- Email: [email protected]
Theoretical Studies on the Structures of Natural and Alkylated Cyclodextrins *
Theoretical Studies on the Structures of Natural and Alkylated Cyclodextrins* NICHOLAS S.BOD OR^^^, MING-JUHUANG~, AND JOHND. WATTS5 Received June 24, 1994, from the 'Center for Drug Discovery, College of Pharmacy, Box 100497, Health Science Center,
Gainesville, FL 32610-0497, and Quantum Theory Project, P.0. Box 118435, 362 Williamson Hall, University of Florida, Accepted for publication December 14, 1994@. Gainesville, FL 3261 1-8435. Abstract 0 A series of semiempirical molecular orbital calculations using the AM1 method have been performed on isolated natural and alkylated a and p-cyclodextrins. For natural cyclodextrins, three geometries were considered: (i) molecular mechanics (MM2); (ii) AM1 fully optimized geometry; (iii) X-ray structures based on the experimental coordinates for heavy atoms with positions of hydrogen atoms optimized by AMI. Large differences between AM1 calculated properties of geometries i-iii were found. The differences between ii and iii are smaller and reflect the intermolecular%crystal packing forces. Comparisons are made between ii and iii and properties determined therefrom, such as cavity diameter, outer diameter, and height. In addition, AM1 semiempirical (hydroxypropyl)-/3calculations were performed on the mixed (2,3,6) cyclodextrin, 2,6-dimethyl-p-cyclodextrin,and 2,6-bis(hydroxypropyl)-/?cyclodextrin. The results were compared with the substituent effects on monoglucose. It was found that the alkylation and methyl and 2-(hydroxypropyl) functions on bcyclodextrin does not introduce significant steric hindrance.
Introduction Cyclodextrins (CDs) or cycloamyloses comprise a family of cyclic oligosaccharides obtained from starch by enzymatic degradation. Up to now, a-, /?-,y-, and 8-cyclodextrins,which are composed of six (a-CD), seven (B-CD),eight (y-CD), and nine (6-CD)a-1,4-linked a-D-glucopyranosylresidues, respectively, have been isolated by selective precipitation with appropriate organic compounds. Cyclodextrins with 10-13 a-D-gluCOpyranOSyl residues have also been identified by chromatographic methods. Cyclodextrins composed of less than six glucose units are not known to exist due to steric hindrance. The number of glucose units determines the dimension and size of the cavity. The cavity is lined by the hydrogen atoms and the glycosidic oxygen bridges. The nonbonding electron pairs of the glycosidic oxygen bridges are directed toward the inside of the cavity, producing a high electron density and lending it some Lewis base character. As a result of this special arrangement of the functional groups in the cyclodextrin molecules, the cavity is relatively hydrophobic compared t o water, while the external faces are hydrophilic. Because of these properties, cyclodextrins are able to bind a large number of guest molecules. In cyclodextrin molecules, a ring of hydrogen bonds is also formed intramolecularly between the 2-hydroxyl and the 3-hydroxyl groups of adjacent glucose units. This hydrogen bonding ring gives the cyclodextrins a remarkably rigid structure. Investigations of cyclodextrin chemistry have been on the increase for several decades. The reasons for the enormous effort in the study of cyclodextrins are (a) such molecules have inherent interest, that is, their physical and chemical properties merit study; (b) they are the first and probably the most
* This paper was presented in part at The 7th International Cyclodextrins Symposium, April 25-28, 1994, Tokyo, Japan. Abstract published in Advance ACS Abstracts, February 1, 1995. @
330 / Journal of Pharmaceutical Sciences Vol. 84, No. 3, March 1995
Table 1-Comparison of X-ray vs Optimized a-and /3-Cyclodextrins
(kcal/mol)
dipole (D)
HOMO (eV)
LUMO-HOMO
Compound
(a) a-cyclodextrin (X-rayPb (a)a-cyclodextrin (X-ray)".," (b) a-cyclodextrin (MM2) (d) a-cyclodextrin (AMI) (a)j3-cyclodextrin(X-ray)"," (b) j3-cyclodextrin(MM2) (c)j3-cyclodextrin(SYM) (d) /?-cyclodextrin(AMI)
-1 368.7 -1374.1 -1361.6 -1414.0 -1613.4 -1592.5 -1 644.8 -1647.5
13.3 14.3 13.8 10.4 8.8 11.7 8.5 7.5
-10.27 -10.19 -9.99 -10.21 -10.36 -9.96 -10.30 -10.35
11.32 11.19 11.42 11.55 11.53 11.40 11.77 11.79
AH
(ev)
a The experimental heavy atom X-ray frame was kept rigid, but all 0-H and C H bond lengths and bond angles were optimized using AM1 . The experimental heavy atom X-ray frame is from ref 26. ,"Theexperimental heavy atom X-ray frames are from refs 27 and 28.
