Population synchrony in small-world networks

Network topography ranges from regular graphs (linkage between nearest neighbours only) via small-world graphs (some random connections between nodes) to completely random graphs. Small-world linkage is seen as a revolutionary architecture for a wide range of social, physical and biological networks, and has been shown to increase synchrony between oscillating subunits. We study small-world topographies in a novel context: dispersal linkage between spatially structured populations across a range of population models. Regular dispersal between population patches interacting with density-dependent renewal provides one ecological explanation for the large-scale synchrony seen in the temporal fluctuations of many species, for example, lynx populations in North America, voles in Fennoscandia and grouse in the UK. Introducing a small-world dispersal kernel leads to a clear reduction in synchrony with both increasing dispersal rate and small-world dispersal probability across a variety of biological scenarios. Synchrony is also reduced when populations are affected by globally correlated noise. We discuss ecological implications of small-world dispersal in the frame of spatial synchrony in population fluctuations.     

Analyzing protein-protein interaction networks

The advent of the "omics" era in biology research has brought new challenges and requires the development of novel strategies to answer previously intractable questions. Molecular interaction networks provide a framework to visualize cellular processes, but their complexity often makes their interpretation an overwhelming task. The inherently artificial nature of interaction detection methods and the incompleteness of currently available interaction maps call for a careful and well-informed utilization of this valuable data. In this tutorial, we aim to give an overview of the key aspects that any researcher needs to consider when working with molecular interaction data sets and we outline an example for interactome analysis. Using the molecular interaction database IntAct, the software platform Cytoscape, and its plugins BiNGO and clusterMaker, and taking as a starting point a list of proteins identified in a mass spectrometry-based proteomics experiment, we show how to build, visualize, and analyze a protein-protein interaction network.     

Sensitivity-dependent model of protein-protein interaction networks

The scale free structure p(k)-k(-gamma) of protein-protein interaction networks can be reproduced by a static physical model in simulation. We inspect the model theoretically, and find the key reason for the model generating apparent scale free degree distributions. This explanation provides a generic mechanism of 'scale free' networks. Moreover, we predict the dependence of gamma on experimental protein concentrations or other sensitivity factors in detecting interactions, and find experimental evidence to support the prediction.     

Robust emergence of small-world structure in networks of spiking neurons

Spontaneous activity in biological neural networks shows patterns of dynamic synchronization. We propose that these patterns support the formation␣of a small-world structure—network connectivity␣optimal for distributed information processing. We␣present numerical simulations with connected Hindmarsh–Rose neurons in which, starting from random connection distributions, small-world networks evolve as a result of applying an adaptive rewiring rule. The rule connects pairs of neurons that tend fire in synchrony, and disconnects ones that fail to synchronize. Repeated application of the rule leads to small-world structures. This mechanism is robustly observed for bursting and irregular firing regimes.     

Global and local synchrony of coupled neurons in small-world networks

Synchronous firing of neurons is thought to play important functional roles such as feature binding and switching of cognitive states. Although synchronization has mainly been investigated so far using model neurons with simple connection topology, real neural networks have more complex structures. Here we examine the behavior of pulse-coupled leaky integrate-and-fire neurons with various network structures. We first show that the dispersion of the number of connections for neurons influences dynamical behavior even if other major topological statistics are kept fixed. The rewiring probability parameter representing the randomness of networks bridges two spatially opposite frameworks: precise local synchrony and rough global synchrony. Finally, cooperation of the global connections and the local clustering property, which is prominent in small-world networks, inforces synchrony of distant neuronal groups receiving coherent inputs.Acknowledgments. We thank M. Watanabe, Y. Tsubo, and\linebreak C. van Leeuwen for helpful discussions. This work is partially supported by the Japan Society for the Promotion of Science and by the Advanced and Innovational Research program in Life Sciences and a Grant-in-Aid no. 15016023 on priority areas (C) Advanced Brain Science Project from the Ministry of Education, Culture, Sports, Science, and Technology, the Japanese Government.     

