Active site design in a chemzyme: Development of a highly asymmetric and remarkably temperature-independent catalyst for the imino aldol reaction

Article abstract of DOI:10.1002/1521-3773(20010618)40:12<2271::AID-ANIE2271>3.0.CO;2-N

Unusually robust: A remarkably temperature-independent catalyst has been developed for the imino aldol reaction of imines derived from ortho-aminophenols (see scheme). This catalyst is prepared from two equivalents of the VAPOL ligand and a zirconium tetraalkoxide. From a consideration of likely intermediates in the catalytic cycle it was deduced that a methyl substituent ortho to the phenol (R¹) should enhance induction. This resulted in asymmetric inductions in excess of 98% ee at room temperature as well as at 100°C. TMS=trimethylsilyl.

Full text of DOI:10.1002/1521-3773(20010618)40:12<2271::AID-ANIE2271>3.0.CO;2-N

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were performed by using the TEXSAN[13] crystallographic software Table 1. Reactions of imine 1 with acetal 2 with various catalysts.[a]
package. Crystallographic data (excluding structure factors) for the
structure reported in this paper have been deposited with the
Cambridge Crystallographic Data Centre as supplementary publica-
tion no. CCDC-153832. Copies of the data can be obtained free of
charge on application to CCDC, 12 Union Road, Cambridge
CB21EZ, UK (fax: (‡44)1223-336-033; e-mail: deposit@ccdc.cam.
ac.uk).
OH
OTMS
cat.
NH
O
+
N
Ph
OMe
Ph
OMe
OH
3
1
2
[10] Nomenclature of Inorganic Chemistry, Recommendation 1990 (Ed.:
G. J. Leigh), Blackwell, Oxford, 1990.
[11] a) J. Lorberth, W. Massa, M. E. Essawi, L. Labib, Angew. Chem. 1988,
100, 1194 ± 1195; Angew. Chem. Int. Ed. Engl. 1988, 27, 1160 ± 1161;
b) B. Longato, G. Bandoli, G. Trovo, E. Marasciulo, G. Valle, Inorg.
Chem. 1995, 34, 1745 ± 1750.
[12] C. White, A. Yates, P. M. Maitlis, Inorg. Synth. 1992, 29, 228 ± 234.
[13] TEXSAN-TEXRAY Structure Analysis Package, Molecular Struc-
ture Corporation, Houston, TX, 1985 and 1992.
Entry Ligand
mol% cat. T [8C] t [h] Solvent
Yield 3 [%] % ee
1
2
3
4
5
S-VAPOL
S-VAPOL
S-VAPOL
S-VAPOL
S-VAPOL
R-BINOL[e]
R-BINOL[e]
20
20
20
2
45
45
25
40
41
45
25
45
25
25
10
20
15
6
CH2Cl2
toluene
toluene[b] 94
toluene[b] 100
50
92
80
91
89[c]
86[d]
85
0.5
20
20
19
19
4
19
4
toluene
CH2Cl2
CH2Cl2
CH2Cl2
CH2Cl2
toluene
60
80
6
7
36
100
87
28
86
8
9
10
R-Br2BINOL[f] 10
R-Br2BINOL[f] 20
R-Br2BINOL[f] 10
87
48
18
95
62
[a] Catalyst generated from Zr(OiPr)4/iPrOH, (S)-VAPOL (2.2 equiv) and
1.2 equiv N-methyl imidazole (NMI) in either CH2Cl2 or toluene at 258C for 1 h.
Unless otherwise specified, all reactions were performed with 1.2 equiv of 2 and
0.125m in imine. [b] 15:1 toluene:CH2Cl2. [c] 0.5m in imine. [d] 1.0m in imine.
[e] Catalyst generated from Zr(OiPr)4/iPrOH, R-BINOL (2.2 equiv) and 1.2 equiv
NMI in CH2Cl2 at 258C for 1 h. [f] Catalyst generated from Zr(OtBu)4, (R)-6,6'-
dibromoBINOL (2.2 equiv) and 1.2 equiv NMI in CH2Cl2 at 258C for 1 h.
