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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

Abstract

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 

Nomenclature

asp

Specific surface area (m2/cm3)

Deff

Effective diffusion coefficiente of substrate (cm2/s)

dp

Average pore diameter (nm)

EM

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

E(r)

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

E(ρ)

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

f(ρ)

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

kcat

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

K

Intrinsic Michaelis constant for the insolubilized enzyme (μM)

r

Distance from the center of the particle (μm)

R

Particle radius (μm)

S0

Substrate concentration in bulk solution (μM)

S(r)

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

v

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

Υ

S(r)/S 0

ρ

K m/S0

ϕ

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

ϕM

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

ϕ(ρ)

R(k cat · E(ρ)/KDeff)sO58u21/2

ϕsh

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

ϕapp

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

η

Effectiveness factor

η1η0

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

ρ

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

ρc

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

ρeq

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

ρcq(kin)

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

ρeq(flu)

ρc obtained from scanning fluorescence microscopy┐

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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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