Tài liệu Báo cáo khoa học: Mechanism of protection of peroxidase activity by oscillatory dynamics docx

Mechanism of protection of peroxidase activity by oscillatory dynamics Lars F. Olsen 1,2 , Marcus J. B. Hauser 3 and Ursula Kummer 1 1 European Media Laboratory, Heidelberg, Germany; 2 CelCom, Institute of Biochemistry and Molecular Biology, Syddansk Universitet, Odense, Denmark; 3 Institut fu ¨ r Experimentelle Physik, Abteilung Biophysik, Otto-von-Guericke Universita ¨ t, Magdeburg, Germany The peroxidase–oxidase reaction is known to involve react- ive oxygen species as intermediates. These intermediates inactivate many types of biomolecules, including peroxidase itself. Previously, we have shown that oscillatory dynamics in the peroxidase–oxidase reaction seem to protect the enzyme from inactivation. It was suggested that this is due to a lower average concentration of reactive oxygen species in the oscillatory state compared to the steady state. Here, we studied the peroxidase–oxidase reaction with either 4-hydroxybenzoic acid or melatonin as cofactors. We show that the protective effect of oscillatory dynamics is present in both cases. We also found that the enzyme degradation depends on the concentration of the cofactor and on the pH of the reaction mixture. We simulated the oscillatory beha- viour, including the oscillation/steady state bistability observed experimentally, using a detailed reaction scheme. The computational results confirm the hypothesis that pro- tection is due to lower average concentrations of superoxide radical during oscillations. They also show that the shape of the oscillations changes with increasing cofactor concentra- tion resulting in a further decrease in the average concen- tration of radicals. We therefore hypothesize that the protective effect of oscillatory dynamics is a general effect in this system. Keywords: peroxidase; superoxide radical; hydrogen per- oxide; oscillations; enzyme degradation. Within the last 30 years the number of reports on oscillating biochemical processes has grown considerably [1]. From the first observations of oscillations in glycolysis in yeast and muscle cells [2,3] through measurements of oscillations in secondary messengers such as cyclic AMP [4] and cytosolic Ca 2+ [5] to recent observations of oscillations in intracel- lular NAD(P)H, pH, hydrogen peroxide, and superoxide in migrating neutrophils [6,7] we are beginning to understand that temporal behaviours, that is dynamics, play important roles in cell metabolism. Thus, it might be appropriate to suggest that in addition to its genome and proteome a given cell should also be characterized by the diversity of its dynamic behaviours. In spite of their universal occurrence the functions of metabolic oscillations in cells are still not well understood. It is not certain whether some biochemical oscillations occur as harmless side-effects of the nonlinear properties of metabolic enzymes or whether they always serve one or more important functions. Over the years many different roles have been proposed for oscillations. It has been suggested that they provide metabolism with an increased thermodynamic efficiency [8]. Furthermore, oscillations, e.g. those of second messengers such as calcium ions, are believed to have information stored in their frequency [9]. Roles as biological time-keepers [1] and encoders of transmembrane signalling have also been proposed [10]. Presumably, oscillations serve many functions in cell metabolism. Here we wish to explore further another potential role of oscillating biochemical processes, namely the protection of proteins against otherwise harmful substances such as reactive oxygen species that are produced during cell metabolism or cell signalling. This idea is not new; it has already been speculated that oscillations in cytosolic calcium were originally meant to prevent the precipitation of calcium phosphates in cytoplasm [11]. However, this hypothesis has, to our knowledge, never been verified experimentally. Nevertheless, in a recent article [12] we have demonstrated experimentally and by computer simulations that oscillations may protect an enzyme from catalyzing its self-destruction by free radicals produced during the catalytic cycle. The peroxidase–oxidase reaction entails the oxidation of an organic electron donor (typically NADH) by molecular oxygen [13]: 2 NADH þ O 2 þ 2H þ ! 