Linking conformational flexibility and kinetics: Catalytic 1,4-type friedel-crafts reactions of phenols utilizing 1,3-diamine-tethered guanidine/bisthiourea organocatalysts

Article abstract of DOI:10.1002/asia.201100363

Herein, we present details of our conformationally flexible, 1,3-diamine-tethered guanidine/bisthiourea organocatalysts for chemo-, regio-, and enantioselective 1,4-type Friedel-Crafts reactions of phenols. These organocatalysts show a unique stereo-discrimination governed by the differential activation entropy (δδS⁺), rather than by the differential activation enthalpy (δδH⁺). Extensive kinetic analyses using Eyring plots for a series of guanidine/bisthiourea organocatalysts revealed the key structural motif in the catalysts associated with a large magnitude of differential activation entropy (δδS ⁺). A plausible guanidine-thiourea cooperative mechanism for the enantioselective Friedel-Crafts reaction is proposed. Copyright

Full text of DOI:10.1002/asia.201100363

DOI: 10.1002/asia.201100363
Linking Conformational Flexibility and Kinetics: Catalytic 1,4-Type Friedel–
Crafts Reactions of Phenols Utilizing 1,3-Diamine-Tethered Guanidine/
Bisthiourea Organocatalysts
Yoshihiro Sohtome,*[a] Bongki Shin,[a] Natsuko Horitsugi,[a] Keiichi Noguchi,[b] and
Kazuo Nagasawa*[a]
Abstract: Herein, we present details of
our conformationally flexible, 1,3-dia-
the differential activation enthalpy
(DDH°). Extensive kinetic analyses
using Eyring plots for a series of guani-
dine/bisthiourea organocatalysts re-
vealed the key structural motif in the
catalysts associated with a large magni-
tude of differential activation entropy
(DDS°). A plausible guanidine–thiour-
ea cooperative mechanism for the
enantioselective Friedel–Crafts reac-
tion is proposed.
mine-tethered
guanidine/bisthiourea
organocatalysts for chemo-, regio-, and
enantioselective 1,4-type Friedel–Crafts
reactions of phenols. These organocata-
lysts show a unique stereo-discrimina-
tion governed by the differential acti-
vation entropy (DDS°), rather than by
Keywords: asymmetric synthesis ·
entropy · Friedel–Crafts reaction ·
organocatalysis · phenols
Introduction
tropy both play significant roles in governing the conforma-
tional changes that occur in the enzyme and the substrate.[4]
Inspired by the well defined, but diverse ways in which en-
zymes function, enormous effort has been devoted to the ex-
ploration of new chiral hydrogen-bond donors that could
serve as asymmetric catalysts.[5–7] However, very few effec-
tive asymmetric hydrogen-bond-donor catalysts with confor-
mationally flexible scaffolds have been found.[8–11] The diffi-
culty in employing acyclic organic molecules as asymmetric
organocatalysts may arise mainly from free bond rotation.[12]
The small barrier to rotation about single bonds connecting
two sp3 carbon atoms often results in rapid and reversible
generation of an infinite number of conformers.[13] This is
one of the reasons why most organocatalysts reported to
date have a conformationally rigid chiral backbone (e.g.,
proline, cinchona alkaloids, cyclohexanediamines, and 1,1’-
bi-2,2’-naphthyl scaffolds) that participates in a structurally
rigid transition state.[5,6] In contrast, our group has shown
that conformationally flexible organocatalysts 1 are effective
for the construction of a variety of chiral environments for
asymmetric organocatalysis,[14] facilitating several classes of
catalytic asymmetric 1,2-additions, including nitroal-
dol,[9,14b–e] nitro-Mannich,[14g] Mannich,[14h,k] and Friedel–
Crafts (FC) reaction of phenols.[14j] The high stereoselectivi-
ties are attributed to chemoselective dual activation of both
the nucleophile and electrophile reacting partners in asym-
metric space.[14,15] Herein, we describe our mechanistic stud-
In enzyme-catalyzed reactions, precise regulation of the
enzyme structure is essential to control the various specifici-
ties (e.g., substrate and stereochemical specificities) com-
monly observed in these processes.[1] The cooperativity of
weak hydrogen-bonding interactions[2] in
a polypeptide
allows the flexible control of the transition-state architecture
required to achieve the target reaction.[3] Enthalpy and en-
[a] Dr. Y. Sohtome,+ B. Shin, N. Horitsugi, Prof. Dr. K. Nagasawa
Department of Biotechnology and Life Science
Faculty of Technology, Tokyo University of Agriculture and Technol-
ogy
2-24-16 Naka-cho, Koganei, Tokyo 184-8588 (Japan)
Fax : (+81)42-388-7295
E-mail: knaga@cc.tuat.ac.jp
[b] Prof. Dr. K. Noguchi
Instrumentation Analysis Center
Tokyo University of Agriculture
and Technology Institution
2-24-16 Naka-cho, Koganei, Tokyo 184-8588 (Japan)
[+] Present address:
RIKEN Advanced Science Institute
2-1 Hirosawa, Wako-shi Saitama 351-0198 (Japan)
Fax : (+81)48-467-4666
E-mail: sohtome@riken.jp
Supporting information for this article is available on the WWW
under http://dx.doi.org/10.1002/asia.201100363.
