Kinetic rotating droplet electrochemistry: A simple and versatile method for reaction progress kinetic analysis in microliter volumes

Article abstract of DOI:10.1021/ja405415q

Here, we demonstrate a new generic, affordable, simple, versatile, sensitive, and easy-to-implement electrochemical kinetic method for monitoring, in real time, the progress of a chemical or biological reaction in a microdrop of a few tens of microliters, with a kinetic time resolution of ca. 1 s. The methodology is based on a fast injection and mixing of a reactant solution (1-10 μL) in a reaction droplet (15-50 μL) rapidly rotated over the surface of a nonmoving working electrode and on the recording of the ensuing transient faradaic current associated with the transformation of one of the components. Rapid rotation of the droplet was ensured mechanically by a rotating rod brought in contact atop the droplet. This simple setup makes it possible to mix reactants efficiently and rotate the droplet at a high spin rate, hence generating a well-defined hydrodynamic steady-state convection layer at the underlying stationary electrode. The features afforded by this new kinetic method were investigated for three different reaction schemes: (i) the chemical oxidative deprotection of a boronic ester by H₂O₂, (ii) a biomolecular binding recognition between a small target and an aptamer, and (iii) the inhibition of the redox-mediated catalytic cycle of horseradish peroxidase (HRP) by its substrate H₂O₂. For the small target/aptamer binding reaction, the kinetic and thermodynamic parameters were recovered from rational analysis of the kinetic plots, whereas for the HRP catalytic/inhibition reaction, the experimental amperometric kinetic plots were reproduced from numerical simulations. From the best fits of simulations to the experimental data, the kinetics rate constants primarily associated with the inactivation/reactivation pathways of the enzyme were retrieved. The ability to perform kinetics in microliter-size samples makes this methodology particularly attractive for reactions involving low-abundance or expensive reagents.

Full text of DOI:10.1021/ja405415q

Article
pubs.acs.org/JACS
Kinetic Rotating Droplet Electrochemistry: A Simple and Versatile
Method for Reaction Progress Kinetic Analysis in Microliter Volumes
Lylian Challier,†,§ Rebeca Miranda-Castro,
and Benoît Limoges*
†,‡,§
‡
†
,‡
̈
́
Damien Marchal, Vincent Noel, Franc o̧ is Mavre,*
,
‡
†
‡
ITODYS, UMR 7086 CNRS, and Laboratoire d’Electrochimie Molec
́ ́
ulaire, UMR 7591 CNRS, Universite Paris Diderot, Sorbonne
Paris Cite,
́
15 rue Jean-Antoine de Baïf, F-75205 Paris Cedex 13, France
*
S Supporting Information
ABSTRACT: Here, we demonstrate a new generic, afford-
able, simple, versatile, sensitive, and easy-to-implement
electrochemical kinetic method for monitoring, in real time,
the progress of a chemical or biological reaction in a
microdrop of a few tens of microliters, with a kinetic time
resolution of ca. 1 s. The methodology is based on a fast
injection and mixing of a reactant solution (1−10 μL) in a
reaction droplet (15−50 μL) rapidly rotated over the surface
of a nonmoving working electrode and on the recording of the
ensuing transient faradaic current associated with the trans-
formation of one of the components. Rapid rotation of the
droplet was ensured mechanically by a rotating rod brought in
contact atop the droplet. This simple setup makes it possible to mix reactants efficiently and rotate the droplet at a high spin rate,
hence generating a well-defined hydrodynamic steady-state convection layer at the underlying stationary electrode. The features
afforded by this new kinetic method were investigated for three different reaction schemes: (i) the chemical oxidative
deprotection of a boronic ester by H O , (ii) a biomolecular binding recognition between a small target and an aptamer, and (iii)
2
2
the inhibition of the redox-mediated catalytic cycle of horseradish peroxidase (HRP) by its substrate H O . For the small target/
2
2
aptamer binding reaction, the kinetic and thermodynamic parameters were recovered from rational analysis of the kinetic plots,
whereas for the HRP catalytic/inhibition reaction, the experimental amperometric kinetic plots were reproduced from numerical
simulations. From the best fits of simulations to the experimental data, the kinetics rate constants primarily associated with the
inactivation/reactivation pathways of the enzyme were retrieved. The ability to perform kinetics in microliter-size samples makes
this methodology particularly attractive for reactions involving low-abundance or expensive reagents.
INTRODUCTION
Surprisingly, despite the many practical advantages of
electrochemical detection methods including high temporal
resolution, sensitivity, low cost, and simplicity, only a scarce
number of kinetic methods combining rapid mixing of reactants
with an electrochemical readout have been so far reported. One
■
(
Monitoring the progress of a chemical or biochemical reaction
e.g., by following the reactant conversion or product formation
over time) with an appropriate kinetic technique is essential to
determine the rate laws of reactions and to aid in elucidation of
10
1
−4
example, recently described, is based on a segmented flow
microfluidic platform in which microdroplets generated from
the mixing of two reagents at a T-junction are moved through a
microchannel and, at some positions downstream, the electro-
active content of the microdroplets is amperometrically
detected by wire electrodes inserted into the microchannel.
The method was illustrated with the kinetic analysis of the
enzymatic decomposition of H O by catalase. This technique
reaction mechanisms.
This may be accomplished by a wide
range of kinetic methods, the most common of which take
advantage of changes in optical signals, such as UV−visible
absorbance or fluorescence, which often accompany a reaction.
5
For monitoring fast reactions on time scales ranging from
milliseconds to several tens of seconds, rapid mixing techniques
are required (e.g., stopped-flow, quenched flow, or continuous
flow). In these examples, two or more reactant solutions are
rapidly mixed in a chamber, and the ensuing reaction solution is
monitored by an appropriate real-time detection method. A
major strength of rapid mixing methods is that they can be
readily combined with a wide range of detection methods, and
though optical techniques have been predominantly imple-
2
2
has the advantage of using low sample volumes (a few tens of
microliters), with the possibility to reach a time resolution
down to 50 ms. However, the principle is inherently limited by
a low sampling rate because of the restricted number of
electrodes that could be inserted into the microfluidic channel,
3
,5
6,7
mented, nonoptical detections such as NMR, isothermal
8
9
titration calorimetry, or small-angle X-ray scattering have
been proven useful alternatives.
Received: May 30, 2013
Published: August 28, 2013
©
2013 American Chemical Society
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Journal of the American Chemical Society
Article
leading thus to rather poorly defined kinetic plots. The other
examples are all based on the use of a rotating disk electrode
microdrop is an alternative route to perform hydrodynamic
electrochemistry in small sample volumes. It was advanta-
27
(
RDE), generally mounted in a standard closed electrochemical
geously applied to magnetic microbead-based enzyme immuno-
11−15
28,29
cell containing a few milliliters of solution.
The RDE
assays.
However, apart from the possibility of working in
ensures rapid mixing of the reactant injected into the cell
small volumes, the approach shows the same limitations as
conventional RDEs.
(
sometimes this is accompanied by magnetic stirring or
12
bubbling with an inert gas ), as well as fast and controlled
mass transport of the reactant to the electrode surface. Under
these conditions, a mixing time shorter than 0.5 s has been
reported. The technique was successfully applied to the
electrochemical characterization of homogeneous and hetero-
In the present work, a new affordable, simple, versatile,
robust, and easy-to-implement electrochemical kinetic method
has been developed for monitoring, in real time, the progress of
a chemical or biological reaction in a few tens of microliters
with a kinetic time resolution of ca. 1 s. The principle basically
consists of rapidly injecting and mixing a reactant solution (1−
10 μL) in a small drop of a reaction solution (15−50 μL) that is
rapidly spinning over the surface of a nonmoving working
electrode polarized at an appropriate potential. The ensuing
transient faradaic current associated with the consumption or
production of one of the components in the microdrop reactor
is subsequently recorded. Rapid rotation of the droplet was
ensured mechanically by a rotating rod (in fact a standard RDE
that was here just used as a mechanical rotator) brought in
contact atop the droplet. As it will be shown, this simple setup
makes it possible to efficiently mix and rotate the sandwiched
droplet at high spin rate and hence to generate a well-
controlled hydrodynamic steady-state convection layer at the
underlying stationary working electrode. This new config-
uration also eliminates all problems related to the moving
electrical contact in the RDE and provides a high degree of
freedom in the choice and design of the working electrode. In
the present work, disposable screen-printed electrodes have
been used, which is very convenient for reproducing a large
number of experiments with fresh electrode surfaces without
need of surface polishing. These electrodes also possess a
remarkably low capacitance, which is advantageous for
1
2
11
12,14
geneous
kinetics of enzyme reactions, as well as to
quantitative analysis of the heterogeneous binding kinetics of
1
3,15
a ligand in solution to a receptor immobilized on the RDE.
It is interesting to note that these hydrodynamic electro-
chemical kinetic methods can be subdivided in two categories:
those in which the fluid is in motion with respect to a static
electrode, and those in which the electrode itself is moving
relative to the solution. Whatever the strategy, each provided a
convective regime (or more rigorously, a chaotic advection in
the case of microdroplets flowing through a winding micro-
1
0
channel ) that has the purpose to rapidly mix the reactants of
the sample solution and at the same time to promote fast
diffusion rate of species to the sensing electrode surface. Thus
the capacity to determine rapid reaction rates and the ability to
sensitively and accurately detect the consumption or
production of one of the participants depend on the efficiency
of these processes.
