Solution Structures of r-Cyclodextrin Complexes with Propanol and PropanesulfonateEstimated from NMR and Molecular Surface Area

Noriaki Funasaki,* Seiji Ishikawa, and Saburo NeyaKyoto Pharmaceutical UniVersity, Misasagi, Yamashina-ku, Kyoto 607-8414, Japan

ReceiVed: December 31, 2001; In Final Form: April 1, 2002

The complex formation ofR-cyclodextrin (R-CD) with propanesulfonate (PS) and propanol (PrOH) wasinvestigated 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 propylâ-methylene protons on theR-CDconcentration to be 23.0 and 21.3 M-1 for PS and PrOH. Quantitative analysis of the ROESY spectra showedthat the propyl groups of PS and PrOH penetrate from the secondary alcohol side ofR-CD. This penetrationside of PrOH is opposite to that in the crystal. The observed vicinal spin-spin coupling constant of theHC(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 HCR-CâH system of PS-R-CD indicated that the sulfur and Cγ atoms are restricted around the trans arrangementbecause of the hindered rotation of the CR-Câ bond, although the CR-Câ bond of PrOH in the complexrotates freely. These ROESY and coupling constant data allowed us to propose the solution structures of thecomplexes. Furthermore, three molecular surface area decreases with docking were calculated as a functionof the penetration depth of the propyl group. For the solution structures of these complexes, the matchinghydrophobic and hydrophilic surface areas,∆Aoo and ∆Aww, of the R-CD and guest molecules exhibitedmaxima, and the mismatching hydrophobic and hydrophilic surface area,∆Aow, had a minimum. These arevery stable structures from the viewpoint of hydrophobic and hydrophilic interactions. The concept of molecularrecognition 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 groupsare found at the wide rim. The toroidal structure ofR-CD hasa hydrophilic surface, making it water-soluble, whereas thecavity is composed of the glucoside oxygens and methinehydrogens, giving it a hydrophobic character. As a consequence,CD is capable of forming inclusion complexes with compoundsthe sizes of which are compatible with the dimensions of theircavity. Geometrical rather than chemical factors are decisivein determining the types of guest molecules that can penetrateinto the CD cavity.1-3 The included molecules are normallyoriented in the host in such a position as to achieve themaximum contact between the hydrophobic part of the guestand the apolar CD cavity.4,5 The hydrophilic part of the guestmolecule remains, as far as possible, at the outer face of thecomplex.3

The crystal structures of many CD complexes are availablein the Cambridge Crystallographic Data Center.6-8 The solutionstructures of such complexes have been estimated by NMR andcircular dichroism spectroscopy.2,9,10These crystal and solutionstructures 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 complexationis different in the solution and solid states.9 Rough solutionstructures have been inferred from the complexation-inducedchemical shifts and intermolecular NOE data with molecularmodeling techniques.9,10 Although fine solution structures of

the complexes of benzene derivatives with CDs have beendetermined from quantitative analysis of chemical shift data,5,9,10

such detailed analyses are not easy for aliphatic guests. Whilewe were investigating the crystal structures of complexes ofaliphatic guests and CDs, we noticed that the crystal structureof the complex ofR-CD and sodium propanesulfonate (PS)12

is different from that of propanol (PrOH) andR-CD.13 The PSmolecule is incorporated from the secondary alcohol side (widerim) of the CD, as is the case for most complexes, but PrOH isincorporated from the primary side (narrow rim). This differenceprompted us to investigate the solution structures of thesecomplexes. Furthermore, we have proposed a molecular surfacearea approach to predict the stereo structures and bindingconstants of CD complexes including the PrOH-R-CD com-plex.4,5 This approach must be pursued for complexes of moreCD and aliphatic guests.

In the present study, we determined the binding constants ofR-CD with PS and PrOH from NMR chemical shift data. Thesolution structures of the 1:1 complexes ofR-CD with PS andPrOH were estimated on the basis of vicinal coupling constantsand ROESY spectra. Furthermore, the contact between guestand host in the complexes was investigated from the viewpointof hydrophobic and hydrophilic molecular surface areas.