2 NAD þ þ 2H 2 O ð1Þ catalyzed by peroxidase. When NADH and O 2 are supplied continuously to a stirred aqueous solution with a pH between 5 and 6.5 containing peroxidase, a suitable aromatic compound and methylene blue, the reaction starts to oscillate [14,15]. During the reaction hydrogen peroxide and superoxide are formed as intermediates [13]. Correspondence to L. F. Olsen, CelCom, Institute of Biochemistry and Molecular Biology, Syddansk Universitet, Campusvej 55, DK5230 Odense M, Denmark. Fax: + 45 65502467, Tel.: + 45 65502482, E-mail: lfo@bmb.sdu.dk Enzyme: horseradish peroxidase (EC 1.11.1.7) Note: The mathematical model described here has been submitted to the Online Cellular Systems Modelling Database and can be accessed free of charge at http://jjj.biochem.sun.ac.za/database/olsen/index.html (Received 6 February 2003, accepted 8 May 2003) Eur. J. Biochem. 270, 2796–2804 (2003) Ó FEBS 2003 doi:10.1046/j.1432-1033.2003.03655.x These reactive oxygen species were considered as unde- sired in cellular metabolism, because of their ability to oxidize a number of biochemical substances, such as enzymes and membrane lipids. For example, it has been shown that high concentrations of hydrogen peroxide can lead to the inactivation of peroxidase through reactions of H 2 O 2 with peroxidase compound I [16,17]. On the other hand, reactive oxygen species may also be useful to the organism. They are used by neutrophils and other phagocytic white blood cells to eliminate invading path- ogens, such as bacteria [18–20]. Recently, it has been shown that reactive oxygen species also seem to function as secondary messengers in certain cell signalling processes [7,21]. Thus, the cell faces the problem of handling a substance with both a beneficial and a harmful effect. While our previous study [12] was aimed at demonstrating the protective role of oscillatory dynamics, the present work concentrates on the mechanism of inactivation of theenzymebyfreeradicalintermediatesandtheroleof aromatic species in this mechanism. The mathematical model described here has been submitted to the Online Cellular Systems Modelling Database and can be accessed free of charge at http:// jjj.biochem.sun.ac.za/database/olsen/index.html. Experimental procedures Experiments were conducted as described previously [22,23] at 28 (± 0.1) °Cina2.0· 2.0 · 4.3 cm 3 quartz cuvette fitted with a thermostating jacket. The cuvette was connec- ted to a Zeiss S10 diode array spectrophotometer through optical fibers. Oxygen in the solution was measured with a Clark-type oxygen electrode (Microelectrodes Inc.). The reaction mixture consisted of an 8-mL well-stirred homo- genous aqueous solution containing 0.1 M sodium acetate, pH 4.5–5.8, 1.1–1.3 l M horseradish peroxidase (Boehringer Mannheim), 0.1 l M methylene blue (Merck), and 600– 900 l M 4-hydroxybenzoic acid or 50–300 l M melatonin (Aldrich, 99.5%). Entry of O 2 to the reaction mixture was from a 1.05% (v/v) O 2 /N 2 gas mixture supplied to the approximately 9 mL gas head space above the liquid. The rate of oxygen diffusion v O 2 into the liquid is given by the equation: v O 2 ¼ Kð½O 2  eq À½O 2 Þ ð2Þ where [O 2 ]and[O 2 ] eq are the actual oxygen concentration in the liquid and the oxygen concentration at equilibrium between the gas and the liquid, respectively. The oxygen transfer constant K depends on the surface area, the energy dissipation by the stirrer, and hence on the stirring rate. K was typically 3.5)6.0 · 10 )3 s )1 corresponding to stirring rates of 800–1000 r.p.m. NADH (Boehringer Mannheim) was supplied by infusion of a 0.1 M NADH solution into the reaction mixture through a capillary whose tip was below the surface of the liquid. The infusion was mediated by a Harvard Apparatus, model 22, syringe pump, and the infusion rate was typically 35 lLÆh )1 . We recorded the time series of the absorbencies in the range 350–600 nm (1 nm resolution) and the O 2 concentra- tion every 2 s, and stored the data on a computer for later analysis. Specifically, the absorbencies at wavelengths cor- responding to NADH (360 nm), ferric peroxidase (403 nm), compound III (418 nm), and ferrous peroxidase (439 nm) were used for spectral deconvolution of the absorbance measurements to concentrations of these four species [24]. Their concentrations were determined by solving the system of linear equations: A ¼ l  e  c ð3Þ where A is a vector containing the absorbencies at wave- lengths 360 nm, 403 nm, 418 nm and 439 nm, l is the length of the light path through the sample, e is a 4 · 4matrix containing the molar extinction coefficients of NADH, ferric peroxidase, ferrous peroxidase, and compound III at the four wavelengths and c is the vector of the concentrations of these four species. The molar extinction coefficients e used in the calculations of c have been