1
6,17
The RDE
remains the workhorse of hydrodynamic
electrochemical methods (even though a wide range of
alternative hydrodynamic approaches have been developed
18−22
during the last 20 years
). It exhibits a number of
advantages such as a high degree of control of the diffusion
flux through fine-tuning of the electrode rotation rate, allowing
one to record a steady-state current with high precision and
reproducibility. However, it has also a number of drawbacks.
For a conventional RDE, only macrosamples of solution are
accessible (typically a few milliliters), consequently prohibiting
reaction kinetic studies of low-abundant and expensive reagents
30
detecting low concentrations. Moreover, because of the
highly favorable hydrodynamic conditions and short response
time of the amperometric measurement, it makes it possible to
electrochemically monitor reaction progress continuously, from
zero-time, with a high sampling rate (up to 1 MHz with
standard commercialized potentiostats).
To evaluate the hydrodynamic properties of the rotating
droplet system, we have first examined the effect of the rod spin
rate on the electrochemical response, as well as the influence of
several geometric parameters such as the gap height separating
the rotating rod from the underlying stationary working
electrode, the volume of the rotated droplet, and the working
electrode area-to-droplet volume ratio. The mixing time
required to homogenously disperse the injected reactant was
also carefully assessed. Thereafter, the relevance and features of
the electrochemical method for reaction progress kinetic
analysis in low-volume samples were investigated for three
different illustrating reaction schemes: (i) an irreversible
bimolecular chemical reaction based on the oxidative
(
e.g., biomolecules). Moreover, the electrical noise, which
determines the ability to reach low detection limits, is attendant
to the electrical contacts between rapidly moving and
nonmoving parts in the electrode. Additionally, the screening
of RDEs made of different conductive materials, different
surface modifications, and various shapes or geometries is in
practice not simple to achieve (note that it is the reason that
the hanging-meniscus rotating disk technique has been
expressly developed and applied to hydrodynamic electro-
2
3,24
chemistry at metal single crystals
). The implementation of
an equivalent of RDE for performing hydrodynamic electro-
chemistry in microliter samples and in a configuration that
would facilitate the screening of different electrode designs and
materials is therefore of great interest. In that vein, Gratzl and
colleagues have described a system that addresses these
31
deprotection of an aryl boronic ester by hydrogen peroxide,
ii) a reversible biomolecular binding reaction through the
enantiospecific molecular recognition of the small target L-
(
2
5,26
issues.
The system consists of applying a small sample
32
tyrosinamide by its 49-mer aptamer, and (iii) a more complex
reaction with the reversible inhibition of the catalytic cycle of
horseradish peroxidase (HRP) by its substrate hydrogen
droplet (20 μL) over a gold ring working electrode and then, by
using a mild gas jet directed tangentially to the droplet of
solution, forcing it to rotate, thereby generating a steady-state
current. This rotating sample strategy was shown to be as
effective as a rotating electrode system. The approach however
suffers from rather fast evaporation of the sample, thus
complicating the current response analysis as a function of
time. Introduction of a RDE directly over the top of an aqueous
3
3,34
peroxide.
MATERIALS AND METHODS
■
Reagents. MgCl ·6H O (Sigma), L-tyrosinamide (Aldrich),
2
2
LiClO4 (Aldrich), hydrogen peroxide (30 wt % reagent grade;
1
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Prolabo), bovine serum albumin (BSA; Sigma), p-aminophenol
primary silver layer was deposited onto the polyethylene terephthalate
surface to form the electrical contacts and the internal reference
electrode pattern using a 230 mesh-count per inch screen. The silver
layer was cured for 15 min in an oven at a temperature of 120 °C. The
carbon layer was next deposited to form the working and counter
electrode patterns using a 230 mesh-count per inch screen. After the
ink leveled for a few minutes at room temperature, the layer was dried
in an oven at 120 °C for 15 min. Finally, a last layer of a thick film
curable dielectric (Vinilfast 36, Kiian, Italy) was printed through a 230
mesh screen to form the reaction well (circular well of 5-mm
diameter) and to insulate the conductive paths of the electrodes. The
insulating layer was cured in an oven at 120 °C for 15 min. The layer
thicknesses were determined with a profilometer (model Alpha-Step
500, KLA-Tencor, USA) (Figure S1, Supporting Information). The
thickness of the silver and the carbon layers were 10 ± 0.5 and 6 ± 0.5
μm, and the insulating layer thickness was 15 ± 0.5 μm. The diameter
of the sensing area of the working carbon electrode was 1.5 mm (i.e., S
(
Prolabo), p-aminophenyl boronic acid pinacol ester (Tokyo Chemical
Industry), and ferrocene methanol (Aldrich) were used without
II
II
further purification. The [Os (bpy) pyCl]PF and [Os (bpy) ](PF )
6 2
2
6
3
3
5
were synthesized according to a published procedure. Lyophilized
HRP was purchased from Sigma (type VI-A, RZ = 3.5) and used
without further purification. The concentration of HRP was
spectrophotometrically determined at 403 nm using a Soret extinction
−1
−1
coefficient of 102 mM cm . The enzyme reaction buffer (EB, pH
.4) was prepared from 4.3 mM NaH PO , 15.1 mM Na HPO , 50
7
2
4
2
4
mM NaCl, and 1 mg/mL BSA. Adding BSA to the enzyme buffer
allows minimization of the loss or denaturation of the enzyme at the
air/liquid or solid/liquid interfaces. The Tris buffer (TB, pH 7.4) used
for the aptamer binding experiments was made of 5 mM Tris buffer,
1
0 mM MgCl , and 50 mM NaCl.
2
The oligonucleotides were synthesized and HPLC-purified by
Eurogentec (Angers, France) and their concentration was controlled
by UV−visible spectroscopy using a Nanodrop 2000 spectropho-
tometer (ThermoFisher). The aptamer oligonucleotide sequence was
2
= 0.0177 cm ), but a few experiments were also performed with a
2
larger diameter of 3 mm (i.e., S = 0.071 cm ).
3
6
(
from 5′ to 3′) Apt , AATTCGCTAGCTGGAGCTTGGATT-
Unless otherwise stated, all potentials indicated in the text are
expressed versus the silver-based screen-printed pseudo-reference
electrode (i.e., Eref ≈ +0.3 V vs SHE).
49
GATGTGGTGTGTGAGTGCGGTGCCC.
Milli-Q water (18.2 MΩ cm, TKA MicroPure UV) was used to
prepare all aqueous solutions.
Instrumentation and Electrodes. Electrochemical measure-
ments were carried out with a computer-controlled AutoLab PGSTAT
Experimental Setup. The experimental setup is schematically
depicted in Figure 1. The planar three-electrode electrochemical
microcell fabricated by screen printing is affixed flat over a multiaxis
translational mechanical stage (Sutter Instrument Company). The
droplet of the reaction solution (15−50 μL) is simply deposited over
the three-electrode microcell and then maintained in place by the
hydrophobic screen-printed insulating layer, which defines a sort of
circular microwell (5-mm diameter) centered on the screen-printed
carbon working electrode. Proper choice of the inner diameter of the
hydrophobic layer ensured a hemispherical-shaped drop. With the help
of the multiaxis translational mechanical stage, the deposited droplet
was brought in contact perpendicular to the rotating rod and centered
to the axial axis of the shaft; thereby forming a sandwiched sand-clock-
shaped droplet between the screen-printed working electrode and the
base of the rotating rod (unless otherwise stated, the distance between
the extremity of the rod and the screen-printed electrodes was set to
12 potentiostat interfaced to a GPES 4.9 software (EcoChemie B.V.
Utrecht, The Netherlands).
Thick-film screen printing was used to shape the reaction well and
the three-electrode cell according to the final design shown in Figure
1A. A DEK model-65 semiautomatic screen-printer (Presco, USA) was
used to deposit the successive thick film layers on planar polyethylene
terephthalate films through stainless-steel wire mesh screens. The
working and counter carbon-based screen-printed electrodes were
prepared from the carbon ink Electrodag PF-407A (Acheson Colloids
Co), whereas the silver-based pseudo-reference electrode was obtained
from the silver ink Electrodag 418 S (Acheson Colloids Co). A
2
.5 mm). The rotating rod was a standard glassy carbon RDE tip
(made of a carbon disk electrode of 5-mm diameter embedded in an
inert and insulating Teflon cylinder) mounted on a shaft attached to
an adjustable speed rotator AFMSRX (Pine Research Instrumentation,
USA). Since the glassy carbon RDE is not used during the
experiments, it was disconnected from the shaft to avoid any leakage
current. According to the relatively high surface tension and strong
capillary forces exerted at the scale of the aqueous drop, transmission
of the mechanical rotating movement from the cylindrical tip to the
droplet sample was possible. As it will be shown, this simple setup
permits rotation of the droplet at a spin rate up to 3500 rpm with a
high degree of control and reproducibility.
