Fast Flux Module Detection Using Matroid Theory
Flux balance analysis (FBA) is one of the most often applied methods on genome-scale metabolic networks. Although FBA uniquely determines the optimal yield, the pathway that achieves this is usually not unique. The analysis of the optimal-yield flux space has been an open challenge. Flux variability analysis is only capturing some properties of the flux space, while elementary mode analysis is intractable due to the enormous number of elementary modes. However, it has been found by Kelk et al. 2012, that the space of optimal-yield fluxes decomposes into flux modules. These decompositions allow a much easier but still comprehensive analysis of the optimal-yield flux space.
Using the mathematical definition of module introduced by Müller and Bockmayr 2013, we discovered that flux modularity is rather a local than a global property which opened connections to matroid theory. Specifically, we show that our modules correspond one-to-one to so-called separators of an appropriate matroid. Employing efficient algorithms developed in matroid theory we are now able to compute the decomposition into modules in a few seconds for genome-scale networks. Using that every module can be represented by one reaction that represents its function, in this paper, we also present a method that uses this decomposition to visualize the interplay of modules. We expect the new method to replace flux variability analysis in the pipelines for metabolic networks.
Keywordsmetabolic networks FBA flux modules matroid theory
Unable to display preview. Download preview PDF.
- 4.Cunningham, W.H.: A combinatorial decomposition theory. PhD thesis, University of Waterloo, Ontario, Canada (1973)Google Scholar
- 15.Müller, A.C., Bockmayr, A.: Flux modules in metabolic networks. Journal of Mathematical Biology (2013) (in press, preprint), http://nbn-resolving.de/urn:nbn:de:0296-matheon-12084
- 22.Schellenberger, J., Que, R., Fleming, R.M.T., Thiele, I., Orth, J.D., Feist, A.M., Zielinski, D.C., Bordbar, A., Lewis, N.E., Rahmanian, S., Kang, J., Hyduke, D.R., Palsson, B.Ø.: Quantitative prediction of cellular metabolism with constraint-based models: the COBRA toolbox v2.0. Nature Protocols 6(9), 1290–1307 (2011)CrossRefGoogle Scholar
- 25.Terzer, M.: Large scale methods to enumerate extreme rays and elementary modes. PhD thesis, Diss., Eidgenössische Technische Hochschule ETH Zürich, Nr. 18538, 2009 (2009)Google Scholar
- 27.Truemper, K.: Partial matroid representations. European Journal of Combinatorics (1984)Google Scholar