Reactions of OOH Radical with β-Carotene, Lycopene, and Torulene

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J. Phys. Chem. B 2009, 113, 11338–11345

Reactions of OOH Radical with β-Carotene, Lycopene, and Torulene: Hydrogen Atom Transfer and Adduct Formation Mechanisms Annia Galano*,† and Misaela Francisco-Marquez‡ Departamento de Quı´mica, UniVersidad Auto´noma Metropolitana-Iztapalapa, San Rafael Atlixco 186, Col. Vicentina, Iztapalapa, C. P. 09340, Me´xico D. F. Me´xico, and Laboratorio de Quı´mica Computacional, FES-Zaragoza, UniVersidad Nacional Auto´noma de Me´xico (UNAM), C.P.09230 Iztapalapa, Me´xico, D.F., Me´xico ReceiVed: May 1, 2009; ReVised Manuscript ReceiVed: June 29, 2009

The relative free radical scavenging activity of β-carotene, lycopene, and torulene toward OOH radicals has been studied using density functional theory. Hydrogen atom transfer (HAT) and radical adduct formation (RAF) mechanisms have been considered. All the possible reaction sites have been included in the modeling, and detailed branching ratios are reported for the first time. The reactions of hydrocarbon carotenoids (Car) with peroxyl radicals, in both polar and nonpolar environments, are predicted to proceed via RAF mechanism, with contributions higher than 98% to the overall OOH + Car reactions. Lycopene and torulene were found to be more reactive than β-carotene. In nonpolar environments the reactivity of the studied carotenoids toward peroxyl radical follows the trend LYC > TOR > BC, whereas in aqueous solutions it is TOR > LYC > BC. OOH adducts are predicted to be formed mainly at the terminal sites of the conjugated polyene chains. The main addition sites were found to be C5 for β-carotene and lycopene and C30 for torulene. The general agreement between the calculated magnitudes and the available experimental data supports the predictions from this work. Introduction Carotenoids (Car) are naturally occurring organic pigments, abundant in human diet. Among their diverse functions in living organisms,1 their free radical scavenging ability stands out.2,3 Peroxyl radicals, on the other hand, are considered potentially more dangerous than many other types of radicals, due to the selectivity of their reactions and their ability to diffuse in biological systems.4 In fact it has been suggested that these species may be implicated in a variety of pathological events, such as heart diseases, cancer, and the process of aging.5 Three viable mechanisms are generally accepted for carotenoids’ free radical scavenging activity:

Electron transfer (ET):

R• + Car f R- + Car•+

Radical adduct formation (RAF):

Hydrogen atom transfer (HAT):

R• + Car f [R - Car]• R• + Car f RH + Car(-H)•

(I)

(II)

(III)

However, it has also been proposed that the antiradical activity of carotenoids can also occur through ET from the radical to the carotenoid; that is, Car can either donate or accept electrons in the process.6 The relative importance of the different reaction channels will depend on diverse factors including the nature of * To whom correspondence should be addressed. E-mail: agalano@ prodigy.net.mx. † Universidad Auto´noma Metropolitana-Iztapalapa. ‡ Universidad Nacional Auto´noma de Me´xico.

the reacting free radical, the structural features of the carotenoid,7,8 and, in biological systems, the location and orientation of the carotenoid within the membrane.8 It should be noticed that the reactions of Car with free radicals can also take place by more than one pathway simultaneously.9 Burton and Ingold10 suggested that β-carotene reacts with peroxyl radicals via an addition reaction. Liebler and McClure11 identified β-carotene-radical adducts as oxidation products associated with antioxidant reactions. In a more recent work, Mortensen12 has shown that carotenoids scavenge peroxyl radicals that are not highly reactive by adduct formation and not by electron transfer. In a previous work from our group,13 single electron transfer reactions from 19 carotenoids to nine different free radicals have been studied. It was found that among the peroxyl radicals only those with electron withdrawing groups are able to react with carotenoids, via electron transfer reaction. The ET reactions involving HOO•, CH3OO•, and C6H5CH2OO• were found to be endergonic (∆G > 0) in both polar and nonpolar environments,13 ruling out the hypothesis that in heterogeneous systems Car radical cations could be formed because they could be solvated at the lipid-water interface. These results are also in line with the reduction potential of the β-carotene radical cation that has been recently determined to be 1.06 V.14 Comparing this value with that of peroxyl radicals (about 0.7 V15) the ET process from β-carotene to peroxyl radicals is highly unfavorable. Mortensen12 has also concluded that Car may also scavenge peroxyl radicals by hydrogen atom transfer, albeit this reaction seems to be much less important than adduct formation. Woodwall et al.16 support hydrogen abstraction as one of the possible mechanisms occurring when carotenoids are exposed to peroxyl radicals. From a theoretical point of view, there are no previous reports on mechanism (II) for Car + peroxyl radicals reactions, in spite of the fact that the experimental results mentioned above support

