Enzymatic Electrocatalysis in a Micellar Environment: Glucose Oxidase Catalysis Mediated by Ferrocene Solubilized by Addition of n-Octyl-β-D-glucoside

Article abstract of DOI:10.1021/jp953120f

In the presence of the neutral n-octylglucoside surfactant the reduced form P of the ferrocene mediator is solubilized by micellization in aqueous solution.Then it can be used in the mediation of the electrochemically driven oxidation of glucose catalyzed by glucose oxidase.The validity of the assumption that P is the only micellized species is ascertained by the analysis of the experimental results.The micellization of the water-soluble ferrocenium Q can be neglected.The apparent diffusion coefficient D_P of ferrocene can be controlled by the micelle concentration while the diffusion coefficient D_Q of ferrocenium is only affected by the accompanying changes in the viscosity of the medium.Accordingly, the kinetics of the enzymatic electrocatalysis, investigated by means of cyclic voltammetry, depends on D_P and the ratio δ = D_P/D_Q.A thorough quantitative analysis of the observed behavior enabled us to carry out the complete kinetic characterization of the process and to show that all the rate constants involved in the enzyme kinetics are unaffected by the presence of the surfactant.

Full text of DOI:10.1021/jp953120f

J. Phys. Chem. 1996, 100, 5063-5069
5063
Enzymatic Electrocatalysis in a Micellar Environment: Glucose Oxidase Catalysis Mediated
by Ferrocene Solubilized by Addition of n-Octyl-â-D-glucoside
Christophe Deshaies,1a Joe1l Chopineau,1a Jacques Moiroux,1b and Christian Bourdillon*,1a
Laboratoire de Technologie Enzymatique, Unite´ Associe´e au CNRS No. 1442, UniVersite´
de Technologie de Compie`gne, B.P. 529, 60205 Compie`gne Cedex, France, and the Laboratoire
d’Electrochimie Mole´culaire, Unite´ Associe´e au CNRS No. 438, UniVersite´ Paris 7sDenis Diderot,
2 place Jussieu, 75251 Paris Cedex 05, France
ReceiVed: October 23, 1995; In Final Form: January 3, 1996X
In the presence of the neutral n-octylglucoside surfactant the reduced form P of the ferrocene mediator is
solubilized by micellization in aqueous solution. Then it can be used in the mediation of the electrochemically
driven oxidation of glucose catalyzed by glucose oxidase. The validity of the assumption that P is the only
micellized species is ascertained by the analysis of the experimental results. The micellization of the water-
soluble ferrocenium Q can be neglected. The apparent diffusion coefficient DP of ferrocene can be controlled
by the micelle concentration while the diffusion coefficient DQ of ferrocenium is only affected by the
accompanying changes in the viscosity of the medium. Accordingly, the kinetics of the enzymatic
electrocatalysis, investigated by means of cyclic voltammetry, depends on DP and the ratio δ ) DP/DQ. A
thorough quantitative analysis of the observed behavior enabled us to carry out the complete kinetic
characterization of the process and to show that all the rate constants involved in the enzyme kinetics are
unaffected by the presence of the surfactant.
The amphiphilic structure of surfactants and their aggregating
properties in aqueous solutions provide a multifunctional
environment for the solubilization and partition of molecules
whose water solubility is rather low. For instance, microhet-
erogeneous solutions have been extensively used in the fields
of chemical catalysis,2 electrocatalysis,3 or enzymatic catalysis.4
The present paper deals with an example of redox enzymatic
catalysis involving a water-insoluble cosubstrate. Addition of
a surfactant at a higher concentration than the critical micelle
Figure 1. The electrocatalytic scheme.
concentration (cmc) creates micelles which can solubilize the
cosubstrate. Thus, the enzymatically catalyzed process can be
enacted efficiently. The cosubstrate is an electroactive mediator
whose enzymatically active form is electrochemically regener-
ated giving birth to the occurrence of an electrocatalytic process.
The partitioning of the cosubstrate in the structure can affect
significantly its apparent thermodynamic characteristics as well
as its apparent rate of diffusion.5 As a result, remarkable
changes in the kinetics of the process are observable and can
be analyzed quantitatively. In the following, we report such a
quantitative analysis of micellar effects on the mediated coupling
between enzymatic and electrochemical reactions.
The electrocatalytic system, which can be considered as a
model, is schematically described in Figure 1. Ferrocene
derivatives have been extensively used as mediators, or cosub-
strates, since the pioneering works of ref 6, particularly, water-
soluble ferrocene derivatives.7
Recently, the electrochemical glucose oxidase catalyzed
oxidation of glucose mediated by one-electron cosubstrates was
studied by means of cyclic voltammetry, the enzyme being
present in the bulk of the solution.8 Then it was shown that
the complete quantitative characterization of the enzyme kinetics
could be achieved. The process consists of the following
sequence of reactions:
standard potential is E°P/Q
.
