Scanning Electrochemical Microscopy of Quinoprotein Glucose

May 4, 2004 - sample. A number of attempts have been made to replace oxygen .... site-selective supply by microfluidic networks,25,26 and local ... su...
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Anal. Chem. 2004, 76, 3145-3154

Scanning Electrochemical Microscopy of Quinoprotein Glucose Dehydrogenase Chuan Zhao and Gunther Wittstock*

Department of Chemistry and Institute of Chemistry and Biology of the Marine Environment, Carl Von Ossietzky University of Oldenburg, D-26111 Oldenburg, Germany

The activity of immobilized glucose dehydrogenase (GDH), a typical PQQ-dependent quinoprotein, was studied qualitatively and quantitatively by scanning electrochemical microscopy (SECM). PQQ-dependent GDH is of interest because of its high activity and independence of dissolved oxygen in catalyzing the transfer of electrons from glucose to an electron mediator. Biotinylated glucose dehydrogenase was bound to streptavidin-coated paramagnetic beads (surface concentration g 1.8 × 10-11 mol cm-2) which were deposited as microscopic microspots on a hydrophobic surface. The catalytic activity of immobilized GDH was mapped in SECM feedback mode and generation-collection mode using ferrocenemethanol, ferrocenecarboxylic acid, p-aminophenol, and ferricyanide as electron mediators, respectively. The apparent steady-state kinetics of catalysis were measured under conditions of high D-glucose concentration using the theory developed for the SECM feedback and generation collection (GC) modes. In feedback mode, curves of the kinetically controlled substrate current against normalized distance were plotted, and it was found that GDH catalysis follows pseudo-first-order kinetics. In GC mode detection, the catalysis follows zero-order kinetics in the presence of high concentration of both substrates for GDH. The turnover rate obtained for immobilized GDH is lower than that of native GDH but much higher than that generally observed for glucose oxidase. In the development of enzyme-based amperometric biosensors, oxidases have been most commonly used as the biological recognition element. The main drawback of the oxidase-based biosensor is its dependence on oxygen concentration in the sample. A number of attempts have been made to replace oxygen with an artificial electron acceptor, but the problem remains since artificial electron acceptors exhibiting a high enough chemical affinity and capability to compete with oxygen have not been found yet. Significant improvement was achieved when oxidases were replaced by quinoproteins, which catalyze the transfer of electrons from the substrate to an electron acceptor other than oxygen.1 Quinoproteins are a large class of enzymes which use one of four different quinone-containing prosthetic groups, tryptophan tryptophylquinone (TTQ), topa-quinone (TPQ), lysine tyrosylquinone * Corresponding author. Phone: (+49-441) 7983971. Fax: (+49-441) 7983979. E-mail: [email protected]. (1) Duine, J. A. J. Biosci. Bioeng. 1999, 88, 231. 10.1021/ac035492n CCC: $27.50 Published on Web 05/04/2004

© 2004 American Chemical Society

(LTQ), and pyrroloquinoline quinone (PQQ), to convert a vast variety of alcohols and amines to their corresponding aldehydes/ lactones.2 Proteins containing the cofactor PQQ constitute the best characterized and largest quinoprotein subclass,3 of which electrons must pass from the reduced PQQ to redox center in the protein domain. Glucose dehydrogenase (GDH) is the classic example of PQQ-dependent quinoproteins. Two different types of quinoprotein glucose dehydrogenase exist, soluble and membranebound.2 The soluble type has so far only been detected in Acinetobacter calcoaceticus strains, while the membrane-bound one is widely distributed among Gram-negative bacteria, including A. calcoaceticus. The soluble GDH has been cloned, and an efficient expression of the apo-enzyme was obtained in a recombinant Escherichia coli strain. It is referred to as GDH here (EC 1.1.99.17). Reconstitution of apo- to holo-enzyme requires the presence of PQQ and Ca2+, which are firmly bound to the protein.4 GDH has a very high catalytic activity. For example, approximately 3 mmol of glucose is oxidized per minute per milligram of protein with 2,6-dichlorophenol indophenol, which is up to 20 times the activity of pure glucose oxidase.5 The high activity and independence of oxygen make GDH extremely interesting for the use in developing biosensors and immunoassay.5-9 Scanning electrochemical microscopy (SECM) appears to be a promising technique for the study of biological systems, e.g., metabolic activity of cells, whole organisms, subcellular particles, and enzymes.10-12 In particular, much attention has been devoted to imaging the activity of immobilized enzymes on patterned surfaces because of their practical significance for the prototyping of integrated and miniaturized biosensors and chip-based assays.13 (2) Anthony, C. Biochem. J. 1996, 320, 697. (3) Salisbury, S. A.; Forrest, H. S.; Cruse, W. B. T.; Kennard, O. Nature 1979, 280, 843. (4) Duine, J. A.; Frank, J.; Jongejan, J. A. Anal. Biochem. 1983, 133, 239. (5) Ye, L.; Ha¨mmerle, M.; Olsthoorn, A. J. J.; Schuhmann, W.; Schmidt, H. L.; Duine, J. A.; Heller, A. Anal. Chem. 1993, 65, 238. (6) Burestedt, E.; Nistor, C.; Schagerlo¨f, U.; Emneus, J. Anal. Chem. 2000, 72, 4171. (7) Nistor, C.; Rose, A.; Wollenberger, U.; Pfeiffer, D.; Emneus, J. Analyst 2002, 127, 1076. (8) Rose, A.; Scheller, F. W.; Wollenberger, U.; Pfeiffer, D. Fresenius’ J. Anal. Chem. 2001, 369, 145. (9) Alkasrawi, M.; Popescu, I. C.; Laurinavicius, V.; Mattiasson, B.; Cso ¨regi, E. Anal. Commun. 1999, 36, 395. (10) Bard, A. J.; Fan, F.-R. F.; Pierce, D. T.; Unwin, P. R.; Wipf, D. O.; Zhou, F. Science 1991, 254, 68. (11) Horrocks, B. R.; Wittstock, G. In Scanning Electrochemical Microscopy; Bard, A. J., Mirkin, M. V., Eds.; Marcel Dekker: New York, 2001; Chapter 11. (12) Pierce, D. T.; Unwin, P. R.; Bard, A. J. Anal. Chem. 1992, 64, 1795. (13) Wittstock, G. Fresenius’ J. Anal. Chem. 2001, 370, 303.

