mathematical model for the luminol chemiluminescence reaction catalyzed by peroxidase

Mathematical Model for the Luminol Chemiluminescence Reaction Catalyzed by Peroxidase

Lin Li,' Mark A. Arnold,'* and Jonathan S. Dordick2 'Department of Chemistry, *Department of Chemical and Biochemical Engineering, University of Iowa, Iowa City, Iowa 52242

Received August 24, 1992/Accepted December 29,

A kinetic model that accurately describes intensity vs. time reaction profiles for the chemiluminescence reaction between luminol and hydrogen peroxide, as catalyzed by horseradish perioxdase, is derived and evaluated. A set of three differential equations is derived and solved to provide intensity time information for the first 200 seconds of the reaction. The model accurately predicts intensity-time profiles when literature values are used for al l but one of the reaction rate constants. Furthermore, the model predicts a nonlinear curve for plots of light intensity versus the initial hydrogen peroxide concentration. Experimental data confirm that such plots are nonlinear. Finally, a linear double-reciprocal plot is predicted by the model and the experimental data verify this relationship. 0 1993 John Wiley & Sons, Inc. Key words: luminol chemiluminescence - peroxidase hydrogen peroxide

INTRODUCTION

Chemiluminescence (CL) is a phenomenon that provides for rapid and sensitive analytical measurements. Light generated by biocatalytic approaches offers high selectivity in combination with reasonable quantum yields at near neutral pH levels. Peroxidases are known to catalyze light generation upon the oxidation of luminol in the presence of hydrogen peroxide. This is particularly useful in coupled reactions with oxidases to measure a wide variety of clinically, biomedically, and chemically important

The mechanism of CL catalyzed by horseradish peroxidase (HRP) has been studied extensively over the past two decades. The individual reaction steps and their kinetics that comprise the catalytic mechanism have been identified (see Scheme I) and fall into three distinct c a t e g ~ r i e s . ~ ~ , ' ~ Initially, luminol (LH2) is oxidized by the peroxidatic pathway of HRP to generate a luminol radical (LH.) (steps 1 through 3). This is followed by a series of nonenzymatic reactions involving luminol radical, oxygen, and H202 (steps 4 through 9). Finally, light generation occurs in step 10 involving an intermediate luminol peroxide adduct (L02H-) and this step is in competition with several unproductive non-light-generating termination reactions (steps 11 through 14). According to this mechanism, an excited

compounds. 1 7 2 7 5 7 11,13

* Author to whom all correspondence should be addressed.

1992

state 3-aminophthalate (3-AP) is the light emitting species that forms directly from LO*H-.

Because 3-AP can be generated by a number of different, and simultaneous reaction steps, the observed generation of light at a given temperature depends upon several system variables including the concentrations of enzyme, luminol, hydrogen peroxide, and oxygen, as well as the pH of the solution. The complexity of this reaction mechanism and its analytical potential motivate us to develop a mathematical model that describes the time-dependent generation of light as a function of system variables. Such a model may be expanded to include oxidase-catalyzed reactions, thereby providing a means to better understand and control these important analytical systems.

In this study, we present a kinetic model that describes the relationship between the CL intensity and concentrations of HRP, luminol, and hydrogen peroxide. Our ultimate objective is to develop an optical method for the continuous, in situ detection of analytes of physiological significance. The reaction conditions maintained in this work have been selected with such applications in mind. For example, the solution pH has been restricted to the physiological value of 7.5.

MATERIALS AND METHODS

Materials

Luminol, hydrogen peroxide (30%), HRP (type 11, E.C. 1.11.1.7, 220 units/mg, pH 6.0, 20°C) and superoxide dismutase (E.C. 1.15.1.1, 3250 units/mg, pH 7.8, 25°C) were obtained from Sigma Chemical Co. (St. Louis, MO). The water used for all solutions was type-I reagent grade obtained from a Milli-Q Reagent Water System (Millipore, Bedford, MA). Hydrogen peroxide solutions were standard- ized by titration with thio~ulfate.~

Instrumentation and Procedures

All CL measurements were made by using the detector op- tics of an SLM-Aminco SPF-5OOC spectrofluorometer. The emission monochromator was set to pass 430 nm radiation with a 10-nm bandpass. The photomultiplier (PMT) supply voltage was set at 1000 V.

