Zeros of the Partition Function and Pseudospinodals in Long-Range Ising Models

The relation between the zeros of the partition function and spinodal critical points in Ising models with long-range interactions is investigated. We find the spinodal is associated with the zeros of the partition function in four-dimensional complex temperature/magnetic field space. The zeros approach the real temperature/magnetic field plane as the range of interaction increases.Comment: 20 pages, 9 figures, accepted to PR

Line Graphs of Weighted Networks for Overlapping Communities

In this paper, we develop the idea to partition the edges of a weighted graph in order to uncover overlapping communities of its nodes. Our approach is based on the construction of different types of weighted line graphs, i.e. graphs whose nodes are the links of the original graph, that encapsulate differently the relations between the edges. Weighted line graphs are argued to provide an alternative, valuable representation of the system's topology, and are shown to have important applications in community detection, as the usual node partition of a line graph naturally leads to an edge partition of the original graph. This identification allows us to use traditional partitioning methods in order to address the long-standing problem of the detection of overlapping communities. We apply it to the analysis of different social and geographical networks.Comment: 8 Pages. New title and text revisions to emphasise differences from earlier paper

Detection and phasing of single base de novo mutations in biopsies from human in vitro fertilized embryos by advanced whole-genome sequencing

Currently, the methods available for preimplantation genetic diagnosis (PGD) of in vitro fertilized (IVF) embryos do not detect de novo single-nucleotide and short indel mutations, which have been shown to cause a large fraction of genetic diseases. Detection of all these types of mutations requires whole-genome sequencing (WGS). In this study, advanced massively parallel WGS was performed on three 5- to 10-cell biopsies from two blastocyst-stage embryos. Both parents and paternal grandparents were also analyzed to allow for accurate measurements of false-positive and false-negative error rates. Overall, >95% of each genome was called. In the embryos, experimentally derived haplotypes and barcoded read data were used to detect and phase up to 82% of de novo single base mutations with a false-positive rate of about one error per Gb, resulting in fewer than 10 such errors per embryo. This represents a ∼ 100-fold lower error rate than previously published from 10 cells, and it is the first demonstration that advanced WGS can be used to accurately identify these de novo mutations in spite of the thousands of false-positive errors introduced by the extensive DNA amplification required for deep sequencing. Using haplotype information, we also demonstrate how small de novo deletions could be detected. These results suggest that phased WGS using barcoded DNA could be used in the future as part of the PGD process to maximize comprehensiveness in detecting disease-causing mutations and to reduce the incidence of genetic diseases.Brock A. Peters, Bahram G. Kermani, Oleg Alferov, Misha R. Agarwal, Mark A. McElwain, Natali Gulbahce, Daniel M. Hayden, Y. Tom Tang, Rebecca Yu Zhang, Rick Tearle, Birgit Crain, Renata Prates, Alan Berkeley, Santiago Munné and Radoje Drmana

Structuring heterogeneous biological information using fuzzy clustering of k-partite graphs

<p>Abstract</p> <p>Background</p> <p>Extensive and automated data integration in bioinformatics facilitates the construction of large, complex biological networks. However, the challenge lies in the interpretation of these networks. While most research focuses on the unipartite or bipartite case, we address the more general but common situation of <it>k</it>-partite graphs. These graphs contain <it>k </it>different node types and links are only allowed between nodes of different types. In order to reveal their structural organization and describe the contained information in a more coarse-grained fashion, we ask how to detect clusters within each node type.</p> <p>Results</p> <p>Since entities in biological networks regularly have more than one function and hence participate in more than one cluster, we developed a <it>k</it>-partite graph partitioning algorithm that allows for overlapping (fuzzy) clusters. It determines for each node a degree of membership to each cluster. Moreover, the algorithm estimates a weighted <it>k</it>-partite graph that connects the extracted clusters. Our method is fast and efficient, mimicking the multiplicative update rules commonly employed in algorithms for non-negative matrix factorization. It facilitates the decomposition of networks on a chosen scale and therefore allows for analysis and interpretation of structures on various resolution levels. Applying our algorithm to a tripartite disease-gene-protein complex network, we were able to structure this graph on a large scale into clusters that are functionally correlated and biologically meaningful. Locally, smaller clusters enabled reclassification or annotation of the clusters' elements. We exemplified this for the transcription factor MECP2.</p> <p>Conclusions</p> <p>In order to cope with the overwhelming amount of information available from biomedical literature, we need to tackle the challenge of finding structures in large networks with nodes of multiple types. To this end, we presented a novel fuzzy <it>k</it>-partite graph partitioning algorithm that allows the decomposition of these objects in a comprehensive fashion. We validated our approach both on artificial and real-world data. It is readily applicable to any further problem.</p

