Quasi-steady-state kinetics at enzyme and substrate concentrations in excess of the Michaelis-Menten constant

Journal of Theoretical Biology

Volumn 245, Issue 4, 2007, Pages 737-748

  Rami Tzafriri, A ^a   Edelman, Elazer R ^a,b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b BRIGHAM AND WOMEN S HOSPITAL   (United States)

Author keywords

Enzyme kinetics; Michaelis Menten; Quasi steady state approximation; Rate equations

Indexed keywords

CATALYSIS; ENZYME ACTIVITY; REACTION KINETICS; STEADY-STATE EQUILIBRIUM; STOCHASTICITY;

ARTICLE; CONCENTRATION (PARAMETERS); CONTROLLED STUDY; ENZYME ANALYSIS; ENZYME KINETICS; ENZYME SUBSTRATE COMPLEX; MATHEMATICAL ANALYSIS; MICHAELIS CONSTANT; PRIORITY JOURNAL; STEADY STATE; STOCHASTIC MODEL; VALIDITY;

ANIMALS; CATALYSIS; ENZYMES; MATHEMATICS; MODELS, CHEMICAL; SUBSTRATE SPECIFICITY;

EID: 33947359087     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2006.12.005     Document Type: Article

References (44)

1. Albe K.R., Butler M.H., and Right B.E. Cellular concentrations of enzymes and their substrates. J. Theor. Biol. 143 (1990) 163-195
2. Aranyi P., and Toth J. A full stochastic description of the Michaelis-Menten reaction for small systems. Acta Biochim. Biophys. Acad. Sci. Hung. 12 (1977) 375-388
3. Bailey J.E., and Ollis D.F. Biochemical Engineering Fundamentals (1986), McGraw-Hill, New York (Chapter 3)
4. Borghans J.A.M., De Boer R.J., and Segel L.A. Extending the quasi-steady state approximation by changing variables. Bull. Math. Biol. 58 (1996) 43-63
5. Briggs G.E., and Haldane J.B.S. A note on the kinetics of enzyme action. Biochem. J. 19 (1925) 338-339
6. Carbonell R.G., and Kostin M.D. Enzyme kinetics and engineering. AIChE J. 18 (1972) 1-12
7. Cha S., and Cha C.-J.M. Kinetics of cyclic enzyme systems. Mol. Pharmacol. 1 (1965) 178-189
8. Cha S. Kinetic behavior at high enzyme concentrations. J. Biol. Chem. 245 (1970) 4814-4818
9. Chance B. The kinetics of the enzyme-substrate compound of peroxidase. J. Biol. Chem. 151 (1943) 553-577
10. De Boer R.J., and Perelson A.S. Towards a general function for T cell proliferation. J. Theor. Biol. 175 (1995) 567-576
11. Fersht A. Enzyme Structure and Mechanism (1985), W.H. Freeman, New York (Chapter 4)
12. Goldstein A. The mechanism of enzyme-inhibitor-substrate reactions. J. Gen. Physiol. 27 (1944) 529-580
13. Goutsias J. Quasiequilibrium approximation of fast reaction kinetics in stochastic biochemical systems. J. Chem. Phys. 122 (2005) 184102
14. Hammes G.G. Enzyme Catalysis and Regulation (1982), Academic Press, New York (Chapter 6)
15. Henri V. The orie ge ne rale de l'action de quelques diastases. C. R. Hebd. Acad. Sci. 135 (1902) 916-919
16. Herman R.A., Korjagin V.A., and Schafer B.W. Quantitative measurement of protein digestion in simulated gastric fluid. Reg. Toxicol. Pharmacol. 41 (2005) 175-184
17. Hertel K.J., Herschlag D., and Uhlenbeck O.C. A kinetic and thermodynamic framework for the hammerhead ribozyme reaction. Biochemistry 33 (1994) 3374-3385
18. Hiromi K. Kinetics of Fast Enzyme Reactions: Theory and Practice (1979), Halsted Press, New York pp. 1-19
19. Karmac M., Amarowicz R., and Kostyra H. Effect of temperature and enzyme/substrate ratio on the hydrolysis of pea protein isolates by trypsin. Czech J. Food Sci. 20 (2002) 1-6
