Electrochemical quantification of accelerated FADGDH rates in aqueous nanodroplets

Significance

For centuries, scientists have assumed that chemical reactivity in bulk, continuous water is conserved at all levels in nature, from reactions in the ocean to enzymatic digestion in a lysosome. There is growing evidence using mass spectrometry that chemical reaction rates are enhanced by orders of magnitude in micro- and nanodroplets. In this study, we use nanoelectrochemistry to track the enzymatic oxidation of glucose in single attoliter (10⁻¹⁸ L) aqueous nanodroplets, one nanodroplet at a time. When a nanodroplet irreversibly adsorbs onto an ultramicroelectrode surface, the enzymatic reaction can be traced due to the electrochemical regeneration of the enzyme cofactor. We demonstrate the enzymatic reaction rate increases up to 100× for nanodroplets under 1 μm in radius.

Abstract

Enzymes are molecules that catalyze reactions critical to life. These catalysts are often studied in bulk water, where the influence of water volume on reactivity is neglected. Here, we demonstrate rate enhancement of up to two orders of magnitude for enzymes trapped in submicrometer water nanodroplets suspended in 1,2-dichloroethane. When single nanodroplets irreversibly adsorb onto an ultramicroelectrode surface, enzymatic activity is apparent in the amperometric current-time trace if the ultramicroelectrode generates the enzyme cofactor. Nanodroplet volume is easily accessible by integrating the current-time response and using Faraday’s Law. The single nanodroplet technique allows us to plot the enzyme’s activity as a function of nanodroplet size, revealing a strong inverse relationship. Finite element simulations confirm our experimental results and offer insights into parameters influencing single nanodroplet enzymology. These results provide a framework to profoundly influence the understanding of chemical reactivity at the nanoscale.

Chemical reactions in submicrometer water droplets (water nanodroplets) have displayed striking differences from reactions in bulk, continuous water (1, 2). One such difference is enhanced homogeneous reaction rates. In 2011, Cooks and coworkers first reported accelerated bimolecular reactions in microdroplets formed from desorption electrospray ionization mass spectrometry (3). The group has since explored a vast array of accelerated organic reactions in microdroplets (4). Zare and coworkers demonstrated accelerated reactions in microdroplets (5) and ultrafast enzymatic digestion (6). In these reports, mass spectrometry was used to track the progress of a reaction over time. A limitation of electrospray is the generation of droplets of various sizes, prohibiting robust quantification of reaction rates as a function of droplet size. To mitigate this limitation, groups have developed thermal and electromagnetic methods of levitating microliter droplets in conjunction with mass spectrometry analysis for the study of confined reactions (7–9). Methods for quantification of reactivity within single attoliter-nanoliter droplets are still needed to rigorously address nanodroplet reactivity.

Recently, electrochemical techniques have emerged as a robust and sensitive means to study reactivity within single aqueous micro- (10) and nanodroplets (11–14). In these experiments, aqueous nanodroplets suspended in an oil continuous phase irreversibly adsorb onto an ultramicroelectrode surface, where activity can be tracked in real time (15). We have previously used aqueous nanodroplets to track the growth kinetics of a single nanoparticle (16, 17), study the electrocatalysis of small clusters of atoms (18), and observe the electrochemistry of very small numbers of molecules using the radical annihilation amplification strategy (19).

Enzymes are molecules in cells that are responsible for catalyzing reactions necessary for life. Classical studies regarding enzyme catalysis have been performed in bulk water; however, this system may not provide a realistic depiction of enzyme behavior in nature. In a cell, for instance, lysosomes that are ∼100 nm in radius (constituting a volume of attoliter, 10⁻¹⁸ L) concentrate degradative enzymes. Classical enzymology does not consider the effect of nanoconfinement on enzymatic reactivity. Here, we demonstrate enhanced enzyme reactivity as a function of nanodroplet size on a nanodroplet-by-nanodroplet basis. We use a flavin adenine dinucleotide-dependent glucose dehydrogenase enzyme (FADGDH) as a model system. In these experiments, a buffered solution of potassium hexacyanoferrate (II) (ferrocyanide), glucose, and the enzyme is emulsified in 1,2-dichloroethane (DCE) using ultrasonication.

