Introduction

Nanostructuration of electrodes seems to play a crucial role in the development of biodevices, such as biosensors and enzymatic fuel cells (EFCs) [1, 2], which are based on a direct electron transfer (DET) communication between the biological material and the electrode [3, 4]. In most cases, redox enzymes immobilized onto “planar” electrodes show slow electron transfer (ET) rate constants between the redox cofactor and the unmodified electrode and very small electrocatalytical currents in the presence of substrate, while gold nanoparticles (AuNPs) offer the possibility to wire the redox protein to the electrode producing a favorable orientation improving so far both the ET rate and the electrocatalytical current [5, 6].

Many papers present effective bioelectrocatalytical processes, where several mono- and multi-cofactor redox enzymes [7], such as cellobiose dehydrogenase [5, 8, 9], horseradish peroxidase, superoxide dismutase, fructose dehydrogenase [10,11,12], blue multicopper oxidases (MCOs) [13, 14], and human sulfite oxidase [15], have been immobilized onto nanostructured electrodes. Despite the large interest in AuNPs, there are only few reports about the influence of the size (e.g., diameter) and shape of the NPs on the enzymatic reactions occurring at the electrodes, sometimes improving the ET rate or changing the mechanism of the bioelectrocatalytic process [16, 17].

Fructose dehydrogenase (FDH, EC 1.1.99.11) from Gluconobacter japonicus has been widely studied to develop biosensors based on mediated electron transfer and DET as well as bioanodes for enzymatic fuel cells (EFCs) [18, 19]. FDH from Gluconobacter japonicus NCBR 3260 is a membrane-bound flavocytochrome oxidoreductase also belonging to the hemoflavoprotein family and is a heterotrimeric membrane-bound enzyme complex with a molecular mass of 146.4 kDa, consisting of three subunits, viz. subunit I (DHFDH), which is the catalytic dehydrogenase domain with a covalently bound flavin adenine dinucleotide (FAD) cofactor, where d-(-)-fructose is involved in a 2H+/2e− oxidation to 5-dehydro-d-(-)-fructose; subunit II (CYTFDH), a cytochrome domain acting as a built-in electron acceptor with three heme c moieties covalently bound to the enzyme scaffold and two of them are involved, one by one, in the electron transfer pathway; and subunit III, which is not involved in the electron transfer but plays a key role for the stability of the enzyme complex [20, 21].

The suggested electron transfer pathway for FDH when it is immobilized on the electrode surface and in the absence of any competing e− acceptors [22] goes initially through the oxidation of d-(-)-fructose to form 5-keto-d-(-)-fructose and involves a net 2e−/2H+ transfer with the reduction of FAD to form FADH2. It then further proceeds with a partial reoxidation of FADH2 to FADH·, through a first internal electron transfer (IET) through two of the three heme c:s contained in subunit II in direct contact with the electrode surface at which these heme c:s are reoxidized. Finally, the reoxidation of FADH· to FAD gives the second internal electron transfer (IET) reaction through the two involved heme c:s, which in turn are reoxidized at the electrode surface [18]. Recently, several researchers managed to demonstrate that the third heme c is not involved in the ET process, due to its distance from the other two heme c:s contained in subunit II, making the latter step of the ET process energetically unfavored [23,24,25]. Therefore, the electrons are directly transferred from the second heme c to the electrode [23, 26].

The DET reaction between FDH and electrodes has been demonstrated in a large number of publications, immobilizing the enzyme on different electrode materials including both polycrystalline gold electrodes [27] as well as on nanomaterials like single- or multi-walled carbon nanotubes [28] and other carbon nanostructures [29,30,31,32] and gold nanoparticles [33] or by exploiting several immobilization approaches such as self-assembling monolayers (SAMs) [34, 35], polymers, and other cross-linking agents [27]. Moreover, also mediated electron transfer (MET) reactions for FDH were exploited to develop various amperometric biosensors [36,37,38,39,40,41,42,43,44,45,46,47,48].

