Motifs in brain networks

Ranking of network elements based on functional substructures

Centrality analysis has been shown to be a valuable method for the structural analysis of biological networks. It is used to identify key elements within networks and to rank network elements such that experiments can be tailored to interesting candidates. Several centrality measures have been studied, in particular for gene regulatory, metabolic and protein interaction networks. However, these centralities have been developed in other fields of science and are not adapted to biological networks. In particular, they ignore functional building blocks within biological networks and therefore do not consider specific network substructures of interest. We incorporate functional substructures (motifs) into network centrality analysis and present a new approach to rank vertices of networks. A method for motif-based centrality analysis is presented and two extensions are discussed which broaden the idea of motif-based centrality to specific functions of particular motif elements, and to the consideration of classes of related motifs. The presented method is applied to the gene regulatory network of Escherichia coli, where it yields interesting results about key regulators.

Revealing network connectivity from response dynamics

We present a method to infer the complete connectivity of a network from its stable response dynamics. As a paradigmatic example, we consider networks of coupled phase oscillators and explicitly study their long-term stationary response to temporally constant driving. For a given driving condition, measuring the phase differences and the collective frequency reveals information about how the units are interconnected. Sufficiently many repetitions for different driving conditions yield the entire network connectivity (the absence or presence of each connection) from measuring the response dynamics only. For sparsely connected networks, we obtain good predictions of the actual connectivity even for formally underdetermined problems.

neuroConstruct: a tool for modeling networks of neurons in 3D space

Conductance-based neuronal network models can help us understand how synaptic and cellular mechanisms underlie brain function. However, these complex models are difficult to develop and are inaccessible to most neuroscientists. Moreover, even the most biologically realistic network models disregard many 3D anatomical features of the brain. Here, we describe a new software application, neuroConstruct, that facilitates the creation, visualization, and analysis of networks of multicompartmental neurons in 3D space. A graphical user interface allows model generation and modification without programming. Models within neuroConstruct are based on new simulator-independent NeuroML standards, allowing automatic generation of code for NEURON or GENESIS simulators. neuroConstruct was tested by reproducing published models and its simulator independence verified by comparing the same model on two simulators. We show how more anatomically realistic network models can be created and their properties compared with experimental measurements by extending a published 1D cerebellar granule cell layer model to 3D.

Dynamical origin of independent spiking and bursting activity in neural microcircuits

The relationship between spiking and bursting dynamics is a key question in neuroscience, particularly in understanding the origins of different neural coding strategies and the mechanisms of motor command generation and neural circuit coordination. Experiments indicate that spiking and bursting dynamics can be independent. We hypothesize that different mechanisms for spike and burst generation, intrinsic neuron dynamics for spiking and a modulational network instability for bursting, are the origin of this independence. We tested the hypothesis in a detailed dynamical analysis of a minimal inhibitory neural microcircuit (motif) of three reciprocally connected Hodgkin-Huxley neurons. We reduced this high-dimensional dynamical system to a rate model and showed that both systems have identical bifurcations from tonic spiking to burst generation, which, therefore, does not depend on the details of spiking activity.

Topological Determinants of Epileptogenesis in Large-Scale Structural and Functional Models of the Dentate Gyrus Derived From Experimental Data

In temporal lobe epilepsy, changes in synaptic and intrinsic properties occur on a background of altered network architecture resulting from cell loss and axonal sprouting. Although modeling studies using idealized networks indicated the general importance of network topology in epilepsy, it is unknown whether structural changes that actually take place during epileptogenesis result in hyperexcitability. To answer this question, we built a 1:1 scale structural model of the rat dentate gyrus from published in vivo and in vitro cell type–specific connectivity data. This virtual dentate gyrus in control condition displayed globally and locally well connected (“small world”) architecture. The average number of synapses between any two neurons in this network of over one million cells was less than three, similar to that measured for the orders of magnitude smaller C. elegans nervous system. To study how network architecture changes during epileptogenesis, long-distance projecting hilar cells were gradually removed in the structural model, causing massive reductions in the number of total connections. However, as long as even a few hilar cells survived, global connectivity in the network was effectively maintained and, as a result of the spatially restricted sprouting of granule cell axons, local connectivity increased. Simulations of activity in a functional dentate network model, consisting of over 50,000 multicompartmental single-cell models of major glutamatergic and GABAergic cell types, revealed that the survival of even a small fraction of hilar cells was enough to sustain networkwide hyperexcitability. These data indicate new roles for fractionally surviving long-distance projecting hilar cells observed in specimens from epilepsy patients.