important example of inclusion complex formation with other organic molecules; (c) they are excellent models of enzymes, which has led to their use as catalysts, both in enzymatic and nonenzymatic reactions; and (d) they are natural products and readily available t o most researchers. Pharmaceutical applications of cyclodextrins as additive and drug-complexing agents have been rapidly growing. Many drug molecules are capable of residing partially within the central cavity of a CD molecule, thus forming an inclusion complex. The interaction of guest molecules with CDs may induce useful modification of the chemical and physical properties of the guest molecule, which may lead to improved stability, solubility in the aqueous medium, and bioavailability. Poorly water soluble drugs can be orally administered in the complex form by taking advantage of the well-established low toxicity of CDs by the oral route. Therefore, experimental and theoretical information on the geometry and structural features of the CD inclusion complexes, as well as on the topology of the host-guest interactions, is increasingly important. Modern computers with graphical capabilities are valuable new tools for obtaining information on the structure and geometry of the inclusion compounds. A previous theoretical study of the conformational differences between a-cyclodextrin in aqueous solution and in crystalline form was performed using molecular dynamics simulation by Koehler et a1.l In additim, several molecular dynamics studies of cyclodextrins have been reported.2-6 A molecular modeling study of structural effects on the binding of m i n e drugs with the diphenylmethyl functionality to cyclodextrins has been reported by Tong et al.' A molecular modeling study of ,&cyclodextrin complexes with nootropic drugs with the MM2 molecular mechanics force field method in the MacroModel program for energy minimization of geometries and conformations of the isolated host and guest molecules has been presented by Amato et al.8 Conformational analysis of 8-cyclodextrin complexes using the MM2 force field in the MacroModel program has been performed by Kostense et al.9 Some other molecular mechanical studies of cyclodextrins have also been reported.10-20 These studies have all used potential energy functions which are based on a classical "balls and springs" model of a molecule and do not
0022-3549/95/3184-0330$09.00/0
0 1995, American Chemical Society and American Pharmaceutical Association
Table 2-X-ray and AM1 Conformers of aCyclodextrin
Table 3-X-ray and AM1 Conformers of pCyclodextrin 0
0
0 ‘0
‘O
7
H
.
