Understanding the mind of a worm: hierarchical network structure underlying nervous system function in C. elegans

Association of Bidirectional Network Cores in the Brain with Perceptual Awareness and Cognition

The brain comprises a complex network of interacting regions. To understand the roles and mechanisms of this intricate network, it is crucial to elucidate its structural features related to cognitive functions. Recent empirical evidence suggests that both feedforward and feedback signals are necessary for conscious perception, emphasizing the importance of subnetworks with bidirectional interactions. However, the link between such subnetworks and conscious perception remains unclear due to the complexity of brain networks. In this study, we propose a framework for extracting subnetworks with strong bidirectional interactions-termed the "cores" of a network-from brain activity. We applied this framework to resting-state and task-based human fMRI data from participants of both sexes to identify regions forming strongly bidirectional cores. We then explored the association of these cores with conscious perception and cognitive functions. We found that the extracted central cores predominantly included cerebral cortical regions rather than subcortical regions. Additionally, regarding their relation to conscious perception, we demonstrated that the cores tend to include regions previously reported to be affected by electrical stimulation that altered conscious perception, although the results are not statistically robust due to the small sample size. Furthermore, in relation to cognitive functions, based on a meta-analysis and comparison of the core structure with a cortical functional connectivity gradient, we found that the central cores were related to unimodal sensorimotor functions. The proposed framework provides novel insights into the roles of network cores with strong bidirectional interactions in conscious perception and unimodal sensorimotor functions.

A hierarchy index for networks in the brain reveals a complex entangled organizational structure

Networks involved in information processing often have their nodes arranged hierarchically, with the majority of connections occurring in adjacent levels. However, despite being an intuitively appealing concept, the hierarchical organization of large networks, such as those in the brain, is difficult to identify, especially in absence of additional information beyond that provided by the connectome. In this paper, we propose a framework to uncover the hierarchical structure of a given network, that identifies the nodes occupying each level as well as the sequential order of the levels. It involves optimizing a metric that we use to quantify the extent of hierarchy present in a network. Applying this measure to various brain networks, ranging from the nervous system of the nematode Caenorhabditis elegans to the human connectome, we unexpectedly find that they exhibit a common network architectural motif intertwining hierarchy and modularity. This suggests that brain networks may have evolved to simultaneously exploit the functional advantages of these two types of organizations, viz., relatively independent modules performing distributed processing in parallel and a hierarchical structure that allows sequential pooling of these multiple processing streams. An intriguing possibility is that this property we report may be common to information processing networks in general.

Does the brain behave like a (complex) network? I. Dynamics

Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network structure does not entail that the brain actually works as a network. Asking whether the brain behaves as a network means asking whether network properties count. From the viewpoint of neurophysiology and, possibly, of brain physics, the most substantial issues a network structure may be instrumental in addressing relate to the influence of network properties on brain dynamics and to whether these properties ultimately explain some aspects of brain function. Here, we address the dynamical implications of complex network, examining which aspects and scales of brain activity may be understood to genuinely behave as a network. To do so, we first define the meaning of networkness, and analyse some of its implications. We then examine ways in which brain anatomy and dynamics can be endowed with a network structure and discuss possible ways in which network structure may be shown to represent a genuine organisational principle of brain activity, rather than just a convenient description of its anatomy and dynamics.

Bayesian Inference of a Spectral Graph Model for Brain Oscillations

The relationship between brain functional connectivity and structural connectivity has caught extensive attention of the neuroscience community, commonly inferred using mathematical modeling. Among many modeling approaches, spectral graph model (SGM) is distinctive as it has a closed-form solution of the wide-band frequency spectra of brain oscillations, requiring only global biophysically interpretable parameters. While SGM is parsimonious in parameters, the determination of SGM parameters is non-trivial. Prior works on SGM determine the parameters through a computational intensive annealing algorithm, which only provides a point estimate with no confidence intervals for parameter estimates. To fill this gap, we incorporate the simulation-based inference (SBI) algorithm and develop a Bayesian procedure for inferring the posterior distribution of the SGM parameters. Furthermore, using SBI dramatically reduces the computational burden for inferring the SGM parameters. We evaluate the proposed SBI-SGM framework on the resting-state magnetoencephalography recordings from healthy subjects and show that the proposed procedure has similar performance to the annealing algorithm in recovering power spectra and the spatial distribution of the alpha frequency band. In addition, we also analyze the correlations among the parameters and their uncertainty with the posterior distribution which can not be done with annealing inference. These analyses provide a richer understanding of the interactions among biophysical parameters of the SGM. In general, the use of simulation-based Bayesian inference enables robust and efficient computations of generative model parameter uncertainties and may pave the way for the use of generative models in clinical translation applications.

