Kinetic Studies on Enzyme-Catalyzed Reactions: Oxidation of Glucose, Decomposition of Hydrogen Peroxide and Their Combination

Abstract

The kinetics of the glucose oxidase-catalyzed reaction of glucose with O₂, which produces gluconic acid and hydrogen peroxide, and the catalase-assisted breakdown of hydrogen peroxide to generate oxygen, have been measured via the rate of O₂ depletion or production. The O₂ concentrations in air-saturated phosphate-buffered salt solutions were monitored by measuring the decay of phosphorescence from a Pd phosphor in solution; the decay rate was obtained by fitting the tail of the phosphorescence intensity profile to an exponential. For glucose oxidation in the presence of glucose oxidase, the rate constant determined for the rate-limiting step was k = (3.0 ± 0.7) ×10⁴ M⁻¹s⁻¹ at 37°C. For catalase-catalyzed H₂O₂ breakdown, the reaction order in [H₂O₂] was somewhat greater than unity at 37°C and well above unity at 25°C, suggesting different temperature dependences of the rate constants for various steps in the reaction. The two reactions were combined in a single experiment: addition of glucose oxidase to glucose-rich cell-free media caused a rapid drop in [O₂], and subsequent addition of catalase caused [O₂] to rise and then decrease to zero. The best fit of [O₂] to a kinetic model is obtained with the rate constants for glucose oxidation and peroxide decomposition equal to 0.116 s⁻¹ and 0.090 s⁻¹ respectively. Cellular respiration in the presence of glucose was found to be three times as rapid as that in glucose-deprived cells. Added NaCN inhibited O₂ consumption completely, confirming that oxidation occurred in the cellular mitochondrial respiratory chain.

Introduction

We study two enzyme-catalyzed reactions, the oxidation of glucose and the breakdown of hydrogen peroxide, by monitoring oxygen concentration using phosphorescence decay. Previous studies of these reactions did not monitor oxygen concentration; the measurements presented in this study permit confirmation of the values of some rate constants, and show problems in the previously assumed model. We study the combination of the two reactions, and also the combination of the reactions with cellular respiration. The latter gives information about the efficiency of glucose transport into cells in vitro.

Measurement of [O₂] based on quenching of the phosphorescence of Pd (II)-meso-tetra-(4-sulfonatophenyl)-tetrabenzoporphyrin was first introduced by Vanderkooi et al. (1), Rumsey et al. (2), and Pawlowski and Wilson (3). This method, which allows accurate and sensitive determination of [O₂] in biological systems (4), uses the time constant τ for the decay of the phosphorescence of the Pd phosphor in solutions; 1/τ is a linear function of [O₂] (see Eq. 8). We have used the method previously to monitor cellular respiration (mitochondrial O₂ consumption) under various conditions (5–8). This method was also used by us to study rapid chemical oxidation in solutions, in particular the dithionite reaction (9).

We study the glucose oxidase-catalyzed oxidation of glucose, the catalase-accelerated breakdown of hydrogen peroxide, their combination in cell-free culture, and glucose-driven cellular respiration. Previous studies of glucose oxidase and catalase did not involve monitoring changes in [O₂]; by doing this, we can get additional information about the mechanism of the reactions. In addition, values of the rate constants are obtained that, in some cases, differ significantly from those previously published. Given their critical roles in fundamental biochemical and biophysical studies, the kinetic properties of these enzymes deserve more attention from researchers.

Although glucose oxidase is not very specific, its action on glucose is faster than on other sugars (10). The reaction of glucose (C₆H₁₂O₆) with O₂ produces glucono-δ-lactone (C₆H₁₀O₆) and H₂O₂, as follows.

$$\text{glucose}+{\mathrm{O}}_2\to \text{glucono-}\delta \text{-lactone}+{\mathrm{H}}_2{\mathrm{O}}_2\text{.}$$

In aqueous solutions, glucono-δ-lactone (C₆H₁₀O₆) reacts spontaneously with water to form gluconic acid (C₆H₁₂O₇), so the overall reaction is

$${\mathrm{C}}_6{\mathrm{H}}_{12}{\mathrm{O}}_6+{\mathrm{H}}_2\mathrm{O}+{\mathrm{O}}_2\to {\mathrm{C}}_6{\mathrm{H}}_{12}{\mathrm{O}}_7+{\mathrm{H}}_2{\mathrm{O}}_2\text{.}$$ (1)

Glucose oxidase has a unique specificity for β-D-glucose with no action on its α-anomer (10,11). However, in solutions, α-D-glucose mutarotates to β-D-glucose (12,13). Thus, the reaction of β-D-glucose is accompanied by the mutarotation

$$\alpha \text{-D-glucose}\underset{k_{\beta }}{\overset{k_{\alpha }}{\rightleftarrows }}\beta \text{-D-glucose}\text{.}$$

This conversion is catalyzed by acid as well as specific substances (14). A free intermediate with the open-chain aldehyde form equilibrates with both α- and β-D-glucose, but its concentration is negligible (∼26 ppm) (14). The interconversion of the isomers is slow, so we assume an equilibrium mixture, with only the β-D-glucose available for reaction. (Glucose oxidase preparations are sometimes contaminated by mutarotase (13), which accelerates mutarotation of α-D-glucose to β-D-glucose.) The α → β conversion constant k_α is higher than that for β → α, k_β (14). Le Barc'H et al. (15) have reported k_α and k_β at various temperatures and concentrations. Interpolating their values, we find k_α = 1.60 ± 0.09 h⁻¹ and k_β = 1.09 ± 0.07 h⁻¹ at 37°C, so that the mutarotation equilibrium constant K ≡ k_α/k_β is equal to 1.46 ± 0.13, and the equilibrium distribution is 59.3% β-isomer. Initially, one has

$${\left[\beta \text{-}\mathrm{D}\text{-}\text{glucose}\right]}_{\text{eq}}=\frac{K}{1+K}{\left[\text{D-glucose}\right]}_0,$$

where [D-glucose]₀ is the sum of the two anomer concentrations.

In the presence of glucose oxidase, Eq. 1 involves the sequence of reactions (10)

$$E_{\text{ox}}+\beta \mathrm{-D-}\text{glucose}\stackrel{k_1}{\to }{\mathrm{E}}_{\text{red}}{P}_1\stackrel{k_2}{\to }{\mathrm{E}}_{\text{red}}+P_1$$ (2)

$$E_{\text{red}}+{\mathrm{O}}_2\stackrel{k_3}{\to }{E}_{\text{ox}}{P}_2\stackrel{k_4}{\to }{E}_{\text{ox}}+P_2\text{.}$$ (3)

The enzyme oxidizes β-D-glucose to glucono-δ-lactone (P₁), and O₂ re-oxidizes the enzyme, producing H₂O₂ (P₂).

