J. Phys. Chem. B 2002, 106, 6431-6436
6431
Solution Structures of r-Cyclodextrin Complexes with Propanol and Propanesulfonate Estimated from NMR and Molecular Surface Area Noriaki Funasaki,* Seiji Ishikawa, and Saburo Neya Kyoto Pharmaceutical UniVersity, Misasagi, Yamashina-ku, Kyoto 607-8414, Japan ReceiVed: December 31, 2001; In Final Form: April 1, 2002
The complex formation of R-cyclodextrin (R-CD) with propanesulfonate (PS) and propanol (PrOH) was investigated by proton NMR spectroscopy and molecular surface area calculations. The 1:1 binding constant, K1, was determined from dependence of the chemical shift of the propyl β-methylene protons on the R-CD concentration to be 23.0 and 21.3 M-1 for PS and PrOH. Quantitative analysis of the ROESY spectra showed that the propyl groups of PS and PrOH penetrate from the secondary alcohol side of R-CD. This penetration side of PrOH is opposite to that in the crystal. The observed vicinal spin-spin coupling constant of the HC(5)-C(6)HR system of PS-R-CD indicated that the H5 and H6R atoms are in the gauche arrangement, though they are in the trans arrangement in the crystal. The observed vicinal coupling constant of the HCRCβH system of PS-R-CD indicated that the sulfur and Cγ atoms are restricted around the trans arrangement because of the hindered rotation of the CR-Cβ bond, although the CR-Cβ bond of PrOH in the complex rotates freely. These ROESY and coupling constant data allowed us to propose the solution structures of the complexes. Furthermore, three molecular surface area decreases with docking were calculated as a function of the penetration depth of the propyl group. For the solution structures of these complexes, the matching hydrophobic and hydrophilic surface areas, ∆Aoo and ∆Aww, of the R-CD and guest molecules exhibited maxima, and the mismatching hydrophobic and hydrophilic surface area, ∆Aow, had a minimum. These are very stable structures from the viewpoint of hydrophobic and hydrophilic interactions. The concept of molecular recognition by hydrophobic and hydrophilic interactions in water will be applicable to other complexes.
Introduction The primary hydroxyl groups of cyclohexaamylose (R-CD) are located at the narrow rim and the secondary hydroxyl groups are found at the wide rim. The toroidal structure of R-CD has a hydrophilic surface, making it water-soluble, whereas the cavity is composed of the glucoside oxygens and methine hydrogens, giving it a hydrophobic character. As a consequence, CD is capable of forming inclusion complexes with compounds the sizes of which are compatible with the dimensions of their cavity. Geometrical rather than chemical factors are decisive in determining the types of guest molecules that can penetrate into the CD cavity.1-3 The included molecules are normally oriented in the host in such a position as to achieve the maximum contact between the hydrophobic part of the guest and the apolar CD cavity.4,5 The hydrophilic part of the guest molecule remains, as far as possible, at the outer face of the complex.3 The crystal structures of many CD complexes are available in the Cambridge Crystallographic Data Center.6-8 The solution structures of such complexes have been estimated by NMR and circular dichroism spectroscopy.2,9,10 These crystal and solution structures are very similar to each other for most complexes, although they are different for a limited number of complexes.9-11 For some rare systems, even the stoichiometry of complexation is different in the solution and solid states.9 Rough solution structures have been inferred from the complexation-induced chemical shifts and intermolecular NOE data with molecular modeling techniques.9,10 Although fine solution structures of * Corresponding author. Fax: +81-75-595-4762. E-mail: funasaki@ mb.kyoto-phu.ac.jp.
the complexes of benzene derivatives with CDs have been determined from quantitative analysis of chemical shift data,5,9,10 such detailed analyses are not easy for aliphatic guests. While we were investigating the crystal structures of complexes of aliphatic guests and CDs, we noticed that the crystal structure of the complex of R-CD and sodium propanesulfonate (PS)12 is different from that of propanol (PrOH) and R-CD.13 The PS molecule is incorporated from the secondary alcohol side (wide rim) of the CD, as is the case for most complexes, but PrOH is incorporated from the primary side (narrow rim). This difference prompted us to investigate the solution structures of these complexes. Furthermore, we have proposed a molecular surface area approach to predict the stereo structures and binding constants of CD complexes including the PrOH-R-CD complex.4,5 This approach must be pursued for complexes of more CD and aliphatic guests. In the present study, we determined the binding constants of R-CD with PS and PrOH from NMR chemical shift data. The solution structures of the 1:1 complexes of R-CD with PS and PrOH were estimated on the basis of vicinal coupling constants and ROESY spectra. Furthermore, the contact between guest and host in the complexes was investigated from the viewpoint of hydrophobic and hydrophilic molecular surface areas. Experimental Section Materials. Commercial samples of R-CD, PrOH, methanol, tetramethylammonium chloride (TMA, Nacalai Tesque Co., Kyoto), and 99.9 at. % D deuterium oxide (Aldrich) were used as received, and PS (Tokyo Kasei Organic Chemicals Co.) was recrystallized from a 50%-50% mixture of water and ethanol.