Before experiments, the surface of the glassy carbon disk embedded
in the rod as well as the overall screen-printed carbon electrodes were
passively coated with a layer of BSA by spreading a droplet of 1 mg/
mL solution over the electrodes for 15 min at room temperature. The
BSA coating offers the advantage to increase the wettability of the two
opposite surfaces in contact with the droplet and also to reduce the
nonspecific adsorption of molecules on these surfaces, without
significantly hindering the accessibility and heterogeneous electron
transfer properties of small redox molecules to the underlying working
electrode surface. The marked contrast between the hydrophilic BSA-
coated interfaces and the surrounding hydrophobic materials (i.e.,
Teflon cylinder of the rod and insulating dielectric layer of the
microcell), at both sides of the sandwiched droplet, helps to maintain a
good drop adhesion to the rotating rod and circular microcell. After
BSA coating, the screen-printed working electrodes were systemati-
cally cycled in a 0.1 M phosphate buffer (between 0.0 and 0.8 V at v =
Figure 1. (A) Graphic representation (1:1 drawing scale) of the
screen-printed three-electrode electrochemical microcell. WE = carbon
working electrode; ref = silver reference electrode; CE = carbon
counter-electrode. (B) Cross-sectional view of a 50 μL droplet
deposited over the electrochemical microcell delimited by the circular
dielectric layer (2:1 drawing scale). (C) Cross-sectional view of the
rotating droplet system (1:1 drawing scale). On the right is shown the
micropipet ready for the injection of a reactant solution. (D)
Schematic representation of the streamlines of recirculating flow
inside the rotated droplet (cross-sectional view of the sandwiched
droplet).
−1
0.05 V s ) until the capacitive background current was stabilized. All
rotating droplet experiments were done at room temperature (∼20
°C).
1
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Gold-plated screen-printed electrodes were produced by electro-
shaped diffusion-controlled reversible wave obtained under
stationary conditions in CV is converted into a typical sigmoid-
shaped wave under mechanical motion of the rotating rod
deposition of gold at −0.5 V (vs. SCE) for 240 s in a 0.1 M HCl
−1
solution containing 4 g L HAuCl .
4
The spectroscopic kinetics determination of the oxidative
deprotection of the p-aminophenyl boronic acid pinacol ester by
hydrogen peroxide was performed with a UV−visible AnalytikJena
Specord S600 spectrophotometer. The temperature of the standard
quartz cell (1-cm path length) was maintained at 20 °C. The time-
course absorbance change resulting from the conversion of the boronic
ester (0.1 mM in 0.1 M phosphate buffer, pH 7.4) into p-aminophenol
(
Figure 2A). The limiting plateau current witnesses the steady-
was monitored at 292 nm for different concentrations of H O2
2
(
ranging from 1 to 5 mM). From the slope of the dependence of
the initial rate of absorbance change as a function of H O
2
2
−
1
concentration, a second order rate constant of k = 4.1 ± 0.2 M
−
1
s
was obtained.
Numerical Simulations. Simulations of the homogeneous
aptamer binding kinetics by numerical resolution of the rate
3
7
differential equations were carried out with the Gepasi 3.30 freeware.
Simulations of the transient amperometric catalytic currents resulting
Figure 2. (A) CVs (v = 0.1 V/s) recorded at a 50 μL rotated droplet
(50 μM FcMeOH in 0.1 M LiClO ) sandwiched (l = 2.5 mm)
from the redox mediated catalytic reaction scheme of HRP were
3
8
4
performed with the DigiElch 7D software from ElchSoft (Germany).
between the rotating rod and a screen-printed electrochemical
In order to simulate a steady-state mass transport through a constant
diffusion layer thickness, the chronoamperometric mode at a microdisk
electrode was selected in DigiElch. The size of the microdisk electrode
used for the simulation was selected in such a way to have a steady-
state mass transport equivalent to the one obtained experimentally at
the rotating droplet system. This was achieved from comparison of the
magnitude of simulated steady-state current densities to those
obtained experimentally at a given mediator concentration and rod
rotation rate. A microdisk electrode of 30 μm diameter was used, for
2
microcell (S = 0.0177 cm ) and for different rod rotation rates:
(
from bottom to top CV) ω = 0, 1000, 1600, 2400, and 2800 rpm. (B)
1
/2
CV plateau current densities (v = 0.1 V/s) as a function of ω for
(red square) a standard working RDE in a 5 mL of 50 μM FcMeOH,
(black open circle) a standard working RDE on top of a 50 μL droplet
of 50 μM FcMeOH, and (blue circle) a 50 μL-rotated droplet under
the same conditions as in panel A. Lines represent the best linear
−
6
2
1/2
2
regressions [RDE slope = (2.51 ± 0.01) × 10 A/cm /(rad/s) ; r =
−
6
2
0
.9997; rotated droplet slope = (1.88 ± 0.01) × 10 A/cm /(rad/
1/2 2
example, because it affords a simulated steady-state current density of
2
s) ; r = 0.9996; RDE on top of the microdrop slope = (1.87 ± 0.01)
7
4
.6 μA/cm for a 20 μM redox species having a diffusion coefficient of
−6 2 1/2 2
−
6
2
−1
× 10 A/cm /(rad/s) ; r = 0.9991].
.5 × 10 cm s , which typically corresponds to the value
II
+
experimentally obtained for the [Os (bpy) pyCl] oxidized at a 2000-
2
rpm-rotated droplet. Once the size of the simulated microdisk
electrode was selected, the overall reactions of the HRP mechanism
including their associated kinetic rate constants, as well as the
concentrations and diffusion coefficients of each species were input to
the DigiElch program for simulating the chronoamperometric
responses. Because the DigiElch software does not allow simulation
of the injection of a reagent at a well-defined time, we have overcome
this problem by starting (i.e., at t = 0) both the experiments and
simulations from the reduced form of the redox mediator. Under these
conditions, the simulated and experimental currents could effectively
start from a zero current value. For the simulations, the different
enzyme forms were considered as practically immobile by setting the
state diffusion rate of the redox species at the electrode surface
through a constant diffusion boundary layer of thickness δ.
Besides, plateau current densities (j ) were observed to vary
pl
proportionally to the concentration of FcMeOH (compare
Figure 2A and Figure S2, Supporting Information) and linearly
with the square root of the rod spin rate (ω) (Figure 2B) but
1/2
with a slope dj /dω lower than at a conventional RDE in a
pl
standard electrochemical cell (i.e., in 5 mL of 50 μM
FcMeOH).
In an attempt to better understand why the hydrodynamic
convection obtained at a conventional RDE does not
completely transpose in our system, the glassy carbon disk
embedded in the Teflon rotating rod was used momentarily as
diffusion coefficient at an arbitrarily low value of 10− cm s ,
whereas the diffusion coefficient of the reduced and oxidized forms of
the mediator were the same as those experimentally determined (i.e.,
10
2
−1
−6
2
−1
−6
2
−1
3
9
DQ = 4.5 × 10 cm s and D = 3.2 × 10 cm s ), and the
P
a working electrode on the top of the microdrop. Under these
−
5
2
−1 33
diffusion coefficient of H O was taken to be 1.6 × 10 cm s .
1/2
2
2
conditions, the resulting linear plot of j as a function of ω
pl
was observed to perfectly overlay the plot previously obtained
with the rotated droplet configuration (Figure 2B). This result
underlines the production of an identical hydrodynamic
convection at the two opposite interfaces of the sandwiched
droplet, thereby suggesting a high symmetry in the fluid
movement induced from the spinning rod. By analogy to the
recirculation flow patterns generated at a conventional RDE
immersed in a cell of restricted volume (i.e., in a configuration
where the walls and the bottom of the cell are close to the
RESULTS AND DISCUSSION
■
Characterization of the Hydrodynamic Properties of
the Rotating Droplet System. Under the experimental
conditions schematically depicted in Figure 1, the hydro-
dynamic conditions settled at the droplet/working electrode
interface were examined by cyclic voltammetry (CV) at a 50 μL
droplet solution of ferrocene methanol (FcMeOH, 50 μM)
deposited over a screen-printed electrochemical microcell and
for different rod spin rates (ranging from 0 to 3500 rpm). The
gap height (l) separating the extremity of the rotating rod from
the underlying screen-printed working electrode was set at a
value of 2.5 ± 0.2 mm. Under these conditions, the strong
capillary forces and surface tension occurring at the scale of the
4
0,41
RDE),
it can be assumed that the flow generated by the
rotation of the rod on top of the droplet similarly induces a
symmetrical recirculation of the liquid inside the droplet. This
would mean that, as schematically depicted in Figure 1D, the
rotating unit should drag the fluid by a flow normal to its
surface and, because of the centrifugal force created by the
rotating disk in contact with the liquid, should throw the
solution outward from the center in a radial direction.
5
0 μL aqueous droplet help to maintain the solution between
the upper base of the rod and the underlying surface of the
microcell, up to a 3500-rpm rotation rate. The classical peak-
1
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4
0
Consequently when the liquid laterally displaced by the rotating
rod reaches the external air/liquid walls of the droplet, it must
change direction by moving downward to the bottom working
electrode. At this point, it changes direction again and moves
toward the center of the droplet where it meets the flow
coming from the opposite air/liquid wall, to finally moves
upward to the rotating disk, forming thus a recirculating
convective flow inside the droplet. As a result, fluid motion
transmits symmetrically from the moving interface up to the
opposite nonmoving surface. This flow pattern was clearly
discerned and confirmed experimentally from a simple visual
inspection of the movement of the colored liquid that was
generated from the dissolution of a small crystal of potassium
permanganate added to a droplet under rotation.
layer), we have found it reasonable to assume that the Levich
equation also holds in the present case, but for the reasons of
the peculiar hydrodynamic resistances occurring at the scale of
the rotated droplet, it needs to be corrected by an appropriate
empirical term in the expression of δ to take into account the
25% loss of mass transport efficiency compared with a
conventional RDE. Therefore we have
nFSDC0
δcorr
= 0.465nFSD2/3ν−1/6 1/2C0
ω
ipl,corr
=
(2)
(3)
1/3
1/6ω−1/2
ν
where δcorr = 2.15D
From eq 2 and the slope of the linear fit in Figure 2B, the
diffusion coefficient of FcMeOH can be calculated using υ =
0.01 cm s . A value of a D = 7.6 × 10 cm s was obtained,
which is consistent with that previously determined for
At a conventional RDE, expression of the steady-state plateau
16
current, i , is given by the Levich equation:
2
−1
−6
2 −1
pl
nFSDC0
FcMeOH in aqueous solution (ca. 7 × 10− cm s ),
confirming thus the validity of eq 2. With this diffusion
coefficient in eq 3, a steady-state diffusion layer thickness of
12.4 μm can be calculated at ω = 2400 rpm. This value is
therefore much lower than the gap height l (2.5 mm), and it
may explain why the plateau currents are independent of the
value of l.
