Reconstructing Metabolic Networks Using Interval Analysis

  • Warwick Tucker
  • Vincent Moulton
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3692)


Recently, there has been growing interest in the modelling and simulation of biological systems. Such systems are often modelled in terms of coupled ordinary differential equations that involve parameters whose (often unknown) values correspond to certain fundamental properties of the system. For example, in metabolic modelling, concentrations of metabolites can be described by such equations, where parameters correspond to the kinetic rates of the underlying chemical reactions. Within this framework, the increasing availability of time series data opens up the attractive possibility of reconstructing approximate parameter values, thus enabling the in silico exploration of the behaviour of complex dynamical systems. The parameter reconstruction problem, however, is very challenging – a fact that has resulted in a plethora of heuristics methods designed to fit parameters to the given data.

In this paper we propose a completely deterministic method for parameter reconstruction that is based on interval analysis. We illustrate its utility by applying it to reconstruct metabolic networks using S-systems. Our method not only estimates the parameters very precisely, it also determines the appropriate network topologies. A major strength of the proposed method is that it proves that large portions of parameter space can be disregarded, thereby avoiding spurious solutions.


Network Topology Boolean Function Metabolic Network Interval Analysis Metabolic Modelling 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Akutsu, T., Miyano, S., Kuhara, S.: Inferring qualitative relations in genetic networks and metabolic pathways. Pacific Symposium on Biocomputing 5, 120–301 (2000)Google Scholar
  2. 2.
    Alefeld, G., Herzberger, J.: Introduction to Interval Computations. Academic Press, New York (1983)zbMATHGoogle Scholar
  3. 3.
    Alves, R., Savageau, M.A.: Comparing systemic properties of ensembles of biological networks by graphical and statistical methods. Bioinformatics 16(6), 527–533 (2000)CrossRefGoogle Scholar
  4. 4.
    CXSC – C++ eXtension for Scientific Computation, version 2.0., Available from
  5. 5.
    de Jong, H.: Modeling and Simulation of Genetic Regulatory Systems: A Literature Review. J. Comp. Biol. 9(1), 67–103 (2002)CrossRefGoogle Scholar
  6. 6.
    Enright, W.H.: A New Error-Control for Initial Value Solvers. Applied Mathematics and Computation 31, 288–301 (1998)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Hlavacek, W.S., Savageau, M.A.: Rules for Coupled Expressions of Regulator and Effector Genes in Inducible Circuits. J. Mol. Biol. 255, 121–139 (1996)CrossRefGoogle Scholar
  8. 8.
    INTLAB – INTerval LABoratory, version 4.1.2. Available from
  9. 9.
    Kell, D.: Current Opinion in Microbiology, vol. 7, pp. 296–307 (2004)Google Scholar
  10. 10.
    Kikuchi, S., Tominaga, D., Arita, M., Takahashi, K., Tomita, M.: Dynamic modeling of genetic networks using genetic algorithm and S-system. Bioinformatics 19(5), 643–650 (2003)CrossRefGoogle Scholar
  11. 11.
    Kulisch, U.W., Miranker, W.L.: Computer Arithmetic in Theory and Practice. Academic Press, New York (1981)zbMATHGoogle Scholar
  12. 12.
    Moore, R.E.: Interval Analysis. Prentice-Hall, Englewood Cliffs (1966)zbMATHGoogle Scholar
  13. 13.
    Moore, R.E.: Methods and Applications of Interval Analysis. SIAM Studies in Applied Mathematics. Philadelphia (1979)Google Scholar
  14. 14.
    PROFIL/BIAS – Programmer’s Runtime Optimized Fast Interval Library/Basic Interval Arithmetic Subroutines. Available from
  15. 15.
    Torres, N.V., Voit, E.O.: Pathway Analysis and Optimization in Metabolic Engeneering. Cambridge University Press, Cambridge (2002)CrossRefGoogle Scholar
  16. 16.
    Tsai, K., Wang, F.: Evolutionary optimization with data collocation for reverse engineering of biological networks Bioinformatics. Advance Access published online on October 28 (2004)Google Scholar
  17. 17.
    Voit, E.O.: Computational Analysis of Biochemical Systems. Cambridge University Press, Cambridge (2000)Google Scholar
  18. 18.
    Voit, E.O., Almeida, J.: Decoupling dynamical systems for pathway identification from metabolic profiles. Bioinformatics 20(11), 1670–1678 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Warwick Tucker
    • 1
  • Vincent Moulton
    • 2
  1. 1.Department of MathematicsUppsala UniversityUppsalaSweden
  2. 2.School of Computing SciencesUniversity of East AngliaNorwichUK

Personalised recommendations