learning algorithms. In the present study, we postulate a novel approach on modeling single neurons and synapses to study the mechanisms underlying learning in the C. elegans nervous system. In this regard, we construct a precise mathematical model of sensory neurons where we include multi-scale details from genes, io…
We exploit flow propagation on the directed neuronal network of the nematode Caenorhabditis elegans to reveal dynamically relevant features of its connectome. We find flow-based groupings of neurons at different levels of granularity, which we relate to functional and anatomical constituents of its nervous system. A systematic in silico evaluation of the full set of single and double neuron ablations is used to identify deletions that induce the most severe disruptions of the multi-resolution flow structure. Such ablations are linked to functionally relevant neurons, and suggest potential cand…
Experiments of pain with human subjects are difficult, subjective, and ethically constrained. Since the molecular mechanisms of pain transduction are reasonably conserved among different species, these problems are partially solved by the use of animal models. However, animals cannot easily communicate to us their own pain levels. Thus progress depends crucially on our ability to quantitatively and objectively infer the perceived level of noxious stimuli from the behavior of animals. Here we develop a quantitative model to infer the perceived level of thermal nociception from the stereotyped n…
Recent efforts in neuroscience research seek to obtain detailed anatomical neuronal wiring maps as well as information on how neurons in these networks engage in dynamic activities. Although the entire connectivity map of the nervous system of C. elegans has been known for more than 25 years, this knowledge has not been sufficient to predict all functional connections underlying behavior. To approach this goal, we developed a two-photon technique for brain-wide calcium imaging in C. elegans using wide-field temporal focusing (WF-TEFO). Pivotal to our results was the use of a nuclear-localized,…
The locomotion of Caenorhabditis elegans exhibits complex patterns. In particular, the worm combines mildly curved runs and sharp turns to steer its course. Both runs and sharp turns of various types are important components of taxis behavior. The statistics of sharp turns have been intensively studied. However, there have been few studies on runs, except for those on klinotaxis (also called weathervane mechanism), in which the worm gradually curves toward the direction with a high concentration of chemicals; this phenomenon was discovered recently. We analyzed the data of runs by excluding sh…
Determining neuronal identity in imaging data is an essential task in neuroscience, facilitating the comparison of neural activity across organisms. Cross-organism comparison, in turn, enables a wide variety of research including whole-brain analysis of functional networks and linking the activity of specific neurons to behavior or environmental stimuli. The recent development of three-dimensional, pan-neuronal imaging with single-cell resolution within Caenorhabditis elegans has brought neuron identification, tracking, and activity monitoring all within reach. The nematode C. elegans is often…
The nematode Caenorhabditis elegans, with information on neural connectivity, three-dimensional position and cell linage provides a unique system for understanding the development of neural networks. Although C. elegans has been widely studied in the past, we present the first statistical study from a developmental perspective, with findings that raise interesting suggestions on the establishment of long-distance connections and network hubs. Here, we analyze the neuro-development for temporal and spatial features, using birth times of neurons and their three-dimensional positions. Comparisons…
An Artificial Neural Network for Image Classification Inspired by Aversive Olfactory Learning Circuits in Caenorhabditis Elegans
Beijing Normal University（北京师范大学）；International Academic Center of Complex Systems, Beijing Normal University（北京师范大学复杂系统国际学术中心）；School of Systems Science, Beijing Normal University（北京师范大学系统科学学院）；School of Computer Science and Engineering, Tianjin University of Technology（天津理工大学计算机科学与工程学院）
Neural networks show a progressive increase in complexity during the time course of evolution. From diffuse nerve nets in Cnidaria to modular, hierarchical systems in macaque and humans, there is a gradual shift from simple processes involving a limited amount of tasks and modalities to complex functional and behavioral processing integrating different kinds of information from highly specialized tissue. However, studies in a range of species suggest that fundamental similarities, in spatial and topological features as well as in developmental mechanisms for network formation, are retained acr…
The connectome, or the entire connectivity of a neural system represented by network, ranges various scales from synaptic connections between individual neurons to fibre tract connections between brain regions. Although the modularity they commonly show has been extensively studied, it is unclear whether connection specificity of such networks can already be fully explained by the modularity alone. To answer this question, we study two networks, the neuronal network of C. elegans and the fibre tract network of human brains yielded through diffusion spectrum imaging (DSI). We compare them to th…
