Estimating parameters for generalized mass action models using constraint propagation

Mathematical Biosciences

Volumn 208, Issue 2, 2007, Pages 607-620

  Tucker, Warwick ^a   Kutalik, Zoltán ^b   Moulton, Vincent ^c  

^a UPPSALA UNIVERSITY   (Sweden)

^b UNIVERSITY OF LAUSANNE   (Switzerland)

^c UNIVERSITY OF EAST ANGLIA   (United Kingdom)

Author keywords

Biochemical systems; Constraint propagation; GMA systems; Interval analysis; Metabolic modelling; Parameter estimation; S systems

Indexed keywords

COMPUTATIONAL METHODS; DIFFERENTIAL EQUATIONS; EVOLUTIONARY ALGORITHMS; MATHEMATICAL MODELS; OPTIMIZATION; PARAMETER ESTIMATION;

BIOCHEMICAL SYSTEMS; CONSTRAINT PROPAGATION; GMA SYSTEMS; INTERVAL ANALYSIS; METABOLIC MODELING;

MOLECULAR BIOLOGY;

BIOCHEMISTRY; ESTIMATION METHOD; EVOLUTIONARY BIOLOGY; GENETIC ALGORITHM; METABOLISM; MOLECULAR ANALYSIS; NUMERICAL MODEL; OPTIMIZATION; TOPOLOGY;

ARTICLE; CHEMICAL ANALYSIS; EXPERIMENTAL MODEL; MASS ACTION; MATHEMATICAL COMPUTING; METABOLIC REGULATION; MOLECULAR BIOLOGY;

BIOCHEMISTRY; KINETICS; MATHEMATICS; METABOLISM; MODELS, BIOLOGICAL; MOLECULAR BIOLOGY;

EID: 34547118379     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2006.11.009     Document Type: Article

References (23)

1. Alefeld G., and Herzberger J. Introduction to Interval Computations (1983), Academic Press, New York
2. CXSC - C++ eXtension for Scientific Computation, version 2.0. Available from .
3. Forte Developer 7: C++ Interval Arithmetic Programming Reference. Available from .
4. INTLAB - INTerval LABoratory, version 4.1.2. Available from .
5. Jaulin L., Kieffer M., and Didrit O. Applied Interval Analysis (2001), Springer, London
6. Jaulin L. Nonlinear bounded-error state estimation of continuous-time systems. Automatica 38 6 (2002) 1079
7. Kell D. Metabolomics and systems biology: making sense of the soup. Curr. Opin. Microbiol. 7 (2004) 296
8. Kikuchi S., Tominaga D., Arita M., Takahashi K., and Tomita M. Dynamic modeling of genetic networks using genetic algorithm and S-system. Bioinformatics 19 5 (2003) 643
9. Mendes P., and Kell D. Non-linear optimization of biochemical pathways: applications to metabolic engineering and parameter estimation. Bioinformatics 14 10 (1998) 869
10. Moore R.E. Interval Analysis (1996), Prentice-Hall, Englewood Cliffs, New Jersey
11. Moore R.E. Methods and Applications of Interval Analysis (1979), SIAM Studies in Applied Mathematics, Philadelphia
12. Polisetty P.K., Voit E.O., and Gatzke E.P. Identification of metabolic system parameters using global optimization methods. Theor. Biol. Med. Model. (2006). http://www.tbiomed.com/content/3/1/4 3:4. Available from
13. PROFIL/BIAS - Programmer's Runtime Optimized Fast Interval Library/Basic Interval Arithmetic Subroutines. Available from .
14. Raïssi T., Ramdani N., and Candau Y. Set membership state and parameter estimation for systems described by nonlinear differential equations. Automatica 40 10 (2004) 1771
15. Savageau M.A. Biochemical systems analysis. I. Some mathematical properties of the rate law for the component enzymatic reactions. J. Theor. Biol. 25 (1969) 365
16. Savageau M.A. Biochemical systems analysis. II. The steady-state solutions for an n-pool system using a power-law approximation. J. Theor. Biol. 25 (1969) 370
17. Savageau M.A. Biochemical systems analysis. 3. Dynamic solutions using a power-law approximation. J. Theor. Biol. 26 (1970) 215
18. Torres N.V., and Voit E.O. Pathway Analysis and Optimization in Metabolic Engineering (2002), Cambridge University Press, Cambridge
19. Tsai K., and Wang F.-S. Evolutionary optimization with data collection for reverse engineering of biological networks. Bioinformatics 21 (2005) 1180
20. Tucker W., and Moulton V. Reconstructing metabolic networks using interval analysis. Lect. Notes Comput. Sci. 3692 (2005) 192
21. Voit E.O. Computational Analysis of Biochemical Systems (2000), Cambridge University Press
22. Voit E.O., and Almeida J. Decoupling dynamical systems for pathway identification from metabolic profiles. Bioinformatics 20 11 (2004) 1670
23. W.G. Walster, E. Hansen, Global Optimization Using Interval Analysis, Series in Pure and Applied Mathematics, vol. 264, CRC Press, 2003.