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Pseudo-equilibrium approach to the design and use of enzyme-based amperometric biosensors evaluated using a sensor for hydrogen peroxide
Analytica Chimica Acta 409 (2000) 123–130
Pseudo-equilibrium approach to the design and use of enzyme-based amperometric biosensors evaluated using a sensor for hydrogen peroxide Weibin Chen, Harry L. Pardue ∗ Department of Chemistry, 1393 BRWN Bldg., Purdue University, West Lafayette, IN 47907-1393, USA Received 9 April 1999; received in revised form 21 July 1999; accepted 23 July 1999
Abstract This paper describes a pseudo-equilibrium approach to the measurement and data-processing steps in the use of enzyme-based amperometric biosensors for substrates. The goal of the method is to obtain the response corresponding to reaction of all substrate in a fixed volume of solution with the expectation that this will improve the linear range and ruggedness relative to the conventional steady-state option. The biosensor is used in a rotating disk mode such that data for current versus time can be monitored with and without rotation of the sensor. With the sensor rotating at moderately high speed, current is monitored until an initial steady-state response is obtained after which the rotation is stopped and current is monitored until a second steady-state response is obtained. Under controlled conditions, the transition form the first to the second steady-state condition corresponds to reaction of virtually all of the substrate in a small fixed volume of solution controlled by the dimensions of the diffusion layer. Integration of current as a function of time yields the charge corresponding to reaction of substrate in the fixed volume established by the diffusion process. Evaluation of this pseudo-equilibrium option using a peroxidase-based sensor for hydrogen peroxide yielded a linear range extending to at least four times the Michaelis constant and a pH dependence approximately 40-fold less than steady-state currents obtained from the same data sets. ©2000 Elsevier Science B.V. All rights reserved. Keywords: Pseudo-equilibrium approach; Biosensors
1. Introduction Research in a variety of laboratories in recent years has resulted in the development of enzyme-based amperometric biosensors for a variety of substrates [1]. Most applications of these biosensors are based on steady-state responses. Advantages of the steady-state approach include simplicity and, in most cases, speed. Disadvantages include reduced sensitivity as ∗ Corresponding author. Tel.: +1-765-494-5320; fax: +1-765-496-1200. E-mail address: [email protected] (H.L. Pardue).
the substrate concentration approaches and exceeds Michaelis constants and large dependencies on experimental variables such as temperature, pH, activators, inhibitors and time-dependent changes in enzyme activity. The limited linear ranges and large dependencies on experimental variables result from the fact that steady-state responses result from balances between two or more competing rate processes such as rates of chemical reactions and mass transport processes. When chemical reaction is one of the limiting processes, the steady-state response is analogous to an initial rate in homogeneous solution methods. As
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such, calibration plots tend to curve toward the concentration axis as expected from Michaelis–Menten behavior and steady-state responses depend not only on substrate concentration but also on variables that affect the activity of the immobilized enzyme. On the one hand, research in several laboratories has shown that alternative measurement/data-processing methods can be used to reduce or eliminate these problems in connection with kinetic-based methods in homogeneous solution [2–6]. On the other hand, limited attention has been focused on similar problems associated with enzyme-based biosensors. One approach to improving the linear range and ruggedness of enzyme-based amperometric biosensors has been to use these devices in a pseudo-equilibrium mode [7,8]. In this mode, experiments are designed to permit the measurement of signals corresponding to reaction of all the substrate in a small fixed volume of solution. The resulting equilibrium-based results exhibit linear calibration plots for substrate concentrations exceeding Michaelis constants by factors of at least five fold and have much smaller dependencies on experimental variables than results based on steady-state responses. Initial implementations of this pseudo-equilibrium option have involved the incorporation of the biosensor into a thin-layer flow cell [7,8]. Although the thin-layer flow cell permits the measurement of responses corresponding to reaction of all the substrate in the thin layer of solution in close proximity to the reactor–sensor surface, the approach is inconvenient and slow. The present study was undertaken in an attempt to improve the simplicity and speed of the pseudo-equilibrium option. Briefly stated, the aim of this study was to determine if diffusion could be exploited to produce the thin layer of solution in which substrate concentration would be depleted during the measurement process. The enzyme was immobilized on the surface of an electrode mounted on a shaft that could be rotated at high speed and then stopped abruptly. Rotation at the desired speed was begun, polarizing voltage was applied to the rotating electrode and current was monitored until a first steady-state response was obtained [9]. Then the rotation was stopped abruptly and the electrolysis current was measured as a function of time until a second steady-state response was obtained.
Current versus time data during the period from the time when rotation was stopped until the second steady-state response was obtained was used to implement the pseudo-equilibrium option. The principal question we were attempting to answer is whether the thickness of the diffusion layer which developed after the flow was stopped would be sufficiently reproducible to permit quantitation of substrate in the same manner as used with the thin-layer flow cell [7,8]. If the diffusion layer is reproducible among different samples, then it should be possible to use current versus time data to obtain the charge corresponding to reaction of substrate in the fixed volume of solution represented by the dimensions of the diffusion layer. Substrate concentrations computed using this charge should vary linearly with concentration over ranges exceeding the Michaelis constant and should be virtually independent of variables that affect enzyme activity and reaction rates at the reactor/sensor surface. Results reported below for a model sensor system support these expectations.
