Simulation of Lipid Peroxidation in Low-Density Lipoprotein by a Basic

Chem. Res. Toxicol. 1995,8, 753-763

753

Simulation of Lipid Peroxidation in Low-Density Lipoprotein by a Basic "Skeleton"of Reactions Peter M. Abuja* and Hermann Esterbauer Institute of Biochemistry, University of Graz, Schubertstrasse 1,A-8010 Graz, Austria Received March 6, 1995@

A minimal kinetic model describing lipid peroxidation in low-density lipoprotein (LDL) has been set up. Models have been calculated by numeric integration of the differential equations describing this system consisting of seven reactions and eleven reactants in a single compartment. The model describes the usually observed behavior of the reaction system, showing that the crucial intermediate is the lipid peroxyl radical (LOO). During different stages of the reaction, depending on the presence of antioxidants (a-tocopherol), different pathways in the reaction scheme become active. Simulation also demonstrates that tocopherolmediated propagation can occur under certain conditions, i.e., a low rate of initiation. This, however, does not mean that tocopherol enhances lipid peroxidation in LDL, as without tocopherol the process would be much faster. Further extension of the basic model by inclusion of a hypothetical antioxidant leads to a model which is capable of describing Cu2+-induced LPO over the whole lag phase up to full propagation.

Introduction It is currently believed that oxidative modification of low-density lipoprotein (LDL)l plays an important role in the development of atherosclerosis (1,2).Considerable effort has, therefore, been put into the elucidation of the molecular mechanism of this process. Many studies suggest that oxidative modification of LDL is intimately linked to a lipid peroxidation (LPO)process taking place in the LDL particle. As such, LDL oxidation possesses the general characteristics of a lipid peroxidation chain reaction initiated and driven by free radicals. In vitro, oxidation can be initiated by cells, free radicals, and redox-active transition metal ions. Antioxidants and certain metal ion chelators inhibit or delay the process. When LDL is oxidized by radical generating substances such as AAPHl or AMVNl or by Cu2+ ions, three consecutive phases of the reaction can be observed in kinetic experiments by measuring compositional changes of LDL. Initially, LPO proceeds with a low rate because the antioxidants contained in LDL inhibit the chain reaction-this period is called the lag phase or lag time. As the antioxidants are used up, the propagation phase begins and the rate of LPO rapidly accelerates. This second phase is then followed by the decomposition phase where the lipid hydroperoxides formed break down to a wide range of products. In a simplified form the overall LPO process in LDL involves oxidation of lipids (LH) by molecular oxygen to lipid hydroperoxides (LOOH)which subsequently decompose: LH 0, LOOH decomposition products

+

-

-

The measurement of oxygen consumption and the measurement of lipid hydroperoxide formation are con-

* Author

to whom correspondence should be addressed. E-mail:

[email protected]. Abstract published in Advance ACS Abstracts, June I, 1995. Abbreviations: LDL, low-density lipoprotein; PUFA, polyunsaturated fatty acid; AAPH,2,2'-azobis(2-amidinopropanehydrochloride); AM",2,2'-azobis(2,4-dimethylvaleronitrile);LPO,lipid peroxidation; RMG. reactive methvlene ETOUD of a PUFA TMF'. tocoDhero1-mediated propagation; ODE, -ordinary differential 'equation; CD, conjugated dienes. @

venient methods to follow the overall lipid peroxidation process in LDL oxidation experiments (3). The lipid hydroperoxides contain conjugated double bonds, and therefore, their accumulation can be readily followed spectrophotometrically by recording the W absorption at 234 nm (4). The mechanistic interpretation of the overall LPO process measured by such conjugated diene vs time curves is rather difficult, mainly due to the involvement of free radical intermediates and the particle nature of LDL. Studies using simple model systems provided insight into the elementary reactions and the associated rate constants contributing to lipid peroxidation reactions. Such model systems comprise homogeneous solution (5-81, submicellar aqueous solution (9), liposomes (IO),and micellar systems (9, 11). We assume, therefore, that it should be possible to simulate the overall LPO process mathematically using a set of those elementary reactions. Besides reproducing the overall process of LPO in LDL, such simulations will provide insight into the elementary reactions and their interaction within LDL. Such an approach could also contribute to solve controversial issues such as the relative importance of antioxidants, the role of initiating radicals, and potential prooxidative effects of antioxidant radicals generated within LDL. Similar model systems have already been set up for lipid peroxidation in membrane systems, in particular the inner mitochondrial membrane (12-14). The purpose of this paper is first to set up a basic model for LPO in LDL that describes the overall process as usually observed in experiments where LDL is fully oxidized within several hours. The second goal is to examine the influence of the rate of initiation and the concentration of the major antioxidant a-tocopherol on the kinetics of the overall process and the elementary reactions. Third, by a slightly extended model we will examine the possibility of tocopherol-mediated propagation of the lipid-peroxidation chain reaction. This is currently an extremely important and controversial issue

Q893-228x/95l27Q8-Q753~Q9.QQ/Q 0 1995 American Chemical Society

Abuja and Esterbauer

754 Chem. Res. Toxicol., Vol. 8, No. 5, 1995

LOO

LOOH XH Figure 1. Schema of the reactions used to simulate lipid peroxidation in LDL. The numbering of the reactions is used throughout the paper. The TMP reaction 8 is included in this scheme although it is not part of the base model.

which also has clinical relevance for the use of high doses of vitamin E t o prevent LDL oxidation in vivo. Finally, we will demonstrate that inclusion of a hypothetical antioxidant in the base model can describe and account for the fact that in Cu2+-mediatedLDL oxidation the lag time usually extends beyond the lifetime of a-tocopherol.

