Model assessment and refinement using strategies from biochemical systems theory: Application to metabolism in human red blood cells

Journal of Theoretical Biology

Volumn 179, Issue 4, 1996, Pages 329-368

  Ni, Ta Chen ^a   Savageau, Michael A ^a  

^a UNIVERSITY OF MICHIGAN MEDICAL SCHOOL   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

2,3 DIPHOSPHOGLYCERIC ACID; ADENOSINE; ADENOSINE DIPHOSPHATE; ERYTHROCYTE ENZYME; FRUCTOSE 6 PHOSPHATE; HEXOKINASE; INOSINE; PHOSPHATE; PHOSPHORIBOSYL PYROPHOSPHATE; RIBOSEPHOSPHATE PYROPHOSPHOKINASE;

ALGORITHM; ENZYME REGULATION; ERYTHROCYTE METABOLISM; EXPERIMENTAL MODEL; HUMAN; MEMBRANE TRANSPORT; NEGATIVE FEEDBACK; NUCLEOTIDE METABOLISM; NUCLEOTIDE TRANSPORT; PRIORITY JOURNAL; REVIEW; SYSTEM ANALYSIS;

ALGORITHMS; ERYTHROCYTES; HUMANS; MODELS, BIOLOGICAL; NUCLEOTIDES;

EID: 0029902666     PISSN: 00225193     EISSN: None     Source Type: Journal    
DOI: 10.1006/jtbi.1996.0072     Document Type: Article

References (70)