Stability and dynamics of a spectral graph model of brain oscillations

We explore the stability and dynamic properties of a hierarchical, linearized, and analytic spectral graph model for neural oscillations that integrates the structural wiring of the brain. Previously, we have shown that this model can accurately capture the frequency spectra and the spatial patterns of the alpha and beta frequency bands obtained from magnetoencephalography recordings without regionally varying parameters. Here, we show that this macroscopic model based on long-range excitatory connections exhibits dynamic oscillations with a frequency in the alpha band even without any oscillations implemented at the mesoscopic level. We show that depending on the parameters, the model can exhibit combinations of damped oscillations, limit cycles, or unstable oscillations. We determined bounds on model parameters that ensure stability of the oscillations simulated by the model. Finally, we estimated time-varying model parameters to capture the temporal fluctuations in magnetoencephalography activity. We show that a dynamic spectral graph modeling framework with a parsimonious set of biophysically interpretable model parameters can thereby be employed to capture oscillatory fluctuations observed in electrophysiological data in various brain states and diseases.

A Data-Driven Simulation of the Trophallactic Network and Intranidal Food Flow Dissemination in Ants

Food sharing can occur in both social and non-social species, but it is crucial in eusocial species, in which only some group members collect food. This food collection and the intranidal (i.e., inside the nest) food distribution through trophallactic (i.e., mouth-to-mouth) exchanges are fundamental in eusocial insects. However, the behavioural rules underlying the regulation and the dynamics of food intake and the resulting networks of exchange are poorly understood. In this study, we provide new insights into the behavioural rules underlying the structure of trophallactic networks and food dissemination dynamics within the colony. We build a simple data-driven model that implements interindividual variability and the division of labour to investigate the processes of food accumulation/dissemination inside the nest, both at the individual and collective levels. We also test the alternative hypotheses (no variability and no division of labour). The division of labour, combined with inter-individual variability, leads to predictions of the food dynamics and exchange networks that run, contrary to the other models. Our results suggest a link between the interindividual heterogeneity of the trophallactic behaviours, the food flow dynamics and the network of trophallactic events. Our results show that a slight level of heterogeneity in the number of trophallactic events is enough to generate the properties of the experimental networks and seems to be crucial for the creation of efficient trophallactic networks. Despite the relative simplicity of the model rules, efficient trophallactic networks may emerge as the networks observed in ants, leading to a better understanding of the evolution of self-organisation in such societies.

A Perspective on Information Optimality in a Neural Circuit and Other Biological Systems

The nematode worm Caenorhabditis elegans has a relatively simple neural system for analysis of information transmission from sensory organ to muscle fiber. Consequently, this study includes an example of a neural circuit from the nematode worm, and a procedure is shown for measuring its information optimality by use of a logic gate model. This approach is useful where the assumptions are applicable for a neural circuit, and also for choosing between competing mathematical hypotheses that explain the function of a neural circuit. In this latter case, the logic gate model can estimate computational complexity and distinguish which of the mathematical models require fewer computations. In addition, the concept of information optimality is generalized to other biological systems, along with an extended discussion of its role in genetic-based pathways of organisms.

Hierarchical networks of food exchange in the black garden ant Lasius niger

In most eusocial insects, the division of labor results in relatively few individuals foraging for the entire colony. Thus, the survival of the colony depends on its efficiency in meeting the nutritional needs of all its members. Here, we characterize the network topology of a eusocial insect to understand the role and centrality of each caste in this network during the process of food dissemination. We constructed trophallaxis networks from 34 food-exchange experiments in black garden ants (Lasius niger). We tested the influence of brood and colony size on (i) global indices at the network level (i.e., efficiency, resilience, centralization, and modularity) and (ii) individual values (i.e., degree, strength, betweenness, and the clustering coefficient). Network resilience, the ratio between global efficiency and centralization, was stable with colony size but increased in the presence of broods, presumably in response to the nutritional needs of larvae. Individual metrics highlighted the major role of foragers in food dissemination. In addition, a hierarchical clustering analysis suggested that some domestics acted as intermediaries between foragers and other domestics. Networks appeared to be hierarchical rather than random or centralized exclusively around foragers. Finally, our results suggested that networks emerging from social insect interactions can improve group performance and thus colony fitness.

Emergence of canonical functional networks from the structural connectome

How do functional brain networks emerge from the underlying wiring of the brain? We examine how resting-state functional activation patterns emerge from the underlying connectivity and length of white matter fibers that constitute its “structural connectome”. By introducing realistic signal transmission delays along fiber projections, we obtain a complex-valued graph Laplacian matrix that depends on two parameters: coupling strength and oscillation frequency. This complex Laplacian admits a complex-valued eigen-basis in the frequency domain that is highly tunable and capable of reproducing the spatial patterns of canonical functional networks without requiring any detailed neural activity modeling. Specific canonical functional networks can be predicted using linear superposition of small subsets of complex eigenmodes. Using a novel parameter inference procedure we show that the complex Laplacian outperforms the real-valued Laplacian in predicting functional networks. The complex Laplacian eigenmodes therefore constitute a tunable yet parsimonious substrate on which a rich repertoire of realistic functional patterns can emerge. Although brain activity is governed by highly complex nonlinear processes and dense connections, our work suggests that simple extensions of linear models to the complex domain effectively approximate rich macroscopic spatial patterns observable on BOLD fMRI.

