An enzyme rate equation for the overall rate of reaction of gel-immobilized glucose oxidase particles under buffered conditions. I. Pseudo-one substrate conditions

Modelling the Current Response and Sensitivity of Oxidase Enzyme Electrodes, Monitored Amperometrically by the Consumption of Oxygen

Biosensor behaviour is characterised by non-linear differential equations that describe well-defined physical, chemical, and biological processes. Mathematical modelling of these biosensors is highly desirable since they have many applications. These models enable the prediction of a variety of their properties. In this study, the cyclic conversion of the substrate in an amperometric biosensor with an oxidase enzyme membrane electrode is studied using a mathematical model. The governing parameters for the Michaelis–Menten kinetics of enzymatic reactions are the enzyme kinetic and diffusion rates across the enzymatic layer. In this paper, we solved the non-linear equations analytically and numerically for all experimental values of parameters. This problem is simulated in MATLAB® v2016b software using the PDE solver. Our analytical solutions are compared to simulation results to validate the proposed model.

Determination of the intrinsic kinetic constants of immobilized glucose oxidase and catalase

Models of membrane systems containing immobilized glucose oxidase and catalase operating together or independently have been developed. A rotated disk electrode apparatus was employed with novel electrochemical operating conditions to experimentally determine mass transfer and intrinsic kinetic parameters of enzyme-containing membranes. The value of a mass transfer parameter that describes internal and external diffusion was first determined under conditions that do not permit the enzyme reactions. In a subsequent experiment with the reaction allowed, kinetic parameters corresponding to the intrinsic maximal velocity and Michaelis constants of the immobilized enzymes were estimated by regression analysis of data based on an appropriate two- or three- parameter model. It was found that immobilization reduced the maximal intrinsic velocity but had no detectable effect on the Michaelis constants. In all but one case- these methods for membrane characterization are nondestructive and can be used repeatedly on a given membrane. These techniques provide the means for quantitative comparisons of immobilization methods and make possible temporal studies of immobilized enzyme inactivation.

Investigations of Reaction Kinetics for Immobilized Enzymes-Identification of Parameters in the Presence of Diffusion Limitation

A method is proposed for identification of kinetic parameters when diffusion of substrates is limiting in reactions catalyzed by immobilized enzymes. This method overcomes conventional sequential procedures, which assume immobilization does not affect the conformation of the enzyme and, thus, consider intrinsic and inherent kinetics to be the same. The coupled equations describing intraparticle mass transport are solved simultaneously using numerical methods and are used for direct estimation of kinetic parameters by fitting modeling results to time-course measurements in a stirred tank reactor. While most traditional procedures were based on Michaelis-Menten kinetics, the method presented here is applicable to more complex kinetic mechanisms involving multiple state variables, such as ping-pong bi-bi. The method is applied to the kinetic resolution of (R/S)-1-methoxy-2-propanol with vinyl acetate catalyzed by Candida antarctica lipase B. A mathematical model is developed consisting of irreversible ping-pong bi-bi kinetics, including competitive inhibition of both enantiomers. The kinetic model, which fits to experimental data over a wide range of both substrates (5-95%) and temperatures (5-56 degrees C), is used for simulations to study typical behavior of immobilized enzyme systems.

Immobilized glucose oxidase--catalase and their deactivation in a differential-bed loop reactor

Glucose oxidase containing catalase was immobilized with a copolymer of phenylenediamine and glutaraldehyde on pumice and titania carrier to study the enzymatic oxidation of glucose in a differential-bed loop reactor. The reaction rate was found to be first order with respect to the concentration of limiting oxygen substrate, suggesting a strong external mass-transfer resistance for all the flow rates used. The partial pressure of oxygen was varied from 21.3 up to 202.6 kPa. The use of a differential-bed loop reactor for the determination of the active enzyme concentration in the catalyst with negligible internal pore diffusion resistance is shown. Catalyst deactivation was studied, especially with respect to the presence of catalase. It is believed that the hydrogen peroxide formed in the oxidation reaction deactivates catalase first; if an excess of catalase is present, the deactivation of glucose oxidase remains small. The mathematical model subsequently developed adequately describes the experimental results.

Characteristics of unbuffered gel-immobilized urease particles. I. Internal pH

The overall rate of reaction of a gel-immobilized urease particle necessarily depends upon the hydrogen ion concentrations within the particle. When the particle is unbuffered, the internal hydrogen ion concentrations are a consequence of the local rates of reaction and the rate of egress of the products of hydrolysis. A simple apparatus has been devised which allows a fairly rapid determination of the hydrogen ion concentration in the center of a particle for any given size, enzyme concentration, substrate concentration, and external pH. The products of urea hydrolysis are self-buffering in the region of pH 8.83 and for an external pH less than the self-buffering pH, the pH within the particle is increased because of the reaction. When the external pH is greater than the self-buffering pH, the converse occurs. The pH at the center of the particle approaches the self-buffering pH with an increase in particle size and enzyme concentration. The external increase in the external substrate concentration has a limited effect, simply rendering the local rates of reaction to be of zero order. The center-line pH and therefore all internal hydrogen ion concentrations depend upon the parameter L square root pe and the external pH. Differences between the external and center-line pH values of the order of units are unexceptional. The implications of the internal pH profiles on the local and overall rates of reaction are explored.

An immobilized two-enzyme system for the activation of the lactoperoxidase antibacterial system in milk

Lactoperoxidase catalyzes the oxidation of thiocyanate by hydrogen peroxide and an intermediary product is formed with antibacterial properties. The components of this system, with the exception of hydrogen peroxide, are present in milk. H2O2 may be introduced by means of enzymatic generation and thus make the system complete. A two-enzyme system consisting of beta-galactosidase and glucose oxidase has been developed for this purpose. The coupled enzyme reaction is shown to work with high efficiency at the neutral pH of milk although the enzymes as such, particularly lactases suitable for immobilization, have optimal activities at much lower pH values. The results indicate that the lactoperoxidase system may in this way be employed to inactivate bacteria present in milk.