A graph-theoretical approach in brain functional networks. Possible implications in EEG studies

Abstract Background Recently, it was realized that the functional connectivity networks estimated from actual brain-imaging technologies (MEG, fMRI and EEG) can be analyzed by means of the graph theory, that is a mathematical representation of a network, which is essentially reduced to nodes and connections between them. Methods We used high-resolution EEG technology to enhance the poor spatial information of the EEG activity on the scalp and it gives a measure of the electrical activity on the cortical surface. Afterwards, we used the Directed Transfer Function (DTF) that is a multivariate spectral measure for the estimation of the directional influences between any given pair of channels in a multivariate dataset. Finally, a graph theoretical approach was used to model the brain networks as graphs. These methods were used to analyze the structure of cortical connectivity during the attempt to move a paralyzed limb in a group (N=5) of spinal cord injured patients and during the movement execution in a group (N=5) of healthy subjects. Results Analysis performed on the cortical networks estimated from the group of normal and SCI patients revealed that both groups present few nodes with a high out-degree value (i.e. outgoing links). This property is valid in the networks estimated for all the frequency bands investigated. In particular, cingulate motor areas (CMAs) ROIs act as ‘‘hubs’’ for the outflow of information in both groups, SCI and healthy. Results also suggest that spinal cord injuries affect the functional architecture of the cortical network sub-serving the volition of motor acts mainly in its local feature property. In particular, a higher local efficiency El can be observed in the SCI patients for three frequency bands, theta (3-6 Hz), alpha (7-12 Hz) and beta (13-29 Hz). By taking into account all the possible pathways between different ROI couples, we were able to separate clearly the network properties of the SCI group from the CTRL group. In particular, we report a sort of compensatory mechanism in the SCI patients for the Theta (3-6 Hz) frequency band, indicating a higher level of “activation” Ω within the cortical network during the motor task. The activation index is directly related to diffusion, a type of dynamics that underlies several biological systems including possible spreading of neuronal activation across several cortical regions. Conclusions The present study aims at demonstrating the possible applications of graph theoretical approaches in the analyses of brain functional connectivity from EEG signals. In particular, the methodological aspects of the i) cortical activity from scalp EEG signals, ii) functional connectivity estimations iii) graph theoretical indexes are emphasized in the present paper to show their impact in a real application.

A decaying factor accounts for contained activity in neuronal networks with no need of hierarchical or modular organization

The mechanisms responsible for containing activity in systems represented by networks are crucial in various phenomena, for example, in diseases such as epilepsy that affect the neuronal networks and for information dissemination in social networks. The first models to account for contained activity included triggering and inhibition processes, but they cannot be applied to social networks where inhibition is clearly absent. A recent model showed that contained activity can be achieved with no need of inhibition processes provided that the network is subdivided into modules (communities). In this paper, we introduce a new concept inspired in the Hebbian theory, through which containment of activity is achieved by incorporating a dynamics based on a decaying activity in a random walk mechanism preferential to the node activity. Upon selecting the decay coefficient within a proper range, we observed sustained activity in all the networks tested, namely, random, Barabasi-Albert and geographical networks. The generality of this finding was confirmed by showing that modularity is no longer needed if the dynamics based on the integrate-and-fire dynamics incorporated the decay factor. Taken together, these results provide a proof of principle that persistent, restrained network activation might occur in the absence of any particular topological structure. This may be the reason why neuronal activity does not spread out to the entire neuronal network, even when no special topological organization exists.

Schizophrenia, brain disease and meta-analyses: Integrating the pieces and testing Fusar-Poli`s hypothesis

This paper aims to discuss and test the hypothesis raised by Fusar-Poli [Fusar-Poli P. Can neuroimaging prove that schizophrenia is a brain disease? A radical hypothesis. Medical Hypotheses in press, corrected proof] that ""on the basis of the available imaging literature there is no consistent evidence to reject the radical and provocative hypothesis that schizophrenia is not a brain disease"". To achieve this goal, all meta-analyses on `fMRI and schizophrenia` published during the current decade and indexed in Pubmed were summarized, as much as some other useful information, e.g., meta-analyses on genetic risk factors. Our main conclusion is that the literature fully supports the hypothesis that schizophrenia is a syndrome (not a disease) associated with brain abnormalities, despite the fact that there is no singular and reductionist pathway from the nosographic entity (schizophrenia) to its causes. This irreducibility is due to the fact that the syndrome has more than one dimension (e.g., cognitive, psychotic and negative) and each of them is related to abnormalities in specific neuronal networks. A psychiatric diagnosis is a statistical procedure; these dimensions are not identically represented in each diagnosticated case and this explains the existence of more than one pattern of brain abnormalities related to schizophrenia. For example, chronification is associated with negativism while the first psychotic episode is not; in that sense, the same person living with schizophrenia may reveal different symptoms and fMRI patterns along the course of his life, and this is precisely what defines schizophrenia since the time when it was called Dementia Praecox (first by pick then by Kraepelin). It is notable that 100% of the collected meta-analyses on `fMRI and schizophrenia` reveal positive findings. Moreover, all meta-analyses that found positive associations between schizophrenia and genetic risk factors have to do with genes (SNPs) especially activated in neuronal tissue of the central nervous system (CNS), suggesting that, to the extent these polymorphisms are related to schizophrenia`s etiology, they are also related to abnormal brain activity. (C) 2009 Elsevier Ltd. All rights reserved.

