Formation and decay dynamics of vitamin e radical in the antioxidant reaction of vitamin E

Article abstract of DOI:10.1246/bcsj.82.494

In order to understand the dynamics of antioxidant actions of vitamin E (α-, β-, γ-, and δ-tocopherols, TocH) in biological systems, kinetic study of the formation and decay reactions of vitamin E radicals (α-, β-, γ-, and γ- tocopheroxyls, Toc ?) has been performed in organic solvents, using stopped-flow spectrophotometry. By mixing α-, β-, γ-, and δ-TocH with aryloxyl radical (ArO ?) in ethanol, the peaks of the UV-vis absorption due to α-, β-, γ-, and δ-Toe? radical appeared rapidly at ca. 430-340 nm, showed maxima, and then decayed gradually. The second-order rate constants (κ_a and 2κ_d) for the formation and decay (that is, bimolecular disproportionation) reactions of a-Toe were determined by comparing the observed curves with the simulation ones obtained by the numerical calculation of differential equations related to the above reactions. From the results, the wavelengths of absorption maxima (λ_max ⁱ) and molar extinction coefficients (ε) (i = 1-4) of the optical spectra were determined for α-Toc? radical. Notable solvent effects have been observed for the reaction rates (κ_f and 2κ_d) and absorption spectra (λ_max ⁱ and ε_i) of α-Toc? radical. The scheme of the formation and decay reactions of α-, β-, γ-, and δ-Toc? radicals has been discussed based on the results obtained.

Full text of DOI:10.1246/bcsj.82.494

494
Bull. Chem. Soc. Jpn. Vol. 82, No. 4, 494–503 (2009)
© 2009 The Chemical Society of Japan
Formation and Decay Dynamics of Vitamin E Radical
in the Antioxidant Reaction of Vitamin E
Kazuo Mukai,*1 Aya Ouchi,*1 Akiko Mitarai,1 Keishi Ohara,1 and Chihiro Matsuoka2
1Department of Chemistry, Faculty of Science, Ehime University, Matsuyama 790-8577
2Department of Physics, Faculty of Science, Ehime University, Matsuyama 790-8577
Received October 27, 2008; E-mail: mukai@chem.sci.ehime-u.ac.jp
In order to understand the dynamics of antioxidant actions of vitamin E (¡-, ¢-, £-, and ¤-tocopherols, TocH) in
biological systems, kinetic study of the formation and decay reactions of vitamin E radicals (¡-, ¢-, £-, and ¤-
tocopheroxyls, Toc●) has been performed in organic solvents, using stopped-flow spectrophotometry. By mixing ¡-, ¢-,
£-, and ¤-TocH with aryloxyl radical (ArO●) in ethanol, the peaks of the UV-vis absorption due to ¡-, ¢-, £-, and
¤-Toc● radical appeared rapidly at ca. 430-340 nm, showed maxima, and then decayed gradually. The second-order rate
constants (kf and 2kd) for the formation and decay (that is, bimolecular disproportionation) reactions of ¡-Toc● were
determined by comparing the observed curves with the simulation ones obtained by the numerical calculation of
differential equations related to the above reactions. From the results, the wavelengths of absorption maxima (-maxi) and
molar extinction coefficients (¾i) (i = 1-4) of the optical spectra were determined for ¡-Toc● radical. Notable solvent
effects have been observed for the reaction rates (kf and 2kd) and absorption spectra (-maxi and ¾i) of ¡-Toc● radical. The
scheme of the formation and decay reactions of ¡-, ¢-, £-, and ¤-Toc● radicals has been discussed based on the results
obtained.
Vitamin E (¡-, ¢-, £-, and ¤-tocopherols, TocH) is well
Detailed kinetic studies have been performed for reactions 1
and 5, and the mechanism involved has been studied
extensively by several investigators.1-4,11,20-22 However, exam-
ples of the measurement of the rate constants (k2, k3, k4, and
known to scavenge active free radicals (LOO● and LO●)
generated in biological systems. The antioxidant actions of the
tocopherols have been ascribed to the hydrogen abstraction
reaction from a phenolic hydroxy group, producing corre-
sponding tocopheroxyl (Toc●) radicals (Figure 1 and reac-
tion 1).1-4 The Toc● radicals produced may combine with
another peroxyl (LOO●) radical (reaction 2).1 If tocopherols
exist in biomembranes and oils, the Toc● radicals may react
with unsaturated lipids (LH) (reaction 3) and lipid hydro-
peroxides (LOOH) (reaction 4).5-9 These reactions 3 and 4 are
known as prooxidant reactions, which induce the degradation
of unsaturated lipids. Toc● radicals may be regenerated to
O
O
C16H33
C16H33
O
O
α-Toc •
β-Toc •
O
O
¹
TocH by vitamin C (ascorbate anion, AsH ) (reaction 5)2,3,10,11
C16H33
C16H33
and/or ubiquinol12 in biological systems, to protect the above
prooxidant effects. Further, Toc● radicals disappear by bimo-
lecular reaction with another Toc● to give non-radical products
(NRP) (reaction 6).1,13-19
O
O
γ-Toc •
δ-Toc •
kinh
LOOꢀ þ TocH ꢁꢁꢁ! LOOH þ Tocꢀ
ð1Þ
ð2Þ
ð3Þ
ð4Þ
ð5Þ
ð6Þ
k2
Tocꢀ þ LOOꢀ ꢁꢁꢁ! Toc-OOL
k3
O
Tocꢀ þ LH ꢁꢁꢁ! TocH þ Lꢀ
O
OCH3
k4
Tocꢀ þ LOOH ꢁꢁꢁ! TocH þ LOOꢀ
O
kr
Tocꢀ þ AsHꢁ ꢁꢁꢁ! TocH þ Asꢀꢁ
2kd
5,7-Di-iPr-Toc • model
ArO •
Tocꢀ þ Tocꢀ ꢁꢁꢁ! No-radical products ðNRPÞ
As described above, ¡-, ¢-, £-, and ¤-Toc● radicals are
important key radicals, which appear in the process of the
antioxidant and prooxidant actions of ¡-, ¢-, £-, and ¤-TocH.
Figure 1. Molecular structures of ¡-, ¢-, £-, and ¤-
tocopheroxyl (Toc●), 5,7-diisopropyltocopheroxyl model
(5,7-Di-i-Pr-Toc●), and aryloxyl (ArO●) radical.
