Advertisement

Extracting Biochemical Reaction Kinetics from Time Series Data

  • Edmund J. Crampin
  • Patrick E. McSharry
  • Santiago Schnell
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3214)

Abstract

We consider the problem of inferring kinetic mechanisms for biochemical reactions from time series data. Using a priori knowledge about the structure of chemical reaction kinetics we develop global nonlinear models which use elementary reactions as a basis set, and discuss model construction using top-down and bottom-up approaches.

Keywords

Basis Function Time Series Data Elementary Reaction Model Size Bimolecular Reaction 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Mendes, P., Kell, D.B.: Non-linear optimization of biochemical pathways: applications to metabolic engineering and parameter estimation. Bioinformatics 14, 869–883 (1998)CrossRefGoogle Scholar
  2. 2.
    Moles, C.G., Mendes, P., Banga, J.R.: Parameter estimation in biochemical pathways: A comparison of global optimization methods. Genome Res. 13, 2467–2474 (2003)CrossRefGoogle Scholar
  3. 3.
    Crampin, E.J., Schnell, S., McSharry, P.E.: Mathematical and computational techniques to deduce complex biochemical reaction mechanisms. Prog. Biophys. Mol. Biol (in press, 2004)Google Scholar
  4. 4.
    Kantz, H., Schreiber, T.: Nonlinear Time Series Analysis. Cambridge University Press, Cambridge (1997)zbMATHGoogle Scholar
  5. 5.
    Almeida, J.S.: Predictive non-linear modeling of complex data by artificial neural networks. Curr. Opin. Biotech. 13, 72–76 (2002)CrossRefGoogle Scholar
  6. 6.
    Érdi, P., Tóth, J.: Mathematical Models of Chemical Reactions: Theory and Applications of Deterministic and Stochastic Models. Princeton University Press, Princeton (1989)zbMATHGoogle Scholar
  7. 7.
    Fersht, A.R.: Structure and Mechanism in Protein Science: A Guide to Enzyme Catalysis and Protein Folding. W. H. Freeman and Co., New York (1999)Google Scholar
  8. 8.
    Judd, K., Mees, A.: On selecting models for nonlinear time series. Physica D 82, 426–444 (1995)zbMATHCrossRefGoogle Scholar
  9. 9.
    Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T.: Numerical Recipes in C, 2nd edn. Cambridge University Press, Cambridge (1992)zbMATHGoogle Scholar
  10. 10.
    Farmer, J.D., Sidorowich, J.J.: Predicting chaotic time series. Phys. Rev. Lett. 59(8), 845–848 (1987)CrossRefMathSciNetGoogle Scholar
  11. 11.
    McSharry, P.E., Smith, L.A.: Consistent nonlinear dynamics: identifying model inadequacy. Physica D 192, 1–22 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Akaike, H.: A new look at the statistical identification model. IEEE Trans. Automat. Contr. 19, 716–723 (1974)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Lawson, C.L., Hanson, R.J.: Solving Least Squares Problems. In: Number 15 in Classics in Applied Mathematics, SIAM, Philadelphia (1995)Google Scholar
  14. 14.
    Rissanen, J.: Consistent order estimates of autoregressive processes by shortest description of data. In: Jacobs, O.L.R., et al. (eds.) Analysis and Optimisation of Stochastic Systems, Academic Press, New York (1980)Google Scholar
  15. 15.
    McSharry, P.E., Ellepola, J.H., von Hardenberg, J., Smith, L.A., Kenning, D.B.R., Judd, K.: Spatio-temporal analysis of nucleate pool boiling: identification of nucleation sites using non-orthogonal empirical functions. Int. J. Heat Mass Transfer 45, 237–253 (2002)zbMATHCrossRefGoogle Scholar
  16. 16.
    Hendry, D.F., Krolzig, H.M.: New developments in automatic general-to-specific modelling. In: Stigum, B.P. (ed.) Econometrics and the Philosophy of Economics, Princeton University Press, Princeton (2003)Google Scholar
  17. 17.
    Vance, W., Arkin, A., Ross, J.: Determination of causal connectivities of species in reaction networks. Proc. Natl. Acad. Sci. U.S.A. 99, 5816–5821 (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Edmund J. Crampin
    • 1
  • Patrick E. McSharry
    • 2
    • 3
  • Santiago Schnell
    • 4
    • 5
  1. 1.Bioengineering InstituteThe University of AucklandAucklandNew Zealand
  2. 2.Mathematical InstituteOxfordUK
  3. 3.Department of Engineering ScienceUniversity of OxfordOxfordUK
  4. 4.Centre for Mathematical BiologyMathematical InstituteOxfordUK
  5. 5.Christ ChurchOxfordUK

Personalised recommendations