measured previously [24]. Results The peroxidase–oxidase reaction shows a variety of dynamic behaviours depending on the reaction conditions [25]. The dynamics include stationary (nonoscillatory) and oscillatory states. In addition, the peroxidase–oxidase system is known to display bistability, that is, two different coexisting dynamic states are simultaneously stable for the same experimental parameters. Which of these dynamic states is approached depends on the ÔhistoryÕ ofthereaction system. Depending on how the experimental parameters inside a bistable domain are approached, the reaction may settle on either one of the two coexisting stable dynamic states. Experimentally this means that for exactlythe same experimental parameters and very similar initial conditions the reaction may converge on either one of the two stable dynamic regimes. Examples are (a) two coexisting steady states [26] and (b) a steady state coexisting with periodic oscillations [27]. Here we study the dynamics of the peroxidase–oxidase reaction under experimental conditions where the system settles either on an oscillatory or on a stationary (non- oscillatory) state [27]. This allows us to explore the inactivation of the enzyme when the reaction is either oscillating or stationary, while all other parameters, such as oxygen and NADH inflow, pH, temperature, etc., are the same. The graphs in Fig. 1A,B show time series of the concentration of O 2 for a typical experiment where the peroxidase–oxidase reaction is either in a stationary state or in an oscillatory state. The experiment is started by infusion of NADH into a solution equilibrated with O 2 in the gas phase and containing the enzyme and the two modifiers, 4-hydroxybenzoic acid and methylene blue. In Fig. 1A the oxygen concentration in the liquid reaches a stationary value of approximately 2.5 l M corresponding to a constant rate of oxidation of NADH. This rate remains essentially the same throughout the experiment, i.e. for more than 10000s.InFig.1Bweshowthetimeseriesof[O 2 ]foran experiment where the peroxidase–oxidase reaction is in an oscillatory state. It is worth emphasizing that the two experiments only differ in the dynamics shown by the peroxidase–oxidase reaction. The average rates of oxidation of NADH were shown to be the same [12]. We recorded the spectra of the enzyme during the nonoscillatory and the oscillatory states and some examples are shown in Fig. 1C,D, respectively. In Fig. 1C we show the spectra of the enzyme before the onset of the NADH inflow and 750 s Ó FEBS 2003 Protection of peroxidase activity (Eur. J. Biochem. 270) 2797 after starting the NADH inflow. The first spectrum has a peak at 403 nm and is typical for ferric peroxidase, while the latter is typical for compound III (oxyferrous peroxidase). Inspection of the spectra in the visible region (500–600 nm) showed no evidence for enzyme intermediates other than ferric peroxidase, ferrous peroxidase, and compound III. Figure 1D shows spectra of the enzyme at various phases of the oscillatory cycle. Again we observe no evidence for enzyme intermediates other than ferric peroxidase, ferrous peroxidase, and compound III. Furthermore, a phase plot where the concentration of ferric peroxidase is plotted against compound III defined an almost straight line, indicating that compound III and ferric peroxidase are by far the dominant species during the oscillations. Thus, we conclude that these three intermediates represent more than 90% of the total amount of enzyme present in the reaction mixture. In Fig. 1E we have plotted the sum of the concentrations of the three enzyme intermediates calculated from Fig. 1A,B. The sum of concentrations from the experiment showing steady state kinetics decreases at an almost constant rate. The rate of inactivation of the enzyme is calculated as 44.6 p M Æs )1 . The sum of concentrations from the experiment showing oscillatory kinetics also decreases, but at a much lower rate compared to the steady state experiment. The small periodic deviations from a smooth decline in concentrations, especially in the trace for oscilla- tory dynamics, is either an artifact due to inaccurate estimates of the extinction coefficients or they represent the oscillations in concentrations of compound I and compound II [24], which are two enzyme intermediates that are also believed to participate in the reaction. The rate of inactivation of the enzyme in the oscillatory state is calculated as 14.2 p M Æs )1 . We have conducted approximately 50 experiments showing oscillations and 50 experiments showing nonoscil- latory behaviour using