Active Site Design in a Chemzyme:
Development of a Highly Asymmetric and
Remarkably Temperature-Independent
Catalyst for the Imino Aldol Reaction**
Song Xue, Su Yu, Yonghong Deng, and
William D. Wulff*
protocol, the catalyst was prepared by reaction of the ligand
with 0.5 equivalents of zirconium tetraalkoxide in the pres-
ence of 0.6 equivalents of N-methyl imidazole at room
temperature for 1 h.[2] The VAPOL catalyst could be prepared
in either methylene chloride or toluene, but for solubility
reasons, the BINOL catalysts were prepared in methylene
chloride. The VAPOL and Br2BINOL catalysts were superior
to the BINOL catalyst at 458C. The asymmetric induction
dropped for the Br2BINOL catalyst when the temperature
was raised from 458C to room temperature, but curiously,
the asymmetric induction for the VAPOL catalyst was
essentially unchanged over this same temperature range.
Only a small drop-off is noted (85% ee) when the temper-
ature is raised to 418C and the substrate-to-catalyst ratio is
raised to 200:1 (entry 5). Both the R enantiomers of BINOL
and Br2BINOL ligands give the R enantiomer of the product
3, whereas with the VAPOL ligand, it is the S enantiomer that
gives the R product. This reversal is not unexpected given the
structures of the ligands where the zirconium is in the minor
groove of the BINOL ligands and in the major groove of the
VAPOL ligand.[6, 7]
The asymmetric aldol reaction of an enolate or enolate
equivalent with an imine is a reaction of established synthetic
importance for the synthesis of chiral amines in general and b-
amino esters in particular.[1] The development of chiral
catalysts for this reaction has proven to be a difficult task
and had eluded all attempts until recently when Kobayashi
and co-workers examined imines derived from o-aminophe-
nol.[2±4] Their method involves the catalysis of the reactions of
these imines and ketene acetals with a catalyst generated from
zirconium(iv) tert-butoxide and two equivalents of (R)-6,6'-
dibromoBINOL (BINOL ˆ 1,1'-binaphth-2-ol). Our interest
in the synthesis of chiral amines led us to investigate the use of
VAPOL-derived catalysts[5] (see Figure 1) for this reaction.
Here we report the development of a remarkably temper-
ature-independent and highly asymmetric method for this
process that was guided by an analysis of models of
intermediates that are suspected to be involved in the
reaction.
A comparison of catalysts prepared from BINOL, 6,6'-
dibromoBINOL and VAPOL ligands on the asymmetric
induction in the reaction of the phenyl-substituted imine 1 and
acetal 2 is summarized in Table 1. Following the Kobayashi
The mechanism that has been proposed for the catalytic
cycle for the Br2BINOL ± zirconium-mediated reaction in-
volves a catalyst bearing two Br2BINOL ligands on one
zirconium and the coordination of the o-hydroxyphenylimine
to the zirconium as a bidentate ligand.[2g] It is clear from the
examination of space-filling CPK models that it is possible to
bind two VAPOL ligands to one zirconium atom but only with
a facial arrangement of the four oxygen atoms as is illustratred
[*] Prof. W. D. Wulff, Dr. S. Xue, Dr. S. Yu, Dr. Y. Deng
Department of Chemistry
Michigan State University
East Lansing, MI 48824 (USA)
Fax : (‡1)517-353-1793
1
by structure 6 in Scheme 1. This is supported by H NMR
E-mail: wulff@cem.msu.edu
experiments on a catalyst generated from zirconium tetraiso-
propoxide and VAPOL in the presence of two equivalents of
N-methyl imidiazole. A clean spectrum is only observed with
two equivalents of VAPOL relative to zirconium and the
spectrum is consistent with a single C2-symmetrical species
[**] This work was supported by a grant from UOP Company. We would
like to thank Thomas Malloy, Timothy Brandvold and Beth McCul-
loch for stimulating discussions.
Supporting information for this article is available on the WWW under
http://www.angewandte.com or from the author.
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OTMS
OMe
2
OH
N
O
N
O
O
O
O
Ph
Zr
H
1
Ph
NMI
4
O
X
O
O
NH
O
O
MeO
O
O
O
Zr
H
Zr
OTMS
O
NMI
Ph
NMI
6
7
X = open
X = NMI
5
OTMS
NH
OMe
O
N
Ph
OMe
9
Ph
8
Scheme 1. Proposed mechanism for the reaction of imine 1 with acetal 2.
which is tentatively identified as structure 7 bearing mutually
trans NMI ligands bound to the zirconium.[8, 9] An approach of
imine 1 to the open apical position in intermediate 6 is
proposed to lead to intermediate 4 in which a phenol
exchange has occurred. In support of this is the observation
that the catalysis of the reaction of the O-methylated imine 9
with acetal 2 under the conditions in entry 3 in Table 2 gave 3
in 5% yield and 0% ee.[10] The requirement for NMI then can
be explained as that of a monodentate ligand that binds to the
other apical site and maintains an octahedral geometry.
