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-β-D-glucoside Christophe Deshaies,1a Joe1 l 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 watersoluble 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, microheterogeneous 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 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 regenerated 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 cosubstrates, since the pioneering works of ref 6, particularly, watersoluble 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:
P a Q + eP/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
Figure 1. The electrocatalytic scheme.
standard potential is E°P/Q. k1
FAD + G {\ } FADG k -1
k2
FADG 98 FADH2 + GL k3
FADH2 + 2Q 98 FAD + 2P
(1) (2) (3)
where E-FAD and E-FADH2 are the oxidized and reduced forms of the glucose oxidase flavoenzyme respectively, G is β-Dglucose, 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 wellknown 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, © 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. 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. Formal Aspects 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. For the partition of P in the presence of micelles M:
P + M a PM
(4)
the equilibrium constant K is expressed as
K ) CPM/CPCM
(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)
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. 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. Then, taking into account the sole partition of P, its apparent diffusion coefficient DP in the micellar solution is given by3,10,11
DP )
DMKCM DP,W + 1 + KCM 1 + KCM
(IV)
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
RT RT DP ln(1 + KCM) + ln E°′P/Q ) E°P/Q + F 2F DQ
(V)
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 Catalyzed 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
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:
∂CP ∂2CP ) DP 2 + ∂t ∂x
2k3C°ECQ 1 k-1 + k2 1 + k3 + C k2 k1k2CG Q
∂2CQ ∂CQ ) DQ 2 ∂t ∂x
2k3C°ECQ 1 k-1 + k2 1 + k3 + C k2 k1k2CG Q
(
)
(
)
(VI)
(VII)
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. 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:
t ) 0, x g 0, and t g 0, x f ∞ t g 0, x ) 0
(CQ)x)0 (CP)x)0
CQ ) 0
[RTF (E - E°′P )]
) exp
/Q
The anodic i current flowing through the working electrode surface (area ) S) is obtained from the concentration gradients of P or Q according to
( )
i ) -FSDQ
∂CQ ∂x
x)0
) FSDP
( ) ∂CQ ∂x
x)0
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. It is convenient to render the above formulations dimensionless by means of the following changes in variables and parameters8b
τ ) (FV/RT)t and ξ ) (F/RT)(E - E°′P/Q) Thus τ ) ξ + 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).
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
σ ) k3C°P[(1/k2) + (1/kredC°G)]
or
i°p ) 0.446FSC°P(δDQFV/RT)1/2
Thus14 2
The ratio ip/i°p is a measure of the catalytic efficiency. At the plateau current, the catalytic efficiency is given by
2
∂p λq λq ∂p ∂q ∂ q )δ 2+ and ) 2∂t 1 + σq ∂t 1 + σq ∂y ∂y with
τ ) 0, y g 0 and τ g 0, y f ∞
with
τ g 0, y ) 0
{ [
q)0
qy)0 ) exp(ζ) py)0
( )() DQFV RT
1/2
∂q ∂y
y)0
) FSC°Pδ
ipl 1 ) (λδ)1/2, when σδ , 1 i°p 0.446
( )() DQFV RT
1/2
∂p ∂y
y)0
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. At the level of the plateau: (∂p/∂τ)pl ) (∂q/∂τ)pl ) 0. Thus (∂p/∂τ)pl + (∂q/∂τ)pl ) δ(∂ 2p/∂y2)pl + (∂ 2q/∂y2)pl ) 0 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
qy)0,pl )
δ )δ 1 + δexp(-ξ)
since ξ 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
(∂q∂y)
y)0,pl
{ [
λ 1 ) - 2 qy)0,pl - ln(1 + σqy)0,pl) σ σ
]}
1/2
when σqy)0,pl is not very small and therefore
ipl ) FSC°P
( ){ [ FVDQ RT
1/2
]}
λ 1 2 δ - ln(1 + σδ) σ σ
1/2
or
( )
ipl ) FSC°P
FVDQ RT
1/2
or
The current is then given by
i ) -FSC°P
]}
ipl 1 λ 1 ) 2 1 - ln(1 + σδ) i°p 0.446 σ σδ
1/2
(λ)1/2δ
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
Obviously, the catalytic efficiency at the plateau depends on δ1/2, i.e., on the ratio δ of the diffusion coefficients DP and DQ. The catalytic efficiency ip/i°p, measured at the peak current, 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 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. 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
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 2. Viscosity, at 25 °C, of the micellar solutions of noctylglucoside 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; DP,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.
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 dependence 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 concentration 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. 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(micellized)/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
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 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.
