Abstract
A general model of zymogen activation is proposed and explicit kinetic equations for the time courses of the various species and products involved are given. These equations are valid for the whole course of the reaction and therefore for both the transient phase and the steady state. This model is sufficiently general to include mechanisms possessing one or more steps of zymogen activation besides possible steps of inhibition (reversible or irreversible) or inactivation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature
Christensen, U. 1977. Kinetic studies of the urokinase-catalysed conversion of NH2-terminal lysine plasminogen to plasmin.Biochim. Biophys. Acta 481, 638–647.
Chock, P. B. and E. R. Stadtman. 1977. Superiority of interconvertible enzyme cascades in metabolic regulation: Analysis of multicyclic systems.Proc. natn. Acad. Sci. U.S.A. 74, 2766–2770.
Chock, P. B. and E. R. Stadtman. 1980. Covalently interconvertible enzyme cascade systems. InMethods in Enzymology, Vol. 64, pp. 297–325. London: Academic Press.
Darvey, I. G. 1977. Transient phase kinetics of enzyme reactions where more than one species of enzyme is present at the start of the reaction.J. theor. Biol. 65, 465–478.
Davie, E. W. and K. Fujikawa. 1975. Basic mechanisms in blood coagulation.Ann. Rev. Biochem. 44, 798–829.
Galindo, J. D., R. Peñafiel, R. Varón, E. Pedreño, F. García Carmona and F. García Cánovas. 1983. Kinetic study of the activation process of frog epidermis protyrosinase by trypsin.Int. J. Biochem. 15, 633–637.
Gálvez, J. and R. Varón. 1981. Transient phase kinetics of enzyme reactions.J. theor. Biol. 19, 1–17.
Garrido del Solo, C., R. Varón and F. García-Cánovas. Programa de ordenador para simular el comportamiento cinético de las reacciones enzimáticas.An. Quim., submitted.
Gerald, C. F. 1989.Applied Numerical Analysis, 4th edn, pp. 367–373. Reading, Massachusetts: Addison-Wesley.
Hadorn, B. 1974. Pancreatic proteinases.Med. Clin. N. Am. 58, 1319–1331.
Havsteen, B. and R. Varón. 1990. Kinetics of the classical complement activation cascade.J. theor. Biol. 145, 47–64.
Holzer, H. and P. C. Heinrich. 1980. Control of proteolysis.Ann. Rev. Biochem. 49, 63–91.
Löffler, G. and P. E. Petrides. 1988.Physiologische Chemie, pp. 832–843. Berlin: Springer.
Mann, K. G., R. J. Jenny and S. Krishnaswamy. 1988. Cofactor proteins in the assembly and expression of blood clotting enzyme complexes.Ann. Rev. Biochem. 57, 915–956.
Mihalyi, E. 1972.Application of Proteolytic Enzymes to Protein Structure Studies. CRC Press, Cleveland: CRC Press.
Müller-Eberhard, H. J. 1988. Molecular organization and function of the complement system.Ann. Rev. Biochem. 57, 321–347.
Neurath, H. and K. A. Walsh. 1976.Proteolysis and Physiological Regulation. E. W. Ribbous and K. Brew (eds), pp 29–40. New York: Academic Press.
Rånby, M. 1982. Studies on the kinetics of plasminogen activation by tissue plasminogen activator.Biochim. Biophys. Acta 704, 461–469.
Rhodes, C. J., A. Zumbrunn, E. M. Bailyes, E. Shaw and J. C. Hutton. 1989. The inhibition of proinsulin-processing endopeptidase activities by active-site-directed peptides.Biochem. J. 258, 305–308.
Shacter, E., P. B. Chock, S. G. Rhee and E. R. Stadtman. 1986.The Enzymes, Vol. XVII, pp. 21–42. London: Academic Press.
Segel, L. A. 1988. On the validity of the steady state assumption of enzyme kinetics.Bull. math. Biol. 50, 579–593.
Segel, L. A. and M. Slemrod. 1989. The quasi-steady-state assumption: a case study in perturbation.Sian Rev. 31, 446–477.
Stadtman, E. R. and P. B. Chock. 1977. Superiority of interconvertible enzyme cascades in metabolic regulation: analysis of monocyclic systems.Proc. natn. Acad. Sci. U.S.A. 74, 2761–2765.
Varón, R. and B. Havsteen. 1990 Kinetics of the transient-phase and steady-state of the monocyclic enzyme cascades.J. theor. Biol. 14, 397–413.
Varón, R., A. Román, F. Garvía Cánovas and F. García Carmona. 1986. Transient phase kinetics of the activation of human plasminogen.Bull. math. Biol. 48, 149–166.
Varón, R., F. García Cánovas, F. García Carmona, J. Tudela, M. García, A. Vázquez and E. Valero. 1987. Kinetics of a general model for enzyme activation through a limited proteolysis.Math. Biosci. 87, 31–45.
Varón, R., F. García Cánovas, F. García Carmona, J. Tudela, A. Román and A. Vázquez. 1988. Kinetics of a model for zymogen activation: the case of high activating enzyme concentrations.J. theor. Biol. 132, 51–59.
Varón, R., B. Havsteen, M. García-Moreno, F. García-Cánovas and J. Tudela. 1990. Computer program for the expression of the kinetic equations of enzyme reactions as functions of the rate constants and the initial concentrations.Biochem. J. 270, 825–828.
Wohl, R. C., L. Summaria and K. C. Robbins. 1980. Kinetic of activation of human plasminogen by different activator species at pH 7.4 and 37°C.J. biol. Chem. 255, 2005–2013.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Havsteen, B.H., Garcia-Moreno, M., Valero, E. et al. The kinetics of enzyme systems involving activation of zymogens. Bltn Mathcal Biology 55, 561–583 (1993). https://doi.org/10.1007/BF02460651
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02460651