Methodology Experimental Results Used To Set Up the Base Case. Initial Conditions. LDL is a spherical particle, the size of which varies with lipid content with an average diameter of 22 nm and an average volume of 5575 nm3. On average, it contains (wt %) 22.3% phospholipids, 5.9% triglycerides, 9.6% free cholesterol, 42.2% cholesterol esters, and 22% protein (2). The average content of polyunsaturated fatty acids (PUFA's) bound in the different lipid species is 1280 mol/mol of LDL, comprising linoleic acid (86%), arachidonic acid (12%),and docosahexaenoic acid (2%). Regarding reactive methylene groups (RMG), which constitute the oxidizable substrate in LDL, this results in 1100 RMG's from linoleic acid, 461 from arachidonic acid, and 128 from docosahexaenoic acid, in total 1689 RMG's. The major identified antioxidant components are tocopherol with an average value of 6.9 mol/mol of LDL (92% a-tocopherol, 8% y-tocopherol), carotenoids (-0.8 mol/mol of LDL), and ubiquinol-10 (-0.1-0.5 mol/mol of LDL). For the base model it is assumed that of these constituents only tocopherol and the PUFA's (LH) participate in the LPO process, where RMGs of PUFA's and PUFA-containing lipids are treated as one single species LH-in this paper PUFA, LH, and RMG are treated as synonyms. Reactions of ubiquinol, carotenoids, saturated and monounsaturated fatty acids, cholesterol, and the apolipoprotein B were deliberately excluded in order to keep the base case as simple as possible. Oxidation experiments are frequently carried out with an LDL concentration of 0.1 yM, which is equal to an apparent global concentration of -0.7 yM tocopherol and -130 pM PUFA's. The constituents of LDL are, however, tightly bound within the particle, and free diffusion via the aqueous phase is probably slow if not negligible. We therefore assume that all elementary reactions take place within the particle and exchange of any (e.g., radical) species occurs fast and by direct contact of LDL rather than via the aqueous surroundings. In that case local concentrations are effective and have to be used for a correct mechanistic description of the kinetics of the LPO process. Preliminary studies t o this paper showed that a correct

simulation in terms of global concentrations is not possible (data not shown). Based on the available data, two approaches were made to calculate local concentrations within the LDL particle: using a lipid content of 78 wt %, a density of -1.0 g and an average molecular mass of 2500 kDa together with the PUFA content, local concentrations of LH and tocopherol amount to 0.65 M and 3.5 x M, respectively (1 L of lipid phase corresponds to 513 pmol of LDL). Calculation based on total LDL volume resulted in values of 0.57 M for LH and 3.0 x M for tocopherol. In the base model we use an initial PUFA concentration of [LHIo = 0.6 M and an initial tocopherol concentration of [TocOHIo = 3 x M. Oxygen can freely diffise through lipid and aqueous phases, and it is assumed that its concentration in LDL is constant and similar to the oxygen concentration in the aqueous phase under atmospheric pressure: in the base case it is 1 x lo-* M. The initial concentrations of all other reactants are zero. Reaction Scheme, Reaction Equations, and Rate Constants. The reaction scheme we use to describe the base model of LDL oxidation is shown in Figure 1. The participating elementary reactions and the associatedrate constants are listed in Table 1. We will briefly describe the elementary reactions and the reason for selecting or assuming certain rates or rate constants. Reaction 1. This is an arbitrary reaction which feeds radicals X' with a constant rate 01 into the system. The assumption for the simulation of the base case is as follows: u1 M s-l. As will be shown, such a rate leads to = 2 x consumption of tocopherol (=lag time) and oxidation of half of the LDL PUFA's within 50 and 150 min, respectively. This is in the range of values observed in experiments where LDL was oxidized with AAF'H or Cu2+ions (2).Based on the volume of the LDL particle, it can be readily calculated that a 01 of 2 x 10-6 M ssl means that an LDL particle is hit by an initiating radical every 3.8 min. Reaction 2. The initiating radical x'abstracts a hydrogen atom from one of the PUFA's, yielding a carbon-centered lipid radical. The rate constant for this reaction depends, of course, on the nature of X' and therefore on the type of prooxidant under consideration. From the reaction scheme, it is, however, obvious that this reaction will not be rate-limiting as long as izz[LHl is much higher than 01. In the simulation, therefore, we chose an arbitrary value of kz = 3 M-I s-l. The hydrogen abstraction occurs a t the CH2 group of the pentadienyl system, and the generated free lipid radical b is resonance stabilized:

Simulation of Lipid Peroxidation in LDL reaction no. 1

2 3 4 5

6 7 8

Chem. Res. Toxicol., Vol. 8, No. 5, 1995 755

Table 1. Reactions and Rate Constants Used in the Model for Lipid Peroxidation in LDL' rate constant reaction (M-l s-l) revcomment XH-x' constant rate v1 (radical influx) = 2.0 x M s-l not rate-limiting; a value of 3.0 M-l s-l was used x'+LH-L' L' 0 2 -LOO' 3 x 108 ref 9 2LOO' NRP + 0 2 1 105 ref 5 LOO' LH LOOH L' 31 ref 14 1 x 106 ref 6 LOO' +TocOH LOOH TocO' LOO' + TocO'- NRP2 2.5 x lo6 ref 8 TocO' LH TocOH + L' 7 x 10-2 ref 7; this reaction is not included in the base case model

+

- + -

+

+

+

a Reaction 8 was not used in the base case model by setting K S = 0 M-' s-l. The initial concentrations used were [LHIo = 0.6 M, [TocOHlo = 3 x M; all other initial concentrations were 0. M, and [021const = 1 x