Reaction of species 4 with the ketene acetal would give
intermediate 5 and then release of the product would
regenerate the unsaturated species 6 and complete the cycle.
A space-filling CPK model of intermediate 6 is shown in
Figure 1 and illustrates the binding cleft that is available for
the docking with imine 1. There are a number of possible
Figure 1. CPK models of intermediate 6 and of two imines complexed with
intermediate 6.
orientations of 1 in the cleft of 6 and these are largely
associated with changes in the Zr-O-C bond angle that has the
effect of rocking the imine back and forth in the cleft. Rocking
the imine down into the cleft should provide a conformation
that provides a greater facial selectivity of attack on the imine
since it should provide greater shielding of the re-face by the
phenanthrene unit on the right side of the molecule as viewed
in Figure 1. CPK models reveal that a methyl group on the
imine ortho to the phenol function should be sufficient to push
the imine down into the cleft. This methyl group is presented
in red in the imine complex with intermediate 6, and as
illustrated in Figure 1 this methyl group makes close contacts
with the floor of the cleft even when the imine is rotated down
into the cleft and this results in greatly restricted movement
about the Zr± O ± C unit to the imine moiety. This model thus
predicts that imines with a methyl substituent ortho to the
phenol function in imine 1 should lead to increased asym-
metric induction in the imino aldol reaction whereas methyl
groups at postions meta and para to the phenol should not
have any effect since they do not make close contacts with any
part of the catalyst.
Table 2. Reactions of imines from substituted amino phenols.[a]
R1
R3
R2
20 % S-VAPOL
cat.
R4
N
R2
R1
OH
NH
R3
toluene, 25 oC, 12-18 h
24 % NMI
O
Ph
R4
Ph
OH
OMe
acetal 2
Imine
R1
R2
R3
R4
Product
Yield [%]
% ee
1
H
Me
H
H
H
Me
H
Me
H
H
Me
H
H
H
H
H
H
H
H
Me
H
Me
Cl
Me
H
H
H
H
Me
H
H
H
3
17
18
19
20
21a
22
94[b]
89
89
ꢀ 99
91
95
36
11
12
13
14
15a
16
15a
87[c]
93
80[c]
100
78
ꢀ 98
On the basis of the above predictions, a series of seven
substituted imines were prepared; data from their reactions
with ketene acetal 2 are summarized in Table 2. Indeed, of the
four possible monomethyl-substituted imines, the highest
induction was observed with a methyl group ortho to the
60
21a
93
47[d]
[a] See Table 1. [b] Reaction performed at 0.5m imine in 15:1 toluene/
CH2Cl2. [c] Reaction time of 2 h. [d] Catalyst (10 mol%) generated from
(R)-6,6'-dibromoBINOL according to footnote [f] in Table 1.
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phenol function (R1 ˆ Me). The asymmetric induction in-
creases from 89% ee with imine 1 to >99% ee with imine 11
(entries 1 and 2). The induction significantly drops with imine
14 with a methyl group ortho to the imine which may be a
result of twisting of the imine to expose the re-face. The
introduction of a methyl group at R2 has very little effect and
the slight increase in induction for the methyl group at R3 may
indicate an electronic effect that results in a shortening of the
zirconium oxygen distance. This is corroborated with the
decrease in induction observed for the imine 16 with a chloro
substituent at R3. The catalyst generated from Br2BINOL has
a completely different response to substituents on the imine;
the induction drops with introduction of a methyl group ortho
to the phenol. The catalyst prepared from this ligand gives an
enantiomeric excess of 62% with imine 1 (Table 1, entry 10)
and 47% with the dimethyl-substituted imine 15a (Table 2,
entry 8).