FAD + G {kk } FADG
(1)
1
-1
k2
FADG
9
8 FADH2 + GL
(2)
(3)
k3
FADH2 + 2Q
98 FAD + 2P
where E-FAD and E-FADH2 are the oxidized and reduced forms
of the glucose oxidase flavoenzyme respectively, G is â-D-
glucose, and GL glucono-δ-lactone.
The rate constants which could be determined then were k3,
k2, and kred ) k1k2/(k-1 + k2).8 In the present work, P is
ferrocene, a cosubstrate almost insoluble in water, and a similar
kinetic study is carried out in micellar solutions solubilizing P.
For the choice of the surfactant we took into account the
following two considerations. Enzymes are poorly stable in
concentrated solutions of numerous surfactants, especially ionic
ones.9a The theoretical treatment of the physical chemistry of
the system under study becomes very complex when both P
and Q are involved in partition equilibria. Thus we chose to
operate with n-octylglycoside (OG), a nonionic surfactant well-
known in the field of biological membranes for not affecting
appreciably the catalytic activity of numerous enzymes.9b
Moreover, with such a nonionic surfactant, the partition of a
water-soluble charged species like Q (ferrocenium cation) can
be neglected.6b,10,11 On the other hand, a water-insoluble neutral
species like P partitions between micelles and water. Therefore,
P a Q + e-
P/Q is a redox couple exhibiting a Nernstian behavior; its
X Abstract published in AdVance ACS Abstracts, February 15, 1996.
0022-3654/96/20100-5063$12.00/0 © 1996 American Chemical Society

5064 J. Phys. Chem., Vol. 100, No. 12, 1996
Deshaies et al.
the apparent rate of diffusion of P depends on the micelle
concentration and can be controlled by it.
δ renders the mathematical treatment much more complicated.
According to the catalytic scheme and the enzyme kinetics,8,12
the following equations govern the time (t) and space (x)
distributions of P and Q within the framework of their
semiinfinite diffusions toward or from the working electrode
surface:
The aim of the present study is twofold. First, it consists in
analyzing the observed changes in the enzymatic electrocatalytic
behavior brought about by the fact that the apparent diffusion
coefficients of P and Q (DP and DQ, respectively) differ
markedly. In a second step, a complete characterization of the
enzyme kinetics in the micellar solutions can be performed.
∂C
∂t
∂2CP
∂x2
2k3C°ECQ
P ) DP
+
-
(VI)
Formal Aspects
k-1 + k2
k1k2CG
1
k2
1 + k3
+
CQ
(
)
The Equilibrium of Partition of P. The electrochemical
behavior of a Nernstian redox couple P/Q in a micellar solution
has been described and theoretically analyzed in terms of
distribution coefficients10a,11 or in terms of equilibrium
constants.3,10b,c We used the latter approach.
∂C
∂2CQ
∂x2
2k3C°ECQ
Q ) DQ
(VII)
∂t
k-1 + k2
k1k2CG
1
k2
1 + k3
+
CQ
(
)
For the partition of P in the presence of micelles M:
P + M a PM
the equilibrium constant K is expressed as
K ) CPM/CPCM
(4)
with C°E the sum of the concentrations of all the catalytically
active forms of the enzyme bound flavin12 and CG the glucose
concentration.
Within the series of experiments we have carried out, the
excess of glucose was large enough to ensure that CG ) C°G
(C°G ) glucose bulk concentration) whatever t and x. As in
ref 8, the enzyme is considered immobile as compared to the
mediator. When taken into account in the simulations, the
diffusion of the enzyme does not affect appreciably the
computed current values.
(I)
with CPM, CP, and CM the concentrations of micelle/ferrocene
aggregates, free ferrocene, and free micelles respectively.
For the mass balances of P and M:
CPM + CM ) CMt
(II)
The current response may thus be obtained from the resolution
of the set of equations (VI) and (VII), accompanied by the
following initial and limiting conditions:
CPM + CP + CQ ) C°P
(III)
with CMt and C°P the total concentrations of micelles and
mediator, respectively, and CQ the concentration of the oxidized
form Q of the mediator.
t ) 0, x g 0, and t g 0, x f ∞
CQ ) 0
The theoretical treatment of the phenomenon can be restricted
to the sole set of equations (I), (II), and (III) provided that the
following two conditions are fulfilled:
(i) There is, at the most, one ferrocene P bound per micelle.
This can be achieved when CMt . C°P.
