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 diagram is known. We focus on the organization of the system into modules, i.e., neuronal groups having relatively higher connection density compared to that of the overall network. We show that this mesoscopic feature cannot be explained exclusively in terms of considerations, such as optimizing for resource constraints (viz., total wiring cost) and communication efficiency (i.e., network path length). Comparison with other complex networks designed for efficient transport (of signals or resources) implies that neuronal networks form a distinct class. This suggests that the principal function of the network, viz., processing of sensory information resulting in appropriate motor response, may be playing a vital role in determining the connection topology. Using modular spectral analysis, we make explicit the intimate relation between function and structure in the nervous system. This is further brought out by identifying functionally critical neurons purely on the basis of patterns of intra- and inter-modular connections. Our study reveals how the design of the nervous system reflects several constraints, including its key functional role as a processor of information.
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…
Synthetic lethality, the finding that the simultaneous knockout of two or more individually non-essential genes leads to cell or organism death, has offered a systematic framework to explore cellular function, and also offered therapeutic applications. Yet, the concept lacks its parallel in neuroscience - a systematic knowledge base on the role of double or higher order ablations in the functioning of a neural system. Here, we use the framework of network control to systematically predict the ablation of neuron pairs and triplets. We find that surprisingly small sets of 58 pairs and 46 triplet…
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…
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…
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…
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…
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…
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,…
Spatially-embedded complex networks, such as nervous systems, the Internet and transportation networks, generally have non-trivial topological patterns of connections combined with nearly minimal wiring costs. However the growth rules shaping these economical trade-offs between cost and topology are not well understood. Here we study the cellular nervous system of the nematode worm C. elegans, together with information on the birth times of neurons and on their spatial locations. We find that the growth of this network undergoes a transition from an accelerated to a constant increase in the nu…
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 analyse the neural dynamics and its relation with the emergent behaviour of a robotic vehicle that is controlled by a neural network numerical simulation based on the nervous system of the nematode Caenorhabditis elegans. The robot interacts with the environment through a sensor, that transmits the information to sensory neurons, while motor neurons outputs are connected to wheels. This is enough to allow robot movement in complex environments, avoiding collisions with obstacles. Working with a robotic model makes it possible to keep track simultaneously of the detailed microscopic dynamics…
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…
National Autonomous University of Mexico（墨西哥国立自治大学）；Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学）
The nervous system of the nematode soil worm Caenorhabditis elegans exhibits remarkable complexity despite the worm's small size. A general challenge is to better understand the relationship between neural organization and neural activity at the system level, including the functional roles of inhibitory connections. Here we implemented an abstract simulation model of the C. elegans connectome that approximates the neurotransmitter identity of each neuron, and we explored the functional role of these physiological differences for neural activity. In particular, we created a Hopfield neural netw…
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…
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…
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…
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 …
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…
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）
Self-regulated emergence of heavy-tailed weight distributions in evolving complex network architectures
KU Leuven（荷语鲁汶大学）；Center for Cognitive Science, University of Kaiserslautern-Landau（凯泽斯劳滕-兰道大学认知科学中心）；NICE Research Group, Computer Science Research Centre, University of Surrey（萨里大学计算机研究中心NICE研究组）；Institute of Optics, Spanish National Research Council (CSIC)（西班牙国家研究理事会光学研究所）；Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire des Signaux et Systèmes（巴黎萨克雷大学、法国国家科学研究中心、中央苏佩莱克学院信号与系统实验室）
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…
Neural connectivity at the cellular and mesoscopic level appears very specific and is presumed to arise from highly specific developmental mechanisms. However, there are general shared features of connectivity in systems as different as the networks formed by individual neurons in Caenorhabditis elegans or in rat visual cortex and the mesoscopic circuitry of cortical areas in the mouse, macaque, and human brain. In all these systems, connection length distributions have very similar shapes, with an initial large peak and a long flat tail representing the admixture of long-distance connections …
The glow of a starry night sky, the smell of a freshly brewed cup of coffee or the sound of ocean waves breaking on the beach are representations of the physical world that have been created by the dynamic interactions of thousands of neurons in our brains. How the brain mediates perceptions, creates thoughts, stores memories and initiates actions remains one of the most profound puzzles in biology, if not all of science. A key to a mechanistic understanding of how the nervous system works is the ability to analyze the dynamics of neuronal networks in the living organism in the context of sens…
