Connectomic constraints on computation in feedforward networks of spiking neurons

Several efforts are currently underway to decipher the connectome or parts thereof in a variety of organisms. Ascertaining the detailed physiological properties of all the neurons in these connectomes, however, is out of the scope of such projects. It is therefore unclear to what extent knowledge of the connectome alone will advance a mechanistic understanding of computation occurring in these neural circuits, especially when the high-level function of the said circuit is unknown. We consider, here, the question of how the wiring diagram of neurons imposes constraints on what neural circuits can compute, when we cannot assume detailed information on the physiological response properties of the neurons. We call such constraints—that arise by virtue of the connectome—connectomic constraints on computation. For feedforward networks equipped with neurons that obey a deterministic spiking neuron model which satisfies a small number of properties, we ask if just by knowing the architecture of a network, we can rule out computations that it could be doing, no matter what response properties each of its neurons may have. We show results of this form, for certain classes of network architectures. On the other hand, we also prove that with the limited set of properties assumed for our model neurons, there are fundamental limits to the constraints imposed by network structure. Thus, our theory suggests that while connectomic constraints might restrict the computational ability of certain classes of network architectures, we may require more elaborate information on the properties of neurons in the network, before we can discern such results for other classes of networks.     

From Caenorhabditis elegans to the human connectome: a specific modular organization increases metabolic,functional and developmental efficiency

The connectome, or the entire connectivity of a neural system represented by a network, ranges across 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 the 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 Caenorhabditis elegans and the fibre tract network of human brains obtained through diffusion spectrum imaging. We compare them to their respective benchmark networks with varying modularities, which are generated by link swapping to have desired modularity values. We find several network properties that are specific to the neural networks and cannot be fully explained by the modularity alone. First, the clustering coefficient and the characteristic path length of both C. elegans and human connectomes are higher than those of the benchmark networks with similar modularity. High clustering coefficient indicates efficient local information distribution, and high characteristic path length suggests reduced global integration. Second, the total wiring length is smaller than for the alternative configurations with similar modularity. This is due to lower dispersion of connections, which means each neuron in the C. elegans connectome or each region of interest in the human connectome reaches fewer ganglia or cortical areas, respectively. Third, both neural networks show lower algorithmic entropy compared with the alternative arrangements. This implies that fewer genes are needed to encode for the organization of neural systems. While the first two findings show that the neural topologies are efficient in information processing, this suggests that they are also efficient from a developmental point of view. Together, these results show that neural systems are organized in such a way as to yield efficient features beyond those given by their modularity alone.     

Discovering sparse control strategies in neural activity

Biological circuits such as neural or gene regulation networks use internal states to map sensory input to an adaptive repertoire of behavior. Characterizing this mapping is a major challenge for systems biology. Though experiments that probe internal states are developing rapidly, organismal complexity presents a fundamental obstacle given the many possible ways internal states could map to behavior. Using C. elegans as an example, we propose a protocol for systematic perturbation of neural states that limits experimental complexity and could eventually help characterize collective aspects of the neural-behavioral map. We consider experimentally motivated small perturbations—ones that are most likely to preserve natural dynamics and are closer to internal control mechanisms—to neural states and their impact on collective neural activity. Then, we connect such perturbations to the local information geometry of collective statistics, which can be fully characterized using pairwise perturbations. Applying the protocol to a minimal model of C. elegans neural activity, we find that collective neural statistics are most sensitive to a few principal perturbative modes. Dominant eigenvalues decay initially as a power law, unveiling a hierarchy that arises from variation in individual neural activity and pairwise interactions. Highest-ranking modes tend to be dominated by a few, “pivotal” neurons that account for most of the system’s sensitivity, suggesting a sparse mechanism of collective control.     

Visualizing neuromodulation in vivo: TANGO-mapping of dopamine signaling reveals appetite control of sugar sensing

Behavior cannot be predicted from a "connectome" because the brain contains a chemical "map" of neuromodulation superimposed upon its synaptic connectivity map. Neuromodulation changes how neural circuits process information in different states, such as hunger or arousal. Here we describe a genetically based method to map, in an unbiased and brain-wide manner, sites of neuromodulation under different conditions in the Drosophila brain. This method, and genetic perturbations, reveal that the well-known effect of hunger to enhance behavioral sensitivity to sugar is mediated, at least in part, by the release of dopamine onto primary gustatory sensory neurons, which enhances sugar-evoked calcium influx. These data reinforce the concept that sensory neurons constitute an important locus for state-dependent gain control of behavior and introduce a methodology that can be extended to other neuromodulators and model organisms.     