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Compared to conventional optical microscopic techniques which usually do not quantify or kinetically characterize the reactions catalyzed by the target enzyme, SECM could analyze enzyme kinetics and location simultaneously. In feedback mode, the ultramicroelectrode (UME) probe of SECM is used to initiate and sustain the enzyme reaction because it provides the only resource of a cofactor (electron donor or acceptor). The cofactor electrochemically produced from the bulk form of the mediator is necessary for the enzyme reaction. In this case, the current monitored at the UME gives a well-defined measure of the amount of substrate produced at the UME which is linked to the amount of substrate converted by the enzyme.12 Therefore, the rate of enzyme reaction at which the bulk form of the mediator is catalytically regenerated could be directly transduced into UME current. Feedback mode provides better lateral resolution because the enzyme reaction only occurs in close proximity to the UME. The sensitivity of feedback mode is, however, very limited because the flux generated by the enzymatic reaction must be detected on the background of the hindered mediator diffusion from the bulk phase. As the hindered diffusion may also vary with the sample topography, successful experiments have been restricted to situations where a high enzyme load is probed or the enzyme has very high turnover rates.12-15 In generation-collection (GC) mode, the production of the enzyme-generated product begins when a substrate specific to the enzyme reaction is added to the electrochemical cell so that a concentration profile forms around the enzyme site and extends into the solution. The major technical problems with the GC mode are the need for an independent distance measurement and the absence of a well-defined mass transport rate in some situations.11 This problem can be overcome by using a microfabricated substrate where the enzymatic reaction is confined to a small diskshaped region. The concentration profile of the products of the enzymatic reaction may then be calculated from the diffusion equation.16 With the well-defined steady-state concentration profile, the distance dependence of the UME signal can be used to calibrate the UME-to-surface separation as well as to quantify the flux of analyte.11,16 In GC mode, the enzyme product is generated continuously over the entire surface, and generally, there is no way to switch the enzyme reaction on and off. This situation can lead to the overlap of product diffusion zones from different individual enzyme sites. Such diffusion zone overlap can perturb kinetic measurements when the product diffuses into regions where no enzyme reaction is actually occurring and can seriously blur the SECM image and degrade lateral resolution.17 Patterning of enzymes on surfaces has been explored in a variety of ways including lithographic approaches,18,19 microcontact printing and subsequent modification,20-23 local electrochemical (14) Zaumseil, J.; Wittstock, G.; Bahrs, S.; Steinru ¨ cke, P. Fresenius’ J. Anal. Chem. 2000, 367, 346. (15) Pierce, D. T.; Bard, A. J. Anal. Chem. 1993, 65, 3598. (16) Bath, B. D.; Lee, R. D.; White, H. S.; Scott, E. R. Anal. Chem. 1998, 70, 1047. (17) Zhao, C.; Sinha, J. K.; Wijayawardhana, C. A.; Wittstock, G. J. Electroanal. Chem. 2004, 561, 83-91. (18) Dontha, N.; Nowall, W. B.; Kuhr, W. G. Anal. Chem. 1997, 69, 2619. (19) Pritchard, D. J.; Morgen, H.; Cooper, J. M. Angew. Chem., Int. Ed. Engl. 1995, 34, 91. (20) Chiu, D. T.; Jeon, N. L.; Huang, S.; Kane, R. S.; Wargo, C. J.; Choi, I. S.; Ingber, D. E.; Whitesides, G. M. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 2408.

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activation with electrode arrays as patterned reagent generators,24 site-selective supply by microfluidic networks,25,26 and local modifications with scanning probe techniques.27-30 Recently, we reported a new micropatterning procedure that uses surfacemodified magnetic microbeads to form microscopic agglomerates of beads on hydrophobic surfaces.31 Here, a droplet of bead suspension was brought in contact with a hydrophobic surface mounted on a magnet. Upon retraction of the droplet, the magnetic field and the hydrodynamic forces cause the beads to aggregate in well-defined, mound-shaped microspots. More recently, we explored using this micropatterning procedure to fabricate microbead microspot arrays.17 Using magnetic microbeads provides a convenient way to achieve high enzyme load in a small but well-defined surface area which is, as aforementioned, very important for a successful feedback experiment. Moreover, using magnetic beads could easily form a host of different enzyme microspots by making available a number of simple coupling chemistries for attaching enzyme to beads. In this paper, we report the SECM study of microbeadimmobilized GDH. The conditions, under which the enzyme catalysis reaction can be detected by SECM, were examined for both feedback and GC modes. Using theoretical models for SECM feedback and GC detection, we quantitatively evaluate the catalytic behavior of immobilized GDH and assess the apparent heterogeneous kinetics of the catalytic reaction. EXPERIMENTAL SECTION Materials. Apo-glucose dehydrogenase (PQQ-dependent, apoGDH) from a recombinant Escherichia coli (EC 1.1.99.17, molecular weight ≈ 50 kDa) was purchased from Genzyme (Genzyme Diagnostics, Kent, U.K.). Pyrroloquinoline quinone (PQQ), β-Dglucose, ferrocenecarboxylic acid (FcCOOH), p-aminophenol (PAP), N-(2-hydroxyethyl)-piperazine-N′-(2-ethanesulfonic acid (HEPES), and folin-ciocalteaus phenol reagent were from Sigma (Sigma-Aldrich Chemie GmbH, Schnelldorf, Germany). Ferrocenemethanol (FcCH2OH) was from ABCR (ABCR GmbH & Co. KG, Carlsruhe, Gremany). Streptavidin-coated M-280 Dynabeads (2.8 µm diameter) were from Dynal Inc. (Great Neck, NY) as a monodisperse suspension of 6.7 × 108 beads mL-1. EZ-Link sulfoNHS-LC-biotinylation kit was from Pierce (Pierce, Rockford, IL). Potassium ferricyanide, K2HPO4, NaH2PO4, MgCl2, CaCl2, KCl, CuSO4, Na2CO3, sodium potassium tartrate (Fluka, Deisenhofen, Germany), and Tween 20 (polyethylene glycol sorbitan monolaurate, Sigma, Steinhein, Germany) were used as received. All chemicals used were of analytical reagent grade. Deionized water was used throughout. (21) Yousaf, M. N.; Houseman, B. T.; Mrksich, M. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 5992. (22) Wilhelm, T.; Wittstock, G. Langmuir 2002, 18, 9485. (23) Wilhelm, T.; Wittstock, G. Angew. Chem., Int. Ed. 2003, 42, 2247. (24) Egeland, R. D.; Marken, F.; Southern, E. M. Anal. Chem. 2002, 74, 1590. (25) Delamarche, E.; Bernard, A.; Schmid, H.; Bietsch, A.; Michel, B.; Biebuyck, H. J. Am. Chem. Soc. 1998, 120, 500. (26) Delamarche, E.; Bernard, A.; Schmid, H.; Michel, B.; Biebuyck, H. Science 1997, 276, 779. (27) Wilhelm, T.; Wittstock, G. Electrochim. Acta 2001, 47, 275. (28) Turyan, I.; Matsue, T.; Mandler, D. Anal. Chem. 2000, 72, 3431. (29) Kenseth, J. R.; Harnisch, J. A.; Jones, V. W.; Porter, M. D. Langmuir 2001, 17, 4105. (30) Piner, R. D.; Zhu, J.; Xu, F.; Hong, S.; Mirkin, C. A. Science 1999, 283, 661. (31) Wijayawardhana, C. A.; Wittstock, G.; Halsall, H. B.; Heineman, W. R. Anal. Chem. 2000, 72, 333.