(ii) Micellization of the ferrocenium cation Q is negligible
as usually assumed in similar circumstances.11 In our case, the
validity of the assumption can be ascertained; see the results
reported further in the text.
(C )
F
RT
t g 0, x ) 0
Q x)0 ) exp (E - E°′P/Q)
[
]
(CP)x)0
The anodic i current flowing through the working electrode
surface (area ) S) is obtained from the concentration gradients
of P or Q according to
∂CQ
∂CQ
Then, taking into account the sole partition of P, its apparent
i ) -FSDQ
) FSD
P
(
)
(
)
∂x x)0
∂x x)0
diffusion coefficient DP in the micellar solution is given by3,10,11
The working electrode potential is related to time during the
anodic scan through E ) Ei + Vt. Ei is the starting potential
at which i ) 0, and V is the linear potential scan rate.
DP,W
DMKCM
DP )
+
(IV)
1 + KCM 1 + KCM
It is convenient to render the above formulations dimension-
less by means of the following changes in variables and
parameters8b
DP,W being the diffusion coefficient of a single molecule of P
and DM the diffusion coefficient of the micelle in the solution.
The apparent standard potential E°′P/Q of the P(micellized)/Q
redox couple is
τ ) (FV/RT)t and ê ) (F/RT)(E - E°′P/Q
)
DP
RT
F
RT
E°′P/Q ) E°P/Q
+
ln(1 + KCM) +
ln
2F DQ
(V)
Thus τ ) ê + u, with u ) -(F/RT)(Ei - E°′P/Q) (practically
u f ∞ since the starting potential is poised at the foot of the
wave where the current flowing through the working electrode
is negligible).
In cyclic voltammetry E°′P/Q ) (Epa + Epc)/2, Epa and Epc being
the anodic and cathodic peak potentials, respectively.
Coupling of the Electrochemical and Enzymatically Cata-
lyzed Reactions. As already mentioned, the detailed theoretical
analysis of the catalysis of the electrochemical oxidation of
glucose by glucose oxidase mediated by soluble one-electron
redox cosubstrates has been reported previously.8 In the absence
of surfactant, DP and DQ were taken as equal. In the present
case DP/DQ ) δ e 1. The introduction of the new parameter
y ) x(FV/RTDQ)1/2; q ) CQ/C°P; and p ) CP/C°P
λ ) 2k3C°E(RT/FV)
σ ) (k3C°P/k2)[1 + (k-1 + k2)/k1C°G]

Enzymatic Electrocatalysis in a Micellar Environment
J. Phys. Chem., Vol. 100, No. 12, 1996 5065
reversible wave of the mediator is given by
or
σ ) k3C°P[(1/k2) + (1/kredC°G)]
i°p ) 0.446FSC°P(δDQFV/RT)1/2
Thus14
The ratio ip/i°p is a measure of the catalytic efficiency.
At the plateau current, the catalytic efficiency is given by
∂p
∂t
∂2p
∂y2
λq
1 + σq
∂q ∂2q
∂t
λq
1 + σq
) δ
+
and
)
-
∂y2
1/2
ipl
1
λ
1
)
2 1 - ln(1 + σδ)
{
[
]
}
i°p 0.446
σ
σδ
with
with
τ ) 0, y g 0 and τ g 0, y f ∞
q ) 0
or
q
τ g 0, y ) 0
y)0 ) exp(ú)
py)0
ipl
1
)
(λδ)1/2, when σδ , 1
i°p 0.446
The current is then given by
1/2
1/2
DQFV
RT
DQFV
RT
∂q
∂y y)0
∂p
∂y y)0
Obviously, the catalytic efficiency at the plateau depends on
i ) -FSC°
) FSC° δ
(
) ( )
(
) ( )
P
P
δ
1/2, i.e., on the ratio δ of the diffusion coefficients DP and DQ.
The catalytic efficiency ip/i°p, measured at the peak current,
The resulting voltammogram can be simulated as a function
of the parameters δ, λ, and σ by means of the DigiSim software
(see Experimental Section). As expected,8 they all exhibit a
more or less accentuated peak current (ip being its value)
followed by a plateau current (ipl being its value) observable at
sufficiently positive potentials.
also depends on δ as can be illustrated by the simulations.15
However, ip/i°p cannot be expressed as a simple function of δ1/2
.
Results and Discussion
Assessment of the Solubility of Ferrocene in Aqueous
Buffered Solutions of Glucose. Ferrocene is only sparingly
soluble in water. Reported solubilities in the presence of various
electrolytes lie in the range (3-5) × 10-5 M.10a,11,12 In the
absence of surfactant, the measurement of i°p allowed us to
determine the solubility of ferrocene in the phosphate buffer
before and after addition of 0.5 M glucose. At 25 °C, in the
absence of glucose, the diffusion coefficients DP ) DQ were
At the level of the plateau: (∂p/∂τ)pl ) (∂q/∂τ)pl ) 0.
