Langmuir 1999, 15, 6527-6533
6527
Step-by-Step Avidin-Biotin Construction of Bienzyme Electrodes. Kinetic Analysis of the Coupling between the Catalytic Activities of Immobilized Monomolecular Layers of Glucose Oxidase and Hexokinase Nathalie Anicet,† Christian Bourdillon,‡ Jacques Moiroux,*,† and Jean-Michel Save´ant*,† Laboratoire d’Electrochimie Mole´ culaire, Unite´ Mixte de Recherche Universite´ - CNRS No 7591, Universite´ de Paris 7 - Denis Diderot, 2 place Jussieu, 75251 Paris Cedex 05, France and the Laboratoire de Technologie Enzymatique, UPRESA No 6022, Universite´ de Technologie de Compie` gne, BP 20529, 60205 Compie` gne Cedex, France Received December 15, 1998. In Final Form: May 18, 1999 Avidin-biotin technology is used to achieve the step-by-step construction of electrode coatings in which two monomolecular layers of biotinylated hexokinase are immobilized on top of five monomolecular layers of biotinylated glucose oxidase. The two enzymes compete for the consumption of glucose. Because the reaction of hexokinase with glucose depends on the presence and concentration of ATP in the solution, the electrochemical response is sensitive to the ATP concentration. Such a system illustrates the possibility of translating the catalytic activity of a nonredox enzyme into an electrical signal within a spatially ordered structure. Full kinetic analysis of the electrochemical responses allowed a description of the diffusion controlled communication between the two enzymes over distances that are comparable to those involved in enzyme coupling in cell cytoplasmic systems.
It has been recently shown1 that avidin-biotin technology may be employed successfully to immobilize a series of monomolecular layers of fully active glucose oxidase onto a glassy carbon electrode. A detailed analysis of the cyclic voltammetric responses in the presence of glucose and of ferrocene-methanol used as cosubstrate allowed the determination of the pertinent rate constants and the demonstration that the result of the step-by-step construction is indeed a spatially defined series of successive monomolecular layers. The work reported below was aimed at illustrating the possibility of translating the catalytic activity of a nonredox enzyme into an electrical signal through its coupling, within a spatially ordered structure, with a redox enzyme that communicates with the electrode by means of a mediator. Two monomolecular layers of biotinylated hexokinase were immobilized on top of five monomolecular layers of biotinylated glucose oxidase.2 The two enzymes compete for the consumption of glucose according to Scheme 1. Glucose oxidase catalyzes the oxidation of glucose (G) to glucono-δ-lactone (GL) by the electrochemically generated oxidized form, Q, of the ferrocene-methanol cosubstrate (or mediator), P (FAD and FADH2 are the oxidized and reduced forms of the flavin adenine dinucleotide prosthetic group of glucose oxidase; FADG is the enzyme-substrate complex).3,4 Hexokinase (HK) catalyzes the formation of glucose-6phosphate (G6P) in the presence of the adenosine 5′triphosphate magnesium complex (ATPMg2-) cosubstrate † ‡
Universite´ de Paris 7 - Denis Diderot. Universite´ de Technologie de Compie`gne.
(1) Anicet, N.; Bourdillon, C.; Moiroux, J.; Save´ant, J.-M. J. Phys. Chem. 1998, 102, 9844. (2) The procedure of deposition and the concentrations of the bathing solutions must be carefully adjusted to avoid the effects of the reversibility of the avidin-biotin binding.1 (3) Weibel, M. K.; Bright, H. J. J. Biol. Chem. 1971, 246, 2734. (4) Bourdillon, C.; Demaille, C.; Moiroux, J.; Save´ant, J.-M. J. Am. Chem. Soc. 1993, 115, 2.
Scheme 1
(HKG and HKG6P are the enzyme-substrate and enzyme-product complexes, respectively; ADPMg- is the adenosine 5′-diphosphate magnesium complex).5 The oxidized form of the mediator, Q, is produced at the electrode surface when the electrode potential is set at a more positive value than the standard potential of the P/Q redox couple, E0P/Q. The reaction of Q with glucose oxidase in the presence of glucose regenerates P, thus giving rise to a catalytic current.1 When hexokinase is also present, together with ATP4- and Mg2+, the two enzymes compete for the consumption of their common substrate, glucose. A decrease of the catalytic current ensues, which is a function of several parameters: the catalytic activities of the two enzymes and their relative spatial distribution, the concentrations of mediator, glucose, ATP4- and Mg2+, the pH, and the buffer composition. Glucose oxidase catalyzed oxidation of glucose can be triggered by imposing an adequately selected potential to the electrode, whereas the hexokinase-catalyzed phos(5) (a) Hammes, G. G.; Kochavi, D. J. Am. Chem. Soc. 1962, 84, 2069. (b) Hammes, G. G.; Kochavi, D. J. Am. Chem. Soc. 1962, 84, 2073.
