Langmuir 2006, 22, 10807-10815
10807
Cyclic Voltammetric Responses of Horseradish Peroxidase Multilayers on Electrodes† Claude P. Andrieux, Benoıˆt Limoges,* Jean-Michel Save´ant,* and Dounia Yazidi Laboratoire d’Electrochimie Mole´ culaire, UMR CNRS 7591, UniVersite´ de Paris 7-Denis Diderot, 2 place Jussieu, 75251 Paris Cedex 05, France ReceiVed April 30, 2006. In Final Form: June 14, 2006 The catalytic responses obtained with step-by-step neutravidin-biotin deposition of successive monolayers of HRP are analyzed by means of cyclic voltammetry. The theoretical tools that have been developed allowed full characterization of the multilayered HRP coatings by means of a combination between closed-form analysis of limiting behaviors and finite difference numerical computations. An analysis of the experiments in which the number of monolayers was extended to 16 allowed an approximate determination of the average thickness of each monolayer, pointing to a compact arrangement of neutravidin and biotinylated HRP. The piling up of so many monolayers on the electrode allowed an improvement of the catalytic current by a factor of ca. 10, leading to very good sensitivities in term of cosubstrate detection.
Introduction Deposition and analysis of thin organized enzyme films on electrodes have attract attention because of their broad applications in analytical biochemistry with the development of biosensors1 as well as in the field of biotechnological processes.2 Various attachment methods aimed at achieving ordered enzyme multilayer films with a high protein density, such as LangmuirBlodgett deposition methods,3 step-by-step covalent enzyme layer attachment,4 alternate layer assembly of oppositely charged macromolecules,5 and biospecific interactions such as antigenantibody recognition6 and avidin-biotin binding,7 have been implemented. Potentially, these strategies offer the possibility of building very thin enzymatic films with nano- to micrometer thicknesses, with a precision better than a few nanometers and a well-defined molecular composition and organization. Among these immobilization strategies, the biospecific approaches are particularly attractive because they allow the building of spatially ordered multilayer films from a relatively low bulk concentration of the enzyme during the binding step, thus minimizing nonspecific adsorption and aggregation of denatured enzyme †
Part of the Electrochemistry special issue. * Corresponding authors. E-mail:
[email protected]; saveant@ paris7.jussieu.fr. (1) (a) Armstrong, F. A.; Wilson G. S. Electrochim. Acta 2000, 45, 2623. (b) Wilson G. S., Hu Y. Chem. ReV. 2000, 100, 2693. (d) Brajter-Toth, A.; Chambers, J. Q. Electroanalytical Methods for Biological Materials; Marcel Dekker: New York, 2002. (c) Bernhardt, P. V. Aust. J. Chem. 2006, 59, 233. (2) (a) Simon, H.; Bader, J.; Gunther, H.; Neumann, S.; Thanos, J. Angew. Chem., Int. Ed. Engl. 1985, 24, 539. (b) Bourdillon, C.; Lortie, R.; Laval, J. M. Biotechnol. Bioeng. 1988, 31, 553. (c) Ramsay, G.; Wolpert, S. M. Polym. Mater. Sci. Eng. 1997, 76, 612. (d) Somers, W. A. C.; Van Hartingsveldt, W.; Stigter, E. C. A.; Van Der Lugt, J. P. Agro Food Ind. Hi-Tech 1997, 8, 32. (3) Protein Architecture: Interfacing Molecular Assemblies and Immobilization Biotechnology; Lvov, Y., Mo¨hwald, H., Eds.; Marcel Dekker: New York, 2000. (4) (a) Yoon, H. C.; Kim, H.-S. Anal. Chem. 2000, 72, 922. (b) Zhang, S.; Yang, W.; Niu, Y.; Sun C. Anal. Chim. Acta 2004, 253, 209. (5) (a) Onda, M.; Ariga, K.; Kunitake, T. J. Biosci. Bioeng. 1999, 87, 69. (b) Pishko, M. V.; Katakis, I.; Lindquist, S.-E.; Ye, L.; Gregg, B. A.; Heller, A. Angew. Chem., Int. Ed. 1990, 29, 82. (c) Lvov, Y.; Caruso, F. Anal. Chem. 2001, 73, 4212. (d) Calvo, E. J.; Danilowicz, C. B.; Wolosiuk, A. Phys. Chem. Chem. Phys. 2005, 7, 1800. (6) (a) Bourdillon, C.; Demaille, C.; Moiroux, J.; Saveant, J. M. J. Am. Chem. Soc. 1994, 116, 10328. (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. (7) (a) Anicet, N. Bourdillon, C. Moiroux, J. Save´ant, J.-M. J. Phys Chem. B 1998, 102, 9844. (b) Anzai, J.; Takeshita, H.; Kobayashi, Y.; Osa, T.; Hoshi, T. Anal. Chem. 1998, 70, 811. (c) Hoshi, T.; Anzai, J.; Osa, T. Anal. Chem. 1995, 67, 770.
