Catalytic and Inhibitory Kinetic Behavior of Horseradish Peroxidase on the Electrode Surface

Enzymatic biosensors are often used to detect trace levels of some specific substance. An alternative methodology is applied for enzymatic assays, in which the electrocatalytic kinetic behavior of enzymes is monitored by measuring the faradaic current for a variety of substrate and inhibitor concentrations. Here we examine a steady-state and pre-steady-state reduction of H2O2 on the horseradish peroxidase electrode. The results indicate the substrate-concentration dependence of the steady-state current strictly obeys Michaelis-Menten kinetics rules; in other cases there is ambiguity, whereby he inhibitor-concentration dependence of the steady-state current has a discontinuity under moderate concentration conditions. For pre-steady-state phases, both catalysis and inhibition show an abrupt change of the output current. These anomalous phenomena are universal and there might be an underlying biochemical or electrochemical rationale.


Introduction
Enzymatic electrodes are not only used to detect trace levels of specific substances, but also used to assay enzyme activities. Peroxidases participate in numerous physiological processes, such as cell wall synthesis, plant defence and activation of oxygen. Horseradish peroxidase (HRP) is a representative peroxidase; the mechanisms of peroxidase-catalyzed reactions have been widely studied using HRP, especially in understanding the biological behavior of the catalyzed oxidation of analytes by H 2 O 2 [1−4]. Many H 2 O 2 biosensors have been constructed using HRP due to its ready availability in high purity and OPEN ACCESS low cost [5−7]. The amperometric biosensors with various enzymes are very useful for the determination of analytes with a very low concentration [8−15]. Enzymatic sensors based on electrochemical reduction of H 2 O 2 [16−18] and oxidation of NADH [19−21] are now available for clinical and environmental detection of glucose, pyruvate, hypoxanthine, alcohol and formaldehyde.
The use of the rotating disk electrode for the study of an electrochemical mechanism was derived by Levich [22]. The output currents obtained are elucidated using the Koutecky-Levich formalism and the ping-pong kinetic scheme for peroxidase [23−25]. In recent years, a large body of research has focused on the mathematical modeling of enzymatic biosensors. Baronas and coworkers [26,27] presented a two-dimensional-in-space mathematical model of amperometric biosensors. They developed later a model based on non-stationary diffusion equations containing a non-linear term related to the Michaelis-Menten kinetics of amperometric enzyme electrodes [28]. Subsequently, they also provided another model of the biosensor based on the mixed enzyme kinetics and diffusion limitations in the case of substrate inhibition [29], the system of non-linear reaction-diffusion equations [30], and the synergistic substrate determination [31]. Andreu and coworkers [32] formulated analytical expressions describing the voltammetric response of a reagentless mediated enzyme electrode operated under rotating disk conditions. Patre and Sangam [33] built a model based on a diffusion mechanism related to Michaelis-Menten kinetics, which can be used in a membrane of the biosensor. Loghambal and Rajendran [34] worked out a steady-state non-linear reaction/diffusion equation. They also developed a mathematical model of amperometric and potentiometric biosensor [35]. Recently, Garay and coworkers [36] presented a comprehensive numerical treatment of the diffusion and reactions within a sandwich-type amperometric biosensor.
In our work, the electrochemical behavior of HRP enzyme activity is reexamined using H 2 O 2 reduction on the electrode. This enzymatic biosensor is optimized for the detection of HRP activity, including the catalytic and inhibitory kinetic behaviors in steady-state and pre-steady-state phases. Actually, only enzymatic activity during steady state follows the Michaelis-Menten formalism, and anomalous behaviors could be observed in all other kinetic processes, suggesting that there might be an unknown mechanism for the regulation of mass transfer or/and kinetic rate.

Electrode Modification
Prior to modification, the glassy carbon electrode surface was polished with 0.05 mm alumina paste on a micro-cloth and subsequently ultrasonically cleaned thoroughly with acetone, NaOH (1:1), HNO 3 (1:1), and doubly distilled water and then dried at room temperature. A mixed solution of 2.0 U/mL HRP and 0.5% (w/w) BSA was prepared by dissolving HRP and BSA in 0.2 mL PBS (50 mM, pH 7.0). A volume of 3 mL of the mixed solution was then added dropwise on the surface of the glassy carbon electrode. The surface area of the electrode is 0.28 cm 2 . The HRP/BSA electrode was cross-linked by placing the electrode in a closed vessel contained 25% glutaraldehyde and water vapor for 20 min and dried at room temperature for 1 h and stored at 4 °C until use.

