Asymptotic expansions in enzyme reactions with high enzyme concentrations

Mathematical Methods in the Applied Sciences

Volumn 34, Issue 16, 2011, Pages 1954-1960

  Bersani, Alberto Maria ^a   Dell'Acqua, Guido ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

asymptotic expansions; enzyme kinetics

Indexed keywords

ASYMPTOTIC EXPANSION; CLOSED FORM; ENZYMATIC REACTION; ENZYME CONCENTRATIONS; ENZYME REACTION; MICHAELIS-MENTEN;

ASYMPTOTIC ANALYSIS; ENZYME KINETICS;

EXPANSION;

EID: 80055011149     PISSN: 01704214     EISSN: 10991476     Source Type: Journal    
DOI: 10.1002/mma.1495     Document Type: Article

References (24)

1. Henri V,. Recherches sur la loi de l'action de la sucrase. Comptes rendus hebdomadaires des seances de l'Academie des sciences 1901; 133: 891-899.
2. Henri V,. Über das gesetz der wirkung des invertins. Zeitschrift für Physikalische Chemie 1901; 39: 194-216.
3. Henri V,. Théorie générale de l'action de quelques diastases. Comptes rendus Hebdomadaires des Seances de l'Académie des Sciences de Paris 1902; 135: 916-919.
4. Michaelis L, Menten ML,. Die kinetik der invertinwirkung. Biochemistry Zeitung 1913; 49: 333-339.
5. Grima R, Schnell S,. A systematic investigation of the rate laws valid in intracellular environments. Biophysical Chemistry 2006; 124 (1): 1-10. (Pubitemid 44528094)
6. Crampin EJ, Schnell S, McSharry PE,. Mathematical and computational techniques to deduce complex biochemical reaction mechanisms. Progress in Biophysics and Molecular Biology 2004; 86 (1): 77-212.
7. Bisswanger H,. Enzyme Kinetics: Principles and Methods. Wiley-VCH Verlag GmbH: Weinheim (Federal Republic of Germany), 2002.
8. Segel LA, Slemrod M,. The quasi steady-state assumption: a case study in perturbation. SIAM Review 1989; 31 (3): 446-477.
9. Segel LA,. On the validity of the steady state assumption of enzyme kinetics. Bulletin of Mathematical Biology 1988; 50 (6): 579-593. (Pubitemid 18268676)
10. Hanson SM, Schnell S,. Reactant stationary approximation in enzyme kinetics. Journal of Physical Chemistry A 2008; 112 (37): 8654-8658.
11. Straus OH, Goldstein A,. Zone behavior of enzymes. Journal of General Physiology 1943; 26 (6): 559-585.
12. Srere PA,. Enzyme concentrations in tissues. Science 1967; 158: 936-937.
13. Sols A, Marco R,. Concentrations of metabolites and binding sites. Implications in metabolic regulation. Current Topics in Cellular Regulation 1970; 2: 227-273.
14. Albe KR, Butler MH, Wright BE,. Cellular concentration of enzymes and their substrates. Journal of Theoretical Biology 1990; 143 (2): 163-195. (Pubitemid 20141560)
15. max estimates. Comments on Theoretical Biology 2003; 8: 169-187.
16. Eanes WF, Merritt TJS, Flowers JM, Kumagai S, Sezgin E, Zhu CT,. Flux control and excess capacity in the enzymes of glycolysis and their relationship to flight metabolism in drosophila melanogaster. Proceedings of the National Academy of Sciences of the United States of America 2006; 103: 19413-19418. (Pubitemid 46026045)
17. Cha S,. Kinetic behavior at high enzyme concentrations: magnitude of errors of michaelis-menten and other approximations. Journal of Biological Chemistry 1970; 245 (18): 4814-4818.
18. Schnell S, Maini PK,. Enzyme kinetics at high enzyme concentration. Bulletin of Mathematical Biology 2000; 62 (3): 483-499.
19. Heineken FG, Tsushiya HM, Aris R,. On the mathematical status of the pseudo-steady state hypothesis of biochemical kinetics. Mathematical Biosciences 1967; 1 (1): 95-113.
20. Lin CC, Segel LA,. Mathematics applied to deterministic problems in the natural sciences. Society for Industrial and Applied Mathematics (SIAM): Philadelphia, 1988.
21. Schauer M, Heinrich R,. Analysis of the quasi-steady-state approximation for an enzymatic one-substrate reaction. Journal of Theoretical Biology 1979; 79 (4): 425-442.
22. Borghans J, de Boer R, Segel L,. Extending the quasi-steady state approximation by changing variables. Bulletin of Mathematical Biology 1996; 58 (1): 43-63. (Pubitemid 126690448)
23. Tzafriri AR,. Michaelis-Menten kinetics at high enzyme concentrations. Bulletin of Mathematical Biology 2003; 65 (6): 1111-1129. (Pubitemid 37446847)
24. Dingee JW, Anton AB,. A new perturbation solution to the Michaelis-Menten problem. AIChE Journal 2008; 54 (5): 1344-1357. (Pubitemid 351690885)