fragments. It has been previously shown with the example of glucose oxidase that stable multilayer films containing up to 10-12 enzyme monolayers can be achieved without significant restriction of film permeability to substrates and without any significant loss of enzyme activity.6,7a From the analysis of the cyclic voltammetric catalytic responses of these electrodes, it was possible to unravel the respective roles of enzyme kinetics and cosubstrate mass transport through the multilayer film, leading to an estimate of the average distance between successive monolayers. (We define a monolayer as a layer that has the thickness of one enzyme molecule plus its attaching protein device.) In the present work, we have extended this analysis to horseradish peroxidase (HRP), particularly isoenzyme C, so as to illustrate its applicability to a particularly complex reaction scheme. The choice of this enzyme was also guided by the fact that HRP has been used in the development of many enzymebased biosensors. For example, HRP was coupled with different hydrogen peroxide-producing oxidases, thus providing the opportunity to determine a wide range of biological substrates of analytical interest.8 HRP has also been involved as an efficient enzyme label in electrochemical immunosensors or DNA sensors.9 However, the dependency of the electrochemical signal upon substrate (hydrogen peroxide) concentration is not simple, as a result of substrate inhibition as shown by a solution enzyme cyclic voltammetric investigation that points to the mechanism depicted in Scheme 1.10a The same mechanism has been shown to operate when HRP is immobilized as a monolayer at the surface of an electrode.10b It consists of a three-step main catalytic loop (reactions 1-3), an inhibition step (4), and two regeneration (8) (a) Gorton, L.; Jo¨nsson-Pettersson, G.; Cso¨regi, E.; Johanson, K.; Domı`nquez, E.; Marko-Varga, G. Analyst 1992, 117, 1235. (b) Boguslavsky, L.; Kalash, H.; Xu, Z.; Beckles, D.; Geng, L.; Scotheim, T.; Laurinavicius, V.; Lee, H. S. Anal. Chim. Acta 1995, 311, 15. (c) Narva`ez, A.; Sua`rez, G.; Popescu, I. C.; Katakis, I.; Domı`nguez, E. Biosens. Bioelectron. 2000, 15, 43. (d) Domı`nguez, E.; Rinco´n, O.; Narva´ez, A. Anal. Chem. 2004, 76, 3132. (9) (a) Kasai, S.; Yokota, A.; Zhou, H.; Nishizawa, M.; Niwa, K.; Onouchi, T.; Matsue, T. Anal. Chem. 2000, 72, 5761. (b) Campbell, C. N.; Lumley-Woodyear, T.; Heller, A. Fresenius J. Anal. Chem. 1999, 364, 165. (c) Pritchard, D. J.; Morgan, H.; Cooper, J. M. Anal. Chim. Acta 1995, 310, 251. (d) Kalab T., Skladal P. Anal. Chim. Acta 1995, 304, 361. (e) Deasy, B.; Dempsey, E.; Smyth, M. R.; Egan, D.; Bogan, D.; O’Kennedy, R. Anal. Chim. Acta 1994, 294, 291. (f) Dequaire, M.; Heller, A. Anal. Chem. 2002, 74, 4370. (g) Campbell, C. N.; Gal, D.; Cristler, N.; Banditrat, C.; Heller, A. Anal. Chem. 2002, 74, 158. (h) Azek, F.; Grossiord, C.; Joannes, M.; Limoges, B.; Brossier, P. Anal. Biochem. 2000, 284, 107. (i) Caruana, D. J.; Heller, A. J. Am. Chem. Soc. 1999, 121, 769.
10.1021/la061193s CCC: $33.50 © 2006 American Chemical Society Published on Web 09/14/2006
10808 Langmuir, Vol. 22, No. 25, 2006
Andrieux et al.
Scheme 1
steps (5 and 6). Few examples of a solid surface covered with ordered multilayers of HRP have been described.11 In some cases, increasing the number of HRP layers seems to delay inhibition at high H2O2 concentrations.11b However, no clear interpretation of this observation has been proposed, and no attempt has been made to evaluate its effect on the analytical performance of the HRP electrodes for H2O2 detection. In a preliminary communication,12 we have described a procedure for immobilizing successive monolayers of HRP at a carbon electrode by application of the avidin-biotin interaction strategy as sketched in Scheme 2. A neutravin form of avidin was preferred to plain avidin because of its lower propensity to undergo nonspecific adsorption. In the present article, we report and analyze typical cyclic voltammetric responses of these multilayered HRP electrode coatings so as to characterize catalysis and inhibition in the presence of the natural substrate H2O2 and of [Os(bpy)(py)Cl]2+/+ (bpy ) bipyridine and py ) pyridine) as a one-electron reversible cosubstrate couple, with particular attention paid to their variations with the number of deposited layers and the concentration of substrate.
Results and Discussion We start with films containing a relatively small number of monolayers, for which we expect the properties of the film to be proportional to the number, N, of monolayers. To illustrate this point, Figure 1 shows the cyclic voltammetric responses obtained with a film made of four monolayers as a function of Scheme 2
Figure 1. Cyclic voltammetry of the catalytic reduction of H2O2 at a screen-printed carbon electrode coated with four monolayers of HRP as a function of [H2O2] (in mM, number on each curve) in the presence of 20 µM [Os(bpy)2(py)Cl]2+. Scan rate, 10 mV‚s-1; phosphate buffer, pH 7.4; temperature, 20 °C. Parameters for simulations: E0P/Q ) 0.2 V vs SCE, kS ) 0.04 cm/s, R ) 0.5, Ei ) 0.4, Ef ) -0.1 V vs SCE, DFP) DSP ) 0.45 × 10-5 cm2/s, DFS) DSS ) 1.2 × 10-5 cm2/s, κP ) κQ ) κS ) 1, k1 ) 1.7 × 107 M-1 s-1, k1,2 ) 2180 s-1, k2 ) 2 × 108 M-1 s-1, k3 ) 7.85 × 106 M-1 s-1, K3,M ) 36 µM, k4 ) 15 M-1 s-1, k5 ) 2600 M-1s-1, k6 ) 0.0125 s-1, k0 ) 500 M-1 s-1, L ) 12 nm, C0E ) 8.3 mM, [EMM 2 ]t)0, and [E3]t)0 from eqs 45 and 46, respectively. δ ) 0.04 cm.