Developmental increase of total cell numbers in the murine cerebellum

The cerebellum has been widely used as a paradigm to study basic mechanisms of brain development and cortical histogenesis. Its highly regular structure has always made it particularly attractive to approaches relying on, and yielding, quantitative information, which provide a cornerstone of systems-oriented integrative analyses. Astonishingly, though, a systematic quantification of cell generation during cerebellar development has so far not been provided. Here, we use the isotropic fractionator (i.e., cell counts based on tissue homogenates from anatomically defined regions; cf. Herculano-Houzel S, Lent R., J Neurosci. 2005;25:2518-21) to assess the developmental increase of total cell numbers in the murine cerebellum from embryonic day 17 into early adulthood. Our data show that the quantitative increase of cerebellar cell numbers follows a classical, S-shaped growth curve as described by the Hill-equation. The adult murine cerebellum was found to comprise a total of (44.03+/-0.42) * 10(6) cells, half of which are generated before postnatal day 12+/-0.18. Consistent results were obtained by using two approaches to cell counting, one based on manual assessment, the other on flow cytometry. These data provide a reliable quantitative description of cerebellar growth in the mouse and define a predictive model that should allow their integration with quantitative and qualitative descriptions of cerebellar development.

Cortical functional network organization from autoregressive modeling of local field potential oscillations

A framework is presented for quantifying functional network organization in the brain by spectral analysis based on autoregressive modeling. Local field potentials (LFPs), simultaneously recorded from distributed sites in the cerebral cortex of monkeys, are treated as signals generated by local neuronal assemblies. During the delay period of a visual pattern discrimination task, oscillatory assembly activity is manifested in the LFPs in the beta-frequency range (14-30 Hz). Coherence analysis has shown that these oscillations are phase synchronized in functional networks in the sensorimotor cortex in relation to maintenance of contralateral hand position, and in the visual cortex in relation to anticipation of the visual stimulus. Granger causality analysis has revealed information flow in the sensorimotor network that is consistent with a peripheral sensorimotor feedback loop, and in the visual network that is consistent with top-down anticipatory modulation of assemblies in the primary visual cortex.

Modeling the dentate gyrus

Computational modeling has become an increasingly useful tool for studying complex neuronal circuits such as the dentate gyrus. In order to effectively apply computational techniques and theories to answer pressing biological questions, however, it is necessary to develop detailed, data-driven models. Development of such models is a complicated process, akin to putting together a jigsaw puzzle with the pieces being such things as cell types, cell numbers, and specific connectivity. This chapter provides a walkthrough for the development of a very large-scale, biophysically realistic model of the dentate gyrus. Subsequently, it demonstrates the utility of a modeling approach in asking and answering questions about both healthy and pathological states involving the modeled brain region. Finally, this chapter discusses some predictions that come directly from the model that can be tested in future experimental approaches.

Metastability, criticality and phase transitions in brain and its models

This survey of experimental findings and theoretical insights of the past 25 years places the brain firmly into the conceptual framework of nonlinear dynamics, operating at the brink of criticality, which is achieved and maintained by self-organization. It is here the basis for proposing that the application of the twin concepts of scaling and universality of the theory of non-equilibrium phase transitions can serve as an informative approach for elucidating the nature of underlying neural-mechanisms, with emphasis on the dynamics of recursively reentrant activity flow in intracortical and cortico-subcortical neuronal loops.

Computational aspects of feedback in neural circuits

It has previously been shown that generic cortical microcircuit models can perform complex real-time computations on continuous input streams, provided that these computations can be carried out with a rapidly fading memory. We investigate the computational capability of such circuits in the more realistic case where not only readout neurons, but in addition a few neurons within the circuit, have been trained for specific tasks. This is essentially equivalent to the case where the output of trained readout neurons is fed back into the circuit. We show that this new model overcomes the limitation of a rapidly fading memory. In fact, we prove that in the idealized case without noise it can carry out any conceivable digital or analog computation on time-varying inputs. But even with noise, the resulting computational model can perform a large class of biologically relevant real-time computations that require a nonfading memory. We demonstrate these computational implications of feedback both theoretically, and through computer simulations of detailed cortical microcircuit models that are subject to noise and have complex inherent dynamics. We show that the application of simple learning procedures (such as linear regression or perceptron learning) to a few neurons enables such circuits to represent time over behaviorally relevant long time spans, to integrate evidence from incoming spike trains over longer periods of time, and to process new information contained in such spike trains in diverse ways according to the current internal state of the circuit. In particular we show that such generic cortical microcircuits with feedback provide a new model for working memory that is consistent with a large set of biological constraints. Although this article examines primarily the computational role of feedback in circuits of neurons, the mathematical principles on which its analysis is based apply to a variety of dynamical systems. Hence they may also throw new light on the computational role of feedback in other complex biological dynamical systems, such as, for example, genetic regulatory networks.