10.1021/jp904061q CCC: $40.75  2009 American Chemical Society Published on Web 07/22/2009

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SCHEME 1

the preponderant role of RAF in the overall scavenging activity of Car. There is however a very recent study by Martı´nez and Barbosa17 on the bond dissociation energies of thirteen carotenoids, and their possible relationship with the viability of the HAT mechanism. Detailed studies on the fundamental chemistry of carotenoids with free radicals present in biological systems seem to be the logical way to gain better understanding on the antiradical activity of such species. Accordingly the main goal of the present work is to assess the relative importance of RAF and HAT mechanisms to the overall reactions of carotenoids with peroxyl radicals. In addition a detailed study on the relative reactivity of the different reaction sites of reaction is also intended, as well as estimations on the branching ratios of the reaction products. For such purposes the smallest peroxyl radical has been chosen (•OOH) and three different carotenoids: β-carotene (BC), lycopene (LYC), and torulene (TOR). BC was chosen since it is the most studied and abundant compound of the family, LYC because it has been proposed as the most reactive carotenoid toward free radicals,9,16,18-20 and TOR because it has recently suggested that it is even more efficient than LYC when the reaction occurs by electron transfer.13 Computational Details All of the electronic structure calculations were performed with the Gaussian 0321 package of programs. Full geometry optimizations and frequency calculations were carried out for all of the stationary points using the density functional BPW91 and the 6-31G(d,p) basis set. This functional combines the Becke’s 1988 exchange functional22 (which includes the Slater exchange along with corrections involving the gradient of the density) with Perdew and Wang’s 1991 gradient-corrected correlation functional.23 The much more widely used B3LYP functional was also tested for the OOH reaction with β-carotene and the results obtained that way are in contradiction with the experimental evidence that show site 5 as the most reactive one. Therefore this functional is not suitable for the purposes of the present work. Solvent effects were included by single point calculations at the same level of theory using the polarizable continuum model, specifically the integral-equation-formalism (IEF-PCM),24 with

benzene (ε ) 2.247) and water (ε ) 78.39) as solvents for mimicking nonpolar and polar environments, respectively, i.e., lipid and aqueous phases. Thermodynamic corrections at 298.15 K were included in the calculation of relative energies. Restricted calculations were used for closed shell systems and unrestricted ones for open shell systems. Local minima and transition states were identified by the number of imaginary frequencies (NIMAG ) 0 or 1, respectively). In addition, the vibrational modes with imaginary frequencies were inspected using the GaussView25 program, and it was confirmed that they do connect the corresponding reactants and products. Intrinsic reaction coordinate (IRC) calculations were carried out, for selected paths of reaction, and it was corroborated that the transition states properly connect reactants and products. Results and Discussion Geometries and Energies. The structures of the modeled carotenoids (Car) are shown in Scheme 1, together with the numbering of the reaction sites that is used throughout this manuscript. The reaction pathways for all of the numbered sites have been included in the present work; that is, the HAT mechanism for all methyl groups and RAF for all the sp2 sites have been considered. The conformation for the polyene chains has been chosen as all trans for the three studied carotenoids. The most relevant geometrical parameters involved in H abstractions from the methyl groups in the studied carotenoids are the breaking C-H and the forming O-H bond distances. Their values corresponding to the optimized transition states for all of the sites susceptible to react through the HAT mechanism are reported as Supporting Information (Table S1). For H abstraction reactions the L parameter can be defined for every site of reaction as:26

L)

δ(C-H) δ(O-H)

(1)

where δ(C-H) represents the variation in the breaking bond distance between transition states and reactants, while δ(O-H) represents the variation in the forming bond distance between transition states and products. This parameter can be used to

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Galano and Francisco-Marquez To calculate the Gibbs free energies of reaction (∆G) for RAF paths and the barriers (∆G+) of RAF and HAT mechanisms reported in this work (corresponding to benzene and water solutions), the reference state has been changed from 1 atm, as calculated from the Gaussian program outputs, to 1 M and the solvent cage effects have been included according to the corrections proposed by Okuno,29 taking into account the free volume theory.30 These corrections are in good agreement with those independently obtained by Ardura et al.31 and have been successfully used by other authors.32 The expression used to correct Gibbs free energy is

∆Gsol = ∆Ggas - RT{ln[n10(2n-2)] - (n - 1)}

Figure 1. Relationship between L and Ladd parameters and enthalpies of reaction for HAT (A) and RAF (B) mechanisms.