-

-

-CH=CHCHCH=CH-CHCH=CHCH=CH-CH=CHCH=CHCHThis resonance equilibrium is rapidly established and governs the pattern of isomeric lipid hydroperoxides (e.g., 13-hydroperoxy- and 9-hydroperoxylinoleicacid) yet not the overall rate of the process. Therefore, these reactions were not included in the simulation. Reaction 3. Oxygen adds rapidly to L',yielding a lipid peroxyl radical LOO'. In the simulation, the rate constant of 3 x lo8 M-l s-l obtained by Hasegawa and Patterson (9)is used. This reaction-and the oxygen concentration-are not ratelimiting. Babbs and Steiner (14)used a 30-fold lower rate constant for this reaction-which would not make the reaction rate-limiting, either. Reaction 4. This is a termination reaction which takes place when two LOO' recombine and give rise t o nonradical products NRP and oxygen. This reaction discovered by Russell (15) occurs via an intermediate tetroxide and yields one molecule of ketone in the ground or excited state, one secondary alcohol, and one molecule of oxygen in the singlet or triplet state. We use the value (kq = lo5 M-l s-l) reported by Barclay et al. (5). A value of kg = 3 x lo7 M-l s-l(9) is probably too high for LDL oxidation since simulation shows that such a value would largely prevent the formation of hydroperoxides and slow down propagation, which would not be consistent with experimental results. Reaction 5. In this chain propagation reaction, a hydrogen atom is abstracted from a LH by LOO', yielding lipid hydroperoxide (LOOH) and a new L' radical which can carry on the chain reaction via reaction 3. The rate constants measured by different groups for this important reaction are in very good agreement. We use in simulation the value reported and used by Babbs and Steiner (14)of K g = 31 M-l s-l. It is evident that the maximum rate of LOOH formation during propagation strongly depends on the value of this rate constant. Reaction 6. The LOO' radical is scavenged by tocopherol, yielding LOOH and a tocopheroxyl radical TocO'. This reaction, which has been studied in many systems, has a high rate constant k6 = 1 x lo6 M-' s-l, as found by Niki et al. (6). It is generally assumed that the TocO' radical is resonance stabilized and of low reactivity. Reaction 7. It is well documented that tocopherol scavenges two LOO' radicals with high rate constants, one as shown in reaction 6 and one in reaction 7. The nonradical product NRP2 formed in this reaction has recently been identified clearly as a peroxytocopherone (16). Reaction 8. This reaction is called "tocopherol-mediated propagation" (TMP). Although its rate constant (k8 = 7 x M-l s-l; 8 ) is low, it might be an important source of chain initiation by formation of L'under some circumstances such as low rate of initiation by x'. Reaction 8 is not included in the base case, but its influence on LDL oxidation will be analyzed separately. Mathematical Simulation. Based on the elementary reactions presented above (cf. also Figure 1,Table l), the changes in the concentrations of the reactants are expressed as ordinary first order differential equations (ODES). Numerical integration

was used to solve the set of ODESfor given initial concentrations of reactants (nonzerofor LH, TocOH, and 02)and the given rate constants. The program used for this work was the GEPASI package by Pedro Mendes in the version 2.08 for MS-Windows. This program is in the public domain under the GNU license and freely available on the Internet (e.g., via anonymous FTP). It comes complete with instructions (an extensive help file) and also with the source code, although we used the program unmodified. It was run on a IBM-AT compatible microcomputer equipped with a 80486 DX2-50 processor. The average computing time for the full reaction set described in this paper was about 15-30 s for a "real" time of about 6 h (100 data points). GEPASI employs the LSODA ("Livermore Solver of Ordinary Differential Equations with Automatic Method Switching for Stiff and Nonstiff Problems") algorithm developed by L. Petzold and A. Hindmarsh (17,18). The GEPASI program was chosen because of its particular ease of use. To perform a simulation, it is only required to enter the reaction equations together with the appropriate type of kinetics (mass action for all reactions in this paper) and the rate constants as well as the initial concentrations of the reactants. The program will then calculate concentrations for all reactants and fluxes through all reactions for equidistant time points over a preselected interval. Usually 100 points were calculated over the whole simulation time to give sufficiently detailed results. LDL Oxidation Experiment. Human plasma LDL, prepared by ultracentrifugation, was oxidized with Cu2+ ions as prooxidants, in principle, as previously described (19). In brief, CuSO4 was added t o an LDL solution in PBS (160 mM NaC1, 10 mM sodium phosphate, pH 7.5) to give final concentrations of 0.1 pM LDL (=0.25 mg/mL LDL) and 1.66pM CuSO4. The total volume of the solution was 50 mL. The mixture was incubated a t 30 "C, and samples were withdrawn in 5 min intervals to analyze vitamin E and conjugated dienes (CD). Vitamin E (a- and y-tocopherol)was analyzed by HPLC as described (2, 20). Conjugated dienes were measured spectrophotometrically by the 234 nm absorption and were calculated with a molar absorption coefficient E = 29 500 cm mol-'. The concentration of lipid hydroperoxidesLOOH was calculated by multiplication of CD with 2.05 (data from ref 2). Definition and Normalization of Time Scales and Concentrations. In lipid oxidation experiments including LDL oxidation, the lag time, where lipid oxidation is inhibited, is obtained by graphical analyses of the measured progress curves (e.g., formation of peroxides or dienes, consumption of vitamin E or oxygen). For mathematical modeling we define the lag time as the reaction time when the tocopheroxyl radical TocO' is used up (Figure 2). As [TocO'l does not become exactly zero at any time during simulation (except t = 01, the slope of the TocO' decrease is extrapolated and the intercept with the time axis at [TocO'l = 0 is taken as end of the lag phase. As will be shown, the computed rates of LDL oxidation may differ by several orders of magnitude, depending on rate of initiation. To facilitate graphical presentation of the progress curves, the time scales were in many instances normalized by dividing "real" time by the associated lag time (time axis is given as timelt-lag). Furthermore, concentrations were frequently

756 Chem. Res. Toxicol., Vol. 8, No. 5, 1995 1 .o


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20000 25000 30000 35000 40000

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Figure 2. Progress curves for LH, TocOH, TocO', LOOH, LOOH NRP,and LOO' (inset) for the base case. The initial concentrations and rate constants are given in Table 1. The "lag time"-the time at which [TocO'l becomes zero again-is indicated by the arrow. Table 2. Comparison of the Base Model with a Typical LPO Experimenta model experiment tocopherol lifetime 50 min 60 min lag phase (graph.) 50 min 110 min rate of initiation 2x M s-l 1.7 x M s-l radical hits per minute 0.26 0.23 [LOOHI,, movmol of LDL -900 -500 [NRP],,, movmol of LDL 100 nd Some key parameters permit semiquantitative comparison between a Cu2+-initiatedLPO experiment (2) and the base case simulation. (I

occur in at least two stages: the first stage is readily identified as the lag phase and lasts as long as antioxidants are present. The lag phase is accompanied by a depletion of a-tocopherol. Only when the antioxidants are used up completely can chain propagation run efficiently, leading to a large increase in the rate of hydroperoxide formation. This is governed by the ratios of the rates of the reactions 4, 5 , and 6 and the concentration of the lipid peroxyl radical. Table 3 shows the calculated rates through the three possible reactions originating from the peroxyl radical:

normalized and are given as the ratio to initial concentrations [LHIo or [TocOHIo.