10.1021/la9817213 CCC: $18.00 © 1999 American Chemical Society Published on Web 07/22/1999
6528 Langmuir, Vol. 15, No. 19, 1999
phorylation of glucose does not depend on the electrode potential but is triggered rather by the presence of ATPMg2-. Therefore, reproducible current responses can only be obtained if the rates of mass transport of glucose and ATPMg2- to the immobilized hexokinase active sites are controlled. The mass transport control was achieved by rotating the disk electrode at a precisely defined rate. The same bienzymatic system has already been used in association with an oxygen electrode6a or a hydrogen peroxide electrode,6b onto which membranes containing both enzymes were fixed, or with a ferrocene-mediated graphite-glucose enzyme electrode and hexokinase in solution.6c Our step-by-step construction of a spatially ordered bienzymatic structure was designed to control mass transport throughout the system, thus allowing a quantitative analysis of its dynamics by observation of the decrease of the catalytic current upon addition of ATP. Before undertaking this task, it was necessary to determine the kinetics of the biotinylated enzymes. Results and Discussion Kinetic Characterization of the Biotinylated Enzymes. Biotinylated glucose oxidase with 66% activity and an average of 5.6 biotin heads per glucose oxidase molecule was obtained as reported earlier.1 Biotinylated hexokinase was prepared as described in the Experimental Section. Kinetics of the Biotinylated Glucose OxidaseCatalyzed Reaction. Glucose oxidase-catalyzed oxidation of glucose by the electrochemically generated mediator Q is fully characterized by the following set of rate constants: k2, k3 and kred ) k1k2(k-1+k2).1,4 k1 is the formation rate constant of the Michaelis complex between oxidized glucose oxidase and glucose; k-1 is the rate constant of the reverse reaction. k2 is the rate constant of decomposition of the Michaelis complex into reduced glucose oxidase and gluconolactone, and k3 is the rate constant for the oxidation of reduced glucose oxidase by the oxidized form of the mediator. These rate constants depend on pH and buffer composition.3,4 When the enzyme is present in solution, the rate constants are readily determined by means of cyclic voltammetry.4 In the buffer selected for a convenient use of hexokinase, as defined in the following section, we found k2 ) 300 s-1; k3 ) 106 M-1 s-1, with ferrocene-methanol as the mediator; and kred ) 104 M-1 s-1. Kinetics of the Biotinylated Hexokinase-Catalyzed Reaction. The pKa’s of ATPH3- and ADPH2- are 7 and 6.7, respectively.5,7 Therefore, at pH > 8, the basic forms ATP4- and ADP3- predominate. The stability constants of ATPMg2- and ADPMg- are 104 and 103 M-1, respectively,5,7 that is, high enough to ensure that all of ATP4- and ADP3- are combined with Mg2+ when the magnesium cations are added in an excess of at least 50 times. The stability constant of G6PMg+ is much smaller,5b and the effect of its formation can be neglected provided that G6P is not introduced initially in the reaction mixture. The use of a phosphate buffer, which may trap Mg2+ to produce MgHPO4, must be avoided. Unless otherwise stated, the solutions were buffered at pH ) 8.2 with 0.2 M Tris (hydroxymethyl) aminomethane (Tris) and 0.1 M HCl. In the present work, ADPMg- and G6P are not introduced initially in the solution, and the hexokinase (6) (a) Scheller, F.; Pfeiffer, D. Anal. Chim. Acta 1980, 117, 383. (b) Compagnone, D.; Guilbault, G. G. Anal. Chim. Acta 1997, 340, 109. (c) Davis, M. S.; Green, M. J.; Hill, H. A. O. Enzyme Microb. Technol. 1986, 8, 349. (7) O’Sullivan, W. J.; Perrin, D. D. Biochemistry, 1964, 3, 18.
Anicet et al.
