×

On the relation between reactions and complexes of (bio)chemical reaction networks. (English) Zbl 1368.92072

Summary: Robustness of biochemical systems has become one of the central questions in systems biology although it is notoriously difficult to formally capture its multifaceted nature. Maintenance of normal system function depends not only on the stoichiometry of the underlying interrelated components, but also on the multitude of kinetic parameters. Invariant flux ratios, obtained within flux coupling analysis, as well as invariant complex ratios, derived within chemical reaction network theory, can characterize robust properties of a system at steady state. However, the existing formalisms for the description of these invariants do not provide full characterization as they either only focus on the flux-centric or the concentration-centric view. Here we develop a novel mathematical framework which combines both views and thereby overcomes the limitations of the classical methodologies. Our unified framework will be helpful in analyzing biologically important system properties.

MSC:

92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
92C42 Systems biology, networks
92C40 Biochemistry, molecular biology

Software:

efmtool
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Abrash, H. I., Studies concerning affinity, J. Chem. Educ., 63, 1044-1047 (1986)
[2] Burgard, A. P.; Nikolaev, E. V.; Schilling, C. H.; Maranas, C. D., Flux coupling analysis of genome-scale metabolic network reconstructions, Genome Res., 14, 2, 301-312 (2004), URL \(\langle\) http://dx.doi.org/10.1101/gr.\(1926504 \rangle \)
[3] Clarke, B. L., Stoichiometric network analysis, Cell Biochem. Biophys., 12, 237-253 (1988)
[4] Conradi, C.; Flockerzi, D.; Raisch, J.; Stelling, J., Subnetwork analysis reveals dynamic features of complex (bio)chemical networks, Proc. Natl. Acad. Sci. USA, 104, 49, 19175-19180 (2007), URL \(\langle\) http://dx.doi.org/10.1073/pnas.\(0705731104 \rangle \)
[5] Cox, D.; Little, J.; O’Shea, D., Ideals, Varieties, and Algorithms (2007), Springer
[7] Feinberg, M., The existence and uniqueness of steady states for a class of chemical reaction networks, Arch. Ration. Mech. Anal., 132, 311-370 (1995) · Zbl 0853.92024
[8] Gagneur, J.; Klamt, S., Computation of elementary modesa unifying framework and the new binary approach, BMC Bioinformatics, 5, 175 (2004), URL \(\langle\) http://dx.doi.org/\(10.1186/1471-2105-5-175 \rangle \)
[9] Guldberg, C.; Waage, P., Untersuchungen über die chemischen Affinitäten (1899), Verlag von Wilhelm Engelmann: Verlag von Wilhelm Engelmann Leipzig
[11] Heinrich, R.; Schuster, S., The Regulation of Cellular Systems (1996), Chapman and Hall: Chapman and Hall New York · Zbl 0895.92013
[12] Horn, F.; Jackson, R., General mass action kinetics, Arch. Ration. Mech. Anal., 47, 81-116 (1972)
[13] Kitano, H., Biological robustness, Nat. Rev. Genet., 5, 11, 826-837 (2004), URL \(\langle\) http://dx.doi.org/10.1038/nrg \(1471 \rangle \)
[14] Mahadevan, R.; Schilling, C. H., The effects of alternate optimal solutions in constraint-based genome-scale metabolic models, Metab. Eng., 5, 4, 264-276 (2003)
[15] Marashi, S.-A.; Bockmayr, A., Flux coupling analysis of metabolic networks is sensitive to missing reactions, Biosystems, 103, 1, 57-66 (2011), URL \(\langle\) http://dx.doi.org/10.1016/j.biosystems.\(2010.09.011 \rangle \)
[16] Millán, M. P.; Dickenstein, A.; Shiu, A.; Conradi, C., Chemical reaction systems with toric steady states, Bull. Math. Biol., 74, 1027-1065 (2012), URL \(\langle\) http://dx.doi.org/10.1007/s11538-011-9685-x \(\rangle \) · Zbl 1251.92016
[17] Moore, W. J., Physikalische Chemie (1986), Walter de Gruyter: Walter de Gruyter Berlin, New York
[18] Papin, J. A.; Reed, J. L.; Palsson, B. O., Hierarchical thinking in network biologythe unbiased modularization of biochemical networks, Trends Biochem. Sci., 29, 1), 641-647 (2004), URL \(\langle\) http://dx.doi.org/10.1016/j.tibs.\(2004.10.001 \rangle \)
[19] Schilling, C. H.; Schuster, S.; Palsson, B. O.; Heinrich, R., Metabolic pathway analysisbasic concepts and scientific applications in the post-genomic era, Biotechnol. Prog., 15, 3, 296-303 (1999), URL \(\langle\) http://dx.doi.org/10.1021/bp990048k \(\rangle \)
[20] Schuster, S.; Fell, D. A.; Dandekar, T., A general definition of metabolic pathways useful for systematic organization and analysis of complex metabolic networks, Nat. Biotechnol., 18, 3, 326-332 (2000), URL \(\langle\) http://dx.doi.org/\(10.1038/73786 \rangle \)
[21] Shinar, G.; Feinberg, M., Structural sources of robustness in biochemical reaction networks, Science, 327, 5971, 1389-1391 (2010), URL \(\langle\) http://dx.doi.org/10.1126/science.\(1183372 \rangle \)
[22] Terzer, M.; Stelling, J., Large-scale computation of elementary flux modes with bit pattern trees, Bioinformatics, 24, 19, 2229-2235 (2008), URL \(\langle\) http://dx.doi.org/10.1093/bioinformatics/btn \(401 \rangle \)
[23] Varma, A.; Palsson, B. O., Metabolic flux balancingbasic concepts, scientific and practical use, Nat. Biotechnol., 12, 994-998 (1994)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.