6
2
−1 42−44
i =
pl
δ
(1)
1
/3 1/6 −1/2
where at 25 °C δ = 1.61D ν ω
electrons exchanged, F the Faraday constant, S the electrode
and n is the number of
2
surface area (in cm ), D the diffusion coefficient of FcMeOH
2
−1
0
(
in cm s ), C the bulk concentration of FcMeOH (in mol
−3
cm ), δ the diffusion-convection layer thickness (in cm), ν the
kinematic viscosity of the solvent (in cm s ), and ω the
2
−1
When the CV response of 5 μM FcMeOH at a rotated
droplet is compared to the one obtained at a classical RDE
(Figure S4, Supporting Information), it is obvious that the
particularly low capacitance of the screen-printed carbon-based
electrodes along with the low electrical noise resulting from the
nonmoving working electrode is of great interest for detecting
low concentrations. This is confirmed from the calibration plot
of FcMeOH (Figure S5, Supporting Information), which shows
an excellent detection limit of 0.1 μM FcMeOH (considering a
−
1
angular velocity (in rad s ). The fact that the current density
with the rotated droplet system is systematically 25% lower
than predicted by the Levich equation (Figure 2B) clearly
indicates that the mass transport efficiency is decreased by 25%
with respect to a conventional RDE. In order to determine
whether such a loss of mass transport efficiency may be
influenced by the droplet volume, V, and gap height, l, the
magnitude of the steady-state current at 2500 rpm was
examined for different values of V and l in the ranges 15 ≤ V
2
signal-to-noise ratio of 3 and an average noise of 0.02 μA/cm )
combined with a good linearity (slope = 0.64 μA cm− μM ; r
2
−1
2
≤
50 μL and 1.0 ≤ l ≤ 3.0 mm. The experimental CVs (Figure
S3, Supporting Information) show that, whatever l and V, the
= 0.996), as well as good reproducibility (a relative standard
deviation of 2% was obtained from 10 measurements at 10
different screen-printed electrochemical microcells).
steady-state current remains unchanged, demonstrating that the
25% loss in mass transport efficiency is independent of V and l
within the range of tested values. Such a behavior, although
difficult to interpret without detailed knowledge of the
hydrodynamic flow, is nevertheless in line with the idea of a
centrosymmetric circular convective flow. It also suggests that
the fluid velocity (in particular the axial fluid velocity, or suction
velocity, assumed to primarily control the magnitude of the
steady-state current) is poorly dependent on the geometrical
features of the system (within the narrow ranges here
explored). The independence of the steady-state current on
the distance l is of practical interest because precise control of
this parameter is thus not required. This was also the case for
the position of the center of the working electrode relative to
the axial center of the rotating shaft, since a small offset of the
working electrode from the axis of rotation was observed to not
noticeably change the magnitude of the steady-state current in
CV (not shown). Finally, the experiment obtained at the lowest
volume of solution demonstrates that hydrodynamic electro-
chemistry is achievable in only 15 μL without altered
performance.
Depending on the working electrode size, the electrode
surface-to-droplet volume ratio could be relatively high in the
droplet configuration and the absolute amount of molecules
electrochemically transformed is not negligible. To evaluate this
ending, several experiments were carried out with a larger
2
screen-printed working electrode area (S = 0.071 cm ), and the
2
results were compared with the smaller one (S = 0.0177 cm )
(Figure S6, Supporting Information). The voltammetric S-
shaped wave of FcMeOH at a larger electrode was observed to
progressively and homothetically shift toward cathodic current
values during successive CV scans (0.1 V/s) in 50 μL FcMeOH
solution, whereas for the smaller electrode, the CV response
remained practically unchanged under the same conditions.
This behavior is characteristic of a significant electrolysis of
FcMeOH in its ferrocenium form in the droplet, a direct
consequence of the large electrode surface area-to-sample
−1
volume (S/V = 1.42 cm ) coupled with an efficient mass
transport. The electrochemical transformation however cannot
be complete, even for prolonged successive CV scans, because
the ferrocenium produced at the working electrode during an
anodic voltammetric scan can be in part reversibly reduced at
the counter electrode and vice versa (for exhaustive electrolysis
at a controlled potential, the counter electrode has to be
separated from the sample solution in an independent
On account of the linear dependence of the steady-state
current with ω1/2 and C and on the basis of the high similarity
with the circular convective flows obtained at a RDE in a
confined cell (for which the Levich equation was shown to hold
if the steady-state diffusion boundary layer at the working
electrode is thin and buried within the hydrodynamic boundary
0
2
5,26
electrolyte compartment equipped with a junction
).
1
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Keeping the working electrode area-to-droplet volume ratio as
low as possible is therefore essential to neglect this effect and
hence get a stable signal, especially for prolonged electrode
polarization. At the smaller working electrode, a reasonably
stable signal over several tens of minutes was finally observed,
which also signifies that evaporation of the aqueous droplet is
negligible under these experimental conditions.
value that is here not significantly affected by the composition
of the selected aqueous solutions.
Independently of the mixing time, there are three other
characteristic times that may limit the temporal resolution of
the kinetic method: the instrument response time, the injection
time, and the dead time. As mentioned in the Introduction, the
instrument response time (routinely in the microsecond range)
is far from being rate determining in our conditions (note that
even though higher sampling rate could be easily achieved in
Figure 3, the current was sampled only every 100 ms).
Although not instantaneous, the injection time is also not rate
limiting. This assertion is supported by the sharp instantaneous
current increases that are sometimes observed during the first
2
5
Characterization of the Mixing Efficiency Subsequent
to the Injection of a Reagent in the Rotated Droplet.
The ability to electrochemically monitor the reaction progress
subsequent to the injection of a reactant into the rotated
reaction solution will depend on how fast is the reaction relative
to the mixing. The mixing efficiency of the rotating droplet
system was thus tested by manual injection of 1 μL of hydrogen
peroxide solution into a 49 μL rotated droplet while the
working electrode, poised at a negative potential, was used to
monitor the transient current change related to the electro-
chemical reduction of H O . Since the reduction of H O is
2
00 ms subsequent to the injection of an electrodetectable
reagent but also by the perfect fit of the experimental data to a
simple exponential law (Figure 3 and Figure S8, Supporting
Information), characteristic of an instantaneously perturbed
system that relaxes. Another possible rate limitation that may
ensue if the injection and mixing time are instantaneous is the
time required for a molecule to cross the constant diffusion
layer established at the working electrode interface. This time,
2
2
2
2
45
facilitated at nanoporous gold metal, the working carbon
electrode was electroplated with a thin film of porous gold
(
Figure S7, Supporting Information). The gold-plated screen-
printed electrode led to an efficient reduction of H O at −0.6
2
2
2
represented by t ≈ δ /(2D), is typically the dead time during
V vs Ag/AgCl in acidic solution. At such a negative potential,
dioxygen is also reduced, giving rise to a steady-state cathodic
current before addition of H O . As reported in Figure 3, upon
which no current could theoretically be measured immediately
after an injection. It is directly correlated to the rod spin rate,
which determines the thickness of the diffusion layer.
Considering the value of δ = 17.3 μm, which can be calculated
for H O at 2000 rpm using eq 3, a dead time of ∼95 ms can be
2
2
2
2
estimated (using DH2O2 = 1.6 × 10− cm /s). This rough
5
2
estimation is clearly shorter than the relaxation time of 1.2 s
determined experimentally, allowing us to definitely conclude
that the mixing time is the rate determining factor that
currently sets the kinetic time resolution of the proposed
method.
Kinetic Results with a Bimolecular Chemical Reaction.
As a first case study, the kinetics of the chemospecific
deprotection of p-aminophenylboronic acid pinacol ester
(
PAPB) into p-aminophenol (PAP) by oxidative hydrolysis
with H O has been considered (Scheme 1).
2
2
This deprotection reaction has been recently proposed for
the electrochemical determination of hydrogen peroxide
generated by glucose oxidase in the presence of glucose and
Figure 3. Transient current response obtained at a gold-plated screen-
printed electrode held at −0.6 V (vs Ag/AgCl) during the injection (t
31
dioxygen. The electrochemical monitoring of this reaction is
=
0) of 1 μL of H O (50 mM in water) in a rotated droplet (V = 49
2 2
μL, ω = 2000 rpm) of 0.1 M H SO . The red line is an exponential fit
2
4
to the experimental data using τ = 1.25 s.
Scheme 1. Reaction Scheme of the H O -Mediated Oxidative
2
2
Deprotection of PAPB into an Electrooxidizable PAP
Product
injection of 1 μL of H O (50 mM) in a 49 μL rotated droplet
2
2
of 0.1 M H SO , (ω = 2000 rpm), the initial steady-state
2
4
cathodic current density (j) is instantly exponentially increased
with time until reaching a maximum value (jmax).
