Mesoscopic organization reveals the constraints governing Caenorhabditis elegans nervous system

Critical Regions and Connections Form Pathways and Clusters in the Mouse Brain

Connectome network analysis across multiple species should help identify principles of brain function. Here, we examined three fundamental properties-global efficiency, global betweenness centrality, and global clustering-in the mesoscale tract-tracing data of the mouse connectome; and conducted vulnerability analysis to identify the critical regions and connections based on the loss in network function when each brain region (213) and connection (16,594) was removed. Robustness tests examining noise effects were also conducted. There were five key findings. First, we identified eight critical regions and 38 critical connections, with more central, limbic regions dominant; and with robustness analysis showing (a) the importance of connection strength; and (b) the findings being robust to noise. Second, although critical regions and connections were significantly based on their local network properties, global influences sometimes deviated from local ones (e.g., critical globally but with lower local scores), thereby revealing global-level interactions. Third, the critical components organized into two main pathways (one from piriform cortex to globus pallidus; the other, entorhinal cortex to the amygdala), and two main clusters (centred on caudoputamen and entorhinal cortex). Fourth, for brain function, all main categories from perception to action were represented: e.g., olfaction (piriform cortex), learning and memory (entorhinal cortex), affect (amygdala and caudoputamen), and cognitive and motor processing (caudoputamen, globus pallidus). Finally, the claustrum was intriguingly identified as critical, perhaps for information integration and motor translation. Vulnerability analysis provides a unique approach to characterizing the fundamental structure of nervous systems.

Comprehensive analysis of the C. elegans connectome reveals novel circuits and functions of previously unstudied neurons

Despite decades of research on the Caenorhabditis elegans nervous system based on an anatomical description of synaptic connectivity, the circuits underlying behavior remain incompletely described and the functions of many neurons are still unknown. Updated and more complete chemical and gap junction connectomes of both adult sexes covering the entire animal including the muscle end organ have become available recently. Here, these are analyzed to gain insight into the overall structure of the connectivity network and to suggest functions of individual neuron classes. Modularity analysis divides the connectome graph into 10 communities that can be correlated with broad categories of behavior. A significant role of the body wall musculature end organ is emphasized as both a site of significant information convergence and as a source of sensory input in a feedback loop. Convergence of pathways for multisensory integration occurs throughout the network-most interneurons have similar indegrees and outdegrees and hence disperse information as much as they aggregate it. New insights include description of a set of high degree interneurons connected by many gap junctions running through the ventral cord that may represent a previously unrecognized locus of information processing. There is an apparent mechanosensory and proprioceptive field covering the entire body formed by connectivity of the many mechanosensory neurons of multiple types to 2 interneurons with output connections across the nervous system. Several additional significant, previously unrecognized circuits and pathways are uncovered, some involving unstudied neurons. The insights are valuable for guiding theoretical investigation of network properties as well as experimental studies of the functions of individual neurons, groups of neurons, and circuits.

FUNCTIONS OF C. ELEGANS NEURONS FROM SYNAPTIC CONNECTIVITY

Despite decades of research on the C. elegans nervous system based on an anatomical description of synaptic connectivity, the circuits underlying behavior remain incompletely described and the functions of many neurons are still unknown. Updated and more complete chemical and gap junction connectomes of both adult sexes covering the entire animal including the muscle end organ have become available recently. Here these are analyzed to gain insight into the overall structure of the connectivity network and to suggest functions of individual neuron classes. Modularity analysis divides the connectome graph into ten communities that can be correlated with broad categories of behavior. A significant role of the body wall musculature end organ is emphasized as both a site of significant information convergence and as a source of sensory input in a feedback loop. Convergence of pathways for multisensory integration occurs throughout the network - most interneurons have similar indegrees and outdegrees and hence disperse information as much as they aggregate it. New insights include description of a set of high degree interneurons connected by many gap junctions running through the ventral cord that may represent a previously unrecognized locus of information processing. There is an apparent mechanosensory and proprioceptive field covering the entire body formed by connectivity of the many mechanosensory neurons of multiple types to two interneurons with output connections across the nervous system. Several additional significant, previously unrecognized circuits and pathways are uncovered, some involving unstudied neurons. The insights are valuable for guiding theoretical investigation of network properties as well as experimental studies of the functions of individual neurons, groups of neurons, and circuits.

