Local structure of directed networks

Previous work on undirected small-world networks established the paradigm that locally structured networks tend to have high density of short loops. On the other hand, many realistic networks are directed. Here we investigate the local organization of directed networks and find, surprisingly, that real networks often have very few short loops as compared to random models. We develop a theory and derive conditions for determining if a given network has more or less loops than its randomized counterpart. These findings carry broad implications for structural and dynamical processes sustained by directed networks

Optimization in Gradient Networks

Gradient networks can be used to model the dominant structure of complex networks. Previous works have focused on random gradient networks. Here we study gradient networks that minimize jamming on substrate networks with scale-free and Erd\H{o}s-R\'enyi structure. We introduce structural correlations and strongly reduce congestion occurring on the network by using a Monte Carlo optimization scheme. This optimization alters the degree distribution and other structural properties of the resulting gradient networks. These results are expected to be relevant for transport and other dynamical processes in real network systems.Comment: 5 pages, 4 figure

Predicting synthetic rescues in metabolic networks

An important goal of medical research is to develop methods to recover the loss of cellular function due to mutations and other defects. Many approaches based on gene therapy aim to repair the defective gene or to insert genes with compensatory function. Here, we propose an alternative, network-based strategy that aims to restore biological function by forcing the cell to either bypass the functions affected by the defective gene, or to compensate for the lost function. Focusing on the metabolism of single-cell organisms, we computationally study mutants that lack an essential enzyme, and thus are unable to grow or have a significantly reduced growth rate. We show that several of these mutants can be turned into viable organisms through additional gene deletions that restore their growth rate. In a rather counterintuitive fashion, this is achieved via additional damage to the metabolic network. Using flux balance-based approaches, we identify a number of synthetically viable gene pairs, in which the removal of one enzyme-encoding gene results in a nonviable phenotype, while the deletion of a second enzyme-encoding gene rescues the organism. The systematic network-based identification of compensatory rescue effects may open new avenues for genetic interventions.Comment: Supplementary Information is available at the Molecular Systems Biology website: http://www.nature.com/msb/journal/v4/n1/full/msb20081.htm

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

Viral Perturbations of Host Networks Reflect Disease Etiology

Many human diseases, arising from mutations of disease susceptibility genes (genetic diseases), are also associated with viral infections (virally implicated diseases), either in a directly causal manner or by indirect associations. Here we examine whether viral perturbations of host interactome may underlie such virally implicated disease relationships. Using as models two different human viruses, Epstein-Barr virus (EBV) and human papillomavirus (HPV), we find that host targets of viral proteins reside in network proximity to products of disease susceptibility genes. Expression changes in virally implicated disease tissues and comorbidity patterns cluster significantly in the network vicinity of viral targets. The topological proximity found between cellular targets of viral proteins and disease genes was exploited to uncover a novel pathway linking HPV to Fanconi anemia

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

Comparison of an expanded ataxia interactome with patient medical records reveals a relationship between macular degeneration and ataxia

Spinocerebellar ataxias 6 and 7 (SCA6 and SCA7) are neurodegenerative disorders caused by expansion of CAG repeats encoding polyglutamine (polyQ) tracts in CACNA1A, the alpha1A subunit of the P/Q-type calcium channel, and ataxin-7 (ATXN7), a component of a chromatin-remodeling complex, respectively. We hypothesized that finding new protein partners for ATXN7 and CACNA1A would provide insight into the biology of their respective diseases and their relationship to other ataxia-causing proteins. We identified 118 protein interactions for CACNA1A and ATXN7 linking them to other ataxia-causing proteins and the ataxia network. To begin to understand the biological relevance of these protein interactions within the ataxia network, we used OMIM to identify diseases associated with the expanded ataxia network. We then used Medicare patient records to determine if any of these diseases co-occur with hereditary ataxia. We found that patients with ataxia are at 3.03-fold greater risk of these diseases than Medicare patients overall. One of the diseases comorbid with ataxia is macular degeneration (MD). The ataxia network is significantly (P= 7.37 × 10−5) enriched for proteins that interact with known MD-causing proteins, forming a MD subnetwork. We found that at least two of the proteins in the MD subnetwork have altered expression in the retina of Ataxin-7266Q/+ mice suggesting an in vivo functional relationship with ATXN7. Together these data reveal novel protein interactions and suggest potential pathways that can contribute to the pathophysiology of ataxia, MD, and diseases comorbid with ataxia

Interpreting Cancer Genomes Using Systematic Host Perturbations by Tumour Virus Proteins

Genotypic differences greatly influence susceptibility and resistance to disease. Understanding genotype-phenotype relationships requires that phenotypes be viewed as manifestations of network properties, rather than simply as the result of individual genomic variations. Genome sequencing efforts have identified numerous germline mutations associated with cancer predisposition and large numbers of somatic genomic alterations. However, it remains challenging to distinguish between background, or “passenger” and causal, or “driver” cancer mutations in these datasets. Human viruses intrinsically depend on their host cell during the course of infection and can elicit pathological phenotypes similar to those arising from mutations. To test the hypothesis that genomic variations and tumour viruses may cause cancer via related mechanisms, we systematically examined host interactome and transcriptome network perturbations caused by DNA tumour virus proteins. The resulting integrated viral perturbation data reflects rewiring of the host cell networks, and highlights pathways that go awry in cancer, such as Notch signalling and apoptosis. We show that systematic analyses of host targets of viral proteins can identify cancer genes with a success rate on par with their identification through functional genomics and large-scale cataloguing of tumour mutations. Together, these complementary approaches result in increased specificity for cancer gene identification. Combining systems-level studies of pathogen-encoded gene products with genomic approaches will facilitate prioritization of cancer-causing driver genes so as to advance understanding of the genetic basis of human cancer

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