Skip to main content
NCBI home page
Biochemical Journal logoLink to Biochemical Journal
. 1993 Apr 15;291(Pt 2):585–593. doi: 10.1042/bj2910585

Quantitative determination of the steady-state kinetics of multienzyme reactions using the algebraic rate equations for the component single-enzyme reactions.

C D Stoner 1
PMCID: PMC1132564  PMID: 8484738

Abstract

Methods are given whereby the steady-state kinetic characteristics of multienzyme reactions consisting of individual single-enzyme reactions linked by freely diffusible intermediates can be determined quantitatively from the experimentally determined complete algebraic rate equations for the individual reactions. The approach is based on the fact that a valid steady-state rate equation for such a multienzyme reaction, in terms of the rate equations for the individual reactions, can be obtained simply from knowledge of the relative rates of the individual reactions when the multienzyme reaction is in the steady state. A number of model multienzyme reactions, which differ as to structural arrangement of the individual reactions, are examined by this approach. Simple mathematical methods which are applicable to most of these models are given for direct calculation of dependent variables. It is either pointed out or demonstrated with Mathematica that the rate equations for all of these models can be handled very easily with the aid of a personal computer equipped with appropriate equation-solving software. Since the approach permits evaluation of all dependent variables for any specific combination of values for the kinetic parameters and independent variables, numerical values for the flux control coefficients of the individual enzymes can be obtained by direct calculation for a wide variety of conditions and can be compared with those obtained according to the methods of Metabolic Control Analysis. Several such comparisons have been made and in all cases identical results were obtained. The intuitive notion that the individual enzymes of a multienzyme reaction would be equally rate limiting if the total amount of enzyme were being used with maximum efficiency is tested and shown to be incorrect. In the course of this test the flux control coefficient for the individual enzymes were found to be appropriate indicators of relative rate limitation or control by the enzymes and to account properly for differences in specific activity among the enzymes.

Full text

PDF
585

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. CLELAND W. W. The kinetics of enzyme-catalyzed reactions with two or more substrates or products. I. Nomenclature and rate equations. Biochim Biophys Acta. 1963 Jan 8;67:104–137. doi: 10.1016/0006-3002(63)91800-6. [DOI] [PubMed] [Google Scholar]
  2. Cornish-Bowden A., Hofmeyr J. H. MetaModel: a program for modelling and control analysis of metabolic pathways on the IBM PC and compatibles. Comput Appl Biosci. 1991 Jan;7(1):89–93. doi: 10.1093/bioinformatics/7.1.89. [DOI] [PubMed] [Google Scholar]
  3. Fell D. A., Sauro H. M. Metabolic control and its analysis. Additional relationships between elasticities and control coefficients. Eur J Biochem. 1985 May 2;148(3):555–561. doi: 10.1111/j.1432-1033.1985.tb08876.x. [DOI] [PubMed] [Google Scholar]
  4. HIGGINS J. Analysis of sequential reactions. Ann N Y Acad Sci. 1963 May 10;108:305–321. doi: 10.1111/j.1749-6632.1963.tb13382.x. [DOI] [PubMed] [Google Scholar]
  5. Heinrich R., Rapoport T. A. A linear steady-state treatment of enzymatic chains. General properties, control and effector strength. Eur J Biochem. 1974 Feb 15;42(1):89–95. doi: 10.1111/j.1432-1033.1974.tb03318.x. [DOI] [PubMed] [Google Scholar]
  6. Heinrich R., Rapoport T. A. Mathematical analysis of multienzyme systems. II. Steady state and transient control. Biosystems. 1975 Jul;7(1):130–136. doi: 10.1016/0303-2647(75)90050-7. [DOI] [PubMed] [Google Scholar]
  7. Hofmeyr J. H., Kacser H., van der Merwe K. J. Metabolic control analysis of moiety-conserved cycles. Eur J Biochem. 1986 Mar 17;155(3):631–641. doi: 10.1111/j.1432-1033.1986.tb09534.x. [DOI] [PubMed] [Google Scholar]
  8. Hofmeyr J. H., van der Merwe K. J. METAMOD: software for steady-state modelling and control analysis of metabolic pathways on the BBC microcomputer. Comput Appl Biosci. 1986 Dec;2(4):243–249. doi: 10.1093/bioinformatics/2.4.243. [DOI] [PubMed] [Google Scholar]
  9. Kacser H., Burns J. A. MOlecular democracy: who shares the controls? Biochem Soc Trans. 1979 Oct;7(5):1149–1160. doi: 10.1042/bst0071149. [DOI] [PubMed] [Google Scholar]
  10. Kacser H., Burns J. A. The control of flux. Symp Soc Exp Biol. 1973;27:65–104. [PubMed] [Google Scholar]
  11. Kacser H. The control of enzyme systems in vivo: elasticity analysis of the steady state. Biochem Soc Trans. 1983 Jan;11(1):35–40. doi: 10.1042/bst0110035. [DOI] [PubMed] [Google Scholar]
  12. Pettersson G., Pettersson P. Ultimate limits for the reaction flux and metabolite levels that may be evolutionarily reached in a linear metabolic pathway. Eur J Biochem. 1990 Nov 26;194(1):135–139. doi: 10.1111/j.1432-1033.1990.tb19436.x. [DOI] [PubMed] [Google Scholar]
  13. Stoner C. D. An investigation of the relationships between rate and driving force in simple uncatalysed and enzyme-catalysed reactions with applications of the findings to chemiosmotic reactions. Biochem J. 1992 Apr 15;283(Pt 2):541–552. doi: 10.1042/bj2830541. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Stoner C. D., Sirak H. D. Steady-state kinetics of the overall oxidative phosphorylation reaction in heart mitochondria. J Bioenerg Biomembr. 1979 Dec;11(5-6):113–146. doi: 10.1007/BF00743199. [DOI] [PubMed] [Google Scholar]

Articles from Biochemical Journal are provided here courtesy of The Biochemical Society

RESOURCES