In the last decades, many researchers devoted considerable attention toward the synthesis and the application of AuNPs in several fields of chemistry [49]. Among all kinds of nanomaterials, AuNPs play an important role in making electrode modifications, because of their high surface area-to-volume ratios and high surface energy, which facilitate the immobilization of several kinds of proteins, allowing to act as electron conducting pathways between the prosthetic groups of the enzymes and the electrode surface [49,50,51]. Several methods for synthesis of AuNPs have been reported in the literature considering different reducing agents like citric acid, NaBH4, surfactants, reducing sugars, and polyphenols [52,53,54,55,56]. In our previous paper, we reported on the synthesis of metal nanoparticles (MNPs) using quercetin as reducing and stabilizing agent at room temperature [57]. Besides the classical methods and green chemistry–based methods, also surfactants like dimyristoyl-l-phosphatidyl-dl-glycerol (DMPG), alkyltrimethylammonium bromides, or cetylpyridinium chloride have been widely employed [58, 59]. Usually, MNPs can have several 2D or 3D shapes like triangles, spheres, hexagons, and cubes exhibiting different chemical and physical properties in heterogeneous catalysis [60].

In this paper, graphite electrodes have been modified with triangular (AuNTrs) and spherical gold (AuNSphs) nanoparticles to investigate whether the shape of the NPs can affect both the mass transfer–limited and the kinetically limited currents by using two different methods: a rotating disk electrode (RDE) and an electrode mounted in a wall jet flow-through electrochemical cell attached to a flow system. The differently prepared electrodes were further modified by drop-casting FDH directly on the top of the AuNTrs/G and AuNSphs/G electrodes. Finally, both methods allowed quantifying the influence of the shape of the NPs on the mass transfer–limited current and the heterogeneous electron transfer rate constant (kS).

Experimental

Chemicals

d-(-)-Fructose, sodium acetate (NaAc), spherical gold nanoparticles (AuNSphs, d = 100 nm stabilized in citric acid), HAuCl4, hydrochloric acid (HCl), sodium hydroxide (NaOH), H2SO4, and sodium dodecyl sulfate (SDS) were purchased from Sigma-Aldrich (St. Louis, MO, USA). The phospholipids, 1,2-dimyristoyl-sn-glycero-3-phospho-rac-glycerol sodium salt (DMPG-Na), and phosphatidylcholine (PC) were kindly donated by LIPOID AG (Germany). d-Fructose dehydrogenase from Gluconobacter japonicus (FDH; EC 1.1.99.11) was purified from the culture supernatant of Gluconobacter japonicus NBRC 3260 obtained from the National Institute of Technology and Evaluation (Nishinomiya, Hyogo Pref., Japan), and solubilized in PBS buffer pH 6 (50~500 mM) containing 0.1 mM 2-mercaptoethanol and 0.1% v/v Triton X-100 (volumetric activity measured with potassium ferricyanide at pH 4.5 = 420 ± 30 U mL−1, specific activity = 250 ± 30 U mg−1, protein concentration = 1.7 ± 0.2 mg mL−1) [20]. All solutions were prepared using Milli-Q water (ρ = 18.2 MΩ cm at 25 °C; total organic compounds (TOC) < 10 μg L−1, Millipore, Molsheim, France).

Buffer exchange for spherical gold nanoparticles

Five milliliters of a solution containing spherical gold nanoparticles (AuNSphs, d = 100 nm stabilized in citric acid) was centrifuged by using Zeba™ Spin Desalting Columns, 7K MWCO (Thermo Fisher, Life Technologies Europe BV, Stockholm, Sweden). The AuNSph pellet was washed 5 times with Milli-Q water to eliminate all traces of citric acid and redispersed in a 0.150 M SDS aqueous solution. Finally, the AuNSph suspension was stored at 4 °C.

Synthesis, purification, and characterization of gold nanotriangles

A mixture of phospholipids, namely DMPG-Na/PC, was dispersed in water with a ratio of 1:1 w/w and stirred for 72 h at room temperature. Next, the dispersion was sonicated for 1 min. Next, 250 μL of a 2 mM tetrachloroaurate solution was added to the phospholipid mixture and gently stirred overnight in a water bath at 25 °C. The color change from yellow to dark red indicated the formation of AuNPs.

After the reaction was completed, the nanoparticles were centrifuged for 1 h at 4400 rpm. The supernatant was removed and the particles were redispersed in water. The procedure was performed twice centrifuging for 30 min at 4400 rpm. Further, the solution containing a mixture of gold nanotriangles (AuNTrs) and byproducts (spherical particles) was redispersed in 2 mL of pure water and purified by using a depletion-induced flocculation method. The separation of NPs based on shape and size can be obtained by tuning the surfactant micelle concentration to create an entropic, short-ranged depletion attraction between the NPs, resulting in a preferential aggregation and sedimentation of one kind of nanoparticles, leaving the others in solution [61]. Therefore, the depletion-flocculation separation was performed in the presence of SDS micelles at an optimum concentration of 0.150 M of the final solution. The flocculation was completed overnight, removing the supernatant containing the AuNSphs while the precipitated AuNTrs were washed and resuspended in Milli-Q water.