catalyzed reaction is never allowed to proceed to a large extent. Under such conditions, the reversibility of the process as well as its kinetic inhibition by the products3b can be ignored. When the enzyme is added to the solution at a concentration C0HK, the rate, v, of the hexokinasecatalyzed reaction is given by eq 1:6
dCG )ν)dt
kHC0HK KmG KmT KiGKmT 1+ + + CG CT CGCT
(1)
in which (CG and CT are the glucose and ATPMg2concentrations, respectively; kH is a first-order rate constant; and KmG, KmT and KiG are characteristic constants expressed in M. The constants KmG, KmT and KiG of the commercially available hexokinase in Tris buffer were determined as follows. Glucose and ATPMg2-, at concentrations ranging from 0.254 to 1.77 mM, were allowed to react in the presence of hexokinase (4.2 × 10-4 mg/mL) in a buffered solution containing 8.67 mM MgCl2, 0.173 M Tris, 0.0867 M HCl, and ferrocene-methanol (C0P ) 0.867 mM). As detailed in the Experimental Section, the decrease of the glucose concentration versus time was monitored with a glucose sensor made of a glucose oxidase modified glassy carbon electrode; antigen-antibody attachment was then used to immobilize five successive glucose oxidase monomolecular layers built as reported previously.8 In cyclic voltammetry, at a scan rate of 0.04 V/s, a C0P of 0.0867 mM, and a positive enough potential (g 0.4 V vs SCE), the plateau current, ipl, is related to the glucose concentration, CG, by eq 2.8
ipl )
2k3FSΓ0GOCQ 1 1 1 + k3CQ + k2 kredCG
(
)
(2)
S is the geometric electrode area and Γ0GO the total amount of immobilized enzyme per unit surface area. The glucose, ATPMg2-, and hexokinase concentrations are maintained low enough to ensure that the initial rate of the hexokinase-catalyzed reaction vi ) (dCG/dt)tf0 can be derived from the measurement of (dipl/dt)tf0. The linear reciprocal plots of 1/vi vs 1/C0G at a given C0T and 1/vi vs C0T at a given C0G are shown in Figure 1a and 1b, respectively. They are consistent with the previously determined values of kH (7.5 × 102 s-1), KmG (2 × 10-4), KmT (2.2 × 10-4 M), and KiG (4 × 10-4 M) for an enzyme concentration of 1.1 × 10-9 M.5b The catalytic activity of the biotinylated hexokinase was assayed similarly. Its protein content was also assayed,9 the activity of the biotinylated enzyme we prepared appeared to be 50%, the molar weight of hexokinase was 104,000.10 We observed that the values of vi were not affected by the presence of 1 mM G6P and 1 mM ADPMg-, confirming that neither the occurrence of the reverse reaction nor the inhibition by G6P and ADPMg- needs to be taken into account. (8) (a) Bourdillon, C.; Demaille, C.; Gue´ris, J.; Moiroux, J.; Save´ant, J.-M. J. Am. Chem. Soc. 1993, 115, 12264. (b) Bourdillon, C.; Demaille, C.; Moiroux, J.; Save´ant, J.-M. J. Am. Chem. Soc. 1995, 117, 11499. (c) Bourdillon, C.; Demaille, C.; Moiroux, J.; Save´ant, J.-M. Acc. Chem. Res. 1996, 29, 529. (9) Bradford, M. M. Anal. Biochem. 1976, 72, 248. (10) Steitz, T. A.; Anderson, W. F.; Fletterick, R. J.; Anderson, C. M. J. Biol. Chem. 1977, 252, 4494.
Use of Bienzyme Electrodes for Kinetic Analysis
Figure 1. Initial rates of glucose phosphorylation in the presence of ATPMg2- (T) and hexokinase (4.2 × 10-4 mg/mL) in a 0.173 M Tris/ 0.0867 M HCl pH 8.2 buffer containing 8.67 mM MgCl2 at 25 °C. Reciprocal plots (a) at constant C0T ) 8.67 × 10-4M and (b) at constant C0G ) 8.67 × 10-4M. The solid straight lines were computed from the previously determined values of the kinetic constants (see text). Scheme 2. Sketch of the NGO Monolayers of Biotinylated Glucose Oxidase and NHK (NHK ) 2) Monolayers of Biotinylated Hexokinase Immobilized on the Glassy Carbon Surfacea
a A ) adsorbed mouse IgG; Ab ) biotinylated goat antibody to mouse IgG, GO ) glucose oxidase, HK ) hexokinase. l is the average distance between the active sites of two successive monolayers of enzymes, l ) 550 Å, l′ ) 355 Å.1
Step-by-Step Construction of a Bienzyme Electrode and Analysis of the Current Response. The best reproducibility and stability of the enzymatic coverage were obtained according to the procedure summarized in Scheme 2 under the conditions of concentration, time, and temperature reported in the Experimental Section. NGO (NGO e 5) monolayers of glucose oxidase are first immobilized on the electrode. In the absence of mass transport limitations for the mediator and glucose, that is, for C0P g 0.05 mM and C0G g 0.2 mM, the enzymatic reaction is the rate-determining step and, therefore, the cyclic voltammetric plateau current ipl is given by eq 2.8c The measurement of ipl after the attachment of each new monolayer of biotinylated glucose oxidase thus gives access 0 (j ) 1 to NGO) of to the surface concentration ΓGO,j catalytically active glucose oxidase immobilized in the jth monolayer. When the disk is rotated, a plateau current (that we name iplr to distinguish it from the cyclic voltammetric plateau current ipl) is obtained at positive enough potentials. For any NGO and for NHK ) 0, iplr is stable over several hours, (C0G g 0.2 mM) and is not affected by an addition of ATPMg2- to the solution. A first monolayer of biotinylated hexokinase is then immobilized on top of the NGO monolayers of biotinylated glucose oxidase. In the absence of ATPMg2-, iplr remains
