Structural properties of the Caenorhabditis elegans neuronal network

Synaptic polarity and sign-balance prediction using gene expression data in the Caenorhabditis elegans chemical synapse neuronal connectome network

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 predictions for more than two-thirds of these chemical synapses and observed an excitatory-inhibitory (E:I) ratio close to 4:1 which was found similar to that observed in many real-world networks. Our open source tool (http://EleganSign.linkgroup.hu) is simple but efficient in predicting polarities by integrating neuronal connectome and gene expression data.

Network topology of the marmoset connectome

The brain is a complex network of interconnected and interacting neuronal populations. Global efforts to understand the emergence of behavior and the effect of perturbations depend on accurate reconstruction of white matter pathways, both in humans and in model organisms. An emerging animal model for next-generation applied neuroscience is the common marmoset (Callithrix jacchus). A recent open respository of retrograde and anterograde tract tracing presents an opportunity to systematically study the network architecture of the marmoset brain (Marmoset Brain Architecture Project; http://www.marmosetbrain.org). Here we comprehensively chart the topological organization of the mesoscale marmoset cortico-cortical connectome. The network possesses multiple nonrandom attributes that promote a balance between segregation and integration, including near-minimal path length, multiscale community structure, a connective core, a unique motif composition, and multiple cavities. Altogether, these structural attributes suggest a link between network architecture and function. Our findings are consistent with previous reports across a range of species, scales, and reconstruction technologies, suggesting a small set of organizational principles universal across phylogeny. Collectively, these results provide a foundation for future anatomical, functional, and behavioral studies in this model organism.

GABAergic motor neurons bias locomotor decision-making in C. elegans

Proper threat-reward decision-making is critical to animal survival. Emerging evidence indicates that the motor system may participate in decision-making but the neural circuit and molecular bases for these functions are little known. We found in C. elegans that GABAergic motor neurons (D-MNs) bias toward the reward behavior in threat-reward decision-making by retrogradely inhibiting a pair of premotor command interneurons, AVA, that control cholinergic motor neurons in the avoidance neural circuit. This function of D-MNs is mediated by a specific ionotropic GABA receptor (UNC-49) in AVA, and depends on electrical coupling between the two AVA interneurons. Our results suggest that AVA are hub neurons where sensory inputs from threat and reward sensory modalities and motor information from D-MNs are integrated. This study demonstrates at single-neuron resolution how motor neurons may help shape threat-reward choice behaviors through interacting with other neurons.

Statistical analysis of unidirectional and reciprocal chemical connections in the C. elegans connectome

We analyze unidirectional and reciprocally connected pairs of neurons in the chemical connectomes of the male and hermaphrodite Caenorhabditis elegans, using recently published data. Our analysis reveals that reciprocal connections provide communication between most neurons with chemical synapses, and comprise on average more synapses than both unidirectional connections and the entire connectome. We further reveal that the C. elegans connectome is wired so that afferent connections onto neurons with large numbers of presynaptic neighbors (in-degree) comprise an above-average number of synapses (synaptic multiplicity). Notably, the larger the in-degree of a neuron the larger the synaptic multiplicity of its afferent connections. Finally, we show that the male forms two times fewer reciprocal connections between sex-shared neurons than the hermaphrodite, but a large number of reciprocal connections with male-specific neurons. These observations provide evidence for Hebbian structural plasticity in the C. elegans.

Melatonin promotes sleep by activating the BK channel in C. elegans

Melatonin (Mel) promotes sleep through G protein-coupled receptors. However, the downstream molecular target(s) is unknown. We identified the Caenorhabditis elegans BK channel SLO-1 as a molecular target of the Mel receptor PCDR-1-. Knockout of pcdr-1, slo-1, or homt-1 (a gene required for Mel synthesis) causes substantially increased neurotransmitter release and shortened sleep duration, and these effects are nonadditive in double knockouts. Exogenous Mel inhibits neurotransmitter release and promotes sleep in wild-type (WT) but not pcdr-1 and slo-1 mutants. In a heterologous expression system, Mel activates the human BK channel (hSlo1) in a membrane-delimited manner in the presence of the Mel receptor MT₁ but not MT₂ A peptide acting to release free Gβγ also activates hSlo1 in a MT₁-dependent and membrane-delimited manner, whereas a Gβλ inhibitor abolishes the stimulating effect of Mel. Our results suggest that Mel promotes sleep by activating the BK channel through a specific Mel receptor and Gβλ.

Raising the Connectome: The Emergence of Neuronal Activity and Behavior in Caenorhabditis elegans

The differentiation of neurons and formation of connections between cells is the basis of both the adult phenotype and behaviors tied to cognition, perception, reproduction, and survival. Such behaviors are associated with local (circuits) and global (connectome) brain networks. A solid understanding of how these networks emerge is critical. This opinion piece features a guided tour of early developmental events in the emerging connectome, which is crucial to a new view on the connectogenetic process. Connectogenesis includes associating cell identities with broader functional and developmental relationships. During this process, the transition from developmental cells to terminally differentiated cells is defined by an accumulation of traits that ultimately results in neuronal-driven behavior. The well-characterized developmental and cell biology of Caenorhabditis elegans will be used to build a synthesis of developmental events that result in a functioning connectome. Specifically, our view of connectogenesis enables a first-mover model of synaptic connectivity to be demonstrated using data representing larval synaptogenesis. In a first-mover model of Stackelberg competition, potential pre- and postsynaptic relationships are shown to yield various strategies for establishing various types of synaptic connections. By comparing these results to what is known regarding principles for establishing complex network connectivity, these strategies are generalizable to other species and developmental systems. In conclusion, we will discuss the broader implications of this approach, as what is presented here informs an understanding of behavioral emergence and the ability to simulate related biological phenomena.