Biotechnology and Bioengineering, Vol. 41, Pp. 1112-1120 (1993) 0 1993 John Wiley & Sons, Inc. CCC 0006-3592/93/01101112-~9

The HRP catalyzed CL reaction was carried out in the following manner. Initially, 2.20 mL of working buffer was added to a plastic disposable cuvette. The needed volumes of luminol and hydrogen peroxide were then added and the contents were shaken gently. The CL reaction was initiated by adding the required volume of a stock HRP solution. The mixture was quickly shaken and then the cuvette was placed in the sample compartment of the spectrometer. The shutter in front of the emission monochromator was opened and the light intensity was recorded as a function of time. Data collection started 15 seconds after HRP was added. All reactions were run with a 0.05 M phosphate, pH 7.5, working buffer. Nitrogen and oxygen saturated buffers were prepared by purging the working buffer for 10 minutes with the particular gas. Stock solutions of HRP, luminol, and hydrogen peroxide were prepared fresh before each experiment.

A proportionality constant was needed to correlate the calculated intensity in units of photons per second to the measured light intensity which was taken as the output current from the PMT detector in units of nanoamperes. This constant was obtained by dividing the measured output current by the corresponding predicted intensity for a single time point (100 s) along a particular intensity-time profile. The value for this constant was 5.56 X lo9 (nA - s/photon) and this value was used throughout for converting all predicted intensities to nanoampere units.

The rate constants summarized in Scheme 1 were ob-

RESULTS AND DISCUSSION

Simplification of the Reaction Mechanism

The overall luminol/HRP reaction mechanism, shown in Scheme I, can be simplified by removing reactions that are negligible under our experimental conditions. In this regard, steps involving oxygen and the formation of superoxide as

well as various nonluminescent side reactions have been considered. In addition, various rate constants have been adjusted according to the predominant species in solution at pH 7.5.

Lundin7 and Vlasenko12 have reported that the luminol/HRP reaction goes by either a superoxide or diazaquinone reaction pathway. In the superoxide pathway, the luminol-peroxide adduct is formed by a three-reaction process involving the formation of superoxide by a reaction between the luminol radical and molecular oxygen (steps 6 through 8). Alternatively, the luminol-peroxide adduct is formed by a reaction involving a diazaquinone species (L) with a second molecule of hydrogen peroxide. Several reactions lead to the formation of the diazaquinone species (steps 4, 5, and 9). Previous work has shown that the superoxide pathway is only considerable at low HRP concentrations (i.e., M ) . ~ ~

While testing for the relevance of the superoxide pathway, we found that the production of light is insensitive to oxygen levels and that the formation of superoxide could not be detected under our conditions. Light intensity versus time curves were essentially identical in solutions saturated with either nitrogen or oxygen (data not shown). In this experiment, the concentrations of luminol, hydrogen peroxide, and HRP were 0.156 mM, 0.625 mM, and 2.4 nM, respectively, and the reaction was monitored continuously for 200 seconds. Moreover, no differences in intensity-time profiles were detectable when superoxide dismutase was added to the solution (109 units/mL). This enzyme consumes superoxide, therefore, a decrease in intensity would be direct evidence of superoxide formation and the superoxide pathway.

Superoxide dismutase did not affect the amount of light detected at HRP levels of 2.4 and 24 nM when the concentrations of luminol and hydrogen peroxide were 0.125 mM and 0.31 pM, respectively. This low level of hydrogen peroxide was necessary to avoid hydrogen peroxide inhibition of superoxide dismutase.12 The insensitivity to oxygen and superoxide dismutase at HRP levels as low as 2.4 nM suggests that the diazaquinone pathway dominates

(1) H20,+ HRP (2) C, + LH- kzs8.0x10; Complex 11 + LH* (3) G+LH- ')='HRP+LH*

L* + H+ (4) LH*+LH*' iH L + L H ,

L + LH-

' L H + O , (7) LH- +O,c

J-(OzH-) + y 0 2 H - ) + H+

(9) L + HOi

(10) YO,H- ) Ls 3-AP + N, + b J I b 3 - A P + N z + H +

(12) L + OH k1z=4.0x1? Amino-2-Formylbenzoate + N, (13) L + H,O k11=0'45 P Amino-2-Formylbenzoate + N, + Hi (14) L + H202 k14=1.1x1f 3-AP + N, + H*

k1=1.8x10; Complex I (C,)

pffi-7.7 LH*

(') L' + L' H+ k&5x10;

+ k8=2.3x1Q

+ 02' (6) L' + '2 k,=,.lx10g

(8) L' + 0 2 * + H a YOZH' 1 pffi-10.4

L(O,H,) ' (11) YOZH,)

Scheme I

LI, ARNOLD, AND DORDICK PEROXIDASE-CATALYZED LUMINOL CHEMILUMINESCENCE 1113

under our experimental conditions which permits neglecting all reaction steps involving oxygen (steps 6 through 8).

