A reliable Taylor series-based computational method for the calculation of dynamic sensitivities in large-scale metabolic reaction systems: Algorithm and software evaluation

Mathematical Biosciences

Volumn 222, Issue 2, 2009, Pages 73-85

  Shiraishi, Fumihide ^a   Tomita, Tomofumi ^a   Iwata, Michio ^a   Berrada, Aziz A ^b   Hirayama, Hiroshi ^c  

^a KYUSHU UNIVERSITY   (Japan)

^b KYUSHU INSTITUTE OF TECHNOLOGY   (Japan)

^c KANAGAWA INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

Dynamic sensitivity; High accuracy and reliability; Metabolism; Non linear dynamics; Reaction engineering; Simulation

Indexed keywords

BIOCHEMICAL SYSTEMS; COMPUTATION TIME; COMPUTER PROGRAM; DYNAMIC SENSITIVITY; DYNAMIC SENSITIVITY ANALYSIS; FINITE DIFFERENCE; HIGH ACCURACY AND RELIABILITY; MATHEMATICAL OPERATIONS; METABOLIC REACTIONS; METABOLITE CONCENTRATIONS; NON-LINEAR; NON-LINEAR DYNAMICS; NUMERICAL DIFFERENTIATION; NUMERICAL INTEGRATIONS; REACTION ENGINEERING; SOFTWARE EVALUATION; TAYLOR EXPANSIONS;

BIOCHEMISTRY; BIOLOGICAL SYSTEMS; COMPUTATIONAL EFFICIENCY; COMPUTER SOFTWARE SELECTION AND EVALUATION; DIFFERENTIAL EQUATIONS; LARGE SCALE SYSTEMS; METABOLISM; SENSITIVITY ANALYSIS; SYSTEMS ENGINEERING; TAYLOR SERIES;

DYNAMIC ANALYSIS;

ALGORITHM; BIOLOGICAL ANALYSIS; FINITE DIFFERENCE METHOD; METABOLISM; METABOLITE; NUMERICAL MODEL; SENSITIVITY ANALYSIS; SOFTWARE;

ACCURACY; ALCOHOL PRODUCTION; ALGORITHM; ARTICLE; COMPUTER PROGRAM; COMPUTER SIMULATION; CONTROLLED STUDY; DICTYOSTELIUM DISCOIDEUM; MATHEMATICAL COMPUTING; METABOLOMICS; NONLINEAR SYSTEM; PYROLYSIS; RELIABILITY; SENSITIVITY ANALYSIS;

ALGORITHMS; CITRIC ACID CYCLE; COMPUTER SIMULATION; DICTYOSTELIUM; ETHANOL; FERMENTATION; GLUCOSE; KINETICS; METABOLISM; MODELS, BIOLOGICAL; NONLINEAR DYNAMICS; SOFTWARE; SOFTWARE DESIGN; USER-COMPUTER INTERFACE;

EID: 70450223697     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2009.09.001     Document Type: Article

References (32)