establish if a transition state structure is reactant-like (L < 1) or product-like (L > 1) and also to quantify the corresponding trend. Therefore (and according to Hammond’s postulate27) there must be a direct relation between the L value and the heat of reaction of a specific pathway. Since deviations from this postulate have previously been reported for other systems,28 we decided to verify if the reactions studied in the present work are in line with the rule or with the exceptions. Figure 1A shows that, in general, HAT mechanisms involving carotenoids and the OOH free radical obey Hammond’s postulate, i.e., the earlier the transition state the more exothermic the reaction. For OH additions to carotenoids, on the other hand, the most relevant geometrical parameter is the distance of the C-O bond formed in the RAF processes. The value of d(C-O) in the optimized structures of transition states and products are reported as Supporting Information (Table S2). In this case we have defined a new parameter for investigating the relationship between structure and the enthalpy of reaction, the Ladd parameter

Ladd )

1 δ(C-O)

(2)

where δ(C-O) represents the variation in the forming bond distance between addition products and transition states. As Figure 1B shows the RAF processes are also in line with the Hammond’s postulate. Since only one bond distance is considered in the definition of the Ladd parameter, the turning point is not Ladd ) 1. However it remains valid that the lower the value of Ladd the larger the exothermicity of the process. In fact it was found that the frontier value in this case is Ladd ) 2, i.e., if Ladd < 2 the addition transition state can be considered reactantlike and the process is expected to be exothermic, and if Ladd > 2 the TS can be considered product-like and the process is expected to be endothermic.

(3)

where n represents the molecularity of the reaction. According to expression (3), the cage effects in solution cause ∆Gsol to decrease by 2.54 kcal/mol for bimolecular reactions, at 298.15 K, with respect to ∆Ggas. This lowering is expected since the cage effects of the solvent reduce the entropy loss associated with any addition reaction or transition state formation, in reactions with molecularity equal to, or larger than, two. Therefore, if the translational degrees of freedom in solution are treated as in the gas phase, the cost associated with their loss when two or more molecules form a complex system in solution is overestimated, and consequently these processes are kinetically overpenalized in solution leading to rate constants that are artificially underestimated. The enthalpies and Gibbs free energies of reaction, in benzene and water solutions, for the HAT processes are reported in Table 1. The channels with the largest energy release were found to be those involving H abstraction from site 4 for all the studied carotenoids. Accordingly, the main products of reaction through HAT mechanism are expected to be those where the H transfer had occurred from site 4, regardless of the polarity of the solvent. Only the abstractions from sites 4 and 5a were found to be significantly exothermic and exergonic for β-carotene and lycopene. For torulene HAT from sites 30a and 30b were also found to be exothermic and exergonic, in addition to paths 4 and 5a. Some reaction channels are described to have thermal effects lower than 1 kcal/mol: 9a for β-carotene; 3 and 9a for lycopene; and 13a and 26a for torulene. The enthalpies and Gibbs free energies of reaction, in benzene and water solutions, for the RAF reactions are reported in Tables 2 and 3, respectively. As the values in this table show, most of the addition processes were found to be exothermic. The exceptions are the OOH addition to C6 in β-carotene; to C2, C6, and C8 in lycopene; and to C6, C8, and C29 in torulene, for both nonpolar and polar environments. The number of processes with values >0 increases when they are analyzed in terms of Gibbs free energies of reaction. In addition to the endothermic channels described above, additions to C8, C10, and C12 of BC were found to be endergonic. In the same situation are sites 1, 10, and 12 in LYC and 10, 12, 14, 16, 18, 25, and 27 in TOR. Therefore, adducts formed by OOH addition to these sites are unlikely to be observed experimentally. The barriers of reaction in terms of enthalpies and Gibbs free energies are reported in Table 4 for all of the reaction channels that take place trough the HAT mechanism. The lowest barriers for β-carotene and lycopene, in terms of Gibbs free energy, are those corresponding to H abstractions from sites 5a and 4, while for torulene they are those involving sites 30 and 4. The same behavior was found both for polar and nonpolar environments. Therefore for those carotenoids with ciclohexene rings in their structures the most favored site of reaction in the ring is site 4,

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TABLE 1: Enthalpies (∆H) and Gibbs Free Energies of Reaction (∆G) in Benzene and Water Solutions, for the HAT Mechanism, at 298.15 K, All in kcal/mol BC