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 tetrafluoroborate, 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
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 C°OG/ M
η/ cP
C°P/ mM
DP/ cm2 s-1
DQa/ cm2 s-1
C°E/ µM
0 0.0685 0.103 0.103 0.110 0.110 0.137 0.137 0.205 0.205 0.274 0.274
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 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
3.72 1.96 2.62 2.27 2.40 2.40 3.10 3.10 2.20 2.20 2.28 2.28
(0.01)
ip/i°p for (V)/V s-1 (0.025) (0.05) (0.1)
(0.25)
10-6 k3b/ M-1 s-1
ca. 15 5.6 5.5 5.1 4.9 5.2 5.8 5.3 4.5 4.3 4.1 3.65
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. 2.6 1.55 1.6 1.55 1.55 1.5 1.9 1.6 1.6 1.5 1.4 1.35
3.3 ( 0.7c 2.5 2.3 2.6 2.7 3.0 3.6 2.7 3.3 3.2 2.4 2.2
ca. 6.2 2.8 2.7 2.65 2.6 2.6 3.1 2.75 2.5 2.4 2.2 2.05
ca. 4.3 2.2 2.1 2.1 2.1 2.0 2.45 2.1 1.9 2.0 1.8 1.65
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.
TABLE 2: Experiments Carried Out at Low Glucose Concentrations for the Determinations of k2 and kreda ip/i°p V ) 0.05 V s-1 C°G/mM 1.5
2
3
10
k2
/s-1
kred/M-1 s-1
1000 1000 1000 500 1500
1.5 × 104 1.2 × 104 1.8 × 104 1.5 × 104 1.5 × 104
1000 1000 1000 500 1500
1.5 × 104 1.2 × 104 1.8 × 104 1.5 × 104 1.5 × 104
1000 1000 1000 500 1500
1.5 × 104 1.2 × 104 1.8 × 104 1.5 × 104 1.5 × 104
1000 1000 1000 500 1500
1.5 × 104 1.2 × 104 1.8 × 104 1.8 × 104 1.8 × 104
V ) 0.1 V s-1
exp
sim
2.22
2.18 2.10 2.28 2.18 2.18
2.33
2.32 2.21 2.44 2.32 2.32
2.57
2.45 2.37 2.59 2.45 2.45
3.15
3.00 2.85 3.18 3.12 3.23
exp
sim
1.78
1.70 1.64 1.78 1.70 1.70
1.89
1.81 1.74 1.90 1.81 1.81
1.85
1.93 1.85 2.02 1.93 1.93
2.42
2.31 2.20 2.43 2.37 2.47
V ) 0.25 V s-1 exp
sim
1.32
1.32 1.29 1.36 1.32 1.32
1.35
1.38 1.35 1.42 1.38 1.38
1.33
1.44 1.41 1.47 1.44 1.44
1.69
1.61 1.55 1.69 1.64 1.72
a For the experiments (exp): C° ) 0.1 mM. C° ) 3.5 µM. C° P E 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 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 shape of the OG micelles in the 0.1-0.3 M range of C°OG.16,18b,c,19 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.
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 Experimental Section) are also listed in Table 1. That gives k3 ) (2.8 ( 0.5) × 106 M-1 s-1 (mean and standard deviation). This
5068 J. Phys. Chem., Vol. 100, No. 12, 1996 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 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 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. Experimental Section Materials. Ferrocene and ferrocenium tetrafluoroborate were obtained from Aldrich and n-octyl-β-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
Deshaies et al. 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 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 concentration, 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 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. Therefore, 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. References and Notes (1) (a) Universite´ de Technologie de Compie`gne. (b) Universite´ Paris 7sDenis Diderot. (2) Review in: Kinetics and Catalysis in Microheterogeneous Systems; Gra¨tzel, M., Kalyanasundaram, K., Eds.; M. Dekker: New York, 1991. (3) Rusling, J. F. In Electroanalytical Chemistry; Bard, A. J., Ed.; M. Dekker: New York, 1994; Vol. 18, pp 1-88. (4) (a) Martinek, K.; Levashov, A. V.; Klyachko, N. L.; Khmelnitsky, Y. L.; Berezin, I. V. Eur. J. Biochem. 1986, 155, 453. (b) Martinek, K.;