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ies on the chemo-, regio-, and enantioselective FC reaction
of phenols[16–18] catalyzed by the 1,3-diamine-tethered guani-
dine/bisthiourea organocatalysts 2.[19–21]
The chiral phenol unit is a ubiquitous structural motif in
biologically active natural products,[22] as well as chiral li-
gands.[23] Considering the high acidity of phenolic acid
(pKa =9.95 in H2O), C-alkylation through phenolic enolates,
which can be generated from phenols under basic condi-
tions, is potentially one of the most straightforward strat-
egies for the preparation of chiral phenols. However, phe-
nolic enolates currently have limited utility in organic syn-
thesis; this is likely to be because they suffer from ligand ex-
change in metal-based catalysis.[24] Although several bifunc-
tional organocatalyst-based approaches have recently been
reported, direct and catalytic asymmetric 1,4-type FC reac-
tions of phenols remain underdeveloped owing to problems
rooted in reaction selectivities (chemo- and regio-) and reac-
tivities.[25–28] With regards to selectivity, a major challenge is
to obtain mono-ortho-alkylated adducts without second-
ortho or O-alkylation to give difunctionalized products.[25,26]
Lowering the reaction temperature is a common method to
avoid overreaction, but this often causes a decrease in the
reaction rate.[25] In this context, we have recently reported
the development of 1,3-diamine-tethered guanidine/bis-
thiourea organocatalyst 2a, which permitted enantioselec-
tive 1,4-type FC reactions of phenols (Figure 1).[14j] A unique
feature is that stereo-discrimination under optimized condi-
tions is governed by the differential activation entropy
Figure 1. a) Catalytic enantioselective FC reaction of 3 with 4 utilizing 2a
under optimized conditions. b) Eyring plots of the 2a-catalyzed FC reac-
tion of sesamol (3a) with b-nitrostyrene (4a) at various concentrations:
[14j]
~
&
*
0.025 ( ), 0.05 (ꢁ), 0.1 ( ), and 0.2m ( ).
(DDS° =25.4 Jmolꢀ1 Kꢀ1), rather than by the differential ac-
tivation enthalpy (DDH° ꢁ0 kJmolꢀ1), thereby attaining
maximum enantioselectivities without strict temperature
control. Herein, we describe details of kinetic studies utiliz-
ing Eyring plots with a variety of guanidine/bisthiourea or-
ganocatalyst variants. A possible catalytic cycle in 2-cata-
lyzed 1,4-type FC reactions, including a chemoselective dual
activation transition state is also discussed.
Abstract in Japanese:
Results and Discussion
Structure and Catalytic-Activity Relationship Studies
Utilizing 1,2-Diamine-Tethered Guanidine/Bisthiourea
Organocatalysts
Differential activation parameters, including differential ac-
tivation enthalpy (DDH°) and entropy (DDS°), are useful
parameters for determining binding ability and degrees of
randomness in studies of chiral recognition processes, rather
than nominal activation parameters (DH°
and DS°nom).[30]
nom
For example, Jacobsen and co-workers used differential acti-
vation enthalpy (DDH°) and differential activation entropy
(DDS°) to characterize the mechanism of conformationally
constrained, thiourea-catalyzed, cationic polycyclizations.[31]
In their catalytic system, the values of DDH° and DDS°
were both negative, meaning that the stereo-discrimination
in the catalytic reaction was controlled enthalpically. Based
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Linking Conformational Flexibility and Kinetics
on the correlation of the degree of enantioselectivity and
the increasing magnitude of DDH° with increasing size of
polycyclic aromatic hydrocarbon on the catalyst, they pro-
posed a cation–p activation mechanism, which served to
broaden the scope of enantioselective counterion catalysis.