Modification of Magnetic Microbeads and Formation of Microbead Microspot. Apo-GDH was first biotinylated according to the manual by Pierce,32 and a Lowry protein assay was performed afterward to determine the concentration of biotinylated enzyme. Excess of biotinylated apo-GDH (50 µL of 10 µg mL-1 in 0.1 M PBS buffer solution, pH 7.2) was added to 10 µL streptavidincoated M-280 microbeads and 40 µL phosphate buffer (PBS, pH 7.2) to saturate all the binding sites on the beads. The mixture was then agitated gently on a plate-shaker for 30 min. Excess ApoGDH was removed in three rinses with 100 µL of PBS buffer containing 0.5% (v/v) Tween 20. Then, the bead suspension was rinsed three times with 100 µL of 20 mM HEPES (pH 7.5). Between rinses, a magnet pressed against the wall of the tube was used to hold the beads. To reconstitute the holo-GDH from apo-GDH, the beads were taken up in 40 µL of HEPES buffer (pH 7.5), 50 µL of 0.5 mg mL-1 PQQ and 10 µL of 0.1 M CaCl2 were then added to the beads, and the mixture was incubated at room temperature for 30 min. The final concentration of beads in test tube was 4 × 107 beads mL-1. The modified microbeads were then deposited as microspots on the insulating surface according to the previously described procedure.31 Microscope glass slides (ca. 76 × 26 mm2, Carl Roth GmbH, Karlsruhe, Germany) were used as support and were covered by stretched Parafilm (American National Can, Chicago, IL) to obtain a hydrophobic surface. Different sized microbeads’ microspots were deposited on the surface by changing the concentration of the bead suspension. The optical image of the deposited bead microspot was then captured with a CCD camera (Stemmer Imaging GmbH, Puchheim, Germany) combined with a optical microscope. The size of the microspot was compared to a transparent scale (100 µm graduation, Graticules Ltd., Tonbridge, U.K.) viewed with the same setup. SECM Instrumentation and Enzyme Assay Procedure. The SECM measurements were performed on a home-built instrument which was described previously.22 All experiments were carried out with a 25 µm diameter Pt UME (RG ) 10) fabricated according to the method developed by Kranz et al.33 A Pt wire as auxiliary electrode and a Ag|AgCl|3 M KCl reference electrode, to which all potentials are referred, completed the electrochemical cell. The in-house software MIRA was used to process and analyze data. The surface reconstruction was achieved by simulating diffuse reflection of light. Gouraud interpolation was applied within the polygon of the surface.34 In the feedback mode, GDH catalysis at prepared surfaces was monitored in 20 mM HEPES buffer solutions (pH 7.5) containing 50 mM glucose, 30 mM KCl, 1.0 mM CaCl2, and different electron mediators. Two ferrocene deviatives, ferrocenemethanol and ferrocenecarboxylic acid, and p-aminophenol were separately employed to mediate the enzyme reaction. The approach of the microelectrode toward the surface was performed in a lateral distance of several hundred micrometers away from the deposited bead agglomerates while monitoring the negative feedback of ferrocenemethanol oxidation until mechanical contact to the (32) Manual for EZ-Link Sulfo-NHS-LC-Biotinylation Kit; Pierce Biotechnology: Rockford, IL; http://www.piercenet.com. (33) Kranz, C.; Ludwig, M.; Gaub, H. E.; Schuhmann, W. Adv. Mater. 1995, 7, 38. (34) Wittstock, G.; Asmus, T.; Wilhelm, T. Fresenius’ J. Anal. Chem. 2000, 367, 346.

support occurred. The UME was then retracted 30 µm from the glass surface. The images were obtained by translating the UME horizontally at a translation speed of 10 µm s-1. In addition, approach curves were reordered above the center of the bead microspot at a speed of 5 µm s-1. The UME potential, ET, was set at 400 mV, a potential suitable for the oxidation of all the three mediators. In SECM GC mode, GDH catalysis was monitored from 20 mM HEPES buffer solutions (pH 7.5) containing 50 mM glucose, 30 mM KCl, 1.0 mM CaCl2, and 10 mM Fe(CN)63- as electron acceptor. To position the UME in a defined distance over the sample, the tip was approached to the Parafilm-coated surface while monitoring the oxygen reduction current (negative feedback). When mechanical contact to the support occurred, the approach was interrupted, and the electrode was then retracted 30 µm from the surface. The surface images were obtained by translating the UME horizontally at a translation speed of 10 µm s-1. Approach curves were then recorded above the center of bead microspot by translating the UME at z direction at a speed of 5 µm s-1. The UME potential, ET, was set at 500 mV to detect the enzyme reaction product [Fe(CN)6]4-. RESULTS AND DISCUSSION Catalytic Mechanism of GDH. The identity of pyrroloquinoline quinone (PQQ) as a redox cofactor of quinoprotein was revealed about 20 years ago.3 Since the discovery, PQQ has been found in a large number of bacterial proteins.2,35 Two redox states of PQQ are relevant in the catalytic mechanism of GDH. The oxidized quinone state of PQQ can be reversibly converted into the reduced, quinol form (PQQH2) by the transfer of two electrons and two protons.35