Communities in C. elegans connectome through the prism of non-backtracking walks

The fundamental relationship between the mesoscopic structure of neuronal circuits and organismic functions they subserve is one of the major challenges in contemporary neuroscience. Formation of structurally connected modules of neurons enacts the conversion from single-cell firing to large-scale behaviour of an organism, highlighting the importance of their accurate profiling in the data. While connectomes are typically characterized by significant sparsity of neuronal connections, recent advances in network theory and machine learning have revealed fundamental limitations of traditionally used community detection approaches in cases where the network is sparse. Here we studied the optimal community structure in the structural connectome of Caenorhabditis elegans, for which we exploited a non-conventional approach that is based on non-backtracking random walks, virtually eliminating the sparsity issue. In full agreement with the previous asymptotic results, we demonstrated that non-backtracking walks resolve the ground truth annotation into clusters on stochastic block models (SBM) with the size and density of the connectome better than the spectral methods related to simple random walks. Based on the cluster detectability threshold, we determined that the optimal number of modules in a recently mapped connectome of C. elegans is 10, which precisely corresponds to the number of isolated eigenvalues in the spectrum of the non-backtracking flow matrix. The discovered communities have a clear interpretation in terms of their functional role, which allows one to discern three structural compartments in the worm: the Worm Brain (WB), the Worm Movement Controller (WMC), and the Worm Information Flow Connector (WIFC). Broadly, our work provides a robust network-based framework to reveal mesoscopic structures in sparse connectomic datasets, paving way to further investigation of connectome mechanisms for different functions.

Connectivity and network burst properties of in-vitro neuronal networks induced by a clustered structure with alginate hydrogel patterning

Modularity is one of the important structural properties that affect information processing and other functionalities of neuronal networks. Researchers have developed in-vitro clustered network models for reproducing the modularity, but it is still challenging to control the segregation and integration of several sub-populations of them. We cultured clustered networks with alginate patterning and collected the electrophysiological signals to investigate the changes in functional properties during the development. We built inter-connected neuronal clusters using alginate micro-patterning with a circular shape on the surface of the micro-electrode array. The neuronal clusters were enabled to be connected at 3 or 10 days-in-vitro (DIV) by removing the barrier. The neuronal signals from different types of networks were collected from 16 to 34 DIV, and functional characteristics were examined. Connectivity and burst motif analysis were carried out to find out the relation between the structure and function of the networks. Neuronal networks with clustered structure showed different activity properties from the random networks along the development. The clustered networks had more short-range connections compared to the random networks. In the network burst motif analysis, the clustered networks showed more various patterns and a slower propagation of the activation patterns. In this study, we successfully cultured neuronal networks with clustered structure, and the structure affected the functional properties. The network model suggested in this study will be a good solution for observing the effect of structure on function during their development.

Supplementary Information

The online version contains supplementary material available at 10.1007/s13534-023-00289-5.

Mesoscopic architecture enhances communication across the macaque connectome revealing structure-function correspondence in the brain

Analyzing the brain in terms of organizational structures at intermediate scales provides an approach to unravel the complexity arising from interactions between its large number of components. Focusing on a wiring diagram that spans the cortex, basal ganglia, and thalamus of the macaque brain, we identify robust modules in the network that provide a mesoscopic-level description of its topological architecture. Surprisingly, we find that the modular architecture facilitates rapid communication across the network, instead of localizing activity as is typically expected in networks having community organization. By considering processes of diffusive spreading and coordination, we demonstrate that the specific pattern of inter- and intramodular connectivity in the network allows propagation to be even faster than equivalent randomized networks with or without modular structure. This pattern of connectivity is seen at different scales and is conserved across principal cortical divisions, as well as subcortical structures. Furthermore, we find that the physical proximity between areas is insufficient to explain the modular organization, as similar mesoscopic structures can be obtained even after factoring out the effect of distance constraints on the connectivity. By supplementing the topological information about the macaque connectome with physical locations, volumes, and functions of the constituent areas and analyzing this augmented dataset, we reveal a counterintuitive role played by the modular architecture of the brain in promoting global coordination of its activity. It suggests a possible explanation for the ubiquity of modularity in brain networks.

The global neuronal workspace as a broadcasting network

A new strategy for moving forward in the characterization of the global neuronal workspace (GNW) is proposed. According to Dehaene, Changeux, and colleagues (Dehaene, 2014, pp. 304, 312; Dehaene & Changeux, 2004, 2005), broadcasting is the main function of the GNW. However, the dynamic network properties described by recent graph theoretic GNW models are consistent with many large-scale communication processes that are different from broadcasting. We propose to apply a different graph theoretic approach, originally developed for optimizing information dissemination in communication networks, which can be used to identify the pattern of frequency and phase-specific directed functional connections that the GNW would exhibit only if it were a broadcasting network.