Experimental Section

Materials. Commercial samples ofR-CD, PrOH, methanol,tetramethylammonium chloride (TMA, Nacalai Tesque Co.,Kyoto), and 99.9 at. % D deuterium oxide (Aldrich) were usedas received, and PS (Tokyo Kasei Organic Chemicals Co.) wasrecrystallized from a 50%-50% mixture of water and ethanol.

* Corresponding author. Fax:+81-75-595-4762. E-mail: funasaki@mb.kyoto-phu.ac.jp.

6431J. Phys. Chem. B2002,106,6431-6436

10.1021/jp0147170 CCC: $22.00 © 2002 American Chemical SocietyPublished on Web 06/04/2002

NMR Measurements. All 500 MHz proton NMR spectraof deuterium oxide solutions were obtained with a JEOLLambda 500 spectrometer at 298.2 K. The proton chemical shiftsof PS andR-CD, with reference to 1 mmol dm-3 (mM) internalmethanol (MeOH) at 3.343 ppm,14 were determined as afunction ofR-CD concentration (up to 120 mM) in the presenceof 9.99 mM PS. The proton chemical shift of PrOH, withreference to 1 mM internal TMA at 3.176 ppm, was alsodetermined as a function ofR-CD concentration (up to 70 mM)in the presence of 5.695 mM PrOH.

Two-dimensional phase-sensitive nuclear Overhauser effectspectroscopy (ROESY) for a solution containing 40 mM PSand 40 mMR-CD was performed at 500 MHz with the JEOLstandard pulse sequences; data consisted of 8 transients collectedover 2048 complex points. A mixing time of 250 ms, a repetitiondelay of 1.2 s, and a 90° pulse width of 11.0µs were used. TheROESY data set was processed by applying a Gaussian functionin both dimensions and zero-filling to 2048× 2048 real datapoints prior to Fourier transformation. Small cross-peaks, closeto noise, were neglected. The ROESY spectrum for a solutioncontaining 60 mM PrOH and 60 mMR-CD was also recordedunder the same conditions as described above. The ROEintensity was determined with our own software.4

Calculations of Molecular Surface Areas. The three-dimensional structure of the PS-R-CD complex was expressedin Cartesian coordinate systems.12 TheR-CD molecule is almostsymmetric around thex-axis, where the O4 plane is atx ) 0.The side of primary hydroxyl groups has a negativex value,whereas that of secondary hydroxyl groups has a positivexvalue. The atomic coordinates of the free PS molecule and thePS-R-CD complex were taken from the crystal structure ofthe complex of PS-R-CD.12 In the crystal of the complex ofPS-R-CD, theγ-carbon atom (Cγ) of PS is atxCγ ) 0.0128nm. The atomic coordinates of the freeR-CD molecule weretaken from the crystal structure ofR-CD hexahydrate.15 In thecrystal of the complex of PrOH-R-CD, theγ-carbon atom ofPrOH is atxCγ ) 0.0534 nm. The displacement of theγ-carbonatom along thex-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, andrS ) 0.180 nm. The waterradius of 0.14 nm was employed for calculations of water-accessible molecular surface areas. Each area element wasgenerated on a water-accessible surface of a molecule andconsisted of a rectangle with a width of 0.010 nm. A dot wasdrawn on the center of the element for visualization of themolecule.4

All groups constituting a molecule were classified as eitherhydrophilic or hydrophobic. The hydrophilic groups includedthe hydroxyl group, the sulfonate group, and the ether oxygenatom, whereas the hydrophobic groups included the methyl,methylene, and methine groups of PS, PrOH, andR-CD.