This behavior is typical of an instantaneously perturbed
system that exponentially relaxes with time. The exponential
increase of j with time was fitted to eq 4 from which a
characteristic relaxation time value of τ = 1.25 s was obtained.
j = jmax [1 − exp(−t/τ)]
(4)
The same experiment was repeated with two other aqueous
media (0.1 M PBS or 0.1 M PBS containing 0.1% BSA), and
similar relaxation time constants were found (Figure S8,
Supporting Information), giving an average value of τ = 1.23 ±
0
.12 s. This time constant characterizes the mixing time
required to fully homogenize H O in the droplet volume, a
2
2
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Article
possible because of the distinct redox properties of the product
PAP (showing a reversible oxidation at 0 V vs Ag/AgCl at pH
maximal value corresponding to the entire conversion of PAPB
into PAP (current densities were normalized to this maximal
value).
7
.4) from the starting PAPB substrate. This is illustrated in
Figure 4, where PAPB gives an irreversibly anodic peak at +0.5
Given the mixing time constant of 1.2 s determined for H O
2
2
in the precedent part, we may thus neglect it and considered
that the reaction solution is homogeneous during the whole
reaction period. Under assumption of a pseudo-first-order
kinetics and consideration that the current is a direct
measurement of the bulk concentration of PAP through eq 2,
all experimental plots could thus be simply fitted by the first-
order rate law given by eq 5 (an illustrating example is shown in
Figure 5 for the concentration of 2.5 mM H O ).
2
2
j
=
1 − exp(−k t)
obs
j
(5)
max
The resulting plot of kobs as a function of C0
shows a
2 2
H O
perfect linear relationship (Figure 5), confirming the
bimolecular reaction mechanism. From the slope of the linear
regression, the second-order kinetic rate constant, k, was
Figure 4. CVs in phosphate buffer, pH 7.4, of (blue first scan; green
second through fourth scans) 1 mM PAPB and (red) 1 mM PAPB and
inferred and a value of 5.1 ± 0.1 M−
1
s
−1
was found. This is a
2
.5 mM H O after 10 min reaction time at room temperature. Scan
relatively slow rate constant that finally can be comfortably
determined under our conditions. In order to corroborate this
result, the rate constant was also independently determined by
UV−visible spectroscopy (see Materials and Methods). A
2
2
2
rate: 0.05 V/s. S = 0.0177 cm .
V in CV, followed upon reverse scan by the appearance of a
reversible wave at ∼0 V characteristic of the p-aminophenol/
quinoneimine redox couple. For monitoring the chemical
reaction of deprotection by amperometry, it is therefore
essential to carefully choose the potential at which PAP is
detected in order to avoid any interference from the
electrochemical generation of PAP by direct oxidation of
PAPB at the electrode. An applied potential of +0.3 V was thus
selected.
second order rate constant of k = 4.1 ± 0.2 M−
1
s
−1
was
obtained, which is in good agreement with the one determined
by the kinetic rotating droplet electrochemical method. The
value obtained herein slightly outperforms the kinetic rate
constants previously determined for H O -mediated depro-
2
2
tection of different types of arylboronic ester derivatives at
−
1
neutral pH (i.e., k values ranging from 0.07 to 2.2 M
s ).
−
1
46−50
It probably results from a favorable electronic effect
of the amino electron donating group on the para position,
thereby facilitating the oxidative cleavage.
Figure 5 shows the amperometric kinetics traces obtained
0
H
after the injection of different concentrations of H O (C
2
2
2
O
2
Kinetic Results with the Enantiospecific Binding of L-
Tyrosinamide to an Aptamer. As a second example, we have
investigated the enantiospecific and reversible biomolecular
binding kinetics of the small chiral molecule L-tyrosinamide (L-
Tym) to its specific 49-mer D-deoxyribo-oligonucleotide
aptamer (D-Apt ) (eq 6, considering a single binding site per
ranging from 0.2 to 10 mM) in a 50 μL rotated droplet (ω =
000 rpm) of 0.1 mM PAPB. Immediately after the addition of
H O (t = 0), PAP is generated in solution and the current
2
2
2
density at +0.3 V is exponentially increased from zero up to a
49
aptamer).
‐Tym +
with K = k /k
k
on
L
D
‐Apt XooY
L
‐Tym/ ‐Apt49
D
4
9
k
(6)
off
d
off on
For monitoring this binding reaction, we have used the same
electrochemical detection strategy we have recently devel-
32
oped. The principle of detection relies on the intrinsic
electroactive properties of L-Tym that can be oxidized at anodic
potential, but also on the difference of diffusion rates between
the free L-Tym molecule and the L-Tym/aptamer complex.
Moreover, in order to quantitatively and accurately discriminate
the free from the bound L-Tym, the electrochemical detection
was performed under redox-mediated catalysis, a strategy that
not only allows us to obtain well-defined and reproducible
anodic catalytic currents of L-Tym but also avoids electrode
surface fouling or passivation by direct oxidation of the phenol
Figure 5. (left) Normalized amperometric kinetic plots recorded at
+
0.3 V (vs Ag/AgCl) after the injection of 1 μL of different H O
2 2
concentrations in a rotated droplet (V = 49 μL, ω = 2000 rpm) of 0.1
mM PAPB (in a 0.1 M phosphate buffer, pH 7.4). The final
concentration of H O was (black) 0, (orange) 0.2, (green) 1, (pink)
2
2
2.5, (red) 5, and (blue) 10 mM. The dashed line represents an
33,51
derivative.
The redox-mediated catalysis was achieved
exponential function fit to the experimental data at 2.5 mM H O .
2
2
under total catalysis conditions (vide infra) with the addition
(
Right) Pseudo-first-order kinetic rate constant, kobs, as a function of
H O concentration. Plain line: linear regression [slope = (5.1 ± 0.1)
of a minute amount of the one-electron redox mediator
2
M
2
−
1
−1
2
II
2+
s ; r = 0.9994].
[Os (bpy) ] in the reaction solution.
3
1
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Figure 6. (left) Normalized time-course amperometric response recorded at +0.7 V (vs Ag/AgCl) at a rotated droplet (V = 50 μL, ω = 2500 rpm) of
II
2+
5
μM [Os (bpy) ] (in TB, pH 7.4) and for successive injections of, first, 5 μM L-Tym and then different concentrations of D-Apt : (from top to
3
4
9
0
bottom) 0, 1, 2.5, 5, 10, 15, 20, and 25 μM D-Apt . The current was normalized to the catalytic current value, i , recorded just before the aptamer
49
c
injection (t = 0). The dashed plots are the theoretical curves obtained from best fit of eq 10 to the data using a single set of parameters: k = 5200
on
−
1
−1
∞
0
M
s , K = 4 μM, and i /i = 0.33. (right) Simulated kinetic plots taking into account the electrocatalytic consumption of L-Tym. The simulations
were obtained with the following set of parameters: τ = 1.25 s, kcons = 8 × 10 s , k = 5800 M s , k = 2.8 × 10 s , and i /i = 0.33 (see
d c c
−4
−1
−1 −1
−2 −1
∞
0
c
on
off
c
details in the text).
The experimental binding kinetic plots shown in Figure 6
The concentration-dependent current decays observed over a
few tens of seconds after aptamer injection (occurring thus over
a time window significantly longer than the mixing time of L-
Tym) are clearly related to the binding kinetics of L-Tym to its
aptamer, whereas at longer time, the dependence of the limiting
plateau current with the aptamer concentration reflects the
were obtained as follows. A sandwiched (l = 2.5 mm) 48-μL
II
2+
droplet of 5 μM [Os (bpy) ] in TB was rotated at 2500 rpm,
3
while the working screen-printed electrode potential was held
II
2+
III
3+
0
at +0.7 V to oxidize the [Os (bpy) ] into [Os (bpy) ] (E
3
3
51
=
0.58 vs Ag/AgCl ). Once the steady-state anodic current was
stabilized at a value of 1.9 ± 0.2 μA/cm , characteristic of the
diffusion controlled oxidation of [Os (bpy) ] , a 1 μL L-Tym
2
equilibrium of the reaction (K ). Note that the injection of a
d
II
2+ 52
49-mer random DNA sequence does not produce any decrease
of the catalytic current (not shown).