different infusion rates of NADH and different stirring rates, corresponding to different oxygen transfer constants, to compare the rates of inacti- vation of the enzyme during oscillatory and nonoscillatory states. In all cases we found that, irrespective of the average concentrations of O 2 , NADH, and enzyme intermediates, the rate of inactivation of the enzyme is always significantly lower in an oscillatory state than in the corresponding nonoscillatory state. Previously we have shown that in experiments similar to those in Fig. 1 in which the peroxidase–oxidase reaction starts in a stationary state, but following a small random perturbation switches to an oscillatory state, the degradation of the enzyme slows down after the transition from the nonoscillatory to the oscillatory state [12]. Thus, oscillatory kinetics seem to protect the enzyme against degradation. Moreover, during experiments in which no reaction took place due to the absence of NADH,theenzymedidnotdegradeatall.Thesameapplies if we block the peroxidase–oxidase reaction by the addition of a small amount of hydroquinone [28]. In this case we observe an abrupt termination of the degradation of the enzyme [12], because the inhibition of the reaction also blocks the formation of free radicals [28]. Thus, the inactivation of the enzyme can be ascribed to the presence of reactive intermediates such as superoxide radical, hydro- gen peroxide and hydroxyl radical, which are generated during the reaction [13,29,30]. A further understanding of the mechanism for inactiva- tion of the enzyme may come from measurement of the effect of the concentration of the aromatic cofactor responsible for the onset of oscillations. Here we use the fact that melatonin (N-acetyl-5-methoxytryptamine), a hormone synthesized by the pineal gland, may also induce oscillatory behaviour in the peroxidase–oxidase reaction [31]. However, so far we have not been able to demonstrate the same oscillation/steady state bistability with melatonin as a cofactor. Figure 2 shows time series of NADH, O 2 , ferric peroxidase and compound III in the presence of 50 l M melatonin. We note that the oscillations stop after about 10 000 s. Further addition of melatonin to the reaction mixture did not result in a resumption of oscillatory dynamics. However, the addition of more enzyme did restart the oscillations. Increasing the initial amount of melatonin has the effect of prolonging the time over which oscillations are observed [31]. In addition, the rate of inactivation is slowed down by increasing the concentration Fig. 1. Bistability between a stationary state and oscillations in the peroxidase–oxidase reaction. (A,B) Time series of the concentration of oxygen during a stationary state and an oscillatory state, respectively. (C) Absorption spectra at time zero (dashed line) and at time 750 s (solid line) after the start of the experiment in (A). (D) Spectra at time zero (dashed line), at time 544 s (solid line), and at time 558 s (dotted line) after the start of the experiment in (B). (E) Total enzyme con- centration plotted against time. The sum of the concentrations of ferric peroxidase (Per 3+ ), ferrous peroxidase (Per 2+ ), and compound III from the experiments in (A and B) are plotted against time. Stationary state, (  ); oscillatory state, (.). The reaction mixture contained 1.2 l M peroxidase, 900 l M 4-hydroxybenzoic acid, and 0.2 l M methylenebluein8mLofa0.1 M sodium acetate buffer, pH 5.1. Oxygen in the solution was in equilibrium with a 1.05% (v/v) O 2 /N 2 gas phase. The experiment was started by infusion of 0.1 M NADH into the reaction mixture at a rate of 35 lLÆh )1 . The oxygen transfer constant was 5.5 · 10 )3 s )1 . 2798 L. F. Olsen et al.(Eur. J. Biochem. 270) Ó FEBS 2003 of melatonin, as illustrated in Fig. 3. Figure 3A shows time series of the total enzyme concentration in the presence of different concentrations of melatonin, while Fig. 3B shows a plot of the rate of enzyme inactivation against the melatonin concentration. It has been shown previously that melatonin is a powerful scavenger of oxygen and nitrogen- based reactive species such as hypochlorous acid [32], hydroxyl radical [33] and peroxynitrite [34]. Increasing the concentration of 4-hydroxybenzoic acid also resulted in a decrease in the rate of enzyme inactivation. However, when the reaction is in a stationary state, the concentration of the aromatic cofactor does not seem to have any effect on the rate of inactivation, i.e. the rate of inactivation is the same when the steady state rate of NADH consumption is the same, irrespective of the concentration