Calculations and molecular graphics were carried out simul-taneously using our own software with a personal computerrunning Microsoft Windows 2000. The relative positions of thehost and guest can be easily varied on the display.4

Results

Chemical Shifts and Binding Constants.As shown inFigure 1b, the proton signals of HR, Hâ, and Hγ of PrOHappeared as a triplet, a multiplet, and a triplet with chemicalshifts,δ, of 3.5, 1.5, and 0.9 ppm, respectively, with referenceto internal TMA. The assignments of the protons ofR-CD havebeen reported.5 Because the HR signal partially overlapped with

the H4 signal ofR-CD, the chemical shift of HR could not bedetermined accurately. All PrOH proton signals exhibiteddownfield shifts with increasingR-CD concentration. Wedetermined the chemical shift for the PrOH-R-CD system as afunction ofR-CD concentration,CD, while the PrOH concentra-tion was kept constant at 5.695 mM.

Figure 2 shows the chemical shift variation,∆δ, of the Hâproton of PrOH. By curve-fitting analysis of these chemical shiftdata, we determined the equilibrium binding constant (K1) andthe complexation-induced chemical shift (∆δ ) δPD - δP) ofthe Hâ proton for the 1:1 complexation of PrOH (P) andR-CD(D); K1 ) 21.3( 0.15 M-1 and∆δPD (Hâ) ) 0.199 ppm. Here,δP andδPD are chemical shifts of the free and complexed PrOHHâ protons, respectively.

The chemical shifts of the protons of PS andR-CD (Figure1a), with reference to internal MeOH, were determined as afunction of R-CD concentration, where the PS concentrationwas kept at 9.99 mM. All PS proton signals exhibited low-field shifts with increasingR-CD concentration. Because thechemical shift variation of the Hâ proton exhibited the largestchange among all theR-CD and PS protons, it was used todetermine the best fit values ofK1 and ∆δPD; K1 ) 23.0 (1.25 M-1 and∆δPD (Hâ) ) 0.201 ppm.

Vicinal Spin-Spin Coupling Constants.On the basis ofspectral simulations, we determined all vicinal spin-spincoupling constants,3J, of PS, PrOH, andR-CD, together withthe chemical shifts. As shown in Figure 1a, theR-methylenegroup of PS has two protons that differ in the vicinal couplingconstant,3JRâ. This nonequivalence in3JRâ is caused by thehindered rotation around the CR-Câ bond. The vicinal couplingconstants,3JRâ, of PS changed with increasing concentrations

Figure 1. NMR spectra of (a) a 9.99 mM PS and 4.9035 mMR-CDsolution and (b) a 5.695 mM PrOH and 2.1446 mMR-CD solution,with partial expansion of the region of the HR and Hâ protons.

Figure 2. Chemical shift variations of the Hâ protons of PS (triangles)and PrOH (circles) with increasingR-CD concentration in the presenceof 9.99 mM PS or 5.695 mM PrOH. The solid lines were calculatedusing values ofK1 ) 23.0 M-1 and ∆δPD(Hâ) ) 0.201 ppm for thePS-R-CD system and values ofK1 ) 21.3 M-1 and∆δPD(Hâ) ) 0.199ppm for the PrOH-R-CD system.

6432 J. Phys. Chem. B, Vol. 106, No. 25, 2002 Funasaki et al.

of R-CD (data not shown), because they were dependent onthe degree of complexation:

Here,3JP and3JPD denote the vicinal coupling constants in thefree and bound states and are shown in Table 1. We candetermine the best fit3JPD value from eq 1 with the bindingconstant by the nonlinear least-squares method. These3JRâvalues are included in Table 1. We can assume three rotamersthat differ in dihedral angle around the CR-Câ bond; trans (T),gauche+ (G+), and gauche- (G-). The Cγ and sulfur atoms arein the trans arrangement for the T conformer and in the gauchearrangements for the G+ and G- conformers. The two3JRâvalues for the complex indicated that the Cγ and sulfur atomsare very close in the trans arrangement. This arrangement wasclose to that for the crystal structure (Figure 3a), in which thedihedral angle around the CR-Câ bond is 186.4°.12 The two3JRâ values for the free PS ion indicated that the Cγ and sulfuratoms were slightly distant from the trans arrangement.