Results (1) Characteristics of the Base Model. (a) Comparison with Experimental Results. The progress curves for several reactants as simulated using the base model are shown in Figure 2. The base model was set up with actual experiments in mind, so we may compare the simulated curves directly to experiments from the literature where the rate of initiation and the concentrations of the constituents match approximately the simulation (for a review see ref 2). From the tocopherol loss ([TocOHlo = 6 moymol of LDL) the rate of initiation can be calculated (Ri= u1 = 2*d[TocOHYdt) to be 1.7 x M s-l, which is a close enough match to permit qualitative comparison. Table 2 gives a comparison of the key parameters of LDL oxidation in experiments and the base model. The results are in good agreement, except for the large difference of total lag phase. Thus the base model describes many features of the LPO process very well. The question of the difference in the length of the lag phase will be addressed later by a simple extension of our base model. (b) General Observations. From Figure 2 we are able to deduce that the simulated LPO process should

u6 = k,[aTocOHl[LOO'l

(3)

During the lag phase, obviously only the radical scavenging reaction 6 takes place at a significant rate (which at the beginning is 4 orders of magnitude higher than either of the other reactions). From the simulation it can be deduced that the LOO' has a very low, but steadily increasing, concentration as long as antioxidant is present. Practically all radicals fed into the system during the lag phase are converted to hydroperoxides directly via reaction 6. As concentrations of intermediates must build up, a slow increase over time in the rate of LOOH generation can be observed during the lag phase. We therefore may summarize that during the lag phase the simulated LPO process runs via the reactions in the upper half of the diagram in Figure 1 (reactions 1 , 2 , 3 , 6 ,and 7) and via the lower half (reactions 1 , 2 , 3 , 4,and 5) during propagation. The crucial intermediate for this branching behavior is the lipid peroxyl radical. When the LPO process changes between lag phase and propagation, the concentration of LOO' rises by 4 orders of magnitude from 5 x to 3 x M. The reason why [LOO'] is so low during the lag phase can be found


Simulation of Lipid Peroxidation in LDL

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Figure 3. Progress curves for the crucial intermediate LOO' for v 1 in the range of 10-9-10-4 M s-l as a function o ;ime/t-lag. The logarithm of LOO' is plotted to cover the large range of concentrations. The apparent increase in the steepness of the progress curves with decreasing v1 is mainly due to the (required) normalization of the time scale. Table 3. Average Concentrations of Some Reactants and Flux through the Three Reactions (4,5 and 6) Originating from the Intermediate Peroxyl Radical As Given in Figure la lag phase propagation phase

5 x 10-10 3 x 10-6

0.6 '0.6

1.5 x 10-3 0

10-14 10-6

10-8 5.5 x 10-5

10-6 0

a The rate constants for the reactions are given in Table 1. During lag phase only the scavenging reaction 6 takes up radicals at a significant rate; during the propagation phase the termination reaction 4 and the chain propagation reaction 5 are in the same range.

Table 4. Dependence on u1 of Lag Time, Maximum Rate of Propagation, Chain Length, and Ratio of Chain and Recombination Reaction Flux at Maximum Propagation Ratea chain length chain length V I (M 9-l) t-lag ( m i d V, (M s-l) (lag phase) (propagation) (VdU4~max 10-9 100 001 1.2 x 10-6 2.5 1169 2091 10-8 10 000 3.9 x 10-6 1.9 392 742 127 246 10-7 1028 1.3 10-5 1.5 10-6 103.4 4.0 x 10-5 1.3 41.5 80.6 10-6 10.5 1.3 10-4 1 13.8 25.8 10-4 1.1 4.1 10-4 1.1 5.1 8.2 4

The other rate constants and initial concentrations are given in Table 1.

in the scavenging reaction 6, which rapidly converts LOO' to LOOH as long as tocopherol is available. Reaction 6 alone would be sufficient to prevent propagation. Reaction 7 makes an additional contribution to this effect and increases the amount of radicals that can be scavenged. It is this behavior of keeping low the concentration of the intermediate at the branching point of scavenging and propagation which has brought about the term "chain-breaking antioxidant" for tocopherol. We will demonstrate later that this scenario may not be so simple as the chain is probably not "broken" in the true sense of the word. (2) Variation of the Rate of Initiation. By variation of some selected parameters, it is possible to find out more about the relative importance and the interactions of the elementary reactions of the LPO process. Of particular interest is the response of [LOO'] to various rates of initiation. The rate of initiation in experiment is correlated to u1 in our model. Figure 3 shows the effect M s-l to 1 x M s-l. In of increasing u1 from 1 x order to make possible a visualization of the effects of

this large range of reaction rates which yield lag times between 1min and 70 days (cf. Table 41, it was necessary to normalize the time scale with respect to lag time. The result obtained from this series of simulations is that with increasing rate of initiation [LOO'] increases during both lag phase and propagation phase. The concentration jump of LOO' between these two time phases becomes less pronounced with increasing rates of initiation. (The different slopes at t = t-lag are due to normalization.) As a consequence of the dependence of [LOO'] on u l , it follows that with increasing ul: (a) there is only a minor effect on [LOOHI during the lag phase, and (b) there is a substantial decrease of the total amount of LH converted to LOOH. In the graph in Figure 4 the time scale is normalized for lag time; therefore, the rates of LOOH formation appear to be higher for lower u1 where the opposite is the case. During propagation the simulation shows more or less constant levels for L'and LOO'. We may, therefore, set up a steady-state scenario for those reactions which run