Thus (∂p/∂τ)pl + (∂q/∂τ)pl ) δ(∂ p/∂y2)pl + (∂ q/∂y2)pl ) 0
2
2
or δ(∂ 2p/∂y2)pl ) -(∂ 2q/∂y2)pl or δ(∂p/∂y)pl ) -(∂q/∂y)pl
since δ(∂p/∂y)y)0 ) -(∂q/∂y)y)0 which means that δ(1 - py)0,pl
)
) qy)0,pl or δpy)0,pl + qy)0,pl ) δ i.e., there exists, under such
conditions, a simple relationship between py)0,pl and qy)0,pl
.
Then
taken as 6.7 × 10-6 cm2s-1 12
.
After addition of 0.5 M glucose
and consequent change in the viscosity, DP ) DQ were taken
as 5.4 × 10-6 cm2 s-1, a value deduced from the measurement
of the viscosity (η) of the solution and from the use of the Stokes
Einstein equation which predicts that Dη is a constant. Thus
we found solubilities of (3 ( 1) × 10-5 M and (2 ( 0.5) ×
10-5 M in the phosphate buffer without and with glucose,
respectively. Spectrophotometric assays10a gave similar data
although with less accuracy due to the low molar absorbance
of ferrocene, even in the UV region. We checked out that the
solubility of the ferrocenium cation Q, introduced in the solution
as the commercially available tetrafluoroborate salt, is much
greater than 0.1 mM. The ferrocenium cation is not very stable
in aqueous solutions. However, by operating with great care
and freshly prepared solutions, we were able to determine DQ
by means of cyclic voltammetry and we found DQ ) (6.5 (
1.0) × 10-6 cm2 s-1 in the buffer, without glucose.
δ
qy)0,pl
)
) δ
1 + δexp(-ê)
since ê is very large at the plateau. Before reaching the
stationary plateau, there is no simple way of relating py)0 to
qy)0 and that is the main reason why the computations become
so tedious.
Besides, at the plateau level
(∂2q/∂y2)pl ) λqpl/(1 + σqpl)
A simple integration gives
1/2
∂q
λ
σ
1
σ
) - 2 qy)0,pl - ln(1 + σqy)0,pl
)
(
)
{
[
]
}
∂y y)0,pl
when σqy)0,pl is not very small and therefore
Micellar Solutions of n-Octylglucoside. The complete
characterization of the exact structure of the OG micelles has
not been achieved up to now.16 In contrast with other highly
organized assemblies like vesicles, the micelles are of dynamic
nature. The slowest relaxation process, which corresponds to
the stepwise dissolution of the micelles to monomers and their
subsequent reassociation, occurs within the millisecond time
scale.17
Assuming that the micelles are homogeneous in size and that
the aggregation number N is independent of the surfactant
concentration, the micelle concentration CMt for a given total
concentration C°OG of surfactant is given by
1/2
1/2
FVDQ
RT
λ
σ
1
σ
i ) FSC°
2 δ - ln(1 + σδ)
(
) {
}
]
pl
P
[
or
1/2
FVDQ
RT
i ) FSC°
(λ)1/2δ
(
)
pl
P
when σqy)0,pl ) σδ , 1.
As in the absence of micelles,8 ipl is independent of V.
Obviously, the knowledge of the above formulas giving ipl
is very helpful to ensure the relevancies of the computer
simulations. They can also be used for the direct quantitative
analysis of the experimental data when ipl can be measured with
good accuracy. Then no computer simulation is needed.
In the absence of enzymatic catalysis, for example, in the
absence of glucose and/or enzyme, the peak current i°p of the
CMt ) (C°OG - cmc)/N
(VIII)
At 25 °C, cmc was found to be 23 ( 3 mM for OG.18 However,
N is not known with good accuracy. The experimental
determinations reported in the literature depend on both C°OG

5066 J. Phys. Chem., Vol. 100, No. 12, 1996
Deshaies et al.
Figure 4. Influence of the ferrocene micellization on the apparent
standard potential E°′P/Q. CP ) 0.1 mM in pH 6.5 phosphate buffer
(ionic strength ) 0.1 M) plus 0.5 M glucose. The continuous line is
computed according to eq V using for K, CM, and DP the same values
as in Figure 3, DQ being also corrected for viscosity.