The3Jâγ value, obtained from the triplet signal of the methylgroup, is also shown in Table 1. This value was almostindependent of the CD concentration and PS or PrOH andsuggested that the Câ-Cγ bond rotates freely. The3JRâ valuesfor PrOH in the free and bound states, determined from thetriplet signal of theR-methylene signal (Figure 1b), suggestedthat the CR-Câ bond of PrOH rotates freely in these states.

The signals of two protons ofR-CD, H6R and H6S, weredistinguishable from each other. The vicinal coupling constantsof R-CD in the free state, the 84% bound state for PS, and the79% bound state for PrOH are shown in Table 2. Theseconstants remained almost unchanged with increasingR-CDconcentration. This finding showed that the conformation ofR-CD remains almost unchanged upon complex formation withPS and PrOH.

The X-ray structures of theR-CD-PS complex12 and theR-CD-PrOH complex13 are shown in Figure 3. From thesestructures we calculated the dihedral angles around the six HC-CH bonds ofR-CD. The dihedral angle averaged over sixglucose units of anR-CD molecule is shown in Table 2. Thedihedral angles around the H5C-CH6Sand H5C-CH6Rbondsfor the freeR-CD molecule and theR-CD-PrOH complex are

dependent on the glucose unit, although those around the otherbonds remained almost constant. These dependences of dihedralangles on the glucose unit led to asymmetric structures ofR-CDand theR-CD-PrOH complex (structure b in Figure 3). Becauseall dihedral angles ofR-CD for the R-CD-PS complex arealmost independent of the glucose unit,R-CD in this complexhas good symmetry (structure a in Figure 3).

The Karplus-type relationship between the vicinal couplingconstant and the dihedral angle holds true for saccharides.9,10,17,18

1H NMR, IR, and ORD spectra established that the solutionstructure ofR-CD is close to the X-ray structure ofR-CD-6H2O.1,3 The dihedral angles shown in Table 2 are for the crystalstructures. In the crystal, the dihedral angle around the HC5-C6HR bond for theR-CD-PS complex showed that the H5and H6R protons are in the trans position. However, theobserved coupling constant of3JH5H6R indicated that theseprotons in water are between the trans and gauche arrangements.In the crystal of theR-CD-PS complex,R-CD molecules forma head-to-tail channel by hydrogen bonds and the sulfonategroup is hydrogen-bonded to three of the primary hydroxylgroups (O6H) of the neighboringR-CD molecule.12 Thesehydrogen bonds are broken by water, so thatR-CD-PS ionsare formed. In water, a sodium ion is completely dissociatedfrom anR-CD-PS ion and forms an ionic atmosphere aroundthe PS-R-CD ion.

ROESY Spectra. To infer the geometry of the inclusioncomplex from the NOE intensity, we recorded the 500 MHzROESY spectrum of a 40 mM PS and 40 mMR-CD solution.As shown in Figure 4, several intermolecular ROE cross-peakswere observed. Two signals of HR and H4 for a 60 mM PrOHand 60 mMR-CD solution could not be resolved because ofoverlap, so that the ROE intensities for these protons could notbe evaluated separately. The volume (ROE intensity) of thecross-peak was determined by integration and was normalizedto be 100 for the cross-peak between H1 and H5. The ROEintensity of the cross-peak is proportional to the number ofequivalent protons.19 In Table 3 ROE/nDnP is shown, wherenD

and nP denote the numbers of equivalent protons of CD andPrOH or PS. For instance, the ROE/nDnP value for the cross-peak between H1 and H5 is 2.78.

When internal rotations are slower than overall tumbling, wecan expect eq 2:19,20

Here,dDiPj denotes the distance between a proton (Di) of R-CD

Figure 3. X-ray structures of (a) PS-R-CD complex (top and sideviews) and (b) PrOH-R-CD complex (side view). The top view iscross-sectioned by the O6 plane (dashed line in the side view).