of either melatonin or 4-hydroxybenzoic acid. We also investigated the effect of the pH on the enzyme inactivation. Figure 4 shows a plot of the rate of enzyme inactivation against pH. We note that the rate of inactiva- tion increases with decreasing pH. We were not able to measure the rate of inactivation by further decreases in pH, because other factors, such as increased autooxidation of NADH and other acid degradation of this substance [35], seemed to prevent the observation of long time intervals of oscillatory dynamics. Numerical simulations In order to understand the mechanism of protection better andtobeabletodepicttheroleofthearomaticcofactorin this scheme we performed numerical simulations using a new variant of a detailed model [36], which was shown to describe the peroxidase–oxidase reaction reasonably well. Unlike the original model [36], this variant considers the role of the aromatic cofactor in detail. In a previous study [12] we used the original model to simulate the peroxidase– oxidase system and showed that the average concentration Fig. 2. Time series of the concentrations of NADH, ferric peroxidase (Per 3+ ), compound III, and oxygen during an oscillatory state induced by melatonin. The reaction was performed in 0.1 M acetate buffer, pH 5.1. The reaction was started by infusion of NADH (flow rate 34 lLÆh )1 ) to a solution containing 1.2 l M peroxidase, 0.1 l M methylene blue and 50 l M melatonin. The oxygen transfer constant was 4.4 · 10 )3 s )1 . Fig. 3. Effect of the concentration of melatonin on the rate of enzyme decay during oscillatory states. (A) Time series of total enzyme con- centration in the presence of 50 l M , 100 l M and 200 l M melatonin as indicated in the fig- ure. (B) Rate of enzyme decay plotted against the concentration of melatonin. Other experi- mental conditions were as in the legend to Fig. 2. Fig. 4. Effect of pH on the rate of enzyme decay during an oscillatory state. The experiments were conducted in the presence of 300 l M melatonin. Other experimental conditions, except for the pH of the reaction mixture, were as in the legend to Fig. 2. Ó FEBS 2003 Protection of peroxidase activity (Eur. J. Biochem. 270) 2799 of superoxide radical was smaller in the oscillatory compared to the steady state. The modified model involves 12 different chemical species, including five enzyme inter- mediates, hydrogen peroxide and superoxide, as well as the aromatic cofactor and its radical form [37]. Thus, the complete model yields 11 nonlinear first order differential equations (because the aromatic cofactor is not consumed in the reaction [28,31] we need only one differential equation to describe the temporal change of both the reduced and the radical form). The elementary reactions of the model are listed in Table 1. Most of the rate constants listed in Table 1 have been determined experimentally [13]. For a proper set of rate constants, which correspond to the present experi- mental conditions, our model shows bistability similar to that of the experimental system, i.e. depending on the initial conditions the system either settles on a steady state (Fig. 1A) or on a periodic oscillation (Fig. 1B). Steady state concentrations as well as average and maximum concentrations of O 2 – during oscillations as functions of the NADH inflow rate are presented in Fig. 5. Similar to our results with the original model [12], the simulations reveal that although the maximum concentration of superoxide during oscillations is much higher than the values observed in a steady state, the average concentration of this species is several times lower during oscillations than during steady state conditions. In Fig. 6 we show the dependence of the Table 1. Detailed model of the peroxidase–oxidase reaction. Per 3+ and Per 2+ indicate iron(III) and iron(II) peroxidase, respectively. Enzyme intermediates compound I, compound II and compound III are represented as coI, coII and coIII, with ArH and Ar  indicating the aromatic compound (4-hydroxybenzoic acid or melatonin) and its free radical, respectively. Reaction R i Constant 1 NADH + O 2 +H + fi NAD + +H 2 O 2 k 1 [NADH][O 2 ] 3.0 a 2H 2 O 2 +Per 3+ fi coI k 2 [H 2 O 2 ][Per 3+ ] 1.8 · 10 7a 3 coI + ArH fi coII + Ar  k 3 [coI][ArH] 1.5 · 10 5a 4 coII + ArH fi Per 3+ +Ar  k 4 [coII][ArH] 5.2 · 10 3a 5 NAD • +O 2 fi NAD + +O 2 – k 5 [NAD  ][O 2 ] 2.0 · 10 7a 6O 2 – +Per 3+ fi coIII k 6 [O 2 – ][Per 3+ ] 1.7 · 10 7a 72O 2 – +2H + fi H 2 O 2 +O 2 k 7 [O 2 – ] 2 2.0 · 10 7a 8 coIII + NAD  fi coI + NAD + k 8 [coIII][NAD  ] 4.0 · 10 7a 9 2 NAD  fi NAD 2 k 9 [NAD  ] 2 6.0 · 10 7a 10 Per 3+ + NAD  fi Per 2+ + NAD + k 10 [Per 3+ ][NAD  ] 1.8 · 10 6a 11 Per 2+ +O 2 fi coIII k 11 [Per 2+ ][O 2 ] 1.0 · 10 5a 12 fi NADH k 12 Variable 13 O 2 (gas) fi O 2 (liquid) k 13 [O 2 ] eq 6.0 · 10 )3b,c )13 O 2 (liquid) fi O 2 (gas) k -13 [O 2 ] 6.0 · 10 )3b 14 Ar  + NADH fi ArH + NAD  k 14 [Ar  ][NADH] 7.0 · 10 5a a In M )1 Æs )1 . b In s )1 . c The value of [O 2 ] eq is 1.2 · 10 )5 M . Fig. 5. Predicted effect of the inflow rate of NADH (k 12 )onthemaxi- mum and the average superoxide concentration during oscillatory dynamics and the steady state concentration calculated using the model presented in Table 1. The initial concentration of oxygen was 12 l M and the total enzyme concentration was 1.4 l M , while the concentra- tion of the aromatic cofactor was 200 l M . All other initial concen- trations were zero, except for the initial concentration of H 2 O 2 which waseither0.7l M (resulting in steady state behaviour) or 0 l M (resulting in oscillatory behaviour). Fig. 6. Predicted effect of the concentration of the aromatic cofactor on the average superoxide concentration during oscillatory dynamics and the steady state concentration calculated using the model in Table 1. The initial concentration of oxygen was 12 l M and the total enzyme concentration was 1.4 l M , while the flow rate of NADH (k 12 ) was 0.08 l M Æs )1 . All other initial concentrations were zero, except for the initial concentration of H 2 O 2 which was either 0.7 l M (resulting in steady state behaviour) or 0 l M (resulting in oscillatory behaviour). 2800 L. F. Olsen et al.(Eur. J. Biochem. 270) Ó FEBS 2003 average concentration of superoxide during oscillations and the steady state concentration on increasing the concentra- tion of the aromatic cofactor. Note that the steady state concentration of superoxide is essentially independent of the concentration of the cofactor. The difference in steady state and mean oscillatory concentrations is more pronounced with increasing cofactor concentration because the shape of the oscillations changes and the peaks of superoxide radical concentration become higher and narrower (Fig. 7). In order to depict the origin of the lowered average concentration of superoxide during oscillations, we calcula- ted the average concentrations of all intermediates during oscillations and compared those with the respective steady state concentrations (Table 2). With the new detailed model and the parameters displayed in Table 1, the rate of production of NAD + is somewhat smaller during oscilla- tions compared to the steady state. Therefore, for a better comparison with the experimental data, we increased the infusion rate of NADH to obtain a higher rate of production of NAD + (Table 2, osc*). Comparing the two oscillatory states (Table 2, osc and osc*) to the steady state reveals that most of the average concentrations of the intermediates differ. Again, it can be seen that the average concentration of superoxide (the likely reason for the stability of the enzyme during oscillations) is several fold lower during oscillations, even if the production of NAD + is the same. It is also worth pointing out here that the concentrations of hydrogen peroxide and compound I are very similar in the oscillatory states and the steady state, suggesting that the inactivation of the enzyme cannot occur through reaction of hydrogen peroxide with compound I [16,17]. Trying to depict the reason for the decreased superoxide concentration, a somewhat naive approach would be to analyse the rates for the formation and decomposition of superoxide in the system. Superoxide is formed via reaction 5 and decomposed via reactions 6 and 7. The rate of formation depends on the concentration of NAD  and oxygen and it is clear that this should be somewhat higher during oscillations because of the increased concentration of NAD  . On the other hand the rate of superoxide decom- position via reaction 7 only depends on the superoxide concentration, and the rate of decomposition via reaction 6 will be much higher during oscillations due to the higher concentration of the native enzyme (Per 3+ ). So, one could conclude that the increased concentration of native enzyme is the reason for the decrease in superoxide concentration during oscillations. Now, of course, one would have to continue with this analysis and look for the reasons for the increased concen- tration of Per 3+ . This enzyme species is formed via reaction 4. The rate of this reaction hardly changes (when comparing oscillatory to steady state dynamics) due to the very similar concentrations of compound II and the aromate. The