Published on the web April 11, 2009; doi:10.1246/bcsj.82.494

K. Mukai et al.
Bull. Chem. Soc. Jpn. Vol. 82, No. 4 (2009)
495
2.5
2.0
1.5
1.0
0.5
0
2kd) for reactions 2, 3, 4, and 6 are limited, because of the
instability of ¡-, ¢-, £-, and ¤-Toc● radicals. The reaction of
In Ethanol
ArOH
[ArO ] = [ -TocH]
265 nm
LOO● with ¡-Toc● radical (reaction 2) is very fast with a rate
¹1 23
constant of 3 © 108 M¹1 s
.
The reaction rates (k3 and k4)
= [ -Toc ] = [ArOH]
ArO
= 1.00 × 10-4
M
376 nm
have been measured by using more stable 5,7-diisopropyl-
tocopheroxyl (5,7-Di-i-Pr-Toc●) radical (Figure 1), and the
structure-activity relationship has been clarified for reactions 3
and 4.7,24,25
In previous work,26 we measured the reaction rates (ks) of ¡-,
¢-, £-, and ¤-tocopherols with 2,6-di-t-butyl-4-(4-methoxy-
phenyl)phenoxyl (ArO● (abbreviated to aryloxyl, hereafter)
(Figure 1) in ethanol (reaction 7) using stopped-flow
spectrophotometry. ArO● can be regarded as a model for
active oxygen radicals (LOO● and others) in biological
systems.
TocH
292 nm
Toc
428 nm
ArO
580 nm
600
300
400
500
700
ks
ArOꢀ þ TocH ꢁꢁꢁ! ArOH þ Tocꢀ
ð7Þ
Wavelength / nm
The second-order rate constants (ks) obtained were 5.12 © 103
(¡-TocH), 2.24 © 103 (¢-TocH), 2.42 © 103 (£-TocH), and
Figure 2. UV-visible absorption spectra of ArOH, ¡-TocH,
ArO●, and ¡-Toc● with the same concentrations of
1.00 © 10¹4 M in ethanol.
¹1
1.00 © 103 (¤-TocH) M¹1 s in ethanol at 25.0 °C. ArO●-
scavenging rates (ks) increased with increasing the number
of methyl substituents at the phenol ring, that is, the elec-
tron-donating capacity of tocopherols. The relative rates
(¡:¢:£:¤ = 100:44:47:20) agreed well with those obtained in
studies on the reactivity (kinh) of TocH toward poly(peroxy-
styryl)peroxyl radicals (100:41:44:14) in chlorobenzene using
the O2 consumption method (reaction 1).1 The results suggest
that the relative reactivity of TocH in solution probably does
not depend on the type of oxyradicals (ArO● and LOO●)
used.26-28
In the present work, in order to understand the dynamics of
antioxidant actions of vitamin E (¡-, ¢-, £-, and ¤-tocopherols,
TocH) in biological systems, kinetic study of formation and
decay reactions 7 and 6 of vitamin E radicals (¡-, ¢-, £-, and ¤-
Toc●) has been performed in several organic solvents, using
stopped-flow spectrophotometry. By mixing ¡-, ¢-, £-, and ¤-
TocH with ArO● in organic solvents, UV-vis absorption
spectra due to Toc● radicals appeared rapidly in the wavelength
region of 340-430 nm, showed a maximum, and then decayed
gradually. The simulation of the formation and decay curve of
¡-Toc● was performed by the numerical calculation of
differential equations derived from reactions 6 and 7, using
the fourth-order Runge-Kutta method.29 From the results, the
rate constant (2kd) for the decay reaction and the molar
extinction coefficients (¾) of the UV-vis absorption spectra of
¡-Toc● radical were determined.
Results
UV-Vis Absorption Spectra of ¡-, ¢-, £-, and ¤-
Tocopheroxyl Radicals.
The aryloxyl radical (ArO●) is
stable in the absence of ¡-tocopherol, and shows absorp-
tion peaks at -max = 376 nm (¾ = 16900 M¹1 cm¹1; 1 M = 1
mol dm¹3), 580 nm (¾ = 4330 M¹1 cm¹1), and 530 nm (shoul-
der) (¾ = 3100 M¹1 cm¹1) in ethanol solution. The phenol
precursor (ArOH) of ArO● and ¡-tocopherol show absorption
peaks at -max = 265 nm (¾ = 19800 M¹1 cm¹1) and 292 nm
(¾ = 2990 M¹1 cm¹1), respectively, in ethanol; no absorptions
were observed in the visible absorption region, as shown in
Figure 2. By adding the ethanol solution of ¡-tocopherol
(1.88 © 10¹3 M) to the solution of ArO● (3.33 © 10¹5 M) (1:1
in volume) at 25.0 °C, the absorption spectrum of ArO●
disappeared quickly, and changed to that of ¡-tocopheroxyl
with four absorption peaks at -max = 428, 408, 387sh,
and 340sh nm (Figure 3a). ¡-Tocopheroxyl is unstable at
25.0 °C, and its absorption peaks decrease gradually after
passing though the maximum (Figure 4a). The spectrum
of the ¡-Toc● at tmax = 504 ms is shown in Figure 3a. The
absorption spectra of ArOH, ArO●, ¡-TocH, and ¡-Toc●
having the same concentration of 1.00 © 10¹4 M¹1 s are
¹1
shown in Figure 2.
The reactions of ¡-TocH with ArO● were also performed in
dichloromethane, chloroform, diethyl ether, benzene, hexane,
and heptane solvents. The formation and decay curves of ¡-
Toc● in benzene and the absorption spectrum at tmax = 365 ms
are shown in Figures 4c and 3b, respectively. The values of
and ¾ (i = 1-4) obtained for ¡-Toc● radical are listed in
Table 1. The values of ¾ were determined by the analyses of
Experimental
¡-, ¢-, £-, and ¤-Tocopherols used in the present work were
kindly supplied by Eisai Co., Ltd. ArO● radical was prepared
according to the method of Rieker and Scheffler.30
i
-
max
i
i
The kinetic data were obtained with a Unisoku Model RSP-
1000 stopped-flow spectrophotometer by mixing equal volumes of
solutions of antioxidants and ArO● under nitrogen atmosphere.26
The shortest time for mixing two solutions and recording the first
data point (that is, dead time) was 10-20 ms. The reaction was
monitored with either single wavelength detection or photo-diode
array detector attached to the stopped-flow spectrophotometer. All
measurements were performed at 25.0 « 0.5 °C.
the formation and decay curves of the ¡-Toc● radical, as
described later.