The model was further simplified by neglecting the slowest unproductive non-light-generating termination reactions. The rate constants indicate that reaction step 12 is the fastest of these reactions. In fact, the rate constants for steps 13 and 14 are several orders of magnitude lower than for step 12. For this reason, reaction steps 13 and 14 have not been considered in this model.

Several pH-related modifications have been incorporated into the simplified reaction mechanism by considering a constant pH of 7.5. Reaction 5 has been eliminated in favor of reaction 4 because the protonated species is predominant at pH 7.5. In addition, an effective rate constant ( k i ) has been used where k i = k4 * (YHL. and (YHL. is the fraction of the total luminol radical concentration in the protonated form. The (YHL. term has been calculated by using a pKa value of 7.7 for the luminol radical.6 The rate constant for reaction step 9 has also been rewritten in terms of protonated hydrogen peroxide, and the corresponding rate constant has been adjusted by using a pKa of 11.5@

The resulting simplified reaction mechanism is summarized in Scheme 11. The first three steps correspond to the HRP catalyzed reaction to form the luminol radical by consuming 2 mol of luminol and one molecule of hydrogen peroxide. Formation of the diazaquinone species is followed by formation of the luminol-peroxide adduct which requires a second molecule of hydrogen peroxide. The adduct then breaks down to form either an excited 3-AP which rapidly undergoes radiative relaxation to produce a photon or a ground state 3-AP without generation of light. In addition, there is a second nonluminescent reaction that involves removal of the diazaquinone species by reacting with hydroxide.

2

(kh = k9 * (Ka/[H+I)).

Derivation of the Kinetic Model

The following set of differential equations results from the reaction sequence presented in Scheme 11:

-d[H2021 = kl[H202][HRP] + k;[L][H202] (2) dt

(3) dp hotons

dt = In = klo[LOzH-]

These equations can be rewritten as follows by applying a steady-state approximation for all reactions intermediates:

' (5)

where In corresponds to the light intensity which is directly proportional to the rate of photon production (d(hv)/dt) and Ka is the acid dissociation constant of L02H2. In- tensity- time profiles can be calculated for various initial concentrations of HRP, luminol, and hydrogen peroxide by solving Eqs. (4)-(6) simultaneously. Such calculations were made by using the IWAG subroutine of the IMSL software package (IMSL, Inc., Houston, TX). Details con- cerning the derivation of these equations are provided in the Appendix.

Accuracy of the Kinetic Model

The accuracy of our kinetic model has been judged by comparing predicted versus experimental intensity -time profiles. The rate constants used for each of these profiles were the literature values, except for kl2. The fits were improved considerably by slightly changing k12 from the literature value of 4.0 X lo6 to a new value of 1.0 X lo7. This discrepancy is likely caused by the different pH values used in the two experiments (4 X lo6 at pH 7.0 and 1.0 X lo7 at pH 7.5).

Predicted intensity-time profiles closely match the experimental results for all situations of changing HRP, hydrogen peroxide, and luminol concentrations. Figure 1 shows a set of profiles where the HRP concentrations are 72.7, 242, and 727 nM, while the hydrogen peroxide and luminol concentrations are held constant at 0.625 and 9 pM, respectively. Likewise, Figure 2 presents profiles where the concentration of hydrogen peroxide is varied from 0.156 to 1.250 mM, while the HRP and luminol levels are constant at 242 nil4 and 9 pM, respectively. Finally,

(I) H202+ HRP k1=1'8x'o; Complex I (C,) (11) c, + L H kz=8.0x10t Complex I1 (q) + LH* (111) q + L H H R P + L H * (IV) + LH. zli=a'*xlp L + LH, (V) L + HzOz kd=4'3x10; L(02H' ) + H+ (VI) L(0,H) '- 3-AP+N2+ hv

(VIII) L + OH- k12=4.0x10e Amino-2-Formylbenzoate + N,

Scheme 11.