Results and Discussion

Fig. 1A shows a schematic representation of the experiment. When a single aqueous nanodroplet irreversibly adsorbs onto a gold ultramicroelectrode (radius 6.25 µm) biased sufficiently positive to drive the oxidation of ferrocyanide, a current transient indicative of the enzymatic reaction is observed in amperometry. The enzyme will deliver electrons to potassium hexacyanoferrate (III) (ferricyanide) in the presence of glucose. A representative i-t trace is shown in Fig. 1B with an inset to display a general transient. Whereas blips with an exponential decay to baseline are observed for nanodroplets that contain only ferrocyanide [Fig. 1C and SI Appendix, Fig. S1A and previous reports (10)], responses in the presence of enzyme and glucose are more complex: An initial blip is observed, but the current levels off to a new limiting current before returning to baseline. The initial spike can be explained by the rapid turnover of ferrocyanide to ferricyanide at the electrode surface (SI Appendix, Fig. S1). When ferricyanide is electrogenerated, the enzyme will oxidize glucose, reducing ferricyanide back to ferrocyanide and creating a feedback loop. This feedback loop generates a limiting current that is sustained until the available glucose in the nanodroplet is depleted, at which time the transient returns to baseline. More amperometric traces (SI Appendix, Fig. S2) and transient examples (SI Appendix, Fig. S3) are given in the SI Appendix. The new limiting current can be described by the reactivity of the enzyme. Assuming the enzymatic reaction is the rate determining step and the glucose concentration is sufficient to saturate the active site of the enzyme, the new limiting current observed in the transient can be expressed by

$$i_{lim}=q{k}_{turn}n{C}_{enzyme}{V}_{nanodroplet}{N}_A,$$ [1]

where i_lim is the limiting current due to the enzyme turnover, k_turn is the enzymatic turnover rate, q is the elementary charge of an electron, n is the number of electrons transferred during the enzymatic reaction, C_enzyme is the concentration of enzyme, V_nanodroplet is the volume of the nanodroplet, and N_A is Avogadro’s number. Eq. 1 can be easily derived from the Michaelis–Menten equation, and a complete derivation is given in the SI Appendix. The linear dependence of i_lim on V_nanodroplet was also validated by finite element simulations and is given in SI Appendix, Fig. S4. This dependence can be justified if one considers the nanodroplet reaction as surface confined (20). There is an important assumption in this derivation in that the entire volume, V_nanodroplet, must be sampled in a very short amount of time. This assumption is valid because mixing is very fast in nanodroplet environments (vide infra). Using the initial concentration of ferrocyanide and the concentration of glucose that is consumed, the nanodroplet volume can be calculated using Faraday’s Law,

$$V_{nanodroplet}=\frac{Q}{F(n_1{C}_{glucose}+n_2{C}_{ferrocyanide})},$$ [2]

where Q is the integrated charge under the amperometric trace, F is Faraday’s constant, C_glucose is the concentration of glucose (75 mM), n₁ is the number of electrons involved in glucose oxidation (2), C_ferrocyanide is the concentration of ferrocyanide (1 mM), and n₂ is the number of electrons involved in ferrocyanide oxidation (1). The volume of the nanodroplet can be readily used to calculate the diameter/radius, and we found good agreement between the diameter calculated from electrochemical data and dynamic light scattering (DLS) (SI Appendix, Fig. S5). This agreement is evidence that we are observing the enzymatic consumption of glucose within a single aqueous nanodroplet.

Fig. 1.