Eigenvector alignment: Assessing functional network changes in amnestic mild cognitive impairment and Alzheimer's disease

Eigenvector alignment, introduced herein to investigate human brain functional networks, is adapted from methods developed to detect influential nodes and communities in networked systems. It is used to identify differences in the brain networks of subjects with Alzheimer’s disease (AD), amnestic Mild Cognitive Impairment (aMCI) and healthy controls (HC). Well-established methods exist for analysing connectivity networks composed of brain regions, including the widespread use of centrality metrics such as eigenvector centrality. However, these metrics provide only limited information on the relationship between regions, with this understanding often sought by comparing the strength of pairwise functional connectivity. Our holistic approach, eigenvector alignment, considers the impact of all functional connectivity changes before assessing the strength of the functional relationship, i.e. alignment, between any two regions. This is achieved by comparing the placement of regions in a Euclidean space defined by the network’s dominant eigenvectors. Eigenvector alignment recognises the strength of bilateral connectivity in cortical areas of healthy control subjects, but also reveals degradation of this commissural system in those with AD. Surprisingly little structural change is detected for key regions in the Default Mode Network, despite significant declines in the functional connectivity of these regions. In contrast, regions in the auditory cortex display significant alignment changes that begin in aMCI and are the most prominent structural changes for those with AD. Alignment differences between aMCI and AD subjects are detected, including notable changes to the hippocampal regions. These findings suggest eigenvector alignment can play a complementary role, alongside established network analytic approaches, to capture how the brain’s functional networks develop and adapt when challenged by disease processes such as AD.

Leveraging Neural Networks in Preclinical Alcohol Research

Alcohol use disorder is a pervasive healthcare issue with significant socioeconomic consequences. There is a plethora of neural imaging techniques available at the clinical and preclinical level, including magnetic resonance imaging and three-dimensional (3D) tissue imaging techniques. Network-based approaches can be applied to imaging data to create neural networks that model the functional and structural connectivity of the brain. These networks can be used to changes to brain-wide neural signaling caused by brain states associated with alcohol use. Neural networks can be further used to identify key brain regions or neural "hubs" involved in alcohol drinking. Here, we briefly review the current imaging and neurocircuit manipulation methods. Then, we discuss clinical and preclinical studies using network-based approaches related to substance use disorders and alcohol drinking. Finally, we discuss how preclinical 3D imaging in combination with network approaches can be applied alone and in combination with other approaches to better understand alcohol drinking.

A pruning feedforward small-world neural network based on Katz centrality for nonlinear system modeling

Approaching to the biological neural network, small-world neural networks have been demonstrated to improve the generalization performance of artificial neural networks. However, the architecture of small-world neural networks is typically large and predefined. This may cause the problems of overfitting and time consuming, and cannot obtain an optimal network structure automatically for a given problem. To solve the above problems, this paper proposes a pruning feedforward small-world neural network (PFSWNN), and applies it to nonlinear system modeling. Firstly, a feedforward small-world neural network (FSWNN) is constructed according to the rewiring rule of Watts-Strogatz. Secondly, the importance of each hidden neuron is evaluated based on its Katz centrality. If the Katz centrality of a hidden neuron is below the predefined threshold, this neuron is considered to be an unimportant node and then merged with its most correlated neuron in the same hidden layer. The connection weights are trained using the gradient-based algorithm, and the convergence of the proposed PFSWNN is theoretically analyzed in this paper. Finally, the PFSWNN model is tested on some problems for nonlinear system modeling, including the approximation for a rapidly changing function, CATS missing time-series prediction, four benchmark problems of UCI public datasets and a practical problem for wastewater treatment process. Experimental results demonstrate that PFSWNN exhibits superior generalization performance by small-world property as well as the pruning algorithm, and the training time of PFSWNN is shortened owning to a compact structure.

Link prediction in real-world multiplex networks via layer reconstruction method

Networks are invaluable tools to study real biological, social and technological complex systems in which connected elements form a purposeful phenomenon. A higher resolution image of these systems shows that the connection types do not confine to one but to a variety of types. Multiplex networks encode this complexity with a set of nodes which are connected in different layers via different types of links. A large body of research on link prediction problem is devoted to finding missing links in single-layer (simplex) networks. In recent years, the problem of link prediction in multiplex networks has gained the attention of researchers from different scientific communities. Although most of these studies suggest that prediction performance can be enhanced by using the information contained in different layers of the network, the exact source of this enhancement remains obscure. Here, it is shown that similarity w.r.t. structural features (eigenvectors) is a major source of enhancements for link prediction task in multiplex networks using the proposed layer reconstruction method and experiments on real-world multiplex networks from different disciplines. Moreover, we characterize how low values of similarity w.r.t. structural features result in cases where improving prediction performance is substantially hard.

Rich-club in the brain's macrostructure: Insights from graph theoretical analysis

The brain is a complex network. Growing evidence supports the critical roles of a set of brain regions within the brain network, known as the brain’s cores or hubs. These regions require high energy cost but possess highly efficient neural information transfer in the brain’s network and are termed the rich-club. The rich-club of the brain network is essential as it directly regulates functional integration across multiple segregated regions and helps to optimize cognitive processes. Here, we review the recent advances in rich-club organization to address the fundamental roles of the rich-club in the brain and discuss how these core brain regions affect brain development and disorders. We describe the concepts of the rich-club behind network construction in the brain using graph theoretical analysis. We also highlight novel insights based on animal studies related to the rich-club and illustrate how human studies using neuroimaging techniques for brain development and psychiatric/neurological disorders may be relevant to the rich-club phenomenon in the brain network.