Figure 2. Viscosity, at 25 °C, of the micellar solutions of n-
octylglucoside in the pH 6.5 phosphate buffer (ionic strength ) 0.1
M): ([) with 0.5 M glucose, (9) without glucose.
Figure 3. Influence of the micelle concentration CMt on the diffusion
coefficient DP of ferrocene measured by means of cyclic voltammetry.
Ferrocene concentration: C°P ) 0.1 mM. Background: pH 6.5
phosphate buffer (ionic strength ) 0.1 M) plus 0.5 M glucose. ([)
Experimental data. The thick line is computed according to eq IV with
K ) 1.2 × 104 and CM given by eqs I-III knowing C°P and C°OG
;
D
P,W and DM were corrected for viscosity according to eq IX for each
C°OG. The thin line is computed similarly without taking into account
the changes in viscosity.
Figure 5. Catalysis of the electrochemical oxidation of glucose by
glucose oxidase mediated by micellized ferrocene. C°P ) 0.1 mM in
pH 6.5 phosphate buffer (ionic strength ) 0.1 M) plus 0.5 M glucose.
Thin lines are voltammograms recorded in the absence of catalysis.
Thick lines are catalytic voltammograms recorded in the presence of 2
µM glucose oxidase. (A) C°OG ) 0.069 M. (B) C°OG ) 0.274 M.
Potential scan rate V ) 0.025 V s-1. Temperature: 25 °C.
and the method used.18c,19 In the C°OG range investigated in
the present work, it seems reasonable to consider that N ) 80
( 30.
Dependence of the Diffusion Coefficients on the Viscosity
of the Solution. Owing to the large size of the micelles, the
viscosity η of the micellar solution exhibits a marked depen-
dence on C°OG, as can be seen in Figure 2. Consequently, the
diffusion of all types of molecules, even those which are not
micellized, is slowed down. In the range of surfactant concen-
tration explored in the present work, it seemed important to
take that slowdown into account. Therefore, we used the
Stokes-Einstein equation to calculate the diffusion coefficient
Di,η of any species i in the micellar solutions.
Figure 3 for an extended range of C°OG. As DQ can be
calculated through the use of the Stokes-Einstein equation, δ
) DP/DQ is known.
The partition equilibrium constant K was deduced from the
experimental evaluation of E°′P/Q ) (Epa + Epc)/2 at various
C°OG (see Figure 4). We proceeded as follows. In the absence
of OG, we found E°P/Q ) 155 ( 5 mV Vs SCE. Then K was
determined by introducing the value of 1 + KCM given by eq
V into the set of equations (I), (II), (III), and (VIII). Incidentally,
one may notice that the approximation CM ) CMt need not be
made here. The scattering of the data obtained over the whole
range of C°OG being very small, we found K ) (1.2 ( 0.1) ×
104.
It seems reasonable to consider that the remarkably small
scattering of the data justifies the validity of the assumptions
made in the formal treatment. Among them, neglecting the
micellization of Q was the most questionable. We attempted
the measurement of DQ in a micellar solution (C°OG ) 0.137
M) of Q, prepared by dissolution of ferrocenium tetrafluorobo-
rate, by means of cyclic voltammetry. We found DQ ) (4.5 (
1.0) × 10-6 cm2 s-1, instead of the value of 5.56 × 10-6 cm2
s-1 predicted by the use of the Stokes-Einstein equation. The
discrepancy does not exceed significantly the experimental
At 25 °C
Di,η ) Di,0.93(0.93/η)
(IX)
0.93 cP is the viscosity of the buffer and Di,0.93 the diffusion
coefficient of i in the buffer.
Cyclic Voltammetry of the Mediator in the Micellar
Solution. In the absence of enzymatic catalysis the P(micel-
lized)/Q redox couple exhibits always a Nernstian behavior in
cyclic voltammetry, i.e. Epa - Epc ) 60 ( 3 mV and i°p/V1/2 is
constant within experimental uncertainty whatever V (0.01 e V
e 0.25 Vs-1) and C°OG (0 e C°OG e 0.3 M).