(VII) L(O,H,) k11=1.5x10; 3-AP + N, + H+

1114 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 41, NO. 11, MAY 1993

4'00 c

0.80

320

5 2.40 II c 0 - 2 .p 1.60 v)

)I - A

-

C A A A.

, I I 80 120 160 m 0.00 L

0 40 Tirnekec)

Figure 1. of 9 p M and 0.625 mM, respectively. Points represent experimental observations and lines correspond to prediction.

Intensity-time plots for HRP concentrations of: (a) 727 nM; (b) 121 nM; and (c) 72.7 nM with luminol and hydrogen peroxide concentrations

profiles are shown in Figure 3 where the luminol levels vary from 3 to 9 ,uM, while the HRP and hydrogen peroxide concentrations are maintained at 242 mM and 0.625 mM, respectively. Figures 2 and 3 show that the maximum intensity decreases with lower hydrogen peroxide and luminol concentrations, and that the intensities decay in a similar fashion for each of these situations. Figure 1, however, shows that the morphology of the intensity-time profile changes dramatically as the HRP level is increased. At the highest HRP levels tested, the intensity decay is faster than at lower concentrations. As a result, the intensity-time curve for 727 nM HRP intersects the other two curves. Experimentally, these intersection points occur at 84 and

133 seconds. The model predicts this same type of change in the profile morphology with predicted intersection points at 93 and 145 seconds, which are reasonably close to the observed points.

Examination of the proposed simplified reaction scheme indicates that the result of peroxidase action is to produce the luminol radical, which subsequently recombines to give the diazaquinone in step IV. The diazaquinone species can react according to the constructive (with respect to light generation) step V or the destructive step VIII. With an initial hydrogen peroxide concentration of 0.625 mM and a pH of 7.5, the ratio of reaction velocities ( VV/VVIII =

k;[L] [HzOz]/k12[L] [OH-]) is 2.1. As the concentration

*'0° I 1.60 1

0.00 I I I 0 40 80 120 160 zoo

Time(sec1

Figure 2. and HRP concentrations of 9 pM and 242 nM, respectively. Points represent experimental observations and lines correspond to prediction.

Intensity-time plots for hydrogen peroxide concentrations of (a) 1.250 mM; (b) 0.625 mM; (c) 0.312 mM; and (d) 0.156 mM with luminol

LI, ARNOLD, AND DORDICK: PEROXIDASE-CATALYZED LUMINOL CHEMILUMINESCENCE 1115

0.00 , 0 40 80 120 160 200

Time(sec1

Figure 3. Intensity-time plots for luminol concentrations o f (a) 9 p M ; @) 6 pM; and (c) 3 pM with hydrogen peroxide and HRP concentrations of 0.625 mM and 242 nM, respectively. Points represent experimental observations and lines correspond to prediction.

of hydrogen peroxide decreases at later incubation times, this velocity ratio drops and the non-light-generating reaction becomes more significant. The intriguing dependence between intensity-time morphology and HRP concentration is consistent with the fate of species L in steps V and VIII. At higher enzyme levels, the rate of luminol oxidation increases and results in a larger concentration of luminol radical at early incubation times. This condition results in an increase in the generation of species L according to step V and, ultimately, more light by reaction step VI. At later incubation times, however, the reduced luminol concentration lowers the concentration of species L and results in

less light generation. Furthermore, lower concentrations of hydrogen peroxide decrease the VV/VVIII ratio and the light intensity drops even further as the nonproductive reaction predominates.

The quality of fit is evident in all these plots with the best fits obtained with changes in the HRP and hydrogen peroxide concentrations. The poorest fits were obtained at low luminol concentrations. Overall, the model provides good correlations over the first 200 seconds of the reaction for a wide variety of initial conditions. These results indicate the accuracy of the model and justifies the simplified reaction mechanism for our reaction conditions.

I I I 40 80 120 I 6 0 200 0

Time(sec)

figure 4. Sensitivity analysis for kl and kz (solid lines), k3 (dashed line), k$ (dash-dot line), and klz (dashed-dot-dot-dot line) with concentrations of HRP, luminol, and hydrogen peroxide set at 242 d, 9 pM and 0.625 nM, respectively.