The purified AuNTrs were characterized by dynamic light scattering (DLS). Measurements were carried out at 25 °C at a fixed angle of 173° (“backscattering detection”) by using a Nano Zetasizer (Zetasizer Nano ZS90, Malvern Instruments Ltd, Malvern, UK) equipped with a He–Ne laser (λ = 633 nm; 4 mW) and a digital autocorrelator. The zeta potential was determined by means of the Nano Zetasizer based on the electrophoresis principle. Micrographs of NPs formed in the phospholipid dispersion were taken with a Hitachi HT7700 transmission electron microscope (TEM) operated at 100 kV (Hitachi Europe GmbH, Düsseldorf, Germany). Transmission and scanning electron microscopy of purified samples were prepared by blotting the NPs on carbon-coated copper grids and visualized by using a TEM detector on a Hitachi Scanning Microscope (SU8030) at 20–30 kV (Hitachi Europe GmbH, Düsseldorf, Germany). UV-Visible-NIR spectra were recorded with a Shimadzu UV-Vis-NIR-3600 Plus spectrophotometer (Kyoto, Japan) with samples contained in a quartz cuvette, operating at a resolution of 1 nm from 300 to 1100 nm.

Electrochemical measurements

Graphite rods (Alfa Aesar GmbH & Co KG, AGKSP grade, ultra “F” purity, and 3.05 mm diameter, Karlsruhe, Germany) were polished on wet emery paper (Turfbak Durite, P1200) and then carefully rinsed with Milli-Q water. The enzyme-modified electrodes were modified respectively with 5 μL of AuNTrs or 5 μL of AuNSphs and left to dry at room temperature. After, 5 μL of a d-fructose dehydrogenase solution was drop-cast and allowed to physically adsorb on the top of the modified graphite rod electrodes, overnight at 4 °C. Cyclic voltammetry (CV) experiments were carried out using an Autolab potentiostat (model PGSTAT30, Metrohm Autolab B.V. Ecochemie, Utrecht, The Netherlands) equipped with GPES, version 4.9. A conventional three-electrode electrochemical cell was used for all experiments performed with an Ag|AgCl (sat. KCl) as reference electrode, a platinum wire as counter electrode, and a modified graphite electrode as working electrode. The rotating disk electrode (RDE) experiments were carried out using a 616A Electrode Rotator (EC&CG Princeton, GammaData Instruments AB, Uppsala, Sweden). All the CV experiments were carried out under temperature control by using the thermostated electrochemical cell (Cat. 6.1418.150, Metrohm AB, Bromma, Sweden) and a cryostatic bath (T ± 0.01 °C, LAUDA RM6, Delran, NJ, USA). Flow through measurements were performed using an analogue potentiostat (Zäta Elektronik, Höör, Sweden) connected with a strip chart recorder (Kipp & Zonen, Utrecht, The Netherlands). The modified graphite electrode, an Ag|AgCl (0.1 M KCl) reference electrode, and a Pt wire counter electrode were fitted into a wall jet cell. The electrochemical system was equipped with a flow system consisting of a peristaltic pump (Gilson, Villier-le-Bel, France) and a six-port valve electrical injector (Rheodyne, Cotati, CA, USA) [62].

Results and discussion

UV-Vis-NIR and TEM characterization of gold nanotriangles

The synthesis of gold nanotriangle (AuNTr) using a phospholipid mixture as a reducing and stabilizing agent in water is relatively simple and reproducible. The mass ratio between the metal precursor and DMPG-Na/PC was kept constant (1:4) during the synthesis at 25 °C. Under such conditions, the solution turns deep red showing two UV-Vis absorption maxima at 523 nm and 870 nm, as reported in Fig. 1a (before purification), characteristic for the formation of spherical small dimension AuNPs and anisotropic NPs, respectively. The AuNTrs were characterized using transmission electron microscopy before (Fig. 1b) and after purification (Fig. 1d). By considering these TEM pictures, a shape yield higher than 95% was demonstrated, resulting in a green color solution due to the concentration of AuNTrs with sizes of about 50 nm and 200 nm after only one sedimentation and re-dispersion step. Consequently, a maximum at about 870 nm is observed in the UV-Vis-NIR spectrum (Fig. 1c, after purification) confirming that highly concentrated AuNTrs are present. Similar results have been observed by Liebig et al. [63] and Scarabelli et al. [64], using AOT and CTAC micelles, respectively, during the purification of AuNTr obtained by different approaches. As expected, the AuNTrs show a negative zeta potential of − 60 mV as a result of the coating with anionic surfactants (data not shown). Furthermore, AuNSphs were also characterized using transmission electron microscopy (TEM) as reported in Fig. S3 (see Electronic Supplementary Material, ESM), showing a good size distribution.

