Relationship between the critical level of oxidative stresses and the glutathione peroxidase activity

Toxwology, 81 (1993) 89-101 Elsewer Scientific Pubhshers Ireland Ltd

89

Relationship between the critical level of oxidative stresses and the glutathione peroxidase activity Olivier Toussaint, Andr6e Houbion and Jos6 Remacle Laboratozre de blochimw cellulaire, Facult~s Umversttalres N -D de la Patx, Rue de Bruxelles, 61 B-5000 Namur ( Belgmm ) (Received May 15th, 1992, accepted February 28th, 1993)

Summary The production and removal of the various oxygen-derived free radicals is a dynamic and complex process which normally results m a steady state of very low concentrations of these reactwe molecules m the cell The mathematical modelhng of this process showed that any lowering of the glutathlone peroxldase actwlty will increase the steady state level of the hydroperoxldes and wdl decrease the level of organic peroxides necessary to destabdize the system. In this paper, we experimentally tested th~s relationship by the est~maUon of the level of peroxidaUve stresses which lead to cell degeneration m the presence of more or less actwe selenmm-dependent glutathlone peroxidase (GPX) The enzyme was inhibited by mercaptosuccmate (MS) and the cells were submitted to various extents of oxldatwe stress usmg tertbutylhydroperoxlde (TBHP). Crmcal levels of this peroxldatlve molecule could be determined by the deternunation of the concentration leading to 50% cell death. A relationship between this crmcal level of TBHP and the GPX acuwty was estabhshed The crmcal level strongly decreased with the mh~bmon of GPX and was found to be zero when 44% of the GPX acuwty is inhibited Presented in this way, the results clearly show the pattern of the reverse relationship between the susceptlbdlty of the cell to oxldatwe stress and the GPX actwity.

Key words Glutathlone peroxldase, Peroxldatlve stress, tert-butylhydroperoxlde, Anuoxldant enzymes, Critical level

Introduction Organisms living in an aerobic environment are well protected against the various toxic free radical molecules mostly derived from molecular oxygen [1]. At the cellular level, the antioxidant system includes enzymes and non-enzymatic Correspondence to Olivler Toussamt, Laboratolre de blochmue cellulalre, Facult& Umversltalres N -D de la Paix, Rue de Bruxelles, 61 B-5000 Namur, Belgmm Abbrevtanons GPX, glutathlone peroxldase, MS, mercaptosuccmate, ROOH, hpld~c hydroperoxlde, ROO', peroxy radicals, TBHP, tert-butylhydroperoxJde 0300-483X/93/$06.00 © 1993 Elsevier Scientific Pubhshers Ireland Ltd Printed and Pubhshed m Ireland

90 molecules. These are, for instance, a-tocopherol, reduced glutathione [2] and ascorbic acid [3,4]. Antioxidant enzymes are the superoxide dlsmutases, catalase and the peroxidases. Superoxide dismutases (SODs) transform superoxide amons (O2 "t-)) into molecular oxygen and hydrogen peroxide (H202). Eukaryotic cells contain Cu Zn SOD in their cytoplasm and mitochondrial interspace and Mn SOD in the mitochondrial matrix [1]. Catalase detoxifies H202 into H20 and 02. It is located in the peroxisomes and the cytosol [5,6]. Catalase shares this property with peroxidases which can also reduce other lipid peroxides into their corresponding alcohol. Some of these peroxidases are glutathione-dependent and others glutathione-independent. Glutathione peroxidase (GPX) was the most studied and is found in the cytosol and in the mitochondrial matrix. Other enzymes play an indirect part in the antlox~dant pathway. Glutathione reductase reduces oxidized glutathione produced in part by the activity of glutathione peroxidase. Microinjection of the various antioxidant enzymes allowed a quanufication of their efficiency to protect against oxidative stress. Whatever the experimental conditions of the stress like hyperoxia or the presence of a xenobiotic molecule, gluthatione peroxidase was always more efficient than catalase and superoxide dismutase [7-10], the difference being in this latter case several orders of magnitude. The key role of GPX could also be observed using inhibition of the enzymes by antibodies [11] or by chemical inhibitors [8]. In cultivated human WI-38 fibroblasts, an inhibition of 20% of the GPX activity was enough to produce cell toxicity in cells maintained in normal atmosphere. Oxygen-derived free radicals are constantly produced in cells by a multitude of chemical or enzymatical reactions but as we have seen many protections also exist so that a steady state is obtained. A theoretical model was developed taking into account the principal reactions of free radical production and elimination [12]. The model also took into consideration the fact that superoxide dismutase and GPX could be inhibited by some free radical species [13]. In such a model, the equations of the steady state of the free radicals could be obtained as being the sum of the rate of production minus the rate of elimination. The resolution of this theoretical model showed that the system is normally stable but that an unstable domain exists which strongly depends on the level of the GPX activity and of the free radical concentrations. The level of superoxide dismutase does not lead to any destabilisation effect while inhibition of catalase will reinforce the negative effect of the GPX inhibition. One prediction of the theoretical model is that the level of oxidative stress leading to an unstable domain decreases with the lowering of the GPX activity until a critical point below which the system is anyway unstable. In this paper, we wanted to experimentally test if such a relationship existed and what could be the experimental relationship between the GPX activity and the hydroperoxide concentration necessary to lead to an unstable process. For these experiments, we used human pulmonar foetal fibroblasts WI-38 and estimated their susceptibility to the presence of TBHP by the estimation of the critical level of peroxide toxicity. This molecule has already been used to submit different cell types to oxidative stresses, e.g. human erythrocytes [14-17], rat hepatocytes [18-22], rat alveolar macrophages [23], mouse fibroblasts [24], hamster lung fibroblasts [25,26] and rabbit sinoatrial node [27].