The general analytical expression describing the kinetics of a
reversible binding reaction is obtained from the integration of
eq 7 (see Supporting Information):
3
solution was injected in the rotated droplet (final concentration
of C0 = 5 μM). As seen in Figure 6, immediately after L-Tym
Tym
injection, the current was rapidly increased to a maximal value
2
(
absolute value of 5.5 ± 0.3 μA/cm ), characteristic of the
catalytic oxidation of L-Tym at the electrode surface by the
III
3+
d[L‐Tym]
d[L‐Tym/Apt49]
electrochemically generated [Os (bpy) ] . The rate at which
3
−
=
the catalytic current was raised and then stabilized gives a direct
measure of the mixing time required to homogeneously mix L-
Tym throughout the whole droplet volume (an average
relaxation time of 1.1 ± 0.1 s, similar to H O , was found).
dt
dt
dx
0
0
Apt
=
= k (C
− x)(C
− x) − koffx
on Tym
(
7)
dt
which finally leads to
2
2
According to the rather high efficiency of the catalytic oxidation
III
3+
of L-Tym by [Os (bpy) ] and also because of the low excess
3
χf = [
L
‐Tym]
ratio of L-Tym compared with the redox catalyst (i.e., 1:1 ratio),
the resulting steady-state catalytic current is expected to be
entirely controlled by the mass transport of L-Tym to the
0
C
Tym
⎡
1
r2
⎤
⎦⎥
53
r − r exp (r − r ) k t +
ln
2
1
2
1
⎣⎢
on
(
)
⎥
⎦
electrode surface (i.e., total catalysis ) and therefore governed
by an equation similar to eq 2. The occurrence of this limiting
case was verified from the linear dependence of the steady-state
catalytic current vs L-Tym concentration within the range 0−5
{
r2 − r1
r
}
1
1
=
1 − C0
Tym
⎡
1
r
⎤
2
1
− exp (r − r ) k t +
ln
2
1
⎢
⎣
on
( )
{
r2 − r1
r
}
1
54
(8)
μM (Figure S9, Supporting Information). As soon as L-Tym
is well-mixed, 1 μL of D-Apt was injected (t = 0) in the
where χ is the mole fraction of L-Tym, and r and r are the
4
9
f
1
2
0
Apt
2
0
Tym
0
0
0
reaction solution (final C concentration ranging from 0 to 20
roots of the equation x − x(C + C + K ) + C
According to our previous work, the catalytic current (i )
can be considered as a linear combination of the catalytic
currents related to the free and bound L-Tym, which, under
approximation of total catalysis, would lead to
C
= 0.
Apt
d
Tym Apt
3
2
μM), and the change in the catalytic current was recorded. The
overlaid kinetic traces in Figure 6 show a systematic exponential
decay of the catalytic current subsequent to the aptamer
addition until a new concentration-dependent steady-state
current value is reached, characteristic of an equilibrium
binding. Such a behavior is in agreement with that expected
for the specific capture of L-Tym by the aptamer, which hence
c
i = 0.465nFSν−
1/6
ω
1/2C [χ D
0
2/3
f
Tym
+ (1 − χf )
c
Tym
DTym/Apt2/3]
32
(9)
decreases the average diffusion rate of L-Tym to the electrode.
1
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Journal of the American Chemical Society
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From the combination of eqs 8 and 9 and knowledge of the
steady-state catalytic currents determined both in the absence
equations associated with each process were numerically solved
(see Materials and Methods) and the concentration decay of L-
Tym with time thus calculated. Also, to consider the potential
interference of the mixing kinetics on the overall kinetics
(especially at high aptamer concentrations), a first-order mixing
rate process has been included in the simulation, leading thus to
the following global reaction scheme:
0
∞
of aptamer (i ) and at infinite aptamer concentration (i ), we
c
c
can write eq 10, which allows us to predict the normalized
catalytic current decreases as a function of time.
∞
∞
⎛
⎞
⎟
i (t)
= ii + χ ⎜1 −
i
c
c
c
0
0
c
f
0
i
⎝
i ⎠
c
c
(10)
1/τ
A ⎯ ⎯→ ‐Apt49
D
or
k
cons
i (t)
1
c
L
‐Tym ⎯⎯ ⎯→ P
=
1 − C0
0
i
c
Tym
k
on
L‐Tym +
D
‐Apt XooY
L‐Tym/D
‐Apt49
⎡
1
2 −
r2
⎤
49
k
r − r exp (r − r ) k t +
ln
off
2
1
2
1
⎢
⎣
on
(
)
⎥
⎦
⎥
{
r
r
r
⎦
}
1
1
where A represents the aptamer amount initially present in the
micropipet and P the product generated from the irreversible
⎡
1
2 −
r
⎤
2
1
− exp (r − r ) k t +
ln(
2
1
⎢
⎣
on
)
{
i ⎠
r
r
r
1
}
55
1
transformation of L-Tym. This whole set of reactions need
∞
⎛
⎜
⎝
⎞
thus five parameters to simulate and fit the progress curves
1 − i
c
∞
0
c
⎟
shown in Figure 6, that is, τ, kcons, k , k , and i /i . The first
0
c
on off
c
two constants, τ and kcons, were recovered from the previous
experiments. The three others were adjusted by iterative fitting
of the simulated plots to the experimental ones. From the best
fits (Figure 6, right plots), the following values were obtained:
The fit of eq 10 to the experimental data in Figure 6 would
thus give the value of k , K , and i /i . From the theoretical
∞
0
c
on
d
c
plots represented by the four dashed curves on the left graph,
kon = 5800 ± 200 M− s , k = 0.028 ± 0.003 s and i /i =
1
−1
−1
∞
0
−1
−1
∞
0
off c c
values of k = 5200 M s , K = 4 μM, and i /i = 0.33 were
on
d
c
c
0
.33 ± 0.02. The resulting K = k /k = 4.8 ± 0.3 μM is
d
off on
obtained. Although fits of eq 10 to the experimental plots are
almost correct, they are far from being perfect, especially at the
limiting plateau currents. This is because eq 10 does not take
into account the slight nonspecific steady catalytic current
decrease concomitantly recorded during the course of the
specific exponential response decrease. The slight steady
decrease, also observed in the absence of aptamer (black
curve in Figure 6), can be explained by the non-negligible
irreversible consumption of L-Tym as a function of electrolysis
time, with a rate that is directly related to both the electrode
surface-to-droplet volume ratio and the magnitude of the
anodic catalytic current. Assuming that the measured current is
governed by total catalysis and the diffusion layer thickness is
steady while the sample is rotated, we can thus write eq 11,
which describes the L-Tym concentration decay with time at a
constant potential electrolysis:
32
consistent with our previous work (i.e., K = 2.9 μM) and in
d
agreement with those previously determined by isothermal
56
57
titration calorimetry and fluorescence polarization, there-
fore validating the reliability of the method. From the
∞
0
experimental ratio i /i = 0.33 proportional to (DTym/Apt/
DTym
c
c
2/3
) , the calculated value of DTym/Apt/DTym = 0.19 also
compares well to the one (i.e., 0.20) previously found by CV
∞
0
c
under nonhydrodynamic conditions (in this latter case i /i =
c
1
/2 32
(
DTym/Apt/DTym) ).
Knowing the binding kinetics between aptamers and small
ligands is important for understanding their recognition
mechanisms as well as for developing practical affinity binding
assays. A number of studies have been devoted to this end, and
when compared with the rate constants that have been
previously determined for small molecule interactions with
8
,58−61
natural or unnatural aptamers,
the value obtained here
(kon = 5800 M− s ) lies in the average of published values. For
instance, a binding rate constant of kon = 2 × 10 M
been found for the specific interaction between the thiamine
1
−1
d[L‐Tym]
dt
ic
SD
Vδcorr
=
=
[L‐Tym]
4
−1 −1
s
has
nFV
(11)
After integration, eq 11 leads to
pyrophosphate ligand and the RNA riboswitch present in the
8
0
Tym
5′-UTR of the thiC mRNA, a result that was obtained by
[L‐Tym] = C
exp[−(SD/Vδcorr)t]
kinetic isothermal titration calorimetry. This technique is more
universal than ours but requires an expensive instrument
or
8
currently restricted to a response time of ∼3.5 s. Another
⎛
2/3
⎞
ic
= [
L
‐Tym]
SD
example that has been recently investigated by kinetic capillary
electrophoresis is the interaction of quinine with variants of a
= exp⎜−
t⎟
0
0
⎝ 2.15ν1/6ω−1/2V ⎠
i
C
c
Tym
(12)
DNA aptamer for which k values ranging from 340 to 410
on
−1
−1
58
From the fit of eq 12 to the experimental curve obtained in the
absence of aptamer (black curve in Figure 6), a first-order rate
M
s
have been found. The kinetic capillary electro-
phoresis method has the advantage of not requiring the labeling
of one reactant, and it can then be applied theoretically to all
−4 −1
constant, kcons = SD/(Vδcorr) = 8 × 10 s , was found. When
58
the experiment was repeated with a 4-fold larger screen-printed
types of ligands. However in practice, the technique is limited
by the buffer composition that may perturb the electro-osmotic
flow and also by charged ligands that can interact and be
2
working electrode area (S = 0.071 cm ), the steady catalytic
current decrease was enhanced by a factor 4 (Figure S10,
Supporting Information) as expected from eq 12.
To more rigorously take into consideration the concurrent
consumption of L-Tym by aptamer binding and electrochemical
oxidation during the reaction progress, the rate differential
retained on the capillary wall. The other examples of k ,
on
4
5
−1 −1
ranging from 2 × 10 to 2 × 10 M s , were all determined
5
9−61
by stopped-flow fluorescence spectroscopy.
The main
advantage of this technique is that it allows the determination
1
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of fast binding rate constants because of its millisecond time
resolution combined with a good sensitivity. However, this is
once more a rather costly instrument that requires large
amount of biological material for performing a complete set of
kinetic experiments. In contrast to all of these examples, the
present kinetic method has finally the combined advantages of
being affordable, simple, and really easy to implement and using
a very low amount of reagents, which is particularly interesting
for some natural nucleic acids that can only be produced in low
amount by in vivo genetic expression. The electrochemical
detection here profits from the intrinsic electroactivity of the
ligand, but it can be also extended to nonelectroactive ligands
by introducing an extrinsic redox label on the ligand as we have
E1. Since this first reaction step goes through the formation of a
short-lived ES intermediate, it can be kinetically described by a
Michaelis−Menten formalism and the following two key
parameters: a substrate Michaelis constant K1 = (k
+
,M
1,−1
k )/k = 128 μM and a bimolecular rate constant k =
1
,2
1,1
1
7
−1 −1
k k /(k
+ k ) = 1.7 × 10 M s . In the presence of a
1,1 1,2
1,−1
1,2
one-electron donor Q, E is then rapidly reduced to yield the
1
oxyferryl intermediate E and the product P (reaction 2).