2. Model sensor system An enzyme-based sensor for hydrogen peroxide was used as a model for this study. The sensor is similar to that described by Bartlett et al. [10]. In this system, glassy carbon coated with polyaniline is used as a substrate for the adsorption of horseradish peroxidase (HRP). The adsorbed HRP is then immobilized with a layer of poly(1,2-diaminobenzene). Hydrogen peroxide reacts at the electrode surface to produce water and the oxidized form of HRP represented as Compound I in Reaction 1. HRP(Fe3+ ) + H2 O2 → Compound I + H2 O
(1)
The oxidized form of HRP is then reduced electrochemically via electron exchange through the polyaniline as shown in Reaction 2. Compound I + 2H+ + 2e → HRP(Fe3+ )
(2)
The net result is reduction of hydrogen peroxide accompanied by the production of an equivalent amount of electrical charge and regeneration of the reduced form of HRP. This process continues as long as hydrogen peroxide is in contact with the reactor/sensor system.
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3. Mathematical description A mathematical description of the system has been described in detail elsewhere [7]; accordingly, it will suffice to review essential equations here. Given that the first steady-state current is obtained with high-speed stirring, it is expected that the first steady-state current will be limited primarily by the rate of chemical reaction. Assuming Michaelis–Menten behavior for the reaction, the first steady-state current, iss , is expected to depend on concentration as follows Iss Cb (3) iss = 0 K m + Cb in which Cb is the bulk substrate concentration, K 0 m is the apparent Michaelis constant and Iss is the maximum current obtained when Cb K 0 m . This steady-state current which is the most frequently measured response is expected to vary nonlinearly with concentration. We have not attempted to model the early part of the transient behavior after the stirring is stopped. However, after the substrate concentration at the reactor–sensor surface falls below the apparent Michaelis constant, the current versus time response can be described as follows i(t) = k0 Cb + k1 Cb exp(−k3 t)
(4)
in which k0 , k1 and k3 are complex combinations of reaction and mass-transport rate constants. An important feature of this equation is that the current is expected to be characterized by mixed zero- and first-order behavior. Another important feature of the equation is that the second steady-state current which occurs when k3 → ∞ is expected to vary linearly with concentration resulting from the fact that it is a diffusion-controlled current. As noted earlier, we are primarily interested in the electrical charge resulting from reaction after rotation is stopped. The time-dependent charge is obtained by integrating Eq. (4) with respect to time. The result is Q(t) = k0 Cb t + k2 Cb [1 − exp(−k3 t)]
(5)
in which k0 and k3 are as described above and k2 = k1 /k3 . According to Eq. (5), the charge versus time response consists of simultaneous zero-order/first-order
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processes. The zero-order component represents diffusion of substrate from the bulk solution; the first-order component is expected to represent substrate in the small volume represented by the diffusion layer. It is this latter component that is of primary interest in this study. The maximum value of the first-order component, Q∞ , is to be used to quantify the hydrogen peroxide concentrations. As will be shown later, there are at least three different ways to extract the desired first-order component from the zero-order component. 4. Experimental 4.1. Regents and solutions All chemicals were used as received. Reagents used included horseradish peroxidase (E.C. 1.11.1.7, Type VI, 260 u mg−1 , Sigma, St. Louis, MO 63178), Aniline (99.5+%, Aldrich., Milwaukee, WI 53233), 1,4-diaminobenzene (99+%, Aldrich) and 1,2-diaminobenzene (99+%, Aldrich, Milwaukee, WI 53201). All solutions were prepared in doubly distilled water. A pH 5 citrate/phosphate buffer solution (McIlvane) was prepared by mixing appropriate volumes of 0.1 M citric acid solution and 0.2 M sodium phosphate (Na2 HPO4 ) solution. A 3% solution of hydrogen peroxide (Mallinckrodt Specialty Chemical, Paris, KY) was used to prepare 10 mmol l−1 stock solutions in citrate/phosphate buffer. All the stock solutions were prepared daily. 4.2. Rotating disk electrode system A high speed rotator with fast start/stop characteristics (Model AFM SRX, Pine Instruments, Grove City, PA 16127), and speed controller (Model MSRX, Pine Instruments) were used to control the rotating disk electrode. Horseradish peroxidase was immobilized on 5 mm diameter glassy-carbon rotating disk electrodes (Models AFMDI 1980 GC and AC011420, Pine Instruments) as described in the next section. 4.3. Preparation of the sensor Polyaniline and HRP were immobilized on a glassycarbon disk electrode (5 mm diameter) as described
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below. First, a polyaniline film was deposited on the surface of polished glassy carbon electrode according to the procedure published previously [10]. The resulting film was rinsed thoroughly with the pH 5 citrate/phosphate buffer. Then HRP was adsorbed onto the polyaniline-coated glassy carbon electrode by rotating the electrode at 60 rpm for 300 s in a citrate/phosphate buffer solution containing 1 mg ml−1 horseradish peroxidase, 5 mmol l−1 1,2-diaminobenzene and 0.5 mol l−1 sodium sulfate. Then a poly(1,2-diaminobenzene) coating was deposited on the surface by applying a potential of +300 mV versus a silver/silver chloride reference electrode for 240 s. The resulting biosensor was then again washed thoroughly with pH 5 citrate/phosphate buffer solution and was finally rotated for 5 min at 1000 rpm in a pH 5 citrate/phosphate buffer to remove weakly immobilized or physically entrapped HRP. The thickness of the resulting films was estimated to be approximately 12 m [11]. 4.4. Data acquisition Time-dependent currents were monitored with a commercially available voltammetric system (CV-50 W Voltammetric Analyzer, Bioanalytical Systems, West Lafayette, IN 47906) which was interfaced to a laboratory computer (Gateway 2000 4DX2-50V, 610 Gateway Drive, North Sioux City, SD 57049) using electrochemistry software (BAS WindowsTM ). 4.5. Procedure All reactions took place in citrate/phosphate buffer in a water-jacketed cell used for temperature control. Temperature was controlled at 23.0 ± 0.1◦ C for all studies reported below. The biosensor was polarized at +90 mV versus Ag/AgCl reference electrode (Bioanalytical Systems) with a platinum wire serving as the auxiliary electrode. Typically, a 50 ml aliquot of sample containing hydrogen peroxide in buffer was added to the sample cell and the working electrode was rotated for 3 min in the sample solution after which a potential of +90 mV (versus Ag/AgCl) was applied to the electrode. Current was monitored for 150 s which was sufficient time for a first steady-state response to be obtained at which point the rotator was stopped and the response was
monitored for an additional 350 s which was sufficient time for a second steady-state response to be obtained. Data were processed using custom designed curve-fitting software described elsewhere [12].