The generated H₂O₂ (P₂) can further decompose into H₂O + 1/2 O₂ through a thermodynamically favorable process. This process becomes much faster with certain catalysts present, including the transition metal compounds (for instance, Fe³⁺ and Mn⁴⁺) and many peroxidases that contain such ions in their enzymatic structures. As the most common and efficient enzyme, catalase, with its four porphyrin heme subunits, breaks down H₂O₂ at a very high turnover rate. Although the exact mechanism of catalase-accelerated H₂O₂ decomposition remains unclear, a proposed reaction strategy through the transient existence of a catalase-H₂O₂ intermediate has been established (16,17).

$$\text{Fe}\left(\text{III}\right)\text{-catalase}+{\mathrm{H}}_2{\mathrm{O}}_2\stackrel{k_{\mathrm{i}}}{\to }\mathrm{O}=\text{Fe}\left(\text{IV}\right)\text{-catalase}+{\mathrm{H}}_2\mathrm{O}$$ (4)

$${\mathrm{H}}_2{\mathrm{O}}_2+\mathrm{O}=\text{Fe}\left(\text{IV}\right)\text{-catalase}\stackrel{k_{\text{ii}}}{\to }\text{Fe}\left(\text{III}\right)-\text{catalase}+{\mathrm{H}}_2\mathrm{O}+{\mathrm{O}}_2$$ (5)

Fe (III) in the enzyme heme group serves as the electron source, thus rendering one electron to H₂O₂ molecule and forming an intermediate, compound I (16). Then the distorted heme ring reacts with a second H₂O₂ molecule to restore the original ferricatalase. In these two steps, H₂O₂ acts first as an oxidizing, then a reducing agent. Because there exist few reports illustrating the kinetic aspects of the reaction steps or testing the assumptions of the kinetic model, the following studies are of interest.

Materials and Methods

Reagents

The Pd (II) complex of meso-tetra-(4-sulfonatophenyl)-tetrabenzoporphyrin (sodium salt, Pd phosphor) was obtained from Porphyrin Products (Logan, UT); its solution (2.5 mg/mL = 2 mM) was prepared in dH₂O and stored at −20°C in small aliquots. D (+) glucose anhydrous (Lot No. D00003205) was purchased from Calbiochem (La Jolla, CA). Glucose oxidase (from Aspergillus niger; 1,400 units/mL in 100 mM sodium acetate, pH ∼4.0) was purchased from Sigma-Aldrich (St. Louis, MO). Catalase (from bovine liver; 2950 units/mg solid or 4540 units/mg protein) and hydrogen peroxide (30 wt % solutions in water, i.e., ∼10.6 M; Lot No. 04624AH) were both purchased from Sigma (the quality and concentration of H₂O₂ were guaranteed for 2 years). Catalase was made in 10 mg/mL solution immediately before experiments and never frozen for reuse. Working solutions of H₂O₂ (106 mM) were freshly made in dH₂O right before injection. NaCN solution (1.0 M) was freshly prepared in dH₂O and the pH was adjusted to ∼7.0 with 12 N HCl immediately before use. Phosphate buffered salt solution (PBS, without Mg²⁺ and Ca²⁺) and RPMI-1640 cell culture media were purchased from Mediatech (Herndon, VA). T-cell lymphoma (Jurkat) cells were cultured as described (5–8).

The rate equation of glucose oxidase-catalyzed glucose oxidation

If the equilibrium between α- and β-D-glucose is established rapidly, Eqs. 2 and 3 are rate controlling. The reaction rate is R = d[P₁]/dt = d[P₂]/dt = −d[O₂]/dt. At steady state, the rates of all steps are equal, so

$$R=k_1\left[E_{\text{ox}}\right]\left[\beta \text{-}\mathrm{D}\text{-}\text{glucose}\right]=k_2\left[E_{\text{red}}{P}_1\right]=k_3\left[E_{\text{red}}\right]\left[{\mathrm{O}}_2\right]=k_4\left[E_{\text{ox}}{P}_2\right]\text{.}$$

Letting C be the total enzyme concentration (here ∼0.125 μM), i.e., C = [E_ox] + [E_redP₁] + [E_red] + [E_oxP₂], we have

$$C=\frac{k_4\left[E_{\text{ox}}{P}_2\right]}{k_1\left[\beta \text{-D-glucose}\right]}+\frac{k_4\left[E_{\text{ox}}{P}_2\right]}{k_2}+\frac{k_4\left[E_{\text{ox}}{P}_2\right]}{k_3\left[{\text{O}}_2\right]}+\left[E_{\text{ox}}{P}_2\right]\text{.}$$

The rate is R = k₄[E_oxP₂] and the specific rate is v = R/C = −C⁻¹ d[O₂]/dt, so

$$\frac{1}{v}=\frac{\frac{k_4}{k_1\left[\beta \text{-D-glucose}\right]}+\frac{k_4}{k_2}+\frac{k_4}{k_3\left[{\mathrm{O}}_2\right]}+1}{k_4}=\frac{1}{k_1\left[\beta \text{-D-glucose}\right]}+\frac{1}{k_2}+\frac{1}{k_3\left[{\mathrm{O}}_2\right]}+\frac{1}{k_4},$$ (6)

showing 1/ν is a linear function of both [β-D-glucose]⁻¹ and [O₂]⁻¹. The above equations are also valid if the α–β equilibration is slow enough to neglect; in this case only the initial (equilibrium) concentration of [β-D-glucose] is relevant.

The rate equation of catalase-catalyzed decomposition of hydrogen peroxide

Rewriting reactions 4 and 5 with E representing Fe (III)-catalase and I the intermediate, compound I, we have:

$$E+{\mathrm{H}}_2{\mathrm{O}}_2\stackrel{k_{\mathrm{i}}}{\to }I+{\mathrm{H}}_2\mathrm{O}$$

$${\mathrm{H}}_2{\mathrm{O}}_2+I\stackrel{k_{\text{ii}}}{\to }E+{\mathrm{H}}_2\mathrm{O}+{\mathrm{O}}_2\text{.}$$

Let E₀ be the total enzyme (here ∼0.40 μM), i.e., [E₀] = [E] + [I]. The reaction rate (R) is R = d[O₂]/dt. At steady state, the rates of the two steps are equal, so k_i [E][H₂O₂] = k_ii[I][H₂O₂]. This leads to [E₀] = $\frac{k_{\mathrm{i}}+k_{\text{ii}}}{k_{\text{ii}}}\left[E\right]$, or [E] = $\frac{k_{\text{ii}}}{k_{\mathrm{i}}+k_{\text{ii}}}\left[E_0\right]$, and the rate becomes

$$R=k_{\text{ii}}\left[I\right]\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]=k_{\mathrm{i}}\left[E\right]\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]=\frac{k_{\mathrm{i}}{k}_{\text{ii}}}{k_{\mathrm{i}}+k_{\text{ii}}}\left[E_0\right]\left[{\mathrm{H}}_2{\mathrm{O}}_2\right],$$ (7)

and the specific rate, v = R/[E₀] = [E₀]⁻¹d[O₂]/dt, is

$$v=\frac{1}{\left[E_0\right]}\times \frac{d\left[{\mathrm{O}}_2\right]}{dt}=\frac{k_{\mathrm{i}}{k}_{\text{ii}}}{\left(k_{\mathrm{i}}+k_{\text{ii}}\right)}\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]=k_{\text{hp}}\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]\text{.}$$