Structural and developmental principles of neuropil assembly in C. elegans

Neuropil is a fundamental form of tissue organization within the brain¹, in which densely packed neurons synaptically interconnect into precise circuit architecture^2,3. However, the structural and developmental principles that govern this nanoscale precision remain largely unknown^4,5. Here we use an iterative data coarse-graining algorithm termed 'diffusion condensation'⁶ to identify nested circuit structures within the Caenorhabditis elegans neuropil, which is known as the nerve ring. We show that the nerve ring neuropil is largely organized into four strata that are composed of related behavioural circuits. The stratified architecture of the neuropil is a geometrical representation of the functional segregation of sensory information and motor outputs, with specific sensory organs and muscle quadrants mapping onto particular neuropil strata. We identify groups of neurons with unique morphologies that integrate information across strata and that create neural structures that cage the strata within the nerve ring. We use high resolution light-sheet microscopy^7,8 coupled with lineage-tracing and cell-tracking algorithms^9,10 to resolve the developmental sequence and reveal principles of cell position, migration and outgrowth that guide stratified neuropil organization. Our results uncover conserved structural design principles that underlie the architecture and function of the nerve ring neuropil, and reveal a temporal progression of outgrowth-based on pioneer neurons-that guides the hierarchical development of the layered neuropil. Our findings provide a systematic blueprint for using structural and developmental approaches to understand neuropil organization within the brain.

Modelling epilepsy in the mouse: challenges and solutions

In most mouse models of disease, the outward manifestation of a disorder can be measured easily, can be assessed with a trivial test such as hind limb clasping, or can even be observed simply by comparing the gross morphological characteristics of mutant and wild-type littermates. But what if we are trying to model a disorder with a phenotype that appears only sporadically and briefly, like epileptic seizures? The purpose of this Review is to highlight the challenges of modelling epilepsy, in which the most obvious manifestation of the disorder, seizures, occurs only intermittently, possibly very rarely and often at times when the mice are not under direct observation. Over time, researchers have developed a number of ways in which to overcome these challenges, each with their own advantages and disadvantages. In this Review, we describe the genetics of epilepsy and the ways in which genetically altered mouse models have been used. We also discuss the use of induced models in which seizures are brought about by artificial stimulation to the brain of wild-type animals, and conclude with the ways these different approaches could be used to develop a wider range of anti-seizure medications that could benefit larger patient populations.

Summary: This Review discusses the challenges of modelling epilepsy in mice, a condition in which the outward manifestation of the disorder appears only sporadically, and reviews possible solutions encompassing both genetic and induced models.

A Novel Neural Model With Lateral Interaction for Learning Tasks

We propose a novel neural model with lateral interaction for learning tasks. The model consists of two functional fields: an elementary field to extract features and a high-level field to store and recognize patterns. Each field is composed of some neurons with lateral interaction, and the neurons in different fields are connected by the rules of synaptic plasticity. The model is established on the current research of cognition and neuroscience, making it more transparent and biologically explainable. Our proposed model is applied to data classification and clustering. The corresponding algorithms share similar processes without requiring any parameter tuning and optimization processes. Numerical experiments validate that the proposed model is feasible in different learning tasks and superior to some state-of-the-art methods, especially in small sample learning, one-shot learning, and clustering.

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.

Discordant attributes of structural and functional brain connectivity in a two-layer multiplex network

Several studies have suggested that functional connectivity (FC) is constrained by the underlying structural connectivity (SC) and mutually correlated. However, not many studies have focused on differences in the network organization of SC and FC, and on how these differences may inform us about their mutual interaction. To explore this issue, we adopt a multi-layer framework, with SC and FC, constructed using Magnetic Resonance Imaging (MRI) data from the Human Connectome Project, forming a two-layer multiplex network. In particular, we examine node strength assortativity within and between the SC and FC layer. We find that, in general, SC is organized assortatively, indicating brain regions are on average connected to other brain regions with similar node strengths. On the other hand, FC shows disassortative mixing. This discrepancy is apparent also among individual resting-state networks within SC and FC. In addition, these patterns show lateralization, with disassortative mixing within FC subnetworks mainly driven from the left hemisphere. We discuss our findings in the context of robustness to structural failure, and we suggest that discordant and lateralized patterns of associativity in SC and FC may provide clues to understand laterality of some neurological dysfunctions and recovery.

Cliques and cavities in the human connectome

Encoding brain regions and their connections as a network of nodes and edges captures many of the possible paths along which information can be transmitted as humans process and perform complex behaviors. Because cognitive processes involve large, distributed networks of brain areas, principled examinations of multi-node routes within larger connection patterns can offer fundamental insights into the complexities of brain function. Here, we investigate both densely connected groups of nodes that could perform local computations as well as larger patterns of interactions that would allow for parallel processing. Finding such structures necessitates that we move from considering exclusively pairwise interactions to capturing higher order relations, concepts naturally expressed in the language of algebraic topology. These tools can be used to study mesoscale network structures that arise from the arrangement of densely connected substructures called cliques in otherwise sparsely connected brain networks. We detect cliques (all-to-all connected sets of brain regions) in the average structural connectomes of 8 healthy adults scanned in triplicate and discover the presence of more large cliques than expected in null networks constructed via wiring minimization, providing architecture through which brain network can perform rapid, local processing. We then locate topological cavities of different dimensions, around which information may flow in either diverging or converging patterns. These cavities exist consistently across subjects, differ from those observed in null model networks, and - importantly - link regions of early and late evolutionary origin in long loops, underscoring their unique role in controlling brain function. These results offer a first demonstration that techniques from algebraic topology offer a novel perspective on structural connectomics, highlighting loop-like paths as crucial features in the human brain's structural architecture.