10.1021/jp0147170 CCC: $22.00 © 2002 American Chemical Society Published on Web 06/04/2002
6432 J. Phys. Chem. B, Vol. 106, No. 25, 2002 NMR Measurements. All 500 MHz proton NMR spectra of deuterium oxide solutions were obtained with a JEOL Lambda 500 spectrometer at 298.2 K. The proton chemical shifts of PS and R-CD, with reference to 1 mmol dm-3 (mM) internal methanol (MeOH) at 3.343 ppm,14 were determined as a function of R-CD concentration (up to 120 mM) in the presence of 9.99 mM PS. The proton chemical shift of PrOH, with reference to 1 mM internal TMA at 3.176 ppm, was also determined as a function of R-CD concentration (up to 70 mM) in the presence of 5.695 mM PrOH. Two-dimensional phase-sensitive nuclear Overhauser effect spectroscopy (ROESY) for a solution containing 40 mM PS and 40 mM R-CD was performed at 500 MHz with the JEOL standard pulse sequences; data consisted of 8 transients collected over 2048 complex points. A mixing time of 250 ms, a repetition delay of 1.2 s, and a 90° pulse width of 11.0 µs were used. The ROESY data set was processed by applying a Gaussian function in both dimensions and zero-filling to 2048 × 2048 real data points prior to Fourier transformation. Small cross-peaks, close to noise, were neglected. The ROESY spectrum for a solution containing 60 mM PrOH and 60 mM R-CD was also recorded under the same conditions as described above. The ROE intensity was determined with our own software.4 Calculations of Molecular Surface Areas. The threedimensional structure of the PS-R-CD complex was expressed in Cartesian coordinate systems.12 The R-CD molecule is almost symmetric around the x-axis, where the O4 plane is at x ) 0. The side of primary hydroxyl groups has a negative x value, whereas that of secondary hydroxyl groups has a positive x value. The atomic coordinates of the free PS molecule and the PS-R-CD complex were taken from the crystal structure of the complex of PS-R-CD.12 In the crystal of the complex of PS-R-CD, the γ-carbon atom (Cγ) of PS is at xCγ ) 0.0128 nm. The atomic coordinates of the free R-CD molecule were taken from the crystal structure of R-CD hexahydrate.15 In the crystal of the complex of PrOH-R-CD, the γ-carbon atom of PrOH is at xCγ ) 0.0534 nm. The displacement of the γ-carbon atom along the x-axis from the crystal structure is expressed by ∆x. The Bondi atomic radii (r) were used;16 rH ) 0.120 nm, rO ) 0.152 nm, rC ) 0.170 nm, and rS ) 0.180 nm. The water radius of 0.14 nm was employed for calculations of wateraccessible molecular surface areas. Each area element was generated on a water-accessible surface of a molecule and consisted of a rectangle with a width of 0.010 nm. A dot was drawn on the center of the element for visualization of the molecule.4 All groups constituting a molecule were classified as either hydrophilic or hydrophobic. The hydrophilic groups included the hydroxyl group, the sulfonate group, and the ether oxygen atom, whereas the hydrophobic groups included the methyl, methylene, and methine groups of PS, PrOH, and R-CD. Calculations and molecular graphics were carried out simultaneously using our own software with a personal computer running Microsoft Windows 2000. The relative positions of the host and guest can be easily varied on the display.4 Results Chemical Shifts and Binding Constants. As shown in Figure 1b, the proton signals of HR, Hβ, and Hγ of PrOH appeared as a triplet, a multiplet, and a triplet with chemical shifts, δ, of 3.5, 1.5, and 0.9 ppm, respectively, with reference to internal TMA. The assignments of the protons of R-CD have been reported.5 Because the HR signal partially overlapped with
Funasaki et al.