A set of hub neurons and non-local connectivity features support global brain dynamics in C. elegans

The wiring architecture of neuronal networks is assumed to be a strong determinant of their dynamical computations. An ongoing effort in neuroscience is therefore to generate comprehensive synapse-resolution connectomes alongside brain-wide activity maps. However, the structure-function relationship, i.e., how the anatomical connectome and neuronal dynamics relate to each other on a global scale, remains unsolved. Systematically, comparing graph features in the C. elegans connectome with correlations in nervous system-wide neuronal dynamics, we found that few local connectivity motifs and mostly other non-local features such as triplet motifs and input similarities can predict functional relationships between neurons. Surprisingly, quantities such as connection strength and amount of common inputs do not improve these predictions, suggesting that the network's topology is sufficient. We demonstrate that hub neurons in the connectome are key to these relevant graph features. Consistently, inhibition of multiple hub neurons specifically disrupts brain-wide correlations. Thus, we propose that a set of hub neurons and non-local connectivity features provide an anatomical substrate for global brain dynamics.

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.

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.

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.

Hub connectivity, neuronal diversity, and gene expression in the Caenorhabditis elegans connectome

Studies of nervous system connectivity, in a wide variety of species and at different scales of resolution, have identified several highly conserved motifs of network organization. One such motif is a heterogeneous distribution of connectivity across neural elements, such that some elements act as highly connected and functionally important network hubs. These brain network hubs are also densely interconnected, forming a so-called rich club. Recent work in mouse has identified a distinctive transcriptional signature of neural hubs, characterized by tightly coupled expression of oxidative metabolism genes, with similar genes characterizing macroscale inter-modular hub regions of the human cortex. Here, we sought to determine whether hubs of the neuronal C. elegans connectome also show tightly coupled gene expression. Using open data on the chemical and electrical connectivity of 279 C. elegans neurons, and binary gene expression data for each neuron across 948 genes, we computed a correlated gene expression score for each pair of neurons, providing a measure of their gene expression similarity. We demonstrate that connections between hub neurons are the most similar in their gene expression while connections between nonhubs are the least similar. Genes with the greatest contribution to this effect are involved in glutamatergic and cholinergic signaling, and other communication processes. We further show that coupled expression between hub neurons cannot be explained by their neuronal subtype (i.e., sensory, motor, or interneuron), separation distance, chemically secreted neurotransmitter, birth time, pairwise lineage distance, or their topological module affiliation. Instead, this coupling is intrinsically linked to the identity of most hubs as command interneurons, a specific class of interneurons that regulates locomotion. Our results suggest that neural hubs may possess a distinctive transcriptional signature, preserved across scales and species, that is related to the involvement of hubs in regulating the higher-order behaviors of a given organism.

The Influence of Wiring Economy on Nervous System Evolution

The activity and maintenance of neurons requires substantial metabolic energy, resulting in selective pressure to decrease resource consumption by the nervous system. The wiring economy principle proposes that animals have evolved mechanisms that wire circuits efficiently by minimizing neurite length. Computational modeling of neuronal morphology, microcircuit organization, and neural networks reveals that wiring economy is a significant determinant of nervous system layout. The strategies for reducing wiring costs are shared across phyla and point to the possibility of generalizable rules that specify the development of efficient nervous systems. As the developmental mechanisms underpinning wiring economy are only now being elucidated, whether the molecular basis of this phenomenon is the result of conserved genetic programs or convergent evolution remains to be determined.

Micro-connectomics: probing the organization of neuronal networks at the cellular scale

Defining the organizational principles of neuronal networks at the cellular scale, or micro-connectomics, is a key challenge of modern neuroscience. In this Review, we focus on graph theoretical parameters of micro-connectome topology, often informed by economical principles that conceptually originated with Ramón y Cajal's conservation laws. First, we summarize results from studies in intact small organisms and in samples from larger nervous systems. We then evaluate the evidence for an economical trade-off between biological cost and functional value in the organization of neuronal networks. Various results suggest that many aspects of neuronal network organization are indeed the outcome of competition between these two fundamental selection pressures.