the concentration of substrate present in the solution. Qualitatively, the shapes and evolution of the cyclic voltammograms are similar to those observed with a single monolayer (Figure 3 in ref 10b). At low H2O2 concentrations, inhibition is negligible, and the reaction is controlled by reaction 1 and H2O2 diffusion, giving rise to sharp peaks that shift toward positive potentials as [H2O2] is decreased. As the H2O2 concentration increases, the current increases before passing through a maximum and then decreases. Kinetic control in the main catalytic cycle accordingly passes from reaction 1 to reaction 3. The wave progressively becomes S-shaped as the depletion of H2O2 becomes negligible. Hysteresis and trace crossing are related to the time dependence of the regeneration of the active forms of the enzyme during the potential scan according to reactions 5 and 6. Figure 2 summarizes the variation of the peak or plateau current with H2O2 concentration. (10) (a) Dequaire, M.; Limoges, B.; Moiroux, J.; Save´ant, J.-M. J. Am. Chem. Soc. 2002, 124, 240. (b) Limoges, B.; Save´ant, J.-M. Yazidi, D. J. Am. Chem. Soc. 2003, 125, 9192. (11) (a) Kobayashi, Y.; Anzai, J. J. Electroanal. Chem. 2001, 507, 250. (b) Rao, S. V.; Anderson, K. W.; Bachas, L. G. Biotechnol. Bioeng. 1999, 65, 389. (c) Caruso, F.; Schu¨ler, C. Langmuir 2000, 16, 9595. (d) Li, Y.; Chen, Z.; Jiang, X.; Lin X. Chem. Lett. 2004, 33, 564. (12) Limoges, B.; Save´ant, J.-M.;Yazidi, D. Aust. J. Chem. 2006, 59, 257.
Horseradish Peroxidase Multilayers
Langmuir, Vol. 22, No. 25, 2006 10809
For the substrate,
(∂[S] ∂x )
x)0
)0
(3)
Inside the film, 0 e x e L. The various enzyme forms are considered to be immobile, the variations in their concentrations with time being given by the following differential equations: Figure 2. Variation of the peak or plateau current with H2O2 concentration for a four-monolayer HRP electrode (blue squares) or at a monolayer HRP electrode (green dots). The same conditions as in Figure 1 are used.
It also compares these data with the same variation observed in the case of one monolayer.10b It again appears that the variations are similar in both cases. At low H2O2 concentration, the two curves are the same as expected for kinetic control by substrate diffusion, whereas upon increasing [H2O2] the four-layered curve tends to be roughly four times the monolayer curve. As compared to a monolayer electrode, the maximum in the bell-shaped curve is shifted toward higher H2O2 concentrations. This results in an extension of the section of the H2O2 calibration curve where inhibition does not interfere, a favorable feature for devising large dynamic range HRP biosensors. Theoretical Analysis. The simulation of these experimental data, based on the mechanism depicted in Scheme 1, involves the numerical resolution of the following set of partial derivative equations and boundary conditions, noting that we treat the stack of deposited monolayers as a continuum where the average enzyme concentration is constant and within which Fick’s second law modified by appropriate kinetic terms applies. P/Q is the cosubstrate (mediator) couple; S (H2O2) is the substrate. L is the film thickness. The rate constants are defined in Scheme 1. As already discussed,10 reaction 2 is much faster than reaction 3, therefore justifying the sole consideration of reaction 3 with the introduction of a stoichiometric factor of 2. C0E is the total enzyme concentration in the film. C0P and C0S are the bulk concentrations of cosubstrate and substrate, respectively. At the electrode surface, x ) 0:
) ( ) ) -D (∂[Q] ∂x ) RF k exp{- (E - E )}{[P] RT
∂[P] i ) DFP FS ∂x
x)0
S
F P
d[E] ) -k1,1[S][E] + k1,-1[ES] + k3,2[E2Q] + k6[E3] (4) dt d[ES] ) k1,1[S][E] - (k1,-1 + k1,2)[ES] dt
(5)
d[E1] ) -k2,1[Q][E1] + k2,-1[E1Q] + k1,2[ES] + k5[Q][E3] dt (6) d[E1Q] ) k2,1[Q][E1] - (k2,-1 + k2,2)[E1Q] dt
(7)
d[E2] ) -(k3,1[Q] + k4[S])[E2] + k3,-1[E2Q] + k2,2[E1Q] dt (8) d[E2Q] ) k3,1[Q][E2] - (k3,-1 + k3,2)[E2Q] dt
(9)
d[E3] ) k4[S][E2] - (k5[Q] + k6)[E3] dt
(10)
For P, Q, and S, Fick’s second law modified by appropriate kinetic terms applies:
∂2[P] ∂[P] ) DFP 2 + k2,2[E1Q] + k3,2[E2Q] + k5[Q][E3] (11) ∂t ∂x ∂2[Q] ∂[Q] ) DFP 2 - k2,1[Q][E1] + k2,-1[E1Q] - k3,1[Q][E2] + ∂t ∂x k3,-1[E2Q] - k5[Q][E3] (12)
x)0
0 P/Q
x)0
exp
∂[S] ∂2[S] ) DFS 2 - k1,1[S][E] - k4[S][E2] ∂t ∂x
- [Q]x)0
[RTF (E - E )]} (1) 0 P/Q
implying that the electron transfer is assumed to follow Butler0 Volmer kinetics. EP/Q is the standard potential of the mediator couple, R is the transfer coefficient, kS is the standard rate constant, and DFP is the diffusion coefficient of P and Q in the film (assumed to be the same for both species). Starting with a reduction, as is the case here, the electrode potential is scanned linearly from an initial potential Ei in the negative direction at a rate V up to a potential Ef, corresponding to a time tR where the scan is reversed and goes back to the initial potential at the same rate, V:
0 e t e tR : E ) Ei - Vt tR e t e 2tR : E ) Ef + V(t - tR) ) 2Ef - Ei + Vt
(2)
(13)
DFS is the diffusion coefficient of S in the film. For several but not all forms of the enzyme, the steady-state assumption applies as previously discussed (refs 10 and references therein). These are first the Michaelis-Menten complexes, ES, E1Q, E2Q, and also E1 insofar as its conversion to E1Q is fast. Thus in the counting of the concentrations of the various enzyme forms, E1 and E1Q may be neglected whereas the following relationships apply to the other enzyme forms. The addition of eqs 4 and 5 and the application of the steadystate approximation to ES leads to
d[E]MM d([E] + [ES]) ) ) -k1,2[ES] + k3,2[E2Q] + k6[E3] dt dt (14) with
10810 Langmuir, Vol. 22, No. 25, 2006
[E] )
k1,-1 + k1,2
Andrieux et al.