(20 mol% catalyst) and in 76% enantiomeric excess at
1008C (5 mol% catalyst). Similarly, the reaction of imine
15a with 26 gives 23a in 71% ee at 258C (20 mol% catalyst)
and 60% ee at 1008C (2 mol% catalyst). The deprotection of
the amine function in the adduct 23a can be accomplished by
direct treatment with 5 equivalents of ceric ammonium nitrate
at 08C and then warming to room temperature over 3.5 h. The
deprotection of the methyl esters 21a ± e were accomplished
with the same conditions in 60 ± 79% chemical yield
(Scheme 2).
The rate of the reaction of imines with ketene acetals with
the VAPOL catalyst is slower with imines generated from
substituted aminophenols, however, as indicated in Table 3,
this effect can be offset by performing the reaction at higher
Table 3. Temperature dependence of the asymmetric induction in 21.[a]
Me
Me
Zr-(R)-VAPOL cat.
OH
NH
Me
toluene
NMI
N
Me
R
O
OH
acetal 2
OMe
R
21
15
Scheme 2. Products, yields, and optical rotations of the reactions of imine
15 with the ketene acetal 26 and deprotection of 21 and 23.
Series
R
mol% cat. T [8C] Yield 21 [%] % ee 21
a
Ph
20
20
20
20
5
2
2
2
2
25
65
85
100
100
100
100
100
100
100
100[b]
93[c]
94[c]
91[c]
90[c]
95[d]
90[e]
85[e]
85[e]
83[e]
98.0
98.4
98.5
98.5
98.4
98.5
95.4
99.8
96.4
93.0
The VAPOL ± zirconium catalyst described herein is un-
usually robust providing very high asymmetric inductions in
the Mukaiyama type condensation of ketene acetals with
imines. We will report in due course on continuing studies
directed toward experimentally probing the mechanism of
this reaction as well as further development of the scope and
synthetic potential of these reactions.
b
c
d
e
4-Cl-C6H4
4-MeO-C6H4
3,4-(MeO)2-C6H3
1-Naph
2
[a] See Table 1; reaction time 2 ± 3 h. [b] Reaction time 15 h. [c] (S)-
VAPOL used. [d] Reaction time 5 h. [e] Reaction time 24 h.
Received: August 7, 2000
Revised: April 9, 2001 [Z15592]
temperature where greater turnover numbers are observed. It
was quite striking to observe that the induction with imine 15a
shows absolutely no temperature dependence over the range
of 25 to 1008C.[11] Furthermore, the reaction at 1008C can be
performed with an order of magnitude change in catalyst
loading with no loss in induction. The turnover numbers have
not yet been measured, as the minimum time for these
reactions was not investigated. The electronic nature of the
imine has a small effect on the induction at this temperature
with a slight increase noted for a p-methoxy substituent and
slight decrease for a p-chloro substituent.
The reactions of the imines 15 with the ketene acetal 26
mediated by the VAPOL ± zirconium catalyst are slower than
those involving the ketene acetal 2 and do not display the
same temperature independence. The reaction of imine 15e
with 26 gives 23e in 91% enantiomeric excess at 258C
[1] For leading references, see: E. Juaristi, Enantioselective Synthesis of b-
Amino Acids, Wiley-VCH, New York, 1997.
[2] a) H. Ishitani, M. Ueno, S. Kobayashi, J. Am. Chem. Soc. 1997, 119,
7153; b) S. Kobayashi, H. Ishitani, M. Ueno, J. Am. Chem. Soc. 1998,
120, 431; c) S. Kobayashi, Y. Hasegawa, H. Ishitani, Chem. Lett. 1998,
1131; d) S. Kobayashi, K.-I. Kusakabe, S. Komiyama, H. Ishitani, J.
Org. Chem. 1999, 64, 4220; e) H. Ishitani, T. Kitazawa, S. Kobayashi,
Tetrahedron Lett. 1999, 40, 2161; f) S. Kobayashi, H. Ishitani, Chem.
Rev. 1999, 99, 1069; g) H. Ishitani, M. Ueno, S. Kobayashi, J. Am.
Chem. Soc. 2000, 122, 8180.
[3] For other examples, see: a) H. Fujieda, M. Kanai, T. Kambara, A. Iida,
K. Tomioka, J. Am. Chem. Soc. 1997, 119, 2060; b) E. Hagiwara, A.
Fuji, M. Sodaka, J. Am. Chem. Soc. 1998, 120, 2474; c) D. Ferrais, B.
Young, T. Dudding, T. Lectka, J. Am. Chem. Soc. 1998, 120, 4548;
d) D. Ferrais, B. Young, C. Cox, W. J. Drury III, T. Dudding, T. Lectka,
J. Org. Chem. 1998, 63, 6090; e) T. Kambara, M. A. Hussein, H.
Fujieda, A. Iida, K. Tomioka, Tetrahedron Lett. 1998, 39, 9055; f) S.
Yamasaki, T. Iida, M. Shibasaki, Tetrahedron Lett. 1999, 40, 307; g) K.
Angew. Chem. Int. Ed. 2001, 40, No. 12
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Cu2‡ Inhibits the Aggregation of Amyloid
Tomioka, H. Fujieda, S. Hayashi, M. A. Hussein, T. Kambara, Y.
Nomura, M. Kanai, K. Koga, Chem. Commun. 1999, 715; h) D.
Ferraris, T. Dudding, B. Young, W. J. Drury III, T. Lectka, J. Org.
Chem. 1999, 64, 2168; i) A. Fujhii, E. Hagiawara, M. Sodeoka, J. Am.
Chem. Soc. 1999, 121, 5450; j) T. Kambara, K. Tomioka, Chem.
Pharm. Bull. 1999, 720; k) S. Yamasaki, T. Iida, M. Shibasaki,
Tetrahedron 1999, 55, 8857; l) D. Ferraris, B. Young, T. Dudding,
W. J. Drury III, T. Lectka, Tetrahedron 1999, 55, 8869; m) K.-i.
Yamada, S. J. Harwood, H. Gröger, M. Shibasaki, Angew. Chem.
1999, 111, 3713; Angew. Chem. Int. Ed. 1999, 38, 3504; n) S. F. Martin,
O. D. Lopez, Tetrahedron Lett. 1999, 40, 8949; o) M. A. Hussein, A.
Iida, K. Tomioka, Tetrahedron 1999, 55, 11219.
b-Peptide(1 ± 42) in vitro**
Jin Zou, Katsushi Kajita, and Naoki Sugimoto*
Alzheimerꢁs disease (AD) is the most frequent cause of
late-life dementia, with pathological characteristics of extra-
cellular aggregation of amyloid b-peptides (Abs) with 39 ± 43
amino acids, which are proteolytically derived from the
transmembrane amyloid precursor protein (APP).[1] Recent
studies indicate that the amyloid b-peptide(1 ± 42) (Ab(42))
plays a central role in the formation of the b-amyloid fibril
(fAb) in vivo among the different coexisting Ab species.[2]
Further elucidation of the mechanism of Ab(42) aggregation,
and the effect of extrinsic or environmental factors such as
pH, metal ions, ionic strength, membrane-like surfaces, and
solvent hydrophobicity on the aggregation is useful for our
understanding of the pathophysiology and treatment of
Alzheimerꢁs disease and other similar neurodegenerative
diseases.
Some metal ions such as Zn2‡, Cu2‡, etc., are essential in
trace amounts with important fundamental roles in the
biochemistry of human life.[3] It was recently reported that
Cu2‡, Zn2‡, and Fe3‡ are concentrated in the normal neo-
cortex. The concentrations of these cations are more than
doubled in the cerebral amyloid deposits of AD brains
compared with the neuropil of normal age-matched brains.[4]
However, the role of Cu2‡ in neurodegenerative diseases such
as Alzheimerꢁs disease is still not clear, although the effect of
Zn2‡ on the aggregation of Abs has been demonstrated by
several groups in recent years.[5] Our recent study indicated
that the complexation of peptides with Cu2‡ is responsible for
inducing and enhancing the formation of the a-helix con-
formation of the alanine-based peptides with a Trp/His pair in
different geometrical spacings and positions.[6] Herein we
describe the aggregation of Ab(42) and demonstrate for the
first time that Cu2‡ inhibits the aggregation of Ab(42) with
both thioflavin T (ThT) fluorescence assay and atomic force
microscopy (AFM) in vitro.
[4] The first example with a chiral catalyst was reported by Yamamoto
et al. and predated the work of Kobayashi but required stoichiometric
loading. See reference [1] and: K. Ishihara, M. Miyata, K. Hattori, H.