1. Varma A., Morbidelli M., and Wu H. Parametric Sensitivity in Chemical Systems (1999), Cambridge University, Cambridge
2. Rabitz H., Kramer M., and Dacol D. Sensitivity analysis in chemical kinetics. Annu. Rev. Phys. Chem. 34 (1983) 419
3. Seigneur C., Stephanopoulos G., and Carr R.W. Dynamic sensitivity analysis of chemical reaction systems. Chem. Eng. Sci. 37 (1982) 845
4. Shiraishi F., and Hatoh Y. Dynamic sensitivities in chaotic dynamical systems. Appl. Math. Comput. 186 (2007) 1347
5. Ingalls B.P., and Sauro H.M. Sensitivity analysis of stoichiometric networks: an extension of metabolic control analysis to non-steady state trajectories. J. Theor. Biol. 222 (2003) 23
6. Schwacke J.H., and Voit E.O. Computation and analysis of time-dependent sensitivities in generalized mass action systems. J. Theor. Biol. 236 (2005) 21
7. Shiraishi F., Hatoh Y., and Irie T. An efficient method for calculation of dynamic logarithmic gains in biochemical systems theory. J. Theor. Biol. 234 (2005) 79
8. Mauch K., Arnold S., and Reuss M. Dynamic sensitivity analysis for metabolic systems. Chem. Eng. Sci. 52 (1997) 2589
9. Wu S.H., Wang F.S., and Chang M.S. Dynamic sensitivity analysis of biological systems. BMC Bioinf. 9 (2008) S1
10. Irvine D.H., and Savageau M.A. Efficient solution of nonlinear ordinary differential equations expressed in S-system canonical form. SIAM J. Numer. Anal. 27 (1990) 704
11. Savageau M.A., and Voit E.O. Recasting nonlinear differential equations as S-systems: a canonical nonlinear form. Math. Biosci. 87 (1987) 83
12. Shiraishi F., Takeuchi H., Hasegawa T., and Nagasue H. A Taylor-series solution in Cartesian space to GMA-system equations and its application to initial-value problems. Appl. Math. Comput. 127 (2002) 103
13. Shiraishi F. Highly accurate solution of the axial dispersion model expressed in S-system canonical form by Taylor-series method. Chem. Eng. J. 83 (2001) 175
14. Shiraishi F., and Fujiwara S. An efficient method for solving two-point boundary value problems with extremely high accuracy. J. Chem. Eng. Jpn. 29 (1996) 88
15. Shiraishi F., Hasegawa T., and Nagasue H. Numerical solution of the two-point boundary value problem by the combined Taylor series method with a technique for rapidly selecting suitable stepsizes. J. Chem. Eng. Jpn. 28 (1995) 306
16. Miyakawa H., Nagasue H., and Shiraishi F. A highly accurate numerical method for calculating apparent kinetic parameters of immobilized enzyme reactions: 1. Theory. Biochem. Eng. J. 3 (1999) 91
17. Miyakawa H., Nagasue H., and Shiraishi F. A highly accurate numerical method for calculating apparent kinetic parameters of immobilized enzyme reactions: 2. Accuracies of calculated values. Biochem. Eng. J. 3 (1999) 103
18. H. Nagasue, Dissertation, Kyushu University, 1994.
19. Ascher U.M., and Petzold L.R. Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations (1998), SIAM, Philadelphia, PA
20. Shiraishi F., Furuta S., Ishimatsu T., and Akhter J. A simple and highly accurate numerical differentiation method for sensitivity analysis of large-scale metabolic reaction systems. Math. Biosci. 208 (2007) 590
21. Hirayama H., Komiya S., and Sato S. Solving ordinary differential equations by Taylor series. JSIAM 12 (2002) 1
22. Baker G.A., and Graves-Morris P. Padé Approximants. second ed. (1996), Cambridge University, New York
23. Curto R., Sorribas A., and Cascante M. Comparative characterization of the fermentation pathway of Saccharomyces cerevisiae using biochemical systems theory and metabolic control analysis: model definition and nomenclature. Math. Biosci. 130 (1995) 25
24. Albe K.R., and Wright B.E. Systems analysis of the tricarboxylic acid cycle in Dictyostelium discoideum. II. Control analysis. J. Biol. Chem. 267 (1992) 3106
25. Wright B.E., Butler M.H., and Albe K.R. Systems analysis of the tricarboxylic acid cycle in Dictyostelium discoideum. I. The basis for model construction. J. Biol. Chem. 267 (1992) 3101
26. Shiraishi F., and Savageau M.A. The tricarboxylic acid cycle in Dictyostelium discoideum. I. Formulation of alternative kinetic representations. J. Biol. Chem. 267 (1992) 22912
27. Shiraishi F., and Savageau M.A. The tricarboxylic acid cycle in Dictyostelium discoideum. II. Evaluation of model consistency and robustness. J. Biol. Chem. 267 (1992) 22919
28. Shiraishi F., and Savageau M.A. The tricarboxylic acid cycle in Dictyostelium discoideum. III. Analysis of steady-state and dynamic behavior. J. Biol. Chem. 267 (1992) 22926
29. Shiraishi F., and Savageau M.A. The tricarboxylic acid cycle in Dictyostelium discoideum. IV. Resolution of discrepancies between alternative methods of analysis. J. Biol. Chem. 267 (1992) 22934
30. Shiraishi F., and Savageau M.A. The tricarboxylic acid cycle in Dictyostelium discoideum: systemic effects of including protein turnover in the current model. J. Biol. Chem. 268 (1993) 16917
31. Dunker A.M. The decoupled direct method for calculating sensitivities coefficients in chemical kinetics. J. Chem. Phys. 81 (1984) 2385
32. Kramer M.S., Calo J.M., and Rabits H. An improved computational method for sensitivity analysis: Green's function method with AIM. Appl. Math. Model. 5 (1981) 432