Under such conditions, once i°p is measured at given V and
C°OG, the determination of DP is straightforward since i°p )
0.446FSC°P(DPFV/RT)1/2
. The ensuing data are reported in

Enzymatic Electrocatalysis in a Micellar Environment
J. Phys. Chem., Vol. 100, No. 12, 1996 5067
TABLE 1: Experiments Carried Out in the Presence of 0.5 M Glucose for the Determination of k3
10-6 k3 /
a
ip/i°p for (V)/V s-1
b
C°OG
M
/
η/
cP
C°P/
mM
DP/
DQ
/
C°E/
µM
cm2 s-1
cm2 s-1
(0.01)
(0.025)
(0.05)
(0.1)
(0.25)
M-1 s-1
0
1.14
1.24
1.33
1.33
1.36
1.36
1.45
1.45
1.74
1.74
2.09
2.09
ca. 0.02
0.100
0.100
0.103
0.032
0.108
0.100
0.030
0.105
0.0316
0.105
0.0315
5.5 × 10-6
1.1 × 10-6
7.2 × 10-7
6.7 × 10-7
4.9 × 10-7
5.8 × 10-7
4.5 × 10-7
4.3 × 10-7
3.0 × 10-7
2.7 × 10-7
2.7 × 10-7
2.2 × 10-7
5.5 × 10-6
3.72
1.96
2.62
2.27
2.40
2.40
3.10
3.10
2.20
2.20
2.28
2.28
ca. 15
5.6
5.5
5.1
4.9
5.2
5.8
5.3
4.5
ca. 9
3.8
3.65
3.5
3.35
3.6
4.1
3.5
3.2
3.05
2.9
2.6
ca. 6.2
2.8
2.7
2.65
2.6
2.6
3.1
2.75
2.5
2.4
2.2
ca. 4.3
2.2
2.1
2.1
2.1
2.0
2.45
2.1
1.9
2.0
ca. 2.6
1.55
1.6
1.55
1.55
1.5
1.9
1.6
1.6
1.5
3.3 ( 0.7c
2.5
2.3
2.6
2.7
3.0
3.6
2.7
3.3
0.0685
0.103
0.103
0.110
0.110
0.137
0.137
0.205
0.205
0.274
0.274
5.03 × 10-6
4.68 × 10-6
4.68 × 10-6
4.58 × 10-6
4.58 × 10-6
4.30 × 10-6
4.30 × 10-6
3.58 × 10-6
3.58 × 10-6
2.98 × 10-6
2.98 × 10-6
4.3
4.1
3.65
3.2
2.4
2.2
1.8
1.65
1.4
1.35
2.05
a According to eq IX. b Data obtained for the best fit between the experimental and simulated catalytic efficiencies. c Relatively large uncertainty
due to the uncertainty on C°p. Temperature: 25 °C. Phosphate buffer (0.1 M ionic strength), pH 6.5.
a
TABLE 2: Experiments Carried Out at Low Glucose Concentrations for the Determinations of k2 and kred
ip/i°p
V ) 0.05 V s-1
V ) 0.1 V s-1
V ) 0.25 V s-1
C°G/mM
k2/s-1
kred/M-1 s-1
exp
sim
exp
sim
exp
sim
1.5
1000
1000
1000
500
1.5 × 104
1.2 × 104
1.8 × 104
1.5 × 104
1.5 × 104
2.18
2.10
2.28
2.18
2.18
1.70
1.64
1.78
1.70
1.70
1.32
1.29
1.36
1.32
1.32
2.22
1.78
1.32
1500
2
3
1000
1000
1000
500
1.5 × 104
1.2 × 104
1.8 × 104
1.5 × 104
1.5 × 104
2.32
2.21
2.44
2.32
2.32
1.81
1.74
1.90
1.81
1.81
1.38
1.35
1.42
1.38
1.38
2.33
2.57
3.15
1.89
1.85
2.42
1.35
1.33
1.69
1500
1000
1000
1000
500
1.5 × 104
1.2 × 104
1.8 × 104
1.5 × 104
1.5 × 104
2.45
2.37
2.59
2.45
2.45
1.93
1.85
2.02
1.93
1.93
1.44
1.41
1.47
1.44
1.44
1500
10
1000
1000
1000
500
1.5 × 104
1.2 × 104
1.8 × 104
1.8 × 104
1.8 × 104
3.00
2.85
3.18
3.12
3.23
2.31
2.20
2.43
2.37
2.47
1.61
1.55
1.69
1.64
1.72
1500
a For the experiments (exp): C°P ) 0.1 mM. C°E ) 3.5 µM. C°OG ) 0.137 M. Temperature: 25 °C. Phosphate buffer (0.1 M ionic strength),
pH ) 6.5. For the simulations (sim): k3 ) 3 × 106 M-1 s-1, DP ) 0.7 × 10-6 cm2 s-1, DQ ) 5.56 × 10-6 cm2 s-1, DE ) 0.32 × 10-6 cm2 s-1
.
uncertainty. The partition equilibrium constant corresponding
to DQ ) 4.5 × 10-6 cm2 s-1 would be ca. 150, i.e., 80 times
less than the partition equilibrium constant of P. Thus,
neglecting the micellization of Q seemed duly justified.
