Initiating a Mexican wave: An instantaneous collective decision with both short and long range interactions

An interesting example for collective decision making is the so-called Mexican wave during which the spectators in a stadium leap to their feet with their arms up and then sit down again following those to their left (right) with a small delay. Here we use a simple, but realistic model to explain how the combination of the local and global interactions of the spectators produces a breaking of the symmetry resulting in the replacement of the symmetric solution -- containing two propagating waves -- by a single wave moving in one of the two possible directions. Our model is based on and compared to the extensive observations of volunteers filling out the related questionnaire we have posted on the Internet. We find that, as a function of the parameter controlling the strength of the global interactions, the transition to the single wave solution has features reminiscent of discontinuous transitions. After the spontaneous symmetry breaking the two directions of propagation are still statistically equivalent. We investigate also how this remaining symmetry is broken in real stadia by a small asymmetrical term in the perception of spectators.Comment: Main text: 12 pages, 3 figures. Appendices: 18 pages (incl. answers from online survey on Mexican waves). Supplementary website: http://angel.elte.hu/localgloba

Topological basis of signal integration in the transcriptional-regulatory network of the yeast, Saccharomyces cerevisiae

BACKGROUND: Signal recognition and information processing is a fundamental cellular function, which in part involves comprehensive transcriptional regulatory (TR) mechanisms carried out in response to complex environmental signals in the context of the cell's own internal state. However, the network topological basis of developing such integrated responses remains poorly understood. RESULTS: By studying the TR network of the yeast Saccharomyces cerevisiae we show that an intermediate layer of transcription factors naturally segregates into distinct subnetworks. In these topological units transcription factors are densely interlinked in a largely hierarchical manner and respond to external signals by utilizing a fraction of these subnets. CONCLUSION: As transcriptional regulation represents the 'slow' component of overall information processing, the identified topology suggests a model in which successive waves of transcriptional regulation originating from distinct fractions of the TR network control robust integrated responses to complex stimuli

Reverse engineering of linking preferences from network restructuring

We provide a method to deduce the preferences governing the restructuring dynamics of a network from the observed rewiring of the edges. Our approach is applicable for systems in which the preferences can be formulated in terms of a single-vertex energy function with f(k) being the contribution of a node of degree k to the total energy, and the dynamics obeys the detailed balance. The method is first tested by Monte-Carlo simulations of restructuring graphs with known energies, then it is used to study variations of real network systems ranging from the co-authorship network of scientific publications to the asset graphs of the New York Stock Exchange. The empirical energies obtained from the restructuring can be described by a universal function f(k) -k ln(k), which is consistent with and justifies the validity of the preferential attachment rule proposed for growing networks.Comment: 7 pages, 6 figures, submitted to PR

Directed network modules

A search technique locating network modules, i.e., internally densely connected groups of nodes in directed networks is introduced by extending the Clique Percolation Method originally proposed for undirected networks. After giving a suitable definition for directed modules we investigate their percolation transition in the Erdos-Renyi graph both analytically and numerically. We also analyse four real-world directed networks, including Google's own webpages, an email network, a word association graph and the transcriptional regulatory network of the yeast Saccharomyces cerevisiae. The obtained directed modules are validated by additional information available for the nodes. We find that directed modules of real-world graphs inherently overlap and the investigated networks can be classified into two major groups in terms of the overlaps between the modules. Accordingly, in the word-association network and among Google's webpages the overlaps are likely to contain in-hubs, whereas the modules in the email and transcriptional regulatory networks tend to overlap via out-hubs.Comment: 21 pages, 10 figures, version 2: added two paragaph

Signalogs: Orthology-Based Identification of Novel Signaling Pathway Components in Three Metazoans