The catalytic mechanism of the soluble glucose dehydrogenase has been extensively studied using biochemical and kinetic techniques, and the results are in agreement with two reaction mechanisms. The first involves a covalent addition-elimination mechanism including a general base-catalyzed proton abstraction from the oxidizable hydroxyl group, followed by the formation of a covalent substrate-PQQ complex and product elimination.2,36 D-glucose

+ PQQ f [PQQ‚‚‚glucose]

(2)

[PQQ‚‚‚glucose] f PQQH2 + D-gluconolactone

(3)

PQQH2 + GDH(ox) f GDH(red) + PQQ

(4)

GDH(red) + (3 - n)Mox f GDH(ox) + (3 - n)Mred + 2H+ (5) M represents an n-electron mediator (n ) 1, 2). An alternative mechanism involves a general base-catalyzed proton abstraction in concert with a hydride transfer to PQQ, and subsequent Analytical Chemistry, Vol. 76, No. 11, June 1, 2004

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tautomerization to PQQH2.36,37 D-glucose

+ PQQ f PQQH2 + D-gluconolactone (6)

PQQH2 + GDH(ox) f GDH (red) + PQQ

(7)

GDH(red) + (3 - n)Mox f GDH(ox) + (3 - n)Mred + 2H+ (8) These two catalytic mechanisms are all plausible and in agreement with enzyme kinetic and spectroscopic results. It has not been possible to resolve which of these two mechnism is correct, due to the lack of comprehensive structural information. Nevertheless, there seems to be growing evidence for the mechanism with direct hydride transfer according to a recent series of high resolution determinations of several crystal structures of catalytically relevant states of GDH.37 At all events, the actual catalytic scheme for both forms of GDH could be modeled as an alternating two reactant or “ping pong” mechanism where GDH is sequentially reduced and reoxidized within one catalytic circle. In this process, Dglucose acts to reduce the enzyme while the electron-deficient mediator acts as the oxidant. A simplified overall mechanism was proposed as D-glucose

holo-GDH

+ (3 - n)Mox 98 D-gluconolactone + (3 - n)Mred + 2H+ (n ) 1, 2) (9)

Detection of Immobilized GDH in Feedback Mode. The first step toward feedback detection of the catalysis of surfacebound glucose dehydrogenase (GDH) was to immobilize GDH at a small but well-defined surface area. According to a simple enzyme detection criteria for the SECM given as12

kcatΓenz g 10-3DRcR/rT enzymatic detection can be improved either by reducing the combined experimentally controllable factor formed by diffusion coefficient for the mediator (DR), its concentration (cR), and the UME radius (rT), or by increasing the combined enzymedependent factors, which are the product of enzyme turnover rate (kcat) and surface concentration (Γenz). For a given enzyme, Γenz is crucial for successful feedback detection. Among the commonly used methods for the immobilization of enzyme, such as covalent immobilization on insulating materials,38 immobilization in hydrogel membrane,39 and immobilization in Langmuir-Blodgett (LB) films,40 immobilization in hydrogel membranes generally has the highest enzyme load. In our experiment, using microbeads as the host of enzyme in combination with the biotin-avidin chemistry provides an easy but versatile way to achieve high enzyme surface concentration. Using the microspotting procedure, well-defined (35) Oubrie, A. Biochim. Biophys. Acta 2003, 1647, 143. (36) Olsthoorn, A. J. J.; Duine, J. A. Biochemistry 1998, 37, 13854. (37) Oubrie, A.; Rozeboom, H. J.; Kalk, K. H.; Olsthoorn, A. J. J.; Duine, J. A.; Dijkstra, B. W. EMBO J. 1999, 18, 5187. (38) Morris, D. L.; Campbell, J.; Hornby, W. E. Biochem. J. 1975, 147, 593. (39) Pishko, M. V.; Michael, A. C.; Heller, A. Anal. Chem. 1991, 63, 2268. (40) Sun, S.; Ho-Si, P. H.; Harrison, D. J. Langmuir 1991, 7, 727.

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Figure 1. Schematic of the SECM feedback imaging principle. The schematic is not to scale.

mound-shaped bead microspots were formed on a hydrophobic surface with different diameters depending on the concentration of bead suspension applied.30 The surface of each bead is previously coated with streptavidin with an estimated 7 × 105 active molecules (Pierce company, manual for M-280 streptavidin bead). Because each strepavidin can accept four biotin molecules, therefore 2.8 × 106 active sites can be present on each bead. When all the sites are saturated with enzyme, a surface concentration Γenz ) 2.8 × 106 molecules/4πrbead2 ) 1.8 × 10-11 mol cm-2 could be obtained. This value is basically equal to that obtained in 50 wt % hydrogel membranes (0.05 ( 0.01 µm thickness), and is 2 orders of magnitude higher than that in LB films (per monolayer).37 Please note that this value was obtained under the assumption that the microspot and microbead are disk-shaped and only the beads laying at the surface of the mound contribute to the catalysis reaction. The real surface concentration should be much higher than this value because the effective microbead surface and microspot surface are three-dimensional and the beads in the inner layer may also contribute, to a lesser extend, to the catalytic reaction. The SECM feedback detection scheme used to image GDH immobilized on microbeads is illustrated in Figure 1. Briefly, a mound of GDH-coated beads was bathed in a buffered assay solution (HEPES, containing Ca2+ for binding of the PQQ but also for functional dimerization of the protein37), the GDH specific reductant, D-glucose, as well as the reduced form of the mediator (Mred). An UME was then positioned in the solution at a distance of a few electrode radii above the surface, and a potential was applied, at which the oxidized mediator (Mox) is formed. If reduced GDH was present within the diffusion field of the electrode, the mediator was regenerated and fed back by the enzymatic reaction. By maintaining glucose at a sufficiently high concentration (50 mM), the enzyme operates in the regime of saturation kinetics of the glucose-GDH reaction. Figure 2b shows an SECM feedback image obtained with FcCH2OH as mediator at a microspot with a diameter about 100 µm (Figure 2a). In the area where microbeads were deposited, a positive feedback current was observed. The profile across the spot center showed a lateral extension of about 150 µm taken as full width at half-maximum (fwhm). This value was slightly larger than the size of the bead agglomerations taken from optical microscope photograph (Figure 2a), indicating that some diffusional blurring of the image occurred. It was noticed that the successful imaging depends critically on the UME-sample distance. This is due to the combined effect of the local cofactor generation and the measurement of the electrochemical feedback at the UME on the background of the steady-state current controlled by hindered diffusion of the mediator toward the UME.