Instrumentation

The home-made O₂ analyzer was described previously (5,6). In our instrument, the solution containing the phosphor is flashed 10 times per second by a visible (670 nm) light source (flash duration, 100 μs). The intensity of the phosphorescence is recorded every 3.2 μs, and the decreasing part of the intensity profile (after the light source is turned off) is fit to an exponential Ae^−t/τ to find the decay constant τ. DAZYlab (Measurement Computing Corporation, Norton, MA) was used for data acquisition. The data were analyzed by a Microsoft Visual C²⁺ language program (9) that calculated the phosphorescence lifetime (τ) and decay constant (1/τ). A typical phosphorescence profile is shown in Fig. 1. Like most of the measurements described in this study, it was made at 37°C. The sample, in PBS, contained 2 μM Pd-phosphor, 0.5% bovine fat-free albumin, 7 units/mL glucose oxidase, and 800 μM glucose, in sealed vials. For this profile only, intensity was measured every 2 μs. The flash goes on at t = t₀ ∼22.87 ms, stays on with a constant intensity until t = t₁ ∼22.97 ms, and then goes off, so flash duration is 100 μs. To determine τ, we localized the time of the peak intensity and fitted the decreasing part of the profile to an exponential (9). The fit, shown as a solid gray line in Fig. 1, gave the decay rate 1/τ = 3.2 ms⁻¹ or τ = 311 μs. Because O₂ quenches the phosphorescence, the decay rate 1/τ is a linear function of [O₂]:

$$\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\tau $}\right.=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{${\tau }_0$}\right.+k_{\mathrm{q}}\left[{\mathrm{O}}_2\right],$$ (8)

where 1/τ₀ is the decay rate in the absence of O₂ and k_q the quenching constant. The data were composed of a number of profiles like that of Fig. 1. The C²⁺ program screened the data stream for intensities >0.05. In every 0.1 s interval, it located the time of each maximum (t₁), and found the best-fit exponential from data after the maximum. It thus generated 10 decay constants per second, which were averaged.

Figure 1.

A typical phosphorescence profile. The sample, in PBS, contained 2 μM Pd-Phosphor, 0.5% bovine fat-free albumin, 7 units/mL glucose oxidase and 800 μM glucose. Sampling was at 500,000 Hz. The flash goes on at t = t₀ ∼22.87 ms, stays on with a constant intensity until t = t₁ ∼22.97 ms, and then goes off, so flash duration is 100 μs. The decay part of the profile was fit to an exponential A e^−t/τ (gray line) to calculate the lifetime τ. The fit gave τ = 311 μs (decay rate 1/τ = 3.2 ms⁻¹).

Calibration with glucose oxidase

A Clark-type O₂ electrode was used to determine [O₂] in PBS solution containing glucose oxidase (7.0 units/mL), 50–250 μM D-glucose, 2 μM Pd phosphor, and 0.5% fat-free bovine serum albumin. The plot of [O₂] versus [D-glucose] (Fig. 2 A) was linear (r² >0.999), with slope = 1.05 μM O₂ per μM glucose, demonstrating a stoichiometry of 1:1, as in Eq. 1.

Figure 2.

(A) Calibration with glucose oxidase. The solution (at 37°C) in PBS contained 7.0 units/mL glucose oxidase, 0.05–1.0 mM D-glucose, 2 μM Pd phosphor, and 0.5% fat-free bovine serum albumin. A Clark-type O₂ electrode was used to measure dissolved O₂. Apparent stoichiometry (moles O₂ consumed per mole glucose added) was 1.05 (r² >0.999). (B) Establishing stoichiometry from decay rate. Phosphorescence decay was measured in glucose solutions in air-saturated water ([O₂] ∼237 μM) containing glucose oxidase. Values of 1/τ were plotted versus [glucose] and fitted to two lines, the second, horizontal, is for [O₂] = 0; the intersection shows [glucose]/O₂ = 1:1.

We then used our instrument to measure 1/τ for solutions containing D-glucose at concentrations between 0 and 1000 μM. For each concentration, 1/τ was determined as the average of 1000–2000 measurements. Results are shown in Fig. 2 B (error bars show the standard deviations, which are worse for smaller values of τ). The best fit to a two-line function (Fig. 2 B, dashed lines) was

$$\{\begin{array}{l}1/\tau ={\alpha }_1+{\beta }_1\left[\mathrm{D}-\text{glucose}\right],0<\left[\mathrm{D}-\text{glucose}\right]\le 283\mu \mathrm{M}\\ 1/\tau ={\alpha }_2,283<\left[\mathrm{D}-\text{glucose}\right]\le 1000\mu \mathrm{M}\end{array}$$

with α₁ = 43,844 s⁻¹, β₁ = −146.7 μM⁻¹s⁻¹, and α₂ = 4788 s⁻¹, whereas the intersection is ([D-glucose], 1/τ) = (266.2 μM, 4788 s⁻¹). Because [O₂] is 267 μM for air-saturated water at 25°C, this confirms the stoichiometry: [D-glucose]/[O₂] = 1:1. It also determines the value of the quenching rate constant, k_q = 134.5 ± 14.3 μM⁻¹ s⁻¹, and the value of 1/τ₀, 5002 ± 437 s⁻¹.

Stability of hydrogen peroxide

The stability of hydrogen peroxide was checked by high performance liquid chromatography (HPLC). The analysis was carried out on a Beckman reversed-phase HPLC system, which consisted of an automated injector (model 507e) and a pump (model 125). The column, 4.6 × 250 mm Beckman Ultrasphere IP column, was operated at room temperature (25°C) at a flow rate of 0.5 mL/min. The run time was 30 min and the mobile phase was dH₂O. Ten microliters 30 wt % H₂O₂ was diluted in 2 mL dH₂O and 5–50 μL injections were run on HPLC, which corresponded to 260–2600 pmol H₂O₂. The detection wavelength was fixed at 250 nm. A typical HPLC chromatogram is shown in Fig. 3 A.

Figure 3.

Stability of H₂O₂ in solutions checked by HPLC. Samples were run at room temperature (25°C) at a flow rate of 0.5 mL/min. The detection wavelength was 250 nm, the run time was 30 min and the mobile phase was dH₂O. Ten μL of 30 wt. % H₂O₂ was diluted in 2 mL dH₂O; 5–50 μL injections, which corresponded to 260-2600 pmol H₂O₂, were then run on HPLC. (A) Representative HPLC chromatograms of H₂O₂. The three plots, from bottom to top, are due to independent injections of 530 (dotted line), 1060 (dashed line), and 2120 (solid line) pmol H₂O₂. A single peak was observed at retention time ∼300 seconds in three samples; the inset panel shows the peak region. (B) H₂O₂ peak areas (A, arbitrary units) assumed proportional to the injected amount of H₂O₂, are fitted to a linear function A × 10⁻⁶ = 0.00337 [H₂O₂] + 0.551 (r² = 0.976). For each concentration, measurements were taken in two different days covering H₂O₂ usage period. The variations of H₂O₂ peak areas for the same injection were 1.8%–6.7%.

A single peak was always observed at retention time ∼5 min in all the samples. The area of this peak was evaluated. Measurements were carried out in two different days spanning the time period over which the H₂O₂ experiments were carried out. The variations of H₂O₂ peak areas for the same injection were found to be between 1.8% and 6.7%. Thus, it is clear that the hydrogen peroxide used in this study is stable. In addition, H₂O₂ peak areas (A, arbitrary units) were proportional to the injected amount of H₂O₂. The best linear fit to the results, shown in Fig. 3 B, was A × 10⁻⁶ = (0.00337 ± 0.00012) (H₂O₂) + (0.551 ± 0.184) where (H₂O₂) is in pmol and r² = 0.976.