Yamamoto, T. Tada, J. Am. Chem. Soc. 1994, 116, 10520. For an
example with a chiral boron enolate, see: E. J. Corey, C. P. Decicco,
R. C. Newbold, Tetrahedron Lett. 1991, 32, 5287.
[5] For applications of VAPOL catalysts in asymmetric catalytic Diels ±
Alder and aziridination reactions, see: a) J. Bao, W. D. Wulff, A. L.
Rheingold, J. Am. Chem. Soc. 1993, 115, 3814; b) J. Bao, W. D. Wulff,
Tetrahedron Lett. 1995, 36, 3321; c) J. Bao, W. D. Wulff, J. B. Dominy,
M. J. Fumo, E. B. Grant, A. C. Rob, M. C. Whitcomb, S.-M. Yeung,
R. L. Ostrander, A. L. Rheingold, J. Am. Chem. Soc. 1996, 118, 3392;
d) D. P. Heller, D. R. Goldberg, W. D. Wulff, J. Am. Chem. Soc. 1997,
119, 10551; e) J. C. Antilla, W. D. Wulff, J. Am. Chem. Soc. 1999, 121,
5099; f) J. Antilla, W. D. Wulff, Angew. Chem. 2000, 112, 4692; Angew.
Chem. Int. Ed. 2000, 39, 4518.
[6] J. Reeder, P. P. Castro, C. B. Knobler, E. Martinborough, L. Owens, F.
Diederich, J. Org. Chem. 1994, 59, 3151.
[7] For a related observation, see: S. Kobayashi, K.-I. Kusakabe, S.
Komiyama, H. Ishitani, J. Org. Chem. 1999, 64, 4220.
[8] The reaction of VAPOL with 0.5 equivalents of zirconium tetraiso-
propoxide in the presence of two equivalents of NMI produces the
clean formation of a single C2-symmetrical species which is tentatively
assigned by 1H NMR spectroscopy as 7: 1H NMR (C6D5CD3): d ˆ 1.60
(brs, 6H), 4.37 (brs, 2H), 5.57 (brs, 2H), 5.87 (brs, 2H), 6.79 ± 6.84 (m,
12H), 6.98 ± 7.01 (m, 8H), 7.05 (s, 4H), 7.14 (d, 4H, J ˆ 8.7 Hz), 7.19 (d,
4H, J ˆ 8.7 Hz), 7.22 (td, 4H, J ˆ 8.1, 1.1 Hz), 7.41 (dd, 4H, J ˆ 8.1,
1.2 Hz), 7.84 (td, 4H, J ˆ 8.1, 1.5 Hz), 11.33 (d, 4H, J ˆ 8.4 Hz). The
1H NMR spectrum shows that a number of species are generated when
a 1:1 stoichiometry of VAPOL to zirconium is employed.
[9] As reported with the BINOL ± Zr catalyst,[2a] the induction falls off
with a catalyst prepared with a 1:1 stoichiometry of zirconium to
VAPOL (to 60% ee for the reaction indicated in entry 3 in Table 1).
[10] A similar observation has been made for the Br2BINOL catalyst
where this imine gave a good yield but only 5% ee.[2a]
[11] There are several examples of asymmetric reactions that give optimal
inductions above ambient temperature. For examples, see: a) M.
Sugiura, T. Nakai, Angew. Chem. 1997, 109, 2462; Angew. Chem. Int.
Ed. Engl. 1997, 36, 2366; b) H. Gröger, Y. Saida, H. Sasai, K.
Yamaguchi, J. Martens, M. Shibasaki, J. Am. Chem. Soc. 1998, 120,
3089.
[*] Prof. Dr. N. Sugimoto, J. Zou, K. Kajita
Department of Chemistry
Faculty of Science and Engineering
Konan University
8-9-1 Okamoto, Higashinada-ku, Kobe 658-8501 (Japan)
Fax : (‡81)78-435-2539
E-mail: sugimoto@konan-u.ac.jp
Prof. Dr. N. Sugimoto
Other address:
High Technology Research Center
Konan University
8-9-1 Okamoto, Higashinada-ku, Kobe 658-8501 (Japan)
J. Zou
Other address:
Department of Biological Engineering
School of Chemical Engineering
Hebei University of Technology
Tianjin 300130 (PR China)
[**] We thank JEOL for the AFM measurement. This work was supported
in part by Grants-in-Aid from the Japanese Ministry of Education,
Science, Sports, and Culture, and a Grant from ªResearch for the
Futureº Program of the Japan Society for the Promotion of Science to
N.S.
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