Apparatus
Cyclic voltammetry and amperometric experiments were performed with a LabChem 10M electrochemical workstation (Tianjin, China) and a conventional three-electrode system. The modified glassy carbon electrode served as working electrode, a platinum wire as counter electrode, and a saturated calomel electrode (SCE) as reference electrode. A 0.10 M pH 7.0 phosphate buffer solution (PBS) was used as supporting electrolyte. A magnetic stirrer (approximately 400 rpm) was employed during the amperometric measurements. All experiments were carried out at room temperature.

Cyclic Voltammetry Test
The electrochemical properties of the electrode modified were characterized by cyclic voltammetry. Electrochemical experiments were performed in a conventional electrochemical cell containing a three electrode arrangement and the potential swept from −0.4 to 0.2 V (vs. SCE) at a sweeping rate of 0.1 V/s. The cyclic voltammetry experiment was performed in 5 mL pH 7.0 PBS. All experiments were conducted at 25 °C.

Amperometric Assay
Electrochemical experiments were undertaken in the electrochemical cell containing 25 mL of the supporting electrolyte. Amperometric measurements were carried out in a stirred solution (approx. 400 rpm). The electrodes were immersed into a stirred phosphate buffer solution (pH 6.5) containing 1.0 mM hydroquinone as the electron mediator and an initial baseline current was recorded. 0.1 mM H 2 O 2 solution was added to get an increased steady-state current record. Subsequently, solution of increasing phenylhydrazine concentration was added with a micropipette in succession and the current decrease was recorded. All experiments were conducted at 25 °C.

Correlation Analysis
Pearson correlation was a measurement of the strength and direction of a linear relationship between two groups of data. Statistical significance is determined for a p-value <0.05 for all tests. Strong correlation is determined for an absolute r value >0.7; weak correlation > 0.5. The bi-variate correlation analysis was carried out by the R statistical package (version 2.13.0; http://www.r-project.org/) [37]. The linear r version 1.1

The Mo
The al te Suppose that a steady-state current (i ∞ ) is the current when the biosensor system approaches to equilibrium as t → ∞: (4) where i(t) is the current at time t. In practice, the current at the response time t R is assumed as i ∞ . t R is defined as the time when the absolute current slope falls below a given small value (ε < 0.0001) [27], i.e., A reduction current (i ∞ ) observed on electrode is a combination of the mass transport-limited current (i ∞,L ) and the reaction-rate-limited current (i ∞,K ) [40], accords with the Koutecky-Levich equation, i.e., where n is the number of electrons transferred to the enzyme in one catalytic cycle (n = 2). F is the Faraday constant. A is the area of the electrode surface. D is the diffusion coefficient of H 2 O 2 . ν is the kinematic viscosity of water. For a given biosensor that is rotating at a constant angular velocity, i ∞,L is proportional to [H 2 O 2 ], Equation (7) reduces to: where a 1 is constant (a 1 = 0.62nFAD 2/3 ν −1/6 ω 1/2 ).
When the transport of H 2 O 2 is high enough to keep its concentration at the electrode surface equal to that in the bulk solution, the reaction-rate-limited current i ∞,K is governed by the ping-pong kinetic scheme, being expressed by [24,39]: (9) Where Γ is the surface concentration of HRP enzyme. [QH 2 ] is the concentration of hydroquinone.
[ I ] is the concentration of phenylhydrazine inhibitor. Assuming that a 2 = 1/nFAΓk 1 , b = 1/nFAΓk I , and c 1 = (k 2 + k 3 )/(nFAΓk 2 k 3 [QH 2 ])+1/nFAΓ, Equation (9) can be also reduced to: Substituting Equations (8) and (10) into Equation (6), the Koutecky-Levich equation can be reduced to: (11) where a 3 = a 2 + 1/a 1 . in 3) f a en ed Figure 1(a) depicts the cyclic voltammetry curves of the proposed biosensor in the presence and absence of H 2 O 2 . A redox couple is observed in the absence of H 2 O 2 . However, an enhancement of the peak current is observed in the presence of H 2 O 2 . On the other hand, it has been reported that phenylhydrazine is able to inhibit or abrogate HRP activity by competing with the normal hydroquinone [42,43]. The inhibition effect of phenylhydrazine is measured by using the proposed biosensor.
Upon The steep increased (or decreased) in magnitude of the current is observed when H 2 O 2 (or phenylhydrazine) is added into the electrolyte solution, and then the current returns to equilibrium (steady state i ∞ ) following an exponential decay with a certain recovery speed (relaxation time τ). The values of i ∞ and τ are best computed by non-linear regression of data fitted to Equation (2). These values at different substrate concentration are listed in Table S1 (Appendix); they at different inhibitor concentration in Table S2 (Appendix).

