Electrical Communication between Electrodes and Enzymes Mediated

Anal. Chem. 1996, 68, 4186-4193

Electrical Communication between Electrodes and Enzymes Mediated by Redox Hydrogels E. J. Calvo*,† and R. Etchenique

INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabello´ n 2, Ciudad Universitaria, AR-1428 Buenos Aires, Argentina C. Danilowicz and L. Diaz†

Facultad de Farmacia y Bioquimica, Universidad de Buenos Aires, Junin 956, AR-1113 Buenos Aires, Argentina

Different redox polymers based on poly(allylamine) with covalently attached ferrocene and pyridine groups that coordinate iron and ruthenium complexes were prepared, and hydrogels were obtained by cross-linking them with epichlorohydrin. Charge propagation from the underlying electrode, through the redox polymer and electrical communication with the enzyme FADH2 of glucose oxidase, was studied by cyclic voltammetry and electrochemical impedance spectroscopy. The effects of electrolyte composition, concentration of enzyme and substrate, and electrode potential are reported. The role of different redox mediators covalently attached to the polymer backbone is discussed in terms of driving force and electrostatic barriers. Amperometric biosensors have been developed by using different strategies.1 Soluble redox mediators were inadequate for long-term stability devices. An alternative approach involved the use of high molecular weight mediators. In this way, polymeric mediators can effect electron transfer between an enzyme and an electrode with the subsequent decrease of mediator loss. An interesting attempt was the use of conductive polymers such as polypyrrole functionalized with ferrocene moieties.2 The monomer, ferrocene-modified pyrrole, was electropolymerized onto the electrode, and the enzyme was entrapped within the resulting film. It was possible to measure the catalytic current due to glucose oxidation as well as to demonstrate the regeneration of reduced ferrocene attached to the polymer by the entrapped enzyme in an excess of glucose. However, this design leads to unstable electrodes. Another approach for increasing mediators’ molecular weights was the covalent attachment of redox species to enzymes with successful results.3-5 Nevertheless, this case implied the entrapment of the modified enzyme by using semipermeable membranes. † Permanent Research Staff of CONICET (Argentina). (1) Bartlett, P. N.; Tebbutt, P.; Whitaker, R. G. Prog. React. Kinet. 1991, 16, 55-155. (2) Foulds, N. C.; Lowe, C. R. Anal. Chem. 1988, 60, 2473. (3) Degani, Y.; Heller, A. J. Am. Chem. Soc. 1988, 110, 2615. (4) Bartlett, P. N.; Bradford, V. Q.; Whitaker, R. G. Talanta 1991, 38, 57. (5) Badia, A.; Carlini, R.; Fernandez, A.; Battaglini, F.; Mikkelsen, S. R.; English, A. M. J. Am. Chem. Soc. 1993, 115, 7053.

4186 Analytical Chemistry, Vol. 68, No. 23, December 1, 1996

More recently, experiments employing redox polymers have proved to be very promising. These polymers represent a “bridge” between the electrode and the enzyme’s redox site. Three essential effects are involved when measuring the resulting signal: (i) electrical connection between the redox polymer and the electrode, (ii) charge propagation through the polymer, and (iii) connection between redox sites in the polymer and the enzymatic active site. The initial results were obtained with modified electrodes using quinone polymers.6 Polysiloxanes7-9 and other polyquinones10 also proved to be effective for redox mediation. However, in these cases redox polymers were soluble only in organic media, which required introduction of the polymer and the enzyme in two separate steps. Skotheim et al. reported that polysiloxanes with covalently bound ferrocenes with highly flexible chains were effective to prove mediation with GOx.9 The authors showed that the catalytic response depended on the average spacing between redox sites and the length of the alkyl side chains containing the active redox group. Heller introduced a different fruitful strategy by working with soluble redox hydrogels.11 The enzyme was initially immobilized in a two-dimensional structure through electrostatic complexation on the electrode.12 Increased currents could be estimated to be obtained in three-dimensional structures.13 A strong interaction between enzyme and redox polymer was achieved by electrostatic association of both components, and 3D biosensors involved covalent cross-linking with bifunctional reagents.14 This allowed large current densities to be obtained in the presence of freely diffusing substrate under anaerobic conditions. (6) Cenas, N. K.; Pocius, A. K.; Kulys, J. J. Bioelectrochem. Bioeng. 1983, 11, 61. (7) Hale, P. D.; Inagaki, T.; Karan, H. J.; Okamoto, Y.; Skotheim, T. A. J. Am. Chem. Soc. 1989, 111, 3482. (8) Hale, P. D.; Lee, H. S.; Okamoto, Y. Anal. Lett. 1993, 26, 1. (9) Hale, P. D.; Bogulavsky, L.i.; Skotheim, T. A.; Liu, L. F.; Lee, H. S.; Karam, H.J.; Lan, H. L.; Okamoto, Y. In Biosensors and Chemical Sensors; Edelman, P. G., Wang, J., Eds.; ACS Symposium Series 487; American Chemical Society: Washington, DC, 1992; p 111. (10) Kaku, T.; Karan, H. J.; Okamoto, Y. Anal. Chem. 1994, 66, 1231. (11) Heller, A. Acc. Chem. Res. 1990, 23, 128. (12) Degani, Y.; Heller, A. J. Am. Chem. Soc. 1989, 111, 2357. (13) Heller, A. J. Phys. Chem. 1992, 96, 3579. (14) Gregg, B.; Heller, A. J. Phys. Chem. 1991, 95, 5975. S0003-2700(96)00170-9 CCC: $12.00