1. ATAULLAKHANOV, F. I., VITVITSKY, V. M., ZHABOTINSKY, A. M., PICHUGIN, A. V., PLATONOVA, O. V. & KHOLODENKO, B. N. (1981). The regulation of glycolysis in human erythrocytes. The dependence of the glycolytic flux on the ATP concentration. Eur. J. Biochem. 115, 359-365.
2. BECKER, M. A., KOSTEL, P. J. & MEYER, L. J. (1975). Human phosphoribosylpyro-phosphate synthetase. Comparison of purified normal and mutant enzymes. J. Biol. Chem. 250, 6822-6830.
3. BEUTLER, E. (1984) Red Cell Metabolism - A Manual of Biochemical Methods, 3rd edn. Orlando: Grune & Stratton.
4. BODE, H. W. (1945). Network Analysis and Feedback Amplifier Design. Princeton, NJ: Van Nostrand.
5. BREWER, G. J. (1989). The Red Cell - Seventh Ann Arbor Conference. New York: Alan R. Liss Inc.
6. BRUMEN, M. & HEINRICH, R. (1984). A metabolic osmotic model of human erythrocytes. Biosystems 17, 155-169.
7. CHEN, C. (1984). Linear System Theory and Design, New York: Holt, Rinehart & Winston.
8. CLEGG, J. S. (1984). Properties and metabolism of the aqueous cytoplasm and its boundaries. Am. J. Physiol. 246, R133-R151.
9. CRUZ, J. B. (1973). System Sensitivity Analysis. Stroudsburg, PA: Dowden, Hutchinson & Ross, Inc.
10. DEAN, B. M. & PERRETT, D. (1976). Studies on adenine and adenosine metabolism by intact human erythrocytes using high performance liquid chromatography. Biochim. Biophys. Acta 437, 1-5.
11. FOX, I. H. & KELLEY, W. N. (1971). Human phosphoribosylpyrophosphate synthetase. Distribution, purification, and properties. J. Biol. Chem. 246, 5739-5748.
12. FOX, I. H. & KELLEY, W. N. (1972). Human phosphoribosylpyrophosphate synthetase. Kinetic mechanism and end product inhibition. J. Biol. Chem. 247, 2126-2131.
13. GERBER, G., PREISSLER, H., HEINRICH, R. & RAPOPORT, S. M. (1974). Hexokinase of human erythrocytes. Eur. J. Biochem. 45, 39-52.
14. GUCKENHEIMER, J. (1990). Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. New York: Springer-Verlag.
15. HALESTRAP, A. P. (1976). Transport of pyruvate and lactate into human erythrocytes. Biochem. J. 156, 193-207.
16. HEINRICH, R. & RAPOPORT, T. A. (1975). Mathematical analysis of multienzyme systems. II. Steady state and transient control. Biosystems 7, 130-136.
17. HENDERSON, J. F. & PATTERSON, A. R. P. (1973). Nucleotide Metabolism: An Introduction. New York: Academic Press.
18. HOLZHUTTER, H. G., JACOBASCH, G. & BISDORFF, A. (1985). Mathematical modelling of metabolic pathways affected by an enzyme deficiency. A mathematical model of glycolysis in normal and pyruvate-kinase-deficient red blood cells. Eur. J. Biochem. 149, 101-111.
19. JOSHI, A. & PALSSON, B. O. (1989a). Metabolic dynamics in the human red cell. Part I - A comprehensive kinetic model. J. theor. Biol. 141, 515-528.
20. JOSHI, A. & PALSSON, B. O. (1989b). Metabolic dynamics in the human red cell. Part II - Interactions with the environment. J. theor. Biol. 141, 529-545.
21. JOSHI, A. & PALSSON, B. O. (1990a). Metabolic dynamics in the human red cell. Part III - Metabolic reaction rates. J. theor. Biol. 142, 41-68.
22. JOSHI, A. & PALSSON, B. O. (1990b). Metabolic dynamics in the human red cell. Part IV - Data prediction and some model computations. J. theor. Biol. 142, 69-85.
23. LASSEN, U. V. (1967). Hypoxanthine transport in human erythrocytes. Biochim. Biophys. Acta 135, 146-154.
24. LEE, I.-D. & PALSSON, B. O. (1990). A comprehensive model of human erythrocyte metabolism: extensions to include pH effects. Biomed. Biochim. Acta 49, 771-789.
25. LEE, I.-D. & PALSSON, B. O. (1992). A Macintosh software package for simulation of human red blood cell metabolism. Comput. Meth. Prog. Biomed. 38, 195-226.
26. MARSHALL, W. E. & OMACHI, U. A. (1974). Measured and calculated NAD+-NADH ratios in human erythrocytes. Biochim. Biophys. Acta 354, 1-10.