Enzymatic Electrocatalysis in a Micellar Environment Klyachko, N. L.; Kabanov, A. V.; Khmelnitsky, Y. L.; Levashov, A. V. Biochem. Biophys. Acta 1989, 981, 161. (5) (a) Rusling, J. F. Acc. Chem. Res. 1991, 24, 75 and references therein. (b) Texter, J. In Electrochemistry of Colloids and Dispersions; Mackay, R. A., Texter, J., Eds.; VCH Publishers: New York, 1992; pp 195-213. (6) (a) Fujihira, Y.; Kuwana, T.; Hartzell, C. R. Biochem. Biophys. Res. Commun. 1974, 61, 488. (b) Yeh, P.; Kuwana, T. J. Electrochem. Soc. 1976, 123, 1334. (7) (a) Cass, A. E. G.; Davis, G.; Francis, G. D.; Hill, H. A. O.; Aston, W. J.; Higgins, J.; Plotkin, E. V.; Scott, L. D. L.; Turner, A. P. F. Anal. Chem. 1984, 56, 667. (b) Cass, A. E. G.; Davis, G.; Green, M. J.; Hill, H. A. O. J. Electroanal. Chem. 1985, 190, 117. (c) Fraser, D. M.; Zakeeruddin, S. M.; Gra¨tzel, M. Biochim. Biophys. Acta 1992, 1099, 91. (d) Heller, A. Acc. Chem. Res. 1990, 23, 128. (8) (a) Bourdillon, C.; Demaille, C.; Moiroux, J.; Save´ant, J. M. J. Am. Chem. Soc. 1993, 115, 2. (b) In ref 8a, there is a misprint in the definition of ξ; the correct definition is ξ ) (F/RT)(E - E°P/Q) instead of ξ ) (F/RT)(E - Ei). (9) (a) Ananthapadmanabhan, K. P. In Interactions of Surfactants with Polymers and Proteins; Goddard, E. D., Ananthapadmanabhan, K. P., Eds.; CRC Press: Boca Raton, FL, 1993; pp 320-410. (b) Baron, C.; Thomson, T. E. Biochim. Biophys. Acta 1975, 382, 276. (10) (a) Georges, J.; Desmettre, S. Electrochim. Acta 1984, 29, 521. (b) Kaifer, A. E.; Bard, A. J. J. Phys. Chem. 1985, 89, 4876. (c) Rusling, J. F.; Shi, C. N.; Kumosinski, T. F. Anal. Chem. 1988, 60, 1260. (11) (a) Ohsawa, Y.; Aoyagui, S. J. Electroanal. Chem. 1978, 86, 289. (b) Myers, S. A.; Mackay, R. A.; Brajter-Toth, A. Anal. Chem. 1993, 65, 3447. (c) Handbook of Chemistry and Physics, 51st ed.; Weast, R. C., Ed.; The Chemical Rubber Co.; Cleveland, 1971; pp F4, F36.
J. Phys. Chem., Vol. 100, No. 12, 1996 5069 (12) (a) Ohsawa, Y.; Aoyagui, S. J. Electroanal. Chem. 1982, 136, 353. (b) Bond, A. M.; McLennan, E. A.; Stojanovic, R. S.; Thomas, F. G. Anal. Chem. 1987, 59, 2853. (13) Weibel, M. K.; Bright, H. J. J. Biol. Chem. 1971, 246, 2734. (14) q e 1, therefore if σ , 1, the sole parameter related to the enzyme kinetics remaining in the following two equations is λ which depends on the sole enzymatic rate constant k3. Then the catalytic current will be independent of k2, kred, and C°G. (15) (a) In a very recent paper, the electrochemically driven oxidation of glucose catalyzed by glucose oxidase and mediated by ferrocene derivatives, including ferrocene itself, in the presence of anionic, cationic, and neutral surfactants was reported.15b The authors proceeded to the quantitative analysis of the observed catalytic efficiencies in accordance with the approach developed in ref 8. However, they ignored the influence of δ. As a result, their data concerning the k3’s were underestimated by ca. 1 order of magnitude. (b) Ryabov, A. D.; Amon, A.; Gorbatova, R. K.; Ryabova, E.S.; Gnedenko, B. B. J. Phys. Chem. 1995, 99, 14072. (16) Seras, M.; Gallay, J.; Vincent, M.; Ollivon, M.; Lesieur, S. J. Colloid Interface Sci. 1994, 167, 159. (17) Fendler, J. H. Membrane Mimetic Chemistry; J. Wiley: New York, 1982; pp 6-47. (18) (a) Shinoda, K.; Yamaguchi, T.; Hori, R. Bull. Chem. Soc. Jpn. 1961, 34, 237. (b) Kameyama, K.; Takagi, T. J. Colloid Interface Sci. 1990, 137, 1. (c) Lorber, B.; Bishop, J. B.; DeLucas, J. L. Biochim. Biophys. Acta 1990, 1023, 254. (19) Roxby, R. W.; Mills, B. P. J. Phys. Chem. 1990, 94, 456.
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