Vulnerability-Based Critical Neurons, Synapses, and Pathways in the Caenorhabditis elegans Connectome

Determining the fundamental architectural design of complex nervous systems will lead to significant medical and technological advances. Yet it remains unclear how nervous systems evolved highly efficient networks with near optimal sharing of pathways that yet produce multiple distinct behaviors to reach the organism’s goals. To determine this, the nematode roundworm Caenorhabditis elegans is an attractive model system. Progress has been made in delineating the behavioral circuits of the C. elegans, however, many details are unclear, including the specific functions of every neuron and synapse, as well as the extent the behavioral circuits are separate and parallel versus integrative and serial. Network analysis provides a normative approach to help specify the network design. We investigated the vulnerability of the Caenorhabditis elegans connectome by performing computational experiments that (a) “attacked” 279 individual neurons and 2,990 weighted synaptic connections (composed of 6,393 chemical synapses and 890 electrical junctions) and (b) quantified the effects of each removal on global network properties that influence information processing. The analysis identified 12 critical neurons and 29 critical synapses for establishing fundamental network properties. These critical constituents were found to be control elements—i.e., those with the most influence over multiple underlying pathways. Additionally, the critical synapses formed into circuit-level pathways. These emergent pathways provide evidence for (a) the importance of backward locomotion, avoidance behavior, and social feeding behavior to the organism; (b) the potential roles of specific neurons whose functions have been unclear; and (c) both parallel and serial design elements in the connectome—i.e., specific evidence for a mixed architectural design.

One of the most important scientific aims is to uncover the functional design principles of nervous systems. To reach this aim, it is useful to examine a complex nervous system that is both well specified and highly tractable, making the nematode roundworm Caenorhabditis elegans an attractive model system, especially since it is the only complete connectome currently available for analysis. In this computational study, we tested the effects of individual attacks on every neuron and synaptic connection in the C. elegans connectome to identify and characterize the most critical constituents of the network by quantifying the changes in key network properties of the connectome that influence information processing. Our analysis identified 12 neurons and 29 synapses critical to clustering, information integration and propagation. These critical constituents formed circuit-level structures that control network processing in the C. elegans connectome. We believe our study provides a significant advance in the understanding of the network topology of the C. elegans connectome, and provides insights into the fundamental architectural design of complex nervous systems.

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.

One of the goals of systems neuroscience is to elucidate the relationship between the structure of neuronal networks and the functional dynamics that they implement. An ideal model organism to study such interactions is the roundworm C. elegans, which not only has a fully mapped connectome, but has also been the object of extensive behavioural, genetic and neurophysiological experiments. Here we present an analysis of the neuronal network of C. elegans from a dynamical flow perspective. Our analysis reveals a multi-scale organisation of the signal flow in the network linked to anatomical and functional features of neurons, as well as identifying different neuronal roles in relation to signal propagation. We use our computational framework to explore biological input-response scenarios as well as exhaustive in silico ablations, which we relate to experimental findings reported in the literature.

Exploring the topological sources of robustness against invasion in biological and technological networks

For a network, the accomplishment of its functions despite perturbations is called robustness. Although this property has been extensively studied, in most cases, the network is modified by removing nodes. In our approach, it is no longer perturbed by site percolation, but evolves after site invasion. The process transforming resident/healthy nodes into invader/mutant/diseased nodes is described by the Moran model. We explore the sources of robustness (or its counterpart, the propensity to spread favourable innovations) of the US high-voltage power grid network, the Internet2 academic network, and the C. elegans connectome. We compare them to three modular and non-modular benchmark networks, and samples of one thousand random networks with the same degree distribution. It is found that, contrary to what happens with networks of small order, fixation probability and robustness are poorly correlated with most of standard statistics, but they depend strongly on the degree distribution. While community detection techniques are able to detect the existence of a central core in Internet2, they are not effective in detecting hierarchical structures whose topological complexity arises from the repetition of a few rules. Box counting dimension and Rent’s rule are applied to show a subtle trade-off between topological and wiring complexity.

Gibbs distribution for statistical analysis of graphical data with a sample application to fcMRI brain images

This paper develops object-oriented data analysis (OODA) statistical methods that are novel and complementary to existing methods of analysis of human brain scan connectomes, defined as graphs representing brain anatomical or functional connectivity. OODA is an emerging field where classical statistical approaches (e.g., hypothesis testing, regression, estimation, and confidence intervals) are applied to data objects such as graphs or functions. By analyzing data objects directly we avoid loss of information that occurs when data objects are transformed into numerical summary statistics. By providing statistical tools that analyze sets of connectomes without loss of information, new insights into neurology and medicine may be achieved. In this paper we derive the formula for statistical model fitting, regression, and mixture models; test their performance in simulation experiments; and apply them to connectomes from fMRI brain scans collected during a serial reaction time task study. Software for fitting graphical object-oriented data analysis is provided.

