Determination of Enzyme Kinetic Constants for Electrochemically Mediated Enzyme Reactions. Application to the Diaphorase-Nicotinamide Adenine Dinucleotide System with p-Methylaminophenolsulfate as an Electron Carrier Riccarda Antiochia, Irma Lavagnini, and Franco Magno* Dipartimento di Chimica Inorganica, Metallorganica ed Analitica, Universita Á di Padova, Via Marzolo 1, I-35131 Padova, Italy e-mail: Magno@chim02.chin.unipd.it Received: June 26, 2000 Final version: September 18, 2000 Abstract Cyclic voltammetry was successfully applied to the study of the kinetics of the nicotinamide adenine dinucleotide (NADH)/diaphorase (DI)/ p-methylamino-phenolsulfate (MAP) electrochemically mediated enzyme reaction. The voltammetric curves relative to the oxidation of MAP coupled with the enzymatic reaction were simulated by the DigiSim package without any simplifying assumption. The comparison between experimental and calculated curves allowed the determination of the rate constants involved in the various steps. In particular a value of 1.1610 5 M 1 s 1 for the bimolecular rate constant for the reaction between enzyme and mediator and a value of 10M 1 s 1 for the parallel competitive reaction between NADH and mediator were obtained. Other methods reported in the literature for studying the kinetics of enzymatic reactions were employed and the results were in perfect agreement with those obtained with the method based on digital simulation. A critical comparison of the merits of the different approaches is also reported. Keywords: NADH, p-Methylaminophenolsulfate, Diaphorase, Electrocatalysis, Digital simulation 1. Introduction A primary requirement for the proposal and the optimal performance of amperometric redox enzyme electrodes is the understanding of the mechanism of the overall electrochemical reaction and the knowledge of the physicochemical parameters which determine the voltammetric responses. For these reasons electroanalytical techniques, in particular cyclic voltammetry, have been widely applied to the study of electrochemically mediated enzyme reactions and suitable data processing methods have been developed. Referring to the following reaction scheme M red  M ox  2e  M ox  E red ! M red  E ox E ox  S ! E red  P where M red and M ox are the reduced and oxidized form of a two- electron mediator, respectively, E red and E ox the reduced and oxidized form of the enzyme and S is the substrate, the most usual strategy is to assume a steady-state approximation both for the redox enzyme and the redox mediator with a concomitant pseudo-®rst order condition for the catalytically limited regen- eration of the latter. These assumptions lead to sigmoidal vol- tammetric curves independent from the scan rate [1, 2] and to the steady-state catalytic limiting current given by I lim  nFAD M k E 1=2 M * 1 where [M]* is the total concentration of the mediator, [E] is the total enzyme concentration, k is the rate constant of the limiting bimolecular reaction between M ox and E red and the other terms have their usual meaning. Under these simplifying conditions two approaches to evaluate the kinetics have been proposed: ± the determination of the rate constant k from the slope of the plot of the steady-state catalytic current I lim versus the mediator concentration or versus the square root of the enzyme concentration [3, 4]; ± the use of the ratio of the kinetic peak current to the diffusion- controlled peak current obtained in the absence of enzyme, at constant mediator and enzyme concentration but at different scan rates [5]. In the former case a linear regression analysis gives the rate constant k value while in the latter the use of the working curve reported in [2] for ®rst order catalytic reactions is adopted. However, two drawbacks are inherent in these methods: ± a large substrate concentration is not enough to assure a pseudo-®rst order condition since only a suitable combination of kinetic constants and of concentrations of the mediator and the substrate allows the validity of the approximation [6]; ± an overall kinetic constant is determined for the enzymatic reaction, overlooking the single steps in the homogeneous electron transfer reaction. An extension is given by Kano et al. [7] who proposed a more general but empirical equation for the limiting current (see Eq. 4 in [7]) which is valid in a wide mediator concentration range and reduces to Equation 1 at very low mediator concentrations. A signi®cant improvement in the rationalization of the reaction mechanisms studied is the use of the digital simulation technique. An approach has been proposed where the differential equation for the diffusive mass-transfer is coupled to Michaelis-Menten kinetic expressions relative to two-substrate enzyme reactions to represent the so called ping-pong mechanism [6, 8]. This procedure condenses in the Michaelis-Menten notation, several ®rst and second order steps of the enzyme reaction and results very effective in various conditions. The evaluation of the kinetic constant is obtained by the use of appropriate working curves 582 Electroanalysis 2001, 13, No. 7 # WILEY-VCH Verlag GmbH, D-69469 Weinheim, 2001 1040-0397/01/0705±0582 $17.50.50=0