LYC

site

∆H

∆G

site

2 3 4 1a)1b 5a 9a 13a

16.06 14.86 -13.40 19.33 -6.94 0.39 1.57

15.26 14.49 -12.40 17.67 -6.71 -0.48 0.54

3 4 1a)1b 5a 9a 13a

2 3 4 1a)1b 5a 9a 13a

15.43 14.22 -14.21 18.42 -7.72 -0.21 0.87

14.63 13.85 -13.22 16.76 -7.48 -1.09 -0.16

3 4 1a)1b 5a 9a 13a

site

∆H

∆G

Benzene -0.99 -12.46 5.96 -6.72 0.10 1.41

-1.30 -12.56 5.03 -7.07 -1.46 0.21

2 3 4 1a)1b 5a 9a 13a 18a 22a 26a 30a)30b

16.06 14.87 -13.84 19.74 -11.18 -1.49 0.50 2.12 1.47 -0.16 -6.70

15.04 14.42 -14.82 19.53 -11.13 -2.58 -1.72 1.55 0.93 -0.76 -6.98

Water -1.59 -13.09 5.01 -7.28 -0.52 0.71

-1.90 -13.18 4.30 -7.63 -2.07 -0.48

2 3 4 1a)1b 5a 9a 13a 18a 22a 26a 30a)30b

15.43 14.25 -14.60 17.20 -11.48 -1.69 -0.14 1.40 0.81 -0.45 -7.13

14.41 13.80 -15.59 19.03 -11.43 -2.77 -2.37 0.83 0.27 -1.05 -7.40

TABLE 2: Enthalpies (∆H) and Gibbs Free Energies of Reaction (∆G) in Benzene Solutions, for the RAF Mechanism, at 298.15 K, All in kcal/mol BC site

∆H

LYC ∆G

site

∆H

TOR ∆G

∆H

TABLE 3: Enthalpies (∆H) and Gibbs Free Energies of Reaction (∆G) in Water Solutions, for the RAF Mechanism, at 298.15 K, All in kcal/mol

TOR ∆G

site

∆H

BC ∆G

site

∆H

LYC ∆G

site

∆H

TOR ∆G

site

∆H

∆G

5 -17.33 -9.12 1 -0.91 7.14 5 -19.67 -11.36 6 7.70 15.54 2 1.03 8.02 6 5.42 13.12 7 -16.57 -8.74 5 -21.68 -14.22 7 -17.66 -10.33 8 -1.22 5.83 6 3.53 9.78 8 0.07 6.79 9 -11.88 -4.16 7 -12.04 -6.53 9 -13.40 -4.88 10 -3.48 2.92 8 0.21 7.26 10 -3.46 3.47 11 -7.25 -0.90 9 -9.53 -2.61 11 -11.20 -6.95 12 -6.13 0.51 10 -5.17 1.35 12 -3.38 4.13 13 -9.20 -1.68 11 -8.16 -2.25 13 -10.35 -3.69 14 -7.08 -0.69 12 -5.06 1.02 14 -5.18 1.31 15 -6.68 -1.17 13 -8.03 -0.31 15 -8.45 -1.38 14 -6.86 -1.49 16 -4.89 1.88 15 -8.92 -2.21 17 -9.91 -2.94 18 -7.31 0.37 19 -7.33 -0.17 20 -6.75 -0.96 21 -7.83 -1.30 22 -9.53 -2.97 23 -6.40 -0.10 24 -8.40 -2.71 25 -3.40 2.21 26 -9.64 -2.69 27 -2.39 4.35 28 -11.88 -5.30 29 4.06 10.08 30 -21.73 -14.28

5 -16.54 -8.34 1 -0.13 7.92 5 6 8.78 16.62 2 1.93 8.92 6 7 -15.64 -7.82 5 -20.59 -13.12 7 8 -0.74 6.31 6 3.81 10.06 8 9 -10.97 -3.25 7 -11.53 -6.02 9 10 -3.13 3.27 8 1.29 8.34 10 11 -6.48 -0.12 9 -8.83 -1.91 11 12 -5.63 1.02 10 -4.64 1.87 12 13 -8.47 -0.96 11 -7.21 -1.30 13 14 -6.65 -0.26 12 -4.18 1.90 14 15 -6.13 -0.62 13 -6.73 0.98 15 14 -5.94 -0.57 16 15 -8.04 -1.34 17 18 19 20 21 22 23 24 25 26 27 28 29 30

-18.05 -9.74 6.86 14.56 -16.37 -9.03 0.81 7.54 -12.09 -3.58 -3.19 3.75 -9.89 -5.63 -2.12 5.39 -9.69 -3.03 -4.55 1.94 -7.23 -0.16 -3.70 3.06 -9.34 -2.37 -6.44 1.24 -5.99 1.16 -5.67 0.12 -6.32 0.21 -8.60 -2.04 -5.92 0.38 -7.09 -1.40 -2.64 2.97 -9.06 -2.10 -1.93 4.82 -11.12 -4.54 4.44 10.46 -20.29 -12.83

while HAT from the methyl groups in the polyene chain strongly depend on the particular reacting carotenoid and those CH3 groups linked to C atoms at the end of the chain seem to be the most susceptible to react trough HAT processes. From the studied carotenoids the lowest barrier of reaction was found for TOR, which suggests that it should be the most reactive one in terms of H abstractions. However, because the HAT mechanism is susceptible of quantum tunneling, to make a

proper estimation of the relative weight of the different abstraction channels kinetic calculations are required. Barriers of reaction for RAF paths are reported in Tables 5 and 6 for benzene and water solutions, respectively. In the presence of the nonpolar solvent the lowest barriers for the OOH + β-carotene reaction corresponds to OOH addition to C5. However there are other channels with barrier heights close to that of channel 5. Therefore significant contributions to the

