Input-output tables describe the flows of goods and services between the sectors of an economy. These tables can be interpreted as weighted directed networks. At the usual level of aggregation, they contain nodes with strong self-loops and are almost completely connected. We derive two measures of node centrality that are well suited for such networks. Both are based on random walks and have interpretations as the propagation of supply shocks through the economy. Random walk centrality reveals the vertices most immediately affected by a shock. Counting betweenness identifies the nodes where a shock lingers longest. The two measures differ in how they treat self-loops. We apply both to data from a wide set of countries and uncover salient characteristics of the structures of these national economies. We further validate our indices by clustering according to sectors' centralities. This analysis reveals geographical proximity and similar developmental status.

The isthmic organizer mediating differentiation of mid- and hindbrain during vertebrate development is characterized by a well-defined pattern of locally restricted gene expression domains around the mid-hindbrain boundary (MHB). This pattern is established and maintained by a regulatory network between several transcription and secreted factors that is not yet understood in full detail. In this contribution we show that a Boolean analysis of the characteristic spatial gene expression patterns at the murine MHB reveals key regulatory interactions in this network. Our analysis employs techniques from computational logic for the minimization of Boolean functions. This approach allows us to predict also the interplay of the various regulatory interactions. In particular, we predict a maintaining, rather than inducing, effect of Fgf8 on Wnt1 expression, an issue that remained unclear from published data. Using mouse anterior neural plate/tube explant cultures, we provide experimental evidence that Fgf8 in fact only maintains but does not induce ectopic Wnt1 expression in these explants. In combination with previously validated interactions, this finding allows for the construction of a regulatory network between key transcription and secreted factors at the MHB. Analyses of Boolean, differential equation and reaction-diffusion models of this network confirm that it is indeed able to explain the stable maintenance of the MHB as well as time-courses of expression patterns both under wild-type and various knock-out conditions. In conclusion, we demonstrate that similar to temporal also spatial expression patterns can be used to gain information about the structure of regulatory networks. We show, in particular, that the spatial gene expression patterns around the MHB help us to understand the maintenance of this boundary on a systems level.

Nuclear magnetic resonance spectroscopy (NMR) provides robust readouts of many metabolic parameters in one experiment. However, identification of clinically relevant markers in 1H NMR spectra is a major challenge. Association of NMR-derived quantities with genetic variants can uncover biologically relevant metabolic traits. Using NMR data of plasma samples from 1,757 individuals from the KORA study together with 655,658 genetic variants, we show that ratios between NMR intensities at two chemical shift positions can provide informative and robust biomarkers. We report seven loci of genetic association with NMR-derived traits (APOA1, CETP, CPS1, GCKR, FADS1, LIPC, PYROXD2) and characterize these traits biochemically using mass spectrometry. These ratios may now be used in clinical studies.

BackgroundExtensive 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 k-partite graphs. These graphs contain k 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.ResultsSince entities in biological networks regularly have more than one function and hence participate in more than one cluster, we developed a k-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 k-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.ConclusionsIn 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 k-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.