Spontaneous Reaction Silencing in Metabolic Optimization

Metabolic reactions of single-cell organisms are routinely observed to become dispensable or even incapable of carrying activity under certain circumstances. Yet, the mechanisms as well as the range of conditions and phenotypes associated with this behavior remain very poorly understood. Here we predict computationally and analytically that any organism evolving to maximize growth rate, ATP production, or any other linear function of metabolic fluxes tends to significantly reduce the number of active metabolic reactions compared to typical non-optimal states. The reduced number appears to be constant across the microbial species studied and just slightly larger than the minimum number required for the organism to grow at all. We show that this massive spontaneous reaction silencing is triggered by the irreversibility of a large fraction of the metabolic reactions and propagates through the network as a cascade of inactivity. Our results help explain existing experimental data on intracellular flux measurements and the usage of latent pathways, shedding new light on microbial evolution, robustness, and versatility for the execution of specific biochemical tasks. In particular, the identification of optimal reaction activity provides rigorous ground for an intriguing knockout-based method recently proposed for the synthetic recovery of metabolic function.Comment: 34 pages, 6 figure

Community Structure and Multi-Modal Oscillations in Complex Networks

In many types of network, the relationship between structure and function is of great significance. We are particularly interested in community structures, which arise in a wide variety of domains. We apply a simple oscillator model to networks with community structures and show that waves of regular oscillation are caused by synchronised clusters of nodes. Moreover, we show that such global oscillations may arise as a direct result of network topology. We also observe that additional modes of oscillation (as detected through frequency analysis) occur in networks with additional levels of topological hierarchy and that such modes may be directly related to network structure. We apply the method in two specific domains (metabolic networks and metropolitan transport) demonstrating the robustness of our results when applied to real world systems. We conclude that (where the distribution of oscillator frequencies and the interactions between them are known to be unimodal) our observations may be applicable to the detection of underlying community structure in networks, shedding further light on the general relationship between structure and function in complex systems

An integrative approach for a network based meta-analysis of viral RNAi screens.

BACKGROUND: Big data is becoming ubiquitous in biology, and poses significant challenges in data analysis and interpretation. RNAi screening has become a workhorse of functional genomics, and has been applied, for example, to identify host factors involved in infection for a panel of different viruses. However, the analysis of data resulting from such screens is difficult, with often low overlap between hit lists, even when comparing screens targeting the same virus. This makes it a major challenge to select interesting candidates for further detailed, mechanistic experimental characterization. RESULTS: To address this problem we propose an integrative bioinformatics pipeline that allows for a network based meta-analysis of viral high-throughput RNAi screens. Initially, we collate a human protein interaction network from various public repositories, which is then subjected to unsupervised clustering to determine functional modules. Modules that are significantly enriched with host dependency factors (HDFs) and/or host restriction factors (HRFs) are then filtered based on network topology and semantic similarity measures. Modules passing all these criteria are finally interpreted for their biological significance using enrichment analysis, and interesting candidate genes can be selected from the modules. CONCLUSIONS: We apply our approach to seven screens targeting three different viruses, and compare results with other published meta-analyses of viral RNAi screens. We recover key hit genes, and identify additional candidates from the screens. While we demonstrate the application of the approach using viral RNAi data, the method is generally applicable to identify underlying mechanisms from hit lists derived from high-throughput experimental data, and to select a small number of most promising genes for further mechanistic studies. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s13015-015-0035-7) contains supplementary material, which is available to authorized users