Fig. 1
figure 1

a UV-Vis-NIR spectra before the purification. b TEM picture of AuNTrs before the purification. c UV-Vis-NIR spectra after the purification. d TEM picture of AuNTrs after the purification

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Electrochemical characterization of FDH-modified graphite electrode

CV experiments were performed with modified graphite electrodes in absence and in presence of substrate in order to assess the contribution of the electrode nanostructuration using differently shaped AuNPs (spherical and triangular) on the catalytic current related to the oxidation of d-(-)-fructose to 5-keto-d-(-)-fructose catalyzed by FDH.

Figure 2a shows the CVs for a FDH/G-modified electrode in 50 mM NaAc buffer pH 4.5 in the absence (black curve) and in the presence (red curve) of 1 mM d-(-)-fructose. From these CVs, it is clear that the non-turnover case reveals no apparent electroactivity of FDH, and in the presence of fructose, there is only a slight electrocatalytic wave with an onset potential, EONSET, at − 0.050 V vs. Ag|AgClsat rising up to maximum current of 2.5 μA at 0.2 V vs. Ag|AgClsat. The low catalytic current is probably due to a combination of the low roughness of the electrode surface and the random orientation of the enzyme onto the electrode surface.

Fig. 2
figure 2

CVs performed in 50 mM NaAc buffer pH 4.5 in absence (black curves) and in presence of 1 mM d-(-)-fructose (red curves) for a FDH/G, b FDH/AuNSphs/G, and c FDH/AuNTrs/G at scan rate 5 mV s−1. The measurements were carried out after 20 min N2 degassing and T = 25 °C

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Figure 2b depicts CVs for a FDH/AuNSphs/G-modified electrode in non-turnover conditions (black curve) (50 mM NaAc buffer pH 4.5), showing surprisingly no redox waves related to DET of CYTFDH. However, in turnover conditions (1 mM d-(-)-fructose, red curve), the modified electrode showed a higher electrocatalytical wave compared with FDH/G, starting at EONSET = − 0.070 V vs. Ag|AgClsat rising up to 7.6 μA at 0.2 V vs. Ag|AgClsat. In this case, the increase in the electrocatalytical wave is probably due to the enhanced real surface area of the modified electrode, which allows a higher enzyme loading. Nevertheless, it should be taken into account also the SDS layer onto the nanoparticles, which surprisingly creates a favorable environment for the immobilization of FDH.

Finally, Fig. 2c shows the CVs for the FDH/AuNTrs/G-modified electrode in 50 mM NaAc buffer pH 4.5; however, also here, there are no evident redox waves for the DET reaction of CYTFDH. The CV in the presence of substrate (red curve) showed the highest electrocatalytical current compared with the others with an EONSET starting at − 0.103 V vs. Ag|AgClsat rising up to 22.5 μA at 0.2 V vs. Ag|AgClsat. The result is probably ascribable to the efficient packing of AuNTrs onto the electrode surface, which would sensibly enhance the enzyme loading and also the ET rate constant.

Since both kinds of spherical and triangular NPs were covered with a layer of SDS creating an unexpected favorable immobilization environment, we considered a possible influence of the shape of the NPs on the catalytic current caused by FDH [65]. In particular, Compton and his co-workers published a paper reporting on the diffusion-limited currents to NPs of various shapes supported on an electrode by means of a mathematical simulation on spherical and hemispherical shapes [66]. For this reason, we believe that the different behaviors between the FDH/AuNSphs/G and FDH/AuNTrs/G could be explained by the influence of the shape of the NPs on the limiting kinetic current part of the catalytic current. Therefore, in the section below, we reveal the results of our investigation of the influence of the shape of the NPs on the diffusion-limited current related to the catalytic oxidation of d-(-)-fructose by using two different approaches: the rotating disk electrode (RDE) and flow through amperometric wall jet cell [67,68,69].