Modulation of Locomotion and Reproduction by FLP Neuropeptides in the Nematode Caenorhabditis elegans

Neuropeptides function in animals to modulate most, if not all, complex behaviors. In invertebrates, neuropeptides can function as the primary neurotransmitter of a neuron, but more generally they co-localize with a small molecule neurotransmitter, as is commonly seen in vertebrates. Because a single neuron can express multiple neuropeptides and because neuropeptides can bind to multiple G protein-coupled receptors, neuropeptide actions increase the complexity by which the neural connectome can be activated or inhibited. Humans are estimated to have 90 plus neuropeptide genes; by contrast, nematodes, a relatively simple organism, have a slightly larger complement of neuropeptide genes. For instance, the nematode Caenorhabditis elegans has over 100 neuropeptide-encoding genes, of which at least 31 genes encode peptides of the FMRFamide family. To understand the function of this large FMRFamide peptide family, we isolated knockouts of different FMRFamide-encoding genes and generated transgenic animals in which the peptides are overexpressed. We assayed these animals on two basic behaviors: locomotion and reproduction. Modulating levels of different neuropeptides have strong as well as subtle effects on these behaviors. These data suggest that neuropeptides play critical roles in C. elegans to fine tune neural circuits controlling locomotion and reproduction.     

Serotonin and the search for the anatomical substrate of aggression

Abstract

All species of animals display aggression in order to obtain resources such as territories, mates, or food. Appropriate displays of aggression rely on the correct identification of a potential competitor, an evaluation of the environmental signals, and the physiological state of the animal. With a hard-wired circuitry involving fixed numbers of neurons, neuromodulators like serotonin offer adaptive flexibility in behavioral responses without changing the “hard-wiring”. In a recent report, we combined intersectional genetics, quantitative behavioral assays and morphological analyses to identify single serotonergic neurons that modulate the escalation of aggression. We found anatomical target areas within the brain where these neurons appear to form synaptic contacts with 5HT1A receptor-expressing neurons, and then confirmed the likelihood of those connections on a functional level. In this Extra View article, we offer an extended discussion of these recent findings and elaborate on how they can link a cellular and functional mapping of an aggression-regulating circuit at a single-cell resolution level.     

Serotonin and the search for the anatomical substrate of aggression

All species of animals display aggression in order to obtain resources such as territories, mates, or food. Appropriate displays of aggression rely on the correct identification of a potential competitor, an evaluation of the environmental signals, and the physiological state of the animal. With a hard-wired circuitry involving fixed numbers of neurons, neuromodulators like serotonin offer adaptive flexibility in behavioral responses without changing the “hard-wiring”. In a recent report, we combined intersectional genetics, quantitative behavioral assays and morphological analyses to identify single serotonergic neurons that modulate the escalation of aggression. We found anatomical target areas within the brain where these neurons appear to form synaptic contacts with 5HT1A receptor-expressing neurons, and then confirmed the likelihood of those connections on a functional level. In this Extra View article, we offer an extended discussion of these recent findings and elaborate on how they can link a cellular and functional mapping of an aggression-regulating circuit at a single-cell resolution level.     

Dual Color Neural Activation and Behavior Control with Chrimson and CoChR in Caenorhabditis elegans