Flexible motor sequence generation during stereotyped escape responses

Complex animal behaviors arise from a flexible combination of stereotyped motor primitives. Here we use the escape responses of the nematode Caenorhabditis elegans to study how a nervous system dynamically explores the action space. The initiation of the escape responses is predictable: the animal moves away from a potential threat, a mechanical or thermal stimulus. But the motor sequence and the timing that follow are variable. We report that a feedforward excitation between neurons encoding distinct motor states underlies robust motor sequence generation, while mutual inhibition between these neurons controls the flexibility of timing in a motor sequence. Electrical synapses contribute to feedforward coupling whereas glutamatergic synapses contribute to inhibition. We conclude that C. elegans generates robust and flexible motor sequences by combining an excitatory coupling and a winner-take-all operation via mutual inhibition between motor modules.

Explosive Higher-Order Kuramoto Dynamics on Simplicial Complexes

The higher-order interactions of complex systems, such as the brain, are captured by their simplicial complex structure and have a significant effect on dynamics. However, the existing dynamical models defined on simplicial complexes make the strong assumption that the dynamics resides exclusively on the nodes. Here we formulate the higher-order Kuramoto model which describes the interactions between oscillators placed not only on nodes but also on links, triangles, and so on. We show that higher-order Kuramoto dynamics can lead to an explosive synchronization transition by using an adaptive coupling dependent on the solenoidal and the irrotational component of the dynamics.

Efficient communication over complex dynamical networks: The role of matrix non-normality

In both natural and engineered systems, communication often occurs dynamically over networks ranging from highly structured grids to largely disordered graphs. To use, or comprehend the use of, networks as efficient communication media requires understanding of how they propagate and transform information in the face of noise. Here, we develop a framework that enables us to examine how network structure, noise, and interference between consecutive packets jointly determine transmission performance in complex networks governed by linear dynamics. Mathematically, normal networks, which can be decomposed into separate low-dimensional information channels, suffer greatly from readout noise. Most details of their wiring have no impact on transmission quality. Non-normal networks, however, can largely cancel the effect of noise by transiently amplifying select input dimensions while ignoring others, resulting in higher net information throughput. Our theory could inform the design of new communication networks, as well as the optimal use of existing ones.

Deriving pairwise transfer entropy from network structure and motifs

Transfer entropy (TE) is an established method for quantifying directed statistical dependencies in neuroimaging and complex systems datasets. The pairwise (or bivariate) TE from a source to a target node in a network does not depend solely on the local source-target link weight, but on the wider network structure that the link is embedded in. This relationship is studied using a discrete-time linearly coupled Gaussian model, which allows us to derive the TE for each link from the network topology. It is shown analytically that the dependence on the directed link weight is only a first approximation, valid for weak coupling. More generally, the TE increases with the in-degree of the source and decreases with the in-degree of the target, indicating an asymmetry of information transfer between hubs and low-degree nodes. In addition, the TE is directly proportional to weighted motif counts involving common parents or multiple walks from the source to the target, which are more abundant in networks with a high clustering coefficient than in random networks. Our findings also apply to Granger causality, which is equivalent to TE for Gaussian variables. Moreover, similar empirical results on random Boolean networks suggest that the dependence of the TE on the in-degree extends to nonlinear dynamics.

Drug discovery technologies: Caenorhabditis elegans as a model for anthelmintic therapeutics

Helminthiasis is one of the gravest problems worldwide. There is a growing concern on less available anthelmintics and the emergence of resistance creating a major threat to human and livestock health resources. Novel and broad-spectrum anthelmintics are urgently needed. The free-living nematode Caenorhabditis elegans could address this issue through automated high-throughput technologies for the screening of large chemical libraries. This review discusses the strong advantages and limitations for using C elegans as a screening method for anthelmintic drug discovery. C elegans is the best model available for the validation of novel effective drugs in treating most, if not all, helminth infections, and for the elucidation the mode of action of anthelmintic candidates. This review also focuses on available technologies in the discovery of anthelmintics published over the last 15 years with particular attention to high-throughput technologies over conventional screens. On the other hand, this review highlights how combinatorial and nanomedicine strategies could prolong the use of anthelmintics and control resistance problems.

Synthetic ablations in the C. elegans nervous system

Synthetic lethality, the finding that the simultaneous knockout of two or more individually nonessential 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 effects of ablating neuron pairs and triplets on the gentle touch response. We find that surprisingly small sets of 58 pairs and 46 triplets can reduce muscle controllability in this context, and that these sets are localized in the nervous system in distinct groups. Further, they lead to highly specific experimentally testable predictions about mechanisms of loss of control, and which muscle cells are expected to experience this loss.

“Synthetic lethality” in cell biology is an extreme example of the effects of higher order genetic interactions: The simultaneous knockout of two or more individually nonessential genes leads to cell death. We define a neural analog to this concept in relation to the locomotor response to gentle touch in C. elegans. Two or more neurons are synthetic essential if individually they are not required for this behavior, yet their combination is. We employ a network control approach to systematically assess all pairs and triplets of neurons by their effect on body wall muscle controllability, and find that only surprisingly small sets of neurons are synthetic essential. They are highly localized in the nervous system and predicted to affect control over specific sets of muscles.

A Genetic Model of the Connectome

The connectomes of organisms of the same species show remarkable architectural and often local wiring similarity, raising the question: where and how is neuronal connectivity encoded? Here, we start from the hypothesis that the genetic identity of neurons guides synapse and gap-junction formation and show that such genetically driven wiring predicts the existence of specific biclique motifs in the connectome. We identify a family of large, statistically significant biclique subgraphs in the connectomes of three species and show that within many of the observed bicliques the neurons share statistically significant expression patterns and morphological characteristics, supporting our expectation of common genetic factors that drive the synapse formation within these subgraphs. The proposed connectome model offers a self-consistent framework to link the genetics of an organism to the reproducible architecture of its connectome, offering experimentally falsifiable predictions on the genetic factors that drive the formation of individual neuronal circuits.