91 The determination of the critical level of ROOH toxicity was then obtained m cells in which the GPX had been partially inhibited by MS. We could in this way determine the relationship existing between the level of GPX activity and the critical level of peroxidative stress. Materials and methods

Cell culture Human WI-38 fibroblasts were purchased from the American Type Culture Collection and serially cultivated as described by Hayflick [28]. At population doubling levels between 28 and 40, they were subcultivated in a squared Petri dish (Falcon, Becton Dickinson and Company, Oxnard, CA) at a density of 300 cells/cm 2 in Eagle medium (Gibco, UK) supplemented with 10% foetal serum and incubated for 1 day at 37°C under normal atmosphere containing 5% CO2.

Stress under tert-butylhydroperoxide After 1 day of incubation in normal conditions, cells were exposed to a buffered solution (phosphate buffer saline, pH 7.4) containing different concentrations of TBHP (Aldrich Chemicals, Belgium) during times ranging from 2 to 20 min at room temperature. Flasks were then rinsed twice with phosphate buffer saline (pH 7.4) and new medium was provided. Cells attached to the flask were counted individually every day and considered as surviving cells. This method of cell counting was assessed as described earlier [29] using the dye exclusion test of viabihty with orange acridine-ethidlum bromide [30]. The same stress under TBHP was achieved after partial inhibition of GPX with MS (Janssen Chimica, Beerse, Belgium). MS, a specific competitive inhibitor of GPX, was diluted in the stressing solutions. Mercaptosuccinate competes with glutathione during the enzymic cycle by reacting with the selenocysteine present in the active site, giving a thioselenate which inhibits the enzyme [31]. The results were expressed as percentages of surviving cells calculated as follows. First, the number of cells counted every day after the stress was divided by the number of cells present before the corresponding peroxldative stress. This ratio obtained for stressed cells was then divided by the ratio obtained for control cells at the same day after the stress. This calculation takes into account the growth rate of the cell which can slightly vary according to the passage number of the culture Results

Toxicity of tert-butylhydroperoxtde Tert-butylhydroperoxide toxicity was assayed by measuring the percentages of surviving cells after incubation for various periods of time and in the presence of various concentrations of the molecule ranging from 1 mM to 50 mM for 2-20 min Figure 1 gives the percentages of surviving cells 2 days after the stress. The data clearly show that cell loss was correlated with the level of the stress and it was concentration and time-dependent. In order to take into account these two parameters, we calculated a critical value as the product of the molar concentration

92 I00

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~ 60 y40 2O

,001

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TBHP concentrat,on (M) Fig 1 Effect of various concentrations of T B H P on the survwal of h u m a n W1-38 fibroblasts for mcubaUon time of 2 nun (11), 5 m m (D'), 15 mln (@) and 20 mln (O) Results are expressed as percentages of cells survwmg 2 days after the stress under TBHP The results are expressed as percentages of survwmg cells calculated by reference to the number of cells present each day m the control culture (see Materials and Methods)

of TBHP multiplied by the time of incubation which gives 50% of cell survival. These concentrations were estimated by a linear regression between the two experimental values surrounding the 50% values. Those estimated values are reported on Fig. 2 and an inverse relationship betweeen the incubation time and the TBHP concentration is obtained. The critical values for 50% survival calculated from these 4 experi-

0,010 o

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t,me (m,n) Fig 2 Relat,onshlp between the T B H P concentrauons (M) and the incubation times (mm) of the stress which leads to a decrease of 50% of the cell number two days after the stress These data were calculated from results presented m F~g. 1.