In contrast, our findings[14j,k] have, for the first time, uncov-
Substituent Effects on 1,3-Diamine-Tethered Guanidine/
Bisthiourea Organocatalysts
Exploratory studies show that drastic enantioswitching can
occur simply as a result of replacing the substituents (R1 and
R2) on the guanidine moiety in 2.[14j,36] These unique features
of the present catalytic system, along with our wish to charac-
terize the chiral recognition processes that take place in these
asymmetric carbon–carbon bond-forming reactions, prompted
us to conduct kinetic analyses using Eyring plots for selected
1,3-diamine-tethered catalysts 2. According to the differential
Eyring treatment,[31,37–39] the relative rates of formation of
(S)-5aa in the reactions are expressed by Equation (1), in
which DDH° represents the differential activation enthalpy
and DDS° represents the differential activation entropy.
ered
a situation where differential activation entropy
(DDS°) controls the outcome of asymmetric hydrogen-
bond-donor catalysis.[32–34] As the entropy term is known to
be tunable by selecting suitable reaction conditions,[14k,35] it
is particularly important to gain insight into the structural
origin of the catalytic action to attain a large magnitude of
differential activation entropy (DDS°). Therefore, we first
carried out structure–activity relationship (SAR) studies on
guanidine/bisthiourea organocatalysts.
The crucial role played by the 1,3-diamine spacer linking
the two centers in 2a is evident from the Eyring plots of the
FC reaction of 3a with 4a catalyzed by 1a with the corre-
sponding 1,2-diamine spacer, at a substrate concentration of
0.025m. As shown in Table 1, 1a showed completely differ-
lnðkS=kRÞ ¼ ꢀDDH°SꢀR=RTþDDS°SꢀR=R
ð1Þ
In accordance with Equation (1), plots of the natural loga-
rithm of the relative rate of formation of (S)-5aa versus re-
ciprocal temperature were fitted to straight lines with good
correlation coefficients (Figure 2).[40] These observations
confirm that a single mechanism is operating in the catalytic
process over the temperature range explored.[38d] An impor-
tant feature is that 2b–g display broadly similar temperature
and concentration profiles in the FC reaction of 3a with 4a.
At less than a threshold concentration, positive values of
Table 1. Temperature profile of the yield in 1a-catalyzed 1,4-type FC re-
actions of 3a with 4a.
DDH°
and DDS°
are obtained from the negative
SꢀR
SꢀR
slopes and positive y intercept of the plots, respectively.
Thus, differential activation entropy (DDS°SꢀR) contributes
to lowering the value of DDG°
(=DDH°SꢀRꢀTDDS°SꢀR),
SꢀR
with an unfavorable enthalpic contribution (DDH°SꢀR). No-
tably, when 2b and 2c were used as catalysts, the major
enantiomer produced switched from (R)- to (S)-5aa at the
equipodal temperature (T0), and thereafter the S selectivity
continued to increase as the temperature further in-
creased.[40] Enantioswitching in the FC reaction when using
1,3-diamine-tethered guanidine/bisthiourea is a consequence
of the occurrence of the equipodal temperature (T0) in the
temperature range with negative slopes in the Eyring
plots.[41] It is also important to note that stereo-discrimina-
tion catalyzed by 2a (maximum enantiomeric excess (ee) of
(S)-5aa: 91% ee)[14j] and 2g (Figure 2 f, maximum ee of (S)-
Entry
T [8C]
Yield [%][a]
ee [%][b]
1
2
3
4
ꢀ30
ꢀ10
0
30
43
51
69
36
35
31
27
20
[a] Yield of isolated product. [b] Determined by HPLC on a chiral sta-
tionary phase.
