Modularization of biochemical networks based on classification of Petri net t-invariants

<p>Abstract</p> <p>Background</p> <p>Structural analysis of biochemical networks is a growing field in bioinformatics and systems biology. The availability of an increasing amount of biological data from molecular biological networks promises a deeper understanding but confronts researchers with the problem of combinatorial explosion. The amount of qualitative network data is growing much faster than the amount of quantitative data, such as enzyme kinetics. In many cases it is even impossible to measure quantitative data because of limitations of experimental methods, or for ethical reasons. Thus, a huge amount of qualitative data, such as interaction data, is available, but it was not sufficiently used for modeling purposes, until now. New approaches have been developed, but the complexity of data often limits the application of many of the methods. Biochemical Petri nets make it possible to explore static and dynamic qualitative system properties. One Petri net approach is model validation based on the computation of the system's invariant properties, focusing on t-invariants. T-invariants correspond to subnetworks, which describe the basic system behavior.</p> <p>With increasing system complexity, the basic behavior can only be expressed by a huge number of t-invariants. According to our validation criteria for biochemical Petri nets, the necessary verification of the biological meaning, by interpreting each subnetwork (t-invariant) manually, is not possible anymore. Thus, an automated, biologically meaningful classification would be helpful in analyzing t-invariants, and supporting the understanding of the basic behavior of the considered biological system.</p> <p>Methods</p> <p>Here, we introduce a new approach to automatically classify t-invariants to cope with network complexity. We apply clustering techniques such as UPGMA, Complete Linkage, Single Linkage, and Neighbor Joining in combination with different distance measures to get biologically meaningful clusters (t-clusters), which can be interpreted as modules. To find the optimal number of t-clusters to consider for interpretation, the cluster validity measure, Silhouette Width, is applied.</p> <p>Results</p> <p>We considered two different case studies as examples: a small signal transduction pathway (pheromone response pathway in <it>Saccharomyces cerevisiae</it>) and a medium-sized gene regulatory network (gene regulation of Duchenne muscular dystrophy). We automatically classified the t-invariants into functionally distinct t-clusters, which could be interpreted biologically as functional modules in the network. We found differences in the suitability of the various distance measures as well as the clustering methods. In terms of a biologically meaningful classification of t-invariants, the best results are obtained using the Tanimoto distance measure. Considering clustering methods, the obtained results suggest that UPGMA and Complete Linkage are suitable for clustering t-invariants with respect to the biological interpretability.</p> <p>Conclusion</p> <p>We propose a new approach for the biological classification of Petri net t-invariants based on cluster analysis. Due to the biologically meaningful data reduction and structuring of network processes, large sets of t-invariants can be evaluated, allowing for model validation of qualitative biochemical Petri nets. This approach can also be applied to elementary mode analysis.</p

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Reflections on Conditions for Commericail Air-launched Suborbital Flight in Europe - Selected Results of a Study Funded by the European Community (EC)

The achievements of Scaled Composites with their SpaceShipOne (SS1) flights in 2004 in the frame of the Ansari X-Prize competition led the authors to propose an EC study to look into corresponding capabilities and opportunities for suborbital flight in Europe. This study confirmed that space tourism is the major commercial driver for suborbital ballistic flight, as long as the corresponding costs cannot be reduced substantially. The study considered a variety of issues to conclude that technical show stoppers to achieve suborbital flight in Europe do not exist, assuming the composite configuration of an Airbus as carrier plane and a winged space plane as suborbital vehicle. A major stumbling block, in addition to the funding issues, remains with legal issues and to achieve permission to fly such vehicles in Europ

Some Considerations on Suborbital Flight in Europe

Sparked by the achievements of Scaled Composites with their SpaceShipOne flights in 2004, a study was proposed to the EC to look into corresponding capabilities and opportunities for suborbital flight in Europe. This study confirmed that space tourism is the major commercial driver for suborbital ballistic flight, unless the corresponding costs can be reduced substantially. The study considered a variety of issues to conclude that technical show stoppers to achieve suborbital flight iu Europe do not exist, assuming the composite configuration of an Airbus as carrier plane and a winged space plane as suborbital vehicle. A major stumbling block, except for the funding issues, remains to achieve permission to fly such vehicles in Europe