Figure 3. Normalized current-distance curves recorded for different concentrations of FcCH2OH in 20 mM HEPES buffer with 50 mM D-glucose: (a) 0.05 mM, (b) 0.5 mM, (c) 2 mM. rT ) 12.5 µm, RG ) 10, rs ) 100 µm.

Figure 2. SECM feedback images of the glucose dehydrogenase activity: (a) optical microphotography of the spot, (b) SECM feedback image using 2 mM FcCH2OH as electron mediator in 20 mM HEPES buffer with 50 mM D-glucose, (c) same as part b but without D-glucose. rT ) 12.5 µm, d ) 30 µm, rS ) 50 µm, translation speed ) 10 µm s-1.

The UME-substrate distance used in this image is about 30 µm. This is a relatively large distance for an UME with rT ) 12.5 µm, resulting in high background currents due to hindered diffusion of FcCH2OH to the UME without contribution from the enzymatic reaction (Figure 2c). Elimination of enzyme feedback was accomplished by using an assay solution without D-glucose. No obvious increase of current was observed above the area where the positive feedback current is seen in Figure 2b. Furthermore, enhanced diffusional blocking and lower currents were expected when the UME scans over the bead microspot protruding out of

the support surface. However, this was not clearly observed. Although a careful observation shows slight decrease of current in the area of x/µm ) 700, y/µm ) 250, it is still not clear enough to derive the topography of the bead microspot. This is probably due to the relatively large UME-substrate distance which leads to only moderate hindrance of the mediator diffusion and low sensitivity for topographic features. Further decrease of microelectrode-support distance would increase the diffusional hindrance but, at the same time, increase the risk of pushing away the bead agglomerations by the insulation shielding of the microelectrode. On the basis of the enzyme-mediated positive feedback image, the location of the microspot was found on the surface, and current (iT)-distance (d) curves were recorded above the center of the microbead spot by translating the UME vertically away or toward the bead spot. The iT-d curves were then made dimensionless by dividing d by the UME radius (rT) and iT by the steady-state diffusion-limited oxidation current of the mediator in the solution bulk (iT,∞). Figure 3, curve a, shows an obvious, well-defined positive feedback approach curves toward a microspot obtained with a low mediator concentration (0.05 mM FcCH2OH). Normalized feedback currents decrease for a given distance if higher mediator concentration are used (Figure 3, curve b and c). For the highest mediator concentration of 2 mM, the approach curve exhibits a maximum at d/rT ≈ 1.8. Feedback response of this type resembles the current-distance behavior observed for slow electron transfer at electrodes41 and demonstrates that the redox catalysis of immobilized GDH could augment the SECM UME current. It has been shown that a variety of quinone compounds and ferrocene derivatives could serve as electron mediators for GDH.8,42,43 Ferrocenecarboxylic acid (FcCOOH) and p-aminophenol (PAP), which has the highest sensitivity among typical phenolic electron acceptors for GDH-based biosensor,8 were tested in this study as well. Figure 4 shows the normalized approaching curves obtained with 0.05 mM solution of each mediator. All the mediators show obvious positive feedback with SECM which was (41) Wipf, D. O.; Bard, A. J. J. Electrochem. Soc. 1991, 138, 469. (42) D’Costa, E. J.; Higgins, I. J.; Turner, A. P. Biosensors 1986, 2, 71. (43) Razumiene J.; Meskys, R.; Gurevicience, V.; Laurinavicius, V.; Reshetova, M. D.; Ryabov, A. D. Electrochem. Commun. 2000, 2, 307.

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Figure 4. Normalized current-distance curves recorded for different mediators in 20 mM HEPES buffer with 50 mM D-glucose: (a) 0.05 mM FcCH2OH, (b) 0.05 mM FcCOOH, and (c) 0.05 mM PAP. rT ) 12.5 µm, RG ) 10, rs ) 100 µm.

similar to that obtained with FcCH2OH, but with different sensitivity levels. PAP shows the highest feedback among these mediators (curve c). However, the poor long-term stability makes it not very attractive for SECM imaging which generally takes about 30 min or longer. Nevertheless, it still can serve as an efficient electron mediator for GDH if it could be generated in situ. Quantitative Analysis of GDH Catalysis in Feedback Mode. When an oxidoreductase enzyme is immobilized at the sample surface, the UME current, iT, depends on the mass transport rate and the enzyme kinetics. Kinetic information can therefore be obtained from the dependence of iT on d, i.e., an approach curve. When the mediator is fed back under diffusion controlled conditions, the iT-d curves will be identical to that above a conducting surface. In the opposite situation, when the rate of mediator fed back from the sample is much less than the rate of mediator diffusion to the UME from bulk solution, the approach curve will be identical to that above an insulating surface. Between these two limiting case, the approach curve will contain information on the steady-state rate of the enzymatic reaction. It has been found that the whole family of SECM working curve (IT vs L) can be described by the equation44

ITk (L) ) Isk(L) -

ITins(L)Isk(L) ITc(L)

+ ITins(L)

(11a)

where ITc(L), and ITins(L) are the normalized UME currents, iT(L)/iT,∞, for diffusion-controlled regeneration of a redox mediator (pure diffusion-controlled positive feedback), and insulating substrate (pure diffusional blocking, i.e., no mediator regeneration), respectively, at a normalized UME-substrate separation, L ) d/rT. The analytical approximations for ITc(L), and ITins(L) have been given as45

ITc(L) ) ITins(L) )

3150

0.78377 -1.0672 + 0.68 + 0.3315 exp L L

(

)

1 1.5151 -2.4035 0.292 + + 0.6553 exp L L

(

)

Analytical Chemistry, Vol. 76, No. 11, June 1, 2004

(11b) (11c)

Figure 5. Dependence of kinetically controlled substrate current (isk) on normalized working distance (d/rT) and substrate concentration c*FcCH2OH. The assay solution contains 20 mM HEPES buffer, 50 mM D-glucose, and c*FcCH2OH of (a) 0.05 mM, (b) 0.5 mM, and (c) 2 mM; inset isk-c*FcCH2OH curves were for the working distance d/rT ) 0.96 (9), 2.08 (b), 4 (2), 6.08 (+), and 8 (3). rT ) 12.5 µm, RG ) 10, rs ) 100 µm.