© 1996 American Chemical Society

Most of the work was carried out with glucose oxidase (GOx) and poly(vinylpyridine)osmium,15,16 as well as with other enzymes,17,18 and more recently with osmium poly(vinylimidazole).19,20 A different alternative was proposed by Oyama et al. for the entrapment of a redox enzyme in a thermoshrinkable redox polymer.21 In this case, a cold aqueous solution of polymer and enzyme is placed on the electrode, and the resulting mixture becomes insoluble for temperatures higher than the phase separation temperature (∼25 °C). Willner et al. achieved electrical communication for various layers of GOx when developing organized networks on a selfassembled monolayer of functionalized thiols on gold electrodes.22 Enzyme electrodes in a self-assembled monolayer configuration have also proved to be effective for NAD(P)+-dependent enzymes.23 The aim of the present work is to report the application of a polycationic hydrogel24 derivatized with different redox couples in amperometric biosensors. The behavior of such electrodes is analyzed in terms of the mechanisms of charge propagation and enzyme catalysis. EXPERIMENTAL SECTION Materials. Ferrocene- and pyridinecarboxyaldehydes (Aldrich), high molecular weight poly(allylamine) hydrochloride (Aldrich), and sodium borohydride (Riedel-de-Hae¨n) were used as received. Glucose oxidase (GOx, EC 1.1.3.4 type VII-S from Aspergillus niger, 186 kDa) with activity 277 IU mg-1 (Sigma Chemical Co.) was used. [Ru(NH3)5Cl]Cl2 was prepared from RuCl3 according to the procedure described in ref 25. [Fe(CN)5NH3]Na3 was prepared according to ref 26. Glucose and 2-deoxyglucose solutions were prepared from a stock solution equilibrated in the anomers, and kinetics herein refer to the total glucose concentration. Doubly distilled water was further purified from a Milli-Q reagent water system (Millipore). Synthesis of Ferrocene-Allylamine Polymer. Ferrocenecarboxaldehyde was dissolved in methanol and added dropwise within an hour to a methanolic solution of poly(allylamine). Poly(allylamine) was previously dissolved in a slight excess of triethylamine. The mixture was stirred for another hour at room temperature, and sodium borohydride was carefully added in portions at O °C. Stirring continued for 1 h; finally, methanol was removed in vacuum, and the residue was extracted with diethyl ether several times. The aqueous solution was further purified by membrane dialysis (Sigma) against water, and water was further removed by freeze drying. (15) Gregg, B.; Heller, A. Anal. Chem. 1990, 62, 258. (16) Pishko, M. V.; Michael, A. C.; Heller, A. Anal. Chem. 1991, 63, 2268. (17) Katakis, Y.; Heller, A. Anal. Chem. 1992, 64, 1008. (18) Ye, L.; Hammerle, M.; Olsthoorn, A. J. J.; Schuhmann, W.; Schimdt, H. L.; Duine, J. A.; Heller, A. Anal. Chem. 1993, 65, 238. (19) Ohara, T. J.; Rajagolapan, R.; Heller, A. Anal. Chem. 1993, 65, 3512. (20) Ohara, T. J.; Rajagolapan, R.; Heller, A. Anal. Chem. 1994, 66, 2451. (21) Tatsuma, T.; Saito, K.; Oyama, N. Anal. Chem. 1994, 66, 1002. (22) Willner, I.; Riklin, A.; Shoham, B.; Rivenzon, D.; Katz, E. Adv. Mater. 1993, 5, 912. (23) Willner, I.; Riklin, A. Anal. Chem. 1994, 66, 1535. (24) Calvo, E. J.; Danilowicz,C.; Diaz, L. J. Electroanal. Chem. 1994, 369, 279. (25) Chang, J. P.; Fung, E. Y.; Curtis, J. C. Inorg. Chem. 1986, 25, 4233. (26) Kenney, D. J.; Flynn, T. P.; Gallini, J. B. J. Inorg. Nucl. Chem. 1961, 20, 75.