Figure 1. NMR spectra of (a) a 9.99 mM PS and 4.9035 mM R-CD solution and (b) a 5.695 mM PrOH and 2.1446 mM R-CD solution, with partial expansion of the region of the HR and Hβ protons.
Figure 2. Chemical shift variations of the Hβ protons of PS (triangles) and PrOH (circles) with increasing R-CD concentration in the presence of 9.99 mM PS or 5.695 mM PrOH. The solid lines were calculated using values of K1 ) 23.0 M-1 and ∆δPD(Hβ) ) 0.201 ppm for the PS-R-CD system and values of K1 ) 21.3 M-1 and ∆δPD(Hβ) ) 0.199 ppm for the PrOH-R-CD system.
the H4 signal of R-CD, the chemical shift of HR could not be determined accurately. All PrOH proton signals exhibited downfield shifts with increasing R-CD concentration. We determined the chemical shift for the PrOH-R-CD system as a function of R-CD concentration, CD, while the PrOH concentration was kept constant at 5.695 mM. Figure 2 shows the chemical shift variation, ∆δ, of the Hβ proton of PrOH. By curve-fitting analysis of these chemical shift data, we determined the equilibrium binding constant (K1) and the complexation-induced chemical shift (∆δ ) δPD - δP) of the Hβ proton for the 1:1 complexation of PrOH (P) and R-CD (D); K1 ) 21.3 ( 0.15 M-1 and ∆δPD (Hβ) ) 0.199 ppm. Here, δP and δPD are chemical shifts of the free and complexed PrOH Hβ protons, respectively. The chemical shifts of the protons of PS and R-CD (Figure 1a), with reference to internal MeOH, were determined as a function of R-CD concentration, where the PS concentration was kept at 9.99 mM. All PS proton signals exhibited lowfield shifts with increasing R-CD concentration. Because the chemical shift variation of the Hβ proton exhibited the largest change among all the R-CD and PS protons, it was used to determine the best fit values of K1 and ∆δPD; K1 ) 23.0 ( 1.25 M-1 and ∆δPD (Hβ) ) 0.201 ppm. Vicinal Spin-Spin Coupling Constants. On the basis of spectral simulations, we determined all vicinal spin-spin coupling constants, 3J, of PS, PrOH, and R-CD, together with the chemical shifts. As shown in Figure 1a, the R-methylene group of PS has two protons that differ in the vicinal coupling constant, 3JRβ. This nonequivalence in 3JRβ is caused by the hindered rotation around the CR-Cβ bond. The vicinal coupling constants, 3JRβ, of PS changed with increasing concentrations
Solution Structures of R-CD Complexes with PrOH and PS
J. Phys. Chem. B, Vol. 106, No. 25, 2002 6433 TABLE 2: Observed Vicinal Spin-Spin Coupling Constants (Hz) in Aqueous Solutions and Average Dihedral Angles (degree) in Crystals for r-CD, PS-r-CD Complex, and PrOH-r-CD Complex R-CD
Figure 3. X-ray structures of (a) PS-R-CD complex (top and side views) and (b) PrOH-R-CD complex (side view). The top view is cross-sectioned by the O6 plane (dashed line in the side view).