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Figure 4. The influence of u1 on the progress of [LOOH] for the base model in the range 10-9-10-4 M s-l, corresponding to Table 4. The time scale has been normalized with respect to multiples of the lag time (timelt-lag), the concentration of [LOOHI with respect to [LH]o, to facilitate comparison. The actual values for the lag time are given in Table 4. The inset shows [LOOH] vs timelt-lag during the lag phase.

during propagation (i.e., reactions 1 , 2 , 3 , 4 , and 5). We obtain the steady-state concentration of LOO’: (4) and 3.1 x M for the steadywhich is 3.16 x state and the base case simulation, respectively. Thus the concentration of LOO’ during propagation is proportional to the square root of u1 (cf. Table 4). Equation 1 from above simplifies to u4 = u1, and eq 2 which describes the rate of LOOH formation during the propagation phase becomes d[LOOHl/dt,,o,,,

= u5 =

k,[LHlu

11/2

(2k4Y2

(5)

which means that u5 during propagation depends on both PUFA concentration and the square root of the rate of initiation. This also can be verified with the data in Table 4. The amount of LH converted into LOOH at each time of the propagation phase is determined by the quotient of propagation and recombination QPR, that is, the ratio of reactions 4 and 5:

The so-called “radical chain length”, that is, the number of LOOH formed per radical put into the system (viz., the number of turns plus one a radical takes in the chain reaction), can be calculated by

making the chain length proportional to [LH] and indirectly proportional to the square root of u l . Thus the increase in chain length does not compensate for the

lower u1 (which would result in a constant maximum rate of hydroperoxide formation), and the maximum overall rate of LOOH production must decrease. It should be noted that both QPR and CL depend on [LHI which, of course, decreases during the reaction. Maximum values for CL are given in Table 4 for both lag phase and propagation phase. Expression 7 is valid only for propagation, as during the lag phase u4 and u5 will be practically zero [(u4 u5)/u6 is far lower than 0.01 in the base case] and the consumption of LH will mainly occur via reactions 6 and 7. During the lag phase, (d[LHYdt)/ u1 is nevertheless a valid measure for CL which may be even lower than 1when recombination plays a significant role. This, however, is possible only at rather high u1. By comparison with the simulation, it becomes clear that the steady-state setup is sufficient to describe a “propagation-only“ model of a chain reaction including recombination of lipid peroxyl radicals. The initial concentration of LH for such a steady-state kinetics (which is the end concentration of LH after the lag phase), however, can only be determined by simulation, as for the lag phase it is not possible to set up such a comparatively simple steady-state description. (3) The Influence of Tocopherol on the Lag Phase. In order to demonstrate the influence of tocopherol on lag time and the rate of LOOH production during the lag phase, a series of simulations with different initial concentrations of tocopherol ([TocOHIo = 5 x 10-4-1 x M,cf. Table 5) was performed. Figure 5 shows the effect on the LOOH progress curves: the length of the lag phase increases strongly, and there is also a slight increase in the rate of LOOH formationwhich is explained by eq 3. This, however, should not be mistaken for a prooxidative effect, e.g., tocopherolmediated propagation. The ratio

+

(d[LOOHYdt),,, (8) (d[LOOHYdt),,,, increases with increasing a-tocopherol concentration. In eq 8 only the rate during lag time changes whereas the



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Figure 5. Dependence of the formation of LOOH on the initial concentration of a-tocopherol (5 x M, 1 x M, 5 x M, and 1 x 10-2 M) corresponding to Table 4. Note that, even without the TMP reaction, formation of LOOH is slightly enhanced with increasing concentration of a-tocopherol.

Table 5. Dependence of Lag Time and Radical Chain Length (the Number of Cycles a Radical Introduced via Reaction 1 Takes via Reaction 5) on the Initial Concentration of Antioxidanp chain length chain length [aTocOH]o lag time (lad (propagation) (M) (min) 9.5 1.5 30.0 5.0 x 10-4 1.0x 10-3 17.8 1.4 29.9 5.0 x 10-3 84.5 1.1 29.4 169 1.2 28.9 1.0 x 10-2 a The other initial concentrations and the rate constants were as given in Table 1.

rate during propagation (and thus the chain length as given in eq 7 ) remains essentially constant. The length of the lag time is Gag

- 2[TocOHl, -

(9)

u1

which also holds in simulation for low u1 (cf. Tables 4 and 5). It does not do so for high u1, as here substantial recombinationof LOO' may occur already during the lag phase. (4) Extending the Base Model. The basic model presented so far permits us to understand the general behavior of the LPO process. By extension of this model, it is possible to obtain insight into more delicate questions regarding LDL lipid peroxidation. (a) Tocopherol-MediatedPropagation ("MP). It has been claimed (21,221that tocopherol may act as a prooxidant rather than as an antioxidant. This would mean that TocO', instead of scavenging LOO', would transfer its radical electron to LH, thereby generating L',which means propagation of a chain reaction. In order to assess the possibility and impact of TMP, we extend our basic model with reaction 8 in the scheme of Figure 1:

+

-

+

TocO' LH TocOH L' The rate constant €or this reaction has been reported to be in the range of 0.07 M-l (7).

Simulations at different u1, ranging from 1.0 x M s-l to 1.0 x lo-* M s-I, were calculated. At low u1, TocO' is obviously nearly entirely consumed by the TMP M s-l, the effect is still reaction 8. At u1 = substantial whereas at u1 = lo-* M s-l, TMP may be regarded as negligible (Figure 6). The effect of TMP and u1 on the production of LOOH and on the length of the lag phase is shown in Figure 7 . TMP also increases the radical chain length CL = (d[LHYdt)/ul during the lag phase when u1 decreases (Figure 8, Table 6). One strong argument against the possibility of TMP might be raised, namely, the recombination of TocO' by

