The total quasi-steady-state approximation for fully competitive enzyme reactions

Bulletin of Mathematical Biology

Volumn 69, Issue 1, 2007, Pages 433-457

  Pedersen, Morten Gram ^a   Bersani, Alberto M ^b   Bersani, Enrico ^c  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

^c ISMAC Genova   (Italy)

Author keywords

Competitive substrates; Michaelis Menten kinetics; Quasi steady state assumption; Substrate inhibitor system

Indexed keywords

ENZYME;

ARTICLE; BINDING COMPETITION; BIOLOGICAL MODEL; CHEMICAL MODEL; KINETICS; MATHEMATICAL COMPUTING; METABOLISM;

BINDING, COMPETITIVE; ENZYMES; KINETICS; MODELS, BIOLOGICAL; MODELS, CHEMICAL; NUMERICAL ANALYSIS, COMPUTER-ASSISTED;

EID: 33846543728     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-006-9136-2     Document Type: Article

References (38)

1. Albe, K.R., Butler, M.H., Wright, B.E., 1990. Cellular concentrations of enzymes and their substrates. J. Theor. Biol. 143, 163-195.
2. Atkinson, D.E., 1977. Cellular Energy Metabolism and its Regulation. Academic Press, New York.
3. Baker, G.A., Jr., 1975. Essentials of Padé approximants. Academic Press, London.
4. Bhalla, U.S., Iyengar, R., 1999. Emergent properties of networks of biological signaling pathways. Science 283, 381-387.
5. Bisswanger, H., 2002. Enzyme Kinetics. Principles and Methods. Wiley-VCH.
6. Borghans, J., de Boer, R., Segel, L., 1996. Extending the quasi-steady state approximation by changing variables. Bull. Math. Biol. 58, 43-63.
7. Briggs, G.E., Haldane, J.B.S., 1925. A note on the kinetics of enzyme action. J. Biochem. 19, 338-339.
8. Burack, W.R., Sturgill, T.W., 1997. The activating dual phosphorylation of MAPK by MEK is nonprocessive. Biochem. 36, 5929-5933.
9. Ferrell, J.E., Bhatt, R.R., 1997. Mechanistic studies of the dual phosphorylation of mitogen-activated protein kinase. J. Biol. Chem. 272, 19008-19016.
10. Goldbeter, A., Koshland, D.E., Jr., 1981. An amplified sensitivity arising from covalent modification in biological systems. Proc. Natl. Acad. Sci. 78, 6840-6844.
11. Henri, V., 1901a. Recherches sur la loi de l'action de la sucrase. C. R. Hebd. Acad. Sci. 133, 891-899.
12. Henri, V., 1901b. Über das gesetz der wirkung des invertins. Z. Phys. Chem. 39, 194-216.
13. Henri, V., 1902. Théorie générale de l'action de quelques diastases. C. R. Hebd. Acad. Sci. 135, 916-919.
14. Huang, C.-Y.F., Ferrell, J.E., 1996. Ultrasensitivity in the mitogen-activated protein kinase cascade. Proc. Natl. Acad. Sci. 93, 10078-10083.
15. Kholodenko, B.N., 2000. Negative feedback and ultrasensitivity can bring about oscillations in the mitogen-activated protein kinase cascades. Eur. J. Biochem. 267, 1583-1588.
16. Kishore, N., Sommers, C., Mathialagan, S., Guzova, J., Yao, M., Hauser, S., Huynh, K., Bonar, S., Mielke, C., Albee, L., Weier, R., Graneto, M., Hanau, C., Perry, T., Tripp, C.S., 2003. A selective IKK-2 inhibitor blocks NF-κ B-dependent gene expression in interleukin-1β-stimulated synovial fibroblasts. J. Biol. Chem. 278, 32861-32871.
17. Kvålseth, T.O., 1985. Cautionary note about r 2 . The American Statistician 39, 279-285.
18. Markevich, N.I., Hoek, J.B., Kholodenko, B.N., 2004. Signaling switches and bistability arising from multisite phosphorylation in protein kinase cascades. J. Cell Biol. 164, 353-359.
19. Michaelis, L., Menten, M.L., 1913. Die kinetik der invertinwirkung. Biochem. Z. 49, 333-369.
20. Pedersen, M.G., Bersani, A.M., Bersani, E., 2006. Quasi steady-state approximations in intracellular signal transduction - a word of caution. Preprint Me. Mo. Mat. no. 3/2006, Department of Mathematical Methods and Models, "La Sapienza" University, Rome, Italy.
21. Pi, N., Leary, J.A., 2004. Determination of enzyme/substrate specificity constants using a multiple substrate ESI-MS assay. J. Am. Soc. Mass Spectrom. 15, 233-243.
22. Rubinow, S., Lebowitz, J., 1970. Time-dependent Michaelis-Menten kinetics for an enzyme-substrate-inhibitor system. J. Am. Chem. Soc. 92, 3888-3893.
23. Schnell, S., Maini, P., 2000. Enzyme kinetics at high enzyme concentrations. Bull. Math. Biol. 62, 483-499.
24. Schnell, S., Maini, P., 2003. A century of enzyme kinetics: Reliability of the km and vmax estimates. Comm. Theor. Biol. 8, 169-187.
25. Schnell, S., Mendoza, C., 1997. Closed-form solution for time-dependent enzyme kinetics. J. Theor. Biol. 187, 207-212.
26. Schnell, S., Mendoza, C., 1997a. Enzymological considerations for a theoretical description of the quantitative competitive polymerase chain reaction (QC-PCR). J. Theor. Biol. 184, 433-440.
27. Schnell, S., Mendoza, C., 1997b. Theoretical description of the polymerase chain reaction. J. Theor. Biol. 188, 313-318.
28. Schnell, S., Mendoza, C., 2000. Time-dependent closed-form solutions for fully competitive enzyme reactions. Bull. Math. Biol. 62, 321-336.
29. Segel, L., 1988. On the validity of the steady state assumption of enzyme kinetics. Bull. Math. Biol. 50, 579-593.
30. Segel, L.A., Slemrod, M., 1989. The quasi steady-state assumption: A case study in pertubation. SIAM Rev. 31, 446-477.
31. Sols, A., Marco, R., 1970. Concentration of metabolites and binding sites. Implications in metabolic regulation. In: Current Topics in Cellular Regulation, vol. 2. Academic Press, New York.
32. Stayton, M.M., Fromm, H.J., 1979. A computer analysis of the validity of the integrated Michaelis-Menten equation. J. Theor. Biol. 78, 309-323.
33. Straus, O.H., Goldstein, A., 1943. Zone behavior of enzymes. J. Gen. Physiol. 26, 559-585.
34. Turner, T.E., Schnell, S., Burrage, K., 2004. Stochastic approaches for modelling in vivo reactions. Comp. Biol. Chem. 28, 165-178.
35. Tzafriri, A.R., 2003. Michaelis-Menten kinetics at high enzyme concentrations. Bull. Math. Biol. 65, 1111-1129.
36. Tzafriri, A.R., Edelman, E.R., 2004. The total quasi-steady-state approximation is valid for reversible enzyme kinetics. J. Theor. Biol. 226, 303-313.
37. Tzafriri, A.R., Edelman, E.R., 2005. On the validity of the quasi-steady state approximation of bimolecular reactions in solution. J. Theor. Biol. 233, 343-350.
38. Zhao, Y., Zhang, Z.-Y., 2001. The mechanism of dephosphorylation of extracellu-lar signal-regulated kinase 2 by mitogen-activated protein kinase phosphatase 3. J. Biol. Chem. 276, 32382-32391.