Ensemble Classification of Alzheimer's Disease and Mild Cognitive Impairment Based on Complex Graph Measures from Diffusion Tensor Images

The human brain is a complex network of interacting regions. The gray matter regions of brain are interconnected by white matter tracts, together forming one integrative complex network. In this article, we report our investigation about the potential of applying brain connectivity patterns as an aid in diagnosing Alzheimer's disease and Mild Cognitive Impairment (MCI). We performed pattern analysis of graph theoretical measures derived from Diffusion Tensor Imaging (DTI) data representing structural brain networks of 45 subjects, consisting of 15 patients of Alzheimer's disease (AD), 15 patients of MCI, and 15 healthy subjects (CT). We considered pair-wise class combinations of subjects, defining three separate classification tasks, i.e., AD-CT, AD-MCI, and CT-MCI, and used an ensemble classification module to perform the classification tasks. Our ensemble framework with feature selection shows a promising performance with classification accuracy of 83.3% for AD vs. MCI, 80% for AD vs. CT, and 70% for MCI vs. CT. Moreover, our findings suggest that AD can be related to graph measures abnormalities at Brodmann areas in the sensorimotor cortex and piriform cortex. In this way, node redundancy coefficient and load centrality in the primary motor cortex were recognized as good indicators of AD in contrast to MCI. In general, load centrality, betweenness centrality, and closeness centrality were found to be the most relevant network measures, as they were the top identified features at different nodes. The present study can be regarded as a "proof of concept" about a procedure for the classification of MRI markers between AD dementia, MCI, and normal old individuals, due to the small and not well-defined groups of AD and MCI patients. Future studies with larger samples of subjects and more sophisticated patient exclusion criteria are necessary toward the development of a more precise technique for clinical diagnosis.

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.

The C. elegans Connectome Consists of Homogenous Circuits with Defined Functional Roles

A major goal of systems neuroscience is to decipher the structure-function relationship in neural networks. Here we study network functionality in light of the common-neighbor-rule (CNR) in which a pair of neurons is more likely to be connected the more common neighbors it shares. Focusing on the fully-mapped neural network of C. elegans worms, we establish that the CNR is an emerging property in this connectome. Moreover, sets of common neighbors form homogenous structures that appear in defined layers of the network. Simulations of signal propagation reveal their potential functional roles: signal amplification and short-term memory at the sensory/inter-neuron layer, and synchronized activity at the motoneuron layer supporting coordinated movement. A coarse-grained view of the neural network based on homogenous connected sets alone reveals a simple modular network architecture that is intuitive to understand. These findings provide a novel framework for analyzing larger, more complex, connectomes once these become available.

Hierarchical organization of functional connectivity in the mouse brain: a complex network approach

This paper represents a contribution to the study of the brain functional connectivity from the perspective of complex networks theory. More specifically, we apply graph theoretical analyses to provide evidence of the modular structure of the mouse brain and to shed light on its hierarchical organization. We propose a novel percolation analysis and we apply our approach to the analysis of a resting-state functional MRI data set from 41 mice. This approach reveals a robust hierarchical structure of modules persistent across different subjects. Importantly, we test this approach against a statistical benchmark (or null model) which constrains only the distributions of empirical correlations. Our results unambiguously show that the hierarchical character of the mouse brain modular structure is not trivially encoded into this lower-order constraint. Finally, we investigate the modular structure of the mouse brain by computing the Minimal Spanning Forest, a technique that identifies subnetworks characterized by the strongest internal correlations. This approach represents a faster alternative to other community detection methods and provides a means to rank modules on the basis of the strength of their internal edges.

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.

Intelligence, Cognition, and Language of Green Plants

A summary definition of some 70 descriptions of intelligence provides a definition for all other organisms including plants that stresses fitness. Barbara McClintock, a plant biologist, posed the notion of the ‘thoughtful cell’ in her Nobel prize address. The systems structure necessary for a thoughtful cell is revealed by comparison of the interactome and connectome. The plant root cap, a group of some 200 cells that act holistically in responding to numerous signals, likely possesses a similar systems structure agreeing with Darwin’s description of acting like the brain of a lower organism. Intelligent behavior requires assessment of different choices and taking the beneficial one. Decisions are constantly required to optimize the plant phenotype to a dynamic environment and the cambium is the assessing tissue diverting more or removing resources from different shoot and root branches through manipulation of vascular elements. Environmental awareness likely indicates consciousness. Spontaneity in plant behavior, ability to count to five and error correction indicate intention. Volatile organic compounds are used as signals in plant interactions and being complex in composition may be the equivalent of language accounting for self and alien recognition by individual plants. Game theory describes competitive interactions. Interactive and intelligent outcomes emerge from application of various games between plants themselves and interactions with microbes. Behavior profiting from experience, another simple definition of intelligence, requires both learning and memory and is indicated in the priming of herbivory, disease and abiotic stresses.

