Accelerating the Computation of Elementary Modes Using Pattern Trees

  • Marco Terzer
  • Jörg Stelling
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4175)

Abstract

Elementary flux modes (EFMs)—formalized metabolic pathways—are central and comprehensive tools for metabolic network analysis under steady state conditions. They act as a generating basis for all possible flux distributions and, thus, are a minimal (constructive) description of the solution space. Algorithms to compute EFMs descend from computational geometry; they are mostly synonymous to the enumeration of extreme rays of polyhedral cones. This problem is combinatorially complex, and algorithms do not scale well. Here, we introduce new concepts for the enumeration of adjacent rays, which is one of the critical and stubborn facets of the algorithms. They rely on variants of k-d-trees to store and analyze bit sets representing (intermediary) extreme rays. Bit set trees allow for speed-up of computations primarily for low-dimensional problems. Extensions to pattern trees to narrow candidate pairs for adjacency tests scale with problem size, yielding speed-ups on the order of one magnitude relative to current algorithms. Additionally, fast algebraic tests can easily be used in the framework. This constitutes one step towards EFM analysis at the whole-cell level.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Klamt, S., Stelling, J.: Stoichiometric and constraint-based modeling. In: Szallasi, Z., Stelling, J., Periwal, V. (eds.) System Modeling in Cellular Biology, pp. 73–96. MIT Press, Cambridge (2006)Google Scholar
  2. 2.
    Price, N., Reed, J., Palsson, B.: Genome-scale models of microbial cells: Evaluating the consequences of constraints. Nat. Rev. Microbiol. 2, 886–897 (2004)CrossRefGoogle Scholar
  3. 3.
    Gagneur, J., Klamt, S.: Computation of elementary modes: A unifying framework and the new binary approach. BMC Bioinformatics 5, 175 (2004)CrossRefGoogle Scholar
  4. 4.
    Motzkin, T.S., Raiffa, H., Thompson, G., Thrall, R.M.: The double description method. In: Kuhn, H., Tucker, A. (eds.) Contributions to the Theory of Games II. Annals of Math. Studies, vol. 8, pp. 51–73. Princeton University Press, Princeton (1953)Google Scholar
  5. 5.
    Schuster, S., Hilgetag, C.: On elementary flux modes in biochemical reaction systems at steady state. J. Biol. Syst. 2, 165–182 (1994)CrossRefGoogle Scholar
  6. 6.
    Wagner, C.: Nullspace approach to determine the elementary modes of chemical reaction systems. J. Phys. Chem. B 108, 2425–2431 (2004)CrossRefGoogle Scholar
  7. 7.
    Fukuda, K., Prodon, A.: Double description method revisited. In: Combinatorics and Computer Science, pp. 91–111 (1995)Google Scholar
  8. 8.
    Bentley, J.L.: Multidimensional binary search trees used for associative searching. Commun. ACM 18, 509–517 (1975)MATHCrossRefGoogle Scholar
  9. 9.
    Stelling, J., Klamt, S., Bettenbrock, K., Schuster, S., Gilles, E.: Metabolic network structure determines key aspects of functionality and regulation. Nature 420, 190–193 (2002)CrossRefGoogle Scholar
  10. 10.
    Klamt, S., Gagneur, J., von Kamp, A.: Algorithmic approaches for computing elementary modes in large biochemical reaction networks. IEE Proc. Systems Biol. 152, 249–255 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Marco Terzer
    • 1
  • Jörg Stelling
    • 1
  1. 1.Department of Computer ScienceETH ZurichZurichSwitzerland

Personalised recommendations