Similarly, upon mixing of ArO● (6.84 © 10¹5 M) with
excess ¢-TocH (3.56 © 10¹3 M) in ethanol, two absorption
peaks at 431 and 409 nm of ¢-Toc● appeared instantly, showed
a maximum, and then its intensity decreased gradually, as
shown in Figure 5a and Figure 6. Differing from the case of

496
Bull. Chem. Soc. Jpn. Vol. 82, No. 4 (2009)
Formation and Decay Dynamics of Vitamin E Radical
¡-Toc●, the absorption spectrum of ArO● does not disappear
completely by the reaction and weak absorption peaks remain
at 376 and 580 nm, although the concentration of the ArO●
([ArO●]) is less than 5% of the initial concentration of ArO●
([ArO●]t=0 = 6.84 © 10¹5 M).
By reacting £-TocH (4.81 © 10¹3 M) with ArO● (6.97 ©
10¹5 M) in ethanol, the absorption spectrum of £-Toc● was
observed at -max = 432 nm. The absorption spectrum at
tmax = 200 ms is shown in Figure 5b. The concentration of
ArO● remaining at tmax = 200 ms was estimated to be
1.4 © 10¹5 M, which corresponds to about 20% of the initial
concentration of ArO● ([ArO●]t=0). The result indicates the
existence of equilibrium in reaction 7. As shown in Figure 2,
the absorption spectrum of ArO● shows a minimum at 420-
440 nm (¾ = 200 M¹1 cm¹1). Therefore, the absorbance of the
ArO● at 432 nm is very weak, and is almost negligible
compared with that of the £-Toc●. Similarly, weak absorption
spectrum of ¤-Toc● was observed at 432 nm, and decreased
rapidly with time, as shown in Figure 5c and Figure 6,
respectively.
As shown in Figure 6, the same concentration of ArO●
(8.88 © 10¹5 M) was used for the reaction with ¡-, ¢-, £-, and
¤-tocopherols. Therefore, we can expect that the absorption
intensities of ¢-, £-, and ¤-Toc● at tmax are similar to that of ¡-
Toc●, if the values of the molar extinction coefficient (¾) of ¢-,
£-, and ¤-Toc● are similar to that of ¡-Toc●. However, the
intensities of Toc● radicals at tmax decreased rapidly in the
order of ¡-Toc● (Absorbance = 0.408 at -max = 428 nm) > ¢-
Toc● (0.131 at 431 nm) > £-Toc● (0.073 at 432 nm) > ¤-Toc●
(0.034 at 434 nm) in ethanol, as shown in Figure 6. The reason
will be discussed in a later section.
0.3
(a)
Ethanol
Toc
428 nm
= 4370 M-1cm-1
0.2
0.1
0
[ArO ] = 3.33 × 10-5
M
[
-TocH] = 1.88 × 10-3
M
at tmax = 504 ms
350
400
450
500
550
Wavelength / nm
1.0
0.8
0.6
0.4
0.2
0
(b)
Benzene
The Rates of the Aryloxyl-Radical-Scavenging (ks) of ¡-,
¢-, £-, and ¤-Tocopherols in Organic Solvents. Measure-
ments of the rate constant (ks) for the reaction of ArO● radical
with ¡-, ¢-, £-, and ¤-TocH were performed in ethanol solution
(reaction 7). The decay rate of ArO● radical was measured by
following the decrease in absorbance at 376 and/or 580 nm of
the ArO●.26 The pseudo-first-order rate constants (kobsd) at 376
and/or 580 nm were linearly dependent on the concentration of
TocH ([TocH]), and thus the rate equation is expressed as
Toc
424 nm
= 3450 M-1cm-1
[ArO ] = 9.66 × 10-5
-TocH] = 3.71 × 10-4
at tmax = 365 ms
M
[
M
ꢁd½ArOꢀꢂ=dt ¼ kobsd½ArOꢀꢂ ¼ ks½TocHꢂ½ArOꢀꢂ
ð8Þ
350
400
450
500
550
where ks is the second-order rate constant for oxidation of TocH
by ArO● radical. The rate constants (ks) were obtained by
plotting kobsd against [TocH]. The rate constants (ks) of ¡-, ¢-,
£-, and ¤-TocH increase in the order of ¤-TocH < £-TocH µ ¢-
TocH < ¡-TocH, as described in Introduction.26
Wavelength / nm
Figure 3. UV-vis absorption spectra of ¡-Toc● in (a)
ethanol and (b) benzene at tmax = 504 and 365 ms,
respectively.
Table 1. The Values of Dielectric Constant (¾dielectric-constant), UV-Visible Absorption Maxima (-maxi), and Molar
Extinction Coefficients (¾i) (i = 1-4) of the ¡-Tocopheroxyl Radical in Several Organic Solvents
-
1/nma)
-
2/nma)
-
3/nma)
-
4/nma)
max
max
max
max
(¾3/M¹1 cm
Solvent
Ethanol
¾
dielectric-constant
(¾1/M¹1 cm
)
(¾2/M¹1 cm
)
)
(¾4/M¹1 cm
)
¹1
¹1
¹1
¹1
24.58
428 (4370)
426 (3800)b)
427 (4100)
427 (4320)
421 (3500)
424 (3450)
423 (6700)c)
418 (3080)
418 (2500)
3
408 (3010)
387shd) (1630)
340shd) (3790)
Dichloromethane
Chloroform
Diethyl ether
Benzene
8.931
4.806
4.335
2.3
408 (2630)
408 (2920)
400 (2150)
404 (2070)
387 (1150)
387 (1320)
381 (1270)
383shd) (1170)
335 (3120)
345 (3270)
341 (2810)
344 (2620)
Heptane
Hexane
1.924
1.880
398 (1860)
398 (1520)
4
374 (1360)
373 (1290)
345 (2700)
341 (2040)
a) Experimental errors in -max1, -max2, and -max are «1 nm, and in -max are «5 nm. b) See Ref. 19. c) See Ref. 31.
d) sh: Shoulder.