The dependence of mass transfer–limited current on the shape of the NPs: rotating disk electrode and flow through amperometric wall jet cell studies

The reaction of FDH with fructose starts with the oxidation of d-(-)-fructose to form 5-keto-d-(-)-fructose, which corresponds to the 2e−/2H+ reduction of FAD to FADH2 followed by the first internal electron transfer through two cyt c moieties (one heme c is not involved at all) contained in subunit II for the partial regeneration of FADH· in its semi-oxidized state and the delivery of the 1st e−, as reported below (Eqs. (1–4)):

$$ \mathrm{D}-\left(-\right)-\mathrm{fructose}+\mathrm{FAD}\to 5-\mathrm{keto}-\mathrm{D}-\left(-\right)-\mathrm{fructose}+{\mathrm{FADH}}_2 $$
(1)
$$ {\mathrm{FADH}}_2+\mathrm{cyt}{c}_1-{\mathrm{Fe}}^{3+}\to {\mathrm{FADH}}^{\cdotp }+\mathrm{cyt}{c}_1-{\mathrm{Fe}}^{2+} $$
(2)
$$ \mathrm{cyt}{c}_1-{\mathrm{Fe}}^{2+}+\mathrm{cyt}{c}_2-{\mathrm{Fe}}^{3+}\to \mathrm{cyt}{c}_1-{\mathrm{Fe}}^{3+}+\mathrm{cyt}{c}_2-{\mathrm{Fe}}^{2+} $$
(3)
$$ \mathrm{cyt}{c}_2-{\mathrm{Fe}}^{2+}\to \mathrm{cyt}{c}_2-{\mathrm{Fe}}^{3+}+{\mathrm{e}}^{-} $$
(4)

In the last step, equation (4), cyt c2-Fe2+ is re-oxidised to cyt c2-Fe3+ at the electrode surface releasing the 1st e-. The FADH. radical formed in equation (2) is reoxidised to FAD by cyt c1-Fe3+ in equation (5) and the last two steps shown above (equations (3-4)) are repeated a second time for the regeneration of FAD and the protein in its native state, as follows (equations 5-7):

$$ {\mathrm{FADH}}^{\cdotp }+\mathrm{cyt}{c}_1-{\mathrm{Fe}}^{3+}\to \mathrm{FAD}+\mathrm{cyt}{c}_1-{\mathrm{Fe}}^{2+} $$
(5)
$$ \mathrm{cyt}{c}_1-{\mathrm{Fe}}^{2+}+\mathrm{cyt}{c}_2-{\mathrm{Fe}}^{3+}\to \mathrm{cyt}{c}_1-{\mathrm{Fe}}^{3+}+\mathrm{cyt}{c}_2-{\mathrm{Fe}}^{2+} $$
(6)
$$ \mathrm{cyt}{c}_2-{\mathrm{Fe}}^{2+}\to \mathrm{cyt}{c}_2-{\mathrm{Fe}}^{3+}+{\mathrm{e}}^{-} $$
(7)

where equations (6) and (7) are equal to equations (3) and (4), respectively. Equation (7) yields the 2nd e- to the electrode.

The oxidation current for d-(-)-fructose at a FDH-modified electrode can be limited by the mass transfer of d-(-)-fructose to the electrode and/or by the kinetics of the enzymatic reaction. The measured current, I, is a combination of both the mass transfer–limited current, Ilim, the kinetically limited current, Ikin, and the current related to the interfacial electron transfer, IE, according to Eq. (8):

$$ \frac{1}{I}=\frac{1}{I_{\mathrm{lim}}}+\frac{1}{I_{\mathrm{kin}}}+\frac{1}{I_{\mathrm{E}}} $$
(8)

The mass transfer–limited current consists of the current observed when the d-(-)-fructose is consumed by the enzyme reaction much faster than d-(-)-fructose which is transported to the electrode surface. For a rotating disk electrode (RDE), the mass transfer–limited current depends on the angular velocity (ω) and the bulk concentration of d-(-)-fructose (c*) according to the Levich equation [70], as follows in Eq. (9a):

$$ {I_{\mathrm{lim}}}^{\mathrm{planar}}=0.620 nFc\ast {D}^{2/3}{A}_{\mathrm{geo}}{v}^{-1/6}\ {\omega}^{1/2} $$
(9a)

where n and F have their usual meanings, D is the diffusion coefficient for d-(-)-fructose (7 × 10−6 cm2 s−1 [71]), A is the geometrical area of the electrode (0.073 cm2), and v is the kinematic viscosity of water (0.01 cm2 s−1).

