Diffusion control, enzyme electrodes

The advantages of diffusion-control enzyme electrodes over devices controlled by the enzymatic reaction (kinetic-control) are that the linearity is increased above the and the response is no longer dominated by the enzyme reaction. This implies that the enzyme electrode is less sensitive to pH and tern-... 

Increase of the load of enzyme of a highly active enzyme shifts the kinetically controlled enzyme electrode to diffusional limitation. Since diffusion-limiting effects are associated with the immobilization, they may be manipulated by the procedure of coupling an enzyme to the electrode. 

The capability of a diffusion-controlled enzyme membrane to completely convert the substrate permeating the membrane offers an interesting analytical application. In other words, interfering substances are converted into non-disturbing products by "filtering" the analyte flux to the indicator electrode. 

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... 

Many problems involving competitive reaction kinetics may be treated by invoking the steady-state assumption within the digital simulation this has been done in at least two instances [29-34]. The first of these involves the development of a model for enzyme catalysis in the amperometric enzyme electrode [29-31]. In this model, the enzyme E is considered to be immobilized in a diffusion medium covering an electrode that is operated at a fixed potential such that the product (P) of enzyme catalysis is electroactive under diffusion-controlled conditions. (This model has also served as the basis for the simulation of the voltammetric response of the enzyme electrode [35].) The substrate (S) diffuses through the medium that contains the immobilized enzyme and is catalyzed to form P by straightforward enzyme kinetics ... 

A bioelectrode functioning optimally has a short response time, which is often controlled by the thickness of the immmobilized enzyme layer rather than by the sensor as well as many other factors (see Table 7). The biosensor response time depends on (1) how rapidly the substrate diffuses through the solution to the membrane surface, (2) how rapidly the substrate diffuses through the membrane cmd reacts with the biocatalyst at the active site, and (3) how rapidly the products formed diffuse to the electrode surface where they are measured. Mathematical models describing this effea are thoroughly presented in the biosensor literature (5, 68). 

Fig. 10.6. Change of the rate hmiting step in t5rrosinase carbon paste electrodes, (a) ind (b) show the flow rate dependence of steady-state currents for unmediated (a) emd mediated (b) enzyme electrodes. Applied potential — 0.05 V vs. Ag/AgCl for ( ) 1 p.M phenol ind ( ) 0.5 mM ferrocyanide as control of diffusion limited response. Error bars show the standard deviation of six electrodes. The cheinge from kinetic to dififtisional control in mediated electrodes results in higher sensitivity and improved operational stability as demonstrated in (c) where (1) represents the FIA response of mediated electrodes and (2) unmediated with consecutive 20 /rl injections of 10 p,M phenol in a thin-layer cell. Applied potential - 0.05 V vs. Ag/AgCl, mobile phase 0.25 M phosphate buffer pH 6.0 ind flow rate 0.7 ml min . ...

Figure 4-6. (A) A close-up view of the active site of yeast cytochrome c peroxidase showing the residues in the distal pocket at which hydrogen peroxide is reduced to water. Overlaid on the structure of the wild type enzyme are the positions of residues in the W51F mutant (tryptophan is replaced by phenylalanine). (B) Voltammograms of a film of wild type CcP on a PGE electrode, obtained in the absence and presence of H2O2 at ice temperature, pH 5.0. The electrode is rotating at 200 rpm, but the catalytic current in this case continues to increase as the rotation rate is increased therefore under these conditions the electrocatalysis is diffusion controlled and few facts are revealed about the enzyme s chemistry. For the W51F mutant, the signal due to the reversible two-electron couple and the catalytic wave are both shifted >100 mV more positive in potential compared to the wild-type enzyme. Reproduced from ref. 46 and 47 with permission.

At low substrate concentration the sensitivity of kinetically controlled sensors increases linearly with Umax. Consequently, the application of several identical enzyme layers one over the other enhances the measuring signal. When the amount of enzyme becomes sufficiently high as to provide complete substrate conversion the system passes over to diffusion control. Under these conditions a decrease of the diffusion resistance by decreasing the layer thickness results in an increased sensitivity. Nevertheless, a membrane-covered enzyme electrode is only 10 to 50% as sensitive as a bare electrode for an analogous electrode-active substance. 

Owing to differences in the Kyi values and the layer thickness, the transient from kinetic to diffusion control of different enzyme electrodes takes place at rather different enzyme activities. Gelatin-entrapped enzymes exhibit transient values of 0.17 U/cm2 (uricase,iifM= 17 pmol/1), 16 U/cm2 (urease, Kyi = 2 mmol/1) and 1.0 U/cm2 (lactate monooxygenase, Km = 7.2 mmol/1). 

Laval etal. (1984) bound LDH covalently to electrochemically pretreated carbon. The enzyme was fixed by carbodiimide coupling simultaneously with anodic oxidation of the electrode surface. The total amount of immobilized LDH was determined fluorimetrically after removal from the electrode and hydrolysis. The authors found that at a maximal enzyme loading of 13 pmol/cm2 six enzyme layers are formed. The immobilization yield was about 15%. The kinetic constants, pmax and. Km, were not affected by the immobilization. The obtained enzyme loading factor of 10-3 indicates that diffusion in the enzyme layer was of minor influence on the response of the sensor. The layer behaved like a kinetically controlled enzyme membrane, i.e., the NADH oxidation current was proportional to the substrate concentration only far below Km- With increasing enzyme loading the sensitivity for NADH decreased due to masking of the electrode surface. 

The pH increase caused by urea hydrolysis can also be indicated by using pH sensitive glass or metal oxide electrodes. Owing to the dissociation equilibria of NH4 and HCO3 in the neutral range approximately 1 mole of OH- ions is formed per mole of urea. Blaedel et al. (1972) showed that in diffusion controlled potentiometric enzyme electrodes, i.e. when the substrate is completely consumed within the enzyme membrane, the product concentration at the electrode surface depends... 

In enzyme electrodes, which are deliberately operated under conditions of diffusion control, the diffusion limits the sensitivity. Here, the coupling of cyclic enzyme reactions gives rise to a sensitivity enhancement by overcoming the limit set by diffusion. The excess of enzyme present in the membrane is included in the substrate conversion. On the other hand, the upper limit of linearity and the operational stability are decreased. 

Figure 7.11 A theoretical potentiometric enzyme electrode calibration curve based on external diffusion control of the reaction a plot of the logarithm of the product concentration in the enzyme layer versus the logarithm of the bulk substrate concentration. K = 10" the value of kaEV/PsE is given on the curve [24],...

Table 14-7. Transition from kinetic to diffusion control of some enzyme electrodes.

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