Structural Properties of the Caenorhabditis elegans Neuronal Network

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

Flow-Based Network Analysis of the Caenorhabditis elegans Connectome

We exploit flow propagation on the directed neuronal network of the nematode C. 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 candidates for further in vivo investigation. In addition, we use the directional patterns of incoming and outgoing network flows at all scales to identify flow profiles for the neurons in the connectome, without pre-imposing a priori categories. The four flow roles identified are linked to signal propagation motivated by biological input-response scenarios

Neural development features: Spatio-temporal development of the Caenorhabditis elegans neuronal network

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 of growth in C. elegans with random spatial network growth highlight two findings relevant to neural network development. First, most neurons which are linked by long-distance connections are born around the same time and early on, suggesting the possibility of early contact or interaction between connected neurons during development. Second, early-born neurons are more highly connected (tendency to form hubs) than later born neurons. This indicates that the longer time frame available to them might underlie high connectivity. Both outcomes are not observed for random connection formation. The study finds that around one-third of electrically coupled long-range connections are late forming, raising the question of what mechanisms are involved in ensuring their accuracy, particularly in light of the extremely invariant connectivity observed in C. elegans. In conclusion, the sequence of neural network development highlights the possibility of early contact or interaction in securing long-distance and high-degree connectivity

Systems level circuit model of C. elegans undulatory locomotion: mathematical modeling and molecular genetics

To establish the relationship between locomotory behavior and dynamics of neural circuits in the nematode C. elegans we combined molecular and theoretical approaches. In particular, we quantitatively analyzed the motion of C. elegans with defective synaptic GABA and acetylcholine transmission, defective muscle calcium signaling, and defective muscles and cuticle structures, and compared the data with our systems level circuit model. The major experimental findings are: (i) anterior-to-posterior gradients of body bending flex for almost all strains both for forward and backward motion, and for neuronal mutants, also analogous weak gradients of undulatory frequency, (ii) existence of some form of neuromuscular (stretch receptor) feedback, (iii) invariance of neuromuscular wavelength, (iv) biphasic dependence of frequency on synaptic signaling, and (v) decrease of frequency with increase of the muscle time constant. Based on (i) we hypothesize that the Central Pattern Generator (CPG) is located in the head both for forward and backward motion. Points (i) and (ii) are the starting assumptions for our theoretical model, whose dynamical patterns are qualitatively insensitive to the details of the CPG design if stretch receptor feedback is sufficiently strong and slow. The model reveals that stretch receptor coupling in the body wall is critical for generation of the neuromuscular wave. Our model agrees with our behavioral data(iii), (iv), and (v), and with other pertinent published data, e.g., that frequency is an increasing function of muscle gap-junction coupling.Comment: Neural control of C. elegans motion with genetic perturbation

Modular structure in C. elegans neural network and its response to external localized stimuli

Synchronization plays a key role in information processing in neuronal networks. Response of specific groups of neurons are triggered by external stimuli, such as visual, tactile or olfactory inputs. Neurons, however, can be divided into several categories, such as by physical location, functional role or topological clustering properties. Here we study the response of the electric junction C. elegans network to external stimuli using the partially forced Kuramoto model and applying the force to specific groups of neurons. Stimuli were applied to topological modules, obtained by the ModuLand procedure, to a ganglion, specified by its anatomical localization, and to the functional group composed of all sensory neurons. We found that topological modules do not contain purely anatomical groups or functional classes, corroborating previous results, and that stimulating different classes of neurons lead to very different responses, measured in terms of synchronization and phase velocity correlations. In all cases, however, the modular structure hindered full synchronization, protecting the system from seizures. More importantly, the responses to stimuli applied to topological and functional modules showed pronounced patterns of correlation or anti-correlation with other modules that were not observed when the stimulus was applied to ganglia.Comment: 23 pages, 6 figure