Langmuir, Vol. 15, No. 19, 1999 6529
Figure 2. Effect of successive additions of ATPMg2- (see text) on the plateau current iplr, of the rotating disk electrode ($ ) 100 rpm) held at 0.4 V vs. SCE. C0P ) 0.1 mM. C0G ) 0.5 mM. Temperature 25 °C. 0.2 M Tris/ 0.1 M HCl pH 8.2 buffer containing 10 mM MgCl2. One monomolecular layer of hexokinase is immobilized on top of 5 monomolecular layers of glucose oxidase containing 5.7 × 10-13 mol/cm2 each. The addition of 0.8 mM of ATPMg2- induces the decrease represented by the dashed line. During period a, the electrode is washed, and a second monomolecular layer of hexokinase is immobilized on top of the first. After immersion in the glucose/ mediator solution, further addition of 0.8 mM of ATPMg2induces the decrease represented by the dotted line. After washing and immersion in the glucose/mediator solution (period b), successive amounts of ATPMg2- are added, resulting in the series of decreasing curves represented by the solid line and corresponding to the following concentrations: C0T ) 0.1 (1), 0.2 (2), 0.4 (3), 0.6 (4), 0.8 (5), 1.2 (6), 1.6 (7) and 2 (8) mM.
unchanged. Addition of ATPMg2- induces a significant decrease of iplr as can be seen in Figure 2 (dashed curve), indicating that hexokinase has been attached to the protein assembly. Then, a second monolayer of hexokinase is immobilized on top of the first. After introduction of the resulting electrode into a solution containing the same concentrations of mediator and glucose as before, addition of the same amount of ATPMg2- as in the first experiment induces, as expected, a larger decrease of iplr (dotted line in Figure 2). The electrode was then washed and introduced into a solution containing the same concentrations of mediator and glucose as were present initially. Stepwise addition of ATPMg2- then results in the series of successive decreases of iplr shown in Figure 2 (solid line). Deactivation of immobilized biotinylated glucose oxidase is very slow. It does not occur to any appreciable extent over a period of 24 h.1 However, hexokinase is much less stable than glucose oxidase. To measure its deactivation rate, the first experiment of the above series was repeated, with the electrode left in the same solution for a long period of time. It was observed that the plateau current increases progressively up to its original value as a result of the deactivation of hexokinase. Simulation of the value of iplr (see below) at any time allows determination of the amount 0 of hexokinase immobilized in the sixth monolayer, ΓHK,6 -13 2 (starting value: 7.2 × 10 mol/cm ). Following the decay 0 showed that the deactivation process is firstof ΓHK,6 order and corresponds to a half-reaction time of 16 h, the same as the half-deactivation time in solution. The same behavior was found upon repeating similarly the experiment when two monolayers were immobilized on top of the five layers of glucose oxidase. At the time of injection 0 0 ) 6.7 × 10-13 mol/cm2 and ΓHK,7 ) 6.0 1 in Figure 2, ΓHK,6 -13 2 × 10 mol/cm . The simulation of iplr and of its variations upon addition of ATPMg2- were carried out as follows. Because the diffusion layer in the solution is much larger than the enzyme film (4.3 × 10-3 cm at a rotation rate,
6530 Langmuir, Vol. 15, No. 19, 1999
Anicet et al.
$, of 100 rpm vs ≈ 4 × 10-5 cm), the concentration profiles of Q, G, and T can be regarded as linear between two successive enzyme monolayers. The key equations (3-6) for describing the kinetics in the film are those expressing, at each monolayer and for each species, the balance among the diffusion flux entering the layer on one side, the diffusion flux leaving the layer on the other side, and the enzymatic reaction in the enzyme monolayer. In applying these equations, we consider, as shown earlier,1 that there is no partition of either P nor Q between the solution and the avidin-biotin protein film. We likewise assume that there is no partition of G and T. The diffusion coefficients of P and Q are equal and are the same inside and outside the film.1 The same should be true for G and T. We may therefore equate all diffusion coefficients to a common value, noted D.