Brn3/POU-IV-type POU homeobox genes-Paradigmatic regulators of neuronal identity across phylogeny

One approach to understand the construction of complex systems is to investigate whether there are simple design principles that are commonly used in building such a system. In the context of nervous system development, one may ask whether the generation of its highly diverse sets of constituents, that is, distinct neuronal cell types, relies on genetic mechanisms that share specific common features. Specifically, are there common patterns in the function of regulatory genes across different neuron types and are those regulatory mechanisms not only used in different parts of one nervous system, but are they conserved across animal phylogeny? We address these questions here by focusing on one specific, highly conserved and well-studied regulatory factor, the POU homeodomain transcription factor UNC-86. Work over the last 30 years has revealed a common and paradigmatic theme of unc-86 function throughout most of the neuron types in which Caenorhabditis elegans unc-86 is expressed. Apart from its role in preventing lineage reiterations during development, UNC-86 operates in combination with distinct partner proteins to initiate and maintain terminal differentiation programs, by coregulating a vast array of functionally distinct identity determinants of specific neuron types. Mouse orthologs of unc-86, the Brn3 genes, have been shown to fulfill a similar function in initiating and maintaining neuronal identity in specific parts of the mouse brain and similar functions appear to be carried out by the sole Drosophila ortholog, Acj6. The terminal selector function of UNC-86 in many different neuron types provides a paradigm for neuronal identity regulation across phylogeny. This article is categorized under: Gene Expression and Transcriptional Hierarchies > Regulatory Mechanisms Invertebrate Organogenesis > Worms Nervous System Development > Vertebrates: Regional Development.

The hourglass organization of the Caenorhabditis elegans connectome

We approach the C. elegans connectome as an information processing network that receives input from about 90 sensory neurons, processes that information through a highly recurrent network of about 80 interneurons, and it produces a coordinated output from about 120 motor neurons that control the nematode's muscles. We focus on the feedforward flow of information from sensory neurons to motor neurons, and apply a recently developed network analysis framework referred to as the "hourglass effect". The analysis reveals that this feedforward flow traverses a small core ("hourglass waist") that consists of 10-15 interneurons. These are mostly the same interneurons that were previously shown (using a different analytical approach) to constitute the "rich-club" of the C. elegans connectome. This result is robust to the methodology that separates the feedforward from the feedback flow of information. The set of core interneurons remains mostly the same when we consider only chemical synapses or the combination of chemical synapses and gap junctions. The hourglass organization of the connectome suggests that C. elegans has some similarities with encoder-decoder artificial neural networks in which the input is first compressed and integrated in a low-dimensional latent space that encodes the given data in a more efficient manner, followed by a decoding network through which intermediate-level sub-functions are combined in different ways to compute the correlated outputs of the network. The core neurons at the hourglass waist represent the information bottleneck of the system, balancing the representation accuracy and compactness (complexity) of the given sensory information.

Navigable maps of structural brain networks across species

Connectomes are spatially embedded networks whose architecture has been shaped by physical constraints and communication needs throughout evolution. Using a decentralized navigation protocol, we investigate the relationship between the structure of the connectomes of different species and their spatial layout. As a navigation strategy, we use greedy routing where nearest neighbors, in terms of geometric distance, are visited. We measure the fraction of successful greedy paths and their length as compared to shortest paths in the topology of connectomes. In Euclidean space, we find a striking difference between the navigability properties of mammalian and non-mammalian species, which implies the inability of Euclidean distances to fully explain the structural organization of their connectomes. In contrast, we find that hyperbolic space, the effective geometry of complex networks, provides almost perfectly navigable maps of connectomes for all species, meaning that hyperbolic distances are exceptionally congruent with the structure of connectomes. Hyperbolic maps therefore offer a quantitative meaningful representation of connectomes that suggests a new cartography of the brain based on the combination of its connectivity with its effective geometry rather than on its anatomy only. Hyperbolic maps also provide a universal framework to study decentralized communication processes in connectomes of different species and at different scales on an equal footing.

Distinct roles for innexin gap junctions and hemichannels in mechanosensation

Mechanosensation is central to a wide range of functions, including tactile and pain perception, hearing, proprioception, and control of blood pressure, but identifying the molecules underlying mechanotransduction has proved challenging. In Caenorhabditis elegans, the avoidance response to gentle body touch is mediated by six touch receptor neurons (TRNs), and is dependent on MEC-4, a DEG/ENaC channel. We show that hemichannels containing the innexin protein UNC-7 are also essential for gentle touch in the TRNs, as well as harsh touch in both the TRNs and the PVD nociceptors. UNC-7 and MEC-4 do not colocalize, suggesting that their roles in mechanosensory transduction are independent. Heterologous expression of unc-7 in touch-insensitive chemosensory neurons confers ectopic touch sensitivity, indicating a specific role for UNC-7 hemichannels in mechanosensation. The unc-7 touch defect can be rescued by the homologous mouse gene Panx1 gene, thus, innexin/pannexin proteins may play broadly conserved roles in neuronal mechanotransduction.

Brain-wide functional architecture remodeling by alcohol dependence and abstinence

Alcohol abuse and alcohol dependence are key factors in the development of alcohol use disorder, which is a pervasive societal problem with substantial economic, medical, and psychiatric consequences. Although our understanding of the neurocircuitry that underlies alcohol use has improved, novel brain regions that are involved in alcohol use and novel biomarkers of alcohol use need to be identified. The present study used a single-cell whole-brain imaging approach to 1) assess whether abstinence from alcohol in an animal model of alcohol dependence alters the functional architecture of brain activity and modularity, 2) validate our current knowledge of the neurocircuitry of alcohol abstinence, and 3) discover brain regions that may be involved in alcohol use. Alcohol abstinence resulted in the whole-brain reorganization of functional architecture in mice and a pronounced decrease in modularity that was not observed in nondependent moderate drinkers. Structuring of the alcohol abstinence network revealed three major brain modules: 1) extended amygdala module, 2) midbrain striatal module, and 3) cortico-hippocampo-thalamic module, reminiscent of the three-stage theory. Many hub brain regions that control this network were identified, including several that have been previously overlooked in alcohol research. These results identify brain targets for future research and demonstrate that alcohol use and dependence remodel brain-wide functional architecture to decrease modularity. Further studies are needed to determine whether the changes in coactivation and modularity that are associated with alcohol abstinence are causal features of alcohol dependence or a consequence of excessive drinking and alcohol exposure.

