Kinetic Analysis of Wired Enzyme Electrodes. Application to Horseradish Peroxidase Entrapped in a Redox Polymer Matrix Juan Jose Calvente,* ,† Ara ´ ntzazu Narva ´ ez, ‡ Elena Domı ´nguez, ‡ and Rafael Andreu* ,† Departamento de Quı ´mica Fı ´sica, Facultad de Quı ´mica, UniVersidad de SeVilla, 41012-SeVilla, Spain, and Departamento de Quı ´mica Analı ´tica, Facultad de Farmacia, UniVersidad de Alcala ´ , 28871-Alcala ´ de Henares, Madrid, Spain ReceiVed: January 8, 2003 A new approach to the description of the steady-state voltammetric behavior of wired enzyme electrodes in the presence of substrate mass transport polarization is presented. Starting from the exact analytical solutions corresponding to two-dimensional mediator-enzyme structures, experimental conditions are identified where the same equations can be applied to the analysis of the more often encountered three-dimensional catalytic films. These conditions are shown to involve a uniform redox conversion throughout the film. Case diagrams have been developed to assess the validity of this approach and to ascertain the influence of mass transport polarization and electron hopping on the voltammetric response. The relevance of the catalytic half-wave potential, as a direct measure of the ratio of the rates of redox mediation and enzyme turnover, is stressed. The kinetic analysis is applied to the electrocatalytic behavior of taurine-modified horseradish peroxidase, entrapped within a polyvinyl pyridine polymer containing osmium redox centers. This integrated electrochemical system is shown to be characterized by an efficient electronic connection between the catalytic and mediator centers, easy permeation of the substrate through the film, and a low value of the enzyme-substrate Michaelis constant. A sensitivity 20% higher than the maximum value previously reported in the literature for polymer- based peroxidase electrodes is obtained, and it appears to be related to a stronger electrostatic interaction between the negatively charged taurine modified HRP and the positively charged redox polymer. A comparison with kinetic parameters obtained in homogeneous solution (J. Am. Chem. Soc. 2002, 124, 240) suggests that further improvement of this electrode configuration would require a higher fraction of the immobilized enzymes to be effectively connected to the redox network. Introduction Enzyme electrodes have attracted considerable attention be- cause of their ability to transduce a chemical event into an easy- to-use electrical signal. 1 Their strength relies on the high spe- cificity of enzymes for recognizing target molecules and on an efficient renewal of the enzyme active form by means of an electrochemically driven redox reaction. Thus, the catalytic cur- rent measured in the presence of substrate can be used either to estimate the amount of a particular analyte or to gain new insights into the catalytic mechanism. It is well-known that enzymatic redox sites are embedded into a protein matrix, making electron transfer rates prohibitively slow in most orientations. Nevertheless, direct electron transfer between electrodes and enzymes has been reported for small redox proteins, of 2 × 10 4 Da or less, with effective hydrody- namic radii of ∼21 Å. 1b,2 In search of an adequate electronic communication, strategic immobilization can provide the means to orientate the enzyme conveniently, thereby, achieving direct electron transfer through a selective pathway. Irrespective of the success of this approach, direct electron-transfer rates often remain low in comparison to turnover rates of the enzymes, 3 thereby, deteriorating the overall performance of the enzyme electrode. Alternatively, mediated electron transfer, coupled to either diffusing or immobilized redox couples, can provide fast and efficient transduction schemes, though the presence of diffusing components should be avoided in those cases where a reagent- less configuration is required. Several strategies have been developed to build fast electronic links between enzymes and electrodes. They include three basic approaches: (i) the tethering of redox relay groups to the protein providing a pathway for electron hopping, 4 (ii) the specific attachment of redox species to the electrode surface, most commonly by self-assembled heterofunctional monolayers, 5 and (iii) the deposition of bio- electrocatalytic films with either redox 6 or conducting 7 polymers, enabling electron exchange with the protein active center. Irrespective of the electrode configuration, optimization of the biosensor performance requires a separate analysis of each bioelectrocatalytic step, including substrate reaction at the active enzyme site, electron transfer between enzyme and electrode, and substrate mass transport from the solution. An adequate modeling of the electrochemical behavior of these steps opens up the possibility to characterize the different processes that determine the sensor response, thus facilitating its rational design. In this context, Smyth et al. 8 have used the ratio between the turnover number and the Michaelis constant to assess the efficiency of organic phase enzyme electrodes. The boundary value problem associated with electrochemically driven cata- lyzed reactions is complex, because of the interplay of mass transport, charge propagation across the film, and nonlinear Michaelis-Menten kinetics. 9 In general, analytical solutions are not attainable, and two approaches have been adopted to cope with this problem: digital simulation and approximate analytical solutions for a number of limiting cases. 10 Numerical solutions of the relevant diffusion-reaction equa- tions have been reported by using different versions of the finite * To whom correspondence should be addressed. Phone: +34- 954557177. Fax: +34-954557174. E-mail: fonda. pacheco@us.es. † Universidad de Sevilla. ‡ Universidad de Alcala ´. 6629 J. Phys. Chem. B 2003, 107, 6629-6643 10.1021/jp030011p CCC: $25.00 © 2003 American Chemical Society Published on Web 06/12/2003