ent catalytic activity from 2a. 1,2-Diamine-tethered 1a pro-
duced (R)-5aa as a major product, whereas 1,3-diamine-
tethered catalyst 2a predominantly gave (S)-5aa. Further-
more, the reactivity and enantioselectivity of 1a are both
drastically reduced in comparison with 2a. These observa-
tions indicate that the selection of a suitable length of chiral
spacer is critical to synergize the guanidine and thiourea
functionalities in the catalyst and achieve drastic rate accel-
eration and effective stereocontrol. It is also important to
note that the temperature-dependency profiles are different
for the FC reactions catalyzed by 1a and 2a. In the case of
1a, the enantioselectivity increased as the reaction tempera-
ture decreased, indicating that stereo-discrimination cata-
lyzed by 1a is controlled by differential enthalpy (DDH°)
with an unfavorable entropic contribution (DDS°). Thus, we
concluded that the 1,3-diamine spacer played a principal
role in attaining entropy-controlled stereo-discrimination in
the FC reaction catalyzed by 2a.
5aa: 91% ee) is governed by only DDS°
at 0.025m sub-
SꢀR
strate concentration. In the case of catalysts 2e (Figure 2d,
maximum ee of (S)-5aa: 80% ee) and 2 f (Figure 2e, maxi-
mum ee of (S)-5aa: 80% ee), a decrease in the substrate
concentration to 0.01m is effective to increase the magni-
tude of DDS°
for stereo-discrimination and DDH°
ap-
SꢀR
SꢀR
proaches zero. Although further studies to probe the rela-
tionship between kinetics and molecular mechanism are re-
quired, these results suggest that both the six-membered
ring containing the guanidine moiety and the a-branched
substituent on the chiral spacer in 2 are crucial for attaining
the maximum magnitude of differential activation entropy
(DDS°SꢀR) in the stereo-determining processes in the FC re-
action of 3a with 4a.
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Y. Sohtome, K. Nagasawa et al.
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Figure 2. Temperature dependence of the enantioselectivity in the enantioselective FC reaction of 3a with 4a using various catalysts at various concentra-
~
&
*
*
tions: 0.01 ( ), 0.025 ( ), 0.05 (ꢁ), 0.1 ( ), and 0.2m ( ). Bn=benzyl.
Mechanistic Studies
A key assumption in the rationalization of our catalytic
system is that a chemoselective interaction of catalyst 2 and
the substrate in the transition state occurs to control the
ortho- and enantioselective 1,4-addition of 3 with 4. As illus-
trated in the proposed ternary complex (Scheme 1), we an-
ticipate that the electron-deficient thiourea moiety might ac-
tivate 4 through bidentate coordination to the nitro group in
4, and the guanidinium cation would effectively orient the
phenol enolate.[14,42]
To confirm crucial contributions of the guanidine and thi-
ourea functional groups, we initially examined the FC reac-
tion of 3a with 4a using variant catalysts 7 and 8.
The optimized catalyst 2a promoted ortho-selective 1,4-
type FC alkylation reactions of 3a with 4a to give the corre-
sponding FC adduct in 97% yield with 91% ee (Table 2,
entry 1). In contrast, no reaction occurred with 7, in which
the guanidine moiety of 2a was replaced with a thiourea
group (Table 2, entry 2). Compound 8, in which the elec-
tron-deficient thiourea moieties in 2a are replaced with Boc
groups, promoted the FC reaction to afford 5aa in 77%
yield with 3% ee. The drastic decrease in the ee value clear-
ly shows the importance of the thiourea moieties for stereo-
determination in the FC reaction catalyzed by 2a. In addi-
tion, when O-methylsesamol 9a was used in place of sesa-
mol 3a, then 2a displayed no catalytic activity. These obser-
vations suggest that generation of phenolic enolate catalyzed
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Linking Conformational Flexibility and Kinetics
substrate concentrations of both 0.1 and 0.025m (Figure 3).
These results suggest that the enantioselectivity in the FC
reaction in toluene catalyzed by 2a is governed by the inher-
ent structures of the monomeric chiral catalyst 2a without
generation of complex dimers or oligomers,[46] regardless of
substrate concentration.
Scheme 1. Proposed ternary complex involved in the FC reaction of
phenol enolate with 4 catalyzed by 2.
Table 2. Catalytic asymmetric FC reaction of 3a or 9a with 4a.
Entry
Catalyst
Nucleophile
Yield [%][a]
ee [%][b]
1
2
3
4
2a
7
8
3a: R=H
3a: R=H
3a: R=H
9a: R=Me
97
n.r.
77
91
–
3
Figure 3. Relationships between ee values of 2a and (S)-5aa for substrate
concentrations of a) 0.1 and b) 0.025m.
