ARTICLE pubs.acs.org/JPCA
Theoretical Study on Reaction Scheme of Silver(I) Containing 5-Substituted Uracils Bridge Formation Toru Matsui,*,†,‡,§ Hideaki Miyachi,|| Takeshi Baba,^ and Yasuteru Shigeta†,‡ †
)
Department of Materials Engineering Science, Graduate School of Enginnering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan ‡ Core Research for Evolutional Science and Technology, The Japan Science and Technology Agency (JST), Japan § Department of Chemistry, Graduate School of Science, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka 560-0043, Japan School of Medicine, Chiba University, 1-8-1 Inohana, Chuo-ku, Chiba-shi, Chiba, 260-8670, Japan ^ Graduate School of Life Science, University of Hyogo, 3-2-1 Kouto, Kamigori-cho, Ako-gun, Hyogo, 678-1297, Japan
bS Supporting Information ABSTRACT: We present a reaction scheme of silver containing 5-substituted uracils (N) bridge formation with two silver ions to a silver-mediated base pair [N-Ag2-N] by using the conductor-like polarizable continuum model (CPCM)-B3LYP/aug-cc-pVDZ level of theory. The whole reaction scheme is divided into the following three steps: (1) silver ion binding and deprotonation, (2) silver ion transfer, and (3) dimer formation and structural fluctuation. With a new pKa computing scheme proposed in our previous studies, it is found that a silver coordination decreases the pKa of N by 2.53.0 pKa units, which is an important clue for silver-ion selectivity by N. Judging from the calculation, we revealed that the silver ion transfer reaction and the dimerization reaction occur spontaneously. Moreover, both reactions are independent of the C5 ligand in N so that the deprotonation reaction, which is the first step of this scheme, plays a key role in forming the [N-Ag2-N] pairing.
1. INTRODUCTION Deoxyribonucleic acid (DNA) contains genetic information used in the development and functioning of living organisms. From the view of a chemist, the DNA has been recently considered as the simplest template for self-organized molecules or systems with one-dimensional structure. The structure of the DNA attracts many people not only from its beautiful shape of double helix, but also from the expectation for a one-dimensional nanowire. The DNA is rich in π electons because the duplex is occupied by the parallel stack of aromatic nucleobases. In our previous work, we computed the electron conductivity of pseudoion stacked base pairs C(+)G()/G()C(+) (C and G represent cytosine and guanine, respectively), which are derived from proton-transfer reactions in CG/GC (50 -CG-30 ).1,2 Judging from its electron affinity, the electronic conductivity of C(+)G()/G()C(+) depends dramatically on the connection to electrode, although it is almost impossible to reproduce such situation experimentally. If metal ions, which have various electronic states, are captured in the DNA duplex and controlled to systematically array, one can obtain a hybrid material with multifunctions in mesoscopic scale. These days, many researchers have developed such metal DNA systems. There exist two strategies to achieve metal arraying in DNA duplex. The former uses an artificial DNA, which is an analog of DNA. The latter uses a mismatch pair of natural nucleobase and its modification. r 2011 American Chemical Society
With the former strategy, since Tanaka and Shionoya et al. succeeded in synthesizing [H-Cu(II)-H]5 (H: hydroxypyridone) in the DNA duplex,3,4 many artificial DNA have been reported and proposed.59 Clever et al. synthesized a salen-metal artificial base pair that captures Mn(II) or Cu(II) ions.10 The duplex, which includes a Cu(II)-salen base pair, shows an extremely high melting point (Tm) of 82 C. Triple helix formation also can capture a metal ion; for example, three Hs capture an iron(III) cation and form octahedral FeH3 structures.11 As for structures of these systens, Johansen et al. first presented the NMR solution structure of a self-cDNA, which contains a silver-mediated imidazole nucleotide.12 Our group1316 and other theoretical groups1721 also have reported several theoretical calculations on magnetic properties and the vertical distance between artificial nucleobases. With the latter strategy, Ono and his co-workers have demonstrated that a thyminethymine mismatch base pair (T-T) in a DNA duplex captures a mercury ion to form a stable neutral thyminemercurythymine base pair [T-Hg(II)-T].22 Following the work by Ono et al., Tanaka and Clever succeeded in presenting two different metals (Cu and Hg) captured in a duplex consisting of two types of ligands (salen and thymine), Received: January 27, 2011 Revised: May 18, 2011 Published: June 20, 2011 8504