Computing Persistent Homology of Directed Flag Complexes

We present a new computing package Flagser, designed to construct the directed flag complex of a finite directed graph, and compute persistent homology for flexibly defined filtrations on the graph and the resulting complex. The persistent homology computation part of Flagser is based on the program Ripser by U. Bauer, but is optimised specifically for large computations. The construction of the directed flag complex is done in a way that allows easy parallelisation by arbitrarily many cores. Flagser also has the option of working with undirected graphs. For homology computations Flagser has an approximate option, which shortens compute time with remarkable accuracy. We demonstrate the power of Flagser by applying it to the construction of the directed flag complex of digital reconstructions of brain microcircuitry by the Blue Brain Project and several other examples. In some instances we perform computation of homology. For a more complete performance analysis, we also apply Flagser to some other data collections. In all cases the hardware used in the computation, the use of memory and the compute time are recorded.

Spatially Arranged Sparse Recurrent Neural Networks for Energy Efficient Associative Memory

The development of hardware neural networks, including neuromorphic hardware, has been accelerated over the past few years. However, it is challenging to operate very large-scale neural networks with low-power hardware devices, partly due to signal transmissions through a massive number of interconnections. Our aim is to deal with the issue of communication cost from an algorithmic viewpoint and study learning algorithms for energy-efficient information processing. Here, we consider two approaches to finding spatially arranged sparse recurrent neural networks with the high cost-performance ratio for associative memory. In the first approach following classical methods, we focus on sparse modular network structures inspired by biological brain networks and examine their storage capacity under an iterative learning rule. We show that incorporating long-range intermodule connections into purely modular networks can enhance the cost-performance ratio. In the second approach, we formulate for the first time an optimization problem where the network sparsity is maximized under the constraints imposed by a pattern embedding condition. We show that there is a tradeoff between the interconnection cost and the computational performance in the optimized networks. We demonstrate that the optimized networks can achieve a better cost-performance ratio compared with those considered in the first approach. We show the effectiveness of the optimization approach mainly using binary patterns and apply it also to gray-scale image restoration. Our results suggest that the presented approaches are useful in seeking more sparse and less costly connectivity of neural networks for the enhancement of energy efficiency in hardware neural networks.

Developmental trajectory of Caenorhabditis elegans nervous system governs its structural organization

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, lineage and bilateral symmetry-exhibit a preference for connecting to each other. Recognizing the existence of such homophily and their relative degree of importance in determining connection probability within neurons (for example, in synapses, symmetric pairing is the most dominant factor followed by birth time cohort, process length and lineage) helps in connecting specific neuronal attributes to the topological organization of the network. Further, the functional identities of neurons appear to dictate the temporal hierarchy of their appearance during the course of development. Providing crucial insights into principles that may be common across many organisms, our study shows how the trajectory in the developmental landscape constrains the structural organization of a nervous system.

Synaptic Plasticity Shapes Brain Connectivity: Implications for Network Topology

Studies of brain network connectivity improved understanding on brain changes and adaptation in response to different pathologies. Synaptic plasticity, the ability of neurons to modify their connections, is involved in brain network remodeling following different types of brain damage (e.g., vascular, neurodegenerative, inflammatory). Although synaptic plasticity mechanisms have been extensively elucidated, how neural plasticity can shape network organization is far from being completely understood. Similarities existing between synaptic plasticity and principles governing brain network organization could be helpful to define brain network properties and reorganization profiles after damage. In this review, we discuss how different forms of synaptic plasticity, including homeostatic and anti-homeostatic mechanisms, could be directly involved in generating specific brain network characteristics. We propose that long-term potentiation could represent the neurophysiological basis for the formation of highly connected nodes (hubs). Conversely, homeostatic plasticity may contribute to stabilize network activity preventing poor and excessive connectivity in the peripheral nodes. In addition, synaptic plasticity dysfunction may drive brain network disruption in neuropsychiatric conditions such as Alzheimer's disease and schizophrenia. Optimal network architecture, characterized by efficient information processing and resilience, and reorganization after damage strictly depend on the balance between these forms of plasticity.

Synchronous patterns and intermittency in a network induced by the rewiring of connections and coupling

The connection architecture plays an important role in the synchronization of networks, where the presence of local and nonlocal connection structures are found in many systems, such as the neural ones. Here, we consider a network composed of chaotic bursting oscillators coupled through a Watts-Strogatz-small-world topology. The influence of coupling strength and rewiring of connections is studied when the network topology is varied from regular to small-world to random. In this scenario, we show two distinct nonstationary transitions to phase synchronization: one induced by the increase in coupling strength and another resulting from the change from local connections to nonlocal ones. Besides this, there are regions in the parameter space where the network depicts a coexistence of different bursting frequencies where nonstationary zig-zag fronts are observed. Regarding the analyses, we consider two distinct methodological approaches: one based on the phase association to the bursting activity where the Kuramoto order parameter is used and another based on recurrence quantification analysis where just a time series of the network mean field is required.