TABLE 1: Observed Vicinal and Geminal Spin-Spin Coupling Constants for PS and PrOH in the Free and Bound States PS J (Hz) 3J
Rβ
3J
βγ
2J
RR
PrOH
P
PD
P
PD
5.6, 10.0 7.5 -11.8
4.6,12.1 7.4 -9.7
6.7 7.4 -12.1
6.9 7.5 -10.0
of R-CD (data not shown), because they were dependent on the degree of complexation: 3
J ) (3JP[P] + 3JPD[PD])/CP
(1)
Here, 3JP and 3JPD denote the vicinal coupling constants in the free and bound states and are shown in Table 1. We can determine the best fit 3JPD value from eq 1 with the binding constant by the nonlinear least-squares method. These 3JRβ values are included in Table 1. We can assume three rotamers that differ in dihedral angle around the CR-Cβ bond; trans (T), gauche+ (G+), and gauche- (G-). The Cγ and sulfur atoms are in the trans arrangement for the T conformer and in the gauche arrangements for the G+ and G- conformers. The two 3JRβ values for the complex indicated that the Cγ and sulfur atoms are very close in the trans arrangement. This arrangement was close to that for the crystal structure (Figure 3a), in which the dihedral angle around the CR-Cβ bond is 186.4°.12 The two 3J Rβ values for the free PS ion indicated that the Cγ and sulfur atoms were slightly distant from the trans arrangement. The 3Jβγ value, obtained from the triplet signal of the methyl group, is also shown in Table 1. This value was almost independent of the CD concentration and PS or PrOH and suggested that the Cβ-Cγ bond rotates freely. The 3JRβ values for PrOH in the free and bound states, determined from the triplet signal of the R-methylene signal (Figure 1b), suggested that the CR-Cβ bond of PrOH rotates freely in these states. The signals of two protons of R-CD, H6R and H6S, were distinguishable from each other. The vicinal coupling constants of R-CD in the free state, the 84% bound state for PS, and the 79% bound state for PrOH are shown in Table 2. These constants remained almost unchanged with increasing R-CD concentration. This finding showed that the conformation of R-CD remains almost unchanged upon complex formation with PS and PrOH. The X-ray structures of the R-CD-PS complex12 and the R-CD-PrOH complex13 are shown in Figure 3. From these structures we calculated the dihedral angles around the six HCCH bonds of R-CD. The dihedral angle averaged over six glucose units of an R-CD molecule is shown in Table 2. The dihedral angles around the H5C-CH6S and H5C-CH6R bonds for the free R-CD molecule and the R-CD-PrOH complex are
PS-R-CD
PrOH-R-CD
pair
3J
φa
3Jb
φc
3J d
φe
H1H2 H2H3 H3H4 H4H5 H5H6S H5H6R
3.4 10.0 8.8 9.7 2.0 4.8
58 -175 171 -173 -21 99
3.4 10.0 8.7 9.9 2.0 4.7
49 -177 168 -169 63 -174
3.4 10.0 8.8 10.0 2.0 4.8
57 -172 171 -168 -43 76
a Based on the crystal structure of R-CD-6H O.15 b At 84% 2 bindingof R-CD. c Based on the crystal structure of PS-R-CD-9H2O complex.12 d At 79% binding of R-CD. e Based on the crystal structure of PrOH-R-CD-4.8H2O.13
dependent on the glucose unit, although those around the other bonds remained almost constant. These dependences of dihedral angles on the glucose unit led to asymmetric structures of R-CD and the R-CD-PrOH complex (structure b in Figure 3). Because all dihedral angles of R-CD for the R-CD-PS complex are almost independent of the glucose unit, R-CD in this complex has good symmetry (structure a in Figure 3). The Karplus-type relationship between the vicinal coupling constant and the dihedral angle holds true for saccharides.9,10,17,18 1H NMR, IR, and ORD spectra established that the solution structure of R-CD is close to the X-ray structure of R-CD6H2O.1,3 The dihedral angles shown in Table 2 are for the crystal structures. In the crystal, the dihedral angle around the HC5C6HR bond for the R-CD-PS complex showed that the H5 and H6R protons are in the trans position. However, the observed coupling constant of 3JH5H6R indicated that these protons in water are between the trans and gauche arrangements. In the crystal of the R-CD-PS complex, R-CD molecules form a head-to-tail channel by hydrogen bonds and the sulfonate group is hydrogen-bonded to three of the primary hydroxyl groups (O6H) of the neighboring R-CD molecule.12 These hydrogen bonds are broken by water, so that R-CD-PS ions are formed. In water, a sodium ion is completely dissociated from an R-CD-PS ion and forms an ionic atmosphere around the PS-R-CD ion. ROESY Spectra. To infer the geometry of the inclusion complex from the NOE intensity, we recorded the 500 MHz ROESY spectrum of a 40 mM PS and 40 mM R-CD solution. As shown in Figure 4, several intermolecular ROE cross-peaks were observed. Two signals of HR and H4 for a 60 mM PrOH and 60 mM R-CD solution could not be resolved because of overlap, so that the ROE intensities for these protons could not be evaluated separately. The volume (ROE intensity) of the cross-peak was determined by integration and was normalized to be 100 for the cross-peak between H1 and H5. The ROE intensity of the cross-peak is proportional to the number of equivalent protons.19 In Table 3 ROE/nDnP is shown, where nD and nP denote the numbers of equivalent protons of CD and PrOH or PS. For instance, the ROE/nDnP value for the crosspeak between H1 and H5 is 2.78. When internal rotations are slower than overall tumbling, we can expect eq 2:19,20 n D nP
ROE Intensity ) k
dD P -6 ∑ ∑ i)1 j)1 i j
(2)
Here, dDiPj denotes the distance between a proton (Di) of R-CD
6434 J. Phys. Chem. B, Vol. 106, No. 25, 2002
Funasaki et al.
Figure 4. Contour plots of partial 500 MHz ROESY spectra of (a) a 40 mM PS and 40 mM R-CD solution and (b) a 60 mM PrOH and 60 mM R-CD solution.
TABLE 3: Relative Intensities,a ROE/nPnD, of Intermolecular ROE Peaks for the PS-r-CD and PrOH-r-CD Complexes PS-R-CD
PrOH-R-CD
R-CD
HR
Hβ
Hγ
HR
Hβ
Hγ
H3 H5 H6R H6S
3.740 1.445 0.143 0.121
3.717 1.923 0.283 0.195
1.710 2.542 0.560 0.655
xb x x x
2.825 0.993 0.161 0.208
1.440 1.811 0.313 0.295
a Relative intensity of each cross-peak to the H1-H5 cross-peak, at 40% binding of PS and at 41% binding of PrOH. b Because the signals of HR and H4 overlapped with each other, the observed cross-peaks could not be resolved into individual signals.
and a proton (Pj) of the propyl group. For simplicity, the effective distance, deff, is defined as: nD nP
-6
(deff)
) (1/nDnP)
∑ ∑dD P -6 i)1 j)1 i j
(3)
For instance, the effective distance between H1 and H5 is 0.46 nm. From eq 2 we can expect that ROE/nDnP will increase, as two protons become closer. Solution Structures of PS-r-CD and PrOH-r-CD Complexes. Figure 3a shows the crystal structure of the 1:1 PSR-CD complex, where the PS molecule is incorporated from the wider rim (the secondary alcohol side) of R-CD. On the basis of this structure, we calculated the effective distance between the protons of R-CD and PS from eq 3. For instance, the effective interproton distance between HR and H3 was averaged over 12 distances between two HR protons and six H3 protons. The NOE intensities for the PS-R-CD system are roughly correlated with these effective interproton distances as shown in Figure 5a. This agreement suggested that the solution structure of the 1:1 PS-R-CD complex is similar to the X-ray structure. However, the average dihedral angle of the H5C-CH6R bond in the crystal is -174°, inconsistent with the observed vicinal coupling constant of 3JH5H6R ) 4.7 Hz (Table 2). This 3JH5H6R value is independent of complex formation. Therefore, we used dihedral angles of six H5C-CH6R bonds in the crystal structure of R-CD-6H2O to construct a solution structure (Figure 6a). The ROE intensities are plotted against the effective distances for this solution structure in Figure 5a. The ROE intensities
Figure 5. ROE/nPnD intensities plotted against the effective distances of the propyl protons to H3, H5, and H6 of R-CD for (a) the solution (open circles) and crystal (closed squares) structures of the PS-R-CD complex and (b) the solution (open circles) and crystal (closed squares) structures of the PrOH-R-CD complex.
Figure 6. Solution structures of (a) PS-R-CD complex (top and side views) and (b) PrOH-R-CD complex (side view). The top view is sectioned by the O6 plane (dashed line in the side view) that crosses the centers of two O6 atoms and is perpendicular to the axis of symmetry.
were correlated with the solution structure slightly better than with the crystal structure. The propyl group of a PrOH-R-CD complex in the crystal state is oriented in the direction opposite to that of a PS-R-CD
Solution Structures of R-CD Complexes with PrOH and PS
Figure 7. Values of ∆Aoo (circles), ∆Aww (triangles), and ∆Aow (squares) as a function of the penetration depth, ∆x, of the propyl group of PS for (a) the solution structure and (b) the crystal structure, where ∆x denotes displacement of the γ-carbon atom along the x-axis from the crystal structure.
