Effect of diffusional limitations on lineweaver‐burk plots for immobilized enzymes

Abstract

EnzymesLineweaver-Burk plats of reaction rate data obtained with immobilized enzymes need not be liqear even when intrinsic enzyme kinetics follow the simple Michaelis-Menten rate expression. Theoretical calculations show that mass transfer effects mqy cause curvature which is concave or convex to the abscissa, depending upon experimental conditions. Consequently, graphical procedures commonly employed for analysis of soluble enzyme kinetics may yield misleading regults when applied to immobilized enzymes. Three approaches which follow from the behavior of numerical and asymptotic solutions to the problem are proposed for extraction of intrinsic kinetic information. Practical application of enzymatic catalysis often requires that enzymes be immobilized, thereby permitting recovery and continuops use. It is important that the kinetics of immobilized enzymes be well understood to facilitate their economic utilization. In particular, it is necessary to account for the effect of diffusional limitations and to develop procedures which permit extraction of intrinsic kinetic parameters from observed reaction rates. BRUCENative enzymes in sdution typically follow hyperbolic Michaelis-Menten kinetics, Equation (l), which are formally analogous to Langmuir-Hinshelwood kinetics in heterogeneous catalysis. Graphical analysis of kinetic data is commonly carried out on transformed coordinates such as a Lineweaver-Burk plot of reciprocal reaction rate versus reciprocal substrate concentration. This serves to linearize the data so that the maximum reaction rate and the Michaelis constant qan be evaluated directly from the intercept and slope. The same approach is often used with immobilized enzymes, but little attention has been paid to the precise physical meaning of the parameters so determined. Nonlinear Lineweaver-Burk plots have been reported in several experimental studies with enzymes immobilized in porous supports (Lilly and Sharp, 1968;Kay and Lilly, 1970;Bunting and Laidler, 1972); in all cases, the enzymes in solution gave Michaelis-Menten kinetics. It is unclear whether the curvature observed with immobilized enzymes stems from diffusional limitations, from changes in intrinsic enzyme kinetics after immobilization, or from other factors.In this paper we examine through theoretical analysis the effect of diffusional limitations on the observed kinetics of immobilized enzymes. Of particular interest i s the behavior of Lineweaver-Burk plots and the extraction of intrinsic kinetic parameters when diffusional effects are large. The problem considered is substrate diffusion in a homogeneous porous support in the form of a one-dimensional slab or membrane in which an enzyme that catalyzes a reaction following irreversible Michaelis-Menten kinetics is uniformly immobilized. Both internal and external diflusional resistances are considered, and emphasis is placed upon the asymptotic solution which is valid when diffusional effects are important and the modified Thiele modulus is large. CONCLUSIONS A N D SIGN IF ICANCELinewea...

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Diffusional limitations of anaerobic biofilms

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