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Scheme 1. Chemical Structure of 5-Substituted Uracil, Where X Is the Ligand of C5
each in the same duplex.2325 Many experimentalists and theoreticians have reported optical properties and electronic structure of these bridge structures.2629 We have also reported the theoretical UVvis spectra by using TD-DFT30 and confirmed that stacked structures of [T-Hg(II)-T] exist, because the theoretically estimated UVvis spectra of stacked [T-Hg(II)-T] closely agreed with those of experiment. The cytosine (C) dimer can also capture the silver ion and form [C-Ag(I)-C] structure, which leads to an increase in the melting point of whole DNA.31 A recent observation by Ihara et al. has succeeded in synthesizing a silver mediated C+GC in the DNA triplex.32 In 2009, Okamoto et al. succeeded in synthesizing a [N-Ag2N] (N: 5-substituted uracil, see Scheme 1 for chemical structure) bridge by substituting the C5 ligand (X) of deoxyuracil nucleooligomer.33 They have confirmed the formation of the bridge structure by using mass-spectra and UVvis spectra. In the case of F (X = F), the captured metal ion (Hg(II) or Ag(I)) depends on pH in aqueous solution, while [N-Ag2-N] can be formed even in low pH in the case of CN (X = CN). On the other hand, T (X = CH3) does not seem to capture any silver ion due to its high pKa. The [N-Ag2-N] bridge can also be stacked in a duplex, which is expected to be similar to the case of [T-Hg(II)-T] bridges. As far as we know, neither reaction scheme nor geometries of [N-Ag2-N] have been clarified, because there are no X-ray or NMR data for its structure. Our previous study34 focused on [UAg2-U] (U: X = H) bridges and showed following three points by using B3LYP/aug-cc-pVDZ + pseudo potential (PP) and 6-31+ +G(d, p) level of theory: (1) The replacement of an iminoproton with Ag(I) increases the stability of the whole duplex in nucleo-oligomer. (2) There exist four conformations of [N-Ag2N] bridge and three of them can coexist from the view of their potential energies. (3) The energy barriers among three structures are no more than 6 kcal/mol that these structures may fluctuate at room temperature. These results indicated that the replacement of imino-proton with Ag(I) plays a key role in forming [N-Ag2-N] bridges. Coordination of metal complex, a kind of chemical modification, is said to promote a deprotonation in nucleobase. According to an experimental paper from Sigel’s group,35,36 metal ions (e.g., Cu(II), Zn(II)) greatly decrease the pKa value of uracilmethylphosphonate. A similar situation may occur in the case of the silver-mediated N. It is expected that the Ag(I) binding decreases the pKa value of imino-proton, which can promote the bridge forming reaction. Accordingly, we first focused on the change of pKa value due to the coordination of Ag(I) complex. However, it is difficult to obtain the pKa value for the silvermediated N experimentally because the silver bound N is not stable enough to exist in the equilibrium state. Our previous study37 showed that there exists the linear correlation between the observed pKa value and the deprotonation energies in the
Figure 1. Whole reaction scheme from 5-substituted uracil (1, denoted as N) to [N-Ag2-N] bridge (7). Ball in the figure denotes a silver atom.
imino-proton of N. We derived the Gibbs energy of proton in implicit aqueous solution and proposed a new computational scheme with polarizable continuum model (PCM) to obtain calculated pKa. By using this scheme, we can consider the reaction scheme for silver-proton (Ag(I)-H+) exchange reaction. This study aims to understand the mechanism of the silver capturing reaction comprehensively and to discuss the dependency on C5 ligand of N.