The observed decrease of DP with increasing C°OG may now
be analyzed quantitatively through the use of eq IV. The
diffusion coefficient DP,W is corrected by the Stokes-Einstein
The first key parameter controlling the coupling between the
electrochemical and enzymatically catalyzed reactions is the
mobility of the mediator which is modulated by the micellar
partition and the viscosity of the medium as discussed above.
The second key factor is enzyme kinetics. The rate constant
which can be determined first is k3. For that purpose, all the
experiments were carried out in the presence of glucose at rather
high concentration, i.e., C°G ) 0.5 M. Then, we checked out
that the catalytic efficiency (ipl/i°p) at the level of the plateau
current, which could be rather easily observed at the smallest
V, was C°P independent provided that C°P e 0.1 mM, a result
ascertaining experimentally that σq , 1 (see above in the
Formal Aspects section). Then the sole enzymatic rate constant
contributing to the value of the catalytic current is k3.14 In such
circumstances, the catalytic efficiencies ip/i°p were measured
at the peak level at various C°P and C°OG. The ensuing data
are gathered together with the corresponding experimental
conditions in Table 1. The values of k3 giving, for each micellar
solution, the best fit (less than 5% discrepancy) between the
experimental and simulated catalytic efficiencies (see Experi-
mental Section) are also listed in Table 1. That gives k3 )
(2.8 ( 0.5) × 106 M-1 s-1 (mean and standard deviation). This
equation. Hence DM can be calculated at each C°OG
. As
expected, DM is C°OG dependent. However, the product DMη
appears quite constant. When η is taken as 0.93 cP, i.e., in the
buffer alone, DM is (4 ( 1) × 10-7 cm2 s-1. According to the
Stokes-Einstein equation, the hydrodynamic radius of the
equivalent sphere would be 5.8 nm, a much larger value than
the radius of 2.2 nm which can be deduced for N ) 80 from
the partial specific volume of the micelle (0.858 cm3g-1).19 Such
a discrepancy provides a new confirmation of the nonspherical
16,18b,c,19
shape of the OG micelles in the 0.1-0.3 M range of C°OG
.
Enzymatic Electrocatalysis. The cyclic voltammograms
reproduced in Figure 5 illustrate clearly that a poorly water
soluble mediator can be used efficiently in micellar solutions.
However, the catalytic current as well as the catalytic efficiency
depends markedly on the micelle concentrations.

5068 J. Phys. Chem., Vol. 100, No. 12, 1996
Deshaies et al.
value is very close to the one found for ferrocenemethanol at
the same pH.8 That was expected since both mediators are
electrically neutral ferrocene derivatives, in their reduced forms,
and their redox potentials differ by less than 40 mV.8
KCl saturated calomel electrode (SCE) separated from the
micellar solution by a double junction compartment filled with
the buffer. Cyclic voltammetric experiments were performed
by means of a PJT24 Tacussel potentiostat, a Pil101T Tacussel
function generator, and a Kipp & Zonen XY recorder.
A HP 8452 Hewlett-Packard spectrophotometer was used for
the absorption UV-visible assays of the glucose oxidase
concentration.13
Obviously k3 is not significantly affected by the presence of
the neutral OG surfactant at concentrations up to 0.274 M (8
wt %), a result indicating that the presence of OG does not
introduce any new rate determining step in the kinetics of the
reaction between Q and the reduced forms of FAD inside the
enzyme. The value of k3 has been shown to depend on that of
the rate of formation of a precursor complex between Q and
the the active site;8 therefore, the observed nondependence of
k3 on C°OG confirms that the micellization of Q is negligible.
Moreover, it also ascertains that the interactions which may exist
between the enzyme and the neutral surfactant do not involve
the active site or are not strong enough to alter the rate of the
precursor complex formation.