93

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=

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~_.8o 10-7 M MS Q)

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i

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i

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2

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Fig 3. Effect of MS on the survival of h u m a n WI-38 fibroblasts. Cells were cultivated for 4 days with various concentrations of MS (10 -8 M (A), 10 -7 M (1),10 -6 M (Q), 10 -5 M (@) and 10 -4 M (O). The resuits are expressed as percentages of survwmg ceils calculated by reference to the number of cells present each day in the control culture (see Materials and Methods).

mental values were very close to each other with a mean value of 0.021 ± 0.001 M. min. This similarity indicates that the level o f the stress is directly time and concentration related. All these data are based on observations made 2 days after the stress. If observed 3 days after, the critical value obtained was identical:

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175

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Fig 4 Effect of MS on the survival of h u m a n W-38 fibroblasts. Cells were cultivated for 4 days m the presence of various concentrations of MS (10 -8 M (&), 10 -7 M (11), l0 -6 M (El), l0 -5 M (@) and l0 -4 M (O) Control (small &) In this figure, the percentages of surviving cells represent the number of cells in the test the number of cells are divided by the number of cells present at day zero

94 I00(

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Fig. 5. Effect of TBHP 50 mM alone (O) and m the presence of MS 10-8 M (Ilk 10-7 M ( ~ and 10-5 M (0) on the survival of human WI-38 fibroblasts. The results are expressed as percentages of surviving cells calculated by reference to the number of cells present each day m the control culture (see Materials and methods)

0.021 ± 0.005 M.min. The value after 1 day was higher with a mean value of 0.100 ± 0.011 M . m i n which indicates that the influence of the stress on cell death was still going on 1 day after the stress.

Effects of GPX inhibttion by MS on cell survival Mercaptosuccinate is a strong inhibitor of GPX activity and in this way can be detrimental for the cell. Figure 3 shows a Ume curve of cell survival in the presence of various concentrations of MS. A reduction of 50% of the cells is observed within 4 days at 10 -5 M MS and within 2 days at 10 -4 M. The reduction of cell numbers is mainly the result of a reduction in the rate of cell proliferation except for the 'highest concentration which showed a toxic effect 1 day after the stress. This dual effect is better observed when the number of surviving cells is expressed in percentage of the cell number compared to the begmnmg of the experiment (Fig. 4). Previous reports of Michiels and Remacle [8] showed that complete inhibition of purified GPX could be obtained with 5 × 10 -5 M MS. The MS effect obtained here on cultivated fibroblasts is in the same range (10-5-10 -4 M) and is thus well explained by the inhibitory effect of this chemical on the GPX.

Effect of GPX mhtbltion by MS on cell survival in the presence of TBHP The effect of various concentrations of MS on cell survival was first tested in the presence of a high 50 mM concentration of TBHP incubated for various periods of time (Fig. 5). The cell survival was obtained by counting the cells 1 day after the stress because of the high toxicity of these conditions. Tert-butylhydroperoxide alone already had a strong toxic effect with only 50 to 35% cell survival depending on the duration of the stress. However, ad&tlon of MS at 10 -5 M, 10 -7 M and 10 -8

95 TABLE I SYNERGISTIC TOXIC EFFECT OF TBHP AND MS The values presented in this Table are calculated from the experiment presented in Fig 5 The cell loss observed 1 day after the stress with TBHP at 50 mM alone and with MS alone have been deduced from the cell loss observed 1 day after the stress with TBHP and MS incubated together with the cells All these results were expressed as percentages of surviving cells calculated by reference to the number of cells present each day m the control culture (see Materials and methods). The table also mentions the GPX mhabltion obtained by Mlchlels and Remacle [8] from the same WI-38 cells cultwated m the same condmons for the three MS concentrations MS concentration (M)

0 10-8 10-7 10-5

% of GPX mhlbmon

Synergistic effect of TBHP and MS on cell loss (%) for various mcubauon times under TBHP 50 mM (mm)