Results

Kinetics of glucose oxidase-catalyzed glucose oxidation

We first studied the glucose oxidase reaction at 37°C in the presence of D-glucose. If Eqs. 2 and 3 are rate-controlling, the specific rate is given by Eq. 6. This shows 1/ν is a linear function of both [β-D-glucose]⁻¹ and [O₂]⁻¹. If the α–β equilibration is not rapid, the α-to-β conversion reactions must be taken into account. However, if the α-to-β equilibration is extremely slow, it may be neglected, provided that the initial concentration of β-D-glucose only is considered. We do this in the following.

In our experiments, D-glucose was first dissolved in PBS (pH ∼7.4) at 37°C, and then injected into PBS containing glucose oxidase. Measured [O₂] as a function of t is shown in Fig. 4 A for 50 μM ≤ [D-glucose] ≤ 300 μM; the reaction rate is the negative slope of the curve. Each experiment was repeated 3–5 times; the representative plots are shown in Fig. 4 A. Each data set is fit to an exponential Pe^−Qt (Fig. 4 A, lines). The initial rate v_o = −d[O₂]/dt is then PQ. For the lowest glucose concentration, the reaction rate is essentially zero for t > 200 s, so the neglect of the mutarotation is not justified. Thus, for experiments at 50 μM glucose, v_o is calculated from an exponential fit to only the first half of the data (fit not shown in Fig. 4 A). Calculated v_o are shown in Fig. 4 B.

Figure 4.

Kinetics of glucose oxidase.(A) D-glucose was injected into PBS containing glucose oxidase (pH ∼7.4; 50 μM ≤ [D-glucose] ≤ 300 μM) at 37°C. [O₂] as a function of t (solid dots) was fit to an exponential function (gray solid line). (B) Plot of 1/v₀ (v₀ = initial rate) versus 1/[D-glucose]₀ (solid squares). Error bars are the standard deviation from two to three experiments for each concentration. The data were fit to a line with slope = 55.4 ± 3.5 μM s and intercept = 0.032 ± 0.003 s (r² > 0.984). From the slope one gets the mutarotation equilibrium constant for glucose. (C) O₂ consumption in the presence of glucose oxidase. Glucose in excess over O₂ is added at time zero. From left to right, [D-glucose] = 10 mM (triangles), 5 mM (diamonds), 1 mM (circles), respectively. The results are fit to Eq. 10 (solid lines).

The initial specific rate should obey (Eq. 6)

$$\frac{1}{v_0}=\frac{A}{{\left[\text{D-glucose}\right]}_0}+B,$$ (9)

where $A=\frac{1+K}{k_{1}K}\text{and}B=\frac{1}{k_2}+\frac{1}{k_3[{\mathrm{O}}_2]}+\frac{1}{k_4}\text{.}$

A plot of 1/v₀ versus 1/[D-glucose]₀ with 50 ≤ [D-glucose]₀ ≤ 300 μM is shown in Fig. 4 B. It should be noted that the small error bars on the points do not include the errors inherent in the conversion of τ to [O₂]. The best linear fit gives A = 55.4 ± 3.5 μM s and B = 0.032 ± 0.003 s (r² > 0.984). The value of B is essentially zero, implying k₂, k₃, and k₄ are very large. Using the determined value of A with K = 1.46 (15), we find the value of the rate constant k₁ = 0.030 μM⁻¹ s⁻¹ at 37°C, comparable to the reported 0.016 μM⁻¹s⁻¹ (10).

Fig. 4 C shows the O₂ consumption in the presence of glucose oxidase when glucose is present in excess over O₂ (from left to right, [D-glucose] = 10, 5, and 1 mM, respectively). With [glucose] >> [O₂], the exact integral of Eq. 6 from t₀ to t is

$$\alpha \left(\left[{\text{O}}_2\right]-{\left[{\mathrm{O}}_2\right]}_0\right)+b\left(\text{ln}\left[{\mathrm{O}}_2\right]-\text{ln}{\left[{\mathrm{O}}_2\right]}_0\right)=-\left(t-t_0\right)\text{.}$$ (10)

Here, [O₂]₀ corresponds to [O₂] in air-saturated PBS,

$$\alpha =\frac{1}{C}\left(\frac{1}{k_1\left[\text{glucose}\right]}+\frac{k_2+k_4}{k_2{k}_4}\right),$$

and b = (Ck₃)⁻¹. Using the Excel Solver function, we fit the curves of Fig. 4 C to Eq. 10, obtaining {a, b} in {μM⁻¹ s, s} = (−0.034, 11.7), (0.025, 20.4), and (0.295, 22.1) from left to right respectively. (Uncertainty about the zero of time may be the reason the fits are not perfect: note that all the fits could be improved by shifting the times for the experimental points slightly to the left.) The value of a increases as [glucose] decreases, whereas the value of b is relatively constant.

From a linear plot of a versus 1/[glucose], we obtain 1/k₁ = 44.4 ± 3.0 μM s, so that k₁ = (2.3 ± 0.2) × 10⁴ M⁻¹ s⁻¹, and (k₂ + k₄)/k₂k₄ = −0.00734 ± 0.00178 s. (The experiments shown in Fig. 4, A and B, gave k₁ = 3.0 × 10⁴ M⁻¹ s⁻¹.) The very small value of (k₂ + k₄)/k₂k₄ implies large numerical values for k₂ and k₄. Using the average value of b, 18.1 ± 5.6 s, and enzyme concentration C = 0.125 μM, k₃ is calculated as (4.4 ± 1.4) × 10⁵ M⁻¹ s⁻¹. These results may be compared to those reported by Gibson et al. (10), k₁ = 1.6 × 10⁴ M⁻¹ s⁻¹ and k₃ = 2.4 × 10⁶ M⁻¹ s⁻¹ at 38°C.

The initial rate of reaction, obtained by differentiating Eq. 10, is

$${\left(\frac{d\left[{\mathrm{O}}_2\right]}{dt}\right)}_0=-V_0=-{\left(a+\frac{b}{{\left[{\mathrm{O}}_2\right]}_0}\right)}^{-1}\text{.}$$ (11)

Using [O₂]₀ = 225 μM in Eq. 11, we find, for [glucose] = 10, 5, and 1 mM, V₀ = 55.1, 8.7, and 2.5 μM s⁻¹, respectively.

Kinetics of catalase-aided decomposition of hydrogen peroxide

As indicated in Eqs. 4 and 5, catalase reacts with one mole of H₂O₂ to produce the intermediate I, which then reacts with another mole of H₂O₂ to regenerate the enzyme and release one mole of O₂. The reaction rate R = d[O₂]/dt is given by

$$R=k_{\text{ii}}\left[I\right]\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]=k_{\mathrm{i}}\left[E\right]\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]=\frac{k_{\mathrm{i}}{k}_{\text{ii}}}{k_{\mathrm{i}}+k_{\text{ii}}}\left[E_0\right]\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]\text{.}$$

Thus, the specific rate v = R/[E₀] = [E₀]⁻¹d[O₂]/dt, leading to

$$v=\frac{1}{\left[E_0\right]}\times \frac{d\left[{\mathrm{O}}_2\right]}{dt}=\frac{k_{\mathrm{i}}{k}_{\text{ii}}}{\left(k_{\mathrm{i}}+k_{\text{ii}}\right)}\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]=k_{\text{hp}}\left[{\mathrm{H}}_2{\mathrm{O}}_2\right],$$ (12)

with k_hp =$\left(\frac{k_{\mathrm{i}}{k}_{\text{ii}}}{k_{\mathrm{i}}+k_{\text{ii}}}\right)$. According to Eq. 12, ν is proportional to [H₂O₂] and the catalase-catalyzed decomposition of H₂O₂ is a first-order reaction with respect to H₂O₂.