0
0’ ~
X-ray
n’l
OH
AM1 Ave
Bond Length (A) 1.541 1.542 1.520 1.535 1.515 1.540 1.534 1.537 1.509 1.533 1.432 1.432 1.411 1.411 1.407 1.415 1.427 1.414 1.441 1.417 Bond Angle (deg) 107.9 110.0 109.7 110.7 111.4 111.1 112.5 111.8 109.9 111.2 111.9 111.6 109.3 110.2 110.3 109.1 Dihedral Angle (deg) -55.8 -51.5 54.8 50.5 -54.6 -51.7 59.9 57.2 -63.7 -58.8 59.7 54.8 -175.7 -1 72.0 175.4 169.1
Range [1.536,1.544] [1.533, 1.5371 ]1.538,1.542] [I ,536, 1.5381 [I ,531, 1.5361 [ 1.429, 1.4341 [I ,405, 1.4161 [1.411, 1.4211 [1.410, 1.4181 [1.416, 1.4181 [109.3, 111.61 [109.1, 112.7 [109.8, 112.71 [111.2, 112.81 [109.8,112.9] [110.3,112.3] [105.8, 111.7 [106.3,111.5] [-56.0, -43.21 [45.0,54.8] [-56.2, -44.01 [51.4,60.7] [-60.4, -57.61 [48.4,58.4] [-175.6, -165.61 [163.8,173.6]
explicitly consider the electrons. A series of fixed-geometry quantum chemical studies of cyclodextrins have been performed with the semiempirical CNDO or CND012 We now report a series of quantum mechanical calculations on cyclodextrins using the most advanced semiempirical molecular orbital method, namely AMl.25 In contrast to the CNDO studies, in these calculations we have performed complete and unrestricted geometry optimization and conformational analysis. The aim of this study is to (a)compare the X-ray crystalline structure, the MM2-optimized structure, and the AM1optimized conformers of a-and P-cyclodextrins; (b) understand substituent effects on B-cyclodextrin by performing AM1 calculations on the mixed (2,3,6) (hydroxypropy1)-p-cyclodextrin, 2,6-dimethyl-~-cyclodext~n, and 2,6-bis(hydroxypro-
0 ~~~
X-ray c1-c2 c2&3
crc4 C4-C5 cSc6
csos osci c1-01
Cz-On c3-03
cl-C2&
Cz-CrC4 c3-c4-c5
c4-c5-c6
O&-C2
oscscs
OrCrCs orC3-c~
C,-Cz-c3-C4 Cz-C3-C4-C5 C3-C4-C5-05
C4-C5-05-C1
c5-05-c1-c2
05-c,-c2-c3
OrCrCrC4 03-C3-C4-C5
~
AM1 Ave
Bond Length (A) 1.532 1.542 1.51I 1.535 1.524 1.538 1.536 1.537 1.514 1.533 1.450 1.432 1.410 1.411 1.432 1.418 1.426 1.413 1.434 1.417 Bond Angle (deg) 109.5 109.7 108.1 109.4 110.3 110.5 112.3 111.6 110.4 111.6 110.8 111.6 110.8 111.4 107.7 110.6 DihedralAngle (deg) -58.6 -54.9 57.4 54.3 -55.0 -53.2 56.4 55.3 -58.2 -56.5 58.8 55.4 -179.1 -175.1 177.8 172.2
~
~~
Range [I .538,1.545] [I .534,1.535] [I ,536, 1.5391 11.535, 1.5391 [1.530,1.535] [1.429,1.434] [1.405,1.418] [1.413,1.424] [1.407,1.416] [I ,416, 1.4181 [108.1, 110.31 [107.7,110.4] [109.0, Ill.8] [110.4, 113.6] [110.7, 113.1 [108.2, 113.9j [110.5, 112.31 [107.3, 112.21 [-59.7, -51.61 [51.O, 60.11 [-57.4, -48.71 [51.2,59.6] [-58.2, -53.91 [52.6,57.8] [-179.1, -171.7 [168.2, 177.81
py1)-B-cyclodextrin and comparing the results with the substituent effects on mono-glucose. Our present calculations are performed on isolated, uncomplexed molecules and therefore pertain to the gas phase. Information on the free species is essential for the understanding the differences between crystalline structure and free species structure and substituent effects.