Symmetry group factorization reveals the structure-function relation in the neural connectome of Caenorhabditis elegans

The neural connectome of the nematode Caenorhabditis elegans has been completely mapped, yet in spite of being one of the smallest connectomes (302 neurons), the design principles that explain how the connectome structure determines its function remain unknown. Here, we find symmetries in the locomotion neural circuit of C. elegans, each characterized by its own symmetry group which can be factorized into the direct product of normal subgroups. The action of these normal subgroups partitions the connectome into sectors of neurons that match broad functional categories. Furthermore, symmetry principles predict the existence of novel finer structures inside these normal subgroups forming feedforward and recurrent networks made of blocks of imprimitivity. These blocks constitute structures made of circulant matrices nested in a hierarchy of block-circulant matrices, whose functionality is understood in terms of neural processing filters responsible for fast processing of information.

The 302-neuron connectome of the nematode C. elegans has been completely mapped, yet the design principles that explain how the connectome structure determines its function are unknown. Here, the authors show that physical principles of symmetry and mathematical tools of symmetry groups can be used to understand C. elegans neural locomotion circuits.

Neuronal Morphology and Synapse Count in the Nematode Worm

The somatic nervous system of the nematode worm Caenorhabditis elegans is a model for understanding the physical characteristics of the neurons and their interconnections. Its neurons show high variation in morphological attributes. This study investigates the relationship of neuronal morphology to the number of synapses per neuron. Morphology is also examined for any detectable association with neuron cell type or ganglion membership.

Network dependence testing via diffusion maps and distance-based correlations

Deciphering the associations between network connectivity and nodal attributes is one of the core problems in network science. The dependency structure and high dimensionality of networks pose unique challenges to traditional dependency tests in terms of theoretical guarantees and empirical performance. We propose an approach to test network dependence via diffusion maps and distance-based correlations. We prove that the new method yields a consistent test statistic under mild distributional assumptions on the graph structure, and demonstrate that it is able to efficiently identify the most informative graph embedding with respect to the diffusion time. The methodology is illustrated on both simulated and real data.

Refined parcellation of the nervous system by algorithmic detection of hidden features within communities

The nervous system can be represented as a multiscale network comprised by single cells or ensembles that are linked by physical or functional connections. Groups of morphologically and physiologically diverse neurons are wired as connectivity patterns with a certain degree of universality across species and individual variability. Thereby, community detection approaches are often used to characterize how neural units cluster into such densely interconnected groups. However, the communities may possess deeper structural features that remain undetected by current algorithms. We present a scheme for refined parcellation of neuronal networks, by identifying local integrator units (LU) that are contained in network communities. An LU is defined as a connected subnetwork in which all neuronal connections are constrained within this unit, and can be formed for instance by a set of interneurons. Our method uses the Louvain algorithm to detect communities and participation coefficients to discriminate local neurons from global hubs. The sensitivity of the algorithm for discovering LUs with respect to the choice of community detection algorithm and network parameters was tested by simulations of different synthetic networks. The appropriateness of the algorithm for real-world scenarios was demonstrated on weighted and binary Caenorhabditis elegans connectomes. The detected LUs are distinctly localized within the worm body and clearly define functional groups. This approach provides a robust, observer-independent parcellation strategy that is useful for functional structure confirmation and potentially contributes to the current efforts in quantitative whole-brain architectonics of different species as well as the analysis of functional connectivity networks.

The central role of peripheral nodes in directed network dynamics

Many social, technological, and biological systems with asymmetric interactions display a variety of collective phenomena, such as opinion formation and synchronization. This has motivated much research on the dynamical impact of local and mesoscopic structure in directed networks. However, the unique constraints imposed by the global organization of directed networks remain largely undiscussed. Here, we control the global organization of directed Erdős–Rényi networks, and study its impact on the emergence of synchronization and ferromagnetic ordering, using Kuramoto and Ising dynamics. In doing so, we demonstrate that source nodes – peripheral nodes without incoming links – can disrupt or entirely suppress the emergence of collective states in directed networks. This effect is imposed by the bow-tie organization of directed networks, where a large connected core does not uniquely ensure the emergence of collective states, as it does for undirected networks.

A Student's Guide to Neural Circuit Tracing

The mammalian nervous system is comprised of a seemingly infinitely complex network of specialized synaptic connections that coordinate the flow of information through it. The field of connectomics seeks to map the structure that underlies brain function at resolutions that range from the ultrastructural, which examines the organization of individual synapses that impinge upon a neuron, to the macroscopic, which examines gross connectivity between large brain regions. At the mesoscopic level, distant and local connections between neuronal populations are identified, providing insights into circuit-level architecture. Although neural tract tracing techniques have been available to experimental neuroscientists for many decades, considerable methodological advances have been made in the last 20 years due to synergies between the fields of molecular biology, virology, microscopy, computer science and genetics. As a consequence, investigators now enjoy an unprecedented toolbox of reagents that can be directed against selected subpopulations of neurons to identify their efferent and afferent connectomes. Unfortunately, the intersectional nature of this progress presents newcomers to the field with a daunting array of technologies that have emerged from disciplines they may not be familiar with. This review outlines the current state of mesoscale connectomic approaches, from data collection to analysis, written for the novice to this field. A brief history of neuroanatomy is followed by an assessment of the techniques used by contemporary neuroscientists to resolve mesoscale organization, such as conventional and viral tracers, and methods of selecting for sub-populations of neurons. We consider some weaknesses and bottlenecks of the most widely used approaches for the analysis and dissemination of tracing data and explore the trajectories that rapidly developing neuroanatomy technologies are likely to take.