Isk(L) is the normalized kinetically controlled substrate current defined as

Isk(L) ) isk(L)/iT,∞

(12)

To measure the finite kinetics of the GDH surface catalysis, steadystate SECM feedback experiments were carried out on the same bead microspot using a wide range of bulk concentrations (usually 50 µM to 2.0 mM) of three mediators. In all of these experiments, the concentration of D-glucose was kept at high level of 50 mM to ensure that the simplified rate expression for the GDH surface reaction remained valid at all times. This saturating level of D-glucose was consistent with the apparent Michaelis constant of K′M,glu e 24 mM reported for native GDH in solution.46 To tell the apparent reaction order of the immobilized GDH catalysis, the curves of kinetically controlled substrate current (isk(L) ) [IT(L) - ITins(L)]‚iT,∞) against normalized distance (L) were plotted using the normalized iT-d curves obtained for each assay solution. ITins(L) values were calculated according to eq 11c for each L value. Figure 5 shows the isk-L curves obtained for different concentrations of mediator FcCH2OH (c*FcCH2OH). It showed that isk values for three assay solutions increase with the decrease of the working distance owing to increased positive feedback effect. The isk-L curves in Figure 5 were further studied by plotting isk against c*FcCH2OH for different working distances. It was found that, at several selected working distances, isk was proportional to the substrate concentrations, showing an obvious characteristic of firstorder kinetics. Similar results have been observed for the other two mediators. It had been found before that apparent zero-order kinetics are the typical case for immobilized enzymes unless the mediator concentration is low and the enzyme activity is high.12,47 The first-order kinetics observed in this study were mainly (44) Wei, C.; Bard, A. J.; Mirkin, M. V. J. Phys. Chem. 1995, 99, 16033. (45) Mirkin, M. V.; Fan, F.-R. F.; Bard, A. J. J. Electroanal. Chem. 1992, 328, 47 (46) Matsushita, K.; Shinagawa, E.; Adachi, O.; Ameyama, M. Biochemistry 1989, 28, 6276. (47) Shiku, H.; Takeda, T.; Yamada, H.; Matsue, T.; Uchida, I. Anal. Chem. 1995, 67, 312.

Table 1. First-Order Kinetics Obtained for Immobilized GDH Catalysis mediatora (Medred)

[R]/ mM

κc

0.05 0.50 2.0 b FcCH2OH 0.05 0.5 2.0 p-aminophenol 0.05 0.5 2.0

4.0 3.3 3.0 2.5 1.0 0.5 5.0 3.5 1.3

FcCOOHb

apparent turnover numberg REd/ rate constante REf/ % % 103 kf/cm s-1 10-2 kcat/s-1 8 7 7 4 5 10 12 9 8

11 9 8 16 6 3 37 26 9

28 27 27 24 25 30 32 29 28

3 2 2 16 6 3 68 47 17

Figure 6. Schematic of the SECM generation-collection imaging principle. The schematic is not to scale.

a Diffusion coefficients measured in the assay solution were 3.47 × 10-6 cm2/s for FcCOOH, 7.25 × 10-6 cm2 s-1 for FcCH2OH, and 9.2 × 10-6 cm2/s for p-aminophenol, respectively. b A small amount of ethanol was added to dissolve FcCH2OH and FcCOOH. c Normalized rate constants (κ’s) were determined from the normalized SECM current-distance curve by fitting to the calculated curve from eqs 11 and 13. d Relative error of normalized rate constants (κ’s) obtained from the curve fit. e First-order apparent rate constants were obtained from kf ) κDR/rT. f Relative error of apparent rate constants obtained from footnote d and an estimation of 10% uncertainty in rT and 10% uncertainty in DR. g The turnover numbers were estimated from kcat ) kfKM/ΓGDH (for details see text). Experimental conditions: rT ) 12.5 µm, RG ) 10; mediators and 50 mM D-glucose in 20 mM HEPES buffer; rS ) 100 µm, ΓGDH g 1.8 × 10-11 mol cm-2.

contributing to the high catalytic activity of GDH. This is reasonable because GDH used in this study generally shows much higher catalytic activity than glucose oxidase which was used in those previous studies.12,46-48 An approximate analytical treatment for general types of firstorder kinetic process, i.e., electrochemical or enzymatic, at the sample surface has been developed. The normalized tip current for finite substrate kinetics was given (for 0.1 < L < 1.5) as44

I sk )

0.68 + 0.3315 exp(-1.0672/L) 0.78377 + L(1 + 1/Λ) 1 + F(L,Λ)

(13)

where Λ ) kfd/DR, kf is the first-order apparent heterogeneous rate constant [cm s-1]; κ ) kfa/DR, F(L, Λ) ) (11/Λ + 7.3)/(110 - 40L), and DR is the diffusion coefficient of the reduced form of the mediator. The iT-d curves obtained for each assay solution were fitted to the calculated curve from eqs 11 and 13 for firstorder kinetics to obtain apparent rate constants (kf’s). These apparent rate constants are listed in Table 1 for various mediator conditions employed. The apparent turnover number for first-order enzymatic kinetics was obtained from the limiting expression of the Michaelis-Menten equation for small substrate concentrations:

kf )

kcatΓenz KM

(14)

The apparent Michaelis constants (KM’s) for the three mediators were estimated by a Hyperbolic nonlinear fitting of the isk-c*mediator curve at different distances (as shown in Figure 5 for FcCH2OH), (48) Weibel, M. K.; Bright, H. J. J. Biol. Chem. 1971, 124, 801.