(A) Schematic illustrating stochastic droplet collisions at the electrode surface, where the blue represents ferrocyanide, yellow illustrates ferricyanide, and pink signifies DCE. (B) Representative trace showing collisions of droplets containing 1 mM ferrocyanide, 0.12 mM FADGDH, and 75 mM glucose. A collision transient was expanded and background-subtracted to show the current and duration of the event. The red dashed line indicates the steady-state current directed by enzymatic reaction. (C) A transient was background-subtracted to show the current and duration of an event arising from the collision of a 10 mM ferrocyanide droplet (no enzymatic catalysis) suspended in 0.5 M tetrabutylammonium perchlorate in DCE. In line with polarographic convention, the anodic current is represented as negative in our plots.

The turnover rate, k_turn, of the FADGDH enzyme in bulk volumes was determined by both electrochemistry and absorbance spectroscopy. Details of these experiments are given in SI Appendix, Fig. S6. For direct comparison to the droplet k_turn values, the bulk k_turn value was determined by absorbance measurements in a bulk solution (250 µL) under the same conditions as the nanodroplet experiments. The k_turn was determined to be 2.25 s⁻¹. This enzyme activity is much lower than reported by the manufacturer and values reproduced in-house (SI Appendix, Fig. S7), suggesting that the oxidative half reaction (dependent on the cofactor) is rate-limiting in this system. Surprisingly, in the nanodroplet experiments, we observed k_turn values ranging from 12 s⁻¹ (droplet radius 2,317 nm) to 265 s⁻¹ (droplet radius 145 nm), suggesting that the turnover rate is enhanced by 5× to over 100× when compared to the bulk values obtained under identical conditions (SI Appendix, Fig. S6 C and D, 2.25 s⁻¹). From our results, the reactivity within an aqueous nanodroplet is always significantly greater than the bulk value. Additional transients are given in the SI Appendix, Fig. S3. These experiments and Eqs. 1 and 2 allow one to rapidly calculate both enzymatic turnover rates and the size of the nanodroplet, respectively. A plot of the limiting current as a function of charge is given in the SI Appendix, Fig. S4C.

From the transients, we can independently measure i_lim and the nanodroplet volume using Eq. 2. Fig. 2 shows the dependence of k_turn on the size of the nanodroplet. There is a clear inverse trend: As the droplet radius gets smaller, the enzymatic activity increases dramatically. While these nanoelectrochemical methods allow one to perform enzymology experiments in a high-throughput manner, there is a striking departure from bulk-determined values that scales inversely with nanodroplet size. The reason for this departure is not completely understood (21). At present, we cannot rule out enzyme anisotropy within the droplet as a contributor to the enhanced kinetics. By fitting current transients in the absence of enzyme with bulk electrolysis theory, we have found that the contact radii are tens of nanometers or smaller. Given the contact radii of the nanodroplets and the radius of the enzyme [∼3.5 nm (22)], we do not expect the enzyme to adsorb significantly to the electrode surface. Even if the enzyme is anisotropically distributed within the droplet, mixing in submicrometer droplets is extremely fast (17). For instance, a small molecule could travel 500 nm in only 0.4 ms (23) and make ∼6,000 round trips by the completion of a 5 s transient (see SI Appendix for further details). Previous reports have indicated the importance of the phase boundary for kinetic amplification (24). Groups have hypothesized that the solvation in such a small volume may enhance activity as well as enzyme orientation at the liquid|liquid phase boundary (25). The interaction of the enzymes with the liquid|liquid interface or the three-phase boundary may influence the observed enhancement and will be the topic of a future investigation.

Fig. 2.

Dependence of k_turn on the radius of the nanodroplet (n = 50). For the bulk measurement, the solution volume is 250 µL, and the plotted k_turn value is 2.25 s⁻¹.

Additionally, a mass transfer argument can be used to indicate that each analyzed transient is the result of a single nanodroplet collision and is not confounded by simultaneous collisions. The concentration of nanodroplets in the continuous phase is low enough such that one would only expect a single nanodroplet to collide within tens to hundreds of seconds (see SI Appendix for complete mass transfer analysis and SI Appendix, Fig. S9 for nanoparticle tracking analysis [NTA] data). Experimental frequencies reported here fell within the range of the expected collision frequency if diffusion is the main source of mass transport to the ultramicroelectrode surface. From these calculations, the probability of more than one nanodroplet colliding simultaneously within the experimental timeframe is low.