To confirm the order of the reaction, we carried out the following experiments. At 37°C, air-saturated PBS solutions containing 2 μM Pd phosphor and 0.1 mg/mL catalase were placed in sealed containers for oxygen measurement. A value of 1/τ was acquired every 0.1 s. Various H₂O₂ concentrations were added at ∼1 min and measurement was continued until >3 min. The measured values of 1/τ, which depends linearly on [O₂], are plotted versus t in Fig. 5 A. Each plot corresponds to an experiment in which H₂O₂ at the indicated concentration was added to air-saturated PBS. The rapid climb in [O₂] when H₂O₂ is injected is evident. Because the reaction rate is independent of [O₂], the plots show an essentially linear increase in 1/τ from t = t_l (l for low O₂ level) to t = t_h (h for high O₂ level). To establish the order with respect to H₂O₂ and to calculate rate constant k_hp, we compare measured rates of reaction for different [H₂O₂]. The analysis used in this study is similar to that in previous studies of dithionite kinetics (9).

Figure 5.

Decomposition of H₂O₂ in the presence of 0.1 mg/mL catalase at (A) 37°C and at (B) 25°C. The reaction (in PBS) contained 2.0 μM Pd phosphor, 0.5% albumin, and 106–636 μM H₂O₂ as labeled. The rapid increase in 1/τ when H₂O₂ is injected corresponds to its catalyzed breakdown to generate O₂. The white solid lines indicate the best fits of experimental data (solid dots) to a three-line function. Slope of middle line gives reaction rate. (C) Logarithms of reaction rates are plotted against logarithms of [H₂O₂] at 25°C (open triangles) and 37°C (solid triangles). Linear fits to the two sets of data are shown. Open triangles fit by the dotted line show the results at 25°C, whereas solid triangles fit by the dashed line represent the results at 37°C.

For each plot, the values of 1/τ before and after the rise in [O₂], 1/τ_l and 1/τ_h, were obtained by averaging 600 measurements at early (0 ≤ t ≤ t_l) and late (t_h ≤ t ≤ 180 s) times, respectively. The value of 1/τ_l should correspond to [O₂] in air-saturated PBS, which is 267 μM at 37°C, whereas the value of 1/τ_h corresponds to total [O₂] after H₂O₂ decomposition, i.e., the sum of original [O₂] and [O₂] produced by the catalase-catalyzed decomposition of H₂O₂. Therefore, the difference between the values of 1/τ_l and 1/τ_h reflects the produced O₂. The white lines in Fig. 5 A are best fits of the experimental data to the two-parameter function,

$$\begin{array}{l}1/\tau =1/{\tau }_{l}t<t_l\\ =1/{\tau }_1+\left(t-t_l\right)\left(1/{\tau }_{\mathrm{h}}-1/{\tau }_l\right)/\left(t_{\mathrm{h}}-t_l\right)t_l\le t\le t_{\mathrm{h}}\\ =1/{\tau }_{\mathrm{h}}\tau >t_{\mathrm{h}}\text{.}\end{array}$$ (13)

Given 1/τ_l and 1/τ_h, we find the values of the two variable parameters t_l and t_h by minimizing the sum of the square deviations of Eq. 13 from experimentally measured 1/τ. The rate R = d[O₂]/dt is obtained by dividing d(1/τ)/dt by k_q (see Eq. 8), the derivative being calculated from the linearly-increasing portion of the plots, i.e.,

$$R=\frac{d\left[{\mathrm{O}}_2\right]}{dt}=\frac{1}{k_{\mathrm{q}}}\left(\frac{1}{{\tau }_{\mathrm{h}}}-\frac{1}{{\tau }_{\mathrm{l}}}\right){\left(t_{\mathrm{h}}-t_{\mathrm{l}}\right)}^{-1}=\left(k_{\text{hp}}\times \left[{\mathrm{E}}_0\right]\right){\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]}^{\mathrm{x}}\text{.}$$ (14)

The value of k_q here is expected to be different from that obtained from the glucose study, because different enzymatic systems are detected here; the new value of k_q can be determined from a regression of (1/τ_h − 1/τ_l) versus generated [O₂] (because the stoichiometry is known to be generated [O₂] = 1/2 [H₂O₂]), and gives 93.0 ± 9.1 μM⁻¹s⁻¹. The same experiments were also carried out at 25°C in PBS solutions, and analyzed in the same way; results are shown in Fig. 5 B.

In Eq. 14 we write the rate as k_hp[E_o] times [H₂O₂]^x where x is the order of the reaction with respect to H₂O₂. To find x, we carry out linear regression of ln(R) versus ln([H₂O₂]) (Fig. 5 C). At 37°C the slope is 1.27 ± 0.14, so that the overall reaction is approximately first order in H₂O₂. This result, x ∼1, agrees with the report by Beers and Sizer (18), who measured the order by monitoring rapid change in H₂O₂ absorptions during the reaction. The rate of the reaction (in μM s⁻¹) is found to be equal to

$$R=\frac{d\left[{\mathrm{O}}_2\right]}{dt}=\text{exp}\left(-3.656+1.266\text{ln}\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]\right)\approx 0.177\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]\text{.}$$ (15)

In contrast, the slope of the linear fit of ln(R) versus ln([H₂O₂]) is 1.69 ± 0.14 for 25°C, suggesting that the reaction becomes 1-1/2-order at the lower temperature. In particular,

$$R=\frac{d\left[{\mathrm{O}}_2\right]}{dt}=\text{exp}\left(-6.615+1.692\text{ln}\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]\right)\approx 4.49\times {10}^{-3}{\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]}^{1.5}$$

at 25°C (all concentrations in units of μM). Not only does the rate constant depend on temperature, but, apparently, so does the reaction order. Other researchers reported the reaction rate in the catalase-catalyzed breakdown of H₂O₂ was only slightly altered with changing temperature (600 cal activation energy) (18). However, those results were acquired from reactions at low ionic strength whereas ours were obtained in phosphate buffer with a high ionic strength. More importantly, we suggest that the importance of the elementary reactions not included in Eqs. 4 and 5 may change with temperature.

Thus, we propose a more general reaction mechanism by including the reverse of Eq. 4, so that the mechanism becomes

$$E+{\mathrm{H}}_2{\mathrm{O}}_2\underset{k_{-\mathrm{i}}}{\overset{k_{\mathrm{i}}}{\leftrightarrow }}I+{\mathrm{H}}_2\mathrm{O}$$ (16)

$${\mathrm{H}}_2{\mathrm{O}}_2+\mathrm{I}\stackrel{k_{\text{ii}}}{\to }E+{\mathrm{H}}_2\mathrm{O}+{\mathrm{O}}_2\text{.}$$

At steady state,

$$\frac{d\left[I\right]}{dt}=k_{\mathrm{i}}\left[E\right]\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]-k_{-\mathrm{i}}\left[I\right]-k_{\text{ii}}\left[I\right]\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]=0,$$

which gives

$$\left[I\right]=\frac{k_{\mathrm{i}}\left[E\right]\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]}{k_{-\mathrm{i}}+k_{\text{ii}}\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]},$$

and the reaction rate is

$$R=\frac{d\left[{\mathrm{O}}_2\right]}{dt}=k_{\text{ii}}\left[I\right]\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]=\frac{k_{\mathrm{i}}{k}_{\text{ii}}\left[E\right]{\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]}^2}{k_{-\mathrm{i}}+k_{\text{ii}}\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]}\text{.}$$

Since $\begin{array}{l}\left[E_0\right]=\left[E\right]+\left[I\right],\end{array}$

$$\begin{array}{l}\left[E_0\right]=\left[E\right]+\frac{k_{\mathrm{i}}\left[E\right]\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]}{k_{-\mathrm{i}}+k_{\text{ii}}\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]}=\left\{\frac{k_{-\mathrm{i}}+(k_{\mathrm{i}}+k_{\text{ii}})\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]}{k_{-\mathrm{i}}+k_{\text{ii}}\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]}\right\}\left[E\right]\end{array}$$

which gives

$$\begin{array}{l}R=\frac{d\left[{\mathrm{O}}_2\right]}{dt}=\frac{k_{\mathrm{i}}{k}_{\text{ii}}{\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]}^2}{k_{-\mathrm{i}}+k_{\text{ii}}\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]}\times \frac{k_{-\mathrm{i}}+k_{\text{ii}}\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]}{k_{-\mathrm{i}}+(k_{\mathrm{i}}+k_{\text{ii}})\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]}\left[E_0\right]=\frac{k_{\mathrm{i}}{k}_{\text{ii}}\left[E_0\right]{\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]}^2}{k_{-\mathrm{i}}+(k_{\mathrm{i}}+k_{\text{ii}})\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]}\text{.}\end{array}$$ (17)

If k_−i is negligible, Eq. 17 becomes

$$R=\frac{d\left[{\mathrm{O}}_2\right]}{dt}=\frac{k_{\mathrm{i}}{k}_{\text{ii}}\left[E_0\right]}{(k_{\mathrm{i}}+k_{\text{ii}})}\left[{\mathrm{H}}_2{\mathrm{O}}_2\right],$$

which is 1st order with respect to H₂O₂. However, if the value of k_−i is large in comparison with (k_i + k_ii)[H₂O₂], the reaction rate approaches $\frac{k_{\mathrm{i}}{k}_{\text{ii}}}{k_{-\mathrm{i}}}\left[E_0\right]{\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]}^2$, which is 2nd order in [H₂O₂]. Thus, if k_−i is not negligible, the reaction order in terms of H₂O₂ should appear to be between 1 and 2. Because the rate constants k_i, k_−I, and k_ii depend on temperature differently, the apparent order of reaction may change with temperature as well. In particular, our results suggest that, when temperature decreases, k_−i becomes more important relative to the other rate constants, raising the reaction order.

By fitting experimental results to Eq. (17, we obtained the best values for all the kinetic constants at 37°C: k_i = 5.0 × 10⁵ M⁻¹s⁻¹, k_−i = 377 s⁻¹, and k_ii = 5.6 × 10⁶ M⁻¹s⁻¹. Because k_ii [H₂O₂] > k_−i except for the lowest value of [H₂O₂] used, the reverse reaction of Eq. 16 is negligible, making the overall reaction appear 1st order. However, the sum of the squared deviations between measured and calculated rates using Eq. 17, which has three parameters, is 5.5 × 10⁵, only slightly below the sum of the squared deviations with the two-parameter function of Eq. 15, 5.9 × 10⁵, so that the exact values of the rate constants cannot be taken very seriously. At 25°C, there are many fewer points and more scatter than at 37°C, so the three-parameter fit is not meaningful (many sets of values for the three parameters give the same difference between measured and calculated rates). However, the fact that the apparent order of the reaction is much greater than one suggests that k_−i exceeds k_ii[H₂O₂] at the lower temperature. Because both rate constants must be lower at 25°C than at 37°C, this implies that k_−i has a lower activation energy than k_ii.

The action of glucose oxidase on glucose followed by the addition of catalase

We next studied the O₂-consuming and O₂-producing reactions together at 37°C. We injected first glucose oxidase (at ∼55 s) and later catalase (at ∼175 s) into RPMI-1640 media containing 10 mM D-glucose, obtaining the results in Fig. 6 A. The first evident drop in [O₂] accompanied injection of glucose oxidase. The best fit to Eq. 10 shows a = −0.159 μM⁻¹ s and b = 28.3 s; the latter differs substantially from the corresponding value in PBS, but is quite in line with the values of b for higher [glucose]. The catalase, injected after O₂ depletion by the glucose oxidation, catalyzed the decomposition of the previously produced H₂O₂, generating O₂, whose concentration climbed to ∼86 μM. Then [O₂] declined again to zero because of the reaction with glucose, present in excess.

Figure 6.

(A) Seven units/mL glucose oxidase was injected at t ∼50 s into 1.0 mL of RPMI-1640 medium containing 10 mM glucose, causing oxygen consumption. At t ∼170 s, 50 μg/mL catalase was injected, causing decomposition of H₂O₂ formed in the first reaction. (B) The data for 150 s < t < 300 s are well fitted by assuming that the original [O₂] was converted into H₂O₂, which decomposes with rate constant k_p to re-form O₂, which is destroyed by reaction with leftover glucose with rate constant k_c. Squares = experimental results, line = fit to Eq. 18 with k_c = 0.116 s⁻¹, k_p = 0.090 s⁻¹.

According to Eq. 1, all of the original O₂ (250 ± 12 μM) should be converted into H₂O₂ in the first reaction and, according to Eqs. 5 and 6, half of the original O₂ should be re-formed by the second reaction; however, the peak concentration was only one-third of the original [O₂]. The decay rate of the second peak was apparently much smaller than that of the first peak, 0.0376 s⁻¹ vs. 0.0846 s⁻¹ (values from exponential fits). Both facts are explained by the competition between O₂ production (from H₂O₂) and consumption (catalyzed by glucose oxidase).

A first check on this involves fitting the points from 184 s to 256 s to an exponential and extrapolating back to 174 s (time at which [O₂] starts to increase); this gives 118 μM, nearly half of the original [O₂]. For a more detailed verification, we write d[O₂]/dt as the result of an O₂-producing reaction with rate constant k_p and an O₂-consuming reaction with rate constant k_c:

$$\frac{d\left[{\mathrm{O}}_2\right]}{dt}=k_{\mathrm{p}}\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]-k_{\mathrm{c}}\left[{\mathrm{O}}_2\right]=k_{\mathrm{p}}{\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]}_0{\mathrm{e}}^{-k_{\mathrm{p}}(t-t_{\mathrm{p}})}-k_{\mathrm{c}}\left[{\mathrm{O}}_2\right],$$ (18)

where t_p is the time at which O₂ production begins (∼174 s) and [H₂O₂]₀ is assumed to be equal to the original [O₂] (see Eq. 1), i.e., 250 μM. The solution to Eq. 17 for t ≥ t_p is

$$\left[{\mathrm{O}}_2\right]=\frac{k_{\mathrm{p}}{\left[{\mathrm{O}}_2{\mathrm{O}}_2\right]}_0}{k_{\mathrm{c}}-k_{\mathrm{p}}}\left[{\mathrm{e}}^{-k_{\mathrm{p}}(t-t_{\mathrm{p}})}-{\mathrm{e}}^{-k_{\mathrm{c}}(t-t_{\mathrm{p}})}\right]\text{.}$$ (19)

In (Fig. 6 B we show that Eq. 19, with k_c = 0.116 s⁻¹ and k_p = 0.090 s⁻¹, gives a good fit to the measured [O₂]. This k_p is comparable to the value of 0.177 s⁻¹ in Eq. 15. The difference apparently reflects the difference between PBS and RPMI media; the latter contains more inorganic salts, and the ionic strength is much higher. Using k_p = 0.177 s⁻¹ in Eq. 18 and choosing k_c to give the best fit, k_c becomes 0.122 s⁻¹, which is not changed significantly from the two-parameter fitting; however, the fit becomes significantly worse.