2a
n.r.
–
[a] Yield of isolated product. [b] Determined by HPLC on a chiral sta-
tionary phase. [c] n.r.=no reaction.
In order to obtain further information on the catalytic
cycle, initial rate kinetic studies at ꢀ30 8C were performed
at 0.025 m substrate concentration.[47] The rate dependencies
of each reaction component are shown in Figure 4. First-
order dependency was observed for the catalyst (Figure 4a),
whereas the reaction rate had zeroth-order dependency for
sesamol (3a, Figure 4b) and b-nitrostyrene (4a, Figure 4c).
The initial kinetics indicate that the rate-determining step is
dissociation of the complex of protonated 2a and nitronate.
by the guanidine base is critical for the enhancement in the
FC reactions of phenols. This is complementary to the situa-
tion in the Brønsted acid catalyzed FC reaction of arenes.[43]
Because the ee values in FC alkylation of 3a with 4a cata-
lyzed by 2a are independent of the percentage conversion,
stereo-discrimination appears to be kinetically governed by
cooperative activation of the substrates by thioureas and
guanidine base in 2a.
We next investigated the re-
lationship between the ee value
of the catalyst and ee value of
FC product 5aa to gain insight
into the assembly state of the
catalyst,[44] because assembly
states generally play a key role
in constructing the ordered con-
formation of acyclic mole-
cules.[45] Indeed, mechanistic
studies and the observation of
nonlinear effects established
the importance of catalyst as-
sembly in catalytic asymmetric
nitroaldol reactions utilizing
1·HCl with a lipophilic long
alkyl chain on the guanidinium
moiety.[14d] In sharp contrast,
linear relationships between the
ee values of 2a and adduct 5aa
were obtained for reactions at Scheme 2. Proposed catalytic cycle in FC reaction of 3 with 4 catalyzed by 2a.
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Y. Sohtome, K. Nagasawa et al.
FULL PAPERS
entropy (DDS°).[48] Finally,
proton transfer between the
guanidinium 2a-H and nitro-
nate intermediate produces 5
and regenerates the catalyst.
Further investigations to broad-
en the utility of the conforma-
tionally flexible guanidine/bis-
thiourea
organocatalysts
2
based on these mechanistic
studies are ongoing.
Conclusion
We have carried out a series of
mechanistic studies on the
chemo-, regio-, and enantiose-
lective FC reaction of phenols
catalyzed by 1,3-diamine-teth-
ered-guanidine/bisthiourea or-
ganocatalysts. Extensive kinetic
studies performed by using
Eyring plots identified that
both the six-membered ring
containing
the
guanidine
moiety and the a-branched sub-
stituent on the chiral spacer in
2 play a pivotal role for attain-
ing the maximum magnitude of
differential activation entropy
(DDS°SꢀR) in the stereo-deter-
mining processes in the FC re-
action of 3a with 4a. Evidence
for the proposed guanidine/thi-
ourea cooperative reaction
mechanism and for the impor-
tance of the 1,3-diamine chiral
spacer in 2a was obtained by
means of experiments with
structural variants of the cata-
lyst. We believe our findings
~
&
*
Figure 4. A) Reaction profiles of the FC reaction for 2a at concentrations of 0.75 ( ), 1.25 ( ), 1.75 ( ), and
~
&
*
2.0 mm (ꢁ). B) Reaction profiles of the FC reaction for 3a at concentrations of 20 ( ), 25 ( ), 27.5 ( ), and
~
&
*
30 mm (ꢁ). C) Reaction profiles of the FC reaction for 4a at concentrations of 20 ( ), 25 ( ), 27.5 ( ), and
30 mm (ꢁ). a) Rate dependency on 2a. y=0.963xꢀ2.97 (R2 =0.983) b) Rate dependency on 3a. y=
ꢀ0.0423xꢀ2.56 c) Rate dependency on 4a. y=ꢀ0.00926xꢀ2.66
On the basis of the series of mechanistic studies described
above, we propose a catalytic cycle for the 1,4-type FC reac-
tion catalyzed by 2a (Scheme 2). The SAR studies with re-
spect to catalytic active sites, summarized in Table 2, suggest
crucial roles of both guanidine and thiourea moieties in 2a.