+

-

TocO' TocO' NRP3 which is not included in our model due to the reasons given below. For the recombination reaction rate constants are reported in the range of lo2M-' s-l to lo4M-I s-l (23,24,8). If this reaction is included in the model, TMP effects become too small to be considered observable in any experiment. We might, of course, simply follow the argumentation line of Bowry and Stocker (22),who postulated a negligible rate of tocopheroxyl recombination due to compartmentalization of the radical within LDL, which would make it very unlikely for one TocO' to encounter another one to recombine with. This hypothesis may be justified, but it is both hard to prove and hard to disprove. There is, however, other and more direct evidence that TocO' recombination is a rare event in LDL. Simulation shows that this reaction eliminates TocO' efficiently enough not only to suppress TMP but also to reduce the radical scavengingpotential of tocopherol to one radical electron in total. This, however, contradicts all experience with tocopherol as a radical scavenger, which is able to take up two radical electrons in succession (reactions 6 and 7 ) (e.g., ref 6). Only when the rate constant of TocO' recombination is made low in simulation ( < 1M-I s-l) is the typical two-radical scavenging behavior restored. That tocopherol scavenges two radicals can also



1.oo

\\

TocOH

0.75

-T 0

0.50

Y

0.25

0.00 0.00

0.50 time I t-lag

0.25

0.75

I.oo

Figure 6. Dependence of a-tocopherol consumption and tocopheroxyl radical formation on u1 a t 1 x 10- M s-l(-), 1 x M s-l (- -), and 1 x 10-4 M s-1(- *. -). TMP was assumed to run with a kg of 0.07 M-l s-l. The amount of tocopheroxyl radical present during the reaction increases with increasing u1. The time scale has been normalized with respect to t-lag, and concentrations are normalized for [TocOHIo.

Table 6. Lagtime, Maximum Rate of LOOH Formation during Lag Time, and the Concentration of LOOH at the End of the Lag Phase Are Compared for the Basic System with and without !l'MP for Different u1 u1

(M s-l) 10-4 10-5 10-6 10-7

t-lagmp (min) 1.02 10.2 102 1017 10169

t-lag (min) 1.02 10.2 102 1017 10000

Vmax,TMP

Vnax

(M s-l) 9.2 x 10-5 1.7 x 5.1 x 1.6 x 10-6 4.9 x 10-7

(M s-l) 8 . y X 10-5 9.2 x

9.6 x 1.1 10-7 1.3 x 10-8

be demonstrated by comparison of simulation and experiment (see next section)-the model fits only without tocopheroxyl recombination. Furthermore, as the rate of initiation can be determined from tocopherol loss experimentally by u1 = n(d[TocOHYdt), where n is the total number of electrons scavenged by tocopherol, we may use eq 5 to determine u1 from the experimental rate of propagation (where the behavior of tocopherol has no more influence). At t = 7000 s (Figure 9, see next section) M s-l, and [LHI we find d[LOOHYdt to be 4.3 x (from simulation) is 0.468 M, resulting in u1= 1.8 x M s-l. As d[TocOHYdt = 9.25 x lo-' M s-l, we obtain for the number of radicals scavenged n = 2. A complication of this analysis may arise if the recombination product of TocO' itself would be capable of scavenging two further radicals. We, however, found no reliable information on this. Once we have made clear that TMP can be explained from the base model by inclusion of reaction 8, we should explain the role of TocO': is it a prooxidant or not? The answer can be found in Figure 7C: TMP produces a large amount of LOOH during the lag phase as compared to the no-TMP simulation. The length of the lag phase remains unchanged. Figure 7C shows an extreme case, of course, as the lag time here is 70 days. Without TocOH, however, there is no lag phase at all and 50% of LH would be converted to LOOH within 3-4 days instead of 27 days when TocOH is present (with TMP)! We may conclude that TocOH itself is certainly chain-breaking (via reaction 6) and TocO' both prevents further radical

[LOOHlmp (M) 4.3 x 10-3 9.7 x 10-3 2.7 x 10-2 8.1 x

2.3 x 10-1

[LOOHI (MI 3.5 10-3 4.9 10-3 9.2 x 10-3 2.2 x 6.8 x lo-*

CL (lag-phase) 1.3 2.2 5.6 16.3 49.8

CL (propagation) 5.1 5.1 40.3 116 271

propagation (reaction 7) and propagates the radical chain (reaction 8). The chain-propagation potential of TocO' is much lower than that of LOO', which is not effective as long as tocopherol is present in LDL by the LOOscavenging reactions of TocOH and TocO' the fast propagation via reaction 5 is abolished with the comparatively harmless side effect of TMP. (b)!l%e Prolonged Lag Phase in Cu2+-Induced W O . The method most widely used for induction of lipid peroxidation in LDL is by addition of Cu2+ions. The advantage of this over induction by azo compounds is that the rate of initiation is easily controlled and the initiator itself does not absorb in the 234 nm region. There is, however, a lag phase to be expected which does not correspond directly to the lifetime of a-tocopherol but is much longer. We want to extend the basic model (including the extension for TMP as shown above) to reflect this behavior. The basic model predicts that propagation can only begin if the antioxidant content of LDL has been depleted. It is therefore evident that the prolonged lag phase observed predominantly in Cu2+-inducedlipid peroxidation is the consequence of the action of an antioxidant other than tocopherol. It is possible to extend the model presented so far by a single reaction and to arrive at a simulation which describes the experimental behavior of copper-induced LPO satisfactorily. The experiment was set up at 30 "C using [Cu2+1= 1.6 pM with a pooled human LDL batch. Diene data


Simulation of Lipid Peroxidation in LDL 0.20

[TocOH]~= 0

-

[TocOHIo= 3 ' 1 0 3 M, with TMP - -

0.15 -[TOCOH]~ = 3'10-3 M, no TMP

8

= 1.0'104 M S-I

VI

0

2

time (min)

6

8

10

1

0.30 1 0.25

1

4

. _ . . _a .