TABLE 1: Observed Vicinal and Geminal Spin-SpinCoupling Constants for PS and PrOH in the Free andBound States

PS PrOH

J (Hz) P PD P PD3JRâ 5.6, 10.0 4.6,12.1 6.7 6.93Jâγ 7.5 7.4 7.4 7.52JRR -11.8 -9.7 -12.1 -10.0

3J ) (3JP[P] + 3JPD[PD])/CP (1)

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, andPrOH-r-CD Complex

R-CD PS-R-CD PrOH-R-CD

pair 3J φa 3Jb φc 3Jd φe

H1H2 3.4 58 3.4 49 3.4 57H2H3 10.0 -175 10.0 -177 10.0 -172H3H4 8.8 171 8.7 168 8.8 171H4H5 9.7 -173 9.9 -169 10.0 -168H5H6S 2.0 -21 2.0 63 2.0 -43H5H6R 4.8 99 4.7 -174 4.8 76

a Based on the crystal structure ofR-CD-6H2O.15 b At 84%bindingofR-CD. c Based on the crystal structure of PS-R-CD-9H2Ocomplex.12 d At 79% binding ofR-CD. e Based on the crystal structureof PrOH-R-CD-4.8H2O.13

ROE Intensity) k ∑i)1

nD

∑j)1

nP

dDiPj

-6 (2)

Solution Structures ofR-CD Complexes with PrOH and PS J. Phys. Chem. B, Vol. 106, No. 25, 20026433

and a proton (Pj) of the propyl group. For simplicity, theeffective distance,deff, is defined as:

For instance, the effective distance between H1 and H5 is 0.46nm. From eq 2 we can expect that ROE/nDnP will increase, astwo protons become closer.

Solution Structures of PS-r-CD and PrOH-r-CD Com-plexes.Figure 3a shows the crystal structure of the 1:1 PS-R-CD complex, where the PS molecule is incorporated fromthe wider rim (the secondary alcohol side) ofR-CD. On thebasis of this structure, we calculated the effective distancebetween the protons ofR-CD and PS from eq 3. For instance,the effective interproton distance between HR and H3 wasaveraged over 12 distances between two HR protons and sixH3 protons.

The NOE intensities for the PS-R-CD system are roughlycorrelated with these effective interproton distances as shownin Figure 5a. This agreement suggested that the solution structureof the 1:1 PS-R-CD complex is similar to the X-ray structure.However, the average dihedral angle of the H5C-CH6R bondin the crystal is-174°, inconsistent with the observed vicinalcoupling constant of3JH5H6R ) 4.7 Hz (Table 2). This3JH5H6R

value is independent of complex formation. Therefore, we useddihedral angles of six H5C-CH6Rbonds in the crystal structureof R-CD-6H2O to construct a solution structure (Figure 6a).The ROE intensities are plotted against the effective distancesfor this solution structure in Figure 5a. The ROE intensities

were correlated with the solution structure slightly better thanwith the crystal structure.

The propyl group of a PrOH-R-CD complex in the crystalstate is oriented in the direction opposite to that of a PS-R-CD

Figure 4. Contour plots of partial 500 MHz ROESY spectra of (a) a 40 mM PS and 40 mMR-CD solution and (b) a 60 mM PrOH and 60 mMR-CD solution.

TABLE 3: Relative Intensities,a ROE/nPnD, ofIntermolecular ROE Peaks for the PS-r-CD andPrOH-r-CD Complexes

PS-R-CD PrOH-R-CD

R-CD HR Hâ Hγ HR Hâ Hγ

H3 3.740 3.717 1.710 xb 2.825 1.440H5 1.445 1.923 2.542 x 0.993 1.811H6R 0.143 0.283 0.560 x 0.161 0.313H6S 0.121 0.195 0.655 x 0.208 0.295

a Relative intensity of each cross-peak to the H1-H5 cross-peak, at40% binding of PS and at 41% binding of PrOH.b Because the signalsof HR and H4 overlapped with each other, the observed cross-peakscould not be resolved into individual signals.