I I I 1 09oM 0 40 80 120 100 200

Time(sec)

Figure 5. Predicted time profile curves for luminol (dash-dot line) and hydrogen peroxide (solid line) at HRP concentrations of (A) 72.7 nM; (B) 121 nM; and (C) 727 nM. The initial luminol and hydrogen peroxide concentrations are 9 p M and 0.625 mM. Note that the scales of both y-axes are the same.

This model is not able to predict the intensity-time curve at short times just after mixing the reagents. The inability to predict at short times is a result of the fact that the model does not contain terms to account for mixing or instrumental factors such as the time constant associated with the spectrometer. For this reason, all experimental measurements start 15 seconds after mixing, which permits equilibration in terms of reagent mixing.

In addition, predictions are not accurate at high lumi- no1 concentrations. When the luminol levels are above 0.02 mM, predicted light intensities are lower than experimentally observed values. The fact that the model under predicts the measured intensities implies that a reaction that favors light generation has not been included in the model. None of the reactions deleted from Scheme I would account for this behavior. A given intensity -time profile can be matched at any luminol concentration by adjusting the value for k12.

Model Predictions

The degree to which individual reaction steps influence light generation was studied by using sensitivity analysis. The steady-state expressions for light generation implicitly require values for k l , k2, k3, k i , k10, kll and k12 (see preceding section and Appendix). The sensitivity of the individual rate constants k l , k2, k3, k;, and k12 on light generation was measured systematically by increasing the literature value by one order of magnitude and comparing the resulting intensity-time profile to the baseline value. Luminol, H202, and enzyme concentrations were fixed at 0.125 mM, 0.625 mM, and 2.42 X M, respectively. The sensitivity of klo and kll was not evaluated explic-

itly because, according to Eq. (6), these constants should demonstrate the same sensitivity as ki and k l z , respectively.

The differences in intensity-time profiles for the afore- mentioned rate constants are shown in Figure 4. While changing kl and k2 has no effect on light generation, time-intensity curves are affected by the other three rate constants. The most significant reaction is the HRP-complex 11-catalyzed oxidation of luminol to the luminol radical (step 111 in Scheme 11). At early times, an increase in the rate constant of this reaction results in a dramatic increase in the intensity of generated light as previously described. At later times, however, the faster rate of radical production results in the faster decay of luminol in solution and the intensity drops lower than that expected with the baseline value of k3. Hence, a negative sensitivity effect is observed after approximately 40 seconds.

The dependence of light generation on reaction 111 as opposed to reactions I or I1 is consistent with peroxidase kinetics. Oxidation of a substrate via complex I1 is well-known to be the rate-determining step in peroxidatic reactions. Literature values for the individual rate constants in reactions I to I11 indicate that the reduction of complex I1 to the native enzyme is the rate-determining step in catalysis. Hence, this step must also be the most sensitive in initiating the light-generation pathway. The slight positive effect of kh is consistent with a direct correlation between reaction step V and light emission (step VI). Finally, the negative effect of k12 indicates that this reaction scavenges free L, which is required for reaction step V and, hence, light generation. Similarly, a positive effect from klo and a negative effect from kll are expected because reaction VI is a light generation step and reaction VII is the same reaction without light generation.

LI, ARNOLD, AND DORDICK: PEROXIDASE-CATALYZED LUMINOL CHEMILUMINESCENCE 1117

1.60 I I I I I

128

: OP6 E 0 lu c CI)

- 0.64

0.32

0.00 0.000 0250 0.500 0.750 1 .ooo 1250

Concentration of Hydrogen Peroxide (mM) Figure 6. Calibration plot for hydrogen peroxide showing predicted (solid line) and experimental (solid squares) intensity values measured 15 seconds after the reaction was initiated. Concentrations of HRP and luminol were 242 nM and 9 pM, respectively. Inset shows the corresponding double-reciprocal plot for these data.

The model can be used to predict the consumption of substrates as a function of time. Figure 5 shows the predicted consumption of luminol and hydrogen peroxide at three different HRP concentrations. As expected, higher enzyme levels result in faster consumption of these substrates. This figure also illustrates that the luminol is consumed faster than the hydrogen peroxide. A 1: 1 reaction stoichiometry is expected according to the light- generating reaction. The additional luminol consumption corresponds to a nonluminescent side reaction (reaction step VIII in Scheme 11) which consumes luminol but not hydrogen peroxide. The model predicts a luminol to hydrogen peroxide reaction stoichiometry of 1.4 : 1.