Topological organization of connectivity strength in the rat connectome

The mammalian brain is a complex network of anatomically interconnected regions. Animal studies allow for an invasive measurement of the connections of these networks at the macroscale level by means of neuronal tracing of axonal projections, providing a unique opportunity for the formation of detailed 'connectome maps'. Here we analyzed the macroscale connectome of the rat brain, including detailed information on the macroscale interregional pathways between 67 cortical and subcortical regions as provided by the high-quality, open-access BAMS-II database on rat brain anatomical projections, focusing in particular on the non-uniform distribution of projection strength across pathways. First, network analysis confirmed a small-world, modular and rich club organization of the rat connectome; findings in clear support of previous studies on connectome organization in other mammalian species. More importantly, analyzing network properties of different connection weight classes, we extend previous observations by showing that pathways with different topological roles have significantly different levels of connectivity strength. Among other findings, intramodular connections are shown to display a higher connectivity strength than intermodular connections and hub-to-hub rich club connections are shown to include significantly stronger pathways than connections spanning between peripheral nodes. Furthermore, we show evidence indicating that edges of different weight classes display different topological structures, potentially suggesting varying roles and origins of pathways in the mammalian brain network.

A Model for Improving the Learning Curves of Artificial Neural Networks

In this article, the performance of a hybrid artificial neural network (i.e. scale-free and small-world) was analyzed and its learning curve compared to three other topologies: random, scale-free and small-world, as well as to the chemotaxis neural network of the nematode Caenorhabditis Elegans. One hundred equivalent networks (same number of vertices and average degree) for each topology were generated and each was trained for one thousand epochs. After comparing the mean learning curves of each network topology with the C. elegans neural network, we found that the networks that exhibited preferential attachment exhibited the best learning curves.

Analysis of core-periphery organization in protein contact networks reveals groups of structurally and functionally critical residues

The representation of proteins as networks of interacting amino acids, referred to as protein contact networks (PCN), and their subsequent analyses using graph theoretic tools, can provide novel insights into the key functional roles of specific groups of residues. We have characterized the networks corresponding to the native states of 66 proteins (belonging to different families) in terms of their core-periphery organization. The resulting hierarchical classification of the amino acid constituents of a protein arranges the residues into successive layers - having higher core order - with increasing connection density, ranging from a sparsely linked periphery to a densely intra-connected core (distinct from the earlier concept of protein core defined in terms of the three-dimensional geometry of the native state, which has least solvent accessibility). Our results show that residues in the inner cores are more conserved than those at the periphery. Underlining the functional importance of the network core, we see that the receptor sites for known ligand molecules of most proteins occur in the innermost core. Furthermore, the association of residues with structural pockets and cavities in binding or active sites increases with the core order. From mutation sensitivity analysis, we show that the probability of deleterious or intolerant mutations also increases with the core order. We also show that stabilization centre residues are in the innermost cores, suggesting that the network core is critically important in maintaining the structural stability of the protein. A publicly available Web resource for performing core-periphery analysis of any protein whose native state is known has been made available by us at http://www.imsc.res.in/ ~sitabhra/proteinKcore/index.html.

Alpha-linolenic acid suppresses dopaminergic neurodegeneration induced by 6-OHDA in C. elegans

Parkinson's disease (PD) is the second most common neurodegenerative disorder characterized by the specific and massive loss of dopamine (DA) containing neurons in the substantia nigra pars compacta (SNpc) and aggregation of protein α-synuclein. There are a few animal studies, which indirectly implicate the neuroprotective action of omega-3 polyunsaturated fatty acids in neurodegenerative diseases. In this study, we exposed Caenorhabditis elegans (both wild type N2, and transgenic strain, UA44) to 6-hydroxydopamine (6-OHDA, the model neurotoxicant) and evaluated the extent of protection offered by alpha-linolenic acid (ALA). Larval stage worms (L1/L2) of N2 and transgenic strains were exposed to 6-OHDA (25 mM) with or without ALA (10, 50 and 100 μM) for 48 h at 20 °C. After 48 h, while the N2 worms were assessed for their responses in terms of locomotion, pharyngeal pumping, lifespan and AChE activity, the transgenic worms were monitored for dopaminergic neuronal degeneration. Worms exposed to 6-OHDA exhibited a significant reduction (48%) in the locomotion rate. Interestingly, supplementation with ALA increased the locomotion rate in 6-OHDA treated worms. A marked decrease (45%) in thrashing was evident in worms exposed to 6-OHDA while thrashing was slightly improved in worms co-exposed to 6-OHDA and higher concentrations of ALA. Interestingly, worms co-exposed to 6-OHDA with ALA (100 μM) exhibited a significant increase in thrashing (66 ± 1.80 thrashes/30s). The pharyngeal pumping rate declined significantly in the case of worms exposed to 6-OHDA (35%). However, the worms co-treated with ALA exhibited significant recovery in pharyngeal pumping. The mean survival for the control worms was 26 days, while the worms exposed to 6-OHDA, showed a marked reduction in survival (21 days). Worms co-exposed to 6-OHDA and ALA showed a concentration-dependent increase in lifespan compared to those exposed to 6-OHDA alone (23, 25 and 26 days respectively). Transgenic worms treated with 6-OHDA showed significant loss of processes of CEP and ADE neurons as evident from visibly marked reduction in GFP expression. Worms co-exposed to 6-OHDA and ALA showed visibly significant reduction in neuronal degeneration in both CEP and ADE. However, worms exposed to 6-OHDA together with ALA showed increased GFP expression within processes of CEP and ADE neurons. Overall, our results demonstrate that ALA significantly suppresses the dopaminergic neurodegeneration and movement disorder induced by 6-OHDA in C. elegans.