0 2k3ΓGO,j CQ,j , 1 1 1 + k3CQ,j + k2 kredCG,j (1 < j < NGO + NHK) (3′′)
D - 2CQ,j + CQ,j+1) ) (C l Q,j-1
D
(
CQ,NGO+NHK-1 - CQ,NGO+NHK l
[( ) ( ) ] ∂CQ ∂x
-
-
0 2k3ΓGO,j CQ,j , + j 1 1 1 + k3CQ,j + k2 kredCG,j (3) (1 e j e NGO + NHK)
∂CQ ∂x
)
(
)
D
[( ) ( ) ] ∂CG ∂x
+
-
0 k3ΓGO,j CQ,j , 1 - j 1 1 + k3CQ,j + k2 kredCG,j (1 e j e NGO) (4)
∂CG ∂x
[( ) ( ) ] ∂CG ∂x
+
For T: ∂CT D ∂x
-
(
)
0 kHΓHK,j , - j KmG KmT KiGKmT 1+ + + CG,j CT,j CG,jCT,j (NGO + 1 e j e NGO + NHK) (5)
∂CG ∂x
)
{( ) ( ) } +
)
-
0 kHΓHK,j , KmG KmT KiGKmT - j 1+ + + CG,j CT,j CG,jCT,j (6) (1 e j e NGO + NHK)
∂CT ∂x
D
For Q: C0P - CQ,1 CQ,1 - CQ,2 ) D l′ l
(
)
CG,2 - CG,1 ) l
(taking into account that CQ,x)0 )
C0P)
) 0 (3′′′)
k3Γ0GO,1CQ,1 1 1 1 + k3CQ,1 + k2 kredCG,1
(
)
(4′)
0 k3ΓGO,j CQ,j , 1 1 1 + k3CQ,j + k2 kredCG,j (1 < j e NGO) (4′′)
D (C - 2CG,j + CG,j-1) ) l G,j+1
(
)
D (C - 2CG,j + CG,j-1) ) l G,j+1 kHΓ0HK,j , KmG KmT KiGKmT 1+ + + CG,j CT,j CG,jCT,j (NGO < j < NGO + NHK) D
(
C0G - CG,NGO+NHK d )
-
(5′)
)
CG,NGO+NHK - CG,NGO+NHK-1 l
0 kHΓHK,N HK
(5′′)
KmG KmT KiGKmT 1+ + + CG,NHK CT,NHK CG,NHK CT,NHK
For T: D
CT,NGO+2 - CT,NGO+1 l
)
0 kHΓHK,N GO+1
KmG
(6′)
KiGKmT 1+ + + CG,NGO+1 CT,NGO+1 CG,NGO+1CT,NGO+1
KmT
(taking into account that (∂CT/∂x)j ) 0, for j e NGO+1, i.e., CT,j-1 ) CT,j.)
D (C - 2CT,j + CT,j+1) ) l T,j-1 0 kHΓHK,j , KmG KmT KiGKmT 1+ + + CG,j CT,j CG,jCT,j
2k3Γ0GO,1CQ,1 (3′) 1 1 1 + k3CQ,1 + k2 kredCG,1
(
d
(taking into account that (∂CG/∂x)0 ) 0, i.e., CG,0 ) CG,1)
)
(The subscripts + and - stand for the right- and left-hand sides of the jth monolayer, respectively). At the plateau current, obtained when the electrode potential is more positive than 0.4 V versus SCE, the concentration of the oxidized form of the mediator at the electrode surface, CQ,x)0, is equal to C0P, the mediator concentration in the bulk of the solution. Because the concentration profiles are linear between each enzyme monolayer, the differential equations (3-6) may be replaced by the following finite difference equations.