and then by taking the averaged values. The KM values obtained were 1.8 mM for FcCH2OH, 0.4 mM for FcCOOH, and 3.3 mM for PAP. The results showed that the values of Michaelis constants depend strongly on the kind of electron acceptor. This indicates that the rate of the overall catalytic reaction is mainly controlled by the reaction step between GDH and the electron acceptors.49 A similar dependence of Michaelis constant has been reported for the native GDH47 in solution and membrane-bound GDH.50,51 From eq 14 and the surface concentration of the bead spot (1.8 × 10-11 mol cm-2), the maximal apparent turnover number of the immobilized enzyme (kcat) was calculated for each mediator (Table 1), yielding an average observed turnover number of 1811 s-1. This value of kcat was lower than the native GDH (5870 s-1, phenazine methosulfate 2,6-dichlorophenolindophenol as electron acceptors at pH 6.8).46 In our system, the small maximal turnover number may result from the practical deactivation of GDH during the biotinylation and immobilization steps. In comparison to glucose oxidase (GO), this value of kcat was about 2 times higher than the intrinsic value reported by Weibel and Bright for solubilized GO,48 and more than 3 orders of magnitudes higher than immobilized GO reported by Pierce et al.,12 indicating a much higher catalytic activity of GDH against GO. Detection of Immobilized GDH in Generation-Collection Mode. As already mentioned, the poor sensitivity in feedback mode is the main obstacle to achieving a good image because the small feedback current is easily submerged in high background current resulting from hindered diffusion. This problem, however, could be effectively solved if a generation-collection (GC) experiment could be constructed. The GDH activity was therefore also studied in the GC mode. As illustrated in Figure 6, in the presence of glucose, the GDH catalyzes the conversion of the added electron mediator [Fe(CN)6]3- to [Fe(CN)6]4-. The reduced form [Fe(CN)6]4-, which is otherwise not present in the solution bulk, is detected at the UME at ET ) 500 mV as a function of the horizontal or vertical UME position. Well-defined mound-shaped bead microspots with the approximate diameter of 150 µm (Figure 7a) were deposited on the surface, and the GDH activity imaging was done on such bead microspots. Figure 7b shows a GC image of the activity of a microspot of GDH-coated beads. Since the bead mound is a microstructure itself, a quasistationary and hemispherical diffusion of [Fe(CN)6]4- develops over the mound. It was noted that the quasistationary diffusion fields were established in about 3 min after the addition of the enzyme substrate. The working distance, (49) Ikeda, T.; Kurosaki, T.; Takayama, K.; Kano, K. Anal. Chem. 1996, 68, 192. (50) Dewanti, A. R.; Duine, J. A. Biochemistry 1998, 37, 6810. (51) Iswantini, D.; Kano, K.; Ikeda, T. Biochem. J. 2000, 350, 917.

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Figure 7. SECM GC image of GDH activity: (a) optical microphotography of the spot, (b) GC image using 10 mM [Fe(CN)6]3- as electron acceptor in 20 mM HEPES buffer with 50 mM D-glucose. rT ) 12.5 µm, d ) 30 µm, rS ) 75 µm, translation speed ) 10 µm s-1.

d, used in the experiment is about 30 µm. While this is a large distance for feedback imaging, it is still very appropriate for GC imaging because the GC mode is less sensitive to variations in the working distance. The possibility of using large working distances reduced the risk of collisions of the UME with the protruding bead mound. Even in Figure 7b, a small feature can be seen beside the main peak that may originate from beads detached from the main mound by the scanning probe illustrating the necessity of working at comparatively large working distances. However, the larger flexibility in the GC mode with regard to d is associated with a lower lateral resolution. In Figure 7b, d ) 30 µm leads to a fwhm of 220 µm in a line scan across the spot center. The UME current dependence on the distance was further studied by recording approach curves above the center of the bead microspot. In the GC experiment at small d under the condition of high enzyme activity and low c*[Fe(CN)6]3-, the UME may actually shield the enzymatically active region from the supply of [Fe(CN)6]3-, similar to the conventional negative feedback.52 Figure 8a shows a typical approach curve for GC detection obtained with small c*[Fe(CN)6]3- ) 1 mM. The UME current initially 3152 Analytical Chemistry, Vol. 76, No. 11, June 1, 2004

rises when approaching the sample but falls sharply after passing through a maximum at d ) 40 µm. The current decrease at a small distance is equivalent to the conventional negative feedback, except that here it is the enzyme reaction at the sample whose conversion is limited by hindered diffusion of [Fe(CN)6]3- from bulk solution to GDH-modified microspot. In contrast to the conventional negative feedback, where the approach curve depends only on the RG of the UME, the ratio between [Fe(CN)6]3bulk concentration and the enzyme activity per unit area of the spot is also important. This “negative feedback” phenomena will become more evident when the turnover number and surface concentration of the enzyme are high and c*[Fe(CN)6]3- is low, as in our case. Nevertheless, the hindered diffusional transport will still provide enough substrate to saturate the enzyme kinetics if the substrate concentration is kept high enough. Another approach curve was recorded under the same conditions except for a much higher c*[Fe(CN)6]3- ) 10 mM. As shown in Figure 8, curve b, a monotonically rising UME current was observed with decreasing d. In this case, the GDH was always saturated even at small d. When looking for low quantities of GDH activity, for instance in

Figure 9. Profile across the GC image (O) of glucose dehydrogenase activity. Experimental parameter c*[Fe(CN)6]3- ) 10 mM, d ) 30 µm, rS ) 75 µm. The solid line was calculated from eqs 15 and 16 with the following parameters: cS,[Fe(CN)6]4- ) 1.69 mM, d ) 30.45 µm, rS ) 74.35 µm, D[Fe(CN)6]3- ) 6.19 × 10-6 cm2 s-1, and a constant current offset of 0.91 nA for all points.

the following form, where rS is the radius of the spot.53

θ)

Figure 8. Approach curves of GC detection obtained with (a) 1.0 mM and (b) 10 mM [Fe(CN)6]3- as the electron acceptor in 20 mM HEPES buffer with 50 mM D-glucose. rT ) 12.5 µm, RG ) 10, rS ) 75 µm, translation speed ) 5 µm s-1. The solid line is a guide to the eyes.

immunoassay applications, this situation is likely to prevail if high substrate concentrations are practicable. Quantitative Analysis of GDH Catalysis in GenerationCollection Mode. The kinetics of immobilized GDH catalysis were investigated using a model originally developed for diffusion to an isolated disk shaped pore.53 Briefly, the UME was assumed as a noninteracting probe. The iT at the UME is given by

iT ) 4nFD[Fe(CN)6]4-rTcS,[Fe(CN)6]4-θ

(15)

where n ) 1 is the number of transferred electrons to the UME per [Fe(CN)6]4-, F is the Faraday constant, D[Fe(CN)6]4- ) 6.19 × 10-6 cm2 s-1 is the diffusion coefficient of [Fe(CN)6]4-,37 rT ) 12.5 µm is the UME radius, cS,[Fe(CN)6]4- is the concentration of the [Fe(CN)6]4- at the surface of the bead mounds, and θ is a dimensionless factor describing the decrease of the c[Fe(CN)6]4- as a function of the lateral distance, r, and vertical distance, d, from the center of the bead spot. For an x scan over the center of the disk-shaped bead mound, the lateral distance of the UME position from the center is r ) ∆x ) x - x0, where x0 is the x-coordinate of the spot center. The factor θ is proportional to the steady-state concentration distribution over a microdisk electrode and assumes (52) Horrocks, B. R.; Schmidtke, D.; Heller, A.; Bard, A. J. Anal. Chem. 1993, 65, 3605. (53) Bath, B. D.; White, H. S.; Scott, E. R. In Scanning Electrochemical Microscopy; Bard, A. J., Mirkin, M. V., Eds.; Marcel Dekker: New York, 2001; Chapter 9.