Feedback to the future: motor neuron contributions to central pattern generator function

Motor behaviors depend on neural signals in the brain. Regardless of where in the brain behavior patterns arise, the central nervous system sends projections to motor neurons, which in turn project to and control temporally appropriate muscle contractions; thus, motor neurons are traditionally considered the last relay from the central nervous system to muscles. However, in an array of species and motor systems, an accumulating body of evidence supports a more complex role of motor neurons in pattern generation. These studies suggest that motor neurons not only relay motor patterns to the periphery, but directly contribute to pattern generation by providing feedback to upstream circuitry. In spinal and hindbrain circuits in a variety of animals - including flies, worms, leeches, crustaceans, rodents, birds, fish, amphibians and mammals - studies have indicated a crucial role for motor neuron feedback in maintaining normal behavior patterns dictated by the activity of a central pattern generator. Hence, in this Review, we discuss literature examining the role of motor neuron feedback across many taxa and behaviors, and set out to determine the prevalence of motor neuron participation in motor circuits.

The Enculturated Move From Proto-Arithmetic to Arithmetic

The basic human ability to treat quantitative information can be divided into two parts. With proto-arithmetical ability, based on the core cognitive abilities for subitizing and estimation, numerosities can be treated in a limited and/or approximate manner. With arithmetical ability, numerosities are processed (counted, operated on) systematically in a discrete, linear, and unbounded manner. In this paper, I study the theory of enculturation as presented by Menary (2015) as a possible explanation of how we make the move from the proto-arithmetical ability to arithmetic proper. I argue that enculturation based on neural reuse provides a theoretically sound and fruitful framework for explaining this development. However, I show that a comprehensive explanation must be based on valid theoretical distinctions and involve several stages in the development of arithmetical knowledge. I provide an account that meets these challenges and thus leads to a better understanding of the subject of enculturation.

Relating network connectivity to dynamics: opportunities and challenges for theoretical neuroscience

We review recent work relating network connectivity to the dynamics of neural activity. While concepts stemming from network science provide a valuable starting point, the interpretation of graph-theoretic structures and measures can be highly dependent on the dynamics associated to the network. Properties that are quite meaningful for linear dynamics, such as random walk and network flow models, may be of limited relevance in the neuroscience setting. Theoretical and computational neuroscience are playing a vital role in understanding the relationship between network connectivity and the nonlinear dynamics associated to neural networks.

Uncovering the Transcriptional Correlates of Hub Connectivity in Neural Networks

Connections in nervous systems are disproportionately concentrated on a small subset of neural elements that act as network hubs. Hubs have been found across different species and scales ranging from C. elegans to mouse, rat, cat, macaque, and human, suggesting a role for genetic influences. The recent availability of brain-wide gene expression atlases provides new opportunities for mapping the transcriptional correlates of large-scale network-level phenotypes. Here we review studies that use these atlases to investigate gene expression patterns associated with hub connectivity in neural networks and present evidence that some of these patterns are conserved across species and scales.

Graphene-Based Nanomaterials: From Production to Integration With Modern Tools in Neuroscience

Graphene, a two-dimensional carbon crystal, has emerged as a promising material for sensing and modulating neuronal activity in vitro and in vivo. In this review, we provide a primer for how manufacturing processes to produce graphene and graphene oxide result in materials properties that may be tailored for a variety of applications. We further discuss how graphene may be composited with other bio-compatible materials of interest to make novel hybrid complexes with desired characteristics for bio-interfacing. We then highlight graphene's ever-widen utility and unique properties that may in the future be multiplexed for cross-modal modulation or interrogation of neuronal network. As the biological effects of graphene are still an area of active investigation, we discuss recent development, with special focus on how surface coatings and surface properties of graphene are relevant to its biological effects. We discuss studies conducted in both non-murine and murine systems, and emphasize the preclinical aspect of graphene's potential without undermining its tangible clinical implementation.

Spectral peculiarity and criticality of a human connectome

We have performed the comparative spectral analysis of structural connectomes for various organisms using open-access data. Our results indicate new peculiar features of connectomes of higher organisms. We found that the spectral density of adjacency matrices of human connectome has maximal deviation from the one of randomized network, compared to other organisms. Considering the network evolution induced by the preference of 3-cycles formation, we discovered that for macaque and human connectomes the evolution with the conservation of local clusterization is crucial, while for primitive organisms the conservation of averaged clusterization is sufficient. Investigating for the first time the level spacing distribution of the spectrum of human connectome Laplacian matrix, we explicitly demonstrate that the spectral statistics corresponds to the critical regime, which is hybrid of Wigner-Dyson and Poisson distributions. This observation provides strong support for debated statement of the brain criticality.

What would a synthetic connectome look like?

A major challenge of contemporary neuroscience is to unravel the structure of the connectome, the ensemble of neural connections that link between different functional units of the brain, and to reveal how this structure relates to brain function. This thriving area of research largely follows the general tradition in biology of reverse-engineering, which consists of first observing and characterizing a biological system or process, and then deconstructing it into its fundamental building blocks in order to infer its modes of operation. However, a complementary form of biology has emerged, synthetic biology, which emphasizes construction-based forward-engineering. The synthetic biology approach comprises the assembly of new biological systems out of elementary biological parts. The rationale is that the act of building a system can be a powerful method for gaining deep understanding of how that system works. As the fields of connectomics and synthetic biology are independently growing, I propose to consider the benefits of combining the two, to create synthetic connectomics, a new form of neuroscience and a new form of synthetic biology. The goal of synthetic connectomics would be to artificially design and construct the connectomes of live behaving organisms. Synthetic connectomics could serve as a unifying platform for unraveling the complexities of brain operation and perhaps also for generating new forms of artificial life, and, in general, could provide a valuable opportunity for empirically exploring theoretical predictions about network function. What would a synthetic connectome look like? What purposes would it serve? How could it be constructed? This review delineates the novel notion of a synthetic connectome and aims to lay out the initial steps towards its implementation, contemplating its impact on science and society.

A quantitative model of conserved macroscopic dynamics predicts future motor commands

In simple organisms such as Caenorhabditis elegans, whole brain imaging has been performed. Here, we use such recordings to model the nervous system. Our model uses neuronal activity to predict expected time of future motor commands up to 30 s prior to the event. These motor commands control locomotion. Predictions are valid for individuals not used in model construction. The model predicts dwell time statistics, sequences of motor commands and individual neuron activation. To develop this model, we extracted loops spanned by neuronal activity in phase space using novel methodology. The model uses only two variables: the identity of the loop and the phase along it. Current values of these macroscopic variables predict future neuronal activity. Remarkably, our model based on macroscopic variables succeeds despite consistent inter-individual differences in neuronal activation. Thus, our analytical framework reconciles consistent individual differences in neuronal activation with macroscopic dynamics that operate universally across individuals.

How can we go about trying to understand an object as complex as the brain? The traditional approach is to begin by studying its component parts, cells called neurons. Once we understand how individual neurons work, we can use computers to simulate the activity of networks of neurons. The result is a computer model of the brain. By comparing this model to data from real brains, we can try to make the model as similar to a real brain as possible.

But whose brain should we try to reproduce? The roundworm C. elegans, for example, has just 302 neurons in total. Advances in brain imaging mean it is now possible to identify each of these neurons and compare its activity across worms. But doing so reveals that the activity of any given neuron varies greatly between individuals. This is true even among genetically identical worms performing the same behavior.

Researchers trying to model the roundworm brain have attempted to model the average activity of each neuron across many worms. They hoped they could use these averages to predict the behavior of other worms from their neuronal activity. But this approach did not to work. Even in roundworms, the coordinated activity of many neurons is required to generate even simple behaviors. Averaging the activity of neurons across worms thus scrambles the information that encodes each behavior.

Brennan and Proekt have now overcome this problem by developing a more abstract model that treats the nervous system as a whole. The model takes into account changes in the activity of neurons, and in the worms’ behavior, over time. A model of this type built using one set of worms can predict the behavior of another set of worms. This approach may work because in evolution natural selection acts at the level of behaviors, and not at the level of individual neurons. The activity of individual neurons can thus vary between animals, even when those neurons encode the same behavior. This means it may also be possible to model the human brain without knowing the activity of each of its billions of neurons.

Whole-animal connectomes of both Caenorhabditis elegans sexes

Knowledge of connectivity in the nervous system is essential to understanding its function. Here we describe connectomes for both adult sexes of the nematode Caenorhabditis elegans, an important model organism for neuroscience research. We present quantitative connectivity matrices that encompass all connections from sensory input to end-organ output across the entire animal, information that is necessary to model behaviour. Serial electron microscopy reconstructions that are based on the analysis of both new and previously published electron micrographs update previous results and include data on the male head. The nervous system differs between sexes at multiple levels. Several sex-shared neurons that function in circuits for sexual behaviour are sexually dimorphic in structure and connectivity. Inputs from sex-specific circuitry to central circuitry reveal points at which sexual and non-sexual pathways converge. In sex-shared central pathways, a substantial number of connections differ in strength between the sexes. Quantitative connectomes that include all connections serve as the basis for understanding how complex, adaptive behavior is generated.

Guided graph spectral embedding: Application to the C. elegans connectome

Graph spectral analysis can yield meaningful embeddings of graphs by providing insight into distributed features not directly accessible in nodal domain. Recent efforts in graph signal processing have proposed new decompositions—for example, based on wavelets and Slepians—that can be applied to filter signals defined on the graph. In this work, we take inspiration from these constructions to define a new guided spectral embedding that combines maximizing energy concentration with minimizing modified embedded distance for a given importance weighting of the nodes. We show that these optimization goals are intrinsically opposite, leading to a well-defined and stable spectral decomposition. The importance weighting allows us to put the focus on particular nodes and tune the trade-off between global and local effects. Following the derivation of our new optimization criterion, we exemplify the methodology on the C. elegans structural connectome. The results of our analyses confirm known observations on the nematode’s neural network in terms of functionality and importance of cells. Compared with Laplacian embedding, the guided approach, focused on a certain class of cells (sensory neurons, interneurons, or motoneurons), provides more biological insights, such as the distinction between somatic positions of cells, and their involvement in low- or high-order processing functions.

Critical excitation-inhibition balance in dense neural networks

The "edge of chaos" phase transition in artificial neural networks is of renewed interest in light of recent evidence for criticality in brain dynamics. Statistical mechanics traditionally studied this transition with connectivity k as the control parameter and an exactly balanced excitation-inhibition ratio. While critical connectivity has been found to be low in these model systems, typically around k=2, which is unrealistic for natural neural systems, a recent study utilizing the excitation-inhibition ratio as the control parameter found a new, nearly degree independent, critical point when connectivity is large. However, the new phase transition is accompanied by an unnaturally high level of activity in the network. Here we study random neural networks with the additional properties of (i) a high clustering coefficient and (ii) neurons that are solely either excitatory or inhibitory, a prominent property of natural neurons. As a result, we observe an additional critical point for networks with large connectivity, regardless of degree distribution, which exhibits low activity levels that compare well with neuronal brain networks.

The importance of the whole: Topological data analysis for the network neuroscientist

Data analysis techniques from network science have fundamentally improved our understanding of neural systems and the complex behaviors that they support. Yet the restriction of network techniques to the study of pairwise interactions prevents us from taking into account intrinsic topological features such as cavities that may be crucial for system function. To detect and quantify these topological features, we must turn to algebro-topological methods that encode data as a simplicial complex built from sets of interacting nodes called simplices. We then use the relations between simplices to expose cavities within the complex, thereby summarizing its topological features. Here we provide an introduction to persistent homology, a fundamental method from applied topology that builds a global descriptor of system structure by chronicling the evolution of cavities as we move through a combinatorial object such as a weighted network. We detail the mathematics and perform demonstrative calculations on the mouse structural connectome, synapses in C. elegans, and genomic interaction data. Finally, we suggest avenues for future work and highlight new advances in mathematics ready for use in neural systems.