20. Lehninger A.L. Biochemistry: The Molecular Basis of Cell Structure and Functions (1975), Worth Publishers, New York pp. 189-195
21. Lin H., Clegg D.O., and Lal R. Imaging real-time proteolysis of single collagen I molecules with an atomic force microscope. Biochemistry 38 (1999) 9956-9963
22. Lowry O.H., Passonneau J.V., Schulz D.W., and Rock M.K. J. Biol. Chem. 236 (1961) 2746-2755
23. Marquardt D.W. An algorithm for least squares estimation for nonlinear parameters. SIAM J. 11 (1963) 431-441
24. Matthews C.K., van Holde K.E., and Ahern K.G. Biochemistry (2000), Harlow, Benjamin Cummings, San Francisco (Chapter 11)
25. Michaelis L., and Menten M.L. Die kinetik der invertinwirkung. Biochem. Z. 49 (1913) 333-369
26. Palsson B.O. On the dynamics of the irreversible Michaelis-Menten reaction mechanism. Chem. Eng. Sci. 42 (1987) 447-458
27. Rao C., and Arkin A. Stochastic chemical kinetics and the quasi-steady-state assumption: application to the Gillespie algorithm. J. Chem. Phys. 118 (2003) 4999-5010
28. Reiner J.M. The Behavior of Enzyme Systems (1959), Van Nostrand Reinhold, New York pp. 54-63
29. M in enzyme reactions. Rate constants for the association of chymotrypsin with substrates. Biochemistry 12 (1973) 4713-4718
30. Salwinski L., and Eisenberg D. In silico simulation of biological network dynamics. Nat. Biotechnol. 22 (2004) 1017-1019
31. Schauer M., and Heinrich R. Analysis of the quasi-steady state approximation for an enzymatic one-substrate reaction. J. Theor. Biol. 79 (1979) 425-442
32. Schnell S., and Maini P.K. Enzyme kinetics at high enzyme concentrations. Bull. Math. Biol. 62 (2000) 483-499
33. max estimates. Comments Theor. Biol. 8 (2003) 169-187
34. Segel L.A. On the validity of the steady-state assumption of enzyme kinetics. Bull. Math. Biol. 50 (1988) 579-593
35. Sicher R.C. Characteristics of light-dependent inorganic carbon uptake by isolated spinach chloroplasts. Plant Physiol. 74 (1984) 962-966
36. Srivastava D.K., and Bernhard S.A. Metabolite transfer via enzyme-enzyme complexes. Science 234 (1986) 1081-1086
37. Stryer L. Biochemistry (1995), W.H. Freeman, New York (Chapter 8)
38. Turner T.E., Schnell S., and Burrage K. Stochastic approaches for modelling in vivo reactions. Comput. Biol. Chem. 268 (2004) 165-178
39. Tzafriri A.R. Michaelis-Menten kinetics at high enzyme concentrations. Bull. Math. Biol. 65 (2003) 1111-1129
40. Tzafriri A.R., and Edelman E.R. The total quasi-steady-state approximation is valid for reversible enzyme kinetics. J. Theor. Biol. 226 (2004) 303-313
41. Tzafriri A.R., and Edelman E.R. Endosomal receptor kinetics determine the stability of intracellular growth factor signaling complexes. Biochem. J. 402 (2004) 537-549
42. Tzafriri A.R., Bercovier M., and Parnas H. Reaction diffusion modeling of the enzymatic erosion of insoluble fibrillar matrices. Biophys. J. 83 (2002) 776-793
43. Wong J.T.-F. On the steady state method of enzyme kinetics. J. Am. Chem. Soc. 87 (1965) 1788-1793
44. Wu J.-W., Wu Y., and Wang Z.-X. Kinetic analysis of a simplified scheme of autocatalytic zymogen activation. Eur. J. Biochem. 268 (2001) 1547-1553