2 arctan π

x(∆x

x2rS 2

+ d2 - rS2) + x(∆x2 + d2 - rS2)2 + 4d2rS2 (16)

To quantify the flux of [Fe(CN)6]4- at the bead mound, a current profile was extracted from the image of Figure 7 including the highest current value that corresponds to the center of the bead spot. It is shown as open symbols in Figure 9 together with the calculated profile given as a solid line. The solid line in Figure 9 was obtained after fitting eqs 15 and 16 to the experimental data using cS,[Fe(CN)6]4- ) 1.69 mM, d ) 30.45 µm, and rS ) 74.35 µm. A constant offset current of 0.91 nA was added to the calculated curve. The calculated curve describes the measured signal perfectly, and the value of cS,[Fe(CN)6]4- confirms that only a small fraction of the provided enzyme substrate c*[Fe(CN)6]3- ) 10 mM is converted. Therefore, the enzyme reactions follow the regime of substrate saturation. The other parameters are in agreement with the experimental settings. It should be noted that the above model developed for the flux of a disk-shaped pore implies a nonuniform flux distribution at the active parts of the sample. Klusmann and Schultze compared this case to a disk with uniform flux distribution.54 Their results indicated that the deviation between both models is less than 10% (see Figures 3 and 4 in ref 54) at our working distances. Unfortunately, the calculation of the model given in ref 54 requires the solution of complicated integral expression for each combination of x, d, and rS values and turns out to be impractical for a numerical fit of experimental data. Moreover, the microelectrode is not a true passive sensor in our experiments. We consider possible deviation by treating an amperometric microelectrode as a passive sensor as a more severe deviation than the rather subtle differences between the assumption of uniform/nonuniform flux distributions at the sample provided the working distance is about half the size or large than (54) Klusmann, E.; Schultze, J. W. Electrochim. Acta 1997, 42, 3123.

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the radius of the bead mound. Nevertheless, it has been demonstrated in a number of studies that this assumption is good enough to allow estimation of chemical fluxes above microscopic sources, for instance, at defects in oxide-covered valve metal electrodes or at micrometer-sized pores.53 From cS,[Fe(CN)6]4-, the total flux Ω of [Fe(CN)6]4- generated at the microspot can be calculated according to eq 1755

Ω ) 4D[Fe(CN)6]4-cS,[Fe(CN)6]4-rs ) 3.14 × 10-13 mol s-1 (17)

Assuming a uniform flux over the entire spot area, this value corresponds to a generation rate related to the projected area of the spot of J ) Ω(πrS2) ) 1.78 × 10-9 mol s-1 cm-2. From eq 14 and the minimum surface concentration of the bead spot (1.8 × 10-11 mol cm-2), the maximum apparent turnover number of the immobilized enzyme (kcat) for the zero-order kinetics was calculated to be 98 s-1. This value of kcat was about 7 times lower than native membrane-bound GDH (727 s-1, using [Fe(CN)6]3- as electron acceptor)51 which generally shows lower catalytic activity than soluble GDH.46 An upper limit of [Fe(CN)6]4- production by a single bead was also estimated to understand how much an individual bead contributes to the [Fe(CN)6]4- flux. Assuming the microspot to be a disk with the geometric area Aspot ) πrS2 and that only those beads lying at the surface and to a lesser extent the ones in the second layer contribute significantly to the [Fe(CN)6]4- flux, an effective number of contributing beads, Nb,eff, was estimated by assuming that sum of the cross section of the beads Nb,eff Across,bead ) Nb,effπrbead2 ) Aspot. This leads to Nb,eff ) rS2/rbead2 ) (75 µm)2/ (1.42 µm)2 ) 2790. This leads to an upper estimate of the flux from one bead Ωbead ) Ω/Nb,eff ) 1.1 × 10-16 mol s-1 ) 6.9 × 107 molecules s-1 and participating bead. A comparison between the maximum number of GDH molecules per beads in our experiment (2.8 × 106) and the upper limit of the flux per bead indicate that nearly all the immobilized GDH on the outer beads effectively contributes to the flux of [Fe(CN)6]4-. This is in accordance with the saturation kinetics under the condition of the very high c*[Fe(CN)6]3-. It should also be noticed that the assumption of (55) Saito, Y. Rev. Polarogr. 1968, 15, 177.

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uniform flux over the bead spot is likely to be very approximate because the microspots are mound-shaped and the buried beads in the center of the mound will also contribute to the flux although to a lesser extent than the beads at the outer surface simply because of diffusional shielding by the presence of the other beads. Further studies are on the way to verify or more accurately determine the estimated numbers (enzymes per bead, shielding effects of the beads to each other, etc.). CONCLUSION A classic quinoprotein, glucose dehydrogenase immobilized on the surface of magnetic microbeads, was studied by SECM. On the bead’s surface, immobilized GDH catalyzes the oxidation of D-glucose to D-glucoselactone by a number of one- and twoelectron mediator oxidants. The catalytic activity of the immobilized enzyme was imaged using four different electron mediators. Among them, p-aminophenol showed the highest sensitivity. GDH kinetics were studied by using the theories developed for SECM feedback mode and GC mode. The complementing advantages/disadvantages of both modes could be demonstrated. The apparent turnover number was found to be lower than that of the native enzyme in solution due to the deactivation during the biotinylation and immobilization steps, but still much higher than that of immobilized glucose oxidase. High activity and independence of oxygen make GDH a very promising substitute for glucose oxidase as the recognition element in glucose sensors and as labeling enzyme in chip-based bioassays. Further work is on the way to perform GDH-labeled immunoassays by SECM. ACKNOWLEDGMENT We gratefully thank Prof. A. J. Bard (University of Texas at Austin) for supplying an Excel file for estimation of kinetic parameters of feedback approach curves. Helpful advice and discussions with Oleg Sklyar (University of Oldenburg) are gratefully acknowledged. This research was supported by Deutsche Forschungsgemeinschaft (Wi 1617/1-3). Received for review December 17, 2003. Accepted March 26, 2004. AC035492N