Circuits of neurons in the brain have an abundance of feedback connections, both on the level of local microcircuits and on the level of synaptic connections between brain areas. But the functional role of these feedback connections is largely unknown. We present a computational theory that characterizes the gain in computational power that feedback can provide in such circuits. It shows that feedback endows standard models for neural circuits with the capability to emulate arbitrary Turing machines. In fact, with suitable feedback they can simulate any dynamical system, in particular any conceivable analog computer. Under realistic noise conditions, the computational power of these circuits is necessarily reduced. But we demonstrate through computer simulations that feedback also provides a significant gain in computational power for quite detailed models of cortical microcircuits with in vivo–like high levels of noise. In particular it enables generic cortical microcircuits to carry out computations that combine information from working memory and persistent internal states in real time with new information from online input streams.

The immune-body cytokine network defines a social architecture of cell interactions

Background

Three networks of intercellular communication can be associated with cytokine secretion; one limited to cells of the immune system (immune cells), one limited to parenchymal cells of organs and tissues (body cells), and one involving interactions between immune and body cells (immune-body interface). These cytokine connections determine the inflammatory response to injury and subsequent healing as well as the biologic consequences of the adaptive immune response to antigens. We informatically probed the cytokine database to uncover the underlying network architecture of the three networks.

Results

We now report that the three cytokine networks are among the densest of complex networks yet studied, and each features a characteristic profile of specific three-cell motifs. Some legitimate cytokine connections are shunned (anti-motifs). Certain immune cells can be paired by their input-output positions in a cytokine architecture tree of five tiers: macrophages (MΦ) and B cells (BC) comprise the first tier; the second tier is formed by T helper 1 (Th1) and T helper 2 (Th2) cells; the third tier includes dendritic cells (DC), mast cells (MAST), Natural Killer T cells (NK-T) and others; the fourth tier is formed by neutrophils (NEUT) and Natural Killer cells (NK); and the Cytotoxic T cell (CTL) stand alone as a fifth tier. The three-cell cytokine motif architecture of immune system cells places the immune system in a super-family that includes social networks and the World Wide Web. Body cells are less clearly stratified, although cells involved in wound healing and angiogenesis are most highly interconnected with immune cells.

Conclusion

Cytokine network architecture creates an innate cell-communication platform that organizes the biologic outcome of antigen recognition and inflammation. Informatics sheds new light on immune-body systems organization.

Reviewers

This article was reviewed by Neil Greenspan, Matthias von Herrath and Anne Cooke.

Topological relationships between brain and social networks

Brains are complex networks. Previously, we revealed that specific connected structures are either significantly abundant or rare in cortical networks. However, it remains unknown whether systems from other disciplines have similar architectures to brains. By applying network-theoretical methods, here we show topological similarities between brain and social networks. We found that the statistical relevance of specific tied structures differs between social "friendship" and "disliking" networks, suggesting relation-type-specific topology of social networks. Surprisingly, overrepresented connected structures in brain networks are more similar to those in the friendship networks than to those in other networks. We found that balanced and imbalanced reciprocal connections between nodes are significantly abundant and rare, respectively, whereas these results are unpredictable by simply counting mutual connections. We interpret these results as evidence of positive selection of balanced mutuality between nodes. These results also imply the existence of underlying common principles behind the organization of brain and social networks.

Tools for knowledge acquisition within the NeuroScholar system and their application to anatomical tract-tracing data

Background

Knowledge bases that summarize the published literature provide useful online references for specific areas of systems-level biology that are not otherwise supported by large-scale databases. In the field of neuroanatomy, groups of small focused teams have constructed medium size knowledge bases to summarize the literature describing tract-tracing experiments in several species. Despite years of collation and curation, these databases only provide partial coverage of the available published literature. Given that the scientists reading these papers must all generate the interpretations that would normally be entered into such a system, we attempt here to provide general-purpose annotation tools to make it easy for members of the community to contribute to the task of data collation.