The interplay between microscopic and mesoscopic structures in complex networks

Understanding a complex network's structure holds the key to understanding its function. The physics community has contributed a multitude of methods and analyses to this cross-disciplinary endeavor. Structural features exist on both the microscopic level, resulting from differences between single node properties, and the mesoscopic level resulting from properties shared by groups of nodes. Disentangling the determinants of network structure on these different scales has remained a major, and so far unsolved, challenge. Here we show how multiscale generative probabilistic exponential random graph models combined with efficient, distributive message-passing inference techniques can be used to achieve this separation of scales, leading to improved detection accuracy of latent classes as demonstrated on benchmark problems. It sheds new light on the statistical significance of motif-distributions in neural networks and improves the link-prediction accuracy as exemplified for gene-disease associations in the highly consequential Online Mendelian Inheritance in Man database.     

Large-scale prediction of protein-protein interactions from structures

Background  

The prediction of protein-protein interactions is an important step toward the elucidation of protein functions and the understanding of the molecular mechanisms inside the cell. While experimental methods for identifying these interactions remain costly and often noisy, the increasing quantity of solved 3D protein structures suggests that in silico methods to predict interactions between two protein structures will play an increasingly important role in screening candidate interacting pairs. Approaches using the knowledge of the structure are presumably more accurate than those based on sequence only. Approaches based on docking protein structures solve a variant of this problem, but these methods remain very computationally intensive and will not scale in the near future to the detection of interactions at the level of an interactome, involving millions of candidate pairs of proteins.     

Fast and robust image segmentation by small-world neural oscillator networks

Inspired by the temporal correlation theory of brain functions, researchers have presented a number of neural oscillator networks to implement visual scene segmentation problems. Recently, it is shown that many biological neural networks are typical small-world networks. In this paper, we propose and investigate two small-world models derived from the well-known LEGION (locally excitatory and globally inhibitory oscillator network) model. To form a small-world network, we add a proper proportion of unidirectional shortcuts (random long-range connections) to the original LEGION model. With local connections and shortcuts, the neural oscillators can not only communicate with neighbors but also exchange phase information with remote partners. Model 1 introduces excitatory shortcuts to enhance the synchronization within an oscillator group representing the same object. Model 2 goes further to replace the global inhibitor with a sparse set of inhibitory shortcuts. Simulation results indicate that the proposed small-world models could achieve synchronization faster than the original LEGION model and are more likely to bind disconnected image regions belonging together. In addition, we argue that these two models are more biologically plausible.     

Domain-domain interactions underlying herpesvirus-human protein-protein interaction networks

Protein-domains play an important role in mediating protein-protein interactions. Furthermore, the same domain-pairs mediate different interactions in different contexts and in various organisms, and therefore domain-pairs are considered as the building blocks of interactome networks. Here we extend these principles to the host-virus interface and find the domain-pairs that potentially mediate human-herpesvirus interactions. Notably, we find that the same domain-pairs used by other organisms for mediating their interactions underlie statistically significant fractions of human-virus protein inter-interaction networks. Our analysis shows that viral domains tend to interact with human domains that are hubs in the human domain-domain interaction network. This may enable the virus to easily interfere with a variety of mechanisms and processes involving various and different human proteins carrying the relevant hub domain. Comparative genomics analysis provides hints at a molecular mechanism by which the virus acquired some of its interacting domains from its human host.     

Excitement and synchronization of small-world neuronal networks with short-term synaptic plasticity

Excitement and synchronization of electrically and chemically coupled Newman-Watts (NW) small-world neuronal networks with a short-term synaptic plasticity described by a modified Oja learning rule are investigated. For each type of neuronal network, the variation properties of synaptic weights are examined first. Then the effects of the learning rate, the coupling strength and the shortcut-adding probability on excitement and synchronization of the neuronal network are studied. It is shown that the synaptic learning suppresses the over-excitement, helps synchronization for the electrically coupled network but impairs synchronization for the chemically coupled one. Both the introduction of shortcuts and the increase of the coupling strength improve synchronization and they are helpful in increasing the excitement for the chemically coupled network, but have little effect on the excitement of the electrically coupled one.     