/ y

0.05

0.00 0.0

, //

L

0.5

2.0

time (h) l.5

2.5

///

/

/--

I "

0

25

time (d) 50

'

a

I 1

c

75

~

3

~

100

Figure 7. Production of LOOH a t u 1 = (A) 1 x (B) 1 x lo+, and (C) 1 x M s-1, Each graph shows the formation of LOOH with (- -1 and without TMP (- -) (ks = 0.07 M-l s-l) and without tocopherol (-). Note that the time scales vary from (A) minutes over (B) hours to (C) days!

were multiplied by a factor of 2 to give peroxide concentrations. [LH]o was estimated from the LDL concentration (100 nM) to be 0.573M. [TocOHIo was extrapolated M (all from experiment to t = 0 to be 1.9 x concentrations given as local concentrations). Ri = u1 was calculated from the average d[TocOHYdt to be 1.85 x M s-l. The reaction to be included in our model is

AntiOxH

+ LOO' - Antiox' + LOOH

The reaction rate exhibited by such a hypothetical antioxidant AntiOxH (Uantiox = [AntiOxHlkantiox)must be lower than u6 = k~[TocOHlo(otherwise it would prevent a-tocopherol from being oxidized) and clearly higher than the rate of the propagation reaction (otherwise propagation would start immediately aRer a-tocopherol has been used up). As during the second part of the lag phase a higher rate of LOOH formation can be observed, kantiox is probably nearer to k5 than to k6. AntiOxH need not represent one single antioxidant species, and kantiox may be composed of several different rate constants in reality. From the experimental curves and some known relations (3), it is possible to estimate the average concentra-

tion of AntiOxH: t-lag+u [AntiOxHl, = 7

(10)

where &lag+means the length of the lag phase beyond the existence of a-tocopherol and n denotes the number of electrons that can be scavenged. With n = 1 and an "additional" lag time &lag+ of 3800 s estimated from experiment, we obtain [AntiOxHIo = 7.0 x M (local concentrations). The approximate kantioxcan be obtained from the average d[LOOHYdt during that phase by

h . = antlox

k&LHlu, [AntiOxHl,(d[LOOHYdt)

(11)

-

With the result for [AntiOxHIo, [LHI [LHlo, and M s-l, we obtain a kantioxof 920 d[LOOHYdt = 5.1 x M-l s-l, which meets the required conditions. The curves for the simulation and the corresponding experiment are shown in Figure 9.

Discussion In this paper we give a description of a minimal reaction system which describes the overall LPO process



300 1

250

200

6

150

100

50

0 0.0

1.o

0.5

1.5

2.0

time / t-lag

Figure 8. The chain length (CL = (d[LHYdt)/ul)of the LPO process including TMP. With decreasing u1, CL becomes higher during the lag phase. 0.25

0.002

8 0.000 t

0.20

L

0.15

0.000 1000

0

0.10 20/ A

/ 0

2000

4000

model experimental

-t

0.05

A

I

I

I

6000

8000

10000

0.00

time Is] Figure 9. Using a hypothetical additional antioxidant, it is possible to reproduce the prolonged lag phase exhibited by most Cu2+initiated LPO experiments. Experimental data for [LOOHI and [TocOHl (A)are compared to the simulation (-),

in terms of its elementary reactions. From the behavior of the base model it follows that in LPO the crucial intermediate is LOO’, the concentration of which governs the switch from lag phase to propagation. The propagation phase alone can be described by a steady-state model and by simulation equally well; the complete process including the lag phase, however, does not permit this kind of simplified steady-state treatment. The question whether tocopherol is a chain-breaking antioxidant or a prooxidant has been addressed in some detail in this paper. We extended our base model with a single reaction to include so-called “tocopherol-mediated propagation”. It shows that tocopherol may actually cany a radical chain reaction similar to “normal”propa-

gation. There is, however, one important difference: the chain driven by the tocopheroxyl radical via reaction 7 (LH TocO’ L’ TocOH) is much slower than the propagation chain reaction 5 (LOO’ LH LOOH

+

L‘).

-. +

+

-

+

It is certainly wrong to claim that TMP leads to faster destruction of LDL. In fact, TMP does not significantly reduce the length of the lag phase, and if there were no tocopherol present at all, propagation would start immediately, leading to a much faster destruction of LDL. This is most strikingly evident from the graph in Figure M s-l: without 9 showing LOOH formation at a u1 of tocopherol LH is consumed in 20% of the time that would be required in the presence of TocOH with TMP.



We probably have to change our concept of what an antioxidant (in the case of tocopherol) is and how it acts: antioxidant capacity of tocopherol including TMP means that a fast chain reaction (LOO' LH LOOH L')is prevented (very effectively) by two successive reactions which scavenge LOO'. In these reactions tocopherol and tocopheroxyl radical act as true chain-breaking antioxidants. As a side effect, tocopheroxyl radical can be the starting point of a very slow propagative cycle. With decreasing rate of initiation, the TMP effects are more pronounced although TMP itself becomes slower: the decrease in TMP rate does not compensate for the increasing interval between two exogenous radical hits. So an internal radical has more time to cycle between two external radical hits, which results in an increase of the chain length during the lag phase (Figure 8). Comparison to experiment reveals that the length of the lag phase cannot be explained by the known antioxidants (predominantly a-tocopherol)alone, particularly when initiating with copper. It is possible to estimate the amount of antioxidant "missing" in current hypotheses (-7 mM, about 15 mollmol of LDL) and even an average K value (920 M-l s-l) for the reaction of this unknown antioxidant with-supposedly-LOO'. The nature of this antioxidant is not known so far. It might be plasmalogens, carotenoids, or certain amino acids of ApoB100. The simulation of such an extended model shows very good correlation with experimental results. Recent preliminary experimental results together with a tentative kinetic model for Cu2+-inducedradical formation are also compatible with this hypothesis: in any case tocopherol is consumed long before the end of the lag phase. The results presented here suggest that all important elementary reactions contributing to the LPO process have been included in the model and that the rate constants used describe the reaction within LDL correctly.

+

-

+

Acknowledgment. This work was supported by the Osterreichischer Fonds zur Forderung der wissenschaftlichen Forschung FWF Project SO 7102 MED and by the Association of International Cancer Research (AICR), U.K.