Colored Motifs Reveal Computational Building Blocks in the C. elegans Brain

Background: Complex networks can often be decomposed into less complex sub-networks whose structures can give hints about the functional organization of the network as a whole. However, these structural motifs can only tell one part of the functional story because in this analysis each node and edge is treated on an equal footing. In real networks, two motifs that are topologically identical but whose nodes perform very different functions will play very different roles in the network. Methodology/Principal Findings: Here, we combine structural information derived from the topology of the neuronal network of the nematode C. elegans with information about the biological function of these nodes, thus coloring nodes by function. We discover that particular colorations of motifs are significantly more abundant in the worm brain than expected by chance, and have particular computational functions that emphasize the feed-forward structure of information processing in the network, while evading feedback loops. Interneurons are strongly over-represented among the common motifs, supporting the notion that these motifs process and transduce the information from the sensor neurons towards the muscles. Some of the most common motifs identified in the search for significant colored motifs play a crucial role in the system of neurons controlling the worm's locomotion. Conclusions/Significance: The analysis of complex networks in terms of colored motifs combines two independent data sets to generate insight about these networks that cannot be obtained with either data set alone. The method is general and should allow a decomposition of any complex networks into its functional (rather than topological) motifs as long as both wiring and functional information is available

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

Information flow through a model of the C. elegans klinotaxis circuit

Understanding how information about external stimuli is transformed into behavior is one of the central goals of neuroscience. Here we characterize the information flow through a complete sensorimotor circuit: from stimulus, to sensory neurons, to interneurons, to motor neurons, to muscles, to motion. Specifically, we apply a recently developed framework for quantifying information flow to a previously published ensemble of models of salt klinotaxis in the nematode worm C. elegans. The models are grounded in the neuroanatomy and currently known neurophysiology of the worm. The unknown model parameters were optimized to reproduce the worm's behavior. Information flow analysis reveals several key principles underlying how the models operate: (1) Interneuron class AIY is responsible for integrating information about positive and negative changes in concentration, and exhibits a strong left/right information asymmetry. (2) Gap junctions play a crucial role in the transfer of information responsible for the information symmetry observed in interneuron class AIZ. (3) Neck motor neuron class SMB implements an information gating mechanism that underlies the circuit's state-dependent response. (4) The neck carries non-uniform distribution about changes in concentration. Thus, not all directions of movement are equally informative. Each of these findings corresponds to an experimental prediction that could be tested in the worm to greatly refine our understanding of the neural circuit underlying klinotaxis. Information flow analysis also allows us to explore how information flow relates to underlying electrophysiology. Despite large variations in the neural parameters of individual circuits, the overall information flow architecture circuit is remarkably consistent across the ensemble, suggesting that information flow analysis captures general principles of operation for the klinotaxis circuit

Characterizing Self-Developing Biological Neural Networks: A First Step Towards their Application To Computing Systems

Carbon nanotubes are often seen as the only alternative technology to silicon transistors. While they are the most likely short-term one, other longer-term alternatives should be studied as well. While contemplating biological neurons as an alternative component may seem preposterous at first sight, significant recent progress in CMOS-neuron interface suggests this direction may not be unrealistic; moreover, biological neurons are known to self-assemble into very large networks capable of complex information processing tasks, something that has yet to be achieved with other emerging technologies. The first step to designing computing systems on top of biological neurons is to build an abstract model of self-assembled biological neural networks, much like computer architects manipulate abstract models of transistors and circuits. In this article, we propose a first model of the structure of biological neural networks. We provide empirical evidence that this model matches the biological neural networks found in living organisms, and exhibits the small-world graph structure properties commonly found in many large and self-organized systems, including biological neural networks. More importantly, we extract the simple local rules and characteristics governing the growth of such networks, enabling the development of potentially large but realistic biological neural networks, as would be needed for complex information processing/computing tasks. Based on this model, future work will be targeted to understanding the evolution and learning properties of such networks, and how they can be used to build computing systems

Si elegans: a computational model of C. elegans muscle response to light

It has long been the goal of computational neuroscientists to understand animal nervous systems, but their vast complexity has made it very difficult to fully understand even basic functions such as movement. The C. elegans nematode offers the opportunity to study a fully described connectome and link neural network to behaviour. In this paper a model of the responses of the body wall muscle in C. elegans to a random light stimulus is presented. An algorithm has been developed that tracks synapses in the nematode nervous system from the stimulus in the phototaxis sensory neurons to the muscles cells. A linear second order model was used to calculate the isometric force in each of the C. elegans body wall muscle cells. The isometric force calculated resembles that of previous investigations in muscle modelling