While these data indicate an inverse relationship between the k_turn and droplet radius (26), we do not know the cause of variability in k_turn values for droplets that are nearly the same size (for binned data analysis, please see SI Appendix, Fig. S10). We ensure experimental reproducibility through careful analytical technique, use of control experiments, and vigilant choice of baseline for transient integration. The variability may be due to how the nanodroplet wets the electrode surface, the role of the exterior glass surrounding the ultramicroelectrode, and molecular orientation heterogeneities at the water|DCE interface or water|DCE|electrode three-phase boundary.

To validate experimental results, we used COMSOL Multiphysics to model the current transients. This model considers flux within the aqueous nanodroplet and Michaelis–Menten kinetics, which account for the change in the enzymatic reaction rate as the glucose is consumed by the enzyme (for more information, see the SI Appendix, Fig. S11). Fig. 3A displays a common transient observed when the enzymatic reaction occurs, where the limiting current region is indicated by dashed lines and the i_lim value used in Eq. 1 is indicated by an enlarged red point. Fig. 3B shows modulation of the k_turn parameter, and Fig. 3C shows the COMSOL fit, where red dashes overlaying the experimental transient decay are the simulated physics. Importantly, these simulations are performed with the nanodroplet volumes calculated using Eq. 2. In these simulations, we take the Michaelis constant, K_M, to be 15 mM, which falls within the range established by manufacturer specifications (22 mM), bulk in-house measurements (15.8 mM, SI Appendix, Fig. S7), calculations over 10 nanodroplets (11.3 mM, details in the SI Appendix, Fig. S8), and prior literature values (27, 28). We note that K_M values have been shown to change in confined volumes (25) and may be different if the oxidative half reaction is rate limiting; however, we did not observe the dependence of K_M on nanodroplet size (SI Appendix, Fig. S8). In these simulations, the only adjustable parameter is k_turn. In this study, we did not independently evaluate the contact radius. Importantly, the contact radius does not influence kinetic quantification because the enzymatic reaction is much slower than the heterogeneous oxidation of ferrocyanide. The influence of important fitting parameters is discussed in the SI Appendix, Fig. S12. In fitting simulations to experiments, we found that the k_turn value used in the simulation is generally ∼15% larger than the k_turn calculated from Eq. 1, indicating that Eq. 1 is sufficient for estimating relative enzymatic turnover. This slight deviation may also be due to the concentration of glucose used in our experiments relative to the K_M (i.e., one cannot assume the substrate concentration is infinitely high compared to K_M due to the limitations in the amount of buffer added to nanodroplets and nanodroplet stability).

Fig. 3.

(A) Example of a background-subtracted amperometric transient for a nanodroplet (r = 611 nm) containing 5 mM ferrocyanide, 75 mM glucose, and 0.5 mM FADGDH. The portion of the transient enclosed by the dashed line illustrates the limiting current region, where the limiting current is largely determined by the k_turn. The red point near the beginning of this region indicates the $i_{lim}$ used to determine k_turn by Eq. 1. In line with polarographic convention, the anodic current is represented as negative in our plots. (B) Simulated influence of the k_turn parameter, where the simulations shown used the experimental parameters described above, contact radius = 4 nm, and K_M = 15 mM. (C) Plot showing the experimental decay (black), where time = 0 is set as the peak current, overlayed with the simulation (dashed red). The simulation shown used the experimental parameters described above, and k_turn = 79 s⁻¹, contact radius = 4 nm, and K_M = 15 mM.