5. Results and discussion Unless stated otherwise, imprecisions are reported at level of one standard deviation (±1SD) throughout this paper. 5.1. Rotation rate As implied by Eq. (3), a goal was to have the first steady-state response controlled primarily by reaction kinetics. To this end, a rotation rate was chosen above which the steady-state current was independent of rotation rate. Preliminary studies of rotation rates up to 1800 rpm using a 0.5 mmol l−1 solution showed that the first steady-state current increased for rotation rates up to about 500 rpm and were independent of rotation rate above this value. Accordingly, a rotation rate of 500 rpm was used for all studies reported below. 5.2. Current response curves Experiments were performed with 0, 0.02, 0.04, 0.1, 0.2, 0.5, 0.76, 1.09, 1.68 and 2.86 mmol l−1 hydrogen peroxide. Fig. 1 includes typical response curves for hydrogen peroxide from 0 to 2.86 mmol l−1 . In all cases, the potential was applied at t = 0, and the rotator was stopped at t = 150 s. The first decrease in current for each concentration corresponds to the establishment of the first steady-state response. The second abrupt decrease in current at 150 s corresponds to the point at which rotation was stopped. Responses for all concentrations decrease to a finite, non-zero background current after about 350 s. At this point, substrate is reacting immediately reaches the reactor/sensor surface, resulting in a diffusion-limited current. As expected from Eq. (5), the amplitudes of these diffusion-limited currents increase with the increasing of hydrogen peroxide concentrations. It was found that the initial decrease in current prior to the first steady-state signal conformed reasonably well to first-order behavior. Plots of ln(i − iss ) versus
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Fig. 1. Experimental response curves for several hydrogen peroxide concentrations. Conditions: pH = 5; T = 23.0◦ C; Stirring rate = 500 rpm; hydrogen peroxide (bottom to top) = 0, 0.04, 0.1, 0.2, 0.5, 0.76, 1.09, 1.68, 2.86 mmol l−1 .
t were linear throughout the concentration range studied. A mean value of 0.19 s−1 was obtained for the rate constant for the initial current decay, corresponding to a half-life of 3.6 s. Accordingly, the 150 s rotation period corresponds to approximately 40 half-lives of the first decay process ensuring that the process was complete before the rotation was stopped. Similarly, the latter parts of the decay curves after rotation was stopped were fit reasonably well by a first-order model. The mean value of the first-order rate constant was k3 = 1.9 × 10−2 s−1 corresponding to a half-life of the decay process is 37 s. Accordingly, the data collection time of 350 s after the rotation was stopped corresponds to 9.4 half-lives during which the exponential decay would be about 99% complete. Therefore, it is expected that the exponential term in Eq. (4) should be negligible and that the background current, I0 , should vary linearly with substrate concentration. 5.3. Current versus concentration relationships As noted earlier, the first steady-state current should vary nonlinearly with concentration (Eq. (3)) and the
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Fig. 2. Calibration plot for steady-state current (a) and charge (b) vs. hydrogen peroxide concentration. Both plots: Triplicate runs at each concentration. (a) Steady-state currents ( ) are averages for last 30 data points during the first steady-state region. Solid line is a fit of Eq. (3) to data. (b) Maximum charge, Q∞ , obtained as first-order component of fit of Eq. (5) to data in Fig. 3.
second steady-state current should vary linearly with concentration (Eq. (4) with t → ∞). Fig. 2 includes a plot of the first steady-state current versus concentration. As expected, the sensitivity for the first steady-state current (Plot a) decreases continuously with concentration. The solid curve is a fit of Eq. (3) to the data supporting the expectation that the steady-state currents conform to Michaelis–Menten kinetics. Fitting parameters were Iss = 0.113 ± 0.007 mA and K 0 m = 0.75 ± 0.16 mmol l−1 . In contrast to the steady-state response before the rotation is stopped, a plot of steady-state response after the rotation is stopped versus concentration is linear. Least-squares parameters for a fit of a linear model to the data correspond to CH2 O2 i0 = 2.382 ± 0.208 A + (8.53 ± 0.18 A) (mmol l−1 ) with a standard error of the estimate (syx ) of 0.52 A and a correlation coefficient (r) of 0.998 for the full concentration range studied (0–2.86 mmol l−1 ). These results support the expected behavior of the measurement approach.
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5.4. Charge versus time relationships According to Eq. (5), data for charge versus time for the decay period after rotation is stopped should follow combined zero-order/first-order behavior. Fig. 3 includes one set of data for charge versus time for each of the concentrations studied. It should be noted that zero time on this plot has been shifted to the time at which rotation was stopped. Points represent experimental data and solid curves represent fits of Eq. (5) to the data. It is observed that Eq. (5) fits all the data quite well, again supporting the expected behavior. As an alternative processing option, the mean value of the second steady-state current was subtracted from each data point along each current versus time response prior to integrating the data. Integration of the background-subtracted data yielded responses for charge versus time for which the fits of a first-order model were at least as good as the fits in Fig. 3.