XPS studies of the ferrocene-allylamine polymer revealed a N/Fe ratio of 10.5 as compared to ferrocene nitrile, used as reference, which yielded 0.93 under similar conditions. Atomic absorption analysis of iron in the polymer confirmed the ratio 1:10 of ferrocene modified to unmodified monomeric units. Synthesis of Pyridine-Allylamine Polymer. Pyridinecarboxaldehyde was dissolved in methanol and then poured into a methanolic solution of poly(allylamine). The reaction was allowed to proceed at room temperature, and after an hour, reduction by sodium borohydride was achieved under conditions similar to those used for the ferrocene polymer. After removal of methanol, the solid residue was further washed with diethyl ether. Finally, the aqueous solution of the modified polymer was purified by membrane dialysis, and water was removed by freeze drying. 1HNMR from the pyridine-modified polymer shows, after integration of the respective signals, 50% of covalent attached pyridine comparing the aromatic protons to the aliphatic signals. Preparation of Hydrogel-Modified Electrodes. Glassy carbon electrodes were chemically modified with the soluble ferrocene-poly(allylamine) polymer or poly(allylamine)-pyridine polymer as follows: 5 mL of a 1-4% solution of the polymer was mixed with an equal amount of 0.4-2% GOx solution in 10 mM Tris buffer (Sigma) of pH 9. The cross-linking agent, epichlorohydrin (1 mL), was finally added, and the mixture was left for 48 h at room temperature. Admittance analysis of EQCM data at 10 MHz has shown that the sol-gel process by which the hydrogel is formed takes more than 15 h for the viscous resistance to increase to half its final value. Coordination of Metal Centers to Polymer Pyridines. In both cases, the electrodes were initially modified with 5 mL aliquots of 3-10% pyridine-poly(allylamine) polymer mixed with an equal aliquot of 0.5% GOx solution in 20 mM Tris buffer (pH 9) and finally cross-linked with 1 mL of epichlorohydrin. The mixture was left to react for 48 h at room temperature. For the ruthenium complex, the modified electrodes were immersed in a 10 mM [Ru(NH3)5Cl](CF3COO)2 solution of pH 4.9 in contact with amalgamated Zn and were kept under argon for 90 min. For coordination of the pentacyanoiron complex, the modified electrodes were immersed in a 10 mM solution of [Fe(CN)5NH3]Na3 for 10 min and then thoroughly washed. The coordinated ammonium in the iron complex is relatively labile and undergoes aquation to yield the aquopentacyanoferrate(II) anion, which generates the pentacyanoferrate(II) pyridine complex in the presence of modified poly(allylamine) by ligand exchange. Electrodes with 25 and 125 mmol dm-3 GOx are reported below, with the total enzyme concentration referred to the total volume of precursor solution. The thickness of the hydrogel membrane is affected by swelling changes upon oxidationreduction; however, RDE experiments27 allowed us to estimate a thickness of ∼10 µm. Furthermore, using Heller’s estimation20 of hydrogel thickness based on a density of 1 g cm-3 and the total mass of material deposited onto the electrode, a dry thickness close to 5 µm could be evaluated. Oxygen removal from the working solutions was achieved by purging with nitrogen. Electrochemical experiments were described elsewhere;24 electrodes of 0.2 cm2 were employed. All (27) Battaglini, F.; Calvo, E. J. J. Chem Soc., Faraday Trans. 1994, 90, 987.

Analytical Chemistry, Vol. 68, No. 23, December 1, 1996

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Scheme 1. Scheme of Reactions

Table 1. Data Obtained with Cyclic Voltammetry

potentials in this paper are quoted with respect to the saturated calomel electrode (SCE). redox couple

RESULTS Poly(allylamine) (PAA) was modified according to two different procedures: ferrocene was covalently attached to the polymer, purified, and further cross-linked on the electrodes, while ruthenium and iron pentacyano complexes were introduced directly to polymer-modified electrodes. In this latter case, pyridine was previously attached to poly(allylamine), and this polymer was cross-linked on the electrode surfaces (see Scheme 1). Figures 1-3 show the cyclic voltammograms of electrodes modified with hydrogels of ferrocene, [Ru(NH3)5py]2+/3+, and [Fe(CN)5py]2-/3-, respectively, with similar redox charge and enzyme load (see Table 1). Figures 1 and 2 also depict the catalytic waves for the oxidation of glucose catalyzed by GOx immobilized in the gels. The sigmoidal oxidation waves centered at the respective E1/2 (0.350 V for ferrocene and 0.033 V for 4188 Analytical Chemistry, Vol. 68, No. 23, December 1, 1996

FcCH2NH-R Ru(NH3)5py3+/2+ -R Fe(CN)5py3-/2- -R

E1/2 Ep - Ep/2 (mV) (mV) 350 33 214

59(67) 57 71

Qa (µC)

Γ (nmol cm-2)

13-62 0.7-3.3 90-105 4.5-5.5 30-96 1.5-5.0

cDe1/2 × 1010 b (mol cm-2 s-1/2) 3-7 5 1.3-2

a Integration at low sweep rate. b Randles-Sevcik equation. c Values in parentheses after prolonged oxidation-reduction cycles.

ruthenium complex) prove effective mediation by the redox centers attached to the polymer backbones.24 It should be noted that, for iron pentacyano complex attached to the PAA polymer, there is no enzyme catalysis, in spite of the oxidation-reduction potential of this redox couple in the polymer (0.25 V). However, addition of ferrocene ammonium monosulfonate as soluble mediator to the solution in contact with the iron pentacyano polymer proved that the enzyme was active toward glucose oxidation.

Figure 1. Catalytic wave for the oxidation of glucose in 20 mM phosphate buffer of pH 7 and 0.10 M KNO3 at redox polymer-GOxmodified electrodes. CV of (a,solid line) 0.93 mC ferrocene-redox polymer-GOx (25 µM)-coated electrode in glucose-free electrolyte and (b, dashed line) 0.10 M glucose. v ) 0.005 V s-1.

Figure 2. (a, dotted line) CV of 0.10 mC [Ru(NH3)5Py]3+/2+redox polymer-GOx (25 µM) in 0.10 M KNO3. (b, dashed line) Catalytic wave for the oxidation of 0.10 M glucose in the same solution. v ) 0.005 V s-1.

Figure 3. CV of 0.39 mC [Fe(CN)5]2-/3- redox polymer-GOx (25 µM) in 0.10 M KNO3 and 20 mM phosphate buffer of pH 7: (a) 0.05, (b) 0.10, and (c) 0.20 V s-1.

Note in Figures 1-3 that current never reaches zero at the extremes of the potential scans; therefore, the redox polymers are never fully oxidized nor fully reduced at any measured sweep rate. When propagation of charge in the polymer has a diffusion-

Figure 4. Cyclic voltammetry of 1 mM NH4[FeCp2SO3] in pH 7.0 buffer at poly(allylamine)-GOx-epichlorohydrin-modified glassy carbon electrode at different sweep rates (bottom to top): (a) 0.01, (b) 0.02, (c) 0.05, (d) 0.10, and (e) 0.20 V s-1.

type behavior, the extent of polymer oxidation or reduction will depend on sweep rate. Cyclic voltammetry in background electrolyte shows linear ip vs v1/2 plots for all three hydrogels, which indicates propagation of charge in the volume of the polymer network by a diffusionlike process (De, electron diffusion coefficient), such as electron hopping between neighboring redox sites or counterion motion. Figure 4 shows cyclic voltammograms of a glassy carbon electrode modified with poly(allylamine), GOx, and epichlorohydrin under analogous conditions but containing no fixed redox groups, in contact with 1 mM ferrocene ammonium monosulfonate solution. Typical curves of soluble redox species are apparent, with a diffusion coefficient of 8 × 10-7 cm2 s-1 calculated from linear ip vs v1/2 plots.28 This value is 20% the value of the diffusion coefficient in aqueous solution. Similar results have been obtained for other hydrogels, such as BSA cross-linked with GOx and glutaraldehyde, with a value of 2.4 × 10-6 cm2 s-1 for ferrocene monosulfonate.27 Diffusion of counterions inside the film to compensate charge when the hydrogel is oxidized or reduced has been ruled out as the rate-determining step of charge propagation, since redox anions in the external electrolyte can easily diffuse through the hydrogel and their electrochemistry can be recorded. Table 1 shows values of cDe1/2 (c is the volume concentration of redox sites) in the range of 10-10 mol cm-2 s-1/2, calculated with the Randles-Sevcik equation for semiinfinite diffusion in a reversible system. Electron transfer under diffusion control suggests for these polymers charge propagation beyond the first layer, which for ferrocene and ruthenium polymers implies a threedimensional wired enzyme. For a reversible redox reaction, Ep - Ep/2 should be 56.5/n mV at 25 °C, and E1/2 can be calculated as Ep/2 + 28/n mV at 25 °C.28 In the present case, the ruthenium complex follows a Nernstian behavior, and the other couples were considered almost reversible for E1/2 calculation. Table 1 summarizes the data obtained from cyclic voltammetry in 0.1 M KNO3 solution. The values of the formal reversible potentials of the redox systems covalently attached to the hydrogels can be compared (28) Bard, A. J.; Faulkner, L. R. Electrochemical Methods. Fundamentals and Applications; John Wiley & Sons: New York, 1980; Chapter 5.