The small-world dynamics of tree networks and data mining in phyloinformatics

MOTIVATION: A noble and ultimate objective of phyloinformatic research is to assemble, synthesize, and explore the evolutionary history of life on earth. Data mining methods for performing these tasks are not yet well developed, but one avenue of research suggests that network connectivity dynamics will play an important role in future methods. Analysis of disordered networks, such as small-world networks, has applications as diverse as disease propagation, collaborative networks, and power grids. Here we apply similar analyses to networks of phylogenetic trees in order to understand how synthetic information can emerge from a database of phylogenies. RESULTS: Analyses of tree network connectivity in TreeBASE show that a collection of phylogenetic trees behaves as a small-world network-while on the one hand the trees are clustered, like a non-random lattice, on the other hand they have short characteristic path lengths, like a random graph. Tree connectivities follow a dual-scale power-law distribution (first power-law exponent approximately 1.87; second approximately 4.82). This unusual pattern is due, in part, to the presence of alternative tree topologies that enter the database with each published study. As expected, small collections of trees decrease connectivity as new trees are added, while large collections of trees increase connectivity. However, the inflection point is surprisingly low: after about 600 trees the network suddenly jumps to a higher level of coherence. More stringent definitions of 'neighbour' greatly delay the threshold whence a database achieves sufficient maturity for a coherent network to emerge. However, more stringent definitions of 'neighbour' would also likely show improved focus in data mining. AVAILABILITY: http://treebase.org     

Abnormal reorganization of functional cortical small-world networks in focal hand dystonia

We investigated the large-scale functional cortical connectivity network in focal hand dystonia (FHD) patients using graph theoretic measures to assess efficiency. High-resolution EEGs were recorded in 15 FHD patients and 15 healthy volunteers at rest and during a simple sequential finger tapping task. Mutual information (MI) values of wavelet coefficients were estimated to create an association matrix between EEG electrodes, and to produce a series of adjacency matrices or graphs, G, by thresholding with network cost. Efficiency measures of small-world networks were assessed. As a result, we found that FHD patients have economical small-world properties in their brain functional networks in the alpha and beta bands. During a motor task, in the beta band network, FHD patients have decreased efficiency of small-world networks, whereas healthy volunteers increase efficiency. Reduced efficient beta band network in FHD patients during the task was consistently observed in global efficiency, cost-efficiency, and maximum cost-efficiency. This suggests that the beta band functional cortical network of FHD patients is reorganized even during a task that does not induce dystonic symptoms, representing a loss of long-range communication and abnormal functional integration in large-scale brain functional cortical networks. Moreover, negative correlations between efficiency measures and duration of disease were found, indicating that the longer duration of disease, the less efficient the beta band network in FHD patients. In regional efficiency analysis, FHD patients at rest have high regional efficiency at supplementary motor cortex (SMA) compared with healthy volunteers; however, it is diminished during the motor task, possibly reflecting abnormal inhibition in FHD patients. The present study provides the first evidence with graph theory for abnormal reconfiguration of brain functional networks in FHD during motor task.     

Driving and driven architectures of directed small-world human brain functional networks

Recently, increasing attention has been focused on the investigation of the human brain connectome that describes the patterns of structural and functional connectivity networks of the human brain. Many studies of the human connectome have demonstrated that the brain network follows a small-world topology with an intrinsically cohesive modular structure and includes several network hubs in the medial parietal regions. However, most of these studies have only focused on undirected connections between regions in which the directions of information flow are not taken into account. How the brain regions causally influence each other and how the directed network of human brain is topologically organized remain largely unknown. Here, we applied linear multivariate Granger causality analysis (GCA) and graph theoretical approaches to a resting-state functional MRI dataset with a large cohort of young healthy participants (n = 86) to explore connectivity patterns of the population-based whole-brain functional directed network. This directed brain network exhibited prominent small-world properties, which obviously improved previous results of functional MRI studies showing weak small-world properties in the directed brain networks in terms of a kernel-based GCA and individual analysis. This brain network also showed significant modular structures associated with 5 well known subsystems: fronto-parietal, visual, paralimbic/limbic, subcortical and primary systems. Importantly, we identified several driving hubs predominantly located in the components of the attentional network (e.g., the inferior frontal gyrus, supplementary motor area, insula and fusiform gyrus) and several driven hubs predominantly located in the components of the default mode network (e.g., the precuneus, posterior cingulate gyrus, medial prefrontal cortex and inferior parietal lobule). Further split-half analyses indicated that our results were highly reproducible between two independent subgroups. The current study demonstrated the directions of spontaneous information flow and causal influences in the directed brain networks, thus providing new insights into our understanding of human brain functional connectome.     