Conclusions

In sum, we have developed a quantitative method to study enzyme kinetics in a single aqueous nanodroplet using nanodroplets ranging from 100 nm to >1,000 nm in radius. Our main finding is that enzyme reactivity enhances by one to two orders of magnitude as the nanodroplets get smaller, and we used finite element simulations to validate this observation. We demonstrate that a clear inverse relationship exists between the enzymatic turnover rate and nanodroplet size. Previously, groups have reported semiquantitative observations indicating enzyme reactivity is enhanced in micelles and inverse emulsions (29–34). Our results at the single nanodroplet level unambiguously validate these findings while presenting a highly quantitative simulation for nanodroplet enzyme kinetics.

Our electrochemical experiments for studying enhanced reaction rates are complementary to mass spectrometric techniques based on electrospray despite the following notable differences in the two techniques: 1) Electrochemical results are not collected at the air|liquid interface but rather a three-phase interface of two immiscible liquid phases and the electrode surface (10, 35, 36). 2) Whereas single droplets of micrometer to millimeter dimensions can be studied mass spectrometrically using levitated droplets, nanoelectrochemical measurements can account for variations in nanodroplet size by being sensitive enough to measure single nanodroplet reactivity for nanodroplets down to ∼100 nm in radius. 3) The timescale of the electrochemical experiment is on the order of seconds compared to milliseconds using electrospray ionization. However, in principle, submillisecond electrochemical reactivity within nanodroplets is possible (37). Our results add to a growing number of observations regarding surprising reactivity in nanodroplets (1, 38) that are profoundly influencing the understanding of chemical reactivity at the nanoscale.

Materials and Methods

Chemicals and Materials.

Potassium hexacyanoferrate(II) trihydrate (ferrocyanide, ≥99.95%) and Potassium hexacyanoferrate(III) (ferricyanide, 99.98%) were purchased from Sigma-Aldrich. Dextrose (D-Glucose), referred to as glucose, was obtained from Fisher Chemical. Phosphate buffered saline (PBS) was prepared in-house using potassium chloride, sodium chloride, and sodium phosphate dibasic anhydrous from Fisher Chemical, and potassium phosphate monobasic from EM Science. All aqueous solutions were made in 20× PBS (pH 6.4) unless otherwise noted. Deionized water (Millipore Milli-Q, 18.0 MΩ ⋅ cm⁻) was used to prepare aqueous solutions. DCE was obtained from Alfa Aesar. Tetrabutylammonium perchlorate (TBAP, ≥99.0%) was obtained from Sigma-Aldrich. Glucose dehydrogenase (FADGDH-AB) was obtained from Kikkoman Biochemifa Company. The lyophilized enzyme was stored in a dark box in −20 °C. Prepared enzyme solutions were stored in a refrigerator at 4 °C and remade daily. Glucose and ferrocyanide solutions were stored in a dark box at room temperature. Ferrocyanide solutions were remade every 30 min. Gold microelectrodes (r = 6.25 µm) and Silver/Silver chloride (Ag/AgCl) reference electrodes were obtained from CH Instruments (CHI).

For the absorbance measurements following the enzyme manufacturer protocol for determination of kinetic parameters, phenazine methosulfate (PMS) and 2,6-Dichloroindophenol sodium salt dihydrate (DCIP) were obtained from Tokyo Chemical Industry (TCI) Co., Ltd., and D-(+)-glucose was obtained from Sigma-Aldrich.

Instrumentation.

All stock solutions, except the enzyme solution, were sonicated by a bench sonicator from VWR International. Enzyme stock solutions were vortexed using a vortex genie. A horn sonicator (QSONICA Q500, 6.4-mm diameter tip) was used to create all emulsions (500 W, 40% amplitude). The tip was thoroughly cleaned with ethanol before and after each emulsion. DLS was performed by a Zetasizer Nano ZS (Malvern) to determine average droplet size. NTA was accomplished using a NanoSight NS300 with a 532-nm green laser. Ultraviolet visible (UV-Vis) spectra were obtained using a JASCO V-650 spectrophotometer. All amperometric experiments were performed with a CHI 601E potentiostat.

