Skip to main content
SpringerLink
Log in

PoCaB: A Software Infrastructure to Explore Algebraic Methods for Bio-chemical Reaction Networks

  • Conference paper
Computer Algebra in Scientific Computing (CASC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7442))

Included in the following conference series:

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

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Hartwell, L.H., Hopfield, J.J., Leibler, S., Murray, A.W.: From molecular to modular cell biology. Nature 402(6761 suppl.), C47–C52 (1999)

    Google Scholar 

  2. 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)

    Google Scholar 

  3. 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)

    Google Scholar 

  4. 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)

    Google Scholar 

  5. Bray, T., Paoli, J., Sperberg-McQueen, C.M., Maler, E., Yergeau, F.: Extensible markup language (xml) 1.0 (fifth edition). Language (2008)

    Google Scholar 

  6. Horn, F., Jackson, R.: General mass action kinetics. Archive for Rational Mechanics and Analysis 47, 81–116 (1972), 10.1007/BF00251225

    Article  MathSciNet  Google Scholar 

  7. Clarke, B.: Stoichiometric network analysis. Cell Biochemistry and Biophysics 12, 237–253 (1988), 10.1007/BF02918360

    Google Scholar 

  8. Feinberg, M.: Review Article Number 25 Stability of Complex Isothermal Reactors–I. Chemical Engineering 42(10), 2229–2268 (1987)

    Article  Google Scholar 

  9. 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)

    Article  Google Scholar 

  10. 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

    Google Scholar 

  11. 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)

    Google Scholar 

  12. 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)

    Chapter  Google Scholar 

  13. Gatermann, K., Huber, B.: A family of sparse polynomial systems arising in chemical reaction systems. Journal of Symbolic Computation 33(3), 275–305 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  14. 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)

    Article  MathSciNet  MATH  Google Scholar 

  15. Clarke, B.L.: Stability of complex reaction networks. Advances In Chemical Physics, vol. 43 (1980)

    Google Scholar 

  16. 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)

    Article  Google Scholar 

  17. Schuster, S., Hlgetag, C.: On elementary flux modes in biochemical reaction systems at steady state. Journal of Biological Systems 2(2), 165–182 (1994)

    Article  Google Scholar 

  18. 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)

    Article  Google Scholar 

  19. Wagner, C., Urbanczik, R.: The geometry of the flux cone of a metabolic network. Biophysical Journal 89(6), 3837–3845 (2005)

    Article  Google Scholar 

  20. 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)

    Google Scholar 

  21. 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)

    Google Scholar 

  22. 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

    Google Scholar 

  23. JGraphT: A free Java graph library (2009), http://jgrapht.sourceforge.net

  24. Soranzo, N., Altafini, C.: Ernest: a toolbox for chemical reaction network theory. Bioinformatics 25(21), 2853–2854 (2009)

    Article  Google Scholar 

  25. Terzer, M.: Large Scale Methods to Enumerate Extreme Rays and Elementary Modes (18538) (2009)

    Google Scholar 

  26. Kamp, A.V., Schuster, S.: Metatool 5.0: fast and flexible elementary modes analysis. Bioinformatics 22(15), 1930–1931 (2006)

    Article  Google Scholar 

  27. 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

    Google Scholar 

  28. 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)

    Article  Google Scholar 

  29. 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)

    Article  Google Scholar 

  30. Urbanczik, R.: Enumerating constrained elementary flux vectors of metabolic networks. IET Systems Biology 1(5), 274–279 (2007)

    Article  Google Scholar 

  31. Ziegler, G.M.: Lectures on Polytopes. Graduate Texts in Mathematics, vol. 152. Springer (July 2001)

    Google Scholar 

  32. O’Madadhain, J., Fisher, D., White, S., Boey, Y.: The JUNG (Java Universal Network/Graph) Framework. Technical report, UCI-ICS (October 2003)

    Google Scholar 

  33. 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)

    Article  Google Scholar 

  34. Pérez Millán, M., Dickenstein, A., Shiu, A., Conradi, C.: Chemical reaction systems with toric steady states. Bulletin of Mathematical Biology, 1–29 (October 2011)

    Google Scholar 

  35. 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)

    Chapter  Google Scholar 

  36. Clarke, B.L.: Complete set of steady states for the general stoichiometric dynamical system. The Journal of Chemical Physics 75(10), 4970–4979 (1981)

    Article  MathSciNet  Google Scholar 

  37. Anderson, D.: A proof of the global attractor conjecture in the single linkage class case (2011)

    Google Scholar 

  38. Domijan, M., Kirkilionis, M.: Bistability and oscillations in chemical reaction networks. Journal of Mathematical Biology 59(4), 467–501 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  39. 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)

    Chapter  Google Scholar 

  40. Weber, A., Sturm, T., Abdel-Rahman, E.O.: Algorithmic global criteria for excluding oscillations. Bulletin of Mathematical Biology 73(4), 899–917 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  41. 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)

    Chapter  Google Scholar 

  42. 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)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Bonn-Aachen International Center for Information Technology, Universität Bonn, Dahlmannstraße 2, D-53113, Bonn, Germany

    Satya Swarup Samal

  2. Institut für Informatik II, Universität Bonn, Friedrich-Ebert-Allee 144, 53113, Bonn, Germany

    Andreas Weber

Authors
  1. Satya Swarup Samal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hassan Errami
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Andreas Weber
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Laboratory of Information Technologies (LIT), Joint Institute for Nuclear Research (JINR), 141980, Dubna, Russia

    Vladimir P. Gerdt

  2. Institut für Mathematik, Universität Kassel, Heinrich-Plett-Straße 40, 34132, Kassel, Germany

    Wolfram Koepf

  3. Institut für Informatik, Lehrstuhl für Effiziente Algorithmen, Technische Universität München, Boltzmannstraße 3, 85748, Garching, Germany

    Ernst W. Mayr

  4. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

Rights and permissions

Reprints 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)

Publish with us

Policies and ethics

Search

Navigation