Altered small-world brain networks in schizophrenia patients during working memory performance

Impairment of working memory (WM) performance in schizophrenia patients (SZ) is well-established. Compared to healthy controls (HC), SZ patients show aberrant blood oxygen level dependent (BOLD) activations and disrupted functional connectivity during WM performance. In this study, we examined the small-world network metrics computed from functional magnetic resonance imaging (fMRI) data collected as 35 HC and 35 SZ performed a Sternberg Item Recognition Paradigm (SIRP) at three WM load levels. Functional connectivity networks were built by calculating the partial correlation on preprocessed time courses of BOLD signal between task-related brain regions of interest (ROIs) defined by group independent component analysis (ICA). The networks were then thresholded within the small-world regime, resulting in undirected binarized small-world networks at different working memory loads. Our results showed: 1) at the medium WM load level, the networks in SZ showed a lower clustering coefficient and less local efficiency compared with HC; 2) in SZ, most network measures altered significantly as the WM load level increased from low to medium and from medium to high, while the network metrics were relatively stable in HC at different WM loads; and 3) the altered structure at medium WM load in SZ was related to their performance during the task, with longer reaction time related to lower clustering coefficient and lower local efficiency. These findings suggest brain connectivity in patients with SZ was more diffuse and less strongly linked locally in functional network at intermediate level of WM when compared to HC. SZ show distinctly inefficient and variable network structures in response to WM load increase, comparing to stable highly clustered network topologies in HC.     

Tissue-specific alternative splicing remodels protein-protein interaction networks

Alternative splicing plays a key role in the expansion of proteomic and regulatory complexity, yet the functions of the vast majority of differentially spliced exons are not known. In this study, we observe that brain and other tissue-regulated exons are significantly enriched in flexible regions of proteins that likely form conserved interaction surfaces. These proteins participate in significantly more interactions in protein-protein interaction (PPI) networks than other proteins. Using LUMIER, an automated PPI assay, we observe that approximately one-third of analyzed neural-regulated exons affect PPIs. Inclusion of these exons stimulated and repressed different partner interactions at comparable frequencies. This assay further revealed functions of individual exons, including a role for a neural-specific exon in promoting an interaction between Bridging Integrator 1 (Bin1)/Amphiphysin II and Dynamin 2 (Dnm2) that facilitates endocytosis. Collectively, our results provide evidence that regulated alternative exons frequently remodel interactions to establish tissue-dependent PPI networks.     

Detecting overlapping protein complexes in protein-protein interaction networks

We introduce clustering with overlapping neighborhood expansion (ClusterONE), a method for detecting potentially overlapping protein complexes from protein-protein interaction data. ClusterONE-derived complexes for several yeast data sets showed better correspondence with reference complexes in the Munich Information Center for Protein Sequence (MIPS) catalog and complexes derived from the Saccharomyces Genome Database (SGD) than the results of seven popular methods. The results also showed a high extent of functional homogeneity.     

Simulated evolution of protein-protein interaction networks with realistic topology

We model the evolution of eukaryotic protein-protein interaction (PPI) networks. In our model, PPI networks evolve by two known biological mechanisms: (1) Gene duplication, which is followed by rapid diversification of duplicate interactions. (2) Neofunctionalization, in which a mutation leads to a new interaction with some other protein. Since many interactions are due to simple surface compatibility, we hypothesize there is an increased likelihood of interacting with other proteins in the target protein's neighborhood. We find good agreement of the model on 10 different network properties compared to high-confidence experimental PPI networks in yeast, fruit flies, and humans. Key findings are: (1) PPI networks evolve modular structures, with no need to invoke particular selection pressures. (2) Proteins in cells have on average about 6 degrees of separation, similar to some social networks, such as human-communication and actor networks. (3) Unlike social networks, which have a shrinking diameter (degree of maximum separation) over time, PPI networks are predicted to grow in diameter. (4) The model indicates that evolutionarily old proteins should have higher connectivities and be more centrally embedded in their networks. This suggests a way in which present-day proteomics data could provide insights into biological evolution.