Methods AM1 calculations on a-cyclodextrin and @-cyclodextrinand their derivatives were performed using a modified version of the AhPAC program from QCPE.25 The monomers and dimers of glucose and
Journal of Pharmaceutical Sciences / 331 Vol. 84, No. 3, March 1995
Table 4-Selected Geometric Parameters for AMl-Optimized Structures 4 CH2OH
i
Table 5-Molecular Dimensions for AM1-Optimized and X-ray Structure of a-Cyclodextrin Inner Diameter (A)
1,4 2s 3,6 Ave
X-ray
AM1
5.835 5.873 7.326 6.345
5.389 5.986 7.065 6.147
Outer Diameter (A) A a-D-Glucose in CD 1,4 2,5 3,6 Ave
Bond Length (Ap 1.542 1.542 1.537 1.535 1.533 1.540 1.536 1.537 1.531 1.533 1.432 1.432 1.412 1.411 1.408 1.415 Bond Angle (deg) 109.3 110.0 108.5 110.7 108.7 111.1 111.1 111.8 113.8 111.2 111.2 111.6 112.4 110.2 111.9 109.1
ct-c2 c2-c3 c3-c4
c4-CS
cSc6 c5-05
oscc ct-01
c1-c2-c3
cz-crc4 C344-G C4-c&6 OSCI-CZ
oSc6-cS
OTCZ-C~
or&-&
1.542 1.535 1.538 1.537 1.533 1.432 1.41 1 1.418 109.7 109.4 110.5 111.6 111.6 111.6 111.4 110.6
C1-Cz-CrC4 CrCpCrCs CrCrCsOs C~-CS-OS-C~ cd5-c142
05-Ci-c& a
-55.7 59.9 -58.7 55.4 -52.4 51.8
Range
Dihedral Angle (deg) -51.5 [-56.0, -43.21 50.5 [45.0,54.8] -51.7 [-56.2,44.0] 57.2 [51.4,60.7] -58.8 [-60.4, -57.61 54.8 [48.4,58.4]
Ave
Ranqe
-54.9 54.3 -53.2 55.3 -56.5 55.4
[-59.7, -51.61 [51.0,60.1] [-57.4, -48.71 [51.2,59.6] [-58.2, -53.91 [52.6,57.8]
No significant change in bond lengths and bond angles.
related compounds were studied using the MM2 and MOPACZ5 programs on t h e Tektronix CAChe (Computer Assisted Chemistry) workstation. In all cases, the default Broyden-Fletcher-GoldfarbShanno geometry search method was employed to get fully optimized geometries. The X-ray structures for a-cyclodextrin are those of the inclusion complexes a - C N H z 0 given by Lindner and Saenger26for form I and by Klar et al.27 for form 11. The X-ray structure for B-cyclodextrin is that of the inclusion complex j3-CD.llHzO given by Betzel e t al.2s It is anticipated that the water molecules will have only a moderate influence on the structure and conformation, so the X-ray data should be a reasonable model of solid phase CD. Four sets of AM1 calculations were performed on a- and B-CD and the results compared (a) since the X-ray structures for a-and 8-CD only give the coordinates of the C and 0 atoms, we first ran AM1 calculations with the X-ray frame of the C and 0 atoms futed and fully optimized all 0-H and C-H bond lengths and bond angles; (b) we ran single point AM1 calculations on a- and 8-CD at the MM2 (CAChe version) optimized geometry; (c) AM1-optimized geometries were obtained within C, symmetry constraints; (d) fully optimized AM1 geometries with no symmetry constraints or other restrictions were calculated.
332 /Journal of Pharmaceutical Sciences Vol. 84, No. 3, March 1995
X-ray
AM1
X-ray
AM1
X-ray
AM1
12.782 11.300 11.265 11.782
12.472 11.441 10.282 11.398
9.324 7.428 12.763 9.838
8.167 7.794 12.350 9.437
10.341 10.392 9.635 10.123
11.065 11.132 10.170 10.789
1 2 3 4 5 6 Ave
X-ray
AM1
(6.194, 6.812; 6.797) (6.701, 6.642; 6.250) (6.107, 6.549; 7.810) (6.687, 6.61 1; 6.877) (6.135, 6.320; 6.362) (6.270,6.683; 5.431) (6.476; 6.588)
(6.771,6.169; 6.499) (6.677,6.711; 6.040) (6.631,6.154; 6.758) (6.708,6.624; 5.989) (6.222,6.067; 6.312) (6.494,6.160; 5.927) (6.449; 6.254)
Table 6-Molecular Dimensions for AM1-Optimized and X-ray Structure of /?-Cyclodextrin Inner Diameter (A)
