Derivation of nonsteady-state analytical solution for surface enzyme kinetics

Kinetics of enzyme action on surface-attached substrates: a practical guide to progress curve analysis in any kinetic situation

In the present work, exact kinetic equations describing the action of an enzyme in solution on a substrate attached to a surface have been derived in the framework of the Michaelis-Menten mechanism but without resorting to the often-used steady-state approximation. The here-derived kinetic equations are cast in a workable format, allowing us to introduce a simple and universal procedure for the quantitative analysis of enzyme surface kinetics that is valid for any kinetic situation. The results presented here should allow experimentalists studying the kinetics of enzyme action on immobilized substrates to analyze their data in a perfectly rigorous way.

Optimizing electrode-attached redox-peptide systems for kinetic characterization of protease action on immobilized substrates. Observation of dissimilar behavior of trypsin and thrombin enzymes

In this work, we experimentally address the issue of optimizing gold electrode attached ferrocene (Fc)-peptide systems for kinetic measurements of protease action. Considering human α-thrombin and bovine trypsin as proteases of interest, we show that the recurring problem of incomplete cleavage of the peptide layer by these enzymes can be solved by using ultraflat template-stripped gold, instead of polished polycrystalline gold, as the Fc-peptide bearing electrode material. We describe how these fragile surfaces can be mounted in a rotating disk configuration so that enzyme mass transfer no longer limits the overall measured cleavage kinetics. Finally, we demonstrate that, once the system has been optimized, in situ real-time cyclic voltammetry monitoring of the protease action can yield high-quality kinetic data, showing no sign of interfering effects. The cleavage progress curves then closely match the Langmuirian variation expected for a kinetically controlled surface process. Global fit of the progress curves yield accurate values of the peptide cleavage rate for both trypsin and thrombin. It is shown that, whereas trypsin action on the surface-attached peptide closely follows Michaelis-Menten kinetics, thrombin displays a specific and unexpected behavior characterized by a nearly enzyme-concentration-independent cleavage rate in the subnanomolar enzyme concentration range. The reason for this behavior has still to be clarified, but its occurrence may limit the sensitivity of thrombin sensors based on Fc-peptide layers.

The computational modelling of the kinetics of ascorbic acid palmitate hydrolysis by lipase considering diffusion

This paper presents mathematical and computational modelling of kinetics of a bioelectroanalytical system based on the interfacial action of hydrolytic enzyme. A system of non-linear differential equations with diffusion is used to describe the kinetics of Termomyces lanuginosa lipase (TLL) catalyzed hydrolysis of L-ascorbic acid palmitate (AAP). The system was solved numerically, and the kinetic prameters of AAP hydrolysis by the enzyme were determined. The experimental and modelling results show linear dependence of the rate of AAP hydrolysis on the TLL concentration. Complex dependence of the initial rate of bioelectrocatalytic current increase on the thickness of total diffusion layer (hydrodynamic diffusion layer plus thickness of dialysis membrane on the electrode surface) is also demonstrated and explained.