K. Mukai et al.
Bull. Chem. Soc. Jpn. Vol. 82, No. 4 (2009)
497
(b)
10
8
Observed
(a)
(b)
(c)
Simulated
(d)
16
14
12
10
8
(a)
10
9
6
-5
8
[ArO ] = 8.88 10 M
4
(a) [ -TocH] = 6.97 10-3 M
(b) [ -TocH] = 3.49 10-3 M
(c) [ -TocH] = 1.39 10-3 M
(d) [ -TocH] = 3.49 10-4 M
7
2
6
0
0.1 0.2 0.3 0.4 0.5 0.6
Time / s
0
0
1
2
3
4
5
2kd = 0 M-1s-1
2kd = 1.17 × 103 M-1s-1
Time / s
2kd = 1.30 × 103 M-1s-1
2kd = 1.43 × 103 M-1s-1
12
(c)
6
2kd = 0 M-1s-1
10
8
4
2kd = 8.55 × 102 M-1s-1
ks = 5.12 × 103 M-1s-1
[ArO ] = 8.88 × 10-5
Observed
2kd = 9.50 × 102 M-1s-1
2
M
6
2kd = 1.05 × 103 M-1s-1
[
-TocH] = 6.97 × 10-3
M
Ethanol
at 25.0
Observed
4
0
ks = 9.87 × 104 M-1s-1
[ArO ] = 9.66 × 10-5
0
2
4
6
8
10
M
2
Time / s
[
-TocH] = 3.71 × 10-4
M
Benzene
at 25.0
0
0
2
4
6
8
10
Time / s
1
Figure 4. Time dependence of the concentrations of ¡-Toc● radical observed at -max (Table 1) during reaction of ArO● with ¡-
TocH in (a) ethanol, (b) ethanol, and (c) benzene at 25.0 °C (Solid line). Dotted line is a simulation curve. The values of [ArO●]t=0
and [¡-TocH]t=0 are shown in Figures 4a-4c.
In the case of ¡-TocH, the measurements were performed in
ꢁd½ArOꢀꢂ=dt ¼ ks½TocHꢂ½ArOꢀꢂ
d½ArOHꢂ=dt ¼ ks½TocHꢂ½ArOꢀꢂ
ð9Þ
several organic solvents. The reaction rates (ks) increased with
decreasing polarity of solvent (Table 2), as reported in previous
work.33 When the logarithm of the rate constant (log ks) was
plotted as a function of the reciprocal of the solvent dielectric
constants (1/¾dielectric-constant), a linear correlation was ob-
served.33
ð10Þ
ð11Þ
ð12Þ
ð13Þ
ꢁd½TocHꢂ=dt ¼ ks½TocHꢂ½ArOꢀꢂ
d½Tocꢀꢂ=dt ¼ ks½TocHꢂ½ArOꢀꢂ ꢁ 2kd½Tocꢀꢂ
2
2
d½NRPꢂ=dt ¼ 2kd½Tocꢀꢂ
Analysis of the Formation and Decay Reactions of ¡-, ¢-,
£-, and ¤-Tocopheroxyl Radicals in Organic Solvents, Using
the Fourth-Order Runge-Kutta Method. By reacting ¡-
TocH with ArO● in organic solvents (reaction 7), ¡-Toc●
radical is produced rapidly, and disappears by a bimolecular
There are three relations (eqs 14-16) between the concentra-
tions of constituents.
½ArOꢀꢂt þ ½ArOHꢂt ¼ ½ArOꢀꢂt¼0 ¼ c1
½TocHꢂt þ ½Tocꢀꢂt þ 2½NRPꢂt ¼ ½TocHꢂt¼0 ¼ c2
ð14Þ
ð15Þ
reaction (reaction 6).1,13-19
ꢁ½ArOꢀꢂt þ ½TocHꢂt ¼ ꢁ½ArOꢀꢂt¼0 þ ½TocHꢂt¼0 ¼ ꢁc1 þ c2
ð16Þ
Where, for instance, c1 = [ArO●]t=0 is a concentration of ArO●
at t = 0, and [ArO●]t is a concentration of ArO● at t = t.
Therefore, only eqs 9, 12, and 13 are independent equations.
Setting [ArO●]t = X1, [Toc●]t = X2, and [NRP] = X3, we can
obtain
ks
ArOꢀ þ TocH ꢁꢁꢁ! ArOH þ Tocꢀ
(7)
(6)
2kd
Tocꢀ þ Tocꢀ ꢁꢁꢁ! No-radical products ðNRPÞ
Where the rate of ArO●-scavenging (ks) in reaction 7 equals
that of Toc●-formation (kf), that is, ks = kf. Reaction equa-
tions included in the above reactions 6 and 7 are as follows
(eqs 9-13):

498
Bull. Chem. Soc. Jpn. Vol. 82, No. 4 (2009)
Formation and Decay Dynamics of Vitamin E Radical
0.3
0.2
0.1
(a)
(b)
(c)
The simulation of the formation and decay curves of ¡-Toc●
at -max1 = 428 nm in ethanol was performed by varying the
rate (2kd) of bimolecular reaction and the molar extinction
coefficient (¾1), where the concentration of ¡-Toc● radical,
[¡-Toc●]t, was calculated from the absorption spectra, by using
-Toc in Ethanol
Lambert-Beer’s equation (Absorbance (At) = ¾1[¡-Toc●]t).
-Toc
431 nm
¹1 26
The value of ks (=kf = 5.12 © 103 M¹1 s
)
in ethanol was
used for the calculation. As shown in Figure 4b, the concen-
tration (that is, the absorbance) of ¡-Toc● radical at tmax
increases with increasing the concentration of ¡-TocH and
approaches a constant value, because at high concentration of
¡-TocH ¡-Toc● appears rapidly and the decay of ¡-Toc● due
to bimolecular reaction is very small and negligible. Therefore,
[ArO ] = 6.84 × 10-5
M
[
-TocH] = 3.56 × 10-3
M
at tmax = 512 ms
0
we can estimate the ¾ value of ¡-Toc● radical, using the
350
400
450
500
550
1
relation (Absorbance (of ¡-Toc● at tmax) = ¾1 © [ArO●]t=0).
The results of the analysis performed for ¡-Toc● are shown
in Figures 4a and 4b. For comparison, the simulation curve
Wavelength / nm
0.3
¹1
calculated for the case of kd = 0 M¹1 s is also shown in
-Toc in Ethanol
Figure 4a.