BACKGROUND: Uncovering novel components of signal transduction pathways and their interactions within species is a central task in current biological research. Orthology alignment and functional genomics approaches allow the effective identification of signaling proteins by cross-species data integration. Recently, functional annotation of orthologs was transferred across organisms to predict novel roles for proteins. Despite the wide use of these methods, annotation of complete signaling pathways has not yet been transferred systematically between species. PRINCIPAL FINDINGS: Here we introduce the concept of 'signalog' to describe potential novel signaling function of a protein on the basis of the known signaling role(s) of its ortholog(s). To identify signalogs on genomic scale, we systematically transferred signaling pathway annotations among three animal species, the nematode Caenorhabditis elegans, the fruit fly Drosophila melanogaster, and humans. Using orthology data from InParanoid and signaling pathway information from the SignaLink database, we predict 88 worm, 92 fly, and 73 human novel signaling components. Furthermore, we developed an on-line tool and an interactive orthology network viewer to allow users to predict and visualize components of orthologous pathways. We verified the novelty of the predicted signalogs by literature search and comparison to known pathway annotations. In C. elegans, 6 out of the predicted novel Notch pathway members were validated experimentally. Our approach predicts signaling roles for 19 human orthodisease proteins and 5 known drug targets, and suggests 14 novel drug target candidates. CONCLUSIONS: Orthology-based pathway membership prediction between species enables the identification of novel signaling pathway components that we referred to as signalogs. Signalogs can be used to build a comprehensive signaling network in a given species. Such networks may increase the biomedical utilization of C. elegans and D. melanogaster. In humans, signalogs may identify novel drug targets and new signaling mechanisms for approved drugs

SignaLink 2 - a signaling pathway resource with multi-layered regulatory networks

ABSTRACT: BACKGROUND: Signaling networks in eukaryotes are made up of upstream and downstream subnetworks. The upstream subnetwork contains the intertwined network of signaling pathways, while the downstream regulatory part contains transcription factors and their binding sites on the DNA as well as microRNAs and their mRNA targets. Currently, most signaling and regulatory databases contain only a subsection of this network, making comprehensive analyses highly time-consuming and dependent on specific data handling expertise. The need for detailed mapping of signaling systems is also supported by the fact that several drug development failures were caused by undiscovered cross-talk or regulatory effects of drug targets. We previously created a uniformly curated signaling pathway resource, SignaLink, to facilitate the analysis of pathway cross-talks. Here, we present SignaLink 2, which significantly extends the coverage and applications of its predecessor.Description: We developed a novel concept to integrate and utilize different subsections (i.e., layers) of the signaling network. The multi-layered (onion-like) database structure is made up of signaling pathways, their pathway regulators (e.g., scaffold and endocytotic proteins) and modifier enzymes (e.g., phosphatases, ubiquitin ligases), as well as transcriptional and post-transcriptional regulators of all of these components. The user-friendly website allows the interactive exploration of how each signaling protein is regulated. The customizable download page enables the analysis of any user-specified part of the signaling network. Compared to other signaling resources, distinctive features of SignaLink 2 are the following: 1) it involves experimental data not only from humans but from two invertebrate model organisms, C. elegans and D. melanogaster; 2) combines manual curation with large-scale datasets; 3) provides confidence scores for each interaction; 4) operates a customizable download page with multiple file formats (e.g., BioPAX, Cytoscape, SBML). Non-profit users can access SignaLink 2 free of charge at http://SignaLink.org CONCLUSIONS: With SignaLink 2 as a single resource, users can effectively analyze signaling pathways, scaffold proteins, modifier enzymes, transcription factors and miRNAs that are important in the regulation of signaling processes. This integrated resource allows the systems-level examination of how cross-talks and signaling flow are regulated, as well as provide data for cross-species comparisons and drug discovery analyses

SignaLink 2 - a signaling pathway resource with multi-layered regulatory networks.