consumption of Per 3+ occurs via reactions 2, 6, and 10. The rates of reactions 2 and 6 should be smaller during oscillations, while the rate of reaction 10 should be somewhat higher. Reaction 6 shows the strongest change and therefore, should be mainly responsible for the observed effect. The rate of this reaction is determined by the concentrations of superoxide and the enzyme peroxidase. Therefore, this kind of analysis takes us back to the beginning, namely the reduced concentration of superoxide radical. It is obvious that this analysis does not really help in understanding the origin of the phenomenon. The reason is of course that the changes in concentrations are inherent to the reaction system (i.e. they depend on the entire network of elementary reactions) rather than properties of the Fig. 7. Time series of the concentration of superoxide computed using the model in Table 1. The initial concentration of oxygen was 12 l M and the total enzyme concentration was 1.4 l M , while the concentra- tion of the aromatic cofactor was (A) 100 l M and (B) 500 l M .All other initial concentrations were zero. The flow rate of NADH (k 12 ) was 0.08 l M Æs )1 . Table 2. Average concentrations of the reactants in lmolÆL -1 .The values were computed for a time series of 7000 s. ss, Steady state solution; osc, oscillatory solution. For the products NAD + and NAD 2 dimers, end concentrations instead of average concentrations were computed. The inital concentration of melatonin was 300 l M ,k 12 was 0.08 l M Æs )1 for the entries ss and osc, while it was set to 0.12 l M Æs )1 for osc*. This was done to obtain a similar rate of production of NAD + in the ss and osc* sets. Reactant ss osc osc* NADH 0.95 79.8 161.8 O 2 5.33 6.85 5.41 Per 3+ 0.059 0.6 0.6 Per 2+ 1.0 · 10 )4 0.012 0.019 NAD  5.0 · 10 )4 9.0 · 10 )4 1.4 · 10 )3 O 2 – 0.026 8.6 · 10 )4 9.5 · 10 )3 co I 8.9 · 10 )4 7.1 · 10 )4 9.1 · 10 )4 co II 0.026 0.020 0.026 compound III 1.31 0.77 0.75 H 2 O 2 0.013 0.009 0.008 ArH 299.88 299.99 299.99 Ar  0.12 0.0011 9.0 · 10 )4 NAD + 558 435 560 NAD 2 0.12 10.73 16.05 Ó FEBS 2003 Protection of peroxidase activity (Eur. J. Biochem. 270) 2801 individual reactions. In other words, this systemic property cannot be reduced to the effect of a single reaction (or to a subset of the reaction network). One interesting result of this analysis is the observation of an approximately 100-fold increase in the production of the NAD dimer (NAD 2 ) during an oscillatory reaction as compared to a reaction in steady state (Table 2). There are only three other species in the system which change their concentrations in a similar dramatic way, two of which are the intermediates Ar  and Per 2+ . The 100-fold increased production of a certain minor product in a reaction pathway corresponds to a switching between different production lines. This can be very useful in responding to different environmental conditions within seconds, rather than waiting for different gene expression, for example. In summary, the bistability allows the system to switch between two states which have similar production rates of the main product NAD + while maintaining, for example, two completely different levels of NADH (although this effect is much more pronounced in the simulations compared to experiments). Furthermore, the production of side products can be switched on while intermediates like the superoxide radical are maintained at very low concen- trations stabilizing the enzyme. Thus, our simulations strongly support our initial hypo- thesis that the explanation for the increased degradation of the enzyme in the steady state is the higher average concentration of toxic reaction intermediates. Discussion We have demonstrated experimentally that oscillatory dynamics seem to protect peroxidases from inactivation. Our simulations corroborate our earlier suggestion [12] that this is because the average concentrations of reactive oxygen species are much lower during oscillatory conditions than during steady state conditions. The inactivation of peroxi- dase does not seem to involve P670 [29,38] as we were unable to find spectral evidence for the formation of this species. Therefore, we suggest that the inactivation occurs through unspecific reactions of reactive oxygen species with amino acid side chains and possible also sugar residues of peroxidase [39]. The exact species responsible for the inactivation cannot be determined here. It may be either superoxide (or rather its protonated form) or it could be the hydroxyl radical. The decrease in inactivation following increases in the concen- tration of melatonin, when