The good agreement between the observed and simulation
curves was obtained for three different concentrations of
¡-TocH ([¡-TocH] = 6.97 © 10¹3, 3.49 © 10¹3, and 1.39 ©
10¹3 M) at t = 0-10 s, if we use the values of ks (=5.12 ©
0.2
0.1
-Toc
432 nm
103 M¹1 s¹1), kd (=1.30 © 103 M¹1 s¹1), and
M
¾
(=4370
1
¹1
¹1 cm at -max1 = 428 nm) (Figure 4b). On the other hand,
[ArO ] = 6.97 × 10-5
TocH] = 4.81 × 10 -3
at tmax = 200 ms
M
when the concentration of ¡-TocH is lower ([¡-TocH] =
3.49 © 10¹4 M), the agreement was not sufficient at t > 1 s.
If the concentration of ¡-TocH is low, the rate of ArO●-
scavenging (¹d[ArO●]/dt) is slow, and thus the ¡-Toc●
radical generated will react with the ArO● radical remaining in
solution, inducing the decrease of the concentration of the
¡-Toc●. As shown in Figure 4a, the concentration of ¡-Toc●
([¡-Toc●]t = 8.71 © 10¹5 M) at tmax = 145 ms is similar to the
initial concentration of ArO● ([ArO●]t=0 = 8.88 © 10¹5 M), if
[
M
0
350
400
450
500
550
Wavelength / nm
0.3
-Toc in Ethanol
¹3
the concentration of ¡-TocH is high ([¡-TocH] = 6.97 © 10
M) and thus ArO● and ¡-Toc● rapidly disappear and appear,
respectively.
0.2
0.1
0
The measurements of the formation and decay curves of ¡-
Toc● radical were performed in several solvents. In dichloro-
methane, chloroform, and benzene, the good agreements
between the observed and simulation curves were obtained at
t = 0-10 s, indicating that the decay of ¡-Toc● radical is due to
bimolecular reaction (Figure 4c). On the other hand, in diethyl
ether, heptane, and hexane, notable disagreements were
observed, if the analyses were performed by assuming a
simple bimolecular reaction, as shown in Figure 7a. Details of
the analyses of the decay reaction of ¡-Toc● in these solvents
will be described in the Discussion.
-Toc
434 nm
[ArO ] = 1.19 × 10-4
TocH] = 1.34 × 10-2
at tmax = 392 ms
M
[
M
ArO
376nm
400
350
450
500
550
Wavelength / nm
Figure 5. UV-vis absorption spectra of (a) ¢-Toc●, (b) £-
Toc●, and (c) ¤-Toc● radicals in ethanol solution at
tmax = 512, 200, and 392 ms, respectively.
Discussion
Optical Spectra (-max and ¾) of ¡-, ¢-, £-, and ¤-
Tocopheroxyl Radicals in Organic Solvents. ¡-, ¢-, £-,
and ¤-Toc● radicals play an important role in the antioxidant
and prooxidant actions of tocopherols (reactions 1-6), as
described in the Introduction. Therefore, the measurements
of the ESR and ENDOR spectra of Toc● radicals were
performed in toluene under vacuum, and the proton hyper-
fine coupling constants (hfcc) (aiH) were correctly deter-
mined.34-36
ꢁdX1=dt ¼ ksðc2 ꢁ X2 ꢁ X3ÞX1
ð17Þ
ð18Þ
ð19Þ
2
dX2=dt ¼ ksðc2 ꢁ X2 ꢁ X3ÞX1 ꢁ 2kdX2
2
dX3=dt ¼ 2kdX2
Equations 17, 18, and 19 were solved numerically using the
fourth-order Runge-Kutta method, as performed by Lucarini
et al.15,29

K. Mukai et al.
Bull. Chem. Soc. Jpn. Vol. 82, No. 4 (2009)
499
12
On the other hand, the measurements of the UV-vis
absorption spectra are difficult, because ¡-, ¢-, £-, and ¤-
Toc● radicals are unstable. We reported the UV-vis absorption
spectrum of a stable 5,7-diisopropyltocopheroxyl radical model
(a)
2kd = 0 M-1s-1
n-Hexane
10
8
i
(Figure 1) in ethanol.37 As listed in Table 3, the values of -max
2kd = 2.00 × 103 M-1s-1
and ¾ (i = 1-4) for ¡-Toc● in ethanol are similar to those of
i
5,7-diisopropyltocopheroxyl model radical, suggesting that the
6
values of ¾ obtained are reasonable. Boguth and Niemann31
Observed
i
and Gregor et al.19 reported the absorption spectrum of ¡-Toc●
obtained by the reaction of ¡-TocH with DPPH radical in
4
ks = 1.79 × 105 M-1s-1
[ArO ] = 9.10 × 10-5
1
benzene and ethanol solution, respectively. The values of -max
(=423 nm in benzene and 426 nm in ethanol) are similar to
those (424 and 428 nm), respectively, observed in the present
work. However, the value of ¾1 (6700 M¹1 cm¹1) in benzene is
about twice as large as that (3420 M¹1 cm¹1) obtained in the
present work. On the other hand, the value (3800 M¹1 cm¹1) in
2
M
[
-TocH] = 4.45 × 10-4
M
at 25.0
4
0
0
2
6
8
10
Time / s
0.5
[ArO ] = 8.88 × 10-5
M
(b)
10
8
-TocH] = 6.84 × 10-3 M
n-Hexane
[
[
[
[
-TocH] = 1.53 × 10-2
M
M
M
0.4
0.3
0.2
0.1
0
-TocH] = 1.49 × 10-2
-TocH] = 3.74 × 10-2
Observed
6
in Ethanol
at 25.0
4
Second-order
First-order
2
0
0
2
4
6
8
10
0
2
4
6
8
10
Time / s
Time / s
Figure 7. Time dependence of the concentrations of ¡-
Toc● radical observed at 418 nm during reaction of ArO●
with ¡-TocH in hexane at 25.0 °C (Solid line). Dotted lines
are simulation curves calculated (a) by assuming a
bimolecular reaction and (b) by assuming first-order and
second-order decays (see text). The values of [ArO●]t=0
and [¡-TocH]t=0 are shown in Figure 7a.
Figure 6. Time dependence of the absorbance of ¡-Toc●
(at 428 nm), ¢-Toc● (at 431 nm), £-Toc● (at 432 nm), and
¤-Toc● (at 434 nm) radicals produced by the reaction
of ¡-, ¢-, £-, and ¤-TocH with ArO● radical in ethanol
at 25.0 °C, respectively. The values of [ArO●]t=0 and
[TocH]t=0 are shown in Figure 6.