Moreover, the mass transfer–limited current was evaluated also by using flow-through amperometry in a wall jet cell, for which the equation derived by Yamada and Matsuda can be applied (Eq. (9b)) [72]:

$$ {I_{\mathrm{lim}}}^{\mathrm{planar}}=0.898 nFc\ast {D}^{2/3}{A_{\mathrm{geo}}}^{3/8}{v}^{-5/12}{V}^{3/4}{a}^{-1/2} $$
(9b)

where V is the volumetric flow rate and a is the radius of the capillary nozzle.

In this regard, we assumed that the AuNTr and the AuNSphs have a different self-packing pattern onto the electrode surface resulting in a different real surface area [73]. This can be determined by scanning the electrodes in H2SO4 and integrating the area under the wave for formation of gold oxide (data not shown). The real surface area (Areal) resulted to be 4.6 ± 0.3 cm2 and 1.1 ± 0.2 cm2 for the AuNTr and the AuNSph modified electrodes, respectively. After this theoretical consideration, both Eqs. (9a) and (9b) were re-formulated as follows:

$$ \frac{I_{\mathrm{lim}}^{\mathrm{real}}}{I_{\mathrm{lim}}^{\mathrm{planar}}}=\frac{0.620 nF{c}^{\ast }{D}^{2/3}{A}_{\mathrm{real}}{v}^{-1/6}{\omega}^{1/2}}{0.620 nF{c}^{\ast }{D}^{2/3}{A}_{\mathrm{geo}}{v}^{-1/6}{\omega}^{1/2}} $$
(10a)
$$ \frac{I_{\mathrm{lim}}^{\mathrm{real}}}{I_{\mathrm{lim}}^{\mathrm{planar}}}=\frac{0.898 nF{c}^{\ast }{D}^{2/3}{A}_{\mathrm{real}}^{3/8}{v}^{-5/12}{V}^{3/4}{a}^{-1/2}}{0.898 nF{c}^{\ast }{D}^{2/3}{A}_{\mathrm{geo}}^{3/8}{v}^{-5/12}{V}^{3/4}{a}^{-1/2}} $$
(10b)

where n, F, c*, D, v, V, a, and ω have their usual meanings while Areal/Ageo is the roughness factor calculated for the two different modified electrodes.

Rotating linear sweep voltammograms (RLSVs) for all the modified electrodes (viz. FDH/G, FDH/AuNSphs/G, and FDH/AuNTrs/G), obtained in presence of 1 mM d-(-)-fructose, are reported in Fig. 3a–c. As can be seen in Fig. 3, d-(-)-fructose oxidation at all modified electrodes resulted in a mass transfer–limited reaction (highly dependent from rotation speed). For a more deeper evaluation of the limiting steps of the performance of the RDE, the currents measured at different rotation speeds were as usually plotted in Koutecky-Levich coordinates (1/1 vs. ω−1/2) [74]. The d-(-)-fructose oxidation currents obtained with one FDH/G, FDH/AuNTrs/G, and FDH/AuNSphs/G at different [d-(-)-fructose] and ω are presented as Koutecky-Levich plots in Fig. 4a–c, for FDH/G, FDH/AuNTrs/G, and FDH/AuNSphs/G, respectively. Nevertheless, we applied the following Koutecky-Levich equation (Eq. (11)):

$$ \frac{1}{I}=\frac{1}{0.620 nF{c}^{\ast }{D}^{2/3}\left({A}_{\mathrm{geo}}\right){v}^{-1/6}{\omega}^{1/2}}+\frac{1}{nF\left(\raisebox{1ex}{${A}_{\mathrm{real}}$}\!\left/ \!\raisebox{-1ex}{${A}_{\mathrm{geo}}$}\right.\right)\Gamma {k}_{\mathrm{cat}}{c}^{\ast }}+\frac{1}{nF\left(\raisebox{1ex}{${A}_{\mathrm{real}}$}\!\left/ \!\raisebox{-1ex}{${A}_{\mathrm{geo}}$}\right.\right)\Gamma \left({k}_{s1}+{k}_{s2}\right)} $$
(11)
Fig. 3
figure 3

LSVs performed in 50 mM NaAc buffer pH 4.5 in presence of 1 mM d-(-)-fructose at different rotation speeds from 0 rpm to 2500 rpm. a FDH/G, b FDH/AuNSphs/G, and c FDH/AuNTrs/G at scan rate 5 mV s−1. The measurements were carried out after 20 min N2 degassing and T = 25 °C