1,4 15 23 2,6 3,6 3,7 4,7 Ave
P
a
ave
C
Height (A)
a-D-Glucosein CD
a-D-Glucose
B
X-ray
AM1
7.821 7.821 7.818 7.821 7.821 7.821 7.822 7.821 Outer Diameter (A)
7.766 7.169 7.556 7.786 7.265 7.797 8.391 7.676
B
A
1,4 1,5 2,5 2,6 3,6 3,7 4,7 Ave
C
X-ray
AM1
X-ray
AM1
X-ray
AM1
11.793 11.286 11.242 11.250 12.239 11.725 12.307 11.692
12.700 13.243 12.141 11.107 12.825 11553 10.100 11.953
13.571 14.023 13.991 13.558 14.299 13.554 14.302 13.900
13.919 12.333 12.929 13.957 12.851 12.742 15.322 13.436
11.017 11.684 11.923 12.634 12.895 12.557 11.679 12.056
11.150 12.382 11.890 11.465 12.717 10.051 9.050 11.244
Height (A) X-ray
AM 1 ~
1 2 3 4 5 6 7 Ave
(6.352,6.252; 5.950) (6.257, 6.352; 6.330) (6.702, 6.576; 6.159) (6.717, 6.598; 6.101) (6.240, 6.331; 7.122) (6.244,6.353; 5.921) (6.245,6.351; 5.918) (6.398; 6.214)
~~~
(6778,6578; 5.933) (6.680,6.630; 6.211) (6,779,6583; 6.464) (6.715,6.623; 5.987) (6.244,6.376; 7.086) (6.276,6.427; 5.854) (6.720,6.646; 6.090) (6.575; 6.232)
Results and Discussion Chemical environment (e.g. the nature of the guest and solvent) and phase (gas, solid, or liquid) influence the geom-
etry and conformation of CDs. These molecules may change geometry and conformation to accommodate a guest molecule. In the solid phase, intermolecular crystalline packing forces will also influence structure and reduce conformational flexibility. Free cyclodextrin molecules in the gas phase have fewer constraints and are expected to have greater conformational freedom. Differences between the structures and conformations of gas phase cyclodextrin molecules and those of their condensed phase, including inclusion complex structures, provide information about the nature of the homogeneous and heterogeneous intermolecular interactions. Cyclodextrins are traditionally depicted as symmetrical molecules of C,, symmetry (n = 6 and 7 for a- and B-CD). Of course, in any inclusion complex, rigorous symmetry will be destroyed, but for free cyclodextrins in the gas phase, symmetrical conformations may be anticipated. However, there is no a priori reason why the most symmetrical free cyclodextrin will be the most stable energetically, and at any finite temperature a free cyclodextrin molecule will sample all accessible regions of conformational space. The AM1 heats of formation, dipole moment, HOMO energy, and LUMO-HOMO gap for geometries a-d of a-and B-CD are shown in Table 1. In all cases, the AM1-optimized conformers (c and d) have the lowest heats of formation, while the MM2-optimized geometry (b) is the least stable. The differences between the heats of formation for geometries a (X-ray structure) and d (MI-optimized conformers) of the a-cyclodextrin and B-cyclodextrin are 45.3 and 35.2 kcal/mol, respectively. The AM1-optimized structures differ somewhat
0
0D,
0
= inner Diameter
DZa = Outer Diameter for group A
~ , =bOuter Diameter for group R DTC= Outer Diameter for group C D, = Height
Figure 1-The definition of the inner diameter, outer diameter, and height of P-cyclodextrin.
CH,OCH,
CHzOH
I
I
H
H
OH
OCH,
AH,= -287.5 kcaVmol
A€& = -302.9 kcaVrnol
M d g ) = AHr (2.6-dimethvl-a-glucose) - AHf (a-glucose)= 15.4 kcaVmol OCH.
0
H,CO
0
AH,= - 1647.5 kcaUmol
AH,= 1547.9 kcaUmol ~
M A c D ) = mf(2.6-dimethylP-cD)- AH, (p-CD) = 99.6 kcal/mol
-
SE = AAHACD) 7 x AAHAg) = -8.2 kcrUmol Figure 2-The stabilization energy for 2,6-dimethyl-8-cyclodextrin.