Activity and High-Order Effective Connectivity Alterations in Sanfilippo C Patient-Specific Neuronal Networks

Induced pluripotent stem cell (iPSC) technology has been successfully used to recapitulate phenotypic traits of several human diseases in vitro. Patient-specific iPSC-based disease models are also expected to reveal early functional phenotypes, although this remains to be proved. Here, we generated iPSC lines from two patients with Sanfilippo type C syndrome, a lysosomal storage disorder with inheritable progressive neurodegeneration. Mature neurons obtained from patient-specific iPSC lines recapitulated the main known phenotypes of the disease, not present in genetically corrected patient-specific iPSC-derived cultures. Moreover, neuronal networks organized in vitro from mature patient-derived neurons showed early defects in neuronal activity, network-wide degradation, and altered effective connectivity. Our findings establish the importance of iPSC-based technology to identify early functional phenotypes, which can in turn shed light on the pathological mechanisms occurring in Sanfilippo syndrome. This technology also has the potential to provide valuable readouts to screen compounds, which can prevent the onset of neurodegeneration.

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Fibroblasts from two Sanfilippo C patients were reprogrammed to obtain iPSCs

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iPSCs were successfully differentiated to neural cells that mimic the disease

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Networks of patients’ neurons show altered activity and connectivity

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Early functional phenotypes are prevented in gene-corrected patients’ neurons

Modular Brain Networks

The development of new technologies for mapping structural and functional brain connectivity has led to the creation of comprehensive network maps of neuronal circuits and systems. The architecture of these brain networks can be examined and analyzed with a large variety of graph theory tools. Methods for detecting modules, or network communities, are of particular interest because they uncover major building blocks or subnetworks that are particularly densely connected, often corresponding to specialized functional components. A large number of methods for community detection have become available and are now widely applied in network neuroscience. This article first surveys a number of these methods, with an emphasis on their advantages and shortcomings; then it summarizes major findings on the existence of modules in both structural and functional brain networks and briefly considers their potential functional roles in brain evolution, wiring minimization, and the emergence of functional specialization and complex dynamics.

Stochastic blockmodeling of the modules and core of the Caenorhabditis elegans connectome

Recently, there has been much interest in the community structure or mesoscale organization of complex networks. This structure is characterised either as a set of sparsely inter-connected modules or as a highly connected core with a sparsely connected periphery. However, it is often difficult to disambiguate these two types of mesoscale structure or, indeed, to summarise the full network in terms of the relationships between its mesoscale constituents. Here, we estimate a community structure with a stochastic blockmodel approach, the Erdős-Rényi Mixture Model, and compare it to the much more widely used deterministic methods, such as the Louvain and Spectral algorithms. We used the Caenorhabditis elegans (C. elegans) nervous system (connectome) as a model system in which biological knowledge about each node or neuron can be used to validate the functional relevance of the communities obtained. The deterministic algorithms derived communities with 4-5 modules, defined by sparse inter-connectivity between all modules. In contrast, the stochastic Erdős-Rényi Mixture Model estimated a community with 9 blocks or groups which comprised a similar set of modules but also included a clearly defined core, made of 2 small groups. We show that the "core-in-modules" decomposition of the worm brain network, estimated by the Erdős-Rényi Mixture Model, is more compatible with prior biological knowledge about the C. elegans nervous system than the purely modular decomposition defined deterministically. We also show that the blockmodel can be used both to generate stochastic realisations (simulations) of the biological connectome, and to compress network into a small number of super-nodes and their connectivity. We expect that the Erdős-Rényi Mixture Model may be useful for investigating the complex community structures in other (nervous) systems.

An anatomical substrate for integration among functional networks in human cortex

The human brain shows several characteristics of an efficient communication network architecture, including short communication paths and the existence of modules interlinked by a small set of highly connected regions. Studies of structural networks comprising macroscopic white matter projections have shown that these putative hubs are densely interconnected, giving rise to a spatially distributed and topologically central collective called the "rich club." In parallel, studies of intrinsic brain activity have consistently revealed distinct functional communities or resting-state networks (RSNs), indicative of specialized processing and segregation of neuronal information. However, the pattern of structural connectivity interconnecting these functional RSNs and how such inter-RSN structural connections might bring about functional integration between RSNs remain largely unknown. Combining high-resolution diffusion weighted imaging with resting-state fMRI, we present novel evidence suggesting that the rich club structure plays a central role in cross-linking macroscopic RSNs of the human brain. Rich club hub nodes were present in all functional networks, accounted for a large proportion of "connector nodes," and were found to coincide with regions in which multiple networks overlap. In addition, a large proportion of all inter-RSN connections were found to involve rich club nodes, and these connections participated in a disproportionate number of communication paths linking nodes in different RSNs. Our findings suggest that the brain's rich club serves as a macroscopic anatomical substrate to cross-link functional networks and thus plays an important role in the integration of information between segregated functional domains of the human cortex.