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Fig. 4
figure 4

Koutecky-Levich plots in 50 mM NaAc buffer pH 4.5 in presence of 0.1 mM (purple), 0.5 mM (blue), 0.75 mM (red), and 1 mM d-(-)-fructose at different rotation speed from 0 rpm to 2500 rpm for a FDH/G, b FDH/AuNSphs/G, and c FDH/AuNTrs/G at scan rate 5 mV s−1. The measurements were carried out after 20 min N2 degassing and T = 25 °C. The current values were detected at E = + 0.4 V vs. Ag|AgClsat

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It can be seen that the electrode current depends on the ω (which is the criterion for diffusion limitation in the bioelectrocatalytic oxidation of d-(-)-fructose) in the range 50–400 μM. However, the data obtained for the FDH/G were fitted according to Eq. (10a) considering the graph 1/1lim vs. [d-(-)-fructose] (data not shown), while the data for FDH/AuNTrs/G and FDH/AuNSphs/G well fitted (Eq. (10a)) taking into account the same graph. In this graph, it should be considered that the slope is proportional to the number of electrons transferred per molecule of d-(-)-fructose oxidized at the modified electrode, which was found to be 1.86 ± 0.02 for FDH/G, 1.93 ± 0.14 for FDH/AuNSphs/G, and 1.89 ± 0.20 for FDH/AuNTrs/G, values actually close to the theoretical value of 2, while kcat (s−1) can be calculated from the intercept. The mass transfer–limited currents were also evaluated by considering Eq. (10b) valid for flow-through setup obtaining similar results. The equivalent Koutecky-Levich plots obtained by the flow-through setup for FDH/G, FDH/AuNSphs/G, and FDH/AuNTrs/G, respectively, are reported in Figs. 5a–c. These results were in great agreement with those reported for RDE as confirmed from the correlation factor R2 = 0.98, as shown in the correlation graph reported in Fig. 5d.

Fig. 5
figure 5

Corresponding plots for the wall jet system performed in 50 mM NaAc buffer pH 4.5 in presence of 0.1 mM (purple), 0.5 mM (blue), 0.75 mM (red), and 1 mM d-(-)-fructose at different flow rates from 0.05 to 2 mL/min for a FDH/G, b FDH/AuNSphs/G, and c FDH/AuNTrs/G. The measurements were carried out by applying E = + 0.4 V vs. Ag|AgClsat. d Correlation plot between the slopes determined for RDE and FIA data obtained for FDH/AuNTrs/G

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The dependence of kinetically limited current on the nanoparticle shape: rotating disk electrode and flow through amperometry studies

Before discussing the data on the kinetically limited current, we should consider the equation for the kinetically limited current, as follows (Eq. (12)):

$$ \frac{1}{I_{\mathrm{kin}}}+\frac{1}{I_{\mathrm{E}}}=\frac{1}{nFA\Gamma}\frac{1}{\left({k}_{\mathrm{cat}}{c}^{\ast }+{k}_{s1}+{k}_{s2}\right)} $$
(12)

The equation above, Eq. (12), is valid for the FDH/G electrode, while for FDH/AuNTrs/G and FDH/AuNSphs/G, a contribution on the enhancement of the electrode area should be considered; therefore, Eq. (12) can be rearranged as follows (Eq. (13)):

$$ \frac{1}{I_{\mathrm{kin}}}+\frac{1}{I_{\mathrm{E}}}=\frac{1}{nF\left(\raisebox{1ex}{${A}_{\mathrm{real}}$}\!\left/ \!\raisebox{-1ex}{${A}_{\mathrm{geo}}$}\right.\right)\Gamma}\frac{1}{\left({k}_{\mathrm{cat}}{c}^{\ast }+{k}_{s1}+{k}_{s2}\right)} $$
(13)

At this stage, we need to further approximate the system in order to determine the catalytic constant, kcat, and the heterogeneous electron transfer rate constant, kSt, considering that the internal electron transfer is not the rate-limiting step in the overall electron transfer mechanism [75]. Thus, we would consider reactions (1), (5), and (9) in order to deeply evaluate the effect of shape of the nanoparticles on kcat and kSt. Finally, Eq. (13) was rearranged as follows (Eq. (14)):

$$ \frac{1}{I_{\mathrm{kin}}}+\frac{1}{I_{\mathrm{E}}}=\frac{1}{nF\left(\raisebox{1ex}{${A}_{\mathrm{real}}$}\!\left/ \!\raisebox{-1ex}{${A}_{\mathrm{geo}}$}\right.\right)\Gamma}\frac{1}{\left({k}_{\mathrm{cat}}{c}^{\ast }+{k}_{\mathrm{St}}\right)} $$
(14)

