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Conservation laws and unidentifiability of rate expressions in biochemical models

Conservation laws and unidentifiability of rate expressions in biochemical models

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New experimental techniques in bioscience provide us with high-quality data allowing quantitative mathematical modelling. Parameter estimation is often necessary and, in connection with this, it is important to know whether all parameters can be uniquely estimated from available data, (i.e. whether the model is identifiable). Dealing essentially with models for metabolism, we show how the assumption of an algebraic relation between concentrations may cause parameters to be unidentifiable. If a sufficient data set is available, the problem with unidentifiability arises locally in individual rate expressions. A general method for reparameterisation to identifiable rate expressions is provided, together with a Mathematica code to help with the calculations. The general results are exemplified by four well-cited models for glycolysis. [Includes supplementary material.]

References

    1. 1)
      • Cedersund, G., Danø, S., Sørensen, P.G., Jirstrand, M.: `From in vitro biochemistry to in vivo understanding of the glycolytic oscillations in ', Proc. BioMedSim'2005, May 2005, Linköping, Sweden, p. 105–114.
    2. 2)
      • F. Hynne , S. Danø , P.G. Sørensen . Full-scale model of glycolysis in Saccharomyces cerevisiae. Biophys. Chem. , 121 - 163
    3. 3)
      • J. Higgins . A chemical mechanism for oscillation of glycolytic intermediates in yeast cells. Proc. Natl Acad. Sci. USA , 989 - 994
    4. 4)
      • M. Rizzi , M. Baltes , U. Theobald , M. Reuss . In vivo analysis of metabolic dynamics in Saccharomyces cerevisiae: II. Mathematical Model. Biotechnol. Bioeng. , 592 - 608
    5. 5)
      • A. Goldbeter . (1996) Biochemical oscillations and cellular rhythms.
    6. 6)
      • C.C. Lin , L.A. Segel . (1988) Mathematics applied to deterministic problems in the natural sciences.
    7. 7)
      • Anguelova, M.: `Nonlinear observability and identifiability: general theory and a case study of a kinetic models for ', 2004, Licentiate, Chalmers University of Technology and Gothenburg University, Sweden, 2004.
    8. 8)
      • I.H. Segel . (1975) Enzyme kinetics.
    9. 9)
      • E.E. Sel'kov . Self-oscillations in glycolysis. A simple kinetic model. Eur. J. Biochem. , 79 - 86
    10. 10)
      • R. Vallabhajosyula , V. Chickarmane , H. Sauro . Conservation analysis of large biochemical networks. Bioinformatics , 3 , 346 - 353
    11. 11)
    12. 12)
      • B. Teusink , J. Passarge , C.A. Reijenga , E. Esgalhado , C.C. van der Weijden , M. Schepper , M.C. Walsh , B. Bakker , K. van Dam , H.V. Westerhoff , J.L. Snoep . Can yeast glycolysis be understood in terms of in vitro kinetics of the constituent enzymes? testing biochemistry. Eur. J. Biochem. , 17 , 5313 - 5329
    13. 13)
    14. 14)
      • G. Margaria , E. Riccomagno , M.J. Chappell , H.P. Wynn . Differential algebra methods for the study of the structural identifiability of rational polynomial state-space models in the biosciences. Math. Biosci. , 1 - 26
    15. 15)
      • B.G. Olivier , J.L. Snoep . Web-based kinetic modelling using JWS Online. Bioinformatics , 2143 - 2144
    16. 16)
      • Diop, S., Fliess, M.: `On nonlinear observability', Proc. First European Control Conf., July 1991, Grenoble, France, p. 152–157.
    17. 17)
      • S. Vajda , K.R. Godfrey , H. Rabitz . Similarity transformation approach to identifiability analysis of nonlinear comportemental models. Math. Biosci. , 2 , 217 - 248
    18. 18)
      • M.J. Chappell , N.D. Evans , K.R. Godfrey , M.J. Chapman . Structural identifiability of controlled state space systems: a quasi-automated methodology for generating identifiable reparameterisations of unidentifiable systems. Symbolic Computation for Control (Ref. No. 1999/088), IEE Colloquium on
    19. 19)
      • Cedersund, G.: `Core-box modelling – theorical contributions and applications to glucose homeostasis related systems', 2006, PhD, Chalmers University of Technology, Sweden, 2006.
    20. 20)
      • M. Lambeth , M.J. Kushmerick . A computational model for glycogenolysis in skeletal muscle’, Ann. Biomed. Eng..
    21. 21)
      • E. Walter . (1987) Identifiability of parametric models.
    22. 22)
      • S. Danø , P.G. Sorensen , F. Hynne . Sustained oscillations in living cells. Nature , 6759 , 320 - 322
    23. 23)
      • Ollivier, F.: `Le problème de l'identifiabilité structurelle globale: approche théorique, méthodes effectives et bornes de complexité', 1990, PhD, École polytechnique, France, 1990.
    24. 24)
      • G.N. Stephanopoulos , A.A. Aristidou , J. Nielsen . (1998) Metabolic Engineering – principles and methodologies.
    25. 25)
      • H. Pohjanpalo . System identifiability based on the power series expansion of the solution. Math. Biosci. , 21 - 33
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