(deff)-6 ) (1/nDnP) ∑

i)1

nD

∑j)1

nP

dDiPj

-6 (3)

Figure 5. ROE/nPnD intensities plotted against the effective distancesof the propyl protons to H3, H5, and H6 ofR-CD for (a) the solution(open circles) and crystal (closed squares) structures of the PS-R-CDcomplex 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 sideviews) and (b) PrOH-R-CD complex (side view). The top view issectioned by the O6 plane (dashed line in the side view) that crossesthe centers of two O6 atoms and is perpendicular to the axis ofsymmetry.

6434 J. Phys. Chem. B, Vol. 106, No. 25, 2002 Funasaki et al.

complex (Figure 3). The effective interproton distances for theX-ray structure of the PrOH-R-CD complex were calculatedin a manner similar to that described for the PS-R-CD complex.The ROE intensities for Hâ and Hγ are plotted against theseeffective distances in Figure 5b. The correlation between themwas rather poor. This disagreement suggested that the penetra-tion direction of the propyl group in the aqueous solution is theopposite of that in the crystal. To construct a solution structureof the PrOH-R-CD complex, we substituted the sulfonate groupfor the hydroxy group in the solution structure of the PrOH-R-CD complex. This solution structure is shown in Figure 6b.On the basis of this solution structure, we calculated effectiveinterproton distances. As shown in Figure 5b, the ROEintensities showed much better correlations with the solutionstructure than with the crystal structure.

Molecular Surface Areas. We have recently developed amethod for calculating various molecular surface areas. Inthese areas,∆Aoo, ∆Aww, and ∆Aow play essential roles indetermining the stable structure of the complex and the bind-ing constant.4 ∆Aoo denotes the hydrophobic (oleophilic)-hydrophobic molecular contact area between guest and hostand ∆Aww denotes the hydrophilic-hydrophilic molecularcontact area between guest and host. These areas stabilize thecomplex.∆Aow denotes the hydrophobic-hydrophilic molecularcontact area between guest and host. This area destabilizes thecomplex.

The molecular surface area is dependent on the molecularconformation. We calculated the values of∆Aoo, ∆Aww, and∆Aow for the solution and crystal structures of theR-CDcomplexes with PS and PrOH (Figures 3 and 6). Figure 7 showsthese areas as a function of penetration depth,∆x, of the propylgroup of PS in theR-CD cavity. Around∆x ) 0, ∆Aoo and∆Aww have maxima and∆Aow has a minimum for the twostructures: these are very stable structures from the viewpointof hydrophobic and hydrophilic interactions.

Figure 8 shows similar plots for the solution and crystalstructures of theR-CD-PrOH complex. Around∆x ) 0, ∆Aoo

and ∆Aww have maxima and∆Aow has a minimum for thesolution 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 crystalstructure. The crystal structure of theR-CD-PrOH complex isstable from the viewpoint of∆Aoo, but is unstable from theviewpoint of ∆Aow and∆Aww.

According to our molecular surface area approach, the 1:1binding constantK1 was well correlated with the maximum of∆Aoo as follows:

This equation was obtained from data for 11 CD inclusionsystems includingR-CD, â-CD, γ-CD, monohydroxy, dihy-droxy, and trihydroxy alcohols, and aromatic guests.4 Using thisequation, we calculated the binding constants of 3.9 and 6.7M-1 from the maximum∆Aoo values for the PS-R-CD andPrOH-R-CD complexes. These theoretical binding constantswere comparable to the observed values.

Discussion

Structure of r-CD Complexes.The sulfonate group in thecrystal structure of the PS-R-CD complex is hydrogen-bondedto three of the primary hydroxyl groups of the neighboringR-CDmolecule.12 In water, however, the sulfonate group is bound towater molecules. The solution structure of the PS-R-CDcomplex (Figure 6a) is stabilized by hydrophobic and hydro-philic interactions (Figure 7a). The CR-Câ bond of PS in thecomplex is restricted in the trans arrangement. The PS moleculewill rotate freely in theR-CD cavity and theR-CD moleculewill always change its shape because of various molecularmotions: the structure shown in Figure 6a should be regardedas one or the average of the most stable structures.