Results

In this paper, we describe an open-source, freely available knowledge management system called 'NeuroScholar' that allows straightforward structured markup of the PDF files according to a well-designed schema to capture the essential details of this class of experiment. Although, the example worked through in this paper is quite specific to neuroanatomical connectivity, the design is freely extensible and could conceivably be used to construct local knowledge bases for other experiment types. Knowledge representations of the experiment are also directly linked to the contributing textual fragments from the original research article. Through the use of this system, not only could members of the community contribute to the collation task, but input data can be gathered for automated approaches to permit knowledge acquisition through the use of Natural Language Processing (NLP).

Conclusion

We present a functional, working tool to permit users to populate knowledge bases for neuroanatomical connectivity data from the literature through the use of structured questionnaires. This system is open-source, fully functional and available for download from [1].

Small-world connectivity, motif composition, and complexity of fractal neuronal connections

Connection patterns of the cerebral cortex consist of pathways linking neuronal populations across multiple levels of scale, from whole brain regions to local minicolumns. This nested interconnectivity suggests the hypothesis that cortical connections are arranged in fractal or self-similar patterns. We describe a simple procedure to generate fractal connection patterns that aim at capturing the potential self-similarity and hierarchical ordering of neuronal connections. We examine these connection patterns by calculating a broad range of structural measures, including small-world attributes and motif composition, as well as some global measures of functional connectivity, including complexity. As we vary fractal patterns by changing a critical control parameter, we find strongly correlated changes in several structural and functional measures, suggesting that they emerge together and are mutually linked. Measures obtained from some modeled fractal patterns closely resemble those of real neuroanatomical data sets, supporting the original hypothesis.

fMRI MODELS OF DENDRITIC AND ASTROCYTIC NETWORKS

In order to elucidate the relationships between hierarchical structures within the neocortical neuropil and the information carried by an ensemble of neurons encompassing a single voxel, it is essential to predict through volume conductor modeling LFPs representing average extracellular potentials, which are expressed in terms of interstitial potentials of individual cells in networks of gap-junctionally connected astrocytes and synaptically connected neurons. These relationships have been provided and can then be used to investigate how the underlying neuronal population activity can be inferred from the measurement of the BOLD signal through electrovascular coupling mechanisms across the blood-brain barrier. The importance of both synaptic and extrasynaptic transmission as the basis of electrophysiological indices triggering vascular responses between dendritic and astrocytic networks, and sequential configurations of firing patterns in composite neural networks is emphasized. The purpose of this review is to show how fMRI data may be used to draw conclusions about the information transmitted by individual neurons in populations generating the BOLD signal.

Operational principles of neurocognitive networks

Large-scale neural networks are thought to be an essential substrate for the implementation of cognitive function by the brain. If so, then a thorough understanding of cognition is not possible without knowledge of how the large-scale neural networks of cognition (neurocognitive networks) operate. Of necessity, such understanding requires insight into structural, functional, and dynamical aspects of network operation, the intimate interweaving of which may be responsible for the intricacies of cognition. Knowledge of anatomical structure is basic to understanding how neurocognitive networks operate. Phylogenetically and ontogenetically determined patterns of synaptic connectivity form a structural network of brain areas, allowing communication between widely distributed collections of areas. The function of neurocognitive networks depends on selective activation of anatomically linked cortical and subcortical areas in a wide variety of configurations. Large-scale functional networks provide the cooperative processing which gives expression to cognitive function. The dynamics of neurocognitive network function relates to the evolving patterns of interacting brain areas that express cognitive function in real time. This article considers the proposition that a basic similarity of the structural, functional, and dynamical features of all neurocognitive networks in the brain causes them to function according to common operational principles. The formation of neural context through the coordinated mutual constraint of multiple interacting cortical areas, is considered as a guiding principle underlying all cognitive functions. Increasing knowledge of the operational principles of neurocognitive networks is likely to promote the advancement of cognitive theories, and to seed strategies for the enhancement of cognitive abilities.

Segregation of the brain into gray and white matter: a design minimizing conduction delays

A ubiquitous feature of the vertebrate anatomy is the segregation of the brain into white and gray matter. Assuming that evolution maximized brain functionality, what is the reason for such segregation? To answer this question, we posit that brain functionality requires high interconnectivity and short conduction delays. Based on this assumption we searched for the optimal brain architecture by comparing different candidate designs. We found that the optimal design depends on the number of neurons, interneuronal connectivity, and axon diameter. In particular, the requirement to connect neurons with many fast axons drives the segregation of the brain into white and gray matter. These results provide a possible explanation for the structure of various regions of the vertebrate brain, such as the mammalian neocortex and neostriatum, the avian telencephalon, and the spinal cord.