Journal of Pharmaceutical Sciences I 333 Vol. 84, No. 3, March 1995
OH
CH2OH
I
C H 2 0 4
I
J
H
OH AHf = -401.2kcaVmol
AHf= -302.9 kcaVrno1
)-
OH
AAHAg) = AHf (2,6-bis(hydroxypmpyl)-u-glucose) - AHf (a-glucose) = -98.3 kc3Urnol 0
O
J
0
AHf= -1647.5 k c a h o l
AHf= -2332.8 kcaUmol
AAHdCD) = AH~(2,6-bis(hydroxypropyl)p-CD) - AHf (p-CD) = -685.3 kcaVmol
SE = MHdCD) - 7 x MH&) = 2.8 kwl/mol Figure 3-The stabilization energy for the 2,6-bis(hydroxypropyl)-B-cyclodextrin.
from the crystalline X-ray forms, which may be due to the intramolecular hydrogen bonds between the 2-hydroxyl and the 3-hydroxyl groups of adjacent glucose units, but are more likely due to the crystalline intermolecular forces which give the X-ray structure a conformationally rigid form. The AM1 C , structures are a few kcavmol higher in energy than the unconstrained structures. This is in agreement with the MM studies of Lipkowitz.20 The large differences between heats of formation of AM1 and MM2 structures call into question the reliability of MM2 for structural optimization of these complex molecules. The difference in dipole moment between the symmetrical and unsymmetrical conformers has been suggested to have implications for the mechanism of incorporation of a guest molecule. Thus, while a large dipole moment will tend to stabilize a complex, it will tend t o create a larger barrier. Hence, a CD molecule may change t o a conformation with a lower dipole moment in order to accommodate a guest. Then, once the guest molecule has been incorporated, the stability of complex may be increased by changing to a high dipole moment conformation. Our AM1 dipole moments differ appreciably for the different conformers c and d, in accord with the suggestion of Kitagawa et al.23 Comparisons of geometric parameters of X-ray and AM1 conformers of a- and p-cyclodextrins are given in Tables 2 and 3. Since the lowest energy AM1 conformers of a- and /?-cyclodextrins are not completely symmetric, Tables 2 and 3
334 / Journal of fharmaceuticaf Sciences Vol. 84, No. 3, March 1995
represent the average values and corresponding range of the bond lengths, bond angles, and dihedral angles. The average C2-C3, C3-C4, and c5-C~bond lengths in the AM1 conformers for a- and P-cyclodextrins are slightly larger than the X-ray values. The average C2-02 and C3-O3 bond lengths in the AM1 conformers for a- and B-cyclodextrins are slightly smaller than the X-ray values. The average C1-C2-C3 bond angle in the AM1 conformer for a-cyclodextrin is larger than the X-ray values, and the average 03-C3-C4bond angle in the AM1 conformers for P-cyclodextrin is also larger than the X-ray value. The remaining average bond angles in the AM1 conformers €or a- and 8-cyclodextrins are very close to the X-ray values. All of the average dihedral angles in the AM1 conformers for a- and P-cyclodextrins are smaller than the X-ray values. The geometric parameters of AM1-optimized structures for a-D-glUCOSe, a-cyclodextrin, and #I-cyclodextrin are given in Table 4. It was found that the average bond lengths and average bond angles of a-D-glucose do not differ significantly from the respective values in a-cyclodextrin and B-cyclodextrin. The dihedral angles C1-C2-C3-Cd, C2-C3-C4-C5, and C3-C4-C5-05 in a- and B-cyclodextrins are smaller than the corresponding angles in a-D-glucose. Dihedral angles C5-05c1-C~and 05-C1-C2-C3 in a- and B-cyclodextrins are larger than those in a-D-glucose. For the dihedral angle C4-C505-C1, the #I-cyclodextrin value is very close to that of a-D-
4 HO
AHf = -302.9 kcaUmol
CHIOH I
CHIOH I
HO
OH
H
OH
CH2OR I
HO
OH H
OR
HO
OH
OH H
OH
R = CH*CH(OH)CH3 AHf = -353.0 kcaVmol
AHf = -347.9 kcaUmol
AHf = -349.4kcaVmol
S6 = AHr (6-hydroxypropyl-a-glucose)- AH[(a-glucose)= -50.1 kcaUmol S2 = AHf (2-hydmxypmpyl-a-glucosc)- AHf (a-glucose)= -46.5 kcaVmol (a-glucose)= -45.0 kcaUmol S, = AHf (3-hydmxypm~yl-a-glucose)-
S - unit substitution
s6 > s, > s,
0
0
0
0
- -(y)
UQ
(4*6 + 2.2 AHf = - 1995.1 kcaUmol
AHf = - 1647.5 kcaUmol MHQ)
= Al& (HP-p-CDmixed) - AHf (p-CD) = -347.6 kcaUmol 4 X S6 2 X S, * 1 X S, = -9.2kcaUmol
SE = MHACD)
-
-
Figure 4-The stabilization energy for the mixed (2,3,6)(hydroxypropy1)-p-cyclodextrin.