Glucose-driven cellular respiration

The last experiments show the action of catalase in the environment of cellular respiration, which involves glucose oxidation. Jurkat cells were washed twice in PBS and incubated in PBS for 16 h to deplete glucose. Cell viability was >90% at this point. The cells (10⁶ per run) were then suspended in PBS, 2 μM Pd phosphor, and 0.5% bovine serum albumin (final volume, 1.0 mL). Temperature was maintained at 37°C throughout. At time zero, 5 μL of glucose or dH₂O was added (final concentration of glucose = 100 μM). [O₂] was measured every 2.0 min, alternately for the two conditions. Results are shown in Fig. 7 (solid circles, with glucose; open circles, no glucose).

Figure 7.

Glucose-driven respiration. Jurkat cells were washed twice in PBS and incubated in PBS for 16 h. The cells (10⁶ per run) were then suspended in PBS, 2 μM Pd phosphor, and 0.5% fat-free bovine serum albumin (final volume, 1.0 mL). Respiration was monitored with (solid circles) and without (open circles) the addition of 100 μM glucose at t = 0. After 38 min, the rate of O₂ consumption in the presence of glucose was three times the rate in the absence of glucose. Other additions included 10 mM NaCN, 7 units glucose oxidase, and 50 μg catalase. NaCN stopped O₂ consumption, showing the O₂ was consumed in the mitochondrial respiratory train. Catalase catalyzed the decomposition of H₂O₂, formed in the earlier oxidation of glucose, releasing O₂.

In the first 38 min, the rate of oxygen consumption (k) for both conditions was 0.14 μM O₂/min, which was similar to the drift rate (0.18 μM O₂/min). After this time (that probably represents the time necessary for glucose or other substrate to enter the cell), k increased for both conditions. From 40 to 140 min, the value of k with no glucose present was 0.32 μM O₂/min ([O₂] dropped from 128 μM to 96 μM); NaCN was added at 140 min. From 38 to 114 min, k with glucose present was 0.79 μM O₂/min ([O₂] dropped from 125 μM to 64 μM), 2-1/2 times as large; NaCN was added at 114 min. The decline in [O₂] in the absence of glucose was due to fatty acids in the albumin preparation used here, which can also drive respiration. (Other experiments showed that, with no albumin, the drop in [O₂] is much smaller.) For both conditions, O₂ consumption was completely inhibited by NaCN, confirming the oxidation occurred in the respiratory chain. Oxygen concentration actually increases slightly in both conditions, possibly due to air introduced with the cyanide injections.

In the suspension without glucose, neither injection of glucose oxidase nor later addition of catalase had any measurable effect on [O₂]. For the glucose-containing suspension, the addition of glucose oxidase (at t = 186 min) led to a decrease, rapid at first, in [O₂], which dropped from 73 μM to 36 μM in 12 min and from 36 μM to 21 μM in 40 min. The leveling-off of [O₂] at 21 μM is probably due to total depletion of glucose. Thus, starting with 100 μM glucose (and residual fatty acids), the total O₂ consumption was 113 μM, i.e., (125–64) + (73–21) μM. The O₂ consumed in the oxidation of fatty acids was 0.32 μM/min (from the data for cells without glucose) × (114 − 38) min, or 24 μM. Therefore, the O₂ consumed in glucose oxidation, extracellular and intracellular, was 89 μM. Because 100 μM glucose was consumed, it seems that intracellular glucose oxidation follows the same stoichiometry as extracellular glucose oxidation. The following calculations confirm this.

By fitting [O₂] for 182 ≤ t ≤ 234 min to the form α + βe^−C(t-182), we find the rate of extracellular O₂ consumption at 182 min to be (β × C) = 8.89 μM/min. The specific rate ν is obtained by dividing by the enzyme concentration, 0.125 μM, so ν = 71.1 min⁻¹ = 1.18 s⁻¹. According to Eq. 9, with B = 0.032 s and A = 55.4 μM s from the experiments of Fig.4 B in cell-free PBS, we obtain the glucose concentration at 182 min as 67.9 μM, so that 100 − 67.9 = 32.1 μM glucose was used to drive cellular respiration for t < 114 min. From the rate of O₂ consumption with glucose present from t = 38 to t = 114 min (0.79 μM O₂/min) we subtract the rate of O₂ consumption without glucose (0.32 μM O₂/min) and multiply by the elapsed time (76 min) to obtain the O₂ consumption associated with glucose oxidation during this period, 36 μM. This is 1.1 times the glucose consumption. Although the uncertainties in this calculation are large, it seems clear that the ratio of uptake of glucose by these cancer cells and the associated O₂ consumption is close to 1:1.

The later addition of catalase at 236 min led to an increase in [O₂] from 21 to 40 μM, due to enzyme-catalyzed decomposition of the H₂O₂ formed in the earlier glucose oxidation. The concentration of newly generated O₂ (19 μM) is less than expected from the H₂O₂ produced by glucose oxidation, which would be 1/2(73 − 21) = 26 μM. This difference could result from the fact that H₂O₂, being a strong oxidant, can react with many of biological molecules.

Discussion

Oxygen concentration in biological solutions can be measured rapidly and repeatedly via the decay rate of phosphorescence from a Pd phosphor in solution (Fig. 1). We used this method to study the glucose oxidase-catalyzed reaction of glucose with O₂, which produces gluconic acid and hydrogen peroxide, and the decomposition of hydrogen peroxide into water and oxygen in the presence of catalase. Previous studies of these reactions (18,19) have monitored [glucose] or [H₂O₂], rather than [O₂]; others have used luminescent probes for their studies in similar systems (20–22).

The decay rate 1/τ should be a linear function of [O₂]. To calibrate the instrument, and to confirm the stoichiometry of the glucose oxidation reaction, we measured 1/τ in a series of solutions of glucose in air-saturated PBS with glucose oxidase present. Measured 1/τ was plotted versus [glucose] (Fig. 2 B). For [glucose] >250 μM, 1/τ was constant at ∼5000 s⁻¹, corresponding to [O₂] = ∼0, i.e., complete consumption of O₂. For [glucose] <250 μM, 1/τ decreased linearly with [glucose]. Because [O₂] in air-saturated PBS at 25°C is 267 μM, ∼267 μM O₂ reacted completely with ∼250 μM glucose, which confirms the 1:1 stoichiometry. From the linear fit of 1/τ versus [glucose], the instrument calibration is established as 1/τ = 134.5[O₂] + 5002, where τ is in μs and [O₂] in μM.