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TABLE 4: Barriers of Reaction in Terms of Enthalpies (∆H+) and Gibbs Free Energies (∆G+) in Benzene and Water Solutions, for the HAT Mechanism, at 298.15 K, All in kcal/mol BC site

∆H+

LYC ∆G+

2 11.94 16.56 3 12.11 17.46 4 1.47 7.28 1a)1b 17.26 22.41 5a 0.34 6.09 9a 3.94 9.26 13a 3.71 10.03

2 3 4 1a)1b 5a 9a 13a

site

TOR

∆H+ ∆G+

Benzene 3 3.27 9.95 4 1.41 7.08 1a)1b 6.27 12.35 5a 6.65 6.25 9a 0.92 9.17 13a 3.00 9.23

12.04 16.66 3 12.00 17.35 4 0.88 6.69 1a)1b 16.82 21.96 5a -0.01 5.73 9a 3.20 8.52 13a 2.91 9.23

Water 3.07 9.75 1.09 6.77 6.09 11.79 0.58 5.90 2.20 8.36 2.48 8.37

site

∆H+ ∆G+

2 11.71 16.94 3 11.62 16.47 4 1.15 6.34 1a)1b 16.86 22.80 5a 3.18 8.90 9a 1.84 7.85 13a 3.53 8.72 18a 3.04 9.21 22a 2.72 9.64 26a 3.31 8.25 30a)30b 0.90 6.01 2 11.71 16.94 3 11.84 16.69 4 1.15 6.34 1a)1b 17.21 23.15 5a 2.68 8.39 9a 1.92 7.93 13a 2.82 8.01 18a 2.97 9.14 22a 2.62 9.55 26a 2.89 7.83 30a)30b 0.37 5.48

TABLE 5: Barriers of Reaction in Terms of Enthalpies (∆H+) and Gibbs Free Energies (∆G+) in Benzene Solutions, for the RAF Mechanism, at 298.15 K, All in kcal/mol BC

LYC

TOR

site

∆H+

∆G+

site

∆H+

∆G+

site

∆H+

∆G+

5 6 7 8 9 10 11 12 13 14 15

-0.66 11.78 0.67 4.91 0.95 4.72 3.43 4.16 1.09 3.35 1.28

6.80 19.64 7.48 12.96 7.34 12.36 9.51 10.88 10.78 9.25 10.58

1 2 5 6 7 8 9 10 11 12 13 14 15

6.91 9.75 -0.32 8.69 0.72 7.38 1.77 4.01 1.86 3.28 1.49 2.93 1.81

13.84 16.58 5.55 16.18 7.40 13.14 8.63 11.16 7.67 8.70 7.90 9.02 6.56

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

-1.47 13.60 0.49 6.63 0.48 4.83 1.69 4.22 1.25 3.26 2.30 2.88 2.03 3.69 2.49 2.30 2.57 1.32 4.36 2.87 3.90 1.51 5.81 0.87 10.48 -0.56

6.44 22.52 7.31 14.46 6.82 12.03 7.67 11.86 8.10 9.31 9.52 10.09 8.07 10.81 9.94 9.15 9.07 7.95 10.96 9.03 11.19 8.66 12.70 7.68 16.65 5.60

overall RAF processes from these channels (7 and 9) might also be expected. For lycopene channel 5 shows the lowest barrier, which is about 1 kcal/mol lower than the closest one. Therefore the main contributions to the overall RAF process in this case is expected to come from OOH additions to C5. For the reaction of this radical with torulene the lowest barriers correspond to

TABLE 6: Barriers of Reaction in Terms of Enthalpies (∆H+) and Gibbs Free Energies (∆G+) in Water Solutions, for the RAF Mechanism, at 298.15 K, All in kcal/mol BC site

∆H

5 6 7 8 9 10 11 12 13 14 15

0.14 12.81 0.89 5.33 1.10 4.77 3.58 4.01 0.96 3.18 1.55

+

LYC +

site

∆H

7.60 20.68 7.71 13.39 7.50 12.42 9.67 10.73 10.65 9.07 10.85

1 2 5 6 7 8 9 10 11 12 13 14 15

7.06 9.76 0.25 9.17 0.79 7.18 1.65 3.94 2.19 3.17 1.47 2.59 1.98

∆G

+

TOR ∆G

+

13.98 16.60 6.13 16.65 7.47 12.95 8.51 11.09 8.00 8.59 7.88 8.68 6.74

site

∆H+

∆G+

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

-3.29 13.67 1.09 7.10 0.95 5.22 2.23 4.49 1.52 3.47 2.34 3.01 2.24 3.46 2.73 2.67 2.80 1.63 3.88 2.83 4.18 1.67 6.21 1.17 10.39 0.29