Complete set of types of phase transition in generalized heterogeneous k-core percolation

We study heterogeneous k-core (HKC) percolation with a general mixture of the threshold k, with k(min) = 2 on random networks. Based on the local tree approximation, the scaling behaviors of the percolation order parameter P(∞)(p) are analytically obtained for general distributions of the threshold k. The analytic calculations predict that the generalized HKC percolation is completely described by the series of continuous transitions with order parameter exponents β(n) = 2/n, discontinuous hybrid transitions with β(H) = 1/2 or β(A)(4)) = 1/4, and three kinds of multiple transitions. Simulations of the generalized HKC percolations are carried out to confirm analytically predicted transition natures. Specifically, the exponents of the series of continuous transitions are shown to satisfy the hyperscaling relation 2β(n) + γ(n) = ν(n).

Emergence of small-world anatomical networks in self-organizing clustered neuronal cultures

In vitro primary cultures of dissociated invertebrate neurons from locust ganglia are used to experimentally investigate the morphological evolution of assemblies of living neurons, as they self-organize from collections of separated cells into elaborated, clustered, networks. At all the different stages of the culture's development, identification of neurons' and neurites' location by means of a dedicated software allows to ultimately extract an adjacency matrix from each image of the culture. In turn, a systematic statistical analysis of a group of topological observables grants us the possibility of quantifying and tracking the progression of the main network's characteristics during the self-organization process of the culture. Our results point to the existence of a particular state corresponding to a small-world network configuration, in which several relevant graph's micro- and meso-scale properties emerge. Finally, we identify the main physical processes ruling the culture's morphological transformations, and embed them into a simplified growth model qualitatively reproducing the overall set of experimental observations.

Critical phenomena in heterogeneous k-core percolation

k-core percolation is a percolation model which gives a notion of network functionality and has many applications in network science. In analyzing the resilience of a network under random damage, an extension of this model is introduced, allowing different vertices to have their own degree of resilience. This extension is named heterogeneous k-core percolation and it is characterized by several interesting critical phenomena. Here we analytically investigate binary mixtures in a wide class of configuration model networks and categorize the different critical phenomena which may occur. We observe the presence of critical and tricritical points and give a general criterion for the occurrence of a tricritical point. The calculated critical exponents show cases in which the model belongs to the same universality class of facilitated spin models studied in the context of the glass transition.

Chemosensory cue conditioning with stimulants in a Caenorhabditis elegans animal model of addiction

The underlying molecular mechanisms of drug abuse and addiction behaviors are poorly understood. Caenorhabditis elegans (C. elegans) provide a simple, whole animal model with conserved molecular pathways well suited for studying the foundations of complex diseases. Historically, chemotaxis has been a measure used to examine sensory approach and avoidance behavior in worms. Chemotaxis can be modulated by previous experience, and cue-dependent conditioned learning has been demonstrated in C. elegans, but such conditioning with drugs of abuse has not been reported. Here we show that pairing a distinctive salt cue with a drug (cocaine or methamphetamine) results in a concentration-dependent change in preference for the cue that was paired with the drug during conditioning. Further, we demonstrate that pairing of either drug with a distinctive food type can also increase preference for the drug-paired food in the absence of the drug. Dopamine-deficient mutants did not develop drug-paired, cue-conditioned responses. The findings suggest that, like vertebrates, C. elegans display a conditioned preference for environments containing cues previously associated with drugs of abuse, and this response is dependent on dopamine neurotransmission. This model provides a new and powerful method to study the genetic and molecular mechanisms that mediate drug preference.

An optimally evolved connective ratio of neural networks that maximizes the occurrence of synchronized bursting behavior

Background

Synchronized bursting activity (SBA) is a remarkable dynamical behavior in both ex vivo and in vivo neural networks. Investigations of the underlying structural characteristics associated with SBA are crucial to understanding the system-level regulatory mechanism of neural network behaviors.

Results

In this study, artificial pulsed neural networks were established using spike response models to capture fundamental dynamics of large scale ex vivo cortical networks. Network simulations with synaptic parameter perturbations showed the following two findings. (i) In a network with an excitatory ratio (ER) of 80-90%, its connective ratio (CR) was within a range of 10-30% when the occurrence of SBA reached the highest expectation. This result was consistent with the experimental observation in ex vivo neuronal networks, which were reported to possess a matured inhibitory synaptic ratio of 10-20% and a CR of 10-30%. (ii) No SBA occurred when a network does not contain any all-positive-interaction feedback loop (APFL) motif. In a neural network containing APFLs, the number of APFLs presented an optimal range corresponding to the maximal occurrence of SBA, which was very similar to the optimal CR.