and eq 10, as
[E]MM
k1,1[S] + k1,-1 + k1,2
[ES] )
k1,1[S]
[E] (15) k1,1[S] + k1,-1 + k1,2 MM
and thus to
The sum of the three significant enzyme concentrations is equal to the total concentration of enzyme in the film, C0E:
d[E]MM ) dt -
[E]MM + [E2]MM + [E3] ) C0E
k1,2k1,1[S]
[E] + k3,2[E2Q] + k6[E3] (16) k1,1[S] + k1,-1 + k1,2 MM
Likewise, from eqs 8 and 9 and application of the steady-state approximation to E2Q, we may write
d[E2]MM d([E2] + [E2Q]) ) ) dt dt -k3,2[E2Q] + k2,2[E1Q] - k4[S][E2] (17) [E2] )
d[E3] k4[S](k3,-1 + k3,2) ) [E ] - (k5[Q] + k6)[E3] dt k3,1[Q] + k3,-1 + k3,2 2 MM (24)
k3,-1 + k3,2
[E2]MM
k3,1[Q] + k3,-1 + k3,2 [E2Q] )
k3,1[Q] k3,1[Q] + k3,-1 + k3,2
[E2]MM (18)
d[E2]MM k3,2k3,1[Q] )[E ] + k2,2[E1Q] dt k3,1[Q] + k3,-1 + k3,2 2 MM k3,-1 + k3,2 [E ] (19) k4[S] k3,1[Q] + k3,-1 + k3,2 2 MM Application of the steady-state approximation to E1 and E1Q leads to
k2,2[E1Q] ) k1,2[ES] + k5[Q][E3] ) k1,2k1,1[S]
[E]MM + k5[Q][E3] (20)
k1,1[S] + k1,-1 + k1,2 k2,1[Q][E1] )
k2,-1 + k2,2 (k1,2[ES] + k5[Q][E3]) k2,2
(
)
k1,2k1,1[S] k2,-1 + k2,2 [E] + k5[Q][E3] ) k2,2 k1,1[S] + k1,-1 + k1,2 MM (21) and therefore to
k3,2k3,1[Q] d[E2]MM )[E ] + dt k3,1[Q] + k3,-1 + k3,2 2 MM k1,2k1,1[S] [E] + k5[Q][E3] k1,1[S] + k1,-1 + k1,2 MM k3,-1 + k3,2 [E ] (22) k4[S] k3,1[Q] + k3,-1 + k3,2 2 MM In addition, eq 16 may be recast as
k1,2k1,1[S] d[E]MM [E] + )dt k1,1[S] + k1,-1 + k1,2 MM k3,-1 + k3,2 [E ] + k6[E3] (23) k3,2 k3,1[Q] + k3,-1 + k3,2 2 MM
(25)
Therefore, the derivative and partial derivative equations to be numerically computed are eq 24 and the following four equations:
d[E2]MM k1,2k1,1[S] C0 ) dt k1,1[S] + k1,-1 + k1,2 E k3,2k3,1[Q] k1,2k1,1[S] + + k1,1[S] + k1,-1 + k1,2 k3,1[Q] + k3,-1 + k3,2 k4[S](k3,-1 + k3,2) [E ] + k3,1[Q] + k3,-1 + k3,2 2 MM k1,2k1,1[S] k5[Q] [E ] (26) k1,1[S] + k1,-1 + k1,2 3
(
(
)
)
k1,2k1,1[S] ∂2[P] ∂[P] C0E + ) DFP 2 + ∂t k [S] + k + k ∂x 1,1 1,-1 1,2 k1,2k1,1[S] k3,2k3,1[Q] [E ] + k3,1[Q] + k3,-1 + k3,2 k1,1[S] + k1,-1 + k1,2 2 MM k1,2k1,1[S] 2k5[Q] [E ] (27) k1,1[S] + k1,-1 + k1,2 3
(
)
(
)
k1,2k1,1[S] ∂2[Q] ∂[Q] ) DFP 2 C0E ∂t k [S] + k + k ∂x 1,1 1,-1 1,2 k1,2k1,1[S] k3,2k3,1[Q] [E ] k3,1[Q] + k3,-1 + k3,2 k1,1[S] + k1,-1 + k1,2 2 MM k1,2k1,1[S] 2k5[Q] [E ] (28) k1,1[S] + k1,-1 + k1,2 3
(
)
(
)
k1,1[S](k1,-1 + k1,2) 0 ∂2[S] ∂[S] ) DFS 2 C + ∂t k1,1[S] + k1,-1 + k1,2 E ∂x k3,-1 + k3,2 k1,1[S](k1,-1 + k1,2) - k4[S] × k1,1[S] + k1,-1 + k1,2 k3,1[Q] + k3,-1 + k3,2 k1,1[S](k1,-1 + k1,2) [E ] (29) [E2]MM + k1,1[S] + k1,-1 + k1,2 3
{
}
At the film/solution boundary, x ) L:
[P]x)L- ) κP[P]x)L+
(30)
[Q]x)L- ) κQ[Q]x)L+
(31)
[S]x)L- ) κS[S]x)L+
(32)
where κi represents the solution/film partition coefficients of the i subscript species
Horseradish Peroxidase Multilayers
(∂[P] ∂x ) ∂[Q] D( ∂x ) ∂[S] D( ∂x ) DFP F P
x)L-
x)L-
F S
x)L-
Langmuir, Vol. 22, No. 25, 2006 10811