0 5 25 40

2 mm

7 mm

15 mm

20 mm

0 -5 7 18

0 19 12 20

0 34 18 14

0 32 11 14

M e n h a n c e d t h e t o x i c effect. S u c h c o n c e n t r a t i o n s o f M S h a v e b e e n f o u n d t o give, r e s p e c t i v e l y 40%, 2 5 % a n d 5 % i n h i b i t i o n o f G P X i n t h e s a m e e x p e r i m e n t a l c o n d i t i o n s [8]. A t 10 -8 M M S , t h e e f f e c t w a s s t r o n g l y d e p e n d e n t w i t h n o s i g n i f i c a n t diff e r e n c e t o T B H P a l o n e a t 2 m i n b u t w i t h a s y n e r g i s t i c effect o b s e r v e d a t 7 r a i n a n d longer incubation periods. I n T a b l e I, w e c a l c u l a t e f r o m t h e s e d a t a t h e s y n e r g i s t i c t o x i c i t y o f b o t h m o l e c u l e s b y s u b s t r a c t i n g t h e a m o u n t o f cell loss o b s e r v e d in t h e p r e s e n c e o f b o t h m o l e c u l e s from the amount found for each one separated. Except for the 2 min incubation with

TABLE II SYNERGISTIC TOXIC EFFECT OF TBHP AND MS The cell loss observed l day after the stress with TBHP at 5 mM alone and with MS alone have been deduced from the cell loss observed l day after the stress with TBHP and MS incubated together with the cells. All these results were expressed as percentages of survwmg cells calculated by reference to the number of cells present each day in the control culture (see Materials and methods) MS concentrations (M)

Synergistic cell loss of TBHP and MS on cell loss (%) for various lncubaUon times under TBHP 5 mM (nun) 2 mln

0 10-7 10-s

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0 1

0 7

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20 mln

0 14 27

0 19 39 5

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0,02 0,03 0,04 TBHP concentration (M)

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Fig 6 Effect of TBHP 5 mM, 10 mM, 20 mM and 50 mM m the presence of MS 10-5 M (@) and 10-7 M (O) on the survival of human WI-38 fibroblasts. The stress was performed for 2 mm and the results are expressed as percentages of surviving ceils 1 day after the incubation calculated by reference to the number of cells present at day 1 m the control culture (see Materials and methods) and plotted against TBHP concentraUons (M)

M S at 10 -8 M f o r w h i c h n o synergistic t o x i c i t y is o b s e r v e d , all the o t h e r c o m b i n a t i o n s i n v o l v e a synergistic toxicity. T h i s is specially t r u e f o r the l o w e s t 10 -8 M c o n c e n t r a t i o n o f M S w h i c h a l o n e is n o t t o x i c a f t e r 1 d a y (100.9% ± 4.7 o f t h e c o n t r o l ) as o b s e r v e d in Fig. 4 b u t w h e n c o m b i n e d w i t h T B H P s t r o n g l y increases its toxic effect. Since the synergistic effect s e e m s to be m o r e i m p o r t a n t at l o w c o n c e n t r a t i o n s , we tested, in the s a m e m a n n e r , the effect o f M S at the l o w 5 m M T B H P c o n c e n t r a t i o n . T a b l e II s u m m a r i z e s the data. T h e synergistic t o x i c i t y o f T B H P by M S a l r e a d y o b s e r v e d at a h i g h T B H P c o n c e n t r a t i o n is c o n f i r m e d a n d this effect is also clearly t i m e - d e p e n d e n t as a l r e a d y n o t i c e d f o r the l o w 10 -8 M c o n c e n t r a t i o n in T a b l e I. T h e

TABLE IIl CRITICAL VALUES OBTAINED AT DAY l AFTER A 2-mm STRESS UNDER TBHP 5 mM OR 50 mM WITH AND WITHOUT MS l0 -5 M AND l0 -7 M The critical values are the products of the molar TBHP concentrauon by the Ume of lncubaUon which gwes a 50% cell loss compared to the control The calculation was performed from data shown m Fig 6. MS concentrauon (M)

% of GPX lnhlbmon

Crmcal TBHP value (M.mm) at day 1 after the stress

Decrease of the crmcal value (%)