Navigating traditional chinese medicine network pharmacology and computational tools

The concept of "network target" has ushered in a new era in the field of traditional Chinese medicine (TCM). As a new research approach, network pharmacology is based on the analysis of network models and systems biology. Taking advantage of advancements in systems biology, a high degree of integration data analysis strategy and interpretable visualization provides deeper insights into the underlying mechanisms of TCM theories, including the principles of herb combination, biological foundations of herb or herbal formulae action, and molecular basis of TCM syndromes. In this study, we review several recent developments in TCM network pharmacology research and discuss their potential for bridging the gap between traditional and modern medicine. We briefly summarize the two main functional applications of TCM network models: understanding/uncovering and predicting/discovering. In particular, we focus on how TCM network pharmacology research is conducted and highlight different computational tools, such as network-based and machine learning algorithms, and sources that have been proposed and applied to the different steps involved in the research process. To make network pharmacology research commonplace, some basic network definitions and analysis methods are presented.

The rich club of the C. elegans neuronal connectome

There is increasing interest in topological analysis of brain networks as complex systems, with researchers often using neuroimaging to represent the large-scale organization of nervous systems without precise cellular resolution. Here we used graph theory to investigate the neuronal connectome of the nematode worm Caenorhabditis elegans, which is defined anatomically at a cellular scale as 2287 synaptic connections between 279 neurons. We identified a small number of highly connected neurons as a rich club (N = 11) interconnected with high efficiency and high connection distance. Rich club neurons comprise almost exclusively the interneurons of the locomotor circuits, with known functional importance for coordinated movement. The rich club neurons are connector hubs, with high betweenness centrality, and many intermodular connections to nodes in different modules. On identifying the shortest topological paths (motifs) between pairs of peripheral neurons, the motifs that are found most frequently traverse the rich club. The rich club neurons are born early in development, before visible movement of the animal and before the main phase of developmental elongation of its body. We conclude that the high wiring cost of the globally integrative rich club of neurons in the C. elegans connectome is justified by the adaptive value of coordinated movement of the animal. The economical trade-off between physical cost and behavioral value of rich club organization in a cellular connectome confirms theoretical expectations and recapitulates comparable results from human neuroimaging on much larger scale networks, suggesting that this may be a general and scale-invariant principle of brain network organization.

Systematic analysis of neural projections reveals clonal composition of the Drosophila brain

BACKGROUND

During development neurons are generated by sequential divisions of neural stem cells, or neuroblasts. In the insect brain progeny of certain stem cells form lineage-specific sets of projections that arborize in distinct brain regions, called clonal units. Though this raises the possibility that the entire neural network in the brain might be organized in a clone-dependent fashion, only a small portion of clones has been identified.

RESULTS

Using Drosophila melanogaster, we randomly labeled one of about 100 stem cells at the beginning of the larval stage, analyzed the projection patterns of their progeny in the adult, and identified 96 clonal units in the central part of the fly brain, the cerebrum. Neurons of all the clones arborize in distinct regions of the brain, though many clones feature heterogeneous groups of neurons in terms of their projection patterns and neurotransmitters. Arborizations of clones overlap preferentially to form several groups of closely associated clones. Fascicles and commissures were all made by unique sets of clones. Whereas well-investigated brain regions such as the mushroom body and central complex consist of relatively small numbers of clones and are specifically connected with a limited number of neuropils, seemingly disorganized neuropils surrounding them are composed by a much larger number of clones and have extensive specific connections with many other neuropils.

CONCLUSIONS

Our study showed that the insect brain is formed by a composition of cell-lineage-dependent modules. Clonal analysis reveals organized architecture even in those neuropils without obvious structural landmarks.