References (1)Steinberg, D., Parthasarathy, S., Carew, T. E., Khoo J. C., and Witzthum, J. L. (1989)Beyond Cholesterol. Modifications of Lowdensity Lipoprotein that Increase Atherogenicity. N. Eng. J. Med. 320,915-924. (2)Esterbauer, H., Striegl, G., Puhl, H., and Rotheneder, M. (1989) Continuous Monitoring of in Vitro Oxidation of Human Low Density Liporotein. Free Radical Res. Commun. 6 (l), 67-75. (3)Esterbauer, H., and Jurgens, G.(1993)Mechanistic and Genetic Aspects of Susceptibilityof LDL to Oxidation. Curr. Opin. Lipidol. 4,114-124. (4)Esterbauer, H., Gebicki, J., Puhl, H., and Jurgens, G. (1992)The Role of Lipid Peroxidation and Antioxidants in Oxidative Modification of LDL. Free Radical Biol. Med. 13,341-390. ( 5 ) Barclay, L. R. C., Baskin, K. A., Locke S. J., and Vinquist, M. R. (1989)Absolute Rate Constants for Lipid Peroxidation and Inhibition in Model Biomembranes. Can. J. Chem. 68, 2258-

2269.

(6) Niki, E., Saito, T., Kawakami, A., and Kamiya, Y. (1984)Inhibition of Oxidation of Methyl Linoleate in Solution by Vitamin E and Vitamin C. J. Biol. Chem. 259,4177-4182. (7)Remorova, A. A., and Roginsky, V. A. (1991)Rate Constants for the Reaction of a-tocopherol Phenoxy Radicals with Unsaturated Fatty Acid Esters, and the Contribution of this Reaction to the Kinetics of Inhibition of Lipid Peroxidation. Kinet. Catal. 32,726-

731. (8) Kaouadji, M. N., Jore, D., Ferradini, C., and Patterson, L. K.

(1987)Radiolytic Scanning of Vitamin E-Vitamin C OxidationReduction Mechanisms. Bioelectrochem. Bioenerg. 18,59-70. (9)Hasegawa, K., and Patterson, L. K. (1978)Pulse Radiolysis in Model Lipid Systems: Formation and Behaviour of Peroxy Radicals in Fatty Acids. Photochem. Photobiol. 28,817-823. (10)Barclay, L. R. C., Locke, S. J., MacNeil, J. M., van Kessel, J., Burton, G. W., and Ingold, K. U. (1984)Autoxidation of Micelles and Model Membranes. Quantitative Kinetic Measurements Can be Made by Using Either Water-Soluble or Lipid-Soluble Initiators with Either Water-Soluble or Lipid-Soluble Chain-Breaking Antioxidants. J . Am. Chem. SOC. 106,2479-2481. (11) Barclay, L. R. C., Baskin, K. A., Locke, S. J., and Schaefer, T. D. (1987)Benzophenone-photosensitizedAutoxidation of Linoleate in Solution and Sodium Dodecyl Sulfate Micelles. Can. J. Chem. 65,2529-2540. (12)Vladimirov, Y. A.,Olenev, V. I., Suslova, T. B., and Cheremisina, Z. P (1980)Lipid Peroxidation in Mitochondrial Membrane. Adu. Lipid Res. 17,173-249. (13)Salvador A., Antunes, F., Pinto, R. E. (1995)Kinetic Modelling of In Vitro Lipid Peroxidation Experiments-"Low Level" Validation of a Model of In Vivo Lipid Peroxidation. Free Radical Biol. Med. (in press) and references therein. (14)Babbs, C. F., and Steiner, M. G. (1990)Simulation of free radical reactions in biology and medicine: a new two-compartment kinetic model of intracellular lipid peroxidation. Free Radical Biol. Med. 8,471-485 and references therein. (15) Russell, G. A. (1957)Deuterium-Isotope Effects in the Autoxidation of Arylalkyl Hydrocarbons. Mechanism of the Interaction of Peroxy Radicals. J . Am. Chem. SOC. 79,3871-3877. (16)Yamauchi, R., Yagi, Y.,and Kato, K. (1994)Isolation and Characterisation of Addition Products of a-Tocopherol with Peroxyl Radicals of Dilinoleylphosphatidylcholine in Liposomes. Biochim. Biophys. Acta 1212 (l),43-49. (17)Petzold, L. R. (1983)Automatic Selection of Methods for Solving Stiff and Nonstiff Systems of Ordinary Differential Equations. SIAM J. Sci. Stat. Comput. 4,36-148. (18)Hindmarsh, A. C.(1983)ODEPACK, a Systematized Collection of ODE Solvers. In Scientific Computing (Stepleman, R. S., et al., Eds.) pp 55-64, North-Holland, Amsterdam. (19)Puhl, H., Waeg, G., and Esterbauer, H. (1993)Methods to Determine Oxidation of Low-Density Lipoproteins. Methods Enzymol. 233,425-441. (20)Vuilleumier, J.-P., Keller, H. E., Gysel, D., and Hunziker, F. (1983) Clinical Chemical Methods for the Routine Assessment of the Vitamin Status in Human Populations. Int. J . Vitam. Nutr. Res.

53,265-272. (21)Bowry, V. W.,Ingold, K. U., and Stocker, R. (1992)Vitamin E in Human Low-Density Lipoprotein. When and How this Antioxidant Becomes Pro-oxidant. Biochem. J. 288,341-344. (22)Bowry, V. W., and Stocker, R. (1993)Tocopherol-Mediated Peroxidation. The Prooxidant Effect of Vitamin E on the RadicalInitiated Oxidation of Human Low-Density Lipoprotein. J . Am. Chem. SOC. 115,6029-6044. (23)Simic, M. G. (1980)Kinetic and Mechanistic Studies of Peroxy, Vitamin E and Antioxidant Free Radicals by Pulse Radiolysis. In Autoxidation in Food and Biological Systems (Simic, M. G., and Karel, M., Eds.) pp 17-26, Plenum, New York. (24)Rousseau-Richard, C., Richard, C., and Martin, R. (1988)Kinetics of Bimolecular Decay of a-Tocopheroxyl Free Radicals Studies by ESR. FEBS Lett. 233,307-310.

TX950040U

Simulation of Lipid Peroxidation in Low-Density Lipoprotein by a Basic

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