Our kinetic model predicts a nonlinear relationship between the measured light intensity and the initial concentration of hydrogen peroxide. The following expression can be derived considering Eqs. (4)-(6) (see Appendix for details):

- 1 In A[HRP], _ -

where A = K,klo(K,klo + kll[H+]). Eq. (7) reveals that the light intensity is not first order in hydrogen peroxide but that a double-reciprocal plot should be linear. The light intensity measured at 15 seconds is plotted in Figure 6 as a

function of the initial hydrogen peroxide concentration. As predicted, this plot is nonlinear. A double-reciprocal plot of these data (see Fig. 7, inset), however, shows the predicted linear relationship. Eq. (7) predicts a slope of 0.309 and a y-intercept of 0.416. Linear regression analysis of the double-reciprocal plot reveals a slope of 0.266 (+0.004), a y-intercept of 0.52 (-+0.03), and a correlation coefficient of 0.999.

Our model incorporates the most important system variables in the CL reaction catalyzed by HRP; namely, the concentrations of enzyme, hydrogen peroxide, and luminol. These variables result in a significant effect on light generation. The most common change employed in analytical measurements by using peroxidase is in the concentration of hydrogen peroxide. During coupled oxidation of analytes by a specific oxidase, the rate of hydrogen peroxide will depend on the rate of analyte oxidation by the oxidase. This, in turn, dictates the rate of 3-AP produced and the intensity of CL by the simplified reaction scheme presented in this work. The nonlinearity of light intensity with respect to hydrogen peroxide concentration indicates that the mechanism of light generation is complex and that the model can simplify in situ detection and quantification of analyte concentrations in coupled oxidaselperoxidase sensors.

We acknowledge the invaluable assistance provided by Professors Johna Leddy and Victor Rodgers. This work was supported by the Department of the Navy, Office of the Chief of Naval Research, under ONR Grant NOOO14-91-J-1768.


APPENDIX

The derivation of the final algebraic equations for light generation [Eqsl (4)-(6)] and Eq. (7) are described.

Derivation of Eqs. (4146)

The following equations can be obtained if the steady-state assumption is applied to reactions I through VII in Scheme 11:

- = dC1 kl[H202][HRP] - kzCl[LH-] = 0 dt

dCZ - = k2Cl[LH-] - k3CJLH-I = 0 dt

-- d[L1 - ki[LH.I2 - kh[L][H20~] - k12[L][OH-] = 0 dt

= kh[L][H202] - klo[L02H-] = 0 d[ LO2 H -1

dt

These equations can be rewritten as follows:

kl [ HzOJ [ HR PI = k2 C1[ L H -1 = k3 C2[ L H -1 = ki[LH.l2 (a)

ki[LH.]' kh[L][H202] + k1z[L][OH-] (b)

kh[LI CH202I = klo[LOzH-I (c) Based upon the model in Scheme 11, the total enzyme

concentration ([HRPIo) is described as the following equation:

[HRPIo = [HRP] + C1 + C2

where [HRP] is free enzyme concentration. C1 and C2 are the concentrations of Complex I and Complex 11. According to Eq. (a), CI = kl[H202][HRPl/k2[LH-] and CZ = kl[Hz02] [HRP]/k3[LH-]. Then, the equation above can be rewritten as:

From steps I through 111 and IV through V in Scheme 11, the following equations are derived:

-d[H20z1 = kl[H202][HRP] + kh[L][H2Oz] (2) dt

d[ Photon s] dt

= In = klo[LOzH-]

Based on Eq. (a), Eq. (1) can be rewritten as:

= 2Ri[HRP][H202]. -d[LH-]

dt

(3)

Replace [HRP] by Eq. (d). Then Eq. (1) is derived as the final term:

(4) -d[LH-] - - 2[HRPlOkik2k3[LH-I [H2021

dt (kik2 + kik3)[H2021 + kzk3[LH-] Combine Eq. (a) with (b), L can be solved as:

Replace L and [HRP] in Eq. (2) by Eqs. (e) and (d), respectively. Then the final equation for d[H~Ozl/dt is as follows:

dt

Apply Eq. (c) to (3), then d Photonsldt = kh[L][Hz021. Replace L in the above equation by Eq. (e). The following equation is obtained:

Derivation of Eq. (7)

Replace (-d[LH-]ldt) in Eq. (6) by Eq. (4). Then, Eq. (6) can be derived as follows:

Rewrite the above equation as:

Replace k l , k2, and k3 with their literature values, then

(l/k2 + l/k3)/[LH-] = 1/(1.18 X 104[LH-]); l/(kl[H202]) = 1/(1.8 X 1O7[H202]).