Trade-off between multiple constraints enables simultaneous formation of modules and hubs in neural systems

The formation of the complex network architecture of neural systems is subject to multiple structural and functional constraints. Two obvious but apparently contradictory constraints are low wiring cost and high processing efficiency, characterized by short overall wiring length and a small average number of processing steps, respectively. Growing evidence shows that neural networks are results from a trade-off between physical cost and functional value of the topology. However, the relationship between these competing constraints and complex topology is not well understood quantitatively. We explored this relationship systematically by reconstructing two known neural networks, Macaque cortical connectivity and C. elegans neuronal connections, from combinatory optimization of wiring cost and processing efficiency constraints, using a control parameter α, and comparing the reconstructed networks to the real networks. We found that in both neural systems, the reconstructed networks derived from the two constraints can reveal some important relations between the spatial layout of nodes and the topological connectivity, and match several properties of the real networks. The reconstructed and real networks had a similar modular organization in a broad range of α, resulting from spatial clustering of network nodes. Hubs emerged due to the competition of the two constraints, and their positions were close to, and partly coincided, with the real hubs in a range of α values. The degree of nodes was correlated with the density of nodes in their spatial neighborhood in both reconstructed and real networks. Generally, the rebuilt network matched a significant portion of real links, especially short-distant ones. These findings provide clear evidence to support the hypothesis of trade-off between multiple constraints on brain networks. The two constraints of wiring cost and processing efficiency, however, cannot explain all salient features in the real networks. The discrepancy suggests that there are further relevant factors that are not yet captured here.

Modular neuronal assemblies embodied in a closed-loop environment: toward future integration of brains and machines

Behaviors, from simple to most complex, require a two-way interaction with the environment and the contribution of different brain areas depending on the orchestrated activation of neuronal assemblies. In this work we present a new hybrid neuro-robotic architecture based on a neural controller bi-directionally connected to a virtual robot implementing a Braitenberg vehicle aimed at avoiding obstacles. The robot is characterized by proximity sensors and wheels, allowing it to navigate into a circular arena with obstacles of different sizes. As neural controller, we used hippocampal cultures dissociated from embryonic rats and kept alive over Micro Electrode Arrays (MEAs) for 3-8 weeks. The developed software architecture guarantees a bi-directional exchange of information between the natural and the artificial part by means of simple linear coding/decoding schemes. We used two different kinds of experimental preparation: "random" and "modular" populations. In the second case, the confinement was assured by a polydimethylsiloxane (PDMS) mask placed over the surface of the MEA device, thus defining two populations interconnected via specific microchannels. The main results of our study are: (i) neuronal cultures can be successfully interfaced to an artificial agent; (ii) modular networks show a different dynamics with respect to random culture, both in terms of spontaneous and evoked electrophysiological patterns; (iii) the robot performs better if a reinforcement learning paradigm (i.e., a tetanic stimulation delivered to the network following each collision) is activated, regardless of the modularity of the culture; (iv) the robot controlled by the modular network further enhances its capabilities in avoiding obstacles during the short-term plasticity trial. The developed paradigm offers a new framework for studying, in simplified model systems, neuro-artificial bi-directional interfaces for the development of new strategies for brain-machine interaction.

Phase synchronization of bursting neurons in clustered small-world networks

We investigate the collective dynamics of bursting neurons on clustered networks. The clustered network model is composed of subnetworks, each of them presenting the so-called small-world property. This model can also be regarded as a network of networks. In each subnetwork a neuron is connected to other ones with regular as well as random connections, the latter with a given intracluster probability. Moreover, in a given subnetwork each neuron has an intercluster probability to be connected to the other subnetworks. The local neuron dynamics has two time scales (fast and slow) and is modeled by a two-dimensional map. In such small-world network the neuron parameters are chosen to be slightly different such that, if the coupling strength is large enough, there may be synchronization of the bursting (slow) activity. We give bounds for the critical coupling strength to obtain global burst synchronization in terms of the network structure, that is, the probabilities of intracluster and intercluster connections. We find that, as the heterogeneity in the network is reduced, the network global synchronizability is improved. We show that the transitions to global synchrony may be abrupt or smooth depending on the intercluster probability.

Detecting alternative graph clusterings

The problem of graph clustering or community detection has enjoyed a lot of attention in complex networks literature. A quality function, modularity, quantifies the strength of clustering and on maximization yields sensible partitions. However, in most real world networks, there are an exponentially large number of near-optimal partitions with some being very different from each other. Therefore, picking an optimal clustering among the alternatives does not provide complete information about network topology. To tackle this problem, we propose a graph perturbation scheme which can be used to identify an ensemble of near-optimal and diverse clusterings. We establish analytical properties of modularity function under the perturbation which ensures diversity. Our approach is algorithm independent and therefore can leverage any of the existing modularity maximizing algorithms. We numerically show that our methodology can systematically identify very different partitions on several existing data sets. The knowledge of diverse partitions sheds more light into the topological organization and helps gain a more complete understanding of the underlying complex network.