Thus, we assumed that the guanidine base deprotonated 3
and the electron-deficient thiourea moieties might have acti-
vated 4 through bidentate coordination to the nitro group,
thus forming the reactive ternary complex I, in which the
stereoselectivity of the FC reaction should be controlled. Ki-
netic studies performed by using Eyring plots suggested that
the dynamic motion of conformationally flexible 2a in re-
sponse to formation of the ternary complex I leads to exten-
sive desolvation of toluene from the catalyst, resulting in ef-
fective stereocontrol simply due to the differential activation
provide basic information that will be broadly useful in the
design of conformationally flexible architectures and will
extend the utility of asymmetric organocatalysts.
Experimental Section
Nitroolefin 4a (14.9 mg, 0.100 mmol) was added to a mixture of 2a
(4.3 mg, 0.005 mmol) and 3a (13.8 mg, 0.100 mmol) in toluene (4.0 mL)
at 208C. After stirring for 9 h at 208C, the reaction was quenched with a
saturated aqueous solution of NH4Cl. The resulting mixture was diluted
with EtOAc and poured into water. The aqueous layer was extracted
with EtOAc (ꢁ3) and the combined organic layer was washed with brine
and then dried over MgSO4. After removing solvents under reduced pres-
sure, the residue was purified by flash column chromatography (n-
hexane/EtOAc=15:1 to 5:1) to afford (ꢀ)-(S)-5aa (27.8 mg, 97% yield)
and 2a·HCl (4.5 mg, 99% recovery). The ee value of (ꢀ)-(S)-5aa
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Chem. Asian J. 2011, 6, 2463 – 2470

Linking Conformational Flexibility and Kinetics
(91% ee) was determined by means of chiral HPLC analysis (Chiral AD-
Nojiri, N. Kumagai, M. Shibasaki, J. Am. Chem. Soc. 2009, 131,
3779.
H, 0.46 cm (f)ꢁ25 cm (L), n-hexane/2-propanol=90:10, 1.0 mLminꢀ1
,
major 39.4 min, minor 30.4 min).
[12] For example, Lovick and Michael reported that the tethered bisgua-
nidine catalysts in the catalytic nitro-Mannich-type reaction dis-
played sharply decreased enantioselectivity as the length of the
tether was increased: H. M. Lovick, F. E. Michael, Tetrahedron Lett.
2009, 50, 1016.
Acknowledgements
[13] a) E. L. Eliel, S. H. Wilen, L. M. Mander, Stereochemistry of Organic
Compounds, Wiley, New York, 1994; b) P. J. Flory, Statistical Me-
chanics of Chain Molecules, Interscience, New York, 1969.
[14] For our personal account, see: a) Y. Sohtome, K. Nagasawa, Synlett
2010, 1; for other our work utilizing guanidine/bisthiourea organoca-
talysts, see: b) Y. Sohtome, N. Takemura, T. Iguchi, Y. Hashimoto,
K. Nagasawa, Synlett 2006, 144; c) Y. Sohtome, Y. Hashimoto, K.
Nagasawa, Eur. J. Org. Chem. 2006, 2894; d) Y. Sohtome, N. Take-
mura, K. Takada, R. Takagi, T. Iguchi, K. Nagasawa, Chem. Asian J.
2007, 2, 1150; e) K. Takada, N. Takemura, K. Cho, Y. Sohtome, K.
Nagasawa, Tetrahedron Lett. 2008, 49, 1623; f) B. Shin, S. Tanaka, T.
Kita, Y. Hashimoto, K. Nagasawa, Heterocycles 2008, 76, 801; g) K.
Takada, K. Nagasawa, Adv. Synth. Catal. 2009, 351, 345; h) K.
Takada, S. Tanaka, K. Nagasawa, Synlett 2009, 1643; i) S. Tanaka, K.
Nagasawa, Synlett 2009, 667; j) Y. Sohtome, B. Shin, N. Horitsugi, R.
Takagi, K. Noguchi, K. Nagasawa, Angew. Chem. 2010, 122, 7457;
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Takada, T. Yamaguchi, K. Nagasawa, Angew. Chem. 2010, 122,
9440; Angew. Chem. Int. Ed. 2010, 49, 9254.
We thank a Grant-in-Aid for Young Scientist (B) and The Uehara Me-
morial Foundation for financial support. B.S. is grateful for a Sasagawa
Scientific Research Grant.
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Received: April 11, 2011
Published online: July 14, 2011
2470
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