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to the respective formal potentials of the soluble redox couples: FcCH2NH2, 0.36 V;29 [Ru(NH3)5Py]3+/2+, 0.05 V,30 and [Fe(CN)5Py]3+/2+, 0.25 V.31 Polymer microenvironment effects are likely to modify the free energy of the redox sites in these hydrogels. The formal potentials of redox couples in the ferrocene-bound polymer shift with the logarithm of anion activity in the range 0.1-1 M, with a slope lower than the value predicted by a Nernst equation for anion permselectivity, RT/F. Exchange of water upon redox switching the PAA-Fc polymer has also been detected by EQCM.32 According to Oyama et al.33 and Hillman et al.,34 the above evidences suggest that the redox change in the PAA hydrogels can be described by Fcf + t+C+ f + t+Af + t-As + mH2Os S + Fc+ (1) f + Af + t+Cs + mH2Of + e

where subindexes f and s indicate species in the film and in solution, respectively, A- is the anion, C+ the cation, and Fc/Fc+ the ferrocene redox couple in the polymer, and t+ and t- are the transport numbers of cations and anions in the hydrogel. The features of cyclic voltammetry of multilayer-modified electrodes are determined by the charge transfer process at the electrode-polymer interface,35 while the subsequent layers propagate charge by a diffusion-like process.36 For the modified electrodes, ∆Ep exceeds the expected value for a reversible redox couple which is likely to arise from the presence of (i) a bulky molecule such as GOx37 and (ii) a highly charged protein. In the absence of GOx, PAA-Fc cross-linked with epichlorohydrin exhibits a symmetrical surface wave with 30 mV peak separation at low sweep rate and linear ip vs v. The rate of charge transfer at the glassy carbon electrodepolymer interface was studied by electrochemical impedance spectroscopy (EIS). Figures 5-7 depict typical Nyquist plots for the three redox polymers in supporting electrolyte and in the presence of 0.1 M glucose in solution at the formal redox potential. In the absence of glucose, the impedance data for the three hydrogels studied can be analyzed by a simple Randles circuit,38 where Warburg impedance is apparent at low frequencies and confirms the semiinfinite diffusion behavior of charge propagation in the polymer, i.e., (Det)1/2 , L, where De is the diffusion coefficient for charge propagation and L the thickness of the hydrogel. This has been confirmed by chronoamperometric transients which show a Cottrell behavior for ferrocene-modified polymer in 0.1 M KNO3. It should be noted that the low-frequency pure capacitive region characteristic of polymer film electrodes39,40 is never reached in the present polymers in the frequency range (29) Cass, A. E. G.; Davis, G.; Francis, G. D.; Hill, H. A. O.; Aston, W. J.; Higgins, I. J.; Plotkin, E. V.; Scott, L. D. L.; Turner, A. P. F. Anal. Chem. 1984, 56, 667. (30) Koval, C. A.; Anson, F. C. Anal. Chem. 1978, 50, 223. (31) Macartney, D. H. Rev. Inorg. Chem. 1988, 9, 104. (32) Calvo, E. J.; Danilowicz, C.; Etchenique, R. J. Chem. Soc., Faraday Trans. 1995, 91 (22), 4083. (33) Oyama, N.; Tatsuma, T.; Takahashi, K. J. Phys. Chem. 1993, 97, 10504. (34) Clarke, A. P.; Vos, J. G.; Glidle, A.; Hillman, A. R. J. Chem. Soc., Faraday Trans. 1993, 89, 1695. (35) Laviron, E. J. Electroanal. Chem. 1979, 100, 263. (36) Majda, M. In Molecular Design of Electrode Surfaces; Murray, R. W., Ed.; J. Wiley & Sons Inc.: New York, 1992; Chapter IV, p 159. (37) Elmgren, M.; Lindquist, S. T.; Sharp, M.; J. Electroanal. Chem. 1993, 362, 227.

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Figure 5. Impedance plane display for GC electrode modified with ferrocene hydrogel (0.10 mC) and GOx (25 µM) in 20 mM phosphate buffer of pH 7 and 0.1 M KNO3-. E ) 0.35 V; modulation voltage, 10 mV; (a) b, in absence of glucose and (b) O, in 0.10 M glucose solution.

Figure 6. Impedance plane display for GC electrode modified with ruthenium hydrogel (0.10 mC) and GOx (25 µM) in 20 mM phosphate buffer of pH 7 and 0.1 M KNO3-. E ) 0.033 V; modulation voltage, 10 mV; (a) 0, in absence of glucose and (b) b, in 0.10 M glucose solution.

investigated (g0.01 Hz). For a Randles circuit, the low-frequency impedance is given by38

Z ) RΩ + Rct + σω-1/2 - j(2σ2C + σω-1/2)

(2)

with j ) -11/2 and ω ) 2πf, with f the ac perturbation frequency, and σ ) RT/n2F2De1/2c. From a plot of Re(Z) or Im(Z) versus ω-1/2, σ could be evaluated, and the quantity cDe1/2 was calculated. Table 2 summarizes the data from EIS in background electrolyte. The uncompensated resistance, RΩ, takes account of the (38) Sluyters, J. H. Rec. Trav. Chim. Pays-Bas 1960, 79, 1092. (39) Armstrong, R. D. J. Electroanal. Chem. 1986, 198, 177. (40) Lang, G.; Bacskai, J.; Inzelt, G. Electrochim. Acta 1993, 38, 773.

Figure 7. Impedance plane display for GC electrode modified with iron pentacyanopyridine hydrogel (0.10 mC) and GOx (25 µM) in 20 mM phosphate buffer of pH 7, 0.1 M KNO3, and 0.10 M glucose solution.

Figure 8. Steady state catalytic currents for substrate oxidation catalized by ferrocene-25 µM GOx hydrogel in 0.1 M KNO3 and 20 mM phosphate buffer, pH 7, for different substrate concentrations: (b) glucose and (O) deoxyglucose; v) 0.002 V s-1. Solid lines show best fit to eq 8 (see text).

Table 2. Data Obtained with Electrochemical Impedance Spectroscopy redox system FcCH2NH2 Ru(NH3)5py3+/2+ Fe(CN)5py2-/3a

RΩ (Ω) 65 14 98

Rct (Ω) 1400 2877 3841

(7600)a

RfO+e

cDe1/2 × 1010 j0 (mA cm-2) (mol cm-2 s-1/2) 0.092 0.045 0.033

(0.017)a

3.2 2.9 1.4

Values in parentheses after prolonged oxidation-reduction cycles.

KS

kcat

7 8 ER - S 98 ER + P EO + S 9

k

redox system

iLim (µA cm-2)

β

FcCH2NH2 Ru(NH3)5py3+/2+ Fe(CN)5py2-/3-

103 38 none

0.69 1.02

resistance of the hydrogel layer and a negligible contribution of the external solution resistance. The charge transfer resistance, Rct, and the exchange current density, j0 ) RT/FRct, account for the rate of charge transfer between the glassy carbon electrode and the first layer of redox polymer and depends on the surface redox concentration, which is determined by the redox concentration of the polymer and the distribution of polymer redox sites on the surface. For ferrocene hydrogel, prolonged oxidation-reduction cycles of the electrode lead to a decrease of redox charge which results in larger Ep - Ep/2 and Rct values and smaller j0, as shown in Tables 1 and 2 in parentheses. This is thought to arise from the unstable ferricenium species, which can undergo nucleophilic attack and decompose. Enzyme Catalysis. The catalytic waves for the anaerobic oxidation of D-β-glucose substrate, S, in Figures 1 and 2 can be described by the enzymatic catalytic cycle. Redox mediation by cosubstrate attached to the polymer backbone, O, and by the enzyme glucose oxidase, GOx, immobilized in the hydrogel can be represented by eqs 3-6:

(4)

with KS ) k1/k-1 and kcat , k-1. Since FADH2/FAD is a two-electron redox center and O/R a one-electron mediator, the oxidation of GOx involves two oneelectron steps according to the global eq 5.

GOx(FADH2) + 2O 98 GOx(FAD) + 2R

Table 3. Enzyme Catalysis Data

(3)

(5)

The concentrations of oxidized and reduced redox sites in the polymer, soluble substrate, and the different forms of enzyme entrapped in the gel layer are described by CO, CR, CS, CEO, CER, and CET, respectively; CT ) CO + CR, and CET is the total enzyme concentration. Electrode reaction 3 takes place at the electrodegel interface with fast kinetics, and a first-order reaction layer at the electrode surface is established rather than reaction throughout the film, since L . (Det)1/2. For charge propagation in the hydrogel under semiinfinite diffusion conditions and reaction 4 under steady state, the catalytic wave can be described by case II of Pratt and Bartlett41 kinetic analysis:

Icat,II )

2FAx2kDeCETCT exp[β(F/RT)(E - E°′)] 1 + exp[β(F/RT)(E - E°′)]

(6)

and ILim ) 2FA(2kDeCET)1/2CT, where E°′ is the formal redox potential of mediator couple in the polymer, β takes into account the interactions between neighboring redox centers,24 and k is the bimolecular enzyme oxidation coefficient. The potential dependence of the catalytic current results from the potential dependence of the surface concentration of O, which follows a modified Nernstian behavior.24 (41) Bartlett, P. N., Pratt, K. F. E. J. Electroanal. Chem. 1995, 397, 61.


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Results for catalytic activity of all hydrogels studied are summarized in Table 3. Note that, as expected from eq 6, the catalytic current increases with the square root of the total enzyme load, CET1/2, as was previously shown for two GOx concentrations in the redox hydrogel with similar redox concentration.24 The dependence of the catalytic current with substrate concentration can be described for these films by case VII of Pratt and Bartlett:41

x

2CTDekcatCET 1 + KS/CS

Icat,VII ) 2FA

(7)

where the maximum catalytic current for excess substrate is Icat,max ) 2FA(2CTDekcatCET)1/2. Figure 8 depicts the catalytic currents for the anaerobic oxidation of glucose and 2-deoxyglucose as a function of substrate concentration for E . E°′. In this case, the rate-determining step is the enzymatic reaction (eq 4) with fast reoxidation of (FADH2)GOx by the redox mediator. Best fits of eq 7 with data in Figure 8 yield icat, max ) 59.5 ( 3.8 µA cm-2 and KS ) 10.9 ( 2.9 mM for glucose and icat,max ) 16.3 ( 1.2 µA and KS ) 15.2 ( 4.5 mM for deoxyglucose. The difference between both substrates results in a ratio of Icat,max of 3.6, in good agreement with (kcat,glucose/ kcat,deoxy)1/2 ) 4.42,43 Nyquist impedance plots in Figures 5 and 6 show that, in excess glucose, a second semicircle is apparent at low frequency instead of the linear Warburg impedance observed in glucosefree solutions. However, for iron pentacyano complex attached to PAA, no difference in the impedance spectra is observed after addition of 0.1 M glucose (Figure 7), as expected from the lack of catalysis found by voltammetry (Figure 3), and only Warburg impedance characteristic of semiinfinite diffusion of electrical charge in the redox hydrogel was observed. In excess glucose, the reaction scheme depicted in eqs 3-5 can be approximated by an EC′ mechanism,44,45 with fast regeneration of the reduced enzyme and the reoxidation of FADH2(GOx) by ferricenium or [Ru(NH3)5 ]3+ the rate-limiting step. If KS/CS + 1 , KO/CO, the EC′ mechanism is given by eq 3, followed by kf

O + Z 98 R + P

(8)

with kf ) 2kcET and cZ ) cET. The differential equation describing the concentration of the oxidized redox mediator in the hydrogel layer of thickness L . (Det)1/2 is44,45

∂CO ∂2C ) DO 2 - kfCO ∂t ∂x

(9)

with the following initial and boundary conditions: (42) Gibson, Q. H.; Swoboda, B. E. P.; Massey, V. J. Biol. Chem. 1964, 239, 3927. (43) Wilson, R.; Turner, A. P. F. Biosens. Bioelectron. 1992, 7, 165. (44) Battaglini, F.; Calvo, E. J. J. Electroanal. Chem. 1990, 280, 443. (45) Bourdillon, C.; Demaille, C.; Moiroux, J.; Saveant, J. M. J. Am. Chem. Soc. 1993, 115, 2.

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For t ) 0,

CO ) 0 for x g 0

For t > 0, At x ) 0,

∆J ) nFDO[∂CO(0,t)/∂x]x)0 cR(0,t) ) 0 and cO(0,t) ) cR*

At x f ∞,

cO(0,t) ) 0

The expression for the Faradaic impedance for a first-order catalytic CE′ mechanism has been derived by Sluyters-Rebach and Sluyters:46

ZF ) Rct +

σ [(ω2 + kf2)1/2 + kf]1/2 (ω2 + kf2)1/2 j[(ω2 + kf′2)1/2 - kf]1/2 (10)

In the absence of enzyme reaction, for kf ) 0, eq 10 simplifies to

ZF ) Rct + σω-1/2(1 - j)

(11)

and Warburg impedance dominates the low-frequency region, as seen in Figures 5-7. The total impedance of the amperometric enzyme electrode under substrate saturation conditions is given by

Z ) RΩ +

1 jωC + 1/ZF

(12)