Undulatory locomotion is common to nematodes as well as to limbless vertebrates, but its control is not understood in spite of the identification of hundred of genes involved in Caenorhabditis elegans locomotion. To reveal the mechanisms of nematode undulatory locomotion, we quantitatively analyzed the movement of C. elegans with genetic perturbations to neurons, muscles, and skeleton (cuticle). We also compared locomotion of different Caenorhabditis species. We constructed a theoretical model that combines mechanics and biophysics, and that is constrained by the observations of propulsion and…
We propose a data-driven approach to represent neuronal network dynamics as a Probabilistic Graphical Model (PGM). Our approach learns the PGM structure by employing dimension reduction to network response dynamics evoked by stimuli applied to each neuron separately. The outcome model captures how stimuli propagate through the network and thus represents functional dependencies between neurons, i.e., functional connectome. The benefit of using a PGM as the functional connectome is that posterior inference can be done efficiently and circumvent the complexities in direct inference of response p…
Network structure or topology is the basis for understanding complex systems. Recently, higher-order structures have been considered as a new research direction that can provide new perspectives and phenomena. However, most existing studies have focused on simple 1-cycles and triangles, and few have explored the higher-order and non-trivial cycles. The current study focused on the cavity, which is a non-trivial cycle. We proposed a method to compute cavities with different orders based on pruning in the boundary matrix and calculated all cavities of the neural network of Caenorhabditis elegans…
We study the dynamics of the structure of a formal neural network wherein the strengths of the synapses are governed by spike-timing-dependent plasticity (STDP). For properly chosen input signals, there exists a steady state with a residual network. We compare the motif profile of such a network with that of a real neural network of \emph{C. elegans} and identify robust qualitative similarities. In particular, our extensive numerical simulations show that this STDP-driven resulting network is robust under variations of the model parameters.
We demonstrate a spiking neural network for navigation motivated by the chemotaxis network of Caenorhabditis elegans. Our network uses information regarding temporal gradients in the tracking variable's concentration to make navigational decisions. The gradient information is determined by mimicking the underlying mechanisms of the ASE neurons of C. elegans. Simulations show that our model is able to forage and track a target set-point in extremely noisy environments. We develop a VLSI implementation for the main gradient detector neurons, which could be integrated with standard comparator cir…
Brain research has been driven by enquiry for principles of brain structure organization and its control mechanisms. The neuronal wiring map of C. elegans, the only complete connectome available till date, presents an incredible opportunity to learn basic governing principles that drive structure and function of its neuronal architecture. Despite its apparently simple nervous system, C. elegans is known to possess complex functions. The neuronal architecture forms an important underlying framework which specifies phenotypic features associated to sensation, movement, conditioning and memory. I…
To find out the role of the wiring cost in the organization of the neural network of the nematode \textit{Caenorhapditis elegans} (\textit{C. elegans}), we build the neuronal map of \textit{C. elegans} based on geometrical positions of neurons and define the cost as inter-neuronal Euclidean distance \textit{d}. We show that the wiring probability decays exponentially as a function of \textit{d}. Using the edge exchanging method and the component placement optimization scheme, we show that positions of neurons are not randomly distributed but organized to reduce the total wiring cost. Furthermo…
We investigate how locomotory behavior is generated in the brain focusing on the paradigmatic connectome of nematode Caenorhabditis elegans (C. elegans) and on neuronal activity patterns that control forward locomotion. We map the neuronal network of the worm as a multilayer network that takes into account various neurotransmitters and neuropeptides. Using logistic regression analysis, we predict the neurons of the locomotory subnetwork. Combining Hindmarsh-Rose equations for neuronal activity with a leaky integrator model for muscular activity, we study the dynamics within this subnetwork and…
INESC-ID（INESC-ID（里斯本高等工程系统与计算机研究所））；IST Tecnico Lisboa（里斯本高等理工学院）；Universidade de Lisboa（里斯本大学）
