An effective method to increase solvability in biochemical systems using S-system

Mathematical Biosciences

Volumn 201, Issue 1-2, 2006, Pages 125-142

  Hasegawa, Takahiro ^a   Yoshimura, Jin ^a  

^a SHIZUOKA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

BIOCHEMICAL ENGINEERING; CONVERGENCE OF NUMERICAL METHODS; INTEGRATION; NONLINEAR EQUATIONS; PROBLEM SOLVING;

GAUSS INTEGRATION METHOD; IMMOBILIZED ENZYME SYSTEM; NEWTON-LIKE METHOD; NON-LINEAR LEAST SQUARE METHOD;

ENZYMES;

BIOCHEMISTRY; ENZYME; IMMOBILIZATION;

ACCURACY; ARTICLE; CHEMICAL ANALYSIS; DATA ANALYSIS; DERIVATIZATION; INTERMETHOD COMPARISON; MATHEMATICAL COMPUTING; MICHAELIS CONSTANT; NONLINEAR SYSTEM; NORMAL DISTRIBUTION; ORTHOGONAL ROTATION; PERFORMANCE; PROBLEM SOLVING; REACTION TIME; REGRESSION ANALYSIS; STATISTICAL ANALYSIS; STATISTICAL PARAMETERS; SYSTEM ANALYSIS;

ENZYMES, IMMOBILIZED; KINETICS; LEAST-SQUARES ANALYSIS; MODELS, CHEMICAL; SOLUBILITY;

EID: 33646835242     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2005.12.009     Document Type: Article

References (19)

1. Byron Bird R., Stewart W.E., and Lightfoot E.N. Transport Phenomena (1960), Wiley International Edition
2. Press W.H., Teukolsky S.A., Vetteriling W.T., and Flannery B.P. Numerical Rcipes in C (1988), Cambridge University
3. Savageau M.A. Biochemical systems analysis. I. Some mathematical properties of the rate law for the component enzymatic reactions. J. Theoret. Biol. 25 (1969) 365
4. Savageau M.A. Biochemical systems analysis. II. The steady-state solutions for an n-pool system using a power-law approximation. J. Theoret. Biol. 25 (1969) 370
5. Savageau M.A., Voit E.O., and Irvine D.H. Biochemical system theory and metabolic control theory: 1. Fundamental similarities and differences. Math. Biosci. 86 (1987) 127
6. Savageau M.A., Voit E.O., and Irvine D.H. Biochemical system theory and metabolic control theory: 2. The role of summation and connectivity relationships. Math. Biosci. 86 (1987) 147
7. Savageau M.A. Finding multiple roots of nonlinear algebraic equation using s-system methodology. Appl. Math. Comp. 55 (1993) 187
8. Hasegawa T., Takatani H., and Yoshimura J. Application of power-law formalism method to equilibrium computation of vapor growth epitaxy. J. Chem. Eng. Jpn. 32 (1999) 506
9. Savageau M.A., and Voit E.O. Recasting nonlinear differential equations as s-system: a canonical nonlinear form. Math. Biosci. 87 (1987) 83
10. Hasegawa T., Shiraishi F., and Nagasue H. Numerical tests for usefulness of power-law formalism method in parameter optimization problem of immobilized enzyme reaction. J. Chem. Eng. Jpn. 33 (2000) 197
11. Villadsen J.V., and Stewart W.E. Solution of boundary-problems by orthogonal collocation. Chem. Eng. Sci. 22 (1967) 1483
12. Villadsen J., and Sorensen J.P. Solution of parabolic partial differential equations by a double collocation method. Chem. Eng. Sci. 24 (1969) 1337
13. Shiraishi F., Hasegawa T., and Nagasue H. Accuracy of the numerical solution of a two-point boundary value problem by the orthogonal collocation method. J. Chem. Eng. Jpn. 28 (1995) 316
14. Goldstein L., Levin Y., and Katchalski E. A water-insoluble polyanionic derivative of trypsin. II. Effect of the polyelectrolyte carrier on the kinetic behavior of bound trypsin. Biochemistry 3 (1964) 1913
15. Hornby W.E., Lilly M.D., and Crook E.M. Some changes in reactivity of enzymes resulting from their chemical attachment to water-insoluble derivatives of cellulose. Biochem. J. 107 (1968) 669
16. Shuler M.L., Aris A., and Tsuchiya H.M. Diffusive and electrostatic effects with insolubilized enzymes. J. Theor. Biol. 35 (1972) 67
17. Shiraishi F. Substrate-concentration dependencies of apparent maximum reaction rate and apparent Michaelis constant observed in immobilized enzyme reactions. Inter. Chem. Eng. 32 (1992) 140
18. Moo-Young M., and Kobayashi T. Effectiveness factor immobilized-enzyme reaction. Can. J. Chem. 16 (1972) 162
19. Horvath C., and Engasser J.M. External and internal diffusion in heterogeneous enzyme systems. Biotechnol. Bioeng. 16 (1974) 909