4.63 22.59 7.92 14.93 7.29 12.42 8.21 12.13 8.37 9.53 9.57 10.23 8.29 10.58 10.18 9.52 9.30 8.26 10.48 8.98 11.47 8.82 13.09 7.99 16.56 6.45

additions to C30, followed by additions to C5. Therefore the forming adducts are expected to correspond to those RAF channels. The lowest of all the studied RAF paths is that of OOH addition to C5 in lycopene, therefore this carotenoid is expected to have the best free radical scavenging activity through RAF mechanism. The presence of a polar environment seems to modify some of the above-described trends for RAF processes. For BC barriers corresponding to OOH additions to C5, C7 and C9 were found to be of similar height. For LYC the barrier of additions to C15 becomes similar to that involving C5. This suggests a wider product distribution in polar than in nonpolar environments for BC and LYC when reacting with peroxyl radicals. For TOR, on the other the lowest barrier in water solution is that corresponding to additions to C5, followed by additions to C30, i.e., the relative feasibility of these two processes is inverted, compared to when they take place in benzene solutions. Kinetics. Theoretical modeling always involves a delicate balance between the computational cost and the level of theory chosen for the task at hand. In the particular case of the present work the systems under study are large-sized, involving 40 heavy atoms without counting those in the free radical. In addition the possible reaction paths are numerous, 74 to be precise. On top of these difficulties, we are also facing a particular challenging problem: to properly describe the competition between HAT and RAF mechanisms. For example such competition between H abstraction and addition mechanisms has been studied before at CCSD(T)/aug-cc-pVDZ//MP2/6311++G(d,p) for the reaction of atomic radical F with propyne.33 Obviously, such a sophisticated level of theory is out the question in the present work. Therefore we have used a different strategy. Two reference reactions have been studied, and calculated at the same level of theory used for the rest of the calculations: OH + ethane reaction (HAT reference) and OH + ethane reaction (RAF reference). They are also radical-

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molecule reactions involving an oxygenated radical and a hydrocarbon, and have been chosen based on the abundant experimental data available for them. These reference reactions have been used to compute correction factors for each kind of reaction according to:

f HAT )

f

RAF

)

exp kHAT (ethane + OH) calc kHAT (ethane + OH) exp kRAF (ethene + OH) calc kRAF (ethene + OH)

(6)

corr calc kj,RAF (Car + OOH) ) f RAFkj,RAF (Car + OOH)

(7)

In all of the above expressions the calculated rate constants (kcalc) were obtained from Conventional Transition State Theory (TST)35-37 and 1 M standard state as:

(8)

where kB and h are the Boltzman and Planck constants, ∆G+ is the Gibbs free energy of activation, σ represents the reaction path degeneracy (accounting for the number of equivalent reaction paths), and κ is the tunneling correction. We have assumed that once a specific pathway has started it proceeds to completion, independently of the other pathways; that is, there is no mixing or crossover between different pathways. On this basis, the overall HAT and RAF rate coefficients, for each carotenoid, can be estimated by summing up the rate coefficients calculated for the corresponding i HAT channels and j RAF channels as N

Overall kHAT )

corr (Car + OOH) ∑ ki,HAT

(9)

i)1

M

Overall kRAF )

corr (Car + OOH) ∑ kj,RAF

(10)

j)1

The total rate coefficient (for each carotenoid) that accounts for the OOH disappearance, and that should correspond to the experimentally observed one, has then been calculated as Overall Overall kTotal ) kHAT + kRAF

LYC

TOR

HAT RAF total

1.32 × 1003 2.80 × 1005 2.81 × 1005

Benzene 5.94 × 1002 1.69 × 1006 1.69 × 1006

2.51 × 1003 9.44 × 1005 9.47 × 1005

HAT RAF total

7.01 × 1002 5.62 × 1004 5.69 × 1004

Water 3.02 × 1002 3.44 × 1005 3.44 × 1005

1.61 × 1003 1.45 × 1006 1.45 × 1006

(5)

corr calc ki,HAT (Car + OOH) ) f HATki,HAT (Car + OOH)

kBT -(∆G*)/RT e h

BC

(4)