27. MCINTYRE, L. M., THORBURN, D. R., BUBB, W. A. & KUCHEL, P. W. (1989). Comparison of computer simulations of the F-type and L-type non-oxidative hexose monophosphate shunts with 31P-NMR experimental data from human erythrocytes. Eur. J. Biochem. 180, 399-420.
28. MILLS, G. C., SCHMALTIEG, F. C., TRIMMER, K. B., GOLDMAN, A. S. & GOLDBLUM, R. M. (1976). Purine metabolism in adenosine deaminase deficiency. Proc. Natl. Acad. Sci. 73, 2867-2871.
29. NI, T.-C. (1994). Metabolism in human red blood cells: model assessment and refinement using strategies from biochemical systems theory. Cat. No. 9513445, pp. 1-150, Ann Arbor, Mi: UMI-University Microfilms.
30. NI, T.-C. & SAVAGEAU, M. A. (1996). Application of biochemical systems theory to metabolism in human red blood cells: Signal propagation and accuracy of representation. J. Biol. Chem. 271, 7927-7941.
31. OKAMOTO, M. & SAVAGEAU, M. A. (1984). Integrated function of a kinetic proofreading mechanism: steady-state analysis testing internal consistency of data obtained in vivo and in vitro and predicting parameter values. Biochemistry 23, 1701-1709.
32. ORLAND, M. J. & SALTMAN, R. J. (1986). Manual of Medical Therapeutics, 25th edn, Boston: Little, Brown and Co.
33. OTTO, M., HEINRICH, R., KUHN, B. & JACOBASCH, G. (1974). A mathematical model for the influence of F-6-P, ATP, potassium, ammonium and magnesium on the PFK from rat erythrocytes. Eur. J. Biochem. 49, 169-178.
34. PRESS, W. H., FLANNERY, B. P. & TEUKOLSKY, S. A. (1992). Numerical Recipes in C, 2nd edn. New York: Cambridge University Press.
35. RAPOPORT, T. A. & HEINRICH, R. (1975). Mathematical analysis of multienzyme systems. I. Modelling of the glycolysis of human erythrocytes. Biosystems 7, 120-129.
36. RAPOPORT, T. A., HEINRICH, R. & RAPOPORT, S. M. (1976). The regulatory principles of glycolysis in erythrocytes in vivo and in vitro. A minimal comprehensive model describing steady states, quasi-steady states and time-dependent processes. Biochem. J. 154, 449-469.
37. RIJKSEN, G. & STAAL, G. E. (1977). Regulation of human erythrocyte hexokinase. The influence of glycolytic intermediates and inorganic phosphate. Biochim. Biophys. Acta 485, 75-86.
38. SAVAGEAU, M. A. (1969). Biochemical systems analysis II. The steady state solutions for an n-pool system using a power-law approximation. J. theor. Biol. 25, 370-379.
39. SAVAGEAU, M. A. (1976). Biochemical Systems Analysis: A Study of Function and Design in Molecular Biology. Reading, MA: Addison-Wesley.
40. SAVAGEAU, M. A. (1979). Growth of complex systems can be related to the properties of their underlying determinants. Proc. Natl. Acad. Sci. U.S.A. 76, 5413-5417.
41. SAVAGEAU, M. A. (1985) A Theory of alternative designs for biochemical control systems. Biomed. Biochim. Acta 44, 875-880.
42. SAVAGEAU, M. A. (1991a). Reconstructionist molecular biology. New Biologist 3, 190-197.
43. SAVAGEAU, M. A. (1991b). Biochemical systems theory: Operational differences among variant representations and their significance. J. theor. Biol. 151, 509-530.
44. SAVAGEAU, M. A. (1992). A critique of the enzymologist's test tube. In: Fundamentals of Medical Cell Biology (Bittar, E. E., ed.), vol. 3A, pp. 45-108, Greenwich, CT: JAI Press Inc.
45. SAVAGEAU, M. A. (1996a). Power-law formalism: A canonical nonlinear approach to modeling and analysis. In: World Congress of Nonlinear Analysts 92, (Lakshmikantham, V., ed), vol. 4, pp. 3323-3334, Berlin: Walter de Gruyter Publishers.
46. SAVAGEAU, M. A. (1996b). A kinetic formalism for integrative molecular biology: Manifestation in biochemical systems theory and use in elucidating design principles for gene circuits. In Integrative Approaches to Molecular Biology (Collado, J, Magasanik, B., and Smith, T., eds), Cambridge, MA: MIT Press.
47. SAVAGEAU, M. A. & SORRIBAS, A. (1989). Constraints among molecular and systemic properties: Implications for physiological genetics. J. theor. Biol. 141, 93-115.