Conclusions

In a neural network, the evolutionarily selected CR (10-30%) optimizes the occurrence of SBA, and APFL serves a pivotal network motif required to maximize the occurrence of SBA.

Rich-club organization of the human connectome

The human brain is a complex network of interlinked regions. Recent studies have demonstrated the existence of a number of highly connected and highly central neocortical hub regions, regions that play a key role in global information integration between different parts of the network. The potential functional importance of these "brain hubs" is underscored by recent studies showing that disturbances of their structural and functional connectivity profile are linked to neuropathology. This study aims to map out both the subcortical and neocortical hubs of the brain and examine their mutual relationship, particularly their structural linkages. Here, we demonstrate that brain hubs form a so-called "rich club," characterized by a tendency for high-degree nodes to be more densely connected among themselves than nodes of a lower degree, providing important information on the higher-level topology of the brain network. Whole-brain structural networks of 21 subjects were reconstructed using diffusion tensor imaging data. Examining the connectivity profile of these networks revealed a group of 12 strongly interconnected bihemispheric hub regions, comprising the precuneus, superior frontal and superior parietal cortex, as well as the subcortical hippocampus, putamen, and thalamus. Importantly, these hub regions were found to be more densely interconnected than would be expected based solely on their degree, together forming a rich club. We discuss the potential functional implications of the rich-club organization of the human connectome, particularly in light of its role in information integration and in conferring robustness to its structural core.

Tricritical point in heterogeneous k-core percolation

k-core percolation is an extension of the concept of classical percolation and is particularly relevant to understanding the resilience of complex networks under random damage. A new analytical formalism has been recently proposed to deal with heterogeneous k-cores, where each vertex is assigned a local threshold k(i). In this Letter we identify a binary mixture of heterogeneous k-cores which exhibits a tricritical point. We investigate the new scaling scenario and calculate the relevant critical exponents, by analytical and computational methods, for Erdős-Rényi networks and 2D square lattices.

Heterogeneous k-core versus bootstrap percolation on complex networks

We introduce the heterogeneous k-core, which generalizes the k-core, and contrast it with bootstrap percolation. Vertices have a threshold r(i), that may be different at each vertex. If a vertex has fewer than r(i) neighbors it is pruned from the network. The heterogeneous k-core is the subgraph remaining after no further vertices can be pruned. If the thresholds r(i) are 1 with probability f, or k ≥ 3 with probability 1-f, the process can be thought of as a pruning process counterpart to ordinary bootstrap percolation, which is an activation process. We show that there are two types of transitions in this heterogeneous k-core process: the giant heterogeneous k-core may appear with a continuous transition and there may be a second discontinuous hybrid transition. We compare critical phenomena, critical clusters, and avalanches at the heterogeneous k-core and bootstrap percolation transitions. We also show that the network structure has a crucial effect on these processes, with the giant heterogeneous k-core appearing immediately at a finite value for any f>0 when the degree distribution tends to a power law P(q)~q(-γ) with γ<3.

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.

Big ideas for small brains: what can psychiatry learn from worms, flies, bees and fish?

While the research community has accepted the value of rodent models as informative research platforms, there is less awareness of the utility of other small vertebrate and invertebrate animal models. Neuroscience is increasingly turning to smaller, non-rodent models to understand mechanisms related to neuropsychiatric disorders. Although they can never replace clinical research, there is much to be learnt from 'small brains'. In particular, these species can offer flexible genetic 'tool kits' that can be used to explore the expression and function of candidate genes in different brain regions. Very small animals also offer efficiencies with respect to high-throughput screening programs. This review provides a concise overview of the utility of models based on worm, fruit fly, honeybee and zebrafish. Although these species may have small brains, they offer the neuropsychiatric research community opportunities to explore some of the most important research questions in our field.

Environmental exposure, obesity, and Parkinson's disease: lessons from fat and old worms

BACKGROUND

A common link has been exposed, namely, that metal exposure plays a role in obesity and in Parkinson's disease (PD). This link may help to elucidate mechanisms of neurotoxicity.

OBJECTIVE

We reviewed the utility of the nematode, Caenorhabditis elegans, as a model organism to study neurodegeneration in obesity and Parkinson's disease (PD), with an emphasis on the neurotransmitter, dopamine (DA).

DATA SOURCES

A PubMed literature search was performed using the terms "obesity" and any of the following: "C. elegans," "central nervous system," "neurodegeneration," "heavy metals," "dopamine" or "Parkinson's disease." We reviewed the identified studies, including others cited therein, to summarize the current evidence of neurodegeneration in obesity and PD, with an emphasis on studies carried out in C. elegans and environmental toxins in the etiology of both diseases.