2. COMPUTATIONAL DETAILS We computed the fully relaxed geometry optimization (not fixed geometries) and vibrational frequency analyses in order to obtain the Gibbs energy in each compound. As an initial structure of N, we modified the structure of fragment appeared in Gauss View 4.1. We also made an initial structure of [N-Ag2-N] from our previous work. In this study, we performed DFT-B3LYP/ aug-cc-pVDZ level of theory by using Gaussian 03.38 As a basis function for Br and Ag, we adopted Peterson’s aug-cc-pVDZ +PP,39,40 which is available in EMSL site.41,42 We assumed that the reaction occurs in implicit water model described by conductor-like polarizable continuum model (CPCM), where the united atom topological model based on the KohnSham DFT level (UAKS) is adopted. For the sake of reducing the computational cost, we replaced the backbone molecules in DNA with a methyl group, that is, we restricted structural model to 5-substituted uracil that was terminated at C10 in backbone molecule. In the Supporting Information we listed the optimized geometries of all structures. We found that all Ns in silver containing N or [N-Ag2-N] keep the planarity. 3. RESULTS AND DISCUSSION 3.1. Proposed Mechanism for Capturing Silver Ion. First of all, we propose here the reaction mechanism of the following reaction:
2N + 2½AgðH2 OÞ2 + f ½N-Ag2 -N + 4H2 O + 2H+
ð1Þ
We supposed the ligand of silver ion is H2O because there exist many water molucules around the DNA we focused on. Figure 1 shows the whole reaction scheme for (1). A silver ion binds to N (1) and forms a Ag(I)-N complex (2). The reaction from 1 to 2 is a substitution reaction and one of the ligand H2O is supposed to 8505
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Figure 2. Contour plots of electrostatic potential (ESP) for (a) X = CH3 (T), (b) X = Br (Br), (c) X = F (F), and (d) X = CN (CN). The site which has large negative value is a candidate for Ag(I) bound site.
dissociate at this stage. Deprotonation follows at N3-H+ (imino group) and leads to a structure Ag(I)-N (3). Next, the Ag(I) transfers to N3 and forms a N3-Ag(I) coordination (4). Then two structures of 4 produce a 4-4 dimer (5), which forms two coordinations as N3-Ag-O4 and O2-Ag-N3. At this stage, H2O, which is a ligand of Ag, dissociates. The structure of 5 resembles that of “UU 7” proposed by Hobza’s group.43 As pointed out in our previous study, we suggested the existence of the stable conformer 6, where silver ions replace imino protons of UU 7. Finally, the structure of [N-Ag2-N] bridge fluctuates from 5 to 7 through the transition state 6. Therefore, in what follows, we considered three steps: (1) Silver ion binding and the deprotonation reaction in the imino group, (2) Silver ion transfer reaction, and (3) Formation of [NAg2-N] bridge from two Ag-N complexes. 3.2. Silver Ion Binding and Deprotonation Reactions. 3.2.1. Electrostatic Potential in N. To specify the binding site for Ag(I) in N, we computed electrostatic potential (ESP). We showed four contours plots for ESP of N (T, Br, F, CN) in Figure 2. In any case of N, there exists a strong negative potential around O4, which attracts Ag(I). Moreover, it is clear that positive potential is distributed around the ligand of C5 in the case of T and Br. On the other hand, negative potential is distributed around the ligand of C5 in F and CN because of the electron withdrawing properties of the ligands. In particular, CN has a strong negative charge around the ligand of C5 as well as around O4 so that there are two binding sites for silver ion in CN. There exists a weak negative potential around the O2 site, which indicates the possibility of AgO2 coordination. (see Supporting Information for details) However, the energy of the AgO2 coordination is less stable than that of the AgO4 bond by 23
kcal/mol. Therefore, we focused on O4 site (and C5 site in CN) in the following sections. 3.2.2. Binding Free Energy. The binding energy of Ag(I) to N can be estimated as ΔGbind ðNÞ ¼ Gð½AgðH2 OÞ2 Þ + GðNÞ fGðN-Ag-H2 OÞ + GðH2 OÞg
ð2Þ where Ag(I)-N is silver-bound N. At first, we depicted optimized geometries for N-Ag-H2O in Figure 3. As indicated in section 3.2.1, we obtained two optimized geometries for CN-Ag-H2O. From Table 1, remarkable changes were not found so that the ligands of C5 did not affect the geometries around Ag(I). Table 1 also lists the binding energies ΔGbind(N) estimated by eq 2. ΔGbind(N) shows slightly negative value so that the silver-bound N becomes more stable than N. 3.2.3. pKa Value of Silver Containing N. It is necessary to compute the pKa value of silver containing N for understanding whether imino-proton can be deprotonated or not. We focused on the pKa value of the silver-mediated N from the Gibbs energy difference between protonated state G(HA) and deprotonated state G(A). Our previous study37 introduced a new method for predicting pKa values by linear fitting for the Gibbs energy and the experimentally observed pKa values for reference bases. The intercept of the linear fitting indicates the Gibbs energy of the proton in aqueous solution. In this study, the same procedure as our previous study was used. When we use the CPCM-B3LYP/ aug-cc-pVDZ level with the UAKS cavity model, the pKa value can be computed as follows: pKa ¼ C1 fGðA Þ GðHAÞg + C2 8506
ð3Þ
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Table 2. Relative Energies of the Product and Transition State for the Silver Ion Transfer Reaction and the Changes of Ion Exchange Reaction ΔGexch (in kcal/mol) T
Br
F
G(4) G(3)
8.8
8.0
8.9
9.2
ΔGexchb
5.7
3.0
2.4
1.1
a
a b
CN
We calculated the free energy from that of 3 in each compound. ΔGexch is given by eq 5.