At limiting step, by considering 1/IE = 0. The experimental conditions at which 1/IE = 0 are low substrate concentration (C), rotation speed (ω) of the electrode, and applying sufficiently large an electrochemical driving force |E-E0′|. In this way, it was possible to increase the influence of the Levich and the enzymatic component in Eqs. (8) and (14); therefore, the kinetics contribution (1/IE) would be negligible (1/IE = 0). Therefore, we can simplify Eq. (14) as follows (Eq. (15)):

$$ \frac{1}{I_{\mathrm{kin}}}=\frac{1}{nF\left(\raisebox{1ex}{${A}_{\mathrm{real}}$}\!\left/ \!\raisebox{-1ex}{${A}_{\mathrm{geo}}$}\right.\right)\Gamma}\frac{1}{k_{\mathrm{cat}}{c}^{\ast }} $$
(15)

Kinetically limited currents of the oxidation of d-(-)-fructose can be evaluated from the intercepts of the Koutecky-Levich plots. According to the mathematical expression for Ikin (Eq. (14)), the slope of this plot is proportional to the rate of the reaction between d-(-)-fructose and FDH (constant kcat in reaction (1)), while the intercept is proportional to the heterogeneous electron transfer (constant kSt in reactions (2–4) and (5–7)) between reduced FDH and the graphite modified surface (AuNTrs and AuNSphs). To evaluate the rates of these reactions, the surface concentration of FDH on the graphite modified electrode must be known. The theoretical surface coverage resulted in 0.80 nmol cm−2 was considered in this paper for all the modified electrodes, namely FDH/G, FDH/AuNSphs/G, and FDH/AuNTrs/G. Therefore, it was possible to estimate k1, the kinetic constant for reaction (1), and the heterogeneous electron transfer (constant kSt in reactions (2–4) and (5–7)). The results calculated for FDH/G, FDH/AuNSphs/G, and FDH/AuNTrs/G are summarized in Table 1. From these results, it is possible to see that the shape of the NPs had no effect on the catalytic constant (kcat), while the kSt for FDH/AuNTrs/G calculated as 3.8 ± 0.3 s−1 resulted in a 5 times higher value compared with both the NPless graphite electrode 0.7 ± 0.1 s−1 and the AuNSphs/G modified electrode 0.9 ± 0.1 s−1. These results are probably related to the shape of the NPs because the AuNTrs due to their triangular geometry have different self-packing mechanism compared with the spherical ones ensuring a higher real surface area. Nevertheless, it should be taken into account also the interaction between the enzyme molecules and the NPs highlighting that the interaction enzyme-NPs can occur on the edge of the triangle while the spherical shape is limiting the number of enzyme molecules interacting with each NP.

Table 1 Kinetic parameters calculated from the RDE data for FDH/G, FDH/AuNSphs/G, and FDH/AuNTrs/G. n is equal to the number of electrons participating in the reaction
Full size table

As further investigations, we studied also the storage and operational stability of the proposed modified electrodes, namely FDH/G, FDH/AuNSphs/G, and FDH/AuNTrs/G, and the results are reported in Fig. S2A and B (see ESM), showing quite a stable signal for 24 h of continuous injections of substrate into the flow system, while in the storage stability test, it was possible to observe a significant drop in the retained current values of approximately 65% for FDH/AuNTrs/G, 72% for FDH/AuNSphs/G, and 70% for FDH/G (compared with the initial current value) achieved after 20 days.

Conclusions

Finally, we have unequivocally demonstrated that the shape of the NPs had a crucial effect on the catalytic current related to the oxidation of d-(-)-fructose to 5-keto-d-(-)-fructose occurring at the FDH-modified electrode surface. In particular, we have shown that AuNTrs have a higher effect compared with the spherical one. The effect was deeply investigated for each contribution to the total catalytic current (I), namely mass transfer–limited current (Ilim), and kinetically limited current (Ikin), by using two different approaches: RDE and flow through amperometry. The shape of the NPs had no effect on the catalytic constant (kcat), while the kSt for FDH/AuNTrs/G resulted in a 5 times higher value compared with both the NPless graphite electrode and the AuNSphs/G modified electrode. These results can probably be ascribed to the shape because with the triangular NPs, the interaction enzyme-NPs can occur on the edge of the triangle, whereas for the spherical shape, the number of enzyme molecules interacting with NPs is limited. These findings would be of fundamental interest to study the kinetic mechanism of FDH and to develop highly efficient 3rd-generation biosensors and EFC bioanode based on metal NPs of various sizes [17] and shapes.