0 10-7 10-5

0 25 40

0 100 0 040 0 016

60 84

97 combined TBHP and MS effect is clearly shown in Fig. 6 which confirmed the dependency of the toxic effect on both molecules. From this figure, we calculated the experimental conditions for which 50% of the cells are lost. These data are reported in Table III in terms of critical values of TBHP concentration. These critical values were 0.040 and 0.016 M.min, respectively, for MS present at 10 -7 M and 10 -5 M compared to the 0.100 M. min without MS. Such a reduction of 60 and 84% of these critical values represents the increased susceptibility of cells to TBHP due to the inhibition of GPX by MS. Discussion Lipidic hydroperoxides are formed in living cells by lipid peroxidation which depends on the formation of oxygen-derived free radicals by multiple sources like oxidative stresses, enzymatic reactions or xenobiotics. TBHP is an amphiphilic molecule which penetrates easily into the erythrocytes and mimics the toxic effect of peroxidized fatty acids. Peroxy radicals can be generated from TBHP in the cytosol by its interaction with ferrous iron in a reaction similar to the Fenton reaction [16]. Beside its toxicity due to free radical damages, TBHP is also an inhibitor of GPX [13,26] and its presence in the cells lowers the amount of glutathione [20]. Other toxic effects have also been reported like a lowering of the polarlsation of the inner mitochondrial membrane [32], an elevation of the intracytosolic Ca 2+, a release of mitochondrial Ca 2+, an inhibition of DNA synthesis and of mitosis [33] and the appearance of chromosomal alterations [26]. The efficiency of GPX in protecting the cell against free radical species has been very well documented by a series of experiments. For example a small increase of the GPX activity in the cell after microinjection of the enzyme was enough to protect human fibroblasts against oxidative stress caused by high oxygen tension or in the presence of nitrofurantoin. Similar protection was also obtained with catalase and superoxide dismutase but at higher concentrations [7,9]. The reasons for,such efficiency of GPX are diverse and have already been extensively reviewed [34]. Briefly, peroxides can be reduced even at low concentrations especially if the level of glutathione is high. GPX protects both the cytosol and the mitochondria against lipid-derived hydroperoxides but also against hydrogen peroxide. It removes the last products of the oxidative cascade and in this way can be considered as the last barrier against the free radical reactions. A mathematical model taking into account the main intracellular reactions of formation and elimination of free radicals was built in order to test for the stability of the system when the free radical production or the antloxidant level are changed. This model took also into account the inhibition of these enzymes by the various free radicals or derived molecules [12]. Some relevant conclusions for the experiments performed here could be obtained from this theoretical approach. First, a stable steady state of hydroperoxide and of peroxy radicals exists in the cell but if the concentration of these molecules increases too much, an unstable domain could be attained The separation between the stable and unstable domains is dependent on both molecule concentrations and is represented as a bifurcation point. Second, the phase plane, expressing the [ROOH]

98

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o,o~

O, O0 50

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. 60

.

. 70

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. 80

90

I

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ii0

GPX act,wty (% nat,ve act,wty)

Fig. 7. Relationship between the cntmal values of TBHP whmh lead to 50% cell loss and the acUvlty of GPX (data from Table III for MS 10-5 M, 10-7 M and 0 M and Fig. 5 for MS 10-8 M) The representation m based on the mathematmal model relating the GPX activity and the [ROOH] and obtained from the equations taking into account the formaUon and ehnunatlon of free radmals [12] The lower branch ( 0 ) represents the steady state concentration of ROOH m the cell. The upper branch (D) represents the highest concentraUon that a cell can afford given its GPX actwlty The four values of GPX actwlty taken into consideration correspond to the four cntmal values calculated from the data Respectwely, 0%, 5%, 25% and 40% mhlbRlon of GPX correspond to a critical value of 0.100 M. mm, 0 100 M. mm, 0 040 M. nun and 0.016 M. mm, which is the TBHP concentraUon × ume of incubauon gwlng 50% cell lost (M. mm) Thin value is represented as the distance between the upper and the lower branch of the bifurcation The blfureaUon point (CP for Crmcal Point or Crossover Point) gives the lowest GPX acnvlty for whmh the system m stdl stable and m esumated to correspond to 56% GPX acnwty. The 100o/oGPX activity represents the natwe GPX actiwty m the fibroblasts, m thin case 0 0178 U/mg protein [10] The absolute value of [ROOH] for the critical point m, however, not known so that the scale is given as relanve values