Table 2. Second-Order Rate Constants for the Aryloxyl-Radical-Scavenging (ks) of ¡-Tocopherol and for the
Bimolecular Reaction (2kd) of ¡-Tocopheroxyl Radical and Equilibrium Constant (K21) at 25.0 °C in Organic Solvents
¹1 b)
¹1
2kd/M¹1 s
K21 = k¹21/k21
/M
2kd/M¹1 s
¹1 a)
Solvent
ks/M¹1 s
(Present work)
(Previous work)
¹3
Ethanol
CH2Cl2
CHCl3
Diethyl ether
Benzene
Heptane
Hexane
5.12 © 103
3.25 © 104
2.76 © 104
1.47 © 104
9.87 © 104
2.02 © 105
1.79 © 105
1.30 © 103
3.00 © 102
3.00 © 104
1.70 © 103
9.50 © 102
1.70 © 103
1.00 © 103
>10
1.03 © 103,c) 1.4 © 103,d) 1.06 © 103 e)
®
1.9 © 102 f)
®
8.8 © 102,f) 3 © 103,g) 1.1 © 103,h) 6.03 © 103 i)
®
3.12 © 103 e)
¹3
>10
¹3
>10
¹4
5.9 © 10
>10
¹3
¹4
8.6 © 10
¹4
9.2 © 10
a) Experimental errors are «5%. b) Experimental errors are «5%. c) See Ref. 18. The value at 37 °C. d) See Ref. 14. The
value at 20 °C. e) See Ref. 19. The value at 20 °C. Measurement was performed by stopped-flow spectrophotometer. f) See
Ref. 31. The value at 25 °C. g) See Ref. 13. The value at 23 °C. h) See Ref. 32. The value for ¡-tocopheroxyl model radical
at 50 °C. i) See Ref. 15. The value at 25 °C.

500
Bull. Chem. Soc. Jpn. Vol. 82, No. 4 (2009)
Formation and Decay Dynamics of Vitamin E Radical
Table 3. The Values of UV-Visible Absorption Maxima (-maxi) and Molar Extinction Coefficients (¾i) (i = 1-4)
of the ¡-, ¢-, £-, and ¤-Tocopheroxyls and 5,7-Diisopropyltocopheroxyl Radical Model in Ethanol
-
1/nmb)
-
2/nmb)
-
3/nmb)
-
4/nmb)
max
max
(¾1/M¹1 cm
max
(¾2/M¹1 cm
max
(¾3/M¹1 cm
Toc●
¹1
¹1
¹1
¹1
)
)
)
(¾4/M¹1 cm
)
¡-Toc●
¢-Toc●
£-Toc●
428 (4370)
431 (1500)d)
432 (820)d)
434 (380)d)
420 (4010)
408 (3010)
387shc) (1630)
®
340shc) (3790)
409 (1200)d)
®
®
®
®
®
¤- Toc●
®
401 (2490)
®
338 (4100)
5,7-Di-i-Pr-Toc● modela)
380shc) (1490)
3
4
a) See Ref. 37. b) Experimental errors in -max1, -max2, and -max are «1 nm, and in -max are «5 nm. c) sh:
Shoulder. d) The apparent ¾ value (see text).
i
¹1
ethanol shows reasonable agreement with that (4370 M¹1 cm
obtained in the present work.
)
5000
4000
3000
2000
1000
0
Ethanol
Chloroform
Polarity of the reaction fields of ¡-TocH in biological
systems differs from system to system, and thus measurements
were performed in several organic solvents with different
polarity, to study the solvent effect on absorption spectra of ¡-
Benzene
n-Heptane
Dichloromethane
Diethyl ether
1
Toc●. As listed in Table 1, the -max changes from 418 nm in
nonpolar n-hexane solvent to 428 nm in polar ethanol solvent.
Similar behavior was observed for the -max2 and -max3. The red
shifts of absorption maxima suggest that the transitions are ³-
³*.38 The absorption peaks at -max4 are very broad, suggesting
the overlap of two absorptions. The relative values of the molar
extinction coefficients (¾1:¾2:¾3:¾4) are similar to each other in
n-Hexane
these solvents. On the other hand, the values of ¾ (i = 1-4)
0
0.1
0.2
0.3
0.4
0.5
0.6
i
increase with increasing polarity, that is, dielectric constant
dielectric-constant
(¾dielectric-constant) of the solvents; for instance, the ¾ value in
1
Figure 8. Plot of ¾ vs. 1/¾
for ¡-Toc●
ethanol is 1.7 times larger than that in n-hexane. The ¾ vs.
1
dielectric-constant
1
radical.
1/¾
plot is shown in Figure 8.
dielectric-constant
As is clear from the results listed in Table 3, the -max1 values
of ¡-, ¢-, £-, and ¤-Toc● radicals increase in the order of
¡- < ¢- < £- < ¤-Toc● in ethanol. However, the difference in
the -max1 values is small, suggesting that the electronic states of
these tocopheroxyls are similar to each other. The results of the
ESR measurements also indicate that the unpaired electron
distributions on ¡-, ¢-, £-, and ¤-Toc● radicals are similar to
each other in toluene solvent.35 Therefore, we can expect that
¡-, ¢-, £-, and ¤-Toc● radicals have similar molar extinction
coefficients (¾i). However, the intensity of the absorption
peak of Toc● radicals decreased remarkably in the order
of ¡-Toc● (Absorbance = 0.408 at -max = 428 nm) > ¢-Toc●
(0.131 at 431 nm) > £-Toc● (0.073 at 432 nm) > ¤-Toc●
(0.034 at 434 nm) in ethanol, as shown in Figure 6. The reason
will be discussed in the following section.
several solvents, using a stopped-flow spectrophotometer and
by the simulation of a kinetic model (Figure 4).
The values of 2kd obtained in the present work are
summarized in Table 2, together with those reported. The 2kd
value (1.30 © 103 M¹1 s¹1) obtained in ethanol is similar to that
(1.4 © 103 M¹1 s¹1) reported by Richard et al.14 and 1.3 and 1.2
times larger than those (1.03 © 103 and 1.06 © 103 M¹1 s
)
¹1
reported by Watanabe et al.18 and Gregor et al.,19 respectively.
