Multilayer Enzyme Electrodes

Compared with the derivations described so far, models with more than one layer require mathematically completely different approaches. The respective systems of differential equations either have to be solved numerically (Smith, 1965 Lasia, 1983 Bergel and Comtat, 1984) or a new approach must be found. The mathematical problem is that the boundary conditions are not known for each layer. For the interfaces between the different membranes only mass conservation relations are known rather than boundary values and no-flux conditions. They may be written  

Di and Z),-+1 are the diffusion coefficients of the substrate under consideration, H, in the layer i and i + 1, respectively. Each of the l layers is modeled separately, the layer thickness being d, 0 = 1,. .., 1). The equations of mass conservation are considered for fixed times, tj (J - 1, 2.). Then the basic idea of the multilayer approach may be described 

When the values so obtained are inserted into the mass conservation equations, a system of linear equations with respect to the desired parameters is obtained. The solution of this system is therefore the calculation of the concentration profile for the time considered, t i. Since for this calculation the values of the concentration profile at t must be known, a successive calculation from one concentration profile to the other is necessary. Since, furthermore, the use of linear boundary and initial conditions is only an approximation, calculation has to be performed in small steps with respect to both time and space. In other words, if a sufficient refinement of the layer arrangement is chosen (by partition of the given layers) and the time steps are sufficiently small, successive calculation of concentration profiles is possible with high accuracy. This algorithm has been published and illustrated by case studies (Schulmeister, 1987a). An example is given in Fig. 37. 

The linear approach described here is expandable to multienzyme electrodes as well as multilayer electrodes. At least for the stationary case, multilayer models of bienzyme electrodes may be easily treated, too. The whole system is readily adaptable to potentiometric electrodes (Carr and Bowers, 1980). It must be noted, however, that the superiority over purely numerical solution procedures decreases with increasing number of enzyme species and in the multilayer model. The advantage in calculation speed using the sum formulas described (e.g., in Section 2.5.2) amounts to about two orders of magnitude. With multilayer electrodes and formulas containing double and triple sums it is reduced to one order of magnitude. 

In many cases the application of linear models is not possible, namely if  

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FIGURE 5.28. Antigen-antibody construction of a multilayered enzyme electrode (see the text). Adapted from Figure 2 of reference 26b, with permission from the American Chemical... 

Monolayer- or Multilayer-enzyme Electrodes Activated by DifTusional Mediators... 

Bourdillon, C., Demaille, C., Moiroux, J., Saveant, J.M. Step-by-Step immunological constmction of a fully active multilayer enzyme electrode. J. Am. Chem. Soc. 116, 10328-10329 (1994)... 

Equations 2.26 and 2.27 carmot be solved analytically except for a series of limiting cases considered by Bartlett and Pratt [147,192]. Since fine control of film thickness and organization can be achieved with LbL self-assembled enzyme polyelectrolyte multilayers, these different cases of the kinetic case-diagram for amperometric enzyme electrodes could be tested [147]. For the enzyme multilayer with entrapped mediator in the mediator-limited kinetics (enzyme-mediator reaction rate-determining step), two kinetic cases deserve consideration in this system in both cases I and II, there is no substrate dependence since the kinetics are mediator limited and the current is potential dependent, since the mediator concentration is potential dependent. Since diffusion is fast as compared to enzyme kinetics, mediator and substrate are both approximately at their bulk concentrations throughout the film in case I. The current is first order in both mediator and enzyme concentration and k, the enzyme reoxidation rate. It increases linearly with film thickness since there is no... 

Despite the simplicity of DET, current densities are usually limited as only monolayer coverage is possible and enzymes may be electrically insulated due to incorrect orientation on the electrode surface. The simplest way to overcome these limitations is to immobilize the enzyme within a polymeric mediator matrix on the electrode surface. This enables multilayer enzyme coverages and, if the mediator can access the enzyme active site, the orientation of enzyme becomes irrelevant. 

Shoham, B. Migron, Y. Riklin, A. Willner, I. Tartakovsky, B. A bilirubin biosensor based on a multilayer network enzyme electrode. 

Biosensors based on biorecognition events occurring in monolayer or thin-fihn assemblies on electronic transducers represent an important recent advance in bioelectronics [15]. The nano-architecture of the sensing interface in a mono-layer, multilayer, or thin-fihn structures precludes diffusion barriers, and hence the rapid response-times of the sensing devices are achieved. Enzyme-electrodes [16,17], immunosensors [18,19], or DNA sensors [13] were developed by tailoring nanoscale sensing interfaces on the transducer. We will specifically address the development of DNA sensors in monolayer and thin-film confignrations. 

Calvo EJ, Danilowicz CB, Wolosiuk A. Supramolecular multilayer stmctures of wired redox enzyme electrodes. Phys Chem Chem Phys 2005 7 1800-1806. 

Negatively charged species such as carboxylic acid group in acid-treated CNTs can attract positively charged enzymes from solution as long as the pH value of the enzyme solution is controlled to be lower than the iso-electric point of the enzyme thus, multilayer films of the enzyme can be formed by the layer-by-layer technique. For example, five layers of GOx can be immobilized on the electrode surface by alternatively dipping a poly(diallyldimethylammonium chloride (PDDA))-functionalized GC into a CNT solution and a GOx solution (pH 3.8). Figure 15.15 illustrates the preparation process for the formation of a multilayer film of GOx on the electrode. 

Still with an enzyme monolayer, the synthesis and current responses of a system that involves simultaneous attachment of the cosubstrate to the electrode coating are then described. The next step consists in constructing a multilayered coating constituted by successive layers of enzyme built thanks to antigen-antibody interactions. Sensing the diffusion of the cosubstrate through the film thus constructed provides evidence for spatial order and an estimate of the distances between layers. 

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