)
CQ,NGO+NHK
For G:
For G: D
-
)
0 (taking into account that CQ,x)∞ ) 0 and ΓGO,j ) 0 for j ) NGO + 1 to NGO + NHK)
For Q: D
(
)
D
(
(NGO < j < NGO + NHK) C0T - CT,NGO+NHK d
-
)
CT,NGO+NHK - CT,NGO+NHK-1 l
(6′′)
Use of Bienzyme Electrodes for Kinetic Analysis
)
0 kHΓHK,N HK
KmG KmT KiGKmT 1+ + + CG,NHK CT,NHK CG,NHK CT,NHK
Langmuir, Vol. 15, No. 19, 1999 6531
(6′′′)
The plateau current, iplr, is given by eq 7
iplr ) FSD
C0P - CQ,1 l′
(7)
The thickness, d, of the diffusion layer for a rotating disk is given by the Levich equation:12 d ) 15.37D1/3ν1/6$-1/2 (d in cm, D and ν in cm2s-1, $ in rpm). Here, ν ) 0.893 × 10-2 cm2/s,13 and D ) 6.7 × 10-6 cm2/s.11 The plateau current iplr and the concentration profiles are readily obtained from the computation of this series of finite difference equations (see the Appendix for details, including introduction of the appropriate dimensionless variables and depiction of the computational procedures). The distance separating two successive monolayers of biotinylated glucose oxidase was determined in a previous study (l ) 550 Å).1 We assumed that the distance separating two successive monolayers of biotinylated hexokinase equals l. The computations show that the concentration profiles are flat and that iplr is not affected by a 50% change of l in the conditions explored in the present study. We may now simulate the variation of the decrease of iplr and ∆iplr resulting from the successive additions of ATPMg2-, as shown in the solid line of Figure 2 and summarized in Figure 3, which represents the electrode response to changes in ATPMg2- concentration. In this simulation, the deactivation of hexokinase was taken into account, neglecting, however, the variation of its surface concentration during the 15 min following each addition. As seen in Figure 3, the computed curve is a very satisfactory fit to the experimental data. Because of hexokinase deactivation, there is no point in trying to immobilize a third monomolecular layer of biotinylated hexokinase; by the time it is attached, including the duration of the intermediary measurements required for the characterization of the first two monolayers, the first monolayer is already strongly deactivated. The instability of hexokinase prevented the construction of a bienzyme assembly in which the spatial distributions of glucose oxidase and hexokinase monolayers could be designed so as to modulate the competition between the two enzymatic systems. However, with bienzymatic assemblies made of NGO (1 e NGO e 10) biotinylated glucose oxidase monolayers and NHK (NHK ) 1 or 2) biotinylated hexokinase monolayers, the excellent agreement obtained between the measured and computed current responses when $, C0P, C0G, and C0T were varied shows that the substrates, cosubstrates, and products diffuse as freely in the immobilized film as in the solution and that the coupling between diffusion and reactions occurs at the immobilized enzyme sites. We observed that an increase of the rotation rate results in a rapid decrease of ∆iplr. This effect, which is reproduced by simulation, results from the fact that the depletion of glucose caused by its consumption in the hexokinase layers (11) (a) Oshawa, Y.; Aoyagui, S. J. Electroanal. Chem. 1982, 136, 353. (b) Bond, A. M.; McLennan, E. A.; Stojanovic, R. S.; Thomas, F. G. Anal. Chem. 1987, 59, 2853. (c) Handbook of Chemistry and Physics. 78th ed.; Lide, D. R. Ed.; CRC Press: New York, 1997; p 6-207. (12) Levich, V., G. Acta Phys. Chim. URSS 1942, 17, 257. (13) Handbook of Chemistry and Physics. 78th ed.; Lide, D. R. Ed.; CRC Press: New York, 1997; p 6-200.
Figure 3. Dependence of ∆iplr on C0T in the experiment represented by the solid line in Figure 2. The solid line is the simulated curve.
Figure 4. Dependence of ∆iprl/iprl on glucose concentration C0G at two different ATPMg2- concentrations C0T. Rotated disk electrode ($ ) 100 rpm) held at 0.4 V vs. SCE. C0P ) 0.1 mM. Temperature 25 °C, 0.2 M Tris/ 0.1 M HCl pH 8.2 buffer 0 containing 10 mM MgCl2. The ΓGO,j are the same as in Figure 0 0 2. ΓHK,6 and ΓHK,7 are 7 and 6 × 10-13 mol/cm2 respectively. (9): C0T ) 0.1 mM. (b): C0T ) 2 mM. The solid lines represent the computed values.
is compensated by its diffusion from the solution to an extent that increases with the rotation rate. Typical examples of the dependence of ∆iplr/iplr on C0G are shown in Figure 4, together with the simulated curves. There is, again, a good agreement between experiment and theory. Conclusions In summary, the avidin-biotin technology allows the immobilization of successive monomolecular layers of glucose oxidase and hexokinase on the surface of an electrode. In the presence of glucose and of ferrocenemethanol, acting as the redox mediator, the occurrence of the redox glucose oxidase-catalyzed reaction gives rise to a catalytic current that decreases significantly when ATPMg2- is added to the solution as a result of the competition between the two enzymes for their common substrate, glucose. This system illustrates the possibility of translating the catalytic activity of a nonredox enzyme into an electrical signal. Indeed, the rate at which the hexokinase-catalyzed reaction proceeds affects the local rate of the glucose oxidase-catalyzed redox reaction, which is sensed through the consumption of the electrochemically generated oxidized form of the mediator. The electrochemical response is thus sensitive to the concentration of ATP in the solution, although a practical drawback of
6532 Langmuir, Vol. 15, No. 19, 1999
the system is that it cannot be used over a period exceeding a few hours due to spontaneous deactivation of hexokinase. Taking account of its spatial structure, the dynamics of the system may be simulated with good precision, thus confirming the reality of this spatial order. The volume concentration of active enzymes within the protein film assembled in the present work is on the order of 50 mg/ mL, that is, comparable to concentrations in the cytoplasm.14 Also similar to what occurs in the cytoplasm,15 metabolite-sized molecules diffuse as freely in the film as in the solution. Therefore, multi-enzyme assemblies built as described here can be used to study metabolite transport and the corresponding temporal response when site-tosite free diffusion occurs in organized multi-enzyme systems that mimick the organization of enzymes in cells. Experimental Section Chemicals. The mouse IgG (whole molecule) and the biotinconjugated goat antibody to mouse IgG (whole molecule) were obtained from Organon Teknika Cappel. Avidin was purchased from Pierce. Biotinylated glucose oxidase was prepared as described previously.1 Hexokinase (type F-300), ADPNa3 (from a bacterial source), ATPH2Na2 (grade I), and biotinamidocaproic acid 3-sulfo-N-hydroxy-succinimide ester (sulfo-NHS-biotin) were purchased from Sigma. The Sephadex G25, PD-10 column for gel filtration was obtained from Pharmacia Biotech. Between uses, the column was equilibrated with a PBS buffer made of 0.01 M KH2PO4, 0.1 M NaCl, and 0.01% sodium azide; pH was adjusted to 7.5 with 1 M NaOH. All other chemicals were purchased from Aldrich. All reagents were used as received. The stock solutions of glucose were allowed to mutarotate overnight before use. Biotinylated Hexokinase. To obtain biotinylated hexokinase that was as active as possible, we prepared it before use. The attachment of the long chain sulfo-NHS-biotin reagent to the available amino groups of hexokinase was carried out according to the following procedure. Hexokinase (20 µL of a 10.7 mg/mL stock solution in PBS buffer) and sulfo-NHS-biotin (16 µL of a 2.5 mg/mL stock solution in PBS buffer) were allowed to react at 4 °C for 2 h with mild stirring, in the presence of glucose and ADPNa3 (24 µL of a stock solution of 4.8 and 8.8 mg/mL glucose and ADPNa3, respectively, in PBS buffer). After addition of 640 µL of PBS buffer, the mixture was gel filtrated. The ready-foruse solution of biotinylated hexokinase was then obtained by addition of 0.5 mL of a 4% solution of bovine serum albumin (BSA) in PBS to the first 1.95 mL of the elution. A protein assay,7 before BSA addition, gave a biotinylated hexokinase concentration of 80 µg/mL in the ready-for-use solution. A biotin assay16 gave an average of 6.2 biotin heads per hexokinase, assuming a molar weight of 104,000 for the enzyme.10 The solution was stored at - 20 °C. Kinetics of Hexokinase in Solution. At time t ) 0, 0.4 mL of an aqueous solution of hexokinase (31.5 mg/mL) and BSA (1%) was added to 2.6 mL of a solution maintained under nitrogen bubbling and containing glucose and ATPH2Na2 at various concentrations, in addition to ferrocene-methanol (0.1 mM) and the Tris/HCl -MgCl2 buffer mentioned in the text. At regular time intervals (2 min), nitrogen bubbling was stopped, and a cyclic voltammogram was recorded at a potential scan rate of
Anicet et al. 0.04 V/s using a stationary glassy carbon disk electrode that was covered with 5 antigen-antibody-attached monolayers of glucose oxidase.9 The plateau current ipl versus t plot (up to 20 min) is almost linear for t < 10 min; therefore, the determination of (dipl/dt)tf0 is quite easy. Step-by-Step Immobilization of the Enzyme Monolayers. Adsorption of mouse IgG resulted from a 2 h exposure of the electrode surface to a 1 mg/mL solution of the IgG in PBS buffer. The electrode was then thoroughly rinsed, washed with buffer, dipped into a 0.1 mg/mL solution of gelatin in PBS for 15 min, and rinsed again. The biotinylated anti-mouse IgG (20 µg/mL in PBS) was then used for 6 h to recognize the adsorbed mouse IgG. The first avidin/biotin reaction was allowed to proceed during immersion of the electrode for 20 h in a 0.1 mg/mL gelatin -20 µg/mL avidin solution in PBS buffer. After another thorough washing, the electrode was dipped, for 30 min at 4 °C, in a 0.1 mg/mL gelatin plus 10 µg/mL biotinylated glucose oxidase PBS buffered solution and washed. For the immobilization of the next monolayer on top of the first or of any preceding layer, we proceeded as follows. The electrode was first immersed for 15 min in a 0.1 mg/mL gelatin and 20 µg/mL avidin-PBS buffered solution, then was washed and immersed for another 30 min in the 0.1 mg/mL gelatin and 10 µg/mL biotinylated enzyme-PBS buffered solution at 4 °C. When not in use, the electrode was stored at 4 °C in the PBS buffer. Voltammetric Instrumentation. The instruments were the same as previously described.17 The working disk electrode was made by sealing a 3-mm diameter glassy carbon rod from Tokai Corp. with an epoxy resin into a plexiglass ferrule that was adjusted to a Tacussel EDI rotating holder. The disk was carefully polished with diamond pastes (down to 1 µm) and ultrasonically washed before use. The cell was thermostated at 25 °C. All solutions were purged from dioxygen before each voltammetric run.