2
Thereafter, with a second equivalent of Q, the enzyme is
regenerated back to its native resting state E by a subsequent
one-electron/two-proton reduction of E to give a second
2
equivalent of P and water (reaction 3). At sufficiently high
substrate concentration, this third reaction is generally the rate
limiting step of the catalytic cycle of HRP (reaction 2 is 10−20-
32
previously shown with a ferrocene-labeled L-Tym. Besides,
kinetic characterization of strictly nonmodified ligand might
also be carried out by combing redox labeling strategies with
3
3,62
fold faster than reaction 3).
Moreover, its investigation has
shown kinetic evidence for a two-step Michaelis−Menten-type
32
63,64
competitive bindings. Another general aspect of the present
technique lies in the fact that the maximal signal amplitude
between free and bound state is merely set by the relative
change in diffusion coefficients, therefore leading to a
predictable signal change for any new design of a small
target/aptamer binding assay. This is undeniably an advantage
over unpredictable signal change generated by fluorescent
reaction with a wide range of electron donors,
a behavior
II
+
that was also observed with [Os (bpy) pyCl] for which a
2
cosubstrate Michaelis constant of K3,M = (k3,−1 + k )/k = 20
3,2
3,1
μM and a bimolecular rate constant of k = k k /(k + k )
3
3,1 3,2
3,−1
3,2
7
−1 −1
33
= 1.4 × 10 M
s
were obtained. The main loop E → E →
E2 → E is the well-established peroxidatic catalytic cycle of
1
HRP, during which one molecule of H O is converted in two
2
2
57
probes in optical detection methods.
molecules of H O while two molecules of a one-electron donor
2
Kinetic Results with the Reversible Substrate Inhib-
ition of Horseradish Peroxidase. As a last illustrating
example, we have investigated the kinetics of a more complex
are concomitantly oxidized. This fast primary catalytic cycle is
the source of the amplified catalytic current in cyclic
33
voltammetry. However, at high H O concentration, the
2
2
reaction mechanism: the catalytic reduction of H O2 by
intermediate E can competitively react with H O (reaction 4)
2
2
2
2
horseradish peroxidase (HRP). This mechanism was previously
elucidated by cyclic voltammetry under redox-mediated
to yield the inactivated form of HRP, the oxyperoxidase or E
3
−
1
−1 65−67
(with a rate constant k ranging from 16 to 55 M s ),
4
3
3
33
catalysis. The reaction scheme is recalled in Scheme 2
resulting in a catalytic current inhibition. Additional complex-
ity also comes from the two HRP reactivation pathways via E3.
The first one is the spontaneous self-reactivation by
Scheme 2. Global Redox-Mediated Catalytic Reaction
Mechanism of HRP
decomposition of E into the active form E (reaction 6),
3
leading to superoxide ion with a rate constant k ranging from
6
3
−2 −1 33,67,68
2
.2 × 10− to 1.2 × 10 s .
The second one is the
reductive reactivation of E into E by the electron donor Q
3
1
6
9,70
present in solution (reaction 5).
A rate constant k of 1900
was previously found for the reactivation of E by the
3
33
5
−
1 −1
M
[
s
II
+
Os (bpy) pyCl] complex.
2
33
In a previous work, the whole set of kinetic constants
controlling the inactivation/reactivation reactions of HRP was
determined from the analysis of catalytic responses recorded by
CV under stationary conditions. The present rotating droplet
kinetic method offers the opportunity to reexamine these
inactivation/reactivation pathways not only under hydro-
dynamic conditions but also transiently subsequent to the
injection of H O . For such a purpose, a 49 μL droplet
2
2
II
+
containing 1 μM HRP and 20 μM [Os (bpy) pyCl] (in EB,
2
pH 7.4) was rotated at ω = 2000 rpm over a screen-printed
electrochemical cell. The potential of the working electrode was
held first at an anodic value of +0.4 V followed by a rapid
switch at −0.1 V before an aliquot of H O was added. The
III
2+
where P and Q are the oxidized ([Os (bpy) pyCl] ) and
2
2
2
II
+
reduced ([Os (bpy) pyCl] ) forms of the reversible one-
electron redox cosubstrate (or mediator), E is the native
ferriperoxidase, E is the oxyferryl π-cation radical compound I,
E is the oxyferryl compound II, E is the oxyperoxidase
compound III, and ES and E Q are the precursor complexes
that may take place with the reactive form of substrate and
cosubstrate, respectively. In the presence of substrate H O , the
catalytic cycle starts from a rapid oxygen atom transfer
reaction 1) from H O to the ferric heme (Fe ) in E
electrode polarization at +0.4 V provides a steady-state current
resulting from the oxidation of the osmium(II) complex
present in the droplet and thereby allows control if the
concentration and hydrodynamic conditions are right (Figure
7). From the steady-state current, the diffusion coefficient of
2
1
2
3
2
II
+
[Os (bpy) pyCl] can also be determined using eq 3. An
2
−6
2 −1
average value of D = 4.5 × 10 cm s was obtained, which is
2
2
Q
33
in good agreement with that previously published. Upon
switching the electrode potential at −0.1 V, the current density
drops to zero since at this potential the complex remains in its
III
(
(
2 2
−
formally a 2 e oxidation) to form water and the intermediate
1
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Article
Figure 7. (left) Substrate-inhibition kinetics of HRP recorded at a 50 μL droplet (ω = 2000 rpm) rotated over an electrode polarized first at +0.4 V
for 20 s (only the last 8 s are shown) and then at +0.1 V, before an aliquot of H O is injected at t = 0. The starting composition of the droplet is 20
2
2
II
+
μM [Os (bpy) pyCl] + 1 μM HRP in EB (pH 7.4). At time t = 0 (arrow), H O was injected in the droplet in such a way to have a final substrate
2
2
2
concentration of (black) 0, (wine) 0.01, (orange) 0.04, (dark cyan) 0.1, (magenta) 0.4, (dark yellow) 1, (blue) 4, (green) 10, and (pink) 50 mM.
right) Corresponding simulated curves (see text for details).
(
reduced form (E 0P /Q = 0.21 V). Immediately after addition of 1
μL of H O solution (t = 0, final concentration ranging from
the primary peroxidatic catalytic loop of HRP. The rate at
which this process occurs is in fact largely controlled by the
mixing rate because, on the basis of the kinetic rate constants
that were previously determined for the primary catalytic
cycle, the time required for complete enzymatic conversion of
the osmium(II) at the present micromolar concentrations is
theoretically less than 0.5 s (Figure S11, Supporting
Information). After a few seconds of reaction, the resulting
steady-state cathodic current reflects the reduction of the
2
2
0
.01 to 50 mM), the cathodic current is rapidly and
exponentially raised in less than 1.5 s (which is characteristic
of the mixing time), up to a maximal value that depends on the
injected H O concentration (Figure 7). This fast increase of
33
2
2
the catalytic current is concomitant to the rapid and complete
oxidation of the reduced form of the osmium complex in the
droplet, whereas a stoichiometric amount of H O2 is
2
simultaneously consumed. Once the maximum is reached, the
current is decreased in a H O -concentration dependent
osmium(III) from which the diffusion coefficient D can be
retrieved. Assuming that the 20 μM osmium(II) complex in the
P
2
2
manner until a steady-state value is asymptotically reached at
longer time (Figure 7). This behavior is characteristic of the
reversible inhibition of HRP by its substrate H O , which,
droplet is entirely converted into osmium(III), a value of D =
P
3.2 × 10− cm s can be calculated, which is slightly lower
than that for the parent reduced form. It is interesting to note
the rather long time (several seconds) needed to reach the
steady-state current compared with the predicted one (less than
0.5 s), well-illustrating the prejudicial effect of the delay
imposed by the noninstantaneous mixing (the catalytic reaction
rate is in fact convoluted to the mixing rate since both kinetics
are of same order of magnitude, therefore delaying the
complete conversion of osmium(II) into osmium(III)) (see
simulations in Figure S11, Supporting Information).
6
2
−1
2
2
according to reaction 4 in Scheme 2, follows a second-order
rate with the H O concentration. During the course of the
2
2
catalytic reduction of H O by HRP, E2 is progressively
2
2
deviated from the primary catalytic loop through the
competitive reaction 4, which thus allows E to be accumulated.