complex (Figure 3). The effective interproton distances for the X-ray structure of the PrOH-R-CD complex were calculated in a manner similar to that described for the PS-R-CD complex. The ROE intensities for Hβ and Hγ are plotted against these effective distances in Figure 5b. The correlation between them was rather poor. This disagreement suggested that the penetration direction of the propyl group in the aqueous solution is the opposite of that in the crystal. To construct a solution structure of the PrOH-R-CD complex, we substituted the sulfonate group for the hydroxy group in the solution structure of the PrOHR-CD complex. This solution structure is shown in Figure 6b. On the basis of this solution structure, we calculated effective interproton distances. As shown in Figure 5b, the ROE intensities showed much better correlations with the solution structure than with the crystal structure. Molecular Surface Areas. We have recently developed a method for calculating various molecular surface areas. In these areas, ∆Aoo, ∆Aww, and ∆Aow play essential roles in determining the stable structure of the complex and the binding constant.4 ∆Aoo denotes the hydrophobic (oleophilic)hydrophobic molecular contact area between guest and host and ∆Aww denotes the hydrophilic-hydrophilic molecular contact area between guest and host. These areas stabilize the complex. ∆Aow denotes the hydrophobic-hydrophilic molecular contact area between guest and host. This area destabilizes the complex. The molecular surface area is dependent on the molecular conformation. We calculated the values of ∆Aoo, ∆Aww, and ∆Aow for the solution and crystal structures of the R-CD complexes with PS and PrOH (Figures 3 and 6). Figure 7 shows these areas as a function of penetration depth, ∆x, of the propyl group of PS in the R-CD cavity. Around ∆x ) 0, ∆Aoo and ∆Aww have maxima and ∆Aow has a minimum for the two structures: these are very stable structures from the viewpoint of hydrophobic and hydrophilic interactions. Figure 8 shows similar plots for the solution and crystal structures of the R-CD-PrOH complex. Around ∆x ) 0, ∆Aoo and ∆Aww have maxima and ∆Aow has a minimum for the solution structure (Figure 8a). This is a very stable structure. On the other hand, ∆Aoo has a maximum around ∆x ) 0, but ∆Aow and ∆Aww change monotonically regardless of the crystal structure. The crystal structure of the R-CD-PrOH complex is stable from the viewpoint of ∆Aoo, but is unstable from the viewpoint of ∆Aow and ∆Aww.
J. Phys. Chem. B, Vol. 106, No. 25, 2002 6435
Figure 8. Values of ∆Aoo (circles), ∆Aww (triangles), and ∆Aow (squares) as a function of the penetration depth, ∆x, of the propyl group of PrOH for (a) the solution structure and (b) the crystal structure. For the crystal structure, ∆x denotes displacement of the γ-carbon atom along the x-axis from this crystal structure. For the solution structure, ∆x is identical to that in Figure 7.
According to our molecular surface area approach, the 1:1 binding constant K1 was well correlated with the maximum of ∆Aoo as follows:
log K1 ) 1.803∆Aoo - 2.023
(4)
This equation was obtained from data for 11 CD inclusion systems including R-CD, β-CD, γ-CD, monohydroxy, dihydroxy, and trihydroxy alcohols, and aromatic guests.4 Using this equation, we calculated the binding constants of 3.9 and 6.7 M-1 from the maximum ∆Aoo values for the PS-R-CD and PrOH-R-CD complexes. These theoretical binding constants were comparable to the observed values. Discussion Structure of r-CD Complexes. The sulfonate group in the crystal structure of the PS-R-CD complex is hydrogen-bonded to three of the primary hydroxyl groups of the neighboring R-CD molecule.12 In water, however, the sulfonate group is bound to water molecules. The solution structure of the PS-R-CD complex (Figure 6a) is stabilized by hydrophobic and hydrophilic interactions (Figure 7a). The CR-Cβ bond of PS in the complex is restricted in the trans arrangement. The PS molecule will rotate freely in the R-CD cavity and the R-CD molecule will always change its shape because of various molecular motions: the structure shown in Figure 6a should be regarded as one or the