The experimental values used to obtain the correction factors are those proposed by Atkinson et al.:34 1.50 × 108 L mol-1 s-1 for ethane + OH reaction and 5.42 × 109 L mol-1 s-1 for ethane + OH reaction. Once these factors were computed they were used to correct the rate constants corresponding to every HAT and RAF path according to

k ) κσ

TABLE 7: Calculated Rate Constants (L mol-1 s-1) for RAF and HAT Mechanisms, at 298.15 K

nonpolar and polar environments, respectively, for the three studied cases. Since the electron transfer mechanism was previously ruled out13 and the contribution of the HAT mechanism is less than 2%, it can be stated that the RAF mechanism is the main one for the reaction of the studied carotenoids with the OOH radical, these results are in agreement with the previous experimental data.10-12 In particular they are in line with the results of El-Agamey and McGarvey38 who have recently shown that in nonpolar solvents only addition radicals are formed. The values of the overall HAT and RAF rate coefficients, as well as the total rate coefficient for the reactions of OOH radical with the studied carotenoids are reported in Table 7. Both torulene and lycopene were found to be more reactive toward OOH radicals than β-carotene. TOR reacts 3.4 and 1.9 times faster than BC through RAF and HAT mechanisms, respectively, when the reactions take place in a nonpolar environment. In water solutions TOR becomes even more reactive toward OOH with rate constants that are 2.3 (HAT) and 25.8 (RAF) times faster than those of BC. Since TOR was also described as a better antiradical through the ET mechanism,13 it can be definitely proposed as a better fighter than BC against peroxyl radical. LYC reacts with OOH 6 times faster than BC, and 1.8 times faster than TOR through the RAF mechanism in benzene solutions. Even though its reaction is the slowest when the reaction takes place by HAT processes, this last mechanism seems to be of minor importance for the reactions of carotenoids with peroxyl radical. Lycopene was found to be the one with highest antioxidant activity, among the studied carotenoids, when the RAF mechanism is preponderant in the free radical scavenging activity and the reaction takes place in a nonpolar environment. Therefore, and taking into account the very low solubility of carotenoids in water, LYC is proposed as the best choice for fighting peroxyl radicals. Based on the discussion above, the reactivity of the studied carotenoids toward peroxyl radical follows the trend: LYC > TOR > BC in nonpolar environment and TOR > LYC > BC in aqueous solution. However, these results should not be extended to other kind of free radicals since the nature of the latter may influence the relative importance of the HAT, RAF and ET mechanisms in the antioxidant activity of carotenoids, and any other antioxidant for that matter. The branching ratios (Γ) corresponding to each computed path of reaction are provided as Supporting Information (Tables S3 to S5). They were calculated for HAT and RAF paths, respectively, as

(11)

The contributions of the RAF mechanism to the total OOH + Car reactions were found to be greater than 99 and 98%, in

HAT

Γ

)

corr ki,HAT Overall kHAT

× 100

(12)

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Γ

)

corr kj,RAF Overall kRAF

× 100

Galano and Francisco-Marquez

(13)

Even though the branching ratios are reported for benzene and water solutions, for the sake of shortness, and taking into account the much larger solubility of carotenoids in nonpolar solvents, we are going to discuss in detail only the branching ratios for reactions taking place in the latter. OOH hydrogen abstractions from β-carotene mainly involve Overall of 5.2% and 93.8%, sites 4 and 5a with contributions to kHAT respectively. Through the RAF mechanism the main site of reaction in BC was found to be site 5, contributing 57.4% to kOverall RAF . Two other minor, but significant, RAF paths were found: those corresponding to OOH addition to C9 and C7, with contributions to kOverall RAF of 22.8% and 18.0%, respectively. These results are in agreement with previously reported experimental product analysis studies. Different products have been identified for the oxidation of BC, in particular 5,6-epoxy-β-carotene; 5,6,5′,6′-diepoxy-β-carotene; 5,8-epoxy-β-carotene; and 5,8,5′,8′diepoxy-β-carotene.39,40 Since epoxidation of olefins by different peroxyl radicals proceeds via addition reactions,41,42 the abovementioned products not only support the preponderance of RAF mechanism for the reactions of peroxyl radicals with BC, but also that a significant proportion of the reaction involves site 5. HAT processes involving LYC mainly take place from sites Overall , respectively. 4 and 9a contributing 26.8% and 71.5% to kHAT The most reactive sites through the RAF mechanism were found to be C5 and C15 with contributions to the overall RAF rate constant of 77.5% and 14.3%, respectively. All other channels Overall . As far as we of reaction contributes less than 5% to kRAF know there are no previous reports on product analysis for peroxyl reactions with lycopene. However, according to our results the main formed adducts should be at the end and just in the middle of the conjugated chain, i.e., involving sites 5 and 15. Therefore 5,6-epoxy-lycopene, 5′,6′-epoxy-lycopene, 15,15′-epoxy-lycopene, 5,6,5′,6′-diepoxy-lycopene, and probably 5,6,15′,15′-diepoxy-lycopene are expected to be formed. TOR is the only one of the studied carotenoids that does not include two equivalent halves in its structure. Therefore the number of different reactive sites is larger than those of BC and LYC. This might suggest a wider product distribution. However it is not the case. As for the other two studied carotenoids, only two major paths of reaction were identified for HAT processes. They are those involving sites 4 and 30, Overall of 8.8% and 87.6%, respectively. with contributions to kHAT However, when TOR reacts with OOH, through the RAF mechanism, three different paths of reactions were found with Overall larger than 5%. These paths correspond contributions to kRAF to OOH addition to C5, C9, and C30, the latter being the main addition site. Their contributions to the overall adduct formation rate constant are 15.5%, 8.2%, and 64.4%, respectively. There are no previous products analyses reported for peroxyl radicals with torulene. However, based on our results, and on the presence of a cyclohexene moiety identical to that in BC, we can predict the formation of the following epoxidation products: 5,6-epoxy-torulene and 5,8-epoxy-torulene. In addition 29,30epoxy-torulene is also expected to be formed. Moreover this is expected to be the major observable product. Diepoxide products are also possible: at least 5,6,29,30-diepoxy-torulene and 5,8,29,30-diepoxy-torulene. Conclusions Hydrocarbon carotenoids are predicted to react with peroxyl radicals, both in polar and in nonpolar environments, mainly

