Applied Biochemistry and Biotechnology

, Volume 14, Issue 1, pp 49–72 | Cite as

Mixed Enzymic Reaction—Internal Diffusion Kinetics of Nonuniformly Distributed Immobilized Enzymes

The System Agarose-Micrococcal Endonuclease
  • J. M. Guisan
  • J. Serrano
  • F. V. Melo
  • A. Ballesteros
Original Article


Two types of (CNBr-activated) Agarose-staphylococcal endonuclease derivatives have been prepared, one with the enzyme uniformly distributed in the support, and the other with the enzyme preferentially bound in the most external part of the support particles; the latter were obtained using agarose of very small pores and a high degree of activation. Quantitative enzyme distribution has been determined by scanning fluorescence microscopy. With these insoluble enzyme derivatives, a kinetic study for the hydrolysis of a mononucleotide has been carried out. A simple theoretical model for nonuniformly distributed insoluble enzyme derivatives, which considers only the case of mixed enzymic reaction-internal diffusion kinetics, is proposed. The experimental data agree very well with the predictions of the model.

Index entries

CNBr-activated agarose staphylococcal nuclease heterogeneously distributed insolubilized enzymes, preparation of inhomogeneously distributed insolubilized enzymes, preparation of insolubilized enzymes, preparation of inhomogeneously distributed fluorescence, determination of enzyme distribution by 



Specific surface area (m2/cm3)


Effective diffusion coefficiente of substrate (cm2/s)


Average pore diameter (nm)


Amount of enzyme insolublized per unit volume of derivative: average concentration corresponding to a uniform distribution (μM)


Enzyme concentration inside the derivative at a distancer from the center of the particle (μM)


Enzyme concentration at an adimensional distance ρ from the center of the particle (μM)


E(ρ)/E M Adimensional enzyme distribution function in the derivative


Intrinsic catalytic constant for the insolubilized enzyme (min-1)


Intrinsic Michaelis constant for the insolubilized enzyme (μM)


Distance from the center of the particle (μm)


Particle radius (μm)


Substrate concentration in bulk solution (μM)


Substrate concentration inide the derivative at a distance r from the center of the particle (μM)


Actual reaction rate per unit volume in an insolubilized derivative (μM/min)


S(r)/S 0


K m/S0


R(k catE/K mDeff)1/ 22. General formulation of Thiele modulus in mixed enzymic reaction-internal diffusion kinetics


R(k cat · EM/K mDeff) 21/2. Thiele modulus corresponding to an insolubilized derivative in which the enzyme is homogenously distributed


R(k cat · E(ρ)/KDeff)sO58u21/2


ϕm(1-ρ3 C)-1/2. Thiele modulus corresponding to a distribution of enzyme in a spherical segment


of a heterogeneously distributed derivative is the Thiele modulus corresponding to an uniformly distributed derivative, which has the same kinetic behavior


Effectiveness factor


Effectiveness factors corresponding to the limiting cases of first and zero order for enzymic kinetics


r/R Adimensional distance from center of particle

ρc= ρsh

Adimensional distance for which there is no enzyme, in a particle of shell-type nonuniform derivative


Adimensional distance for which there is no enzyme, in a linearly distributed derivative


ρc equivalent of nonuniformly insolubilized enzyme, whatever be the type of distribution


ρeq obtained from the fitting of experimental kinetic data to the theoretical model