average of the most stable structures. The structure of the PrOH-R-CD complex in water (Figure 6b) is much different from that in the crystal (Figure 3b). This solution structure is stabilized by hydrophobic and hydrophilic interactions (Figure 8a). Hydrophobic interactions also play an important role in stabilizing the crystal structure (Figure 8b), while hydrophilic interactions do not. Molecular Surface Area and Binding Constants. Equation 4 takes into consideration the ∆Aoo term alone. However, two other terms, ∆Aww and ∆Aow, will contribute to the stability of the structures of complexes, and thus may also contribute to the binding constant. Then, the binding constant K1 may be better correlated with the three area terms as follows:
log K1 ) a∆Aoo + b∆Aww - c∆Aow + d
(5)
To determine the four coefficients in eq 5, we need detailed structures of more complexes including native and modified cyclodextrins and aliphatic and aromatic guests. The first term will play the predominant role in eq 5, as reported previously.4
6436 J. Phys. Chem. B, Vol. 106, No. 25, 2002 Implications of the Present Approach. The solution structures of cyclodextrin complexes with aromatic guest molecules can be determined more accurately than those with aliphatic guests.1-3,5 The chemical shift provides some information on the structures of the complex cyclodextrin and aromatic guest, although it is less useful for aliphatic guests. The results of the present study demonstrated that the ROE intensity and molecular surface area provide semiquantitative data on the structures of such aliphatic guest complexes. The present approach will serve to estimate the structures and binding constants of cyclodextrin inclusion complexes with long alkyl chain compounds such as surfactants and fatty acids.21,22 Acknowledgment. Thanks are due to Mr. Shigehisa Yatsuda, Mr. Hiroshi Yamaguchi, and Mr. Makoto Fukuba for assistance with NMR measurements and analyses. This work was supported by a Grant-in-Aid for the Frontier Research Program from the Ministry of Education, Culture, Sports, Science, and Technology of Japan. References and Notes (1) Bender, M. L.; Komiyama, M. Cyclodextrin Chemistry; SpringerVerlag: Berlin, 1978; Chapters 2 and 3. (2) Szejtli, J. Cyclodextrin Technology; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1988; Chapters 2 and 3. (3) Saenger, W. Angew. Chem., Int. Ed. Engl. 1980, 19, 344. (4) Ishikawa, S.; Hada, S.; Neya, S.; Funasaki, N. J. Phys. Chem. B 1999, 103, 1208.
Funasaki et al. (5) Funasaki, N.; Yamaguchi, H.; Ishikawa, S.; Neya, S. J. Phys. Chem. B 2001, 106, 760. (6) Saenger, W.; Jacob, J.; Gesseler, K.; Steiner, T.; Hoffmann, D.; Sanbe, H.; Koizumi, K.; Smith, S.; Takaha, T. Chem. ReV. 1998, 98, 1787. (7) Harata, K. In Inclusion Compounds; Atwood, J. L., Davis, J. E. D., MacNicol, D. D., Eds.; Academic Press: London, 1991; Vol. 5, Chapter 9. (8) Harata, K. Chem. ReV. 1998, 98, 1803. (9) Inoue, Y. Ann. Rep. NMR Spectrosc. 1993, 27, 60. (10) Schneider, H.-J.; Hacket, F.; Ru¨diger, V.; Ikeda, H. Chem. ReV. 1998, 98, 1755. (11) Alderfer, J. L.; Eliseev, A. V. J. Org. Chem. 1997, 62, 8225 and references therein. (12) Harata, K. Bull. Chem. Soc. Jpn. 1977, 50, 1259. (13) Saenger, W.; McMullan, R. K.; Fayos, J.; Mootz, D. Acta Crystallogr. B 1974, 30, 2019. (14) Matsui, Y.; M.; Tokunaga, S. Bull. Chem. Soc. Jpn. 1996, 69, 2477. (15) Klar, B.; Hingerty, B.; Saenger, W. Acta Crystallogr. B 1980, 36, 1154. (16) Bondi, A. J. Phys. Chem. 1964, 68, 441. (17) Nishida, Y.; Ohrui, H.; Meguro, H. Tetrahedron Lett. 1984, 25, 1575 and references therein. (18) Streefkerk, D. G.; de Bie, M. J. A.; Vliegenthart, J. F. G. Tetrahedron 1973, 29, 833. (19) Neuhaus, D.; Williamson, M. P. The Nuclear OVerhauser Effect in Structural and Conformational Analysis, 2nd ed.; Wiley-VCH: New York, 2000; Chapters 5 and 12. (20) Kessler, H.; Seip, S. In Two-dimensional NMR Spectroscopy, 2nd ed.; Croasmun, W. R., Carlson, R. M. K., Eds.; Wiley-VCH: New York, 1994; Chapter 5. (21) Funasaki, N.; Yodo, H.; Hada, S.; Neya, S. Bull. Chem. Soc. Jpn. 1992, 65, 1323 and references therein. (22) Ishikawa, S.; Neya, S.; Funasaki, N. J. Phys. Chem. B 1998, 102, 2502.