versus the G P X a c t i v i t y gives a b i f u r c a t i o n w i t h a l o w e r b r a n c h w h i c h i n d i c a t e s the s t e a d y state c o n c e n t r a t i o n o f R O O H p r e s e n t in the system for v a r i o u s G P X a c t i v i t y a n d w i t h the u p p e r b r a n c h w h i c h i n d i c a t e s the m a x i m a l f l u c t u a t i o n in the c o n c e n t r a t i o n o f R O O H t o l e r a t e d for t h e s a m e G P X activity. T h e c r o s s i n g - p o i n t b e t w e e n the u p p e r a n d the l o w e r b r a n c h o f the b i f u r c a t i o n is a critical p o i n t w h i c h r e p r e s e n t s the l o w e s t G P X a c t i v i t y f o r w h i c h t h e s y s t e m is u n s t a b l e in the p r e s e n c e o f a n y f l u c t u a t i o n in the s t e a d y state c o n c e n t r a t i o n o f R O O H . H o w e v e r , such a r e l a t i o n s h i p w a s o n l y t h e o r e t i c a l l y o b t a i n e d a n d n o e x p e r i m e n t a l d a t a w e r e a v a i l a b l e to test for its v a l i d i t y a n d for the c a l c u l a t i o n o f the critical point. I n this p a p e r , we clearly o b s e r v e d t h a t T B H P w a s t o x i c for the cells a n d this t o x i c i t y was c o n c e n t r a t i o n - a n d t i m e - d e p e n d e n t so t h a t the p a r a m e t e r w h i c h g a v e 50% cell loss was c a l c u l a t e d f r o m these t w o p a r a m e t e r s a n d was c o n s i d e r e d as a critical v a l u e o f toxicity. W h e n G P X was p a r t l y i n h i b i t e d , the sensitivity o f cells to the p r e s e n c e o f T B H P was s h a r p l y i n c r e a s e d w i t h a synergistic effect w h i c h was well o b s e r v e d w h e n the t o x i c i t y was n o t t o o p r o n o u n c e d ( T a b l e s I a n d II).

99 When the critical value of TBHP (cc × time) was calculated, a strong reduction of the TBHP critical value was found with a small inhibition of GPX in the presence of MS. Inhibition of 25% of the GPX activity observed with 10 -7 M MS gave a 60% reduction of the critical value while a 40% reduction with 10 -5 M MS gave an 84% reduction. These results allow to determine the shape of the curve showing the dependency between the affordable level of hydroperoxide in the cell and the level of GPX activity. The three values of Table III and one value of Fig. 5 were incorporated m the equation obtained from the theoretical model [12] and are represented in Fig. 7. Such a representation confirms the strong relationship between the GPX activity and the ROOH concentration which is able to destabilize the system. It also allows the estimation of the critical point which was found to be located at 56% of the GPX activity. Below this activity, cells will start to die even in normal conditions. This is exemplified in such a representation as a bifurcation point which shows the limit between the possibility of the system to exist in a stable manner. GPX is a key enzyme for protecting cells against hydroperoxide derivatives but also from more general oxidative stresses and any reduction or inhibition of its acnvity makes cells much more susceptible to such a stress. On the contrary increased activity, as obtained for example by injection of the enzyme in the cells, or in transfected cells [35] gwes a high protection to oxygen or oxygen-derived free radicals [7]. These findings showed that organic peroxides can destabilize the cellular antioxidant system when glutathione peromdase is partly inhibited. However, such a synergistic effect cannot be demonstrated when organic peroxides are replaced by hydrogen peroxide (H202) in concentranons which involved a similar cell death (data not shown); this synergistic effect is also specific of the glutathione peroxidase. The concomitant presence of H202 and the inhibition of catalase by amino-triazole (data not shown) or, the presence of 02" (-) and specific inhibition of superoxide dismutase by micromjected antibodies [11] do not lead to such a synergistic effect. These results are also in accordance with the mathematical model described here above. In this work, an estimation of the increase of the concentration bringing the system from a stable to the unstable domam was obtained. However, on a quantitative basis, we do not know the exact absolute concentration of such hydroperomdes in the cell in its stationary state so that the exact level of hydroperomde at the critical point is also not known. This work attempts a quantitative analysis of the dependency of the oxidative stress on GPX activity. Such studies are only possible with in vitro cultivated cells and they emphasize the need for the determination of the GPX activity when toxicity of oxidative stress is reported.

Acknowledgments O. Toussaint was a Research Assistant of the Fonds National de la Recherche Sc~entlfique, Belgium. This work was supported by a grant from the Fonds de la Recherche Fondamentale Collective, Belgmm and from the Belgian First Minister Service of Science Programme, Belgium. We thank Dr. D. Lambert for relevant discussions on the subject.

100

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