glucose and the a-cyclodextrin value is larger than for a-D-glucose. Molecular dimensions such as inner diameter, outer diameter, and height for the AM1 and X-ray structures of a- and P-cyclodextrins are given in Tables 5 and 6. The definitions of the inner diameter, outer diameter, and height are given in Figure 1. In Tables 5 and 6 the inner diameter is the distance between the hydrogen attached to the C5 of one glucose unit and the corresponding atom of another glucose unit. The outer diameter for group A is the distance between the hydrogen in the secondary alcohol which is attached t o the C2 of one glucose unit and the corresponding atom of another glucose unit. The outer diameter for group B is the distance between the hydrogen in the primary alcohol of one glucose unit and the corresponding atom of another glucose unit. The outer diameter for group C is the distance between the hydrogen in the secondary alcohol which is attached to the C3 of one glucose unit and the corresponding atom of another glucose unit. For height, the first two values in the same row of each glucose unit are the distances between the two hydrogens attached to Cs and the hydrogen in the
secondary alcohol of C2; the third value is the distance between the hydrogen in the primary alcohol and the hydrogen in the secondary alcohol of C2. We found that the average inner diameters for the X-ray structure are slightly greater than for the AM1 structure for a- and /3-cyclodextrins. The inner diameters fqr the AM1 structure of a- and /3-cyclodextrins are 6.1 and 7.7 A, respectively, which are quite close to the values (of unspecified origin) given in Figure 3 of Li and Purdy’s review29 and the approximate dimensions of cyclodextrins shown in Figures 1-9 of Szejtli30 (5.7 and 7.8 A for a- and /3-cyclodextrins,respectively), but quite different from those diameters measured with the aid of Corey-Pauling-Koltun (CPK) models and mpst popular citation reporting cavity diameters of 4.7-5.2 A for the a-cyclodextnn and 6.0-6.4 A for the ,%cyclodextrin,3l One of the reviewers quoted the estimates of 4.8-6.4 A for the cavity diameter for a-CD, a range that includes our result. The difference between CPK estimates emphasizes the value of more rigorous and unambiguous methods such as AM1 for estimating these parameters. If we substrac; twice the van der Wads radius of the hydrogen atom (1.2 A), then the cavity diameter will be 3.7 Journal of Pharmaceutical Sciences / 335 Vol. 84, No. 3, March 7995
and 5.3 A for a- and P-cyclodextrins,respectively. The largest outer diameter for the a-cyclodextrinis from group A of Table 5, which is the distance between the hydrogen in the secondary alcohol of Cz of one glucose unit and the corresponding atom of another glucose unit. The largest outer diameter for the b-cyclodextrin is from group B of Table 6, which is the distance between the hydrogen in the primary alcohol of one glucose unit and the corresponding atom of another glucose unit. The outer diameters for the AM$ structure of the aand B-cyclodextrins are 11.4 and 13.4 A, respectively. If we add twice the van der Waals radius of hydrogen, then the external diameters of the a- and B-cyclodextrins are 13.8and 15.8A, respectively, which are surprisingly close to the values of Li and Purdy’sZ9Figure 3 and the approximate dimensions of Szejtli’s3O Figures 1-9. None of our largest outer diameters are taken from the distance between the hydrogen in the secondary alcohol of C3 of one glucose unit and the corresponding