(∂[P] ∂x ) ∂[Q] )D ( ∂x ) ∂[S] )D ( ∂x ) ) DSP
x)L+
S P
x)L+
S S
x)L+
(33)
We note that addition of eqs 27 and 28 on one hand and eqs 36 and 37 on the other hand shows that
(34)
∂([P] + [Q]) ∂2([P] + [Q]) ) DFP ∂t ∂x2
(35)
throughout the whole space. The integration of eq 47, taking eqs 39, 40, 42, and 43 into account, leads to
and DSi represents the solution diffusion coefficients of the i subscript species. In the solution, L e x e δ:
(47)
[P]x)0 + [Q]x)0 ) C0P
(48)
and, more generally,
2
∂ [P] ∂[P] ) DSP 2 ∂t ∂x
(36)
[P] + [Q] ) C0P
∂[Q] ∂2[Q] ) DSP 2 ∂t ∂x
(37)
The boundary condition at the electrode surface (1) may thus be replaced by
∂[S] ∂2[S] ) DSS 2 ∂t ∂x
(38)
At the natural conVection-diffusion boundary, x ) δ: In standard cyclic voltammetric experiments, the solution bulk boundary conditions are considered to apply at an infinite distance from the electrode. Because rather low scan rates were used here, these conditions should be considered to apply at a finite distance, δ, from the electrode because of the interference of natural convection. That is,
[P]x)δ ) C0P
(39)
[Q]x)δ ) 0
(40)
[S]x)δ ) C0S
(41)
C0P and C0S are the bulk concentrations of the cosubstrate and substrate, respectively. Initial conditions, t ) 0:
[P]t)0 ) C0P
(42)
[Q]t)0 ) 0
(43)
[S]t)0 )
(44)
C0S
In the absence of Q, besides serving as substrate for E, H2O2 is also able to reduce E1 to E2 slowly,13 thus opening a route to substrate inhibition through the conversion of E2 to E3. These reactions occur immediately after immersing the multilayer HRP electrode in a solution containing H2O2. A steady-state distribution of the enzyme between the two forms E2 and E3 is thus rapidly established. Thus, at the start of the voltammetric scan (i.e., at t ) 0),
k6 0 [EMM 2 ]t)0 ) CE k4[S]
(
[E3]t)0 ) C0E 1 -
k6
(45)
)
k4[S]
(46)
(13) Hernandez-Ruiz, J.; Arnao, M. B.; Garcia-Canovas, F.; Acosta, M. Biochem. J. 2001, 354, 107.
(49)
( ) ) RF k exp{- (E - E )}[C - [Q] {1 + RT
∂[Q] i ) -DFP FS ∂x
x)0
0 P/Q
S
0 P
exp
x)0
[RTF (E - E )]}] (50) 0 P/Q
The calculations may thus involve four concentrations only: [Q], [S], [E2], and [E3], using eqs 49 and 3 as electrode surface boundary conditions, eqs 31, 32, 34, and 35 as conditions at the film solution interface, eqs 40 and 41 as natural convectiondiffusion boundary conditions, eqs 43-46 as initial conditions, and eqs 37 and 38 to depict diffusion in the solution. As to the main eqs 24, 26, 28, and 29, they may be recast as
C0E d[E2]MM ) dt 1 1 + k1,2 k1[S]
(
)
k4[S] 1 1 + + [E2]MM 1 1 1 1 [Q] + + 1 + k3,2 k3[Q] k1,2 k1[S] K3,M
(
)
1 - k5[Q] [E3] (51) 1 1 + k1,2 k1[S]
d[E3] ) dt
k4[S] 1+
[Q] K3,M
[E2]MM - (k5[Q] + k6)[E3]
(52)
C0E ∂2[Q] ∂[Q] ) DFP 2 ∂t 1 1 ∂x + k1,2 k1[S] 1 1 [E2]MM 1 1 1 1 + + k3,2 k3[Q] k1,2 k1[S] 1 2k5[Q] [E3] (53) 1 1 + k1,2 k1[S]
(
(
)
)
10812 Langmuir, Vol. 22, No. 25, 2006
Andrieux et al.