To be able to determine k2 and kred, we needed to proceed
under conditions ensuring that σq was no longer very small
compared to 1. Theoretically, this could be achieved by either
decreasing C°G or increasing C°P. However, we did not dare
to increase the latter by fear of endangering the validity of the
simplifying assumptions we made in the theoretical treatment
of the micellization processes. On the other hand, it is easy to
increase σ by decreasing C°G. Then we measured the catalytic
efficiencies at low glucose concentrations lying in the 1.5-10
mM range (see Table 2). The data gathered in Table 2 show
that the simulated catalytic efficiencies are rather sensitive to
the changes in kred and this global rate constant can be
determined with satisfactory accuracy, i.e. kred ) (1.5 ( 0.3) ×
104 M-1 s-1. However, the simulated catalytic efficiencies
exhibit practically no dependence on k2 when C°G e 3 mM
and only a slight sensitivity when C°G ) 3 mM. This is not
surprising since the expression of σ contains the sum of the
two terms 1/k2 and 1/kredCG. The first of these two terms
becomes very small (k2 being ca. 103 s-1) and therefore
ineffective compared to the latter when C°G is small. To
enhance the influence of 1/k2 it would be necessary to decrease
1/kredCG (by increasing C°G) and to increase simultaneously σ
by increasing C°P, a possibility we excluded a priori as
explained above in the presence of OG, and a possiblity which
does not exist at all in the absence of OG due the very low
solubility of ferrocene in water. In consequence, k2 was not
Procedures. The viscosity η of a solution is given by η )
η1Ft/F1t1, η1 being the viscosity of water, F and F1 the respective
volumic weight of the solution and water, and t and t1 the
corresponding outflow times. The volumic weights were
measured by pycnometry. The standard values used for pure
water at 25 °C were F1 ) 0.997 g cm-3 and η1 ) 0.890 cP.11c
Stock solutions of glucose oxidase (ca. 8 µM) were prepared
in 0.01 M acetic buffer at pH 5.5. At low micellar concentra-
tion, dissolution of ferrocene is neither easy nor reproducible.
Thus a solution of 1 mM ferrocene, in concentrated OG (10 wt
%) and pH 6.5 phosphate buffer of 0.13 M ionic strength, was
used as a stock solution. The dissolution was initially assisted
by ultrasonication. All solutions of ferrocene were prepared at
25 °C and stirred overnight at this temperature before use.
For the measurement of ip the protocol was standardized as
follows: a 3 cm3 aliquot of a micellar solution containing for
instance 0.133 mM ferrocene, 0.274 M OG, and 0.66 M glucose
in 0.13 M ionic strength phosphate buffer was introduced in
the thermostated electrochemical cell and deaerated for 10 min
with a flux of wet argon at the surface of the solution maintained
under gentle magnetic stirring. After addition of 1 cm3 of the
stock solution of enzyme, the final solution was deaerated as
before. Then, the final concentrations were C°E ca. 2 µM, C°P
) 0.1 mM, C°OG ) 0.205 M, and C°G ) 0.5 M. The final
ionic strength was 0.1 M and the pH was 6.5. The stirring
was stopped and the voltammograms were recorded 30 s later.
For the measurement of i°p, 1 cm3 of the acetic buffer was added
in place of the enzyme stock solution.
Simulations. The DigiSim 2.0 software of Bioanalytical
Systems, Inc. (1994) by M. Rudolph, and S. W. Feldberg, was
used for the simulations. To take into account the fact that two
Q are needed to oxidize FADH2, the mechanism was written
as detailed in ref 8, i.e., consisting in the following sequence
of reactions: P ) Q + e; Q + FADH2 ) P + (FADH); Q +
(FADH) ) P + FAD; FAD + G ) FADG; FADG ) FADH2
+ GL. (FADH) is the one-electron intermediate in oxidation
of the fully reduced flavin. The second and third steps in the
preceding sequence are both irreversible, their rate constants
being either k3 in both cases or k3 for the second and a greater
rate constant for the third one.8
determined with good accuracy; k2 ) (1 ( 0.5) × 103 s-1
.
As already mentioned for k3, the values found for kred and
even k2, in the present work, are in good agreement with those
found previously with P ) ferrocenemethanol at the same pH
(kred ) 1.3 × 104 M-1 s-1 and k2 ) 900 s-1).8,13 We may then
conclude that all the rate constants characterizing the glucose
oxidase kinetics are not appreciably affected by the presence
of the neutral n-octylglycoside surfactant.
Inputs of k1 and k-1 were required. Those are rate constants
which cannot be determined individually8,13 since only k3, k2,
and the global rate constant kred ) k1k2/(k-1 + k2) are involved
in the kinetics of the enzymatically catalyzed reaction. There-
fore, we entered reasonable values for both k1 and k-1 and we
checked out that the simulations did not depend on changes in
the individual values of k1 and k-1 provided that kred remained
unaffected.
Experimental Section
Materials. Ferrocene and ferrocenium tetrafluoroborate were
obtained from Aldrich and n-octyl-â-D-glucopyrannoside (OG)
was from Sigma. Glucose oxidase (Aspergillus Niger, grade
I) was from Boehringer Mannheim. The stock solutions of
glucose were allowed to mutarotate overnight before use.
Instruments. Viscosities were measured with an Ostwald
viscometer from Prolabo located in a thermostated bath (25 (
1 °C). The inner diameter of the capillary tube was 0.5 mm.
The working electrode was a 3 mm diameter glassy carbon
disk from Tokai Corp. It was polished with aluminas down to
0.1 µm particle size and ultrasonically washed with great care
in the buffer before use. The reference electrode was an aqueous
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JP953120F