Given the inner complexity of the human nervous system, insight into the dynamics of brain activity can be gained from understanding smaller and simpler organisms, such as the nematode C. Elegans. The behavioural and structural biology of these organisms is well-known, making them prime candidates for benchmarking modelling and simulation techniques. In these complex neuronal collections, classical, white-box modelling techniques based on intrinsic structural or behavioural information are either unable to capture the profound nonlinearities of the neuronal response to different stimuli or gen…
Probing the developing neural circuitry in Caenorhabditis elegans has enhanced our understanding of nervous systems. The C. elegans connectome, like those of other species, is characterized by a rich club of densely connected neurons embedded within a small-world architecture. This organization of neuronal connections, captured by quantitative network statistics, provides insight into the system's capacity to perform integrative computations. Yet these network measures are limited in their ability to detect weakly connected motifs, such as topological cavities, that may support the systems cap…
We study external, electrical perturbations and their responses in the brain dynamic network of the \textit{Caenorhabditis elegans} soil worm, given by the connectome of its large somatic nervous system. Our analysis is inspired by a realistic experiment where one stimulates externally specific parts of the brain and studies the persistent neural activity triggered in other cortical regions. In this work, we perturb groups of neurons that form communities, identified by the walktrap community detection method, by trains of stereotypical electrical Poissonian impulses and study the propagation …
The emerging field of optogenetics allows for optical activation or inhibition of neurons and other tissue in the nervous system. In 2005 optogenetic proteins were expressed in the nematode C. elegans for the first time. Since then, C. elegans has served as a powerful platform upon which to conduct optogenetic investigations of synaptic function, circuit dynamics and the neuronal basis of behavior. The C. elegans nervous system, consisting of 302 neurons, whose connectivity and morphology has been mapped completely, drives a rich repertoire of behaviors that are quantifiable by video microscop…
We develop an artificial neural circuit for contour tracking and navigation inspired by the chemotaxis of the nematode Caenorhabditis elegans. In order to harness the computational advantages spiking neural networks promise over their non-spiking counterparts, we develop a network comprising 7-spiking neurons with non-plastic synapses which we show is extremely robust in tracking a range of concentrations. Our worm uses information regarding local temporal gradients in sodium chloride concentration to decide the instantaneous path for foraging, exploration and tracking. A key neuron pair in th…
One of the biggest challenges in biology is to understand how activity at the cellular level of neurons, as a result of their mutual interactions, leads to the observed behavior of an organism responding to a variety of environmental stimuli. Investigating the intermediate or mesoscopic level of organization in the nervous system is a vital step towards understanding how the integration of micro-level dynamics results in macro-level functioning. In this paper, we have considered the somatic nervous system of the nematode Caenorhabditis elegans, for which the entire neuronal connectivity diagra…
We model the neuronal circuit of the C.elegans soil worm in terms of Hindmarsh-Rose systems of ordinary differential equations, dividing its circuit into six communities pointed out by the walktrap and Louvain methods. Using the numerical solution of these equations, we analyze important measures of dynamical complexity, namely synchronicity, the largest Lyapunov exponent, and the $Φ_{\mbox{AR}}$ auto-regressive integrated information theory measure, which has been suggested to reflect different levels of consciousness. We show that $Φ_{\mbox{AR}}$ provides a useful measure of the information …
Neuronal networks provide living organisms with the ability to process information. They are also characterized by abundant recurrent connections, which give rise to strong feedback that dictates their dynamics and endows them with fading (short-term) memory. The role of recurrence in long-term memory, on the other hand, is still unclear. Here we use the neuronal network of the roundworm C. elegans to show that recurrent architectures in living organisms can exhibit long-term memory without relying on specific hard-wired modules. A genetic algorithm reveals that the experimentally observed dyn…
As shown recently (arXiv:0801.3056), several types of neuronal complex networks involving non-linear integration-and-fire dynamics exhibit an abrupt activation along their transient regime. Interestingly, such an avalanche of activation has also been found to depend strongly on the topology of the networks: while the Erdős-Rény, Barabási-Albert, path-regular and path-transformed BA models exhibit well-defined avalanches; Watts-Strogatz and geographical structures present instead a gradual dispersion of activation amongst their nodes. The current work investigates such phenomena by considering …