C0E ∂[S] ∂2[S] + ) DFS 2 1 ∂t 1 ∂x + k1,2 k1[S] k4[S] 1 1 [E3] (54) [E2]MM + 1 1 1 1 [Q] + + k1,2 k1[S] 1 + K3,M k1,2 k1[S]
{
}
after the introduction of the following constants:
k1 )
k1,1k1,2 k1,-1 + k1,2
k3 )
k3,1k3,2 k3,-1 + k3,2
K3,M )
k3,-1 + k3,2 k3,1 (55)
The current-potential responses predicted from this set of differential equations and boundary and initial conditions depend on a large number of parameters, which remain large even after the system has been formulated in dimensionless terms. Fitting of the experimental data would thus require the simultaneous adjustment and estimation of a large number of parameters, making such an endeavor a losing battle. It is thus advisable henceforth to adopt a classical strategy consisting of the search of limiting kinetic behaviors depending on a small number of independent parameters.14 These can then be adjusted with minimal tedium and reasonable accuracy. Once this preliminary analysis is achieved, one may come back to the general simulation for determining the remaining unknown. One such situation is met in the experiments shown in Figures 1 and 2 in the upper domain of the H2O2 concentration range, as indicated by the S shape of the cyclic voltammetric responses and the small degree of hysteresis, which correspond to the establishment of a steady state for all forms of the enzyme. Steady-State Situations. The steady-state approximation is applied to all forms of the enzyme, meaning that the right-hand sides of eqs 4-10 are set equal to zero. The expressions of the enzyme concentrations thus obtained and the resulting kinetic term in eq 12 may be drastically simplified, as previously discussed in detail for monolayer HRP electrodes10 in view of the fact that the time constants involved in the main catalytic cycle are much shorter than those pertaining to substrate inhibition and regeneration of the active forms of the enzyme. It follows that eq 12, 28, or 53 may be replaced by eq 56:
∂[Q] ) ∂t ∂2[Q] DFP 2 ∂x
2C0E k4[S] 1 1 1 1 + + + k3[Q] kcat k1[S] k3[Q] k6 + k5[Q]
(56)
with
1 1 1 ) + kcat k1,2 k3,2
(57)
Steady-state conditions also imply that ∂[Q]/∂t ) 0, leading to the replacement of eq 56 by eq 58. (14) Save´ant, J.-M. Elements of Molecular and Biomolecular Electrochemistry: An Electrochemical Approach to Electron-Transfer Chemistry; WileyInterscience: New York, 2006.
DFP
d2[Q] dx2
)
2C0E k4[S] 1 1 1 1 + + + k3[Q] kcat k1[S] k3[Q] k6 + k5[Q]
(58)
In the experiments shown in Figures 1 and 2 in the upper domain of the H2O2 concentration range, such a steady-state situation is achieved, and the substrate concentration is large enough for its depletion near the electrode to be neglected. Also, with four deposited monolayers, the enzyme film is thin enough, relative to the solution diffusion layer, for the concentration of Q to be practically constant throughout the film. The situation is thus the same as for a monomolecular film except that the total amount of enzyme on the electrode is equal to
Γ0E ) C0EL
(59)
At the plateau, [Q]x)0 ) C0P; therefore, the plateau current, ip, is given by eq 60.
k3 k3 k4C0S 2FSk3Γ0E 1 ) 0+ + + ip CP kcat k1C0S k6 + k5C0P
(60)
In this H2O2 concentration range, k1C0S . k3C0P; therefore,
k3 k4C0S 2FSk3Γ0E 1 ) 0+ + ip CP kcat k6 + k5C0P
(61)
It follows that the reciprocal of the plateau current is predicted to vary linearly with the substrate concentration. That this is indeed the case is shown in Figure 3. The rate characteristics summarized in Table 1 follow from the values of the slopes and intercept of the two linear plots shown in Figure 3. The total enzyme surface concentration Γ0E contained in the four HRP layers was calculated using the values k3 and K3,M previously obtained at an HRP monolayer electrode,10b values that were previously shown to be similar to those obtained for HRP in homogeneous solution.10a We note that the ratio (k6 + k5C0P)/k4, characterizing the extent of inhibition, is definitely larger than in solution (by about a factor of 2). We do not know whether this is caused by a decrease in the substrate inhibition rate constant, k4, and/or by an increase in the regeneration rate constants k5 and k6. This observation is reminiscent of a similar decrease in the global efficiency of inhibition when passing from monomeric to polymeric HRP.15 On these bases, we may now come back to the simulation of the series of curves in Figure 1 by the numerical resolution of eqs 51-54 and 37 and 38 with, as boundary conditions, eqs 50 and 2 for the electrode surface, eqs 31, 32, 34, and 35 for the film solution interface, eqs 40 and 41 for the natural convectiondiffusion boundary, and eqs 43-46 as the initial conditions. The best fits for all H2O2 concentrations were obtained for the parameter values listed in the caption of Figure 1. The computational details are given after the Experimental Section. A peculiar property of H2O2 is that it can serve as a reductant as well as an oxidant of HRP. This is the reason that immediately after the addition of H2O2 a steady-state distribution of the enzyme between the two forms E2 and E3 according to eqs 45 and 46 is rapidly established. This implies the presence of an additional reaction in Scheme 1 (reaction 0, not shown) involving the reduction of E1 by H2O2 to give E2. The introduction of this supplementary reaction into the numerical simulation allows the (15) Hoshino, N.; Nakajima, R.; Yamazaki, I. J. Biochem. 1987, 102, 785.
