Effective parameters determining the information flow in hierarchical biological systems.

Signaling networks are abundant in higher organisms. They play pivotal roles, e.g., during embryonic development or within the immune system. In this contribution, we study the combined effect of the various kinetic parameters on the dynamics of signal transduction. To this end, we consider hierarchical complex systems as prototypes of signaling networks. For given topology, the output of these networks is determined by an interplay of the single parameters. For different kinetics, we describe this by algebraic expressions, the so-called effective parameters.When modeling switch-like interactions by Heaviside step functions, we obtain these effective parameters recursively from the interaction graph. They can be visualized as directed trees, which allows us to easily determine the global effect of single kinetic parameters on the system's behavior. We provide evidence that these results generalize to sigmoidal Hill kinetics.In the case of linear activation functions, we again show that the algebraic expressions can be immediately inferred from the topology of the interaction network. This allows us to transform time-consuming analytic solutions of differential equations into a simple graph-theoretic problem. In this context, we also discuss the impact of our work on parameter estimation problems. An issue is that even the fitting of identifiable effective parameters often turns out to be numerically ill-conditioned. We demonstrate that this fitting problem can be reformulated as the problem of fitting exponential sums, for which robust algorithms exist.

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

BACKGROUND: 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 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. RESULTS: Since 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. CONCLUSIONS: 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 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.

Knowledge-based matrix factorization temporally resolves the cellular responses to IL-6 stimulation.

BACKGROUND: External stimulations of cells by hormones, cytokines or growth factors activate signal transduction pathways that subsequently induce a re-arrangement of cellular gene expression. The analysis of such changes is complicated, as they consist of multi-layered temporal responses. While classical analyses based on clustering or gene set enrichment only partly reveal this information, matrix factorization techniques are well suited for a detailed temporal analysis. In signal processing, factorization techniques incorporating data properties like spatial and temporal correlation structure have shown to be robust and computationally efficient. However, such correlation-based methods have so far not be applied in bioinformatics, because large scale biological data rarely imply a natural order that allows the definition of a delayed correlation function. RESULTS: We therefore develop the concept of graph-decorrelation. We encode prior knowledge like transcriptional regulation, protein interactions or metabolic pathways in a weighted directed graph. By linking features along this underlying graph, we introduce a partial ordering of the features (e.g. genes) and are thus able to define a graph-delayed correlation function. Using this framework as constraint to the matrix factorization task allows us to set up the fast and robust graph-decorrelation algorithm (GraDe). To analyze alterations in the gene response in IL-6 stimulated primary mouse hepatocytes, we performed a time-course microarray experiment and applied GraDe. In contrast to standard techniques, the extracted time-resolved gene expression profiles showed that IL-6 activates genes involved in cell cycle progression and cell division. Genes linked to metabolic and apoptotic processes are down-regulated indicating that IL-6 mediated priming renders hepatocytes more responsive towards cell proliferation and reduces expenditures for the energy metabolism. CONCLUSIONS: GraDe provides a novel framework for the decomposition of large-scale 'omics' data. We were able to show that including prior knowledge into the separation task leads to a much more structured and detailed separation of the time-dependent responses upon IL-6 stimulation compared to standard methods. A Matlab implementation of the GraDe algorithm is freely available at http://cmb.helmholtz-muenchen.de/grade.

Spatial analysis of expression patterns predicts genetic interactions at the mid-hindbrain boundary.

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.

An evolutionary and structural characterization of mammalian protein complex organization.

BACKGROUND: We have recently released a comprehensive, manually curated database of mammalian protein complexes called CORUM. Combining CORUM with other resources, we assembled a dataset of over 2700 mammalian complexes. The availability of a rich information resource allows us to search for organizational properties concerning these complexes. RESULTS: As the complexity of a protein complex in terms of the number of unique subunits increases, we observed that the number of such complexes and the mean non-synonymous to synonymous substitution ratio of associated genes tend to decrease. Similarly, as the number of different complexes a given protein participates in increases, the number of such proteins and the substitution ratio of the associated gene also tends to decrease. These observations provide evidence relating natural selection and the organization of mammalian complexes. We also observed greater homogeneity in terms of predicted protein isoelectric points, secondary structure and substitution ratio in annotated versus randomly generated complexes. A large proportion of the protein content and interactions in the complexes could be predicted from known binary protein-protein and domain-domain interactions. In particular, we found that large proteins interact preferentially with much smaller proteins. CONCLUSION: We observed similar trends in yeast and other data. Our results support the existence of conserved relations associated with the mammalian protein complexes.

Identification and MS-assisted interpretation of genetically influenced NMR signals in human plasma.

Nuclear magnetic resonance spectroscopy (NMR) provides robust readouts of many metabolic parameters in one experiment. However, identification of clinically relevant markers in (1)H 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.

Vertex centralities in input-output networks reveal the structure of modern economies.

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.