atom of another glucose unit, as described by Saenger.31 For the height, the AM1 structure of a-cyclodextrin is slightly smaller than the X-ray structure, but the AM1 structure of the B-cyclodextrinis slightly higher than the X-ray structure. The largest diameters for the a- and j3-cyclodextrins are 6.4 and 6.6 A, respectively. If we add twice of the van der Waals radius of hydrogen, then the heights for the aand B-cycl2dextrins are 8.8 and 9.0 A, respectively, which are about 1.0 A higher than those of Li and Purdy’sZ9Figure 3. The heats of formation of 2,6-dimethyl-a-~-glucose and 2,6dimethyl-b-cyclodextrinare given in Figure 2. The calculated difference between the heats of formation of 2,6-dimethyl-aD-glUCOSe and a-D-ghCOSe is 15.4 kcdmol, and the difference between the heats of formation of 2,6-dimethyl-P-cyclodextrin and ,6-cyclodextrin is 99.6 kcaYmol. Thus, the “stabilization energy“ for the 2,6-dimethyl-~-cyclodextrin is 8.2 kcdmol. The and heats of formation of 2,6-bis(hydroxypropyl)-a-~-glucose 2,6-bis(hydroxypropyl)-~-cyclodextrinare shown in Figure 3. The differences between the heats of formation of 2,6-bis(hydroxypropy1)-a-D-glucose and a-D-glucose and between 2,6bis(hydroxypropyl)-j3-cyclodextrinand P-cyclodextrinare -98.3 and -685.3 kcaumol, respectively. The “stabilization energy” is -2.8 kcdmol. for the 2,6-bis(hydroxypropyl)-~-cyclodextrin The mixed (2,3,6) (hydroxypropy1)-P-cyclodextrinis built in such a way that there is only one hydroxypropyl substituent in each glucose unit: four glucose units have the hydroxypropyl substituent in the 6 position, two glucose units have the hydroxypropyl substituent in the 2 position, and one glucose unit has the hydroxypropyl substituent in the 3 position. The detailed structure of this mixed (2,3,6) (hydroxypropy1)-Bcyclodextrin is shown in Figure 4. Based on our previous the differences between the heats of formation of isomers with the hydroxypropyl substituent in the 6,2, and 3 positions of the a-D-glucose and the a-D-glucose are 50.1, 46.5, and 45.0kcdmol, respectively. The stabilization energy for the mixed (2,3,6)(hydroxypropy1)-b-cyclodextrinis 9.2 k c d mol. In conclusion, compared with X-ray results, AM1-optimized cyclodextrins have a somewhat distorted, less symmetrical structure, with a slightly smaller inner diameter or cavity
336 / Journal of Pharmaceutical Sciences Vol. 84, No. 3, March 1995
diameter. The stabilization energies for the 2,6-dimethyl-Pand mixed cyclodextrin, 2,6-bis(hydroxypropyl)-~-cyclodextrin, (2,3,6) (hydroxypropy1)-/3-cyclodextrinare 8.2, -2.8, and 9.2 kcal/mol, respectively. As a results of these calculations, we found that the alkylation and hydroxylalkylation of the cyclodextrins do not introduce significant steric hindrance.
References and Notes 1. Koehler, J. E. H.; Saenger, W.; van Gunsteren, W. F. J . Mol. Biol. 1988,203, 241-250. 2. Koehler, J. E. H.; Saenger, W.; van Gunsteren, W. F. Eur. Biophys. J . 1987, 15, 197-210. 3. Koehler, J. E. H.; Saenger, W.; van Gunsteren, W. F. Eur. Biophys. J . 1987,15, 211-224. 4. Prabhakaran, M.; Harvey, S. C. Biopolymers 1987,26, 10871096. 5. Koehler, J. E. H.; Saenger, W.; van Gunsteren, W. F. J. BiomoE. Struct. Dvn. 1988. 6 (1). 181-198. 6. Koehler, “J. E. H.’; Saenger, W.; van Gunsteren, W. F. Eur. Biophys. J . 1988,16, 153-168. 7. Tong, W.-Q.; Lach, J. L.; Chin, T.-F.; Guillory, J. K. Pharm. Res. 1991.8. 1307-1312. 8. Amatb, M.E.; Djedaini, F.; Pappalardo, G. C.; Perly, B.; Scarlata,
G. J . Pharm. Sci. 1992,81, 1157-1161. 9. Kostