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Enhanced Direct Electron Transfer of Fructose Dehydrogenase Rationally Immobilized on 2-Amino Anthracene Diazonium Cation Grafted Single-Walled Carbon Nanotube Based Electrode Paolo Bollella, Yuya Hibino, Kenji Kano, Lo Gorton, and Riccarda Antiochia ACS Catal., Just Accepted Manuscript • DOI: 10.1021/acscatal.8b02729 • Publication Date (Web): 27 Sep 2018 Downloaded from http://pubs.acs.org on September 27, 2018
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ACS Catalysis
Enhanced Direct Electron Transfer of Fructose Dehydrogenase Rationally Immobilized on 2-Amino Anthracene Diazonium Cation Grafted Single-Walled Carbon Nanotube Based Electrode Paolo Bollella§,*, Yuya Hibino†, Kenji Kano†, Lo Gorton‡, Riccarda Antiochia§ §
Department of Chemistry and Drug Technologies, Sapienza University of Rome P.le Aldo Moro 5, 00185 – Rome, Italy ‡
Department of Analytical Chemistry/Biochemistry, Lund University, P.O. Box 124, 221 00 – Lund, Sweden
†
Division of Applied Life Sciences, Graduate School of Agriculture, Kyoto University, Sakyo – Kyoto 606-8502, Japan
ABSTRACT: In this paper, an efficient direct electron transfer (DET) reaction was achieved between fructose dehydrogenase (FDH) and a glassy carbon electrode (GCE) where anthracene modified single walled carbon nanotubes were deposited. The SWCNTs were in situ activated with a diazonium salt synthesized through the reaction of 2-amino anthracene with NaNO2 in acidic media (0.5 M HCl) for 5 min at 0 °C. After the in situ reaction, the 2-amino anthracene diazonium salt was electrodeposited by running cyclic voltammograms from +1000 mV to -1000 mV . The anthracene-SWCNT modified GCE was further incubated in an FDH solution allowing enzyme adsorbtion. Cyclic voltammograms of the FDH modified electrode revealed two couple of redox waves possibly ascribed to the heme c1 and heme c3 of the cytochrome domain. In the presence of 10 mM fructose two catalytic waves could clearly be seen and were correlated with two heme c:s (heme c1 and c2), with a maximum current density of 485±21 µA cm-2 at 0.4 V at a sweep rate of 10 mVs-1. In contrast, for the plain SWCNT modified GCE only one catalytic wave and one couple of redox waves were observed. Adsorbing FDH directly onto a GCE showed no non-turn over electrochemistry of FDH and in the presence of fructose only a slight catalytic effect could be seen. These differences can be explained by considering the hydrophobic pocket close to heme c1, heme c2 and heme c3 of the cytochrome domain at which the anthracenyl aromatic structure could interact through π-π interactions with the aromatic side chains of the amino acids present in the hydrophobic pocket of FDH.
KEYWORDS fructose dehydrogenase (FDH), 2-aminoanthracene (2-ANT), diazonium coupling, hydrophobic pocket, single-walled carbon nanotubes (SWCNTs)
INTRODUCTION Recently, the direct electron transfer (DET) mechanism of several redox proteins has been widely investigated in order to gain fundamental bioelectrochemical knowledge but also to develop DET based biosensors and enzymatic fuel cells (EFCs) .1-8 DET reactions have been observed both for smaller electron transfer redox proteins9 such as cytochrome c10, azurin11, ferredoxin, as well as for a whole range of the larger more complex redox enzymes of great relevance in recent studies of biosensors and biofuel cells, e.g., hydrogenases12-14 cellobiose dehydrogenase,15-17 multi-copper oxidases,18-20 peroxidases,21-23 fructose dehydrogenase (FDH)24-28, alcohol PQQ dehydrogenase29-33, sulfite oxidase34-35 etc. Nevertheless, several strategies to improve DET such as deglycosylation36-41 or bioengineering of redox enzymes42-43 and electrode nanostructuration44-45 by using both carbon or metal nanomaterials (e.g. carbon nanotubes, graphene, metal nanoparticles, highly porous gold etc.).46-50 Among the carbon nanomaterials, single-walled carbon nanotubes (SWCNTs) exhibit a cylindrical shepe with a diameter in the nanometer range.
51
Their peculiar properties (e.g. high conductance,
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tensile strength etc.)have attracted great attention for the development of electronic devices.52 Moreover, several methods have been developed for their synthesis and functionalization.
53
However, the nanotubes functionalization will affect the charge delocalization offering different possibilities for proteins/molecules tethering.
54-55
(e.g., SWCNTs can be functionalized by using
EDC-NHS covalent coupling, glutaraldehyde or other cross-linkers, or chemical modification with aryl diazonium salts etc.).56-58 The electrochemical reductive adsorption of aryl diazonium salts onto carbon nanotubes has been widely usedfor the development of new electrode platforms for biosensors and EFCs.59-62 The aryl diazonium salts electroreduction can be performed either in acetonitrile or aqueous acid solutions (pH < 2).63 The aryl diazonium salts electroreduction can be obtained by using cyclic voltammetry.64 This approach to nanostructure the electrode surface has been exploited by Armstrong and coworkers, where 2-anthracenecarboxylic acid was electrodeposited onto a multi-walled carbon nanotube (MWCNT) modified electrode surface to orient laccase from Trametes versicolor through the π-π interaction between the anthracenyl groups available onto the electrode surface and the aromatic groups present in the hydrophobic pocket of the enzyme, greatly facilitating an enhanced DET reaction without enzyme activity loss as well as increasing the long-term stability of the laccase modified electrode.65 This approach has been widely used in the last 10 years to obtain high potential cathodes for EFCs.66-70 In this work we consider a functional group able to access the hydrophobic region of FDH in a similar way as was used for multi-copper oxidases and thus realizing an ‘electric plug’ to achieve a faster DET, useful for biosensors and EFCs development.71 Recently,Gluconobacter japonicus FDH (EC 1.1.99.11) is a membrane-bound flavocytochrome oxidoreductase, whichhas been widely employed to develop DET and MET based electrode platforms.25,
72-75
Gluconobacter japonicus FDH is a heterotrimerer consisting
a catalytic
dehydrogenase domain, DHFDH (subunit I), where D-(-)-fructose oxidationoccurs at flavin cofactor (FAD), then followed by internal electron transfer (IET) to the cytochrome domain ( CYTFDH, subunit II)
29
which contains three heme c moieties coordinated by the enzyme scaffold25, 76; and a
subunit III not involved in the ET process77-78
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Figure 1. Enzymatic sequence of the subunit II (CYTFDH) and interaction with the anthracenyl moieties onto the electrode. (Red marks and green marks for cysteine and methionine, respectively, residues that coordinate the heme c:s and hydrophobic motif underlined).
In this paper, we aim at obtaining an efficient DET reaction pathway between FDH and a SWCNTs/GCE further modified through diazonium coupling of an aromatic compound. In particular, we have electrodeposited anthracene onto SWCNTs through electroreduction of 2aminoanthracene diazonium (2-ANT) by using cyclic voltammetry from +1000 mV to -1000 mV at 100 mV s-1, according to the electrochemical reduction mechanism reported in Figure S1. Next the electrode was further modified through drop-casting an FDH solution onto the electrode surface allowing the interaction between the aromatic anthracenyl groups available onto the electrode surface and the hydrophobic pocket within the enzyme, as shown by the enzymatic sequence reported in Figure 1 (Red marks and green marks for cysteine and methionine, respectively, residues that coordinate the heme c:s and hydrophobic motif underlined). This region is located on subunit II of FDH leading to the improvement of the DET reaction of the enzyme probably shortening the distance between the prosthetic groups (i.e., heme), deeply buried, and the electrode surface.78 The redox potential of each heme was carefully determined both by cyclic and square wave voltammetry in order to establish which of the hemes was highly exposed toward the electrode surface with this modification. Finally, the kinetics and analytical properties of 2ANT/SWCNTs/GC have been thoroughly investigated to prove the advantages of using this electrode platform both as 3rd generation biosensor and EFCs bioanode. ACS Paragon Plus Environment