Horseradish Peroxidase Multilayers
Langmuir, Vol. 22, No. 25, 2006 10813
Figure 3. Reciprocal plot of the data in Figure 2 for a four-monolayer HRP electrode (blue squares) and a monolayer HRP electrode (green dots). Table 1. Compared Characteristics of the Four-Monolayer and One-Monolayer Electrode Coatings Derived from the Data in Figure 3 k3Γ0E (cm/s)a N)4 0.101
N)1 0.023
Γ0E (pM/cm2)b N)4 13.0
N)1 3.0
(k6 + k5C0P)/k4 (mol cm-3)c N)4 3.3 ×
10-6
N)1 2.6 ×
10-6
Electrodes Coated with up to 16 Monolayers. Cyclic voltammetric responses of films obtained by the successive deposition of up to 16 monolayers are shown in Figure 4. The concentrations of substrate and cosubstrate were selected so as to avoid substrate depletion and to ensure the achievement of steady-state conditions. Although the plateau current regularly increases with the number of monolayers, the increase is not linear but tends to bend down, reflecting the interference of cosubstrate diffusion within the film, as previously observed and analyzed for glucose oxidase electrodes.6 Equation 58 is applicable under the conditions selected for these experiments. Taking into account that there is no substrate depletion, it can be recast in a dimensionless form as
( )
d2
[Q] C0P
(x )
dx
k3C0E
)
2
DFP
2
kcat/k3 ) 36 × 10-9 mol cm-3.10 b k3 ) 7.9 × 109 mol-1 cm3 s-1.10 c 1.7 × 10-6 mol cm-3 in solution.10a a
1 + k3C0P
( ) [Q] C0P
(62)
k4C0S
(
)( ) ( )
k5C0P 1 1 [Q] + + k6 kcat k C0 C0 [Q] 1 S P + 0 CP k5C0P
Knowing that 0 e [Q]/C0P e 1, that k3C0P(1/kcat + 1/k1C0S) ) 5.7 × 10-3, and that k6/k5C0P ) 35, it follows that eq 62 may be simplified to give
( )
d2 Figure 4. Cyclic voltammetry of the catalytic reduction of H2O2 by HRP multilayers deposited on a screen-printed carbon electrode. Scan rate, 10 mV s-1; phosphate buffer, pH 7.4; temperature, 20 °C. (a) Variation of the cyclic voltammetric responses with the number of monolayers (number on each curve) in the presence of 0.25 mM H2O2 and 0.2 µM [Os(bpy)2(py)Cl]2+. (b) Plateau current (open blue squares) as a function of the number, N, of monolayers under the same conditions as in part a. Red line, simulation according to eq 65.
prevention of the accumulation of E1 at the start of the scan, when the concentration of Q is not sufficient to convert it efficiently into E2. An approximate value of k0 ) 500 M-1 s-1 was obtained from the literature.16 A high precision value is not required because reduction by Q rapidly takes over when a significant current flows. The thickness of the four-monolayer film is too small for the diffusion of the substrate and/or cosubstrate within the film to interfere in the cyclic voltammetric responses. It follows that, if small enough, the thickness of the film can take an arbitrary value, provided the total concentration of enzyme obeys eq 58, as was determined to be the case. This is to say that the experiments of the type shown in Figures 1 and 2 are of no use for sensing the thickness of the film. We come back to this question in the next section where we examine the responses obtained upon deposition of a much larger number of monolayers onto the electrode. (16) (a) Nakajima, R.; Yamazaki, I. J. Biol. Chem. 1987, 262, 2576. (b) Baker, C. J.; Deahl, K.; Domek, J.; Orlandi, E. W. Arch. Biochem. Biophys. 2000, 382, 232.
[Q] C0P
(x )
2 k3C0E DFP
dx
)
( )
[Q] 2 0 k4CS C0P 1+ k6
(63)
the integration of which, knowing that
i ) FSDFP
(∂[Q] ∂x )
(64)
x)0
and that at the plateau ([Q])x)0 ) C0P, leads to the following expression of the plateau current
ip )
xDQ
FSC0P
(x )
x
2 k C0 tanh L 0 3 E k4CS 1+ k6
k3C0E 2 k4C0S DQ 1+ k6 (65)
or equivalently
ip ) FSC0PxDQ ×
x
m
(x
ΓE 2 k tanh N 0 3 l k4CS 1+ k6
m
)
k3ΓE l 2 (66) 0 D k4CS Q 1+ k6
where l is the average thickness of each monolayer and Γm E is the average amount of enzyme that it contains per unit area.
10814 Langmuir, Vol. 22, No. 25, 2006 Scheme 3
Andrieux et al.
(5) The experiments in which the number of monolayers was extended to 16 allowed an approximate determination of the average thickness of each monolayer. Comparing the value thus found, 5 nm, with the crystallographic sizes of neutravidin and HRP, which are also both on the order of 5 nm,17 points to the arrangement depicted in Scheme 3 rather that the one used in Scheme 2 to explain the step-by-step deposition procedure. The average amount of enzyme (3.5 pM/cm2) contained within the 5 nm thickness of each layer allows us to calculate an impressive enzyme concentration of 7 mM, which is relatively close to the HRP concentration that can be calculated from its crystal form (∼20 mM). Experimental Section
A good fit of the data in Figure 4b is obtained for l ) 5 nm 2 and Γm E ) 3.5 pM/cm , as represented by the red line.