The structure of the PrOH-R-CD complex in water (Figure6b) is much different from that in the crystal (Figure 3b). Thissolution structure is stabilized by hydrophobic and hydrophilicinteractions (Figure 8a). Hydrophobic interactions also play animportant role in stabilizing the crystal structure (Figure 8b),while hydrophilic interactions do not.

Molecular Surface Area and Binding Constants.Equation4 takes into consideration the∆Aoo term alone. However, twoother terms,∆Aww and∆Aow, will contribute to the stability ofthe structures of complexes, and thus may also contribute tothe binding constant. Then, the binding constantK1 may bebetter correlated with the three area terms as follows:

To determine the four coefficients in eq 5, we need detailedstructures of more complexes including native and modifiedcyclodextrins and aliphatic and aromatic guests. The first termwill play the predominant role in eq 5, as reported previously.4

Figure 7. Values of ∆Aoo (circles), ∆Aww (triangles), and∆Aow

(squares) as a function of the penetration depth,∆x, of the propyl groupof PS for (a) the solution structure and (b) the crystal structure, where∆x denotes displacement of theγ-carbon atom along thex-axis fromthe crystal structure.

Figure 8. Values of ∆Aoo (circles), ∆Aww (triangles), and∆Aow

(squares) as a function of the penetration depth,∆x, of the propyl groupof PrOH for (a) the solution structure and (b) the crystal structure. Forthe crystal structure,∆x denotes displacement of theγ-carbon atomalong thex-axis from this crystal structure. For the solution structure,∆x is identical to that in Figure 7.

log K1 ) 1.803∆Aoo - 2.023 (4)

log K1 ) a∆Aoo + b∆Aww - c∆Aow + d (5)

Solution Structures ofR-CD Complexes with PrOH and PS J. Phys. Chem. B, Vol. 106, No. 25, 20026435

Implications of the Present Approach.The solution struc-tures of cyclodextrin complexes with aromatic guest moleculescan be determined more accurately than those with aliphaticguests.1-3,5 The chemical shift provides some information onthe structures of the complex cyclodextrin and aromatic guest,although it is less useful for aliphatic guests. The results of thepresent study demonstrated that the ROE intensity and molecularsurface area provide semiquantitative data on the structures ofsuch aliphatic guest complexes. The present approach will serveto estimate the structures and binding constants of cyclodextrininclusion complexes with long alkyl chain compounds such assurfactants and fatty acids.21,22

Acknowledgment. Thanks are due to Mr. Shigehisa Yatsuda,Mr. Hiroshi Yamaguchi, and Mr. Makoto Fukuba for assistancewith NMR measurements and analyses. This work was sup-ported by a Grant-in-Aid for the Frontier Research Program fromthe Ministry of Education, Culture, Sports, Science, andTechnology of Japan.

References and Notes

(1) Bender, M. L.; Komiyama, M.Cyclodextrin Chemistry; Springer-Verlag: 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.

(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. InInclusion Compounds; Atwood, J. L., Davis, J. E.D., MacNicol, D. D., Eds.; Academic Press: London, 1991; Vol. 5, Chapter9.

(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 andreferences 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.

Tetrahedron1973, 29, 833.(19) Neuhaus, D.; Williamson, M. P.The Nuclear OVerhauser Effect

in Structural and Conformational Analysis, 2nd ed.; Wiley-VCH: NewYork, 2000; Chapters 5 and 12.

(20) Kessler, H.; Seip, S. InTwo-dimensional NMR Spectroscopy, 2nded.; 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.

6436 J. Phys. Chem. B, Vol. 106, No. 25, 2002 Funasaki et al.