Journal of Mathematical Chemistry

, Volume 49, Issue 8, pp 1667–1686 | Cite as

Characterization of unstable enzyme systems which evolve according to a three-exponential equation

  • E. Arribas
  • J. M. Villalba
  • M. Garcia-Moreno
  • M. L. Amo
  • F. Garcia-Sevilla
  • F. Garcia-Molina
  • J. L. Muñoz-Muñoz
  • R. Varon
Original Paper


The time course of an enzyme catalyzed reaction is normally followed either by monitoring the instantaneous concentration or velocity of an enzyme species or a product. In many enzyme catalyzed reactions these time variations are multi-exponential. The accurate fit of the relevant curves to obtain the kinetic parameters involved can be difficult using conventional methods (Galvez et al. in J Theor Biol 89:37–44, 1981; Garcia-Canovas et al. in Biochim Biophys Acta 912:417–423, 1987; Tudela et al. in Biochim Biophys Acta 912:408–416, 1987; Teruel et al. in Biochim Biophys Acta 911:256–260, 1987; Garrido del Solo et al. in Biochem J 294:459–464, 1993; Varon et al. in Int J Biochem 25:1889–1895, 1993; Garrido del Solo et al. in An Quim 89:319–324, 1993; Varon et al. in J Mol Catal 83:273–285, 1993; Garrido del Solo et al. in Biochem J 303(Pt 2):435–440, 1994; Garrido del Solo and Varon in An Quim 91:13–18, 1995; Garrido del Solo et al. in Biosystems 38:75–86, 1996; Garrido del Solo et al. in Int J Biochem Cell Biol 28:1371–1379, 1996; Garrido del Solo et al. in Int J Biochem Cell Biol 30:735–743, 1998; Varon et al. in J Mol Catal 59:97–118, 1990). In order to circumvent such difficulties Arribas et al. (J Math Chem 44:379–404, 2008) proposed an evaluation method which is applicable regardless of the complexity of the kinetic equation. This procedure is based on the numerical determination of statistical moments from experimental time progress curves. The fitting of these experimentally obtained moments to the corresponding theoretical symbolic expressions allows, in most cases, all the individual rate constants involved to be evaluated. In this paper we perform a general analysis that can be applied to any unstable enzyme system described by a three-exponential equation and apply it to a substrates induced enzyme inactivation process that is described by this type of equation. To verify the goodness of the method we have simulated time progress curves and applied the suggested procedure to these curves, obtaining kinetic parameters values very close to those used to obtain simulated curves. Finally, we compare our results with those obtained in previous contributions in which other procedures were used.


Three-exponential equations Statistical moments Enzyme Kinetics Simulated progress curves Numerical integration 


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • E. Arribas
    • 1
  • J. M. Villalba
    • 2
  • M. Garcia-Moreno
    • 3
  • M. L. Amo
    • 3
  • F. Garcia-Sevilla
    • 4
  • F. Garcia-Molina
    • 5
  • J. L. Muñoz-Muñoz
    • 5
  • R. Varon
    • 3
  1. 1.Applied Physics DepartmentUniversity of Castilla-La Mancha (UCLM)AlbaceteSpain
  2. 2.Medical Sciencie DepartmentUCLMAlbaceteSpain
  3. 3.Departamento de Quimica-Fisica, Escuela de Ingenieros Industriales de AlbaceteUCLMAlbaceteSpain
  4. 4.Departamento de Ingenieria Electronica, Electrica, Automatica y ComunicacionesUCLMAlbaceteSpain
  5. 5.Departamento Bioquimica y Biologia Molecular AUniversidad de MurciaMurciaSpain

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