A Shimadzu UV-1800 spectrophotometer was used to obtain absorbance measurements for determination kinetic parameters following the enzyme manufacturer protocol.

Turnover Rate (k_turn) Experiments.

The molarity of the enzyme solution was determined based on the molecular weight, 85 kDa, assuming 100% purity and activity. We note that the apparent activity in this system is much lower than reported by the manufacturer (∼700 U/mg). The turnover rate, k_turn, reported herein describes the enzymatic rate in this system, where the turnover is limited by the enzymatic oxidative half reaction or the reduction of the ferricyanide cofactor. Importantly, after the fast initial electrogeneration of ferricyanide, the ferricyanide concentration is unchanging due to the constant overpotential. We also emphasize that all enzymatic rates were compared against others determined in-house using consistent solution preparation, concentrations, and methodology.

Collision Experiments.

Based on the DLS average, an enzyme concentration range of 0.1 to 0.5 mM is required to load the droplets with hundreds to thousands of enzymes. Furthermore, this concentration of enzyme allows one to observe the amperometric transient with sufficient signal-to-noise when a single nanodroplet is incident on the ultramicroelectrode surface in accordance with Eq. 1.

Amperometric traces were obtained in emulsions using a three-electrode configuration connected to a CHI 601E potentiostat. A gold ultramicroelectrode, a platinum coil, and a Ag/AgCl electrode were used as the working, counter, and reference, respectively. A total of 60 µL of aqueous solution was emulsified into 10 mL DCE using a pulse method (5 s on, 5 s off, 2 cycles). For enzymology experiments, the suspended aqueous phase contained various concentrations of ferrocyanide, 75 mM glucose, and 0.1 to 0.5 mM FADGDH. The dispersant organic phase was comprised of DCE. An oxidizing potential of 0.5 V versus Ag/AgCl was applied to the electrode for 100 s, sampling at 0.016 s. The limiting current (i_lim) was calculated by averaging the measured current from a group of points at the start of the leveled-off region followed by background subtraction.

Background traces were obtained for each prepared aqueous solution under the same conditions but without the addition of glucose. Additional background traces were obtained with aqueous solutions containing ferrocyanide and glucose and FADGDH and glucose (SI Appendix, Fig. S13). Although free FAD is electrochemically active, the structure of Aspergillus flavus–derived FADGDH (afGDH) has FAD buried deeply within the protein suggesting the FADGDH enzyme should not be able to perform direct electron transfer and requires an electron mediator for catalysis (e.g., ferricyanide) (22, 28). To demonstrate the dependence on a chemical cofactor, a trace containing 0.5 mM FADGDH and 75 mM glucose (without ferrocyanide) suspended in DCE is shown in SI Appendix, Fig. S13A, and no events are observed.

For nonenzymatic collision experiments, the suspended aqueous phase contained various concentrations of ferrocyanide emulsified in a dispersant organic phase of 0.5 M tetrabutylammonium perchlorate in DCE. Background traces were collected with the same aqueous solution, excluding tetrabutylammonium perchlorate in the DCE. For all collision experiments, noise levels were reduced by performing the experiments inside a double Faraday cage and pausing the potentiostat fan during collection. For collision experiments that produce two protons/turnover of glucose, a larger buffer capacity was required to account for the expected 150 mM protons released from 75 mM glucose. In all collision experiments, 20× PBS was used.

Simulation.

COMSOL Multiphysics 5.3a was used to compare computational transients to experimental data. A detailed discussion on the performed simulation is provided in the SI Appendix, including information on the model (SI Appendix, Fig. S11) and important computational parameters (SI Appendix, Fig. S12).

The SI Appendix and supporting information includes all raw data, more examples of current transients, and amperometric traces; derivation of Eq. 1; frequency analysis and NTA data; discussion of mass transfer in nanodroplets; control experiments; K_M calculation from nanodroplet transients; histograms of droplet size; bulk experiment discussion and examples; binned data analysis; and COMSOL discussion.

Data Availability

All study data are included in the article and/or supporting information.