BACKGROUND Signaling networks in eukaryotes are made up of upstream and downstream subnetworks. The upstream subnetwork contains the intertwined network of signaling pathways, while the downstream regulatory part contains transcription factors and their binding sites on the DNA as well as microRNAs and their mRNA targets. Currently, most signaling and regulatory databases contain only a subsection of this network, making comprehensive analyses highly time-consuming and dependent on specific data handling expertise. The need for detailed mapping of signaling systems is also supported by the fact that several drug development failures were caused by undiscovered cross-talk or regulatory effects of drug targets. We previously created a uniformly curated signaling pathway resource, SignaLink, to facilitate the analysis of pathway cross-talks. Here, we present SignaLink 2, which significantly extends the coverage and applications of its predecessor. DESCRIPTION We developed a novel concept to integrate and utilize different subsections (i.e., layers) of the signaling network. The multi-layered (onion-like) database structure is made up of signaling pathways, their pathway regulators (e.g., scaffold and endocytotic proteins) and modifier enzymes (e.g., phosphatases, ubiquitin ligases), as well as transcriptional and post-transcriptional regulators of all of these components. The user-friendly website allows the interactive exploration of how each signaling protein is regulated. The customizable download page enables the analysis of any user-specified part of the signaling network. Compared to other signaling resources, distinctive features of SignaLink 2 are the following: 1) it involves experimental data not only from humans but from two invertebrate model organisms, C. elegans and D. melanogaster; 2) combines manual curation with large-scale datasets; 3) provides confidence scores for each interaction; 4) operates a customizable download page with multiple file formats (e.g., BioPAX, Cytoscape, SBML). Non-profit users can access SignaLink 2 free of charge at http://SignaLink.org. CONCLUSIONS With SignaLink 2 as a single resource, users can effectively analyze signaling pathways, scaffold proteins, modifier enzymes, transcription factors and miRNAs that are important in the regulation of signaling processes. This integrated resource allows the systems-level examination of how cross-talks and signaling flow are regulated, as well as provide data for cross-species comparisons and drug discovery analyses

Uncovering the overlapping community structure of complex networks in nature and society

Many complex systems in nature and society can be described in terms of networks capturing the intricate web of connections among the units they are made of. A key question is how to interpret the global organization of such networks as the coexistence of their structural subunits (communities) associated with more highly interconnected parts. Identifying these a priori unknown building blocks (such as functionally related proteins, industrial sectors and groups of people) is crucial to the understanding of the structural and functional properties of networks. The existing deterministic methods used for large networks find separated communities, whereas most of the actual networks are made of highly overlapping cohesive groups of nodes. Here we introduce an approach to analysing the main statistical features of the interwoven sets of overlapping communities that makes a step towards uncovering the modular structure of complex systems. After defining a set of new characteristic quantities for the statistics of communities, we apply an efficient technique for exploring overlapping communities on a large scale. We find that overlaps are significant, and the distributions we introduce reveal universal features of networks. Our studies of collaboration, word-association and protein interaction graphs show that the web of communities has non-trivial correlations and specific scaling properties.Comment: The free academic research software, CFinder, used for the publication is available at the website of the publication: http://angel.elte.hu/clusterin

Statistical mechanics of topological phase transitions in networks

We provide a phenomenological theory for topological transitions in restructuring networks. In this statistical mechanical approach energy is assigned to the different network topologies and temperature is used as a quantity referring to the level of noise during the rewiring of the edges. The associated microscopic dynamics satisfies the detailed balance condition and is equivalent to a lattice gas model on the edge-dual graph of a fully connected network. In our studies -- based on an exact enumeration method, Monte-Carlo simulations, and theoretical considerations -- we find a rich variety of topological phase transitions when the temperature is varied. These transitions signal singular changes in the essential features of the global structure of the network. Depending on the energy function chosen, the observed transitions can be best monitored using the order parameters Phi_s=s_{max}/M, i.e., the size of the largest connected component divided by the number of edges, or Phi_k=k_{max}/M, the largest degree in the network divided by the number of edges. If, for example the energy is chosen to be E=-s_{max}, the observed transition is analogous to the percolation phase transition of random graphs. For this choice of the energy, the phase-diagram in the [,T] plane is constructed. Single vertex energies of the form E=sum_i f(k_i), where k_i is the degree of vertex i, are also studied. Depending on the form of f(k_i), first order and continuous phase transitions can be observed. In case of f(k_i)=-(k_i+c)ln(k_i), the transition is continuous, and at the critical temperature scale-free graphs can be recovered.Comment: 12 pages, 12 figures, minor changes, added a new refernce, to appear in PR

Freezing by Heating in a Driven Mesoscopic System

We investigate a simple model corresponding to particles driven in opposite directions and interacting via a repulsive potential. The particles move off-lattice on a periodic strip and are subject to random forces as well. We show that this model - which can be considered as a continuum version of some driven diffusive systems - exhibits a paradoxial, new kind of transition called here ``freezing by heating''. One interesting feature of this transition is that a crystallized state with a higher total energy is obtained from a fluid state by increasing the amount of fluctuations.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.html and http://angel.elte.hu/~vicsek