by adduct formation processes. They were found to account for more than 98% to the total OOH + Car reactions, regardless of the polarity of the environment. Lycopene and torulene are predicted to be more efficient than β-carotene as peroxyl radical scavengers. The reactivity of the studied carotenoids toward peroxyl radical follows the trend: LYC > TOR > BC when the reactions take place in nonpolar environments and TOR > LYC > BC in aqueous solutions. OOH adducts are predicted to be formed mainly at the terminal sites of the conjugated polyene chains. The main addition sites were found to be C5 for β-carotene and lycopene and C30 for torulene, when the reaction tales place in nonpolar media. Acknowledgment. A.G. thanks project CONACYT 46124 PROMEP and Laboratorio de Visualizacio´n y Co´mputo Paralelo at UAM - Iztapalapa for the access to its computer facilities. M.F.M. thanks the Direccio´n General de Servicios de Co´mputo Acade´mico (DGSCA) at Universidad Nacional Auto´noma de Me´xico, and Instituto de Ciencia y Tecnologı´a del D.F. for a postdoctoral research fellowship. Supporting Information Available: Geometrical parameters of relevant stationary points and branching ratios for each modeled reaction path. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) van der Berg, H.; Faulks, R.; Fernando Granado, H.; Hirschberg, J.; Olmedilla, B.; Sandmann, G.; Southon, S.; Stahl, W. J. Sci. Food Agric. 2000, 80, 880. (2) Krinsky, N. I. Annu. ReV. Nutr. 1993, 13, 561. (3) Edge, R.; McGarvey, D. J.; Truscott, T. G. J. Photochem. Photobiol. 1997, 41, 189. (4) Simic, M. G. Mutat. Res. 1988, 202, 377. (5) Burton, G. W. J. Nutr. 1989, 119, 109. (6) Martinez, A.; Rodriguez-Girones, M. A.; Barbosa, A.; Costas, M. J. Phys. Chem. A 2008, 112, 9037. (7) Everett, S. A.; Dennis, M. F.; Patel, K. B.; Maddix, S.; Kundu, S. C.; Willson, R. L. J. Biol. Chem. 1996, 271, 3988. (8) Woodall, A. A.; Britton, G.; Jackson, M. J. Biochim. Biophys. Acta 1997, 1336, 575. (9) Mortensen, A.; Skibsted, L. H. J. Agric. Food Chem. 1997, 45, 2970. (10) Burton, G. W.; Ingold, K. U. Science 1984, 224, 569. (11) Liebler, D. C.; McClure, T. D. Chem. Res. Toxicol. 1996, 9, 8. (12) Mortensen, A. Free Rad. Res. 2002, 36, 211. (13) Galano, A. J. Phys. Chem. B 2007, 111, 12898. (14) Edge, R.; Land, E. J.; McGarvey, D. J.; Burke, M.; Truscott, T. G. FEBS Lett. 2000, 471, 125. (15) Jonsson, M. J. Phys. Chem. 1996, 100, 6814. (16) Woodall, A. A.; Lee, S. W.-M.; Weesie, R. J.; Jackson, M. J.; Britton, G. Biochim. Biophys. Acta 1997, 1336, 33. (17) Martinez, A.; Barbosa, A. J. Phys. Chem. B 2008, 112, 16945. (18) Bohm, F.; Tinkler, J. H.; Truscott, T. G. Nat. Med. 1995, 1, 98. (19) Henry, L. K.; Puspitasari-Nienaber, N. L.; Jaren-Galan, M.; van Breemen, R. B.; Catignani, G. L.; Schwartz, S. J. J. Agric. Food Chem. 2000, 48, 5008. (20) Kopczynski, M.; Lenzer, T.; Oum, K.; Seehusen, J.; Seidel, M. T.; Ushakov, V. G. Phys. Chem. Chem. Phys. 2005, 7, 2793. (21) Gaussian 03, ReVision D.01, Frisch, M. J. Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, Jr., J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.;

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