Enhancement of neural representation capacity by modular architecture in networks of cortical neurons

Biological networks are ubiquitously modular, a feature that is believed to be essential for the enhancement of their functional capacities. Here, we have used a simple modular in vitro design to examine the possibility that modularity enhances network functionality in the context of input representation. We cultured networks of cortical neurons obtained from newborn rats in vitro on substrate-integrated multi-electrode arrays, forcing the network to develop two well-defined modules of neural populations that are coupled by a narrow canal. We measured the neural activity, and examined the capacity of each module to individually classify (i.e. represent) spatially distinct electrical stimuli and propagate input-specific activity features to their downstream coupled counterpart. We show that, although each of the coupled modules maintains its autonomous functionality, a significant enhancement of representational capacity is achieved when the system is observed as a whole. We interpret our results in terms of a relative decorrelation effect imposed by weak coupling between modules.

Exploring brain function from anatomical connectivity

The intrinsic relationship between the architecture of the brain and the range of sensory and behavioral phenomena it produces is a relevant question in neuroscience. Here, we review recent knowledge gained on the architecture of the anatomical connectivity by means of complex network analysis. It has been found that cortico-cortical networks display a few prominent characteristics: (i) modular organization, (ii) abundant alternative processing paths, and (iii) the presence of highly connected hubs. Additionally, we present a novel classification of cortical areas of the cat according to the role they play in multisensory connectivity. All these properties represent an ideal anatomical substrate supporting rich dynamical behaviors, facilitating the capacity of the brain to process sensory information of different modalities segregated and to integrate them toward a comprehensive perception of the real world. The results here exposed are mainly based on anatomical data of cats’ brain, but further observations suggest that, from worms to humans, the nervous system of all animals might share these fundamental principles of organization.

Cognitive effort drives workspace configuration of human brain functional networks

Effortful cognitive performance is theoretically expected to depend on the formation of a global neuronal workspace. We tested specific predictions of workspace theory, using graph theoretical measures of network topology and physical distance of synchronization, in magnetoencephalographic data recorded from healthy adult volunteers (N = 13) during performance of a working memory task at several levels of difficulty. We found that greater cognitive effort caused emergence of a more globally efficient, less clustered, and less modular network configuration, with more long-distance synchronization between brain regions. This pattern of task-related workspace configuration was more salient in the β-band (16-32 Hz) and γ-band (32-63 Hz) networks, compared with both lower (α-band; 8-16 Hz) and higher (high γ-band; 63-125 Hz) frequency intervals. Workspace configuration of β-band networks was also greater in faster performing participants (with correct response latency less than the sample median) compared with slower performing participants. Processes of workspace formation and relaxation in relation to time-varying demands for cognitive effort could be visualized occurring in the course of task trials lasting <2 s. These experimental results provide support for workspace theory in terms of complex network metrics and directly demonstrate how cognitive effort breaks modularity to make human brain functional networks transiently adopt a more efficient but less economical configuration.

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.

Modular and hierarchically modular organization of brain networks

Brain networks are increasingly understood as one of a large class of information processing systems that share important organizational principles in common, including the property of a modular community structure. A module is topologically defined as a subset of highly inter-connected nodes which are relatively sparsely connected to nodes in other modules. In brain networks, topological modules are often made up of anatomically neighboring and/or functionally related cortical regions, and inter-modular connections tend to be relatively long distance. Moreover, brain networks and many other complex systems demonstrate the property of hierarchical modularity, or modularity on several topological scales: within each module there will be a set of sub-modules, and within each sub-module a set of sub-sub-modules, etc. There are several general advantages to modular and hierarchically modular network organization, including greater robustness, adaptivity, and evolvability of network function. In this context, we review some of the mathematical concepts available for quantitative analysis of (hierarchical) modularity in brain networks and we summarize some of the recent work investigating modularity of structural and functional brain networks derived from analysis of human neuroimaging data.

Cause-effect relationships in medicine: a protein network perspective

Current target-based drug discovery platforms are not able to predict drug efficacy and the full spectrum of drug effects in organisms. Hence, many experimental drugs do not survive the lengthy and costly process of drug development. Understanding how drugs affect cellular network structures and how the resulting signals are translated into drug effects is extremely important for the discovery of new medicines. This requires a greater understanding of cause-effect relationships at the organism, organ, tissue, cellular, and molecular level. There is a growing recognition that this information must be integrated into discovery paradigms, but a 'road map' for obtaining and integrating information about heterogeneous networks into drug-discovery platforms currently does not exist. This review explores recent network-centered approaches developed to investigate the genesis of medicine and disease effects, specifically highlighting protein-protein interaction network models and their use in cause-effect analyses in medicine.