The glucose oxidase-catalyzed oxidation of glucose involves four steps, and hence four rate constants and three intermediates (Eqs. 2 and 3). At steady state, the rates of all steps are equal. Plots of [O₂] versus t for [glucose] = 50–300 μM are shown in Fig. 4 A. Only β-D-glucose reacts with this catalyst, and the conversion of α to β isomer is slow and can be neglected, except for long times when [glucose] = 50 μM. The initial concentration of the β isomer is ∼70% of the total glucose. According to Eq. 4, the reciprocal of the steady-state rate should be a linear function of 1/[glucose]; this is verified in Fig. 4 B. Using 1.46 (15) for the mutarotation constant for glucose, we find the rate constant for the reaction of the catalyst E_ox with glucose, to form the first intermediate E_redP₁, to be k₁ = 3.0 × 10⁴ M⁻¹ s⁻¹.

When initial [glucose] is much larger than initial [oxygen], the equation for d[O₂]/dt can be solved explicitly (Eq. 10). Experimental results of [O₂] versus t are fitted to this solution in Fig. 4 C. From the fits, we find k₁ = 2.3 × 10⁴ M⁻¹ s⁻¹, between the value given by Gibson et al. (10), 1.6 × 10⁴ M⁻¹ s⁻¹, and the value above, 3.0 × 10⁴ M⁻¹ s⁻¹. We can also calculate k₃ = 4.4 × 10⁵ M⁻¹ s⁻¹, significantly smaller than the literature value of 2.4 × 10⁶ M⁻¹ s⁻¹ (10). Le Barc'H et al. (15) used luminescence intensity to monitor [O₂] during the glucose oxidase-catalyzed oxidation of glucose. They reported a Michaelis constant K_m of 38 ± 6 mM, as well as some rate data. Direct comparison of our measured rates with those of Le Barc'H et al. (15) is not possible because our measurements were carried out using a different enzyme, a lower enzyme concentration (0.02 vs. 0.8 mg/mL protein), and a higher temperature (37°C vs. 25°C). If Michaelis-Menten kinetics were followed, V₀ would be proportional to [glucose] for small [glucose] and level off for large [glucose]. Because [glucose] was so low in our measurements, our results (see above) show initial rate proportional to [glucose] with no sign of leveling off, and there is no possibility of measuring K_m. The initial rate V_o is just k₁ times the glucose concentration.

We next studied the catalase-catalyzed H₂O₂ decomposition. The initial rate of reaction was determined from plots of [O₂] versus time obtained from solutions with various [H₂O₂]. Then ln(rate) was plotted versus ln([H₂O₂]) and fitted to a line. The slope, which should be the reaction order with respect to H₂O₂, changed with temperature. At 37°C, it was 1.27 ± 0.14, consistent with the reaction rate d[O₂]/dt being 1st order in [H₂O₂], as in Eq. 7. However, the slope was 1.69 ± 0.14 for 25°C, suggesting that the reaction is $\frac{3}{2}$-order at the lower temperature. Assuming 1st order kinetics, the rate constant for the decomposition of H₂O₂ at 37°C is 0.177 s⁻¹; writing d[O₂]/dt as k^∗[H₂O₂]^3/2 and seeking the best value of k∗ leads to k^∗ = 4.49 M^−1/2 s⁻¹ at 25°C. We believe that the apparently higher reaction order at 25°C is due to increased importance of the dissociation of the H₂O₂-catalase intermediate, as shown in Fig. 8 A. We showed that including this reaction leads to an apparent reaction order with respect to H₂O₂ between 1 and 2.

Figure 8.

Kinetic schemes with rate constants. (A) The catalase-catalyzed decomposition of H₂O₂ involves two steps. If k_ii[H₂O₂] >> k_−i the overall rate is proportional to [H₂O₂], as observed at 37°C. If k_ii[H₂O₂] << k_−i the overall rate is proportional to [H₂O₂]². At 25°C, the rate is proportional to [H₂O₂]^3/2 suggesting that k_ii[H₂O₂] is comparable to k_−i at 25°C. (B) The two enzymatic reactions, one consuming oxygen and producing H₂O₂, and the other producing O₂ from H₂O₂, were combined and the rate constants shown were determined.

We next studied glucose oxidation at 37°C in cell culture medium containing 10 mM D-glucose, for which [O₂] was measured as 250 ± 12 μM. When glucose oxidase was added, [O₂] dropped rapidly (k_c = 0.0846 s⁻¹) to zero. To verify that the O₂ was indeed reduced to H₂O₂ as implied by Eqs. 1 and 3, catalase was added to catalyze the decomposition of H₂O₂; [O₂] rose to 86 μM and then, because of the oxidation of remaining glucose, declined to zero. As shown in Fig. 6 B, the variation of [O₂] with t was completely explained by assuming that 250 μM H₂O₂ was present (equal to the original [O₂]), that the oxidation of glucose occurred with rate constant k_c = 0.116 s⁻¹, and that the reaction H₂O₂ → H₂O + 1/2 O₂ occurred with rate constant k_p = 0.090 s⁻¹. This is indicated in Fig. 8 B.

Having established that our oxygen measurement method gave valid results in cell culture medium, we studied glucose-driven cellular respiration by starved Jurkat cells (Fig. 7). Two conditions, with and without 100 μM glucose, were used. Glucose-driven respiration began at 38 min; respiration driven by residual fatty acids began somewhat later in the sample without glucose. The rate of consumption of O₂ by cells with glucose was three times the rate by the cells without glucose. For both conditions, addition of cyanide inhibited O₂ consumption completely, showing the oxidations occurred in the mitochondrial respiratory chain. The addition of glucose oxidase 1 h after cyanide had stopped respiration had no effect on [O₂] in the glucose-free condition, but produced a sharp decrease in [O₂] in the glucose-present condition. Subsequent addition of catalase had no effect in the former case, and increased [O₂] in the latter. Both the decrease in [O₂] on glucose oxidase addition and the increase in [O₂] with catalase addition resulted from extracellular glucose oxidation, producing H₂O₂, which was, in turn, decomposed to O₂. Quantitative analysis of this experiment showed glucose/oxygen stoichiometry for cellular oxidation was close to the 1:1 ratio characteristic of extracellular oxidation. The rate of the latter was consistent with our previous measurements.

The results of our experiments show that, by monitoring oxygen concentration via phosphorescence lifetime, one can gain information about the kinetics and mechanism of biochemical reactions. For the glucose oxidase-catalyzed oxidation of glucose, we confirmed the stoichiometry and found precise values of several rate constants. (These measurements also established the calibration of our instrument.) For the catalase-catalyzed decomposition of hydrogen peroxide, we showed that, although the simple mechanism (Eqs. 4 and 5) explained the reaction order at 37°C, it failed to do so at 25°C. We suggested that, at 25°C, the reverse reaction to Eq. 4 is important; including it can explain the observed reaction order of 1.67. (Because the reaction order at 37°C, 1.27 ± 0.14, may be significantly greater than unity, this reaction may also be important at 37°C, but less so.) The oxygen-measurement technique also showed its utility in more complicated systems, in which both glucose oxidation and hydrogen peroxide decomposition occurred, or in which there was intracellular as well as extracellular oxidation of glucose. In particular, we showed that the glucose-oxygen ratio for intracellular oxidation was essentially the same as for extracellular (glucose oxidase-catalyzed) oxidation.