Concluding Remarks (1) The step-by-step immobilization procedure described above allows the deposition of up to 16 active monolayers, whereas previous procedures allowed the deposition of only a few monolayers (ranging from 2 to a maximum of 5).11 There is no reason that this number could not be further increased. Improvement of the catalytic sensitivity by a factor on the order of 10 may thus be reached. To illustrate the good sensitivities that can thus be achieved, we may observe in Figure 4 that a cosubstrate concentration as low as 0.2 µM can be easily determined. With a background current of 1.5 nA at 10 mV s-1 and a signalto-noise ratio of 3, this means that the detection limit of the mediator can be as low as 1 nM. Whereas the mediator used in this work is of no analytical interest, it can be easily replaced by a large variety of quinoid compounds known to mediate the electrochemistry of HRP efficiently. For some of them, it should be interesting to dispose of a sensitive analytical method. (2) The theoretical tools that have been developed allowed full characterization of the multilayered HRP coatings by means of a combination between the closed-form analysis of limiting behaviors and finite difference numerical computations. (3) The characteristic rate constants of the multilayered system are not very different from those of a monolayer as well as those in solution. The main difference as compared to the solution data is a small decrease in the efficiency of substrate inhibition. This result emphasizes that the avidin-biotin connector is well suited to attaching multimonolayers of enzymes onto solid surfaces while maintaining the activity of the immobilized enzyme at approximately the same level as in solution. (4) At the lower end of the H2O2 concentration range, where the peak current becomes proportional to the H2O2 concentration, there is no advantage in using a multilayer HRP electrode because catalysis is maximal, producing a current equal to the direct reduction current, albeit occurring at a less demanding potential. In other words, thick coatings are not required to obtain maximal catalytic efficiency for low substrate concentrations. The total extent of accessible concentrations is wider for the multilayer electrode than for the monolayer electrode. The apparent delaying of inhibition by H2O2 for the multilayer electrode is simply a consequence of the rate constants of the multilayered system being about the same as those of a monolayer, resulting in a current that is proportional to the number of layers as long as depletion of the substrate and diffusion of the cosubstrate through the film do not interfere significantly.
Instrumentation, electrodes, and chemicals were the same as previously described,10b with the exception of biotinylated HRP. After unsuccessful attempts to build multilayer of HRP using commercial sources of biotinylated HRP, we chose to prepare this modified enzyme ourselves. A biotin functionalized with a long spacer arm (i.e., the biotin-amidohexanoic acid hydrazide; Sigma) was selected for its attachment to the carbohydrates surrounding HRP. The biotinylation procedure of the HRP has been described in ref 12. Once biotinylated, the modified HRP was recovered in a phosphate buffer, and its concentration was determined spectrophotometrically using the Soret extinction coefficient of 102 mM-1 cm-1 at 403 nm. The catalytic activity of the biotinylated enzyme in solution was determined by cyclic voltammetry, and the biotin contents, by competitive displacement of the 2-(4-hydroxyphenylazo)benzoic acid (or HABA) bonded to avidin.18 The procedure led to a biotinylated HRP containing five to six biotins per protein, retaining full enzymatic activity. The final solution was divided into aliquots and stored below -20 °C. The step-by-step building of the HRP multilayers was also described in ref 12. Briefly, a drop of 8 µL of 0.5 mg mL-1 biotinylated rabbit IgG in a phosphate buffer (pH 7.4) was locally deposited on the sensing area of the carbon electrode and incubated for 2 h in a water-saturated atmosphere. The electrode surface was next rinsed with phosphate buffer, immersed in a solution of 0.1% BSA for 15 min, rinsed again, and then incubated in a solution of 10 µg mL-1 neutravidin for 15 min. Once the first layer of neutravidin was deposited, the electrode was rinsed and immersed in 0.2 µM biotinylated HRP in phosphate buffer for 45 min. The multilayer was obtained by repeating the two last steps as many times as required.
Numerical Computation Procedures For the numerical resolution of eqs 51-54, space and time were divided into intervals of length ∆x and ∆t. We designate any of the four variable concentrations involved, [E2]MM, [E3], [Q], and [S] by [Z]. For time t ) j∆t (0 e j e n) and for x ) i∆x (0 e i e m), the current value of [Z] is denoted [Z]ij. The time and space derivatives are replaced by the following finite difference expressions
∂[Z] [Z]j - [Z]j-1 ) ∂t ∆t i
∂2[Z] ∂x2
)
i
[Z]i+1 - 2[Z]ij + [Z]ij - 1 j ∆x2
(67)
(68)
allowing the calculation of the actual values (j) from the preceding values (j - 1). When nonlinear, the chemical terms are linearized using the preceding values. For example, [Z] × [Z′] is replaced by i i 0.5([Z]j-1 [Z′]ij + [Z]ij [Z′]j-1 ).
Horseradish Peroxidase Multilayers
At each time, the various values of the four concentrations are related by 4(m - 1) linear equations plus two equations for [Q] and [S] at the electrode surface and two at the film/solution boundary, resulting in a set of 4m linear equations for 4m unknowns. (17) (a) Henriksen, A.; Smith, A. T.; Gajhede, M. J. Biol. Chem. 1999, 274, 35005. (b) Pugliese, L.; Coda, A.; Malcovati, M.; Bolognesi, M. J. Mol. Biol. 1993, 231, 698. (18) Green, N. M. In Methods in Enzymology; McCornick, D. B., Wright, L. D., Eds.; Academic Press: New York, 1970; Vol. 18A, p 418.
Langmuir, Vol. 22, No. 25, 2006 10815
In the solution, outside the film a similar discretization of space and time is introduced, and the two diffusion equations with no kinetic terms pertaining to [Q] and [S] are calculated by the explicit method with appropriate boundary conditions. A classical matrix inversion procedure is used for the resolution of the 4m equations, which are repeated for all n’s. Typical values of n and m for the simulation of a cyclic voltammetric curve are n ) 1000 and m ) 20. LA061193S