Electrochemical Enzyme Assay
From Figure 2 In fact, our result shows the steady-state current follows the Michaelis-Menten kinetic model within a broader concentration range. Kinetic constants are determined by fitting the initial rate data to Lineweaver-Burk plot Figure 2(b). Thus, the current is regarded as a relative enzyme reaction rate. This methodology could monitor in real-time subtle changes in enzyme activity.
The pre-steady-state time course of the i → i ∞ process is fitted to Equation (3) for a single exponential decay, in which τ is the apparent relaxation time for output current (i.e., the reciprocal of the apparent first-order rate constant). It is found, however, that τ is not a simple function of the substrate concentration. As shown in Figure 3, τ is low in both the low-and high-concentration regions; a relatively larger τ occurs in at a moderate concentration ([H 2 O 2 ] = 0.8−1.4 mM). This suggests that, within this concentration range, the rate at which the equilibrium is approached is slowed down.
If the kinetic control becomes operative, there is a possible explanation: a "shoulder" appears on the curve of t 0.5 versus [H 2 O 2 ] in the two-dimensional-in-space biosensor model, as has been proposed in reference [27]. Where t 0.5 is the half time (t 0.5 = 0.693τ). Baronas et al. [27]  ]the kinetics undergoes a transition from zero order to first order. This phenomenon is also manifested in inhibition assays, so it is not obvious whether agreement between our data and the shoulder of t 0.5 is not a coincidence. Inhibition kinetics also experiences a transition from zero order to first order, but it is not proof.

Electrochemical Inhibition Assay
Phenylhydrazine can inhibit HRP activity [42,43]. In our biosensor, i ∞ decreased steadily as [ I ] is increased. However, the Lineweaver-Burk plot for the substrate dependence shows that the reaction does not follow Michaelis-Menten kinetics, as the curve connecting the experimental points is clearly curved Figure 4(a). However, there is a more simple linear relationship between i ∞ and [ I ]. The dependence of the rate of i ∞ change on [ I ] is illustrated in Figure 4  A similar phenomenon occurs in the relation between [ I ] and τ as well. In Figure 5, τ increases exponentially as the inhibitor concentration increases. However, in the concentration of 3−4 mM, the points determined experimentally is lower than τ value extrapolated from low concentration and thus the curve displays a drop. Figure 5. Effect of the concentration of phenylhydrazine inhibitor on the relaxation time during pre-steady-state phase. It increased exponentially with increase in concentration. A "depression" appears on the curve in the concentration of 3−4 mM.

Conclusions
We have examined the electrocatalytic behavior of enzymatic biosensors and possibilities for measuring the enzymatic activities. The substrate concentration-dependence of such a steady-state current is governed by the Michaelis-Menten equation under the condition of constant diffusion, suggesting that the output current reflects the relative rate of the enzyme reaction. For our datasets, we find that Michaelis-Menten model does not work well at high inhibitor concentrations and works better at low concentrations, and the enzymatic kinetics gives the best results in the absence of inhibitor. Deviations from this model cause observed sudden changes in the current occurring at intermediate concentrations of inhibitor or substrate. An auto-deceleration of the current occurs when the substrate reaches a specific concentration ([H 2 O 2 ] = 0.7 mM). In contrast, an auto-acceleration occurs when the inhibitor reaches another critical concentration ([ I ] = 3 mM).
Electrochemical enzyme assays provide an extremely sensitive measure but suffer from difficulties in interpretation of the data. At relatively higher concentrations of H 2 O 2 , the steady-state current follows the Michaelis-Menten equation (Figure 2) and the relaxation time is low (Figure 3). These indicate that no significant H 2 O 2 -induced suicide inactivation of HRP enzyme occurs in our experiment. The Levich equation and ping-pong kinetics emphasize that the current should be a monotonically increasing (or decreasing) function of the concentration of substrate (or inhibitor) either under diffusion limitations or under enzyme kinetics. However, peaks, discontinuities and sudden changes appear in Figures 3−5 and their definite mechanism is unknown yet. Also, it is not clear whether the same would be true for other enzymes. Electrochemical biosensors do not provide any microscopic information, and even assignment of the relaxation modes (whether it is the mode of a mass transfer or of a chemical reaction) is not obvious.