ρc obtained from scanning fluorescence microscopy┐


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  1. 1.
    Bordiert, A., and Buchholz, K. (1979),Bioteclmol. Lett. 1, 15.CrossRefGoogle Scholar
  2. 2.
    Buchholz, K. (1979),Bioteclmol. Lett. 1, 451.CrossRefGoogle Scholar
  3. 3.
    Guisán, J. M., Fernández, V. M, and Ballesteros, A. (1980), Distribution of Staphylococcal Nuclease Insolubilized on Sepharose, inEnzyme Engineering, vol. 5, Weetall, H. H., and Royer, G. P., eds., Plenum, New York, NY, pp. 435–438.Google Scholar
  4. 4.
    Buchholz, K., Borchert, A., and Duggal, S. K. (1980), Adsorption of Enzymes in Carriers, inEnzyme Engineering, vol. 5, Weetall, H. H., and Royer, G. P., eds., Plenum, New York, NY, pp. 465–468.Google Scholar
  5. 5.
    Park, S. H., Lee, S. B., and Ryu, D. D. Y. (1981),Bioteclmol. Bioeng. 23, 2591.CrossRefGoogle Scholar
  6. 6.
    Juang, H.-D., and Weng, H.-S. (1984)Bioteclmol. Bioeng. 26, 623.CrossRefGoogle Scholar
  7. 7.
    Borchert, A., and Buchholz, K. (1984)Bioteclmol. Bioeng. 26, 727.CrossRefGoogle Scholar
  8. 8.
    Kohn, J., and Wilchek, M. (1981),Anal. Biochem. 115, 375.CrossRefGoogle Scholar
  9. 9.
    Guisán, J. M, Melo, F. V. and Ballesteros, A. (1981),Appl. Biochem. Biotechnol. 6, 37.CrossRefGoogle Scholar
  10. 10.
    Franks, R. G. E. (1972),Modeling and Simulation in Chemical Engineering, John Wiley and Sons, New York, NY.Google Scholar
  11. 11.
    Aris, R. (1971),Mathematica Theory of Diffusion and Reaction in Permeable Catalysts, vol. 1, Clarendon, Oxford.Google Scholar
  12. 12.
    Wheeler, A. (1951),Adv. Catal. 3, 249.Google Scholar
  13. 13.
    Weekman, V. W., and Gorring, R. L. (1965),J. Catalysis 4, 260–270. vol. 44, Mosbach, K., ed. Academic, New York, NY, pp. 19–45.Google Scholar
  14. 14.
    Porath, J., and Axén, R. (1976), Immobilization of Enzymes to Agar, Agarose and Sephadex Supports, inMethods in Enzymology.Google Scholar
  15. 15.
    Porath, J., Aspberg, K., Drevin, H., and Axén, R. J. (1973),J. Chromatog. 86, 53.CrossRefGoogle Scholar
  16. 16.
    Serrano, J. (1981),Ph. D. Thesis, Autonomous University of Madrid, Spain.Google Scholar
  17. 17.
    Anfinsen, C. B., Cuatrecasas, P., and Taniuchi, H. (1971), Staphylococcal Nuclease, Chemical Properties and Catalysis, inThe Enzymes, vol. 4, Boyer, P. D., ed., Academic, New York, NY, pp. 177–204.Google Scholar
  18. 18.
    Guisán, J. M., and Ballesteros, A. (1979),J. Solid Phase Biochem. 4, 245.CrossRefGoogle Scholar
  19. 19.
    Cuatrecasas, P., Wilchek, M., and Anfinsen, C. B. (1969),Biochemistry 8, 2277.CrossRefGoogle Scholar
  20. 20.
    Lash, J., Iwig, M., and Koelsch, R. (1971),Em: J. Biochem. 27, 431.CrossRefGoogle Scholar
  21. 21.
    Ballesteros, A., Guisán, J.M., and Serrano, J. (1982), Influence of the Activation Degree of the Support on the Properties of Agarose-Nuclease, inEnzyme Engineering, vol. 6, Chibata, I., Fukui, A., and Wingard, L. B., Jr., eds., Plenum, New York, NY, pp. 223–224.3, 313.Google Scholar

Copyright information

© The Humana Press Inc 1987

Authors and Affiliations

  • J. M. Guisan
    • 1
  • J. Serrano
    • 1
  • F. V. Melo
    • 1
  • A. Ballesteros
    • 1
  1. 1.Instituto de Catálisis, CSICMadridSpain

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