Word sense disambiguation via high order of learning in complex networks

Complex networks have been employed to model many real systems and as a modeling tool in a myriad of applications. In this paper, we use the framework of complex networks to the problem of supervised classification in the word disambiguation task, which consists in deriving a function from the supervised (or labeled) training data of ambiguous words. Traditional supervised data classification takes into account only topological or physical features of the input data. On the other hand, the human (animal) brain performs both low- and high-level orders of learning and it has facility to identify patterns according to the semantic meaning of the input data. In this paper, we apply a hybrid technique which encompasses both types of learning in the field of word sense disambiguation and show that the high-level order of learning can really improve the accuracy rate of the model. This evidence serves to demonstrate that the internal structures formed by the words do present patterns that, generally, cannot be correctly unveiled by only traditional techniques. Finally, we exhibit the behavior of the model for different weights of the low- and high-level classifiers by plotting decision boundaries. This study helps one to better understand the effectiveness of the model. Copyright (C) EPLA, 2012

Discriminating Different Classes of Biological Networks by Analyzing the Graphs Spectra Distribution

The brain's structural and functional systems, protein-protein interaction, and gene networks are examples of biological systems that share some features of complex networks, such as highly connected nodes, modularity, and small-world topology. Recent studies indicate that some pathologies present topological network alterations relative to norms seen in the general population. Therefore, methods to discriminate the processes that generate the different classes of networks (e. g., normal and disease) might be crucial for the diagnosis, prognosis, and treatment of the disease. It is known that several topological properties of a network (graph) can be described by the distribution of the spectrum of its adjacency matrix. Moreover, large networks generated by the same random process have the same spectrum distribution, allowing us to use it as a "fingerprint". Based on this relationship, we introduce and propose the entropy of a graph spectrum to measure the "uncertainty" of a random graph and the Kullback-Leibler and Jensen-Shannon divergences between graph spectra to compare networks. We also introduce general methods for model selection and network model parameter estimation, as well as a statistical procedure to test the nullity of divergence between two classes of complex networks. Finally, we demonstrate the usefulness of the proposed methods by applying them to (1) protein-protein interaction networks of different species and (2) on networks derived from children diagnosed with Attention Deficit Hyperactivity Disorder (ADHD) and typically developing children. We conclude that scale-free networks best describe all the protein-protein interactions. Also, we show that our proposed measures succeeded in the identification of topological changes in the network while other commonly used measures (number of edges, clustering coefficient, average path length) failed.

Natural intracellular peptides can modulate the interactions of mouse brain proteins and thimet oligopeptidase with 14-3-3e and calmodulin

Protein interactions are crucial for most cellular process. Thus, rationally designed peptides that act as competitive assembly inhibitors of protein interactions by mimicking specific, determined structural elements have been extensively used in clinical and basic research. Recently, mammalian cells have been shown to contain a large number of intracellular peptides of unknown function. Here, we investigate the role of several of these natural intracellular peptides as putative modulators of protein interactions that are related to Ca2+-calmodulin (CaM) and 14-3-3 epsilon, which are proteins that are related to the spatial organization of signal transduction within cells. At concentrations of 1-50 mu M, most of the peptides that are investigated in this study modulate the interactions of CaM and 14-3-3 epsilon with proteins from the mouse brain cytoplasm or recombinant thimet oligopeptidase (EP24.15) in vitro, as measured by surface plasmon resonance. One of these peptides (VFDVELL; VFD-7) increases the cytosolic Ca2+ concentration in a dose-dependent manner but only if introduced into HEK293 cells, which suggests a wide biological function of this peptide. Therefore, it is exciting to suggest that natural intracellular peptides are novel modulators of protein interactions and have biological functions within cells.

Collective Almost Synchronisation in Complex Networks

This work introduces the phenomenon of Collective Almost Synchronisation (CAS), which describes a universal way of how patterns can appear in complex networks for small coupling strengths. The CAS phenomenon appears due to the existence of an approximately constant local mean field and is characterised by having nodes with trajectories evolving around periodic stable orbits. Common notion based on statistical knowledge would lead one to interpret the appearance of a local constant mean field as a consequence of the fact that the behaviour of each node is not correlated to the behaviours of the others. Contrary to this common notion, we show that various well known weaker forms of synchronisation (almost, time-lag, phase synchronisation, and generalised synchronisation) appear as a result of the onset of an almost constant local mean field. If the memory is formed in a brain by minimising the coupling strength among neurons and maximising the number of possible patterns, then the CAS phenomenon is a plausible explanation for it.