the system is in an oscillatory state, could favour the hydroxyl radical, as melatonin is known to be a powerful scavenger of this radical species [33]. However, our numerical results suggest that the effect of an increase in melatonin concentration is simply due to a further reduction in the average concentration of super- oxide and other radical species. This result also explains the experimental observation that the concentration of the aro- matic cofactor does not seem to have an effect on the rate of inactivation when the system is in a steady state. The pH dependence of the inactivation does not reveal much more about the mechanism of the inactivation. Nevertheless, the fact that the inactivation rate increases rapidly below pH 5 is consistent with the above-described mechanism. The protonated form of superoxide radical has a pK of 4.8 [40] and forms hydroxyl radicals according to the following equation [20,40]: HO  2 þ H 2 O 2 ! OH  þ H 2 O þ O 2 ð4Þ Therefore, a decrease in pH will lead to more hydroxyl radicals and more inactivation due to those. This observation is also consistent with previous results [41], showing that the production of OH  , catalyzed by peroxidase in the presence of NADH, increases with decreasing pH. The mechanism responsible for the production of hydroxyl radical is believed to involve compound III [41]. Hydroxyl radicals are normally not assumed to play a crucial role in the dynamics of the peroxidase–oxidase reaction [13], and therefore they do not appear in most detailed models of the reaction. The pronounced dependence of the stability of the enzyme against inactivation on the type of dynamics (i.e. whether the reaction system shows oscillatory or steady state behaviour) is mainly due to the lower superoxide concentrations found in the oscillatory state. The search for the source of such differences in the superoxide concentra- tion levels have shown that the value of the concentration of superoxide (as well as that of other intermediates) is clearly determined by the entire reaction network rather than by some individual reactions of the network. Hence, the mechanism responsible for the differences in the concentra- tion of this key intermediate is a systemic property that is encoded in the underlying reaction network. We believe that our finding that oscillatory dynamics seem to protect enzymes from inactivation by toxic reaction intermediates is important for the function of peroxidases in vivo. An example is the killing of microorganisms in pathogen-defence mechanisms of neutrophils and other phagocytic white blood cells. The dominating protein in neutrophils is myeloperoxidase [42] and several of these cells also synthesize melatonin [43]. Furthermore, the pH inside the phagocytic vacuole (phagosome) is between 4 and 6 [44], which should favour an oscillating peroxidase–oxidase reaction. Computer simulations of a model of the peroxi- dase–oxidase reaction involving myeloperoxidase predict oscillations in NADPH, oxygen, and reactive oxygen species in neutrophils [45]. This model is a two-compart- ment model and uses the fact that NADPH is formed in the cytosol through the pentose phosphate shunt, while peroxi- dase is situated in the phagosome. Other reactants diffuse across the phagosome membrane. One potential function of such oscillations could be to protect the machinery producing reactive oxygen species against self-destruction. For example, hydroxyl radicals react very fast with certain lipids, proteins and DNA [39,46]. Peroxidases, on the other hand, do not react very fast with the free radicals whose formation they catalyze, and hence the enzyme will decay very slowly under oscillatory conditions. Contrary to this, lipid oxidation and structural changes in DNA may require only brief time intervals of high concentrations of reactive oxygen species. As we have shown here by experiments and simulations oscillatory dynamics offer exactly such conditions. Oscillations in enzymatic systems may also serve another biological function, provided that the dynamic system allows for a bistable regime. Here, the system can switch on or off the production of minor products (in this case the dimeric NAD 2 ) without delay, therefore 2802 L. F. Olsen et al.(Eur. J. Biochem. 270) Ó FEBS 2003 responding immediately to changes in the environmental conditions. To summarize, we have shown that oscillatory dynamics in the peroxidase–oxidase system may serve different physiological purposes, in addition to a role in being associated with signal transduction pathways. 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