DATA EXTRACTION AND DATA SYNTHESIS

Heavy metals and DA have both been linked to diet-induced obesity, which has led to the notion that the mechanism of environmentally induced neurodegeneration in PD may also apply to obesity. C. elegans has been instrumental in expanding our mechanism-based knowledge of PD, and this species is emerging as a good model of obesity. With well-established toxicity and neurogenetic assays, it is now feasible to explore the putative link between metal- and chemical-induced neurodegeneration.

CONCLUSIONS

One side effect of an aging population is an increase in the prevalence of obesity, metabolic disorders, and neurodegenerative orders, diseases that are likely to co-occur. Environmental toxins, especially heavy metals, may prove to be a previously neglected part of the puzzle.

Mesoscopic organization reveals the constraints governing Caenorhabditis elegans nervous system

One of the biggest challenges in biology is to understand how activity at the cellular level of neurons, as a result of their mutual interactions, leads to the observed behavior of an organism responding to a variety of environmental stimuli. Investigating the intermediate or mesoscopic level of organization in the nervous system is a vital step towards understanding how the integration of micro-level dynamics results in macro-level functioning. The coordination of many different co-occurring processes at this level underlies the command and control of overall network activity. In this paper, we have considered the somatic nervous system of the nematode Caenorhabditis elegans, for which the entire neuronal connectivity diagram is known. We focus on the organization of the system into modules, i.e., neuronal groups having relatively higher connection density compared to that of the overall network. We show that this mesoscopic feature cannot be explained exclusively in terms of considerations such as, optimizing for resource constraints (viz., total wiring cost) and communication efficiency (i.e., network path length). Even including information about the genetic relatedness of the cells cannot account for the observed modular structure. Comparison with other complex networks designed for efficient transport (of signals or resources) implies that neuronal networks form a distinct class. This suggests that the principal function of the network, viz., processing of sensory information resulting in appropriate motor response, may be playing a vital role in determining the connection topology. Using modular spectral analysis we make explicit the intimate relation between function and structure in the nervous system. This is further brought out by identifying functionally critical neurons purely on the basis of patterns of intra- and inter-modular connections. Our study reveals how the design of the nervous system reflects several constraints, including its key functional role as a processor of information.

Random distance dependent attachment as a model for neural network generation in the Caenorhabditis elegans

MOTIVATION

The topology of the network induced by the neurons connectivity's in the Caenorhabditis elegans differs from most common random networks. The neurons positions of the C.elegans have been previously explained as being optimal to induce the required network wiring. We here propose a complementary explanation that the network wiring is the direct result of a local stochastic synapse formation process.

RESULTS

We show that a model based on the physical distance between neurons can explain the C.elegans neural network structure, specifically, we demonstrate that a simple model based on a geometrical synapse formation probability and the inhibition of short coherent cycles can explain the properties of the C.elegans' neural network. We suggest this model as an initial framework to discuss neural network generation and as a first step toward the development of models for more advanced creatures. In order to measure the circle frequency in the network, a novel graph-theory circle length measurement algorithm is proposed.

Human brain networks in health and disease

PURPOSE OF REVIEW

Recent developments in the statistical physics of complex networks have been translated to neuroimaging data in an effort to enhance our understanding of human brain structural and functional networks. This review focuses on studies using graph theoretical measures applied to structural MRI, diffusion MRI, functional MRI, electroencephalography, and magnetoencephalography data.

RECENT FINDINGS

Complex network properties have been identified with some consistency in all modalities of neuroimaging data and over a range of spatial and time scales. Conserved properties include small worldness, high efficiency of information transfer for low wiring cost, modularity, and the existence of network hubs. Structural and functional network metrics have been found to be heritable and to change with normal aging. Clinical studies, principally in Alzheimer's disease and schizophrenia, have identified abnormalities of network configuration in patients. Future work will likely involve efforts to synthesize structural and functional networks in integrated models and to explore the interdependence of network configuration and cognitive performance.

SUMMARY

Graph theoretical analysis of neuroimaging data is growing rapidly and could potentially provide a relatively simple but powerful quantitative framework to describe and compare whole human brain structural and functional networks under diverse experimental and clinical conditions.

The Gal4/UAS toolbox in zebrafish: new approaches for defining behavioral circuits

Over recent years, several groundbreaking techniques have been developed that allow for the anatomical description of neurons, and the observation and manipulation of their activity. Combined, these approaches should provide a great leap forward in our understanding of the structure and connectivity of the nervous system and how, as a network of individual neurons, it generates behavior. Zebrafish, given their external development and optical transparency, are an appealing system in which to employ these methods. These traits allow for direct observation of fluorescence in describing anatomy and observing neural activity, and for the manipulation of neurons using a host of light-triggered proteins. Gal4/Upstream Activating Sequence techniques, as they are based on a binary system, allow for the flexible deployment of a range of transgenes in expression patterns of interest. As such, they provide a promising approach for viewing neurons in a variety of ways, each of which can reveal something different about their structure, connectivity, or function. In this study, the author will review recent progress in the development of the Gal4/Upstream Activating Sequence system in zebrafish, feature examples of promising studies to date, and examine how various new technologies can be used in the future to untangle the complex mechanisms by which behavior is generated.