The brain is one of the most studied and highly complex systems in the biological world. It is the information center behind all vertebrate and most invertebrate life, and thus has become a major focus in current research. While many of these studies have concentrated on studying the brain directly, our focus is the structure of the brain itself: at its core an interconnected network of nodes (neurons). A better understanding of the structural aspects of the brain should elucidate some of its functional properties. In this paper we analyze the brain of the nematode Caenorhabditis elegans. Cons…
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] 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 c…
A main goal in the analysis of a complex system is to infer its underlying network structure from time-series observations of its behaviour. The inference process is often done by using bi-variate similarity measures, such as the cross-correlation (CC), however, the main factors favouring or hindering its success are still puzzling. Here, we use synthetic neuron models in order to reveal the main topological properties that frustrate or facilitate inferring the underlying network from CC measurements. Specifically, we use pulse-coupled Izhikevich neurons connected as in the Caenorhabditis eleg…
The detection of neuronal communities is addressed with basis on two important concepts from neuroscience: facilitation of neuronal firing and nearly simultaneous beginning of activation of sets of neurons. More specifically, integrate-and-fire complex neuronal networks are activated at each of their nodes, and the dissemination of activation is monitored. As the activation received by each neuron accumulates, its firing gets facilitated. The time it takes for each neuron, other than the source, to receive the first non-zero input (beginning activation time) and the time for it to produce the …
Early brain connectivity development consists of multiple stages: birth of neurons, their migration and the subsequent growth of axons and dendrites. Each stage occurs within a certain period of time depending on types of neurons and cortical layers. Forming synapses between neurons either by growing axons starting at similar times for all neurons (much-overlapped time windows) or at different time points (less-overlapped) may affect the topological and spatial properties of neuronal networks. Here, we explore the extreme cases of axon formation especially concerning short-distance connectivit…
Transient and equilibrium synchronizations in complex neuronal networks as a consequence of dynamics induced by having sources placed at specific neurons are investigated. The basic integrate-and-fire neuron is adopted, and the dynamics is estimated computationally so as to obtain the activation at each node along each instant of time. In the transient case, the dynamics is implemented so as to conserve the total activation entering the system. In our equilibrium investigations, the internally stored activation is limited to the value of the respective threshold. The synchronization of the act…
In large neuronal networks, it is believed that functions emerge through the collective behavior of many interconnected neurons. Recently, the development of experimental techniques that allow simultaneous recording of calcium concentration from a large fraction of all neurons in Caenorhabditis elegans - a nematode with 302 neurons - creates the opportunity to ask if such emergence is universal, reaching down to even the smallest brains. Here, we measure the activity of 50+ neurons in C. elegans, and analyze the data by building the maximum entropy model that matches the mean activity and pair…
Complex systems in the real world can be modeled as a network of connected components. The human brain, as a network of neurons among which the interactions cause perception, is a complex network. Synchronization is a dynamical phenomenon that can be seen in the brain. The network topology has a remarkable impact on both the function and the dynamics of neural networks. In this research, synchronization of neural networks is scrutinized through creating various topologies. These networks include both excitatory and inhibitory neurons. We investigate the dynamics of different networks by random…
It has been suggested that neural systems across several scales of organization show optimal component placement, in which any spatial rearrangement of the components would lead to an increase of total wiring. Using extensive connectivity datasets for diverse neural networks combined with spatial coordinates for network nodes, we applied an optimization algorithm to the network layouts, in order to search for wire-saving component rearrangements. We found that optimized component rearrangements could substantially reduce total wiring length in all tested neural networks. Specifically, total wi…
The organization of the connectivity between mammalian cortical areas has become a major subject of study, because of its important role in scaffolding the macroscopic aspects of animal behavior and intelligence. In this study we present a computational reconstruction approach to the problem of network organization, by considering the topological and spatial features of each area in the primate cerebral cortex as subsidy for the reconstruction of the global cortical network connectivity. Starting with all areas being disconnected, pairs of areas with similar sets of features are linked togethe…