the reaction, which involves the proton of the nucleobase, we simply defined the deprotonation energy, ΔGdep, as follows: ΔGdep ¼ GðA Þ + GðH+ Þ GðHAÞ
Figure 3. Optimized geometries of silver-mediated N (the ligand of Ag is not shown for simplicity). (a) X = CH3 (T), (b) X = Br (Br), and (c) X = F (F). In the case of X = CN (CN), there are two stable geometries. The former (d) is that Ag binds to O4, which is similar to (ac). The latter (e) is that Ag(I) binds to CN of the ligand of C5.
Table 1. Binding Energy (in kcal/mol) of Ag(I) to N in Each Model and Computed pKa of N (Taken from Ref 37), Predicted pKa of the Silver-Mediated N and ΔGdep (in kcal/ mol) in Each Compound binding energy
a
without Ag
Ag bound
ΔGbind(N)
pKaa
ΔGdep
pKa
ΔGdep
T
0.4
9.66
21.1
6.84
14.9
Br F
0.4 0.1
7.96 7.86
17.4 17.2
5.22 5.13
11.4 11.2
CN (C5)
7.1
6.36
13.9
6.16
13.5
CN (O4)
0.3
3.83
8.4
Taken from ref 37.
where C1 = 0.4583 (mol/kcal) and C2 = 138.05 are determined by the experimental and theoretical values.37 Table 1 lists the computed results for pKa. Predicted pKa values are 6.8 for T and 5.15.2 for Br and F. In the case of CN, whose pKa depends on the position of Ag(I), pKa is 3.8 (when Ag binds to O4) or 6.2 (when Ag binds to C5). In all cases, it is notable that the coordination of silver to the O4 site of N decreases the pKa value of the imino-proton by 2.53.0 pKa units. Judging from these results, we discuss the possibility of deprotonation in silver-mediated N. In the case of T, the deprotonation of the imino-proton cannot occur except for basic domain because of the high pKa value. On the other hand, in Br and F, the deprotonation does not occur in acidic solution, but in neutral solution, according to computed pKa value. As for CN, predicted pKa is low enough to cause the deprotonation of N3H+ in any condition. However, the pKa value did not decrease due to the silver coordination when Ag binds to the C5 site of CN. This fact tells us that Ag(I) bound to the C5 ligand of CN does not affect the deprotonation of the imino-proton. 3.2.4. Gibbs Energies of Deprotonation Reaction. Though many papers have reported the importance of water molecules in
ð4Þ
According to our previous study,37 we estimated the Gibbs energy of the imino-proton of the 5-substituted uracil in aqueous solution as 271.96 kcal/mol, which is referred to as G(H+) for further discussions. Table 1 lists ΔGdep in each ligand. Without the silver ion, ΔGdep shows a large value that ranges from 13.9 (CN) to 21.1 kcal/mol (T) so that it is impossible for the deprotonation reaction to occur without the high activation energy. Judging from Table 1, on the other hand, the silver coordination decreases ΔGdep by 46 kcal/mol. Nevertheless, the deprotonation of Ag-bound T still needs high activation energy such as 14.9 kcal/mol. In the case of Ag-bound CN, it needs 8.4 and 13.5 kcal/mol when Ag(I) binds to O4 and CN of C5 ligand, respectively. These results are equivalent to the change of the pKa value shown in section 3.2.3. Through the stage of the deprotonation, the dependency on C5 ligand makes a difference at most 6.5 kcal/mol, which affects the whole forming reaction of the [N-Ag2-N] bridge. 