Similarly, the 2kd value (9.50 © 102 M¹1 s¹1) in benzene is
1.1 times larger than that (8.8 © 102 M¹1 s¹1) reported by
Boguth and Niemann31 and 1.2, 3.2, and 6.3 times smaller
than those (1.1 © 103, 3 © 103, and 6.03 © 103 M¹1 s¹1) re-
ported by Roginsky and Krasheninnikova,32 Doba et al.,13
and Lucarini et al.,15 respectively. The 2kd value (3.00 © 104
The Rate Constant for the Decay Reaction (2kd) of ¡-
Tocopheroxyl in Organic Solvents. The measurements of the
decay rate of ¡-Toc● radicals in organic solvents have
generally been performed by using ESR techniques.1,13-19,32 It
has been reported that the decay of the ¡-Toc● follows the
bimolecular self-reaction of ¡-Toc● radicals, suggesting the
production of ¡-TocH and ¡-tocopherol-o-quinonemethide
(¡-Toc-QM) (Figure 9b) by disproportionation reaction (reac-
tion 20). However, ¡-Toc-QM is unstable and not isolated.
2kd
M
¹1 s¹1) obtained in chloroform is 160 times larger than that
(1.9 © 102 M¹1 s¹1) reported by Boguth and Niemann.31 The
reason for such a fast decay of ¡-Toc● in chloroform is not
clear at present.
Scheme of the Decay Reaction of ¡-, ¢-, £-, and ¤-
Tocopheroxyl Radicals in Organic Solvents. Most of the
phenoxyl (PhO●) free radicals are unstable, and decay by fast
bimolecular reactions with each other. Bimolecular radical de-
cay of PhO● radical involves dimerization (recombination) and
disproportionation reactions.39 Dimers of some PhO● are stable
in solution and sometimes may be recovered as solids. Most of
such dimers, e.g., dimers of 2,6-di-tert-butyl-4R- or 2,6-diphen-
yl-4R-phenoxyl radicals (for instance, R = CH3 or C2H5), have
¡-Tocꢀ þ ¡-Tocꢀ ꢁꢁꢁ! ¡-TocH þ ¡-Toc-QM
ð20Þ
In the present work, the concentrations (that is, the values of ¾)
and decay rates (2kd) of ¡-Toc● were exactly determined in

K. Mukai et al.
Bull. Chem. Soc. Jpn. Vol. 82, No. 4 (2009)
501
In fact, at low concentration of ¡-Toc● radical (t > 5 s), the
decay of ¡-Toc● radical in hexane may be well explained by a
bimolecular disproportionation reaction with a second-order
rate constant (2kobsd = 2kd = 1.00 © 103 M¹1 s¹1), as shown in
H
H
O
C
C16H33
O
C16H33
O
O
O
L
Figure 7b. At high concentration of ¡-Toc●, the decay follows
O
¹1
first-order kinetics with kobsd = kdk¹21/2k21 = 3.00 © 103 s
.
Similar analyses were performed for the formation and decay
curves observed in diethyl ether and n-heptane solvents. The
2kd and k¹21/k21 values were calculated by assuming the
dimerization and disproportionation model shown in reac-
tion 21 and are listed in Table 2.
(a) α-Toc-OOL (b) α-Toc-o-quinonemethide
(α-Toc-QM)
As described above, the rate constants (kf) for the formation
reaction of ¡-Toc● radical changed remarkably depending on
the polarity of the solvents. The values of kf (=ks) increased
with decreasing polarity of solvent.33 For example, the values
in hexane and benzene are 35 and 19 times larger than those in
ethanol, respectively (Table 2). On the other hand, such a
solvent dependence was not observed for the rate constants
(2kd) of bimolecular reaction. Further, the effect of solvent for
2kd (3.00 © 102-1.70 © 103 M¹1 s¹1) is smaller than that for kf,
except for that in chloroform.
O
C16H33
O
O
R
O
O
O
R
C16H33
The decay curves of ¡-Toc● in polar ethanol, dichloro-
methane, and chloroform solvents were explained by a simple
(c) Quinol ether
(d) α-Toc Dimer
bimolecular reaction without the dimer formation. In fact, the
Figure 9. Molecular structures of (a) ¡-Toc-OOL, (b) ¡-
Toc-o-quinonemethide (¡-Toc-QM), (c) Quinol ether, and
(d) Dimer of ¡-Toc● radical (¡-Toc Dimer).
¹1
values of ¾ obtained are similar (¾1 = 4100-4370 M¹1 cm
)
1
(Table 1). The strong interaction between polar solvent and ¡-
Toc● molecules will hinder the formation of quinol-ether-type
dimer in ¡-Toc● radicals. The nonpolar benzene molecules
with an aromatic ³-system will also interact with ¡-Toc●
radical molecules that also have an aromatic ring, hindering
the formation of dimer. On the other hand, in hexane,
heptane, and diethyl ether solvents, ¡-Toc● radicals are
believed to form dimers quickly, and then disappear gradually
by bimolecular reaction. The relative ratios of the dimer
formation will increase with decreasing polarity of the solvents
structures of quinol ethers (“head-to-tail”) (Figure 9c). Structure
of the dimer has been ascertained by NMR measurement.40
Dimerization reactions of PhO● radicals are fast reactions and
are characterized by large rate constants (k µ 107-109 M¹1 s
in nonviscous solvents at room temperature.
)
¹1
¡-Toc● radical in hexane may also decay in two steps as
observed for PhO● radicals. First, an equilibrium establishes
itself very quickly (with k21 and k¹21), and then disproportio-
nation reaction 20 with 2kd follows (reaction 21), as proposed
(¾dielectric-constant), and thus the values of ¾ decrease from
1
by Doba et al.13 and ascertained by Lucarini et al.15 k21 and k
¾1 = 4370 M¹1 cm¹1 in ethanol to 2500 M¹1 cm¹1 in hexane, as
shown in Figure 8 and as listed in Table 1.
¹21
represent the rate constants for the formation and breakdown of
dimer, respectively.