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EXPERIMENTAL SECTION Reagents and apparatus. 2-aminoanthracene (2-ANT), sodium nitrite (NaNO2), hydrochloric acid (HCl), D-(-)-fructose, sodium acetate (NaAc), sodium hydroxide (NaOH), single-walled carbon nanotubes (SWCNTs) were obtained from Sigma Aldrich (St. Louis, MO, USA). Gluconobacter japonicus FDH (EC 1.1.99.11) was extracted, purified and solubilized in 50 mM PBS buffer pH 6 containing 0.1 mM 2-mercaptoethanol and 0.1% v/v Triton X-100. The enzymatic volumetric activity resulted to be 420±30 U mL−1 at pH 4.5 evaluated by using ferricyanide.75 The working solutions have been prepared by using Milli-Q water (R = 18.2 MΩ cm at 25 °C; TOC < 10 µg L−1, Millipore, Molsheim, France). Cyclic voltammetry (CV) experiments were performed by using an Autolab potentiostat (model PGSTAT30, Metrohm Autolab B.V. Ecochemie, Utrecht, The Netherlands) equipped with GPES, version 4.9. The experiments were carried out using a
three-electrode electrochemical cell
equipped with an Ag|AgCl (sat. KCl) as reference electrode, a Pt wire as counter electrode and a modified GCE as working electrode. All potential values reported in this work are referred to Ag|AgClsat (E= + 199 mV vs. standard hydrogen electrode (SHE))Square wave voltammetry (SWV) experiments were carried out using a PalmSens potentiostat (model Emstat2, Palm Instruments BV, Utrecht, The Netherlands) equipped with PSTrace, version 4.5. All measurements were performed under temperature control by using a thermostat (T ± 0.01 ºC, LAUDA RM6, Delran, NJ, USA). The rotating disk electrode (RDE) experiments were carried out using a 616A Electrode Rotator (EC&CG Princeton, GammaData Instruments AB, Uppsala, Sweden). The amperometric experiments were performed by using a flow-injection setup equipped with a peristaltic pump (Gilson, Villier-le-Bel, France), a six-port valve electrical injector (Rheodyne, Cotati, CA, USA) and a 50 µl-loop mounted onto the injector. The potential was applied by using an analogicpotentiostat (Zäta Elektronik, Höör, Sweden) equipped with a strip chart recorder (Kipp & Zonen, Utrecht, The Netherlands) for signal recording. The enzyme-modified electrode, the reference and counter electrode were placed into a wall-jet cell.79
Electrode Modification. Glassy carbon electrodes (GCEs) (Bioanalytical Systems Inc., West Lafayette, IN, USA, Ø=3 mm; Ageometric=0.073 cm2) were polished with aqueous alumina (Al2O3) slurry (Struers, Copenhagen, Denmark), ultra-sonicated and dried under N2 stream. FDH/GC electrode – 3 µL of an FDH solution were drop-cast onto the electrode surface. FDH/2-ANT/GC electrode – GCE was immersed into an ice cold 1 mM solution of 2aminoanthracene (2-ANT) diazonium cation in situ generated, purged with argon for 20 min to ACS Paragon Plus Environment
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achieve anaerobicity. After, the aryl diazonium cation was electrochemically reduced by scanning the potential between +1000 mV and – 1000 mV at 100 mV s-1 for two cycles. Finally, the electrode was thoroughly rinsed with Milli-Q water, dried under a stream of N2 and 3 µL of FDH solution were drop-cast onto the modified electrode surface.80 FDH/SWCNTs/GC electrode - 3 µL of an SWCNTs aqueous suspension (30 mg mL-1), previously ultra-sonicated for 1 week, was drop-cast onto the electrodes and allowed to dry at room temperature. Thus, 3 µL of an FDH solution were drop-cast onto the electrode surface. FDH/2-ANT/SWCNTs/GC electrode - 3 µL of an SWCNTs aqueous suspension (30 mg mL-1), previously ultra-sonicated for 1 week, was drop-cast onto the electrodes and allowed to dry at room temperature. The modified electrode was further immersed into a 2-aminoanthracene (2-ANT) diazonium cation solution and electrochemically reduced as above. After rinsing, 3 µL of an FDH solution were drop-cast onto the electrode surface.80 The in situ-generated 2-aminoanthracene diazonium cation solution was prepared by mixing a 0.5 mM HCl:ethanol (50 % v/v) solution containing 1 mM 2-aminoanthracene and 5 mM NaNO2 for 5 min, under stirring.
Circular dichroism (CD) measurements. Secondary structure modifications occurring at FDH immobilized onto a bare indium tin oxide (ITO) electrode (cat. CEC007, Präzisions Glas & Optik GmbH, Iserlohn, Germany) and modified with 2-amino-anthracene diazonium salt, were investigated by performing CD measurements using a CD spectrometer (J-815 Circular Dichroic Spectrometer, JASCO, Easton, MD, USA). These measurements were performed by placing the modified electrodes into a 1 cm cuvette containing 50 mM NaAc buffer at pH 4.5.