If [H202]l[LH-] 2 0.66, then

1/(1.18 X 104[LH-]) 2 100(1/(1.18 X 107[HzOz])).

Therefore, the equation above can be derived:

The double-reciprocal plot of (l/In) vs. (l/[H202]) must be linear. With our experimental conditions, the ratio of [H2021/[LH-] is from 7 to 14. Therefore, the nonlinear calibration curve of In vs. [H~OZ] and a linear double- reciprocal plot of (l/In) vs. (l/[H202]) can be obtained.

LI, ARNOLD, AND DORDICK PEROXIDASE-CATALYZED LUMINOL CHEMILUMINESCENCE 1119

References

1. Akimoto, K., Shinmen, Y., Sumida, M., Asami, S., Amachi, T., Yoshizumi, H., Saeki, Y., Shinmizu, S., Yamada, H. 1990. Luminol chemiluminescence reaction catalyzed by a microbial peroxidase. Anal. Biochem. 189 182-185.

2. Bostick, D. T., Hercules, D. H. 1975. Quantitative determination of blood glucose using enzyme induced chemiluminescence of luminol. Anal. Chem. 47: 447-452.

3. Christian, G. 1986. Analytical chemistry. 4th edition. Wiley, New York, pp. 580-581.

4. Corder , M. J., Prichard, P. M. 1968. An investigation of the mechanism of the luminescent peroxidation of luminol by stopped flow techniques. J. Biol. Chem. 243: 4706-4714.

5. Freeman, T. M., Seitz, W. R. 1978. Chemiluminescence fiber optic probe for hydrogen peroxide based on the luminol reaction. Anal. Chem. 50: 1242-1246.

6. Lind, J., MerBnyi, G., Eriksen, T. E. 1983. Chemiluminescence mechanism of cyclic hydrazides such as luminol in aqueous solution. J. Am. Chem. SOC. 105: 7655-7677.

7. Lundin, A., Hallander, L. 0. B. 1987. Mechanisms of horseradish peroxidase catalyzed luminol reaction in presence and absence of various enhancers, pp. 555-558. In: J. Scholmerich, R. Andresen, A. Kapp, M. Emst, and W. G. Woods (eds.), Biochemluminescence and

chemiluminescence. New Perspectives. Wiley, Chichester, UK. 8. Merhyi, G., Lind, J., Eriksen, T.E. 1990. Luminol chemilumi-

nescence: Chemistry, excitation, emitter. J. Biolum. Chemilum. 5:

9. Merinyi, G., Lind, J., Eriksen, T.E. 1986. Nucleophilic addition to diazoquinones. Formation and breakdown of tetrahedral intermediates in relation to luminol chemiluminescence. J. Am. Chem. SOC. 108

10. Merinyi, G., Lind, J., Eriksen, T. E. 1984. The equilibrium reaction of the luminol radical with oxygen and the one-electron-reduction potential of 5-aminophthalazine-l,4-dione. J. Phys. Chem. 88: 2320-2323.

11. Thorpe, G. H. G., Kicka, L. J., Moseley, S. B., Whitehead, T. P. 1985. Phenols as enhancers of the chemiluminescence horseradish peroxidase-lumi,nol-hydrogen peroxide reaction: application in luminescence-monitored enzyme immunoassays. Clin. Chem. 31:

12. Vlasenko, S. B., Arefyev, A. A., Klimov, A. D., Kim, B. B., Gorovits, E. L., Osipov, A. P., Gavrilova, E. M., Yegorov, A.M. 1989. An investigation on the catalytic mechanism of enhanced chemiluminescence: immunochemical applications of this reaction. J. Biochemilum. Chemilum. 4: 164-178.

13. Williams, D.C., Huff, G.F., Seitz, W.R. 1976. Glucose oxidase chemiluminescence measurement of glucose in urine compared with the hexokinase method. Clin. Chem. 22: 372-374.

53-56.

7716-1726.

1335 - 1341.


mathematical model for the luminol chemiluminescence reaction catalyzed by peroxidase

Documents