Equation 12 with ZF given in eq 10 predicts the second semicircle observed in Figure 5 and 6 for glucose-containing solutions as demonstrative of the simulation of eq 12 depicted in Figure 9 for typical values of the diffusion-kinetic parameters obtained in the present work: σ ) 800 Ω cm2 s-1/2, kf ) 0.1 s-1, and De ) 10-9 cm2 s-1. In the absence of catalytic regeneration, low-frequency Warburg behavior is apparent in Figure 9. In this case, not all the polymer film can be oxidized, and therefore the hydrogel behaves like an infinite diffusion medium in the frequency range investigated. In conclusion, the three contributions to electrical transduction at hydrogel-modified electrodes have been separately studied for three redox hydrogels based on poly(allylamine) derivatized with different pendant redox groups, all of them bioencapsulating glucose oxidase with high stability. Electrical connection of the underlying electrode and redox polymer was not hindered, nor was the propagation of charge in the hydrogels by a diffusion-like motion through electron hopping between neighboring redox sites a limiting factor to catalysis. In the absence of enzyme substrate in the external electrolyte, only propagation of charge in the hydrogel by electron hopping between neighboring sites in the polymer is observed for all three redox hydrogels. In the presence of glucose, however, interplay of electron diffusion and reoxidation kinetics of enzymatic FADH2 establishes a steady state catalytic current, and counterions are (46) Sluyters-Rebach, M.; Sluyters, J. H. J. Electroanal. Chem. 1970, 26, 237.

with a higher redox potential than ruthenium, failed to show catalysis due to the strong local repulsive barrier for the formation of FADH2-redox site encounter pair.48 GOx is a highly negatively charged glycoprotein,49 and the redox moiety attached to the polymer backbone must penetrate the funnel leading to the FADH2 redox site buried in the protein structure.50 The electrostatic work to bring the redox mediator at the reaction site can be described by the model of Wherland and Gray,48 with RE and RO the radii of reactants (large GOx and oxidant moiety respectively), r# their sum, κ ) 0.329µ1/2 A-1 (with µ the ionic strength) for water at 25 °C, the dielectric constant of water (78.3 at 25 °C), zO and zE the charge of mediator and enzyme, respectively, and e the unit electrical charge:

W)

Figure 9. Nyquist impedance plane curves simulated with eqs 13 and 11 for C ) 3 × 10-5 F cm-2; RΩ ) 50 Ω, Rct ) 1000 Ω; σ ) 800 Ω cm2 s-1/2; De ) 10-9 cm2 s-1; and kf ) 0 (O) and 0.1 s-1 (b).

expected to be positioned across the hydrogel film.47 This finally results in the oxidation of substrate glucose. The rate of reoxidation, thus, fixes an upper limit for the propagation length of charge by diffusion in the hydrogel with the kinetic length for CS . KS: µ ) (De/2kCET)1/2.27 Higher rates of enzyme catalysis, however, were observed for ferrocene hydrogel than for the ruthenium polymer due to the higher redox potential driving force. Iron pentacyano hydrogel, (47) Surridge, N. A.; Sosnoff, C. S.; Schmehl, R.; Facci, J. S.; Murray, R. W. J. Phys. Chem. 1994, 98, 917. (48) Wherland, S.; Gray, H. B. Proc. Natl. Acad. Sci. U.S.A. 1976, 73, 2950. (49) Frederick, K.; Tung, J.; Emerick, R. S.; Masiarz, F. R.; Chamberlain, S. H.; Vasavada, A.; Rosemberg, S.; Chakraborty, S.; Schopfer, L. M.; Massey, V. J. Biol. Chem. 1990, 265, 3793. (50) Hecht, H. J.; Kalisz, H. M.; Hendle, J.; Schimd, R. D.; Schomburg, D. J. Mol. Biol. 1993, 229, 153.

[

]

e-kRO e-kRE + z z e2e-κr/2r( 1 + kRE 1 + kRO O E

(13)

Equation 13 assumes the protein to be a sphere with a totally symmetric charge distribution, and the electrostatic barrier corresponds to the approximation of the oxidant molecule to the GOx protein, which would result in a very low concentration of reactants at the reaction site, i.e., a fraction e-W/kT. ACKNOWLEDGMENT The authors thank the University of Buenos Aires and Fundacio´n Antorchas (Argentina) for financial support. Also, the supply of iron pentacyanopyridine complex by Dr. F. Cukiernik and fruitful discussions with Dr. F. Battaglini are greatly appreciated. Received for review February 21, 1996. Accepted August 9, 1996.X AC960170N X

Abstract published in Advance ACS Abstracts, October 1, 1996.


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Electrical Communication between Electrodes and Enzymes Mediated

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