3.3. Silver Ion Transfer Reaction. Table 2 shows the relative Gibbs energy of 4 in each ligand. The product is 8.09.2 kcal/ mol more stable than the reactant (3). This reaction is irreversible and exothermic. Table S3 in Supporting Information shows the energy barrier of the silver ion transfer and the stabilization energy in the case of ligand-free Ag(I) as a reference. Compound 4 is considered to be the product of Ag(I)-H+ ion exchange reaction from 1. The Gibbs energy of Ag(I)-H+ exchange reaction ΔGexch is given as follows: ΔGexch ¼ Gð4Þ + GðH+ Þ + GðH2 OÞ Gð1Þ Gð½AgðH2 OÞ2 Þ ð5Þ Table 2 shows the C5 ligand dependence on ΔGexch. ΔGexch of CN (1.1 kcal/mol) is more stable than that of other ligands, which ranges from +2.4 to +5.7 kcal/mol. The difference is derived from the stage of the deprotonation, which depends on the energy of proton in solution. Therefore, the pH of solution may decide whether Ag(I)-H+ exchange reaction occurs or not. 3.4. Dimer Formation and Energy Profiles. 3.4.1. Forming the Dimer Structure and Structural Fluctuation. As mentioned in the Introduction, our previous study revealed that the [U-Ag2-U] bridge has four possible conformers.34 A similar situation would be found in the [N-Ag2-N] bridge. Especially three conformers (5, 7, and 70 depicted in Figure 4) are stable enough to coexist at room temperature from the view of the free energy. Note that we replaced the backbone molecule with a methyl group. The stability of 5 may be overestimated in this model, so the larger model, which includes backbone molecules, should be investigated for further studies. 8507
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Table 3. Gibbs Energy of Dimerization Reaction and Relative Energies of the Stable and Transition States (in kcal/mol) ΔGdim
T
Br
F
CN
15.4
11.3
10.8
8.6
2ΔGexch + ΔGdim 6b
4.0 5.3
5.3 6.5
6.0 5.6
10.8 5.4
7b
a
0.4
0.1
0.1
0.6
60
b
6.8
6.6
6.6
7.0
70
b
2.5
2.0
2.4
2.3
ΔGdim is given by eq 5. b We set zero point as the Gibbs free energy of 5 in each compound. a
Table 4. Gibbs Energy Profiles in Each Compound from 1 (Reactant) to 7 (Product) (in kcal/mol) T
Figure 4. Three stable conformers (5, 7, and 70 ) and two transition states (6 and 60 ) of [N-Ag2-N] bridge (C5 ligand is not shown).
Scheme 2. Dimerization Reaction 2[H2O-Ag-N] f [NAg2-N] + 2H2O (from 4 to 5)
Two bonds N3-Ag-O4 and O2-Ag-N3 are formed in the dimer structure 5 as shown in Scheme 2. The free energy of dimer formation ΔGdim is given as follows: ΔGdim ¼ Gð5Þ + 2GðH2 OÞ 2Gð4Þ
ð6Þ
Table 3 presents the formation energy ΔGdim in each C5 ligand. It is found that the dimer (5) is 2024 kcal/mol more stable than two monomers (4) and that ΔGdim of T is larger than that of CN by 4 kcal/mol. ΔGdim is large enough to prove that the dimer forming reaction is one-sided and irreversible.
a
Br
F
CN
1
0.0
0.0
0.0
0.0
2a
0.4
0.4
0.1
0.3
3 4
14.5 5.7
10.8 2.8
11.3 2.4
8.1 1.1
5b
4.0
5.7
6.0
10.8
6
1.3
0.8
0.4
5.4
7
4.4
5.8
5.9
11.4
Estimated as ΔGbind. b Computed as 2ΔGexch + ΔGdim.