RESULTS AND DISCUSSION Electrochemical reduction of in-situ generated 2-aminoanthracene diazonium cation. GCE and SWCNT/GCEs were grafted with in-situ generated 2-aminoanthracene diazonium cations as described above in order to access directly the hydrophobic region of FDH located in the subunit II close to the heme c moieties and to enhance the DET reaction of FDH occurring at the electrode surface (reported in the reaction scheme shown in Figure S1). After the preliminary in-situ generation of the 2-aminoanthracene diazonium cations, the electrochemical reduction was performed by scanning the potential between +1000 mV and – 1000 mV at 100 mV s-1 for two cycles as outlined in Figures S2A and B (see Supporting Information), on a GCE and a SWCNT/GCE, respectively.
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Figures S2A and B present CVs showing the electroreduction of the 2-aminoanthracene diazonium salt on a GCE and a SWCNT/GCE, respectively. In the first case, the CV showed one wave in the first scan (black curve) with a potential close to -0.090 V , which partially disappeared in the second scan (red curve), meaning that the GCE surface was partially covered by 2-aminoanthracene diazonium salt. In the latter case, the CV showed two waves in the first scan (black curve) with a potential close to +0.280 V and +0.010 V , which can be ascribed to the amino groups of unreacted 2-amino-anthracene molecules and the reduction of 2-amino-anthracene diazonium salt, respectively. The peak for the reduction of 2-amino-anthracene diazonium salt disappeared in the second scan (red curve), meaning that the SWCNT/GCE surface was fully covered by the 2aminoanthracene diazonium salt. Moreover, in the second scan (red curve) two couple of redox peaks are still visible with formal potentials close to +0.395 V and 0.230 V , which can be ascribed to the amino groups of 2-amino-anthracene and the diazonium groups of the non-grafted 2-aminoanthracene diazonium salt. This aryl amine provides a hydrophobic moiety to get access into the hydrophobic region of FDH.
Cyclic Voltammetric Characterization of GC Modified Electrodes. To investigate the role of the anthracenyl groups on the catalytic current density, several CV experiments have been performed in the absence (50 mM NaAc buffer at pH 4.5, non-turnover condition) and in the presence of 10 mM D-(-)-fructose
as substrate (turnover condition). In several papers, it has been proven that the
orientation of the enzyme is a key issue to obtain an efficient DET reaction, especially considering the access to a particular part of the enzyme, e.g., a hydrophobic region due to its structure giving a correct immobilization strategy beneficial both for the development of biosensors and EFCs.65-67 Figure 2A shows the CV for FDH/GC modified electrode in non-turnover conditions (), where it was not possible to observe any redox wave related to a DET reaction of any heme c probably due to FDH molecules randomly oriented onto the electrode surface and the low roughness of GCE not allowing a high enzyme loading.In turnover conditions, the FDH/GC modified electrode showed a slight electrocatalytic wave starting at -0.058 V rising up to 18 µA cm-2 at 0.4 V , as shown in Figure 2B. Afterwards, the GCE was modified through electrodeposition of the 2-aminoanthracene diazonium cation in order to highlight the effect of the anthracenyl group on the orientation of FDH. The CV of the FDH/2-ANT/GCE in non-turnover conditions is depicted in Figure 2C, showing a couple of redox waves with a formal potential of E0’= -0.002 V and another wave in the forward scan at a potential of E= +0.140 , values close to those for heme c1 (E=-0.010 V) and heme c3 (E0’= +0.150 V ), respectively, as reported in the literature76. The results are ascribable to the interaction between
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the anthracenyl groups exposed on the electrode surface and the hydrophobic region of FDH located on the subunit II of the enzyme. Moreover, when the modified electrode was tested in the presence of the substrate it unexpectedly showed a low electrocatalytic wave starting at = + 0.028 V rising up to 13.3 µA cm-2 at 0.4 V , as shown in Figure 2D. Despite the great results obtained in non-turnover conditions for FDH/2-ANT/GCE, the electrocatalytic wave showed lower current density values compared to that of the FDH/GCE probably because there might be some denaturation process occurring to FDH due to the strong interaction between the enzyme and the anthracenyl groups or no space for the substrate to approach the catalytic site due to compact arrangement of the enzyme on the smooth electrode. The denaturation process was demonstrated by using the circular dichroism experiments to verify possible changes occurring at the secondary structure of the enzyme immobilized on different modified electrodes. As shown in Figure S3, it was possible to observe a CD signal for a random coiled secondary structure when immobilized onto an unmodified electrode (black line), while for an anthracenyl modified electrode it was not possible to observe any clear CD signal (red line), meaning a clear denaturation process has occurred certainly due to the strong interaction between the enzyme and the electrode on a smooth electrode. In order to enhance the roughness of the electrode surface, the following experiments have been performed modifying the GCEs with SWCNTs. Figure 3A shows the CV for an FDH/SWCNT/GCE in non-turnover conditions , where it is possible to observe a couple of redox waves with a formal potential of E°’= +0.142 V close to the E°’ of heme c3 (E°’= +0.150 V )76. This result is ascribable to the random orientation of FDH onto the electrode surface and to the position of heme c3, which is probably close to the edge of the enzyme. After the addition of 10 mM D-(-)-fructose,
the FDH/SWCNT/GCE showed a great electrocatalytical wave starting at -0.052 V
rising up to 223 µA cm-2 at 0.4 V , as shown in Figure 3A. The great electrocatalytical wave is probably due to the high enzyme loading directly related with the enhanced roughness of the electrode surface achieved with the deposition of the SWCNTs. From these results it is possible to observe that a couple of redox peaks is visible in both curves (absence and presence of substrate), therefore the heme c3 seems not to be involved in the electron transfer process during the catalysis of D-(-)-fructose oxidation, as also reported in the literature 81-82. Finally, the CV of an FDH/2-ANT/SWCNT/GCE in 50 mM NaAc at pH 4.5 is depicted in Figure 3B, showing two couples of redox waves with E°’= -0.006 V and of E°’= +0.169 V , respectively. In both cases, the E°’ values of the redox waves are in agreement with the E°’ of heme c1 (E=-0.010 V ) and heme c3 (E0’= +0.150 V )76. Afterwards, the modified electrode was tested in the presence of substrate, showing a larger electrocatalytical wave compared to that of the SWCNT/GCE starting
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at = -0.095 V rising up to 485 µA cm-2 at 0.4 V , as shown in Figure 3B. In the overall electrocatalytic wave, it is possible to clearly see that it is divided into three parts: i) the first sigmoidal catalytic wave starting in correspondence to heme c1 of FDH (-0.1 V to +0.050 V ), ii) the second sigmoidal catalytic wave starting in correspondence to heme c2 of FDH not visible in the non-turnover signal (+0.050 V to +0.250 V ) and iii) the mass-transfer limited current due to the limited diffusion of the substrate to the electrode (+0.250 V to +0.550 V ) 83-85. This result could be explained with the enhanced roughness of the electrode surface improving the enzyme loading and the correct orientation of FDH due to the interaction between the anthracenyl group and the hydrophobic part of subunit II. In particular, the interaction occurs between the aromatic rings of the anthracenyl group and the aromatic rings available on the side chain of the amino acids present into the hydrophobic portion of subunit II (π-π interaction).86 The effect of the scan rate of the CVs was investigated for the non-turnover DET reaction of the immobilized FDH at the SWCNT/GCE and 2-ANT/SWCNT/GCE. The CVs at different scan rates for these electrodes are reported in Figures 4A and B, respectively. It is possible to see that the anodic and cathodic peak current densities were linearly dependent on the scan rate in the range between 2 and 100 mV s−1, shown in the insets of both Figures 4A and B, indicating a surface confined electrochemical process. The apparent heterogeneous electron transfer rate constants (ks) has been calculated by considering the peak current for heme c3 for FDH/SWCNT/GCE (Figure 5A), and both peak currents for heme c1 and c3 for FDH/2-ANT/SWCNT/GCE (Figure 5B).87 The α values were found to be 0.43 for the SWCNT/GCE, 0.60 (heme c1) and 0.37 (heme c3) for the 2-ANT/SWCNT/GCE. Thereafter, the ks values have been calculated using Laviron's equation (equation (1)) and resulted in 2.5±0.1 s−1 for the SWCNT/GCE, and 3.7±0.3 s−1 (heme c1) and 4.2±0.6 s−1 (heme c3) for the 2ANT/SWCNT/GCE (ν between 2 and 100 mV s−1):
log = log 1 − + 1 − log − 1 −
∆ .
