Abstract
Given a bio-chemical reaction network, we discuss the different algebraic entities e.g. stoichiometric matrix, polynomial system, deficiency and flux cones which are prerequisite for the application of various algebraic methods to qualitatively analyse them. We compute these entities on the examples obtained from two publicly available bio-databases called Biomodels and KEGG. The computations involve the use of computer algebra tools (e.g. polco, polymake). The results consisting of mostly matrices are arranged in form of a derived database called PoCaB (Platform of Chemical and Biological data). We also present a visualization program to visualize the extreme currents of the flux cone. We hope this will aid in the development of methods relevant for computational systems biology involving computer algebra. The database is publicly available at http://pocab.cg.cs.uni-bonn.de/
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Hartwell, L.H., Hopfield, J.J., Leibler, S., Murray, A.W.: From molecular to modular cell biology. Nature 402(6761 suppl.), C47–C52 (1999)
Bornstein, B., Broicher, A., Nove, N.L., Donizelli, M., Dharuri, H., Li, L., Sauro, H., Schilstra, M., Shapiro, B., Snoep, J.L., Hucka, M.: BioModels Database: a free, centralized database of curated, published, quantitative kinetic models of biochemical and cellular systems. Database 34, 689–691 (2006)
Kanehisa, M., Goto, S., Sato, Y., Furumichi, M., Tanabe, M.: KEGG for integration and interpretation of large-scale molecular data sets. Nucleic Acids Research 40(Database issue), D109–D114 (January 2012)
Caspi, R., Altman, T., Dreher, K., Fulcher, C.A., Subhraveti, P., Keseler, I.M., Kothari, A., Krummenacker, M., Latendresse, M., Mueller, L.A., Ong, Q., Paley, S., Pujar, A., Shearer, A.G., Travers, M., Weerasinghe, D., Zhang, P., Karp, P.D.: The MetaCyc database of metabolic pathways and enzymes and the BioCyc collection of pathway/genome databases. Nucleic Acids Research 40(Database issue), D742–D753 (2012)
Bray, T., Paoli, J., Sperberg-McQueen, C.M., Maler, E., Yergeau, F.: Extensible markup language (xml) 1.0 (fifth edition). Language (2008)
Horn, F., Jackson, R.: General mass action kinetics. Archive for Rational Mechanics and Analysis 47, 81–116 (1972), 10.1007/BF00251225
Clarke, B.: Stoichiometric network analysis. Cell Biochemistry and Biophysics 12, 237–253 (1988), 10.1007/BF02918360
Feinberg, M.: Review Article Number 25 Stability of Complex Isothermal Reactors–I. Chemical Engineering 42(10), 2229–2268 (1987)
Wrzodek, C., Dräger, A., Zell, A.: KEGGtranslator: visualizing and converting the KEGG PATHWAY database to various formats. Bioinformatics (Oxford, England) 27(16), 2314–2315 (2011)
Hucka, M., Finney, A., Sauro, H.M., Bolouri, H., Doyle, J.C., Kitano, H.: The rest of the SBML Forum: Arkin, A.P., Bornstein, B.J., Bray, D., Cornish-Bowden, A., Cuellar, A.A., Dronov, S., Gilles, E.D., Ginkel, M., Gor, V., Goryanin, I.I., Hedley, W.J., Hodgman, T.C., Hofmeyr, J.H., Hunter, P.J., Juty, N.S., Kasberger, J.L., Kremling, A., Kummer, U., Le Novère, N., Loew, L.M., Lucio, D., Mendes, P., Minch, E., Mjolsness, E.D., Nakayama, Y., Nelson, M.R., Nielsen, P.F., Sakurada, T., Schaff, J.C., Shapiro, B.E., Shimizu, T.S., Spence, H.D., Stelling, J., Takahashi, K., Tomita, M., Wagner, J., Wang, J.: The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models. Bioinformatics 19(4), 524–531 (2003), doi:10.1093/bioinformatics/btg015
Hucka, M., Smith, L., Wilkinson, D., Bergmann, F., Hoops, S., Keating, S., Sahle, S., Schaff, J.: The Systems Biology Markup Language (SBML): Language Specification for Level 3 Version 1 Core. Nature Precedings (October 2010)
Gatermann, K.: Counting stable solutions of sparse polynomial systems in chemistry. In: Green, E., et al. (eds.) Symbolic Computation: Solving Equations in Algebra, Geometry and Engineering, vol. 286, pp. 53–69. American Mathematical Society, Providence (2001)
Gatermann, K., Huber, B.: A family of sparse polynomial systems arising in chemical reaction systems. Journal of Symbolic Computation 33(3), 275–305 (2002)
Gatermann, K., Eiswirth, M., Sensse, A.: Toric ideals and graph theory to analyze Hopf bifurcations in mass action systems. Journal of Symbolic Computation 40(6), 1361–1382 (2005)
Clarke, B.L.: Stability of complex reaction networks. Advances In Chemical Physics, vol. 43 (1980)
Schuster, S., Dandekar, T., Fell, D.A.: Detection of elementary flux modes in biochemical networks: a promising tool for pathway analysis and metabolic engineering. Trends in Biotechnology 17(2), 53–60 (1999)
Schuster, S., Hlgetag, C.: On elementary flux modes in biochemical reaction systems at steady state. Journal of Biological Systems 2(2), 165–182 (1994)
