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:
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 />(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. These ÔnewÕ
roles are firstly the protection of the peroxidase activity
against inactivation by reactive reaction intermediates, and
secondly the possibility to act as a tool for rapid adaptation
to changing conditions by inducing immediate changes
between two reaction pathways, without requiring any

involvement of changes in the genetic expression.
Acknowledgements
LFO and UK wish to acknowledge the Klaus Tschira Foundation and
the Danish Natural Science Research Council, while MJBH thanks the
Deutsche Forschungsgemeinschaft, for financial support. The authors
should like to thank Anita Lunding, Torben Christensen, and Søren
Knudsen for valuable technical assistance and Mario Allegra of the
University of Palermo for stimulating discussions.
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