(1)
where all symbols have their usual meanings (F=96.495 C mol−1; T=298 K; R=8.31 J mol−1 K−1).87 By considering the redox peaks of heme c:s depicted in Figure 5A for the SWCNT/GCE and in Figure 5B for the 2-ANT/SWCNT/GCE, it was possible to calculate the enzyme surface coverage using the following equation (equation (2))88 : =
υ Γ
(2)
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Where all symbols have their usual meanings. Γ was evaluated to be 19.4±0.7 nmol cm-2 and 9.1±0.3 nmol cm-2 for the FDH/SWCNT/GCE and the FDH/2-ANT/SWCNT/GCE, respectively. Despite the lower amount of FDH immobilized onto the 2-ANT/SWCNT/GCE, this electrode showed a better performance in terms of electron transfer rate, which resulted in a twice higher value compared to that of the SWCNT/GCE. This result could be ascribed to a correct orientation of the FDH molecules on the 2-ANT/SWCNT/GCE compared to the random orientation of FDH on the SWCNT/GCE, achieved through the interaction between the anthracenyl groups immobilized onto the electrode surface and the aromatic groups present in the hydrophobic portion of subunit II of FDH.
Rotating disk electrode characterization of GC modified electrodes. To elucidate the mechanism of the electrocatalytical current caused by D-(-)-fructose oxidation occurring at the SWCNT/GCE and 2-ANT/SWCNT/GCE modified electrodes, the rotating disc electrode (RDE) approach was used. The currents were obtained using different rotation speeds from 0 to 2500 rpm (Figures 5A and B) and different D-(-)-fructose concentrations (Figures 5C, D and E). The linear sweep voltammograms (LSVs) for FDH/SWCNT/GCE electrode reported in Figure 5A showed a certain mass-transfer limitation, which can be reduced by increasing the rotation speed, resulting in higher limiting currents. Conversely, the LSV for FDH/2-ANT/SWCNT/GCE reported in Figure 5B (black line) displayed not a clear electrocatalytical wave for heme c1 and a clear mass-transfer limitated current for the second electrocatalytical signal at a potential more positive than 0.25 V (rotation speed: 0 rpm). The mass-transfer limitation is strongly reduced by increasing the rotation speed of the RDE showing higher limiting currents for both electrocatalytical signals. The enzymatic electrocatalytic current (Iel) can be described as the combination of three independent contributions, namely the mass-transfer limited current, Ilim, the kinetically limited current, Ikin, and IE, the current related to the interfacial electron transfer between the modified electrodes (SWCNT/GCE and 2-ANT/SWCNT/GCE) according to equation (4):
!"#
=!
#
%$+!
&$'
+!
(4)
"#
The first term is related to the diffusion of the substrate from the bulk solution and the enzyme modified electrode. This term can be determined by studying the rotation speed dependence of the current, which can be described the Levich equation (equation (5)) for a diffusion-controlled process:
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Ilim = 0.620nFc*D2/3Av-1/6 ω1/2
(5)
where n and F have their usual meanings, c* is the concentration of the D-(-)-fructose solution, D is the diffusion coefficient for D-(-)-fructose (7 × 10-6 cm2 s-1
89
), A is the geometrical area of the
electrode (0.0706 cm2), and v is the kinematic viscosity of the electrolyte (1.8 ·10-2 cm2 s-1), and ω is the rotation rate per minute (rpm)., Koutecky-Levich plots were used for the evaluation of the limiting steps (1/Ilim vs. ω-1/2) 90. From the slope of this graph it is possible to calculate the number of electrons transferred during the oxidation of D-(-)-fructose, and from the intercept it is possible to calculate kcat (s-1). The second contribution, which is related to the catalytical properties, can be calculated by exploiting the electrochemical form of the Michaelis-Menten equation (equation (6)):
() =
*Γ(+,- . ∗
(6)
. ∗ 012
Where n, F and A have their usual meaning, kcat is the turnover number for D-(-)-fructose oxidation (s-1) and KM is the Michaelis-Menten constant (mM). The third term can be described by the Butler-Volmer equation (equation (7), for first order reactions at a potential distant from the formal potential E0’):
IE = nFAΓks
(7)
Where ks is the heterogeneous electron transfer rate constant, which has been determined in the previous section for FDH/SWCNT/GCE and FDH/2-ANT/SWCNT/GCE by using the Laviron’s method. For the FDH/SWCNT/GCE modified electrode, by combining equations (4-7) it was possible to obtain a satisfying model that describes the variation of 1/Iel with ω-1/2 for different concentrations of D-(-)-fructose (equation (8)):
!"#
= 3.4356 7∗
8 /: ;