Schilling, C.H., Letscher, D., Palsson, B.O.: Theory for the systemic definition of metabolic pathways and their use in interpreting metabolic function from a pathway-oriented perspective. Journal of Theoretical Biology 203(3), 229–248 (2000)
Wagner, C., Urbanczik, R.: The geometry of the flux cone of a metabolic network. Biophysical Journal 89(6), 3837–3845 (2005)
Llaneras, F., Picó, J.: Which metabolic pathways generate and characterize the flux space? A comparison among elementary modes, extreme pathways and minimal generators. Journal of Biomedicine & Biotechnology 2010, 753904 (2010)
Swainston, N., Smallbone, K., Mendes, P., Kell, D., Paton, N.: The SuBliMinaL Toolbox: automating steps in the reconstruction of metabolic networks. Journal of Integrative Bioinformatics 8(2), 186 (2011)
Dräger, A., Rodriguez, N., Dumousseau, M., Dörr, A., Wrzodek, C., Novère, N.L., Zell, A., Hucka, M.: JSBML: a flexible and entirely Java-based library for working with SBML. Bioinformatics 27(15), 2167–2168 (2011), doi: 10.1093/bioinformatics/btr361
JGraphT: A free Java graph library (2009), http://jgrapht.sourceforge.net
Soranzo, N., Altafini, C.: Ernest: a toolbox for chemical reaction network theory. Bioinformatics 25(21), 2853–2854 (2009)
Terzer, M.: Large Scale Methods to Enumerate Extreme Rays and Elementary Modes (18538) (2009)
Kamp, A.V., Schuster, S.: Metatool 5.0: fast and flexible elementary modes analysis. Bioinformatics 22(15), 1930–1931 (2006)
Gawrilow, E., Joswig, M.: Polymake: a framework for analyzing convex polytopes. In: Kalai, G., Ziegler, G.M. (eds.) Polytopes—Combinatorics and Computation. DMV Seminars, vol. 29, pp. 43–73. Birkhäuser, Basel (2000), 10.1007/978-3-0348-8438-9_2
Palsson, B.O.: The challenges of in silico biology Moving from a reductionist paradigm to one that views cells as systems will necessitate. Nature Biotechnology 18, 1147–1150 (2000)
Covert, M.W., Schilling, C.H., Palsson, B.O.: Regulation of gene expression in flux balance models of metabolism. Journal of Theoretical Biology 213(1), 73–88 (2001)
Urbanczik, R.: Enumerating constrained elementary flux vectors of metabolic networks. IET Systems Biology 1(5), 274–279 (2007)
Ziegler, G.M.: Lectures on Polytopes. Graduate Texts in Mathematics, vol. 152. Springer (July 2001)
O’Madadhain, J., Fisher, D., White, S., Boey, Y.: The JUNG (Java Universal Network/Graph) Framework. Technical report, UCI-ICS (October 2003)
Funahashi, A., Morohashi, M., Kitano, H., Tanimura, N.: Celldesigner: a process diagram editor for gene-regulatory and biochemical networks. BIOSILICO 1(5), 159–162 (2003)
Pérez Millán, M., Dickenstein, A., Shiu, A., Conradi, C.: Chemical reaction systems with toric steady states. Bulletin of Mathematical Biology, 1–29 (October 2011)
Grigoriev, D., Weber, A.: Complexity of Solving Systems with Few Independent Monomials and Applications to Mass-Action Kinetics. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2012. LNCS, vol. 7442, pp. 143–154. Springer, Heidelberg (2012)
Clarke, B.L.: Complete set of steady states for the general stoichiometric dynamical system. The Journal of Chemical Physics 75(10), 4970–4979 (1981)
Anderson, D.: A proof of the global attractor conjecture in the single linkage class case (2011)
Domijan, M., Kirkilionis, M.: Bistability and oscillations in chemical reaction networks. Journal of Mathematical Biology 59(4), 467–501 (2009)
Errami, H., Seiler, W.M., Eiswirth, M., Weber, A.: Computing Hopf Bifurcations in Chemical Reaction Networks Using Reaction Coordinates. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2012. LNCS, vol. 7442, pp. 84–97. Springer, Heidelberg (2012)
Weber, A., Sturm, T., Abdel-Rahman, E.O.: Algorithmic global criteria for excluding oscillations. Bulletin of Mathematical Biology 73(4), 899–917 (2011)
Weber, A., Sturm, T., Seiler, W.M., Abdel-Rahman, E.O.: Parametric Qualitative Analysis of Ordinary Differential Equations: Computer Algebra Methods for Excluding Oscillations (Extended Abstract) (Invited Talk). In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2010. LNCS, vol. 6244, pp. 267–279. Springer, Heidelberg (2010)
Errami, H., Seiler, W.M., Sturm, T., Weber, A.: On Muldowney’s Criteria for Polynomial Vector Fields with Constraints. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2011. LNCS, vol. 6885, pp. 135–143. Springer, Heidelberg (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Samal, S.S., Errami, H., Weber, A. (2012). PoCaB: A Software Infrastructure to Explore Algebraic Methods for Bio-chemical Reaction Networks. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2012. Lecture Notes in Computer Science, vol 7442. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32973-9_25
Download citation
DOI: https://doi.org/10.1007/978-3-642-32973-9_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32972-2
Online ISBN: 978-3-642-32973-9
eBook Packages: Computer ScienceComputer Science (R0)