Acknowledgment. We are indebted to Marc Detcheverry (Universite´ de Technologie de Compie`gne) for his help in the preparation of biotinylated hexokinase. Appendix Simulation of the Catalytic Plateau Currents Equations (3) - (7) may be made dimensionless by introduction of the following variables and parameters:
δ) qj )
0 CQ,j CG,j CT,j ΓGO,j , g ) , t ) , γ ) , γHK,j ) j j GO,j C0P C0P C0P lC0P 0 ΓHK,j
lC0P µ)
, g0 )
C0G 0 C0T ,t ) 0 C0P CP
k3C0P k3 k3C0Pl2 kHl2 , γHK ) ,ν) , γGO ) k2 kred D D κ1 )
(14) Welch, G. R.; Easterby, J. S. TIBS 1994, 19, 193. (15) (a) Mastro, A. M.; Hurley, D. J. In Organization of Cell Metabolism; Welch, G. R., Clegg, J. S., Eds. Plenum Press: New York, 1987; pp 57-74. (b) Fushimi, K.; Verkman, A. S. J. Cell. Biol. 1991, 112, 719. (c) Kao, H. P.; Abney, J. R.; Verkman, A. S. J. Cell. Biol. 1993, 120, 175. (16) (a) Green, N. M. Biochem. J. 1965, 94, 23C. (b) Green, N. M. In Methods in Enzymology; McCormick, D. B., Wright, L. D., Eds.; Academic Press: New York, 1970; Vol. 18A, p 418. (c) Green, N. M. Avidin. In Advances in Protein Chemistry; Anfisen, C. B., Edsall, J. T., Richards, F. M., Eds.; Academic Press: New York, 1975; Vol. 29, pp 85-133. (d) Hermanson, G. T. Bioconjugate Techniques, Academic Press: San Diego, 1996; p. 590.
d l
ζGO,j )
KMG KMT KiGKMT , κ2 ) 0 , κ3 ) 2 0 CP CP C0P γGO,j
(
)
ν 1+ µ+ gj
, ζHK,j )
γHK,j κ1 κ2 κ3 1+ + + gj tj gjtj
(17) Bourdillon, C.; Demaille, C.; Moiroux, J.; Save´ant, J.-M. J. Am. Chem. Soc. 1993, 115, 2. (18) Crank, J. Mathematics of Diffusion; Oxford University Press: London, 1964; pp 789-790.
Use of Bienzyme Electrodes for Kinetic Analysis
The dimensionless expression of the plateau current is:
ψ)
Langmuir, Vol. 15, No. 19, 1999 6533
for j ) NGO + NHK
iprll
qNGO+NHK-1 - qNGO+NHK
FSDC0P
Thus at potentials corresponding to the plateau current of the rotating disk electrode:
q0 ) 1 q 0 - q1 ) q1 - q2 + 2λGOζGO,1q1 1.65 g1 - g0 ) 0 t1 - t0 ) 0 for 1 < j e NGO
qj-1 - qj ) qj - qj+1 + 2 λGOζGO,jqj gj+1 - gj ) gj - gj-1 + λGOζGO,jqj tj+1 - tj ) 0 for NGO < j < NGO + NHK
qj-1 - qj ) qj - qj+1
l
qNGO+NHK δ
0
g - gNGO+NHK δ t0 - tNGO+NHK δ
) gNGO+NHK - gNGO+NHK-1 + λHKζHK,NGO+NHK
) tNGO+NHK - tNGO+NHK-1 + λHKζHK,NGO+NHK
The preceding set of equations is then resolved iteratively to obtain the whole set of q, g, and t values. We started from a set of q, g and t values derived from the equations in which the ζGO,j’s and ζHK,j’s are calculated with q ) 1, g ) g0, and t ) t0. Each equation is thus linear, and the Gauss elimination method18 can therefore be used to compute the starting set of q, g, and t values. These values are then introduced in the ζGO,j and ζHK,j terms. The resulting set of linear equations is resolved again by means of the Gauss method, leading to a new set of q, g, and t values. The procedure is repeated until the relative variation of q1 is less than 10-5, thus leading to ψ and therefore to ipl.
gj+1 - gj ) gj - gj-1 + λHKζHK,j tj+1 - tj ) tj - tj-1 + λHKζHK,j
)
LA9817213