48. SCHAUER, M., HEINRICH, R. & RAPOPORT, S. M. (1981). Mathematical modelling of glycolysis and adenine nucleotide metabolism of human erythrocytes. I. Reaction-kinetic statements, analysis of in vivo state and determination of starting conditions for in vitro experiments. Acta Biol. Med. Ger. 40, 1659-1682.
49. SEGAL, H. L. (1959). The development of enzyme kinetics. In: The Enzymes (Boyer, P. D., Lardy, H., & Myrback, K., eds), vol. I, 2nd edn, pp. 1-48. New York: Academic Press.
50. SEGEL, I. H. (1975). Enzyme Kinetics. New York: Wiley.
51. SHIRAISHI, F. & SAVAGEAU, M. A. (1992a). The tricarboxylic acid cycle in Dictyostelium discoideum I. Formulation of alternative kinetic representations. J. Biol. Chem. 267, 22912-22918.
52. SHIRAISHI, F. & SAVAGEAU, M. A. (1992b). The tricarboxylic acid cycle in Dictyostelium discoideum II. Evaluation of model consistency and robustness. J. Biol. Chem. 267, 22919-22925.
53. SHIRAISHI, F. & SAVAGEAU, M. A. (1992c). The tricarboxylic acid cycle in Dictyostelium discoideum III. Analysis of steady-state and dynamic behavior. J. Biol. Chem. 267, 22926-22933.
54. SHIRAISHI, F. & SAVAGEAU, M. A. (1992d). The tricarboxylic acid cycle in Dictyostelium discoideum IV. Resolution of discrepancies between alternative methods of analysis. J. Biol. Chem. 267, 22934-22943.
55. SHIRAISHI, F. & SAVAGEAU, M. A. (1993). The tricarboxylic acid cycle in Dictyostelium discoideum V. Systemic effects of including protein turnover in the current model. J. Biol. Chem. 268, 16917-16928.
56. SORRIBAS, A. & SAVAGEAU, M. A. (1989a). A comparison of variant theories of intact biochemical systems I: Enzyme-enzyme interactions and biochemical systems theory. Math. Biosci. 94, 161-193.
57. SORRIBAS, A. & SAVAGEAU, M. A. (1989b). A comparison of variant theories of intact biochemical systems II: Flux-oriented and metabolic control theories. Math. Biosci. 94, 195-238.
58. SORRIBAS, A. & SAVAGEAU, M. A. (1989c). Strategies for representing metabolic pathways within biochemical systems theory: Reversible pathways. Math. Biosci. 94, 239-269.
59. SORRIBAS, A., CURTO, R. & CASCANTE, M. (1995). Comparative characterization of the fermentation pathway of Saccharomyces cerevisiae using biochemical systems theory and metabolic control analysis: model validation and dynamic behavior. Math. Biosci. 130, 71-84.
60. SRERE, P., JONES, M. E. & MATTHEWS, C. (1989). Structural and Organizational Aspects of Metabolic Regulation. New York: Liss.
61. SURGENOR, D. M. (1974). The Red Blood Cell, 2nd edn. New York: Academic Press.
62. THORBURN, D. R. & KUCHEL, P. W. (1985). Regulation of the human-erythrocyte hexose-monophosphate shunt under conditions of oxidative stress. A study using NMR spectroscopy, a kinetic isotope effect, a reconstituted system and computer simulation. Eur. J. Biochem. 150, 371-386.
63. VERHULST, F. (1990). Nonlinear Differential Equations and Dynamical Systems. New York: Springer-Verlag.
64. VIDYASAGAR, M. (1978). Nonlinear Systems Analysis. Englewood Cliffs, NJ: Prentice-Hall.
65. VOIT, E. O. (1991). Canonical Nonlinear Modeling: S-System Approach to Understanding Complexity, New York: Van Nostrand Reinhold.
66. VOIT, E. O. & SAVAGEAU, M. A. (1987). Accuracy of alternative representations for integrated biochemical systems. Biochemistry 26, 6869-6880.
67. WALLACH, J. (1986). Interpretation of Diagnostic Tests, 4th edn. Boston: Little, Brown and Co.
68. WEBB, J. L. (1963). Enzyme and Metabolic Inhibitors, vol. I. New York: Academic Press.
69. WERNER, A. & HEINRICH, R. (1985). A kinetic model for the interaction of energy metabolism and osmotic states of human erythrocytes. Analysis of the stationary in vivo state and of time dependent variations under blood preservation conditions Biomed. Biochim. Acta 44, 185-212.
70. YOSHIDA, T. & DEMBO, M. (1990). A thermodynamic model of hemoglobin suitable for physiological applications. Am. J. Phys. 258, C563-C577.