By enabling a tight control of cell excitation, optogenetics is a powerful approach to study the function of neurons and neural circuits. With its transparent body, a fully mapped nervous system, easily quantifiable behaviors and many available genetic tools, Caenorhabditis elegans is an extremely well-suited model to decipher the functioning logic of the nervous system with optogenetics. Our goal was to establish an efficient dual color optogenetic system for the independent excitation of different neurons in C. elegans. We combined two recently discovered channelrhodopsins: the red-light sensitive Chrimson from Chlamydomonas noctigama and the blue-light sensitive CoChR from Chloromonas oogama. Codon-optimized versions of Chrimson and CoChR were designed for C. elegans and expressed in different mechanosensory neurons. Freely moving animals produced robust behavioral responses to light stimuli of specific wavelengths. Since CoChR was five times more sensitive to blue light than the commonly used ChR2, we were able to use low blue light intensities producing no cross-activation of Chrimson. Thanks to these optogenetics tools, we revealed asymmetric cross-habituation effects between the gentle and harsh touch sensory motor pathways. Collectively, our results establish the Chrimson/CoChR pair as a potent tool for bimodal neural excitation in C. elegans and equip this genetic model organism for the next generation of in vivo optogenetic analyses.     

Topological cluster analysis reveals the systemic organization of the Caenorhabditis elegans connectome

The modular organization of networks of individual neurons interwoven through synapses has not been fully explored due to the incredible complexity of the connectivity architecture. Here we use the modularity-based community detection method for directed, weighted networks to examine hierarchically organized modules in the complete wiring diagram (connectome) of Caenorhabditis elegans (C. elegans) and to investigate their topological properties. Incorporating bilateral symmetry of the network as an important cue for proper cluster assignment, we identified anatomical clusters in the C. elegans connectome, including a body-spanning cluster, which correspond to experimentally identified functional circuits. Moreover, the hierarchical organization of the five clusters explains the systemic cooperation (e.g., mechanosensation, chemosensation, and navigation) that occurs among the structurally segregated biological circuits to produce higher-order complex behaviors.     

Illuminating neural circuits and behaviour in Caenorhabditis elegans with optogenetics

The development of optogenetics, a family of methods for using light to control neural activity via light-sensitive proteins, has provided a powerful new set of tools for neurobiology. These techniques have been particularly fruitful for dissecting neural circuits and behaviour in the compact and transparent roundworm Caenorhabditis elegans. Researchers have used optogenetic reagents to manipulate numerous excitable cell types in the worm, from sensory neurons, to interneurons, to motor neurons and muscles. Here, we show how optogenetics applied to this transparent roundworm has contributed to our understanding of neural circuits.     

Functional organization of a neural network for aversive olfactory learning in Caenorhabditis elegans

Many animals use their olfactory systems to learn to avoid dangers, but how neural circuits encode naive and learned olfactory preferences, and switch between those preferences, is poorly understood. Here, we map an olfactory network, from sensory input to motor output, which regulates the learned olfactory aversion of Caenorhabditis elegans for the smell of pathogenic bacteria. Naive animals prefer smells of pathogens but animals trained with pathogens lose this attraction. We find that two different neural circuits subserve these preferences, with one required for the naive preference and the other specifically for the learned preference. Calcium imaging and behavioral analysis reveal that the naive preference reflects the direct transduction of the activity of olfactory sensory neurons into motor response, whereas the learned preference involves modulations to signal transduction to downstream neurons to alter motor response. Thus, two different neural circuits regulate a behavioral switch between naive and learned olfactory preferences.     

Environmental-temperature and internal-state dependent thermotaxis plasticity of nematodes

Thermotaxis behavior of Caenorhabditis elegans is robust and highly plastic. A pair of sensory neurons, AFD, memorize environmental/cultivation temperature and communicate with a downstream neural circuit to adjust the temperature preference of the animal. This results in a behavioral bias where worms will move toward their cultivation temperature on a thermal gradient. Thermotaxis of C. elegans is also affected by the internal state and is temporarily abolished when worms are starved. Here I will discuss how C. elegans is able to modulate its behavior based on temperature by integrating environmental and internal information. Recent studies show that some parasitic nematodes have a similar thermosensory mechanism to C. elegans and exhibit cultivation-temperature-dependent thermotaxis. I will also discuss the common neural mechanisms that regulate thermosensation and thermotaxis in C. elegans and Strongyloides stercoralis.     

Analyzing Self-Similar and Fractal Properties of the C. elegans Neural Network

The brain is one of the most studied and highly complex systems in the biological world. While much research has 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 connectivity of the brain should elucidate some of its functional properties. In this paper we analyze the connectome of the nematode Caenorhabditis elegans. Consisting of only 302 neurons, it is one of the better-understood neural networks. Using a Laplacian Matrix of the 279-neuron “giant component” of the network, we use an eigenvalue counting function to look for fractal-like self similarity. This matrix representation is also used to plot visualizations of the neural network in eigenfunction coordinates. Small-world properties of the system are examined, including average path length and clustering coefficient. We test for localization of eigenfunctions, using graph energy and spacial variance on these functions. To better understand results, all calculations are also performed on random networks, branching trees, and known fractals, as well as fractals which have been “rewired” to have small-world properties. We propose algorithms for generating Laplacian matrices of each of these graphs.     

Graph theoretical model of a sensorimotor connectome in zebrafish

Mapping the detailed connectivity patterns (connectomes) of neural circuits is a central goal of neuroscience. The best quantitative approach to analyzing connectome data is still unclear but graph theory has been used with success. We present a graph theoretical model of the posterior lateral line sensorimotor pathway in zebrafish. The model includes 2,616 neurons and 167,114 synaptic connections. Model neurons represent known cell types in zebrafish larvae, and connections were set stochastically following rules based on biological literature. Thus, our model is a uniquely detailed computational representation of a vertebrate connectome. The connectome has low overall connection density, with 2.45% of all possible connections, a value within the physiological range. We used graph theoretical tools to compare the zebrafish connectome graph to small-world, random and structured random graphs of the same size. For each type of graph, 100 randomly generated instantiations were considered. Degree distribution (the number of connections per neuron) varied more in the zebrafish graph than in same size graphs with less biological detail. There was high local clustering and a short average path length between nodes, implying a small-world structure similar to other neural connectomes and complex networks. The graph was found not to be scale-free, in agreement with some other neural connectomes. An experimental lesion was performed that targeted three model brain neurons, including the Mauthner neuron, known to control fast escape turns. The lesion decreased the number of short paths between sensory and motor neurons analogous to the behavioral effects of the same lesion in zebrafish. This model is expandable and can be used to organize and interpret a growing database of information on the zebrafish connectome.     

Neural network features distinguish chemosensory stimuli in Caenorhabditis elegans

Nervous systems extract and process information from the environment to alter animal behavior and physiology. Despite progress in understanding how different stimuli are represented by changes in neuronal activity, less is known about how they affect broader neural network properties. We developed a framework for using graph-theoretic features of neural network activity to predict ecologically relevant stimulus properties, in particular stimulus identity. We used the transparent nematode, Caenorhabditis elegans, with its small nervous system to define neural network features associated with various chemosensory stimuli. We first immobilized animals using a microfluidic device and exposed their noses to chemical stimuli while monitoring changes in neural activity of more than 50 neurons in the head region. We found that graph-theoretic features, which capture patterns of interactions between neurons, are modulated by stimulus identity. Further, we show that a simple machine learning classifier trained using graph-theoretic features alone, or in combination with neural activity features, can accurately predict salt stimulus. Moreover, by focusing on putative causal interactions between neurons, the graph-theoretic features were almost twice as predictive as the neural activity features. These results reveal that stimulus identity modulates the broad, network-level organization of the nervous system, and that graph theory can be used to characterize these changes.     

The Interscutularis Muscle Connectome

The complete connectional map (connectome) of a neural circuit is essential for understanding its structure and function. Such maps have only been obtained in Caenorhabditis elegans. As an attempt at solving mammalian circuits, we reconstructed the connectomes of six interscutularis muscles from adult transgenic mice expressing fluorescent proteins in all motor axons. The reconstruction revealed several organizational principles of the neuromuscular circuit. First, the connectomes demonstrate the anatomical basis of the graded tensions in the size principle. Second, they reveal a robust quantitative relationship between axonal caliber, length, and synapse number. Third, they permit a direct comparison of the same neuron on the left and right sides of the same vertebrate animal, and reveal significant structural variations among such neurons, which contrast with the stereotypy of identified neurons in invertebrates. Finally, the wiring length of axons is often longer than necessary, contrary to the widely held view that neural wiring length should be minimized. These results show that mammalian muscle function is implemented with a variety of wiring diagrams that share certain global features but differ substantially in anatomical form. This variability may arise from the dominant role of synaptic competition in establishing the final circuit.