Dynamic properties of network motifs contribute to biological network organization

Biological networks, such as those describing gene regulation, signal transduction, and neural synapses, are representations of large-scale dynamic systems. Discovery of organizing principles of biological networks can be enhanced by embracing the notion that there is a deep interplay between network structure and system dynamics. Recently, many structural characteristics of these non-random networks have been identified, but dynamical implications of the features have not been explored comprehensively. We demonstrate by exhaustive computational analysis that a dynamical property—stability or robustness to small perturbations—is highly correlated with the relative abundance of small subnetworks (network motifs) in several previously determined biological networks. We propose that robust dynamical stability is an influential property that can determine the non-random structure of biological networks.

The authors model how network motifs respond to small-scale perturbations and find a strong correlation between motif stability and abundance in a network, suggesting that dynamic properties of network motifs may play a role in overall network structure.

The human connectome: A structural description of the human brain

The connection matrix of the human brain (the human "connectome") represents an indispensable foundation for basic and applied neurobiological research. However, the network of anatomical connections linking the neuronal elements of the human brain is still largely unknown. While some databases or collations of large-scale anatomical connection patterns exist for other mammalian species, there is currently no connection matrix of the human brain, nor is there a coordinated research effort to collect, archive, and disseminate this important information. We propose a research strategy to achieve this goal, and discuss its potential impact.

Signal transduction networks: topology, response and biochemical processes

Conventionally, biological signal transduction networks are analysed using experimental and theoretical methods to describe specific protein components, interactions, and biochemical processes and to model network behavior under various conditions. While these studies provide crucial information on specific networks, this information is not easily converted to a broader understanding of signal transduction systems. Here, using a specific model of protein interaction we analyse small network topologies to understand their response and general properties. In particular, we catalogue the response for all possible topologies of a given network size to generate a response distribution, analyse the effects of specific biochemical processes on this distribution, and analyse the robustness and diversity of responses with respect to internal fluctuations or mutations in the network. The results show that even three- and four-protein networks are capable of creating diverse and biologically relevant responses, that the distribution of response types changes drastically as a function of biochemical processes at protein level, and that certain topologies strongly pre-dispose a specific response type while others allow for diverse types of responses. This study sheds light on the response types and properties that could be expected from signal transduction networks, provides possible explanations for the role of certain biochemical processes in signal transduction and suggests novel approaches to interfere with signaling pathways at the molecular level. Furthermore it shows that network topology plays a key role on determining response type and properties and that proper representation of network topology is crucial to discover and understand so-called building blocks of large networks.

Dynamics of a neural system with a multiscale architecture

The architecture of the brain is characterized by a modular organization repeated across a hierarchy of spatial scales-neurons, minicolumns, cortical columns, functional brain regions, and so on. It is important to consider that the processes governing neural dynamics at any given scale are not only determined by the behaviour of other neural structures at that scale, but also by the emergent behaviour of smaller scales, and the constraining influence of activity at larger scales. In this paper, we introduce a theoretical framework for neural systems in which the dynamics are nested within a multiscale architecture. In essence, the dynamics at each scale are determined by a coupled ensemble of nonlinear oscillators, which embody the principle scale-specific neurobiological processes. The dynamics at larger scales are 'slaved' to the emergent behaviour of smaller scales through a coupling function that depends on a multiscale wavelet decomposition. The approach is first explicated mathematically. Numerical examples are then given to illustrate phenomena such as between-scale bifurcations, and how synchronization in small-scale structures influences the dynamics in larger structures in an intuitive manner that cannot be captured by existing modelling approaches. A framework for relating the dynamical behaviour of the system to measured observables is presented and further extensions to capture wave phenomena and mode coupling are suggested.

Local design principles of mammalian cortical networks

To understand global and local design principles of mammalian cerebral cortical networks, we applied network-theoretical approaches to connectivity data from macaque and cat cortical networks. We first confirmed "small-world" properties and searched for the evidence of hierarchical modularity. To elucidate their local design principles, we then compared these cortical networks, based on the significance profile (SP) of network motifs in the real network compared to randomized networks. We found that SPs of different mammalian cortical networks are highly conserved and robust, suggesting constraints of neocortical development and evolution.