Similar measurements were performed for ¢-, £-, and ¤-
TocH, in order to determine the 2kd values for reaction 20. As
shown in Figure 6, the same concentration of ArO● radical
(8.88 © 10¹5 M) was used for the reaction with ¡-, ¢-, £-,
and ¤-TocH. However, the absorbances of ¡-, ¢-, £-, and
¤-Toc● observed decrease rapidly in the order of ¡-Toc●
(Absorbance = 0.408 at -max = 428 nm) > ¢-Toc● (0.131 at
431 nm) > £-Toc● (0.073 at 432 nm) > ¤-Toc● (0.034 at
434 nm) in ethanol. The smaller absorbance obtained for ¢-,
£-, and ¤-Toc● radicals will be due to the fast formation of
dimer (fast equilibrium with the dimer) (reaction 21) in these
Toc● radical molecules. In fact, the values of 2k21 reported for
PhO● radicals are very fast and 107-109 M¹1 s¹1, as described
above.39 The steric repulsion due to two ortho-methyl groups
on ¡-Toc● radical molecule will hinder the formation of
quinol-ether-type dimer. However, the dimer formation will
become easier with decreasing the number of ortho-methyl
groups. As a result, the values of the absorbance decrease in the
order of ¡-Toc● > ¢-Toc● > £-Toc● > ¤-Toc● radicals in
ethanol solvent. In addition to the interaction between solvent
and Toc● radical molecules, such steric hindrance will also
2k
ꢁ21
Dimer ꢀ ¡-Tocꢀ þ ¡-Tocꢀ
2kd
2k21
ꢁꢁꢁ! ¡-TocH þ ¡-Toc-QM
where dimer is quinol ether (Figure 9d), although it is unstable
and has not been isolated.
Under the condition k21 º kd, we obtain39
ð21Þ
2
ꢁd½¡-Tocꢀꢂ=dt ¼ kd½¡-Tocꢀꢂ =ð1 þ 2k21½¡-Tocꢀꢂ=kꢁ21Þ ð22Þ
If 2k21[¡-Toc●]/k
º 1, radical decay will occur with
¹21
first-order kinetics and kobsd = kdk¹21/2k21.
ꢁd½¡-Tocꢀꢂ=dt ¼ ðkdkꢁ21=2k21Þ½¡-Tocꢀꢂ
For 2k21[¡-Toc●]/k
ð23Þ
¹ 1, radical decay will be a second-
¹21
order reaction with kobsd = kd.
2
ꢁd½¡-Tocꢀꢂ=dt ¼ kd½¡-Tocꢀꢂ
Thus in the case of high concentrations, radicals decay by a
first-order reaction, and in the case of low concentrations, by a
second-order reaction.
ð24Þ

502
Bull. Chem. Soc. Jpn. Vol. 82, No. 4 (2009)
Formation and Decay Dynamics of Vitamin E Radical
have an important effect on the dimer formation. To our regret,
we were unsuccessful in determining the ¾i values for ¢-Toc●,
£-Toc●, and ¤-Toc● radicals. However, we may estimate
important in biological systems. The study is now in progress
in our laboratory.
tentatively the apparent ¾ values (¾apparent = 1500, 820, and
We are grateful to Prof. Fernando Antunes of University of
Lisbon (Portugal) and Prof. Shin-ichi Nagaoka of Ehime
University for their helpful discussions. This work was partly
supported by the Grant-in-Aid for Scientific Research
on Priority Areas “Applications of Molecular Spins” (Area
No. 769, Proposal No. 15087104) from the Ministry of
Education, Culture, Sports, Science and Technology (MEXT),
Japan (to K. M.).
¹1
380 M¹1 cm
(Table 3)) for ¢-, £-, and ¤-Toc● radicals,
respectively, by using the relation (Absorbance (at tmax) =
¾ © [Toc●] = ¾ © [ArO●]t=0). Where the apparent ¾ values
are defined as those for the total molecules which include
both i) Toc● monomer and ii) quinol-ether-type Toc● dimer
(Figure 9d).
It is well known that the orders of relative tocopherol
biopotency using various bioassays41 and scavenging activities
of lipid peroxyl1 and aryloxyl26,42 radicals by TocH are as
follows; ¡-TocH > ¢-TocH ² £-TocH > ¤-TocH. On the other
hand, the reverse is the case for the activity to protect fats and
oils from oxidation;9 ¡-TocH < ¢-TocH < £-TocH < ¤-TocH.
In general biological systems, such as erythrocyte and
mitochondrial membranes, Toc● radicals produced by the
reaction with peroxyl radicals may be regenerated to TocH by
vitamin C2,3,10,11 and/or ubiquinol3,12,20 (reaction 5), to protect
the prooxidant effect (reaction 3). In fats and oils, Toc●
radicals react with unsaturated lipids (reaction 3), and induce
lipid peroxidation.7,9,18 If the Toc● radicals disappear rapidly
by the dimer formation and the disproportionation reaction
(reaction 21), the prooxidant reaction 3 will be suppressed.
This may be one of the reasons why the activity to protect fats
and oils from oxidation increases in the order of ¡-TocH <
¢-TocH < £-TocH < ¤-TocH.9
References
1
G. W. Burton, T. Doba, E. Gabe, L. Hughes, F. L. Lee, L.
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3
E. Niki, Chem. Phys. Lipids 1987, 44, 227.
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5
L. R. C. Barclay, Can. J. Chem. 1993, 71, 1.
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but has received little attention compared with ¡-TocH, the
predominant form of vitamin E in tissues. However, recently it
has been indicated that £-TocH may be important to human
health and that it possesses new attractive functions that
distinguish it from ¡-TocH.43-45 For example, £-TocH has
higher activity than ¡-TocH in inhibition of cycloxygenase
activity, and thus £-TocH supresses anti-inflammation46,47 and
inhibits proliferation of prostate cancer cells.48 As one of the
reason that £-TocH shows higher activity than ¡-TocH, the
suppression of the prooxidant effect in £-TocH may be
considered. However, the details are not clear at present.
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Kinetic study of the formation and decay reactions of
vitamin E radicals (¡-, ¢-, £-, and ¤-tocopheroxyls, Toc●) has
been performed in several organic solvents, using stopped-flow
spectrophotometry. By mixing ¡-, ¢-, £-, and ¤-tocopherols
(TocH) with aryloxyl radical (ArO●) in organic solvents, the
peaks of the UV-vis absorption due to ¡-, ¢-, £-, and ¤-Toc●
appeared rapidly at 340-430 nm, showed a maximum, and then
decayed gradually. We have succeeded in the simulation of the
formation and decay curve of ¡-Toc● radical by the numerical
calculation of differential equations related to the above
reactions, using the fourth-order Runge-Kutta method. From
the results, the second-order rate constants (kf and 2kd) for the
formation and decay reactions of ¡-Toc● and the molar
extinction coefficients (¾) of the UV-vis absorption spectra
were determined. We can develop this method to more complex
reaction systems; for example, the system including ArO●,
tocopherol, and ubiquinol-10 (or vitamin C), which is

K. Mukai et al.
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