3
However, while E is accumulated, a fraction is reactivated
3
through reactions 5 and 6. As observed in Figure 7, once the
inhibition rate equals those of reactivation, the catalytic current
stops at a stationary value, which thus depends on the H O2
In an attempt to analyze the experimental kinetics plots
through an analytical expression of the catalytic current changes
as a function of time (i.e., in a similar way as it was previously
2
concentration according to the following competitive param-
0
0
eter: k C /(k [Q] + k ) (where C is the droplet concentration
4
S
5
6
S
II
+
33
of H O and [Q] is the concentration of [Os (bpy) pyCl]
done in cyclic voltammetry ), we have realized its unfeasibility
2
2
2
generated within the diffusion-reaction layer at the electrode
for the reason that, under our experimental settings, the
catalytic current never reaches pure catalytic kinetic conditions
(the thickness of the catalytic enzyme reaction layer is in fact of
comparable size to the thickness of the steady-state diffusion
layer of the redox mediator, even for the highest catalytic
surface). When only a stoichiometric amount of H O is added
2
2
(
10 μM H O for 20 μM osmium(II) complex; wine curve in
2 2
Figure 7), the cathodic current slowly increases over seconds
and then halts at an absolute value not very different from the
one obtained for the steady-state oxidation of
71
current response). The alternative was then to numerically
solve the overall rate differential equations of the HRP
mechanism with the help of the commercial DigiElch software
dedicated to the simulation of electrochemical processes at
II
+
[
Os (bpy) pyCl] at +0.4 V (note that at these concentrations,
2
substrate inhibition is negligible). This behavior is characteristic
of quantitative conversion of the osmium(II) complex initially
present in the droplet into its osmium(III) form. The measured
current here provides an immediate observation of the
osmium(III) concentration growth within the droplet through
38
electrodes by finite difference computation. Since DigiElch
does not allow simulating an electrochemical response at a
RDE, we have selected the chronoamperometric 2D-simulation
1
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Journal of the American Chemical Society
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mode at a microdisk electrode, which allows simulation of a
current response under steady-state mass transport conditions
equivalent to those achieved at a RDE. In addition to the
overall elementary reactions of HRP reported in Scheme 2, the
mixing rate was included in the simulation via a first-order
reaction in which H O is generated from a virtual compound
U with a rate constant of 1/τ = 0.8 s . The overall parameters
that give best fits to the experimental plots in Figure 7 are
reported in Table 1. For the fitting, only the rate constants k4,
not directly implicate an electrodetectable compound.
Furthermore, the methodology can be extended to reactions
occurring heterogeneously at an electrode surface. For example,
it could be used for studying heterogeneous electrochemical
catalytic reactions at electrodes modified by molecular or
inorganic catalysts, but also for characterizing catalytic reactions
of immobilized enzymes (either through direct or mediated
electron transfer) on different types or shapes of conductive
materials (e.g., nanostructured conductive materials, forests of
nanotubes, transparent conductive metal oxides) or for
investigating either the adsorption kinetics of electroactive
compounds on electrode surfaces or the specific binding of a
ligand to an immobilized receptor in a much easier way than at
a conventional RDE. For these latter applications, the cell
volume is no more an issue but the possibility to easily adapt or
interchange the nature or shape of the working electrode is of
great interest, especially for investigating under hydrodynamic
conditions the heterogeneous electrochemical reactions at
fragile electrode materials or at electrodes having complex
design or shapes.
2
2
−1
Table 1. Kinetic Rate Constants and Parameters Used for
the Simulation of the Redox-Mediated Catalytic Responses
a
of HRP Shown in Figure 7
b
reaction
kinetic rate constants
E + H O /E
k = 1.7 × 10 M s−1; k1,2 = 2.2 × 10 s
7
−1
3
−1
−1
2
2
1
1
k = 2 × 10 M s−1
8
−1
E1 + Q/E
E2 + Q/E
2
2
k = 1.2 × 10 M s−1; k3,2 = 2.8 × 10 s
7
−1
2
3
E + H O /E
k4 = 60 M−
1
s
3
−1
(55 M−1 s−1
)
c
2
2
2
3
E3/E
k6 = 5 × 10− s−1 (1.2 × 10 s−1
−2
)
3
3
−1 −1
(1.9 × 10 M s−1
)
−1
E3 + Q/E1
U/H O
k = 1.2 × 10 M
s
5
While the use of screen-printed technology allows flexible
design (geometries and materials) of disposable and mini-
aturized electrochemical cells, particularly well-adapted to the
method, electrochemical microcells fabricated by other
−1
1/τ = 0.8 s
0
2
2
−
−1
0
d
P + e /Q
k = 10 cm s , α = 0.5, E = 0.21 V
a
b
In parentheses are the values reported in ref 33. At pH 7.4 and ∼20
c
−1 −1
−3 −1
72
°C. Literature values: k = 40 M
s
in ref 65; k = 8 × 10
s
in
4
6
techniques such as photolithography and laser micromachin-
d
0
ref 69. k , standard heterogeneous electron transfer rate; α, transfer
coefficient.
73
ing might also be straightaway used. Another much
appreciated feature of the method is the very easy and fast
sample change, which just requires removal of the droplet by
pipetting and, after washing of electrodes/rod interface and
soaking up with a paper tissue, application of a new one. The
system was demonstrated with aqueous droplets, but it can be
relatively easily transposed to any low-volatile organic solvent
able to form a stable hemispherical droplet on a surface
delimited by an appropriate circular well. The foregoing
features along with the ease-to-implement the system in a
laboratory from the commercially available standard potentio-
stats and adjustable speed rotators is a further reason that
makes the method accessible and attractive.
k , and k were slightly adjusted, whereas the other rate
5
6
33
constants were kept the same as in previous work. Using this
set of values, the time-course amperometric simulations were
finally found, for all substrate concentrations, in excellent
agreement with the experimental ones (right plots in Figure 7).
Even for the experiment performed under stoichiometric
H O /mediator ratio, the current response is well predicted
2
2
by simulation.
These results again demonstrate the relevance of the kinetic
rotating droplet electrochemical method for reaction progress
kinetic analysis in microliter samples and highlight the potential
offered by this method for analyzing kinetics of complex
mechanisms. It also points out its high precision, resolution,
and reproducibility.
In the case of large electrode surface area to volume ratio,
exhaustive electrolysis of the electroactive species in the entire
sample droplet has been shown to be achievable. It therefore
opens the opportunity to determine reaction stoichiometries by
microcoulometry as well as to analyze the electrolyzed content
of the microdrop by separation methods (e.g., HPLC, capillary
electrophoresis). For the development of these applications, the
problem of isolating the counter electrode in an independent
compartment separated from the droplet by a junction has to
be solved. One possibility is to include, similarly as shown by
CONCLUSION
■
In this proof-of-principle work, we have outlined the main
features of the kinetic rotating droplet electrochemical method.
Its 1 s kinetic time resolution combined with a low detection
limit, high reproducibility, ease-to-operate, and ability to
perform kinetics with microliter-size samples are key advantages
that make this methodology particularly attractive and
appropriate for kinetic analysis, especially for reactions
involving low-abundance or expensive reagents.
2
5,26
Gratzl and colleagues,
a junction (e.g., Vycor glass frit) with
an electrolyte compartment somewhere on the nonmoving
support of the working electrode. Another more convenient
approach would be to incorporate the counter electrode
directly inside the body of a hollow rotating rod filled with an
electrolyte and closed at its disk extremity with a junction.
Additionally, independently of microcoulometric and kinetic
applications, the rotating droplet system could be advanta-
geously used for a wide range of analytical purposes (e.g.,
electrochemical enzyme-based bioaffinity assays, anodic strip-
ping voltammetry of heavy metals).
The method has been currently illustrated with three
different types of reactions: an irreversible chemical reaction,
a reversible biomolecular recognition binding, and a substrate
inhibition/reactivation of a catalytic enzyme reaction. It is of
course not restricted to these reaction types. In principle, it can
be extended to any homogeneous reactions involving a change
either in the redox state, formal potential, electron transfer
kinetics, or diffusion rate of one of the reactants or products.
Although not demonstrated here, on the basis of our previous
The work is in progress to improve the mixing time down to
a few tens of milliseconds and to better understand the mass
transport occurring at the rotated droplet/stationary working
electrode interface from numerical simulations. Mechanical
32
work involving a redox labeling strategy, the method can also
be anticipated for kinetic characterizations of reactions that do
1
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Journal of the American Chemical Society
Article
increase of the mixing by trapping small air bubbles within the
rotated droplet or by using a roughened rotating rod interface
are directions that must be considered to improve the mixing
time of the system. Designing a device able to perform fast
nonmanual injection at a well-defined position in the droplet is
another route to explore.
We believed that the kinetic rotating droplet electrochemical
method is not only an alternative as well as a complementary
method to the wide range of existing optical kinetic methods
but also offers new possibilities for getting information
unattainable by other simple means.
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ASSOCIATED CONTENT
Supporting Information
■
(
8
(
*
S
Cross-sectional profile of the screen-printed electrochemical
microcell, CVs for a low FcMeOH concentration at a rotated
droplet, CV comparison with a standard RDE, detection
sensitivity of FcMeOH, effect of electrode area on successive
CV scans at a rotated droplet, SEM images of a gold-plated
screen-printed electrode, transient currents characterizing the
mixing time, verification of the linear relationship between
catalytic current and L-Tym concentration, influence of
electrode area on the catalytic current of L-Tym, simulations
of [Q] decay or [P] growth during redox-mediated HRP
catalysis, and derivation of eq 7 is also reported. This material is
available free of charge via the Internet at http://pubs.acs.org.
(
Electrochemistry; Wiley-VCH Verlag GmbH & Co. KGaA: Weinheim,
Germany, 2007.
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AUTHOR INFORMATION
Corresponding Authors
francois.mavre@univ-paris-diderot.fr
limoges@univ-paris-diderot.fr
■
(
(
2
Author Contributions
̈
llhorn, B.; Degrand, C. Anal. Chem.
§
1
(
L.C. and R.M.-C. contributed equally.
Notes
The authors declare no competing financial interest.
(
́
̈
llhorn, B.;
̈
ACKNOWLEDGMENTS
This work was supported by Agence Nationale pour la
Recherche (ANR ECSTASE project).
■
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