There are two reaction paths from 5. One path forms O4-AgO4 and N3-Ag-N3 coordinations to make 7. The other path forms N3-Ag-N3 and O2-Ag-O2 coordinations to make 70 . Table 3 shows the relative energy of two structures (7 and 70 ) and two energy barriers between 5 and 7 (or 70 ). As shown in our previous work for [U-Ag2-U]34 (U: X = H), the energy difference of 5 and 7 is small, for example, 0.40.1 kcal/mol. Judging from the energy, two conformers 5 and 7 coexist. This fact suggests that the molecular properties of 5 and 7 should mix at room temperature or higher based on the assumption of Boltzmann distribution in this model. Moreover, the relative energy of the TS (6) from 5 to 7 is 5.36.5 kcal/mol while that of TS (60 ) from 5 to 70 is 6.67.0 kcal/mol. Judging from ΔGdim, these reactions should occur easily at the room temperature. On the other hand, the energy of 70 is 2.53.0 kcal/mol higher than that of 7 so that 70 hardly affects the molecular property of the [N-Ag2-N] bridge. 3.4.2. Total Reaction Diagram. Finally, we summarize the energy profile of whole reaction in Table 4 and discuss the dependency on C5 ligand. The value for compound 7 in Table 4 represents the Gibbs energy of the overall reaction 1, which ranges from 4.4 kcal/ mol (T) to 11.4 kcal/mol (CN). In order to proceed to the Ag(I)- H+ exchange, very high energy such as 14.9 kcal/mol is needed for T. In contrast, only 4.4 kcal/mol is needed for CN at least. Therefore, the difference of C5 ligands in CN and T makes a difference in the process of deprotonation, which affect the AgN binding. The free energy difference between 1 and 5 is given by 2ΔGexch +ΔGdim because two conformers 4 are needed for the dimerization. From the row of 5 in Table 4, CN is the most stable conformer among all substituted [N-Ag2-N] bridges. [N-Ag2-N] bridges of the other N (T, Br, and F) are also stable because ΔGdim is large for all ligands. This result indicates that the dimerization occurs spontaneously when two Ag(I)-N (4) 8508
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4. CONCLUSION In this study, we revealed how N captures a silver ion by dividing the whole scheme into three steps. We also showed the reason why the pKa value of N plays a key role of forming [N-Ag2N] bridges. Judging from the contour plots of ESP on N, we specified the binding site for Ag(I). We found that CN has two sites with strong negative potential for capturing Ag(I). Moreover, the energy diagram of the silver ion transfer reaction from N (C5 ligand) to O4 shows that two binding sites are almost equivalent to proceed to the deprotonated structure 3. Therefore, CN has two chances to capture the silver ion, which is different from the other N. This result also corresponds to the fact that [N-Ag2-N] can be easily formed in the case of CN. As for the deprotonation reaction, the coordination of the silver to O4 site of N decreases pKa value of the imino-proton by 2.53.0 pKa units. However, the silver-mediated T keeps high pKa value that the deprotonation cannot occur. On the other hand, in Br and F, it is possible for the deprotonation reaction to occur even in the neutral solution (e.g., pH = 7.0). Moreover, dependency on the C5 ligand makes a difference at most 6.5 kcal/mol, which affects the whole reaction to form the [N-Ag2-N] bridge. In either silver ion transferring reaction or dimerization reaction, we did not find an apparent dependency on the C5 ligands. According to the energy barrier and the Gibbs energies of dimerization, both reactions occur thermally at room temperature in any ligands. Finally, we listed two conditions to form [N-Ag2-N] bridges. (1) The ligand must have a strong electron withdrawing property, which decreases the pKa value of N. (2) It is better that the ligand has a strong negative charge for Ag(I) to bind. ’ ASSOCIATED CONTENT
bS
Supporting Information. All optimized geometries and other topics (such as the geometry of three silver ions containing the N-N pair, the possibility of the Ag-O2 bond and the single silver ion transfer reaction). This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT This research is supported by the Core Research for Evolutional Science and Technology (CREST) Program “High Performance Computing for Multi-Scale and Multi-Physics Phenomena” from the Japan Science and Technology (JST). This research is also partly supported by a Grant-in-Aid for Young Scientists (A) (No. 22685003) from the Japan Society for the Promotion of Science (JSPS). H.M. thanks Chiba Prefecture, Japan, for financial support. We thank Prof. M. Okumura and Dr. Y. Kitagawa in Osaka University and Dr. K. Kamiya in Tsukuba University for fruitful discussions.
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