Fig. 3. Charge vs. time response for different hydrogen peroxide concentrations. Conditions as in Fig. 1. t = 0 is the point at which rotator was stopped. Experimental data ( ); Fitted data, Eq. (5) (—).
5.5. Charge versus concentration relationships The total charge, Q∞ , corresponding to the first-order component of the decay process after the rotation is stopped is expected to vary linearly with concentration (Eq. (5)). Both the curve-fitting process illustrated in Fig. 3 and the background-subtraction approach described above were used to isolate the first-order component of the charge from the zero-order component as described earlier [7,8]. In each case, the determined value of charge varied linearly with concentration. Results obtained using the curve-fitting option are included in Fig. 2. The solid plot is a fit of a linear model to the data. Least-squares parameters for the fit correspond to Q∞ = 0.07 ± 0.02 mC + (1.24 ± 0.02 mC) × CH2 O2 (mmol l−1 ) with a standard error of the estimate of 0.05 mC and a correlation coefficient of 0.999. Similar results were obtained using background-subtracted data as described above. Whereas the sensitivity of the steady-state option changes continuously with concentration, the sensitivity of the charge versus concentration data is constant throughout the range examined which exceeds the apparent Michaelis constant
(K 0 m = 0.75 ± 0.16 mmol l−1 ) by approximately four fold. The important point here is not so much the extension of the linear range but rather the combined effects of the sensitivity and the measurement uncertainty on the determination error at high concentrations. For example, the combined effects of sensitivity and error bars near 3 mmol l−1 correspond to concentration errors of about 0.7 mmol l−1 for the steady-state option and about 0.13 mmol l−1 for the pseudo-equilibrium option. In other words, the pseudo-equilibrium option yields at least a five-fold reduction in concentration error at 3 mmol l−1 . 5.6. pH effects A major objective of this study was to determine if the proposed approach could be used to reduce effects of experimental variables relative to the steady-state option. One variable, pH values, was used to compare the ruggedness of the steady-state and pseudo-equilibrium options. To quantitatively compare the effects of changes in these variables on the
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and temperature. Regardless of the direction in which temperature was changed, the first steady-state current tended to decrease with successive experiments. While we are unable to explain this behavior, the net result is that it is not possible to compensate for temperature changes using this reactor/sensor combination.
6. Conclusions
Fig. 4. Effects of pH on steady-state current (a) and charge (b). Hydrogen peroxide concentration, 0.5 mmol l−1 ; ordinates are ratios of current or charge at each pH to values (55.36 A and 0.840 mC) at pH 4.5.
results, the relative error coefficients (RECs) concept was adapted from a previous publication [13]. Effects of pH on the two options for a fixed concentration of hydrogen peroxide are illustrated in Fig. 4. It is apparent that the pseudo-equilibrium option is much more rugged to changes in pH than is the steady-state option. Differences that are visualized from these plots can be quantified using relative error coefficients (RECs) computed from the slopes of these plots [13]. Numerical values of the relative error coefficients for the steady-state and pseudo-equilibrium options at pH = 4.5 are 0.22 and 0.0049%/pH unit, respectively. This corresponds to a 45-fold improvement in the ruggedness to changes in pH for the pseudo-equilibrium option relative to the steady-state option. 5.7. Temperature effects Effects of temperature in the range from 20◦ C to 36◦ C on steady-state currents and charge were studied using a 0.5 mmol l−1 hydrogen peroxide solution at pH 5. A positive correlation with temperature was expected for both steady-state currents. Whereas the second steady-state exhibited the expected positive correlation with temperature, there was no consistent correlation between values of the first steady-state current
The pseudo-equilibrium approach to the use of enzyme-based biosensors has two important advantages relative to steady-state methods. It maintains constant sensitivity over much wider concentration ranges and it is more rugged to changes in a variety of experimental variables. The principal disadvantages of the pseudo-equilibrium option as implemented to date are the more involved experimental procedures and the longer measurement times. The batch mode implementation as described in the present paper is simpler than the thin-layer stopped-flow approach described earlier [7,8] but still requires longer measurement times than the steady-state option and has one potential limitation relative to the thin-layer stopped-flow option. Whereas the thin-layer stopped-flow option has a fixed reaction layer, the batch-mode option described in this paper depends upon mass-transport processes to establish the reaction layer. As with other mass-transport limited methods, anything that influences mass-transport processes can potentially affect results. In summary, the steady-state option is favored for situations in which speed and simplicity have highest priority and the pseudo-equilibrium option is favored for situations in which extended linear ranges and high degrees of ruggedness to changes in experimental variables have highest priority. References [1] J. Janata, J. Josowicz, P. Vanysek, D.M. DeVanex, Anal. Chem. 70 (1998) 179R. [2] M.D. Love, H.L. Pardue, Anal. Chim. Acta 299 (1994) 195. [3] P.D. Wentzell, S.R. Crouch, Anal. Chem. 58 (1986) 2851. [4] S.A. Engh, F.J. Holler, Anal. Chem. 60 (1988) 545. [5] G.E. Meiling, H.L. Pardue, Anal. Chem. 50 (1978) 1611. [6] R.C. Harris, E. Hultman, Clin. Chem. 29 (1983) 2079. [7] C.E. Uhegbu, K.B. Lim, H.L. Pardue, Anal. Chem. 65 (1993) 2443.
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[8] W. Chen, H.L. Pardue, S. Williams, Anal. Chim. Acta, in press. [9] B.A. Gregg, A.J. Heller, Anal. Chem. 62 (1990) 258. [10] P.N. Barlett, P. Derek, J. Zeng, J. Electrochem. Soc. 144 (1997) 3705.
[11] E.W. Paul, A.J. Ricco, M.S. Wrighton, J. Phys. Chem. 89 (1985) 1441. [12] J.W. Skoug, W.E. Weiser, I. Cyliax, H.L. Pardue, Trends Anal. Chem. 5 (1986) 32. [13] K.B. Lim, H.L. Pardue, Clin. Chem. 39 (1993) 1850.
Pseudo-equilibrium approach to the design and use of enzyme-based amperometric biosensors evaluated using a sensor for hydrogen peroxide Weibin Chen, Harry L. Pardue ∗ Department of Chemistry, 1393 BRWN Bldg., Purdue University, West Lafayette, IN 47907-1393, USA Received 9 April 1999; received in revised form 21 July 1999; accepted 23 July 1999
Abstract This paper describes a pseudo-equilibrium approach to the measurement and data-processing steps in the use of enzyme-based amperometric biosensors for substrates. The goal of the method is to obtain the response corresponding to reaction of all substrate in a fixed volume of solution with the expectation that this will improve the linear range and ruggedness relative to the conventional steady-state option. The biosensor is used in a rotating disk mode such that data for current versus time can be monitored with and without rotation of the sensor. With the sensor rotating at moderately high speed, current is monitored until an initial steady-state response is obtained after which the rotation is stopped and current is monitored until a second steady-state response is obtained. Under controlled conditions, the transition form the first to the second steady-state condition corresponds to reaction of virtually all of the substrate in a small fixed volume of solution controlled by the dimensions of the diffusion layer. Integration of current as a function of time yields the charge corresponding to reaction of substrate in the fixed volume established by the diffusion process. Evaluation of this pseudo-equilibrium option using a peroxidase-based sensor for hydrogen peroxide yielded a linear range extending to at least four times the Michaelis constant and a pH dependence approximately 40-fold less than steady-state currents obtained from the same data sets. ©2000 Elsevier Science B.V. All rights reserved. Keywords: Pseudo-equilibrium approach; Biosensors
1. Introduction Research in a variety of laboratories in recent years has resulted in the development of enzyme-based amperometric biosensors for a variety of substrates [1]. Most applications of these biosensors are based on steady-state responses. Advantages of the steady-state approach include simplicity and, in most cases, speed. Disadvantages include reduced sensitivity as ∗ Corresponding author. Tel.: +1-765-494-5320; fax: +1-765-496-1200. E-mail address: [email protected] (H.L. Pardue).
the substrate concentration approaches and exceeds Michaelis constants and large dependencies on experimental variables such as temperature, pH, activators, inhibitors and time-dependent changes in enzyme activity. The limited linear ranges and large dependencies on experimental variables result from the fact that steady-state responses result from balances between two or more competing rate processes such as rates of chemical reactions and mass transport processes. When chemical reaction is one of the limiting processes, the steady-state response is analogous to an initial rate in homogeneous solution methods. As
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such, calibration plots tend to curve toward the concentration axis as expected from Michaelis–Menten behavior and steady-state responses depend not only on substrate concentration but also on variables that affect the activity of the immobilized enzyme. On the one hand, research in several laboratories has shown that alternative measurement/data-processing methods can be used to reduce or eliminate these problems in connection with kinetic-based methods in homogeneous solution [2–6]. On the other hand, limited attention has been focused on similar problems associated with enzyme-based biosensors. One approach to improving the linear range and ruggedness of enzyme-based amperometric biosensors has been to use these devices in a pseudo-equilibrium mode [7,8]. In this mode, experiments are designed to permit the measurement of signals corresponding to reaction of all the substrate in a small fixed volume of solution. The resulting equilibrium-based results exhibit linear calibration plots for substrate concentrations exceeding Michaelis constants by factors of at least five fold and have much smaller dependencies on experimental variables than results based on steady-state responses. Initial implementations of this pseudo-equilibrium option have involved the incorporation of the biosensor into a thin-layer flow cell [7,8]. Although the thin-layer flow cell permits the measurement of responses corresponding to reaction of all the substrate in the thin layer of solution in close proximity to the reactor–sensor surface, the approach is inconvenient and slow. The present study was undertaken in an attempt to improve the simplicity and speed of the pseudo-equilibrium option. Briefly stated, the aim of this study was to determine if diffusion could be exploited to produce the thin layer of solution in which substrate concentration would be depleted during the measurement process. The enzyme was immobilized on the surface of an electrode mounted on a shaft that could be rotated at high speed and then stopped abruptly. Rotation at the desired speed was begun, polarizing voltage was applied to the rotating electrode and current was monitored until a first steady-state response was obtained [9]. Then the rotation was stopped abruptly and the electrolysis current was measured as a function of time until a second steady-state response was obtained.
Current versus time data during the period from the time when rotation was stopped until the second steady-state response was obtained was used to implement the pseudo-equilibrium option. The principal question we were attempting to answer is whether the thickness of the diffusion layer which developed after the flow was stopped would be sufficiently reproducible to permit quantitation of substrate in the same manner as used with the thin-layer flow cell [7,8]. If the diffusion layer is reproducible among different samples, then it should be possible to use current versus time data to obtain the charge corresponding to reaction of substrate in the fixed volume of solution represented by the dimensions of the diffusion layer. Substrate concentrations computed using this charge should vary linearly with concentration over ranges exceeding the Michaelis constant and should be virtually independent of variables that affect enzyme activity and reaction rates at the reactor/sensor surface. Results reported below for a model sensor system support these expectations.
2. Model sensor system An enzyme-based sensor for hydrogen peroxide was used as a model for this study. The sensor is similar to that described by Bartlett et al. [10]. In this system, glassy carbon coated with polyaniline is used as a substrate for the adsorption of horseradish peroxidase (HRP). The adsorbed HRP is then immobilized with a layer of poly(1,2-diaminobenzene). Hydrogen peroxide reacts at the electrode surface to produce water and the oxidized form of HRP represented as Compound I in Reaction 1. HRP(Fe3+ ) + H2 O2 → Compound I + H2 O
(1)
The oxidized form of HRP is then reduced electrochemically via electron exchange through the polyaniline as shown in Reaction 2. Compound I + 2H+ + 2e → HRP(Fe3+ )
(2)
The net result is reduction of hydrogen peroxide accompanied by the production of an equivalent amount of electrical charge and regeneration of the reduced form of HRP. This process continues as long as hydrogen peroxide is in contact with the reactor/sensor system.
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3. Mathematical description A mathematical description of the system has been described in detail elsewhere [7]; accordingly, it will suffice to review essential equations here. Given that the first steady-state current is obtained with high-speed stirring, it is expected that the first steady-state current will be limited primarily by the rate of chemical reaction. Assuming Michaelis–Menten behavior for the reaction, the first steady-state current, iss , is expected to depend on concentration as follows Iss Cb (3) iss = 0 K m + Cb in which Cb is the bulk substrate concentration, K 0 m is the apparent Michaelis constant and Iss is the maximum current obtained when Cb K 0 m . This steady-state current which is the most frequently measured response is expected to vary nonlinearly with concentration. We have not attempted to model the early part of the transient behavior after the stirring is stopped. However, after the substrate concentration at the reactor–sensor surface falls below the apparent Michaelis constant, the current versus time response can be described as follows i(t) = k0 Cb + k1 Cb exp(−k3 t)
(4)
in which k0 , k1 and k3 are complex combinations of reaction and mass-transport rate constants. An important feature of this equation is that the current is expected to be characterized by mixed zero- and first-order behavior. Another important feature of the equation is that the second steady-state current which occurs when k3 → ∞ is expected to vary linearly with concentration resulting from the fact that it is a diffusion-controlled current. As noted earlier, we are primarily interested in the electrical charge resulting from reaction after rotation is stopped. The time-dependent charge is obtained by integrating Eq. (4) with respect to time. The result is Q(t) = k0 Cb t + k2 Cb [1 − exp(−k3 t)]
(5)
in which k0 and k3 are as described above and k2 = k1 /k3 . According to Eq. (5), the charge versus time response consists of simultaneous zero-order/first-order
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processes. The zero-order component represents diffusion of substrate from the bulk solution; the first-order component is expected to represent substrate in the small volume represented by the diffusion layer. It is this latter component that is of primary interest in this study. The maximum value of the first-order component, Q∞ , is to be used to quantify the hydrogen peroxide concentrations. As will be shown later, there are at least three different ways to extract the desired first-order component from the zero-order component. 4. Experimental 4.1. Regents and solutions All chemicals were used as received. Reagents used included horseradish peroxidase (E.C. 1.11.1.7, Type VI, 260 u mg−1 , Sigma, St. Louis, MO 63178), Aniline (99.5+%, Aldrich., Milwaukee, WI 53233), 1,4-diaminobenzene (99+%, Aldrich) and 1,2-diaminobenzene (99+%, Aldrich, Milwaukee, WI 53201). All solutions were prepared in doubly distilled water. A pH 5 citrate/phosphate buffer solution (McIlvane) was prepared by mixing appropriate volumes of 0.1 M citric acid solution and 0.2 M sodium phosphate (Na2 HPO4 ) solution. A 3% solution of hydrogen peroxide (Mallinckrodt Specialty Chemical, Paris, KY) was used to prepare 10 mmol l−1 stock solutions in citrate/phosphate buffer. All the stock solutions were prepared daily. 4.2. Rotating disk electrode system A high speed rotator with fast start/stop characteristics (Model AFM SRX, Pine Instruments, Grove City, PA 16127), and speed controller (Model MSRX, Pine Instruments) were used to control the rotating disk electrode. Horseradish peroxidase was immobilized on 5 mm diameter glassy-carbon rotating disk electrodes (Models AFMDI 1980 GC and AC011420, Pine Instruments) as described in the next section. 4.3. Preparation of the sensor Polyaniline and HRP were immobilized on a glassycarbon disk electrode (5 mm diameter) as described
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below. First, a polyaniline film was deposited on the surface of polished glassy carbon electrode according to the procedure published previously [10]. The resulting film was rinsed thoroughly with the pH 5 citrate/phosphate buffer. Then HRP was adsorbed onto the polyaniline-coated glassy carbon electrode by rotating the electrode at 60 rpm for 300 s in a citrate/phosphate buffer solution containing 1 mg ml−1 horseradish peroxidase, 5 mmol l−1 1,2-diaminobenzene and 0.5 mol l−1 sodium sulfate. Then a poly(1,2-diaminobenzene) coating was deposited on the surface by applying a potential of +300 mV versus a silver/silver chloride reference electrode for 240 s. The resulting biosensor was then again washed thoroughly with pH 5 citrate/phosphate buffer solution and was finally rotated for 5 min at 1000 rpm in a pH 5 citrate/phosphate buffer to remove weakly immobilized or physically entrapped HRP. The thickness of the resulting films was estimated to be approximately 12 m [11]. 4.4. Data acquisition Time-dependent currents were monitored with a commercially available voltammetric system (CV-50 W Voltammetric Analyzer, Bioanalytical Systems, West Lafayette, IN 47906) which was interfaced to a laboratory computer (Gateway 2000 4DX2-50V, 610 Gateway Drive, North Sioux City, SD 57049) using electrochemistry software (BAS WindowsTM ). 4.5. Procedure All reactions took place in citrate/phosphate buffer in a water-jacketed cell used for temperature control. Temperature was controlled at 23.0 ± 0.1◦ C for all studies reported below. The biosensor was polarized at +90 mV versus Ag/AgCl reference electrode (Bioanalytical Systems) with a platinum wire serving as the auxiliary electrode. Typically, a 50 ml aliquot of sample containing hydrogen peroxide in buffer was added to the sample cell and the working electrode was rotated for 3 min in the sample solution after which a potential of +90 mV (versus Ag/AgCl) was applied to the electrode. Current was monitored for 150 s which was sufficient time for a first steady-state response to be obtained at which point the rotator was stopped and the response was
monitored for an additional 350 s which was sufficient time for a second steady-state response to be obtained. Data were processed using custom designed curve-fitting software described elsewhere [12].
5. Results and discussion Unless stated otherwise, imprecisions are reported at level of one standard deviation (±1SD) throughout this paper. 5.1. Rotation rate As implied by Eq. (3), a goal was to have the first steady-state response controlled primarily by reaction kinetics. To this end, a rotation rate was chosen above which the steady-state current was independent of rotation rate. Preliminary studies of rotation rates up to 1800 rpm using a 0.5 mmol l−1 solution showed that the first steady-state current increased for rotation rates up to about 500 rpm and were independent of rotation rate above this value. Accordingly, a rotation rate of 500 rpm was used for all studies reported below. 5.2. Current response curves Experiments were performed with 0, 0.02, 0.04, 0.1, 0.2, 0.5, 0.76, 1.09, 1.68 and 2.86 mmol l−1 hydrogen peroxide. Fig. 1 includes typical response curves for hydrogen peroxide from 0 to 2.86 mmol l−1 . In all cases, the potential was applied at t = 0, and the rotator was stopped at t = 150 s. The first decrease in current for each concentration corresponds to the establishment of the first steady-state response. The second abrupt decrease in current at 150 s corresponds to the point at which rotation was stopped. Responses for all concentrations decrease to a finite, non-zero background current after about 350 s. At this point, substrate is reacting immediately reaches the reactor/sensor surface, resulting in a diffusion-limited current. As expected from Eq. (5), the amplitudes of these diffusion-limited currents increase with the increasing of hydrogen peroxide concentrations. It was found that the initial decrease in current prior to the first steady-state signal conformed reasonably well to first-order behavior. Plots of ln(i − iss ) versus
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Fig. 1. Experimental response curves for several hydrogen peroxide concentrations. Conditions: pH = 5; T = 23.0◦ C; Stirring rate = 500 rpm; hydrogen peroxide (bottom to top) = 0, 0.04, 0.1, 0.2, 0.5, 0.76, 1.09, 1.68, 2.86 mmol l−1 .
t were linear throughout the concentration range studied. A mean value of 0.19 s−1 was obtained for the rate constant for the initial current decay, corresponding to a half-life of 3.6 s. Accordingly, the 150 s rotation period corresponds to approximately 40 half-lives of the first decay process ensuring that the process was complete before the rotation was stopped. Similarly, the latter parts of the decay curves after rotation was stopped were fit reasonably well by a first-order model. The mean value of the first-order rate constant was k3 = 1.9 × 10−2 s−1 corresponding to a half-life of the decay process is 37 s. Accordingly, the data collection time of 350 s after the rotation was stopped corresponds to 9.4 half-lives during which the exponential decay would be about 99% complete. Therefore, it is expected that the exponential term in Eq. (4) should be negligible and that the background current, I0 , should vary linearly with substrate concentration. 5.3. Current versus concentration relationships As noted earlier, the first steady-state current should vary nonlinearly with concentration (Eq. (3)) and the
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Fig. 2. Calibration plot for steady-state current (a) and charge (b) vs. hydrogen peroxide concentration. Both plots: Triplicate runs at each concentration. (a) Steady-state currents ( ) are averages for last 30 data points during the first steady-state region. Solid line is a fit of Eq. (3) to data. (b) Maximum charge, Q∞ , obtained as first-order component of fit of Eq. (5) to data in Fig. 3.
second steady-state current should vary linearly with concentration (Eq. (4) with t → ∞). Fig. 2 includes a plot of the first steady-state current versus concentration. As expected, the sensitivity for the first steady-state current (Plot a) decreases continuously with concentration. The solid curve is a fit of Eq. (3) to the data supporting the expectation that the steady-state currents conform to Michaelis–Menten kinetics. Fitting parameters were Iss = 0.113 ± 0.007 mA and K 0 m = 0.75 ± 0.16 mmol l−1 . In contrast to the steady-state response before the rotation is stopped, a plot of steady-state response after the rotation is stopped versus concentration is linear. Least-squares parameters for a fit of a linear model to the data correspond to CH2 O2 i0 = 2.382 ± 0.208 A + (8.53 ± 0.18 A) (mmol l−1 ) with a standard error of the estimate (syx ) of 0.52 A and a correlation coefficient (r) of 0.998 for the full concentration range studied (0–2.86 mmol l−1 ). These results support the expected behavior of the measurement approach.
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5.4. Charge versus time relationships According to Eq. (5), data for charge versus time for the decay period after rotation is stopped should follow combined zero-order/first-order behavior. Fig. 3 includes one set of data for charge versus time for each of the concentrations studied. It should be noted that zero time on this plot has been shifted to the time at which rotation was stopped. Points represent experimental data and solid curves represent fits of Eq. (5) to the data. It is observed that Eq. (5) fits all the data quite well, again supporting the expected behavior. As an alternative processing option, the mean value of the second steady-state current was subtracted from each data point along each current versus time response prior to integrating the data. Integration of the background-subtracted data yielded responses for charge versus time for which the fits of a first-order model were at least as good as the fits in Fig. 3.
Fig. 3. Charge vs. time response for different hydrogen peroxide concentrations. Conditions as in Fig. 1. t = 0 is the point at which rotator was stopped. Experimental data ( ); Fitted data, Eq. (5) (—).
5.5. Charge versus concentration relationships The total charge, Q∞ , corresponding to the first-order component of the decay process after the rotation is stopped is expected to vary linearly with concentration (Eq. (5)). Both the curve-fitting process illustrated in Fig. 3 and the background-subtraction approach described above were used to isolate the first-order component of the charge from the zero-order component as described earlier [7,8]. In each case, the determined value of charge varied linearly with concentration. Results obtained using the curve-fitting option are included in Fig. 2. The solid plot is a fit of a linear model to the data. Least-squares parameters for the fit correspond to Q∞ = 0.07 ± 0.02 mC + (1.24 ± 0.02 mC) × CH2 O2 (mmol l−1 ) with a standard error of the estimate of 0.05 mC and a correlation coefficient of 0.999. Similar results were obtained using background-subtracted data as described above. Whereas the sensitivity of the steady-state option changes continuously with concentration, the sensitivity of the charge versus concentration data is constant throughout the range examined which exceeds the apparent Michaelis constant
(K 0 m = 0.75 ± 0.16 mmol l−1 ) by approximately four fold. The important point here is not so much the extension of the linear range but rather the combined effects of the sensitivity and the measurement uncertainty on the determination error at high concentrations. For example, the combined effects of sensitivity and error bars near 3 mmol l−1 correspond to concentration errors of about 0.7 mmol l−1 for the steady-state option and about 0.13 mmol l−1 for the pseudo-equilibrium option. In other words, the pseudo-equilibrium option yields at least a five-fold reduction in concentration error at 3 mmol l−1 . 5.6. pH effects A major objective of this study was to determine if the proposed approach could be used to reduce effects of experimental variables relative to the steady-state option. One variable, pH values, was used to compare the ruggedness of the steady-state and pseudo-equilibrium options. To quantitatively compare the effects of changes in these variables on the
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and temperature. Regardless of the direction in which temperature was changed, the first steady-state current tended to decrease with successive experiments. While we are unable to explain this behavior, the net result is that it is not possible to compensate for temperature changes using this reactor/sensor combination.
6. Conclusions
Fig. 4. Effects of pH on steady-state current (a) and charge (b). Hydrogen peroxide concentration, 0.5 mmol l−1 ; ordinates are ratios of current or charge at each pH to values (55.36 A and 0.840 mC) at pH 4.5.
results, the relative error coefficients (RECs) concept was adapted from a previous publication [13]. Effects of pH on the two options for a fixed concentration of hydrogen peroxide are illustrated in Fig. 4. It is apparent that the pseudo-equilibrium option is much more rugged to changes in pH than is the steady-state option. Differences that are visualized from these plots can be quantified using relative error coefficients (RECs) computed from the slopes of these plots [13]. Numerical values of the relative error coefficients for the steady-state and pseudo-equilibrium options at pH = 4.5 are 0.22 and 0.0049%/pH unit, respectively. This corresponds to a 45-fold improvement in the ruggedness to changes in pH for the pseudo-equilibrium option relative to the steady-state option. 5.7. Temperature effects Effects of temperature in the range from 20◦ C to 36◦ C on steady-state currents and charge were studied using a 0.5 mmol l−1 hydrogen peroxide solution at pH 5. A positive correlation with temperature was expected for both steady-state currents. Whereas the second steady-state exhibited the expected positive correlation with temperature, there was no consistent correlation between values of the first steady-state current
The pseudo-equilibrium approach to the use of enzyme-based biosensors has two important advantages relative to steady-state methods. It maintains constant sensitivity over much wider concentration ranges and it is more rugged to changes in a variety of experimental variables. The principal disadvantages of the pseudo-equilibrium option as implemented to date are the more involved experimental procedures and the longer measurement times. The batch mode implementation as described in the present paper is simpler than the thin-layer stopped-flow approach described earlier [7,8] but still requires longer measurement times than the steady-state option and has one potential limitation relative to the thin-layer stopped-flow option. Whereas the thin-layer stopped-flow option has a fixed reaction layer, the batch-mode option described in this paper depends upon mass-transport processes to establish the reaction layer. As with other mass-transport limited methods, anything that influences mass-transport processes can potentially affect results. In summary, the steady-state option is favored for situations in which speed and simplicity have highest priority and the pseudo-equilibrium option is favored for situations in which extended linear ranges and high degrees of ruggedness to changes in experimental variables have highest priority. References [1] J. Janata, J. Josowicz, P. Vanysek, D.M. DeVanex, Anal. Chem. 70 (1998) 179R. [2] M.D. Love, H.L. Pardue, Anal. Chim. Acta 299 (1994) 195. [3] P.D. Wentzell, S.R. Crouch, Anal. Chem. 58 (1986) 2851. [4] S.A. Engh, F.J. Holler, Anal. Chem. 60 (1988) 545. [5] G.E. Meiling, H.L. Pardue, Anal. Chem. 50 (1978) 1611. [6] R.C. Harris, E. Hultman, Clin. Chem. 29 (1983) 2079. [7] C.E. Uhegbu, K.B. Lim, H.L. Pardue, Anal. Chem. 65 (1993) 2443.
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[11] E.W. Paul, A.J. Ricco, M.S. Wrighton, J. Phys. Chem. 89 (1985) 1441. [12] J.W. Skoug, W.E. Weiser, I. Cyliax, H.L. Pardue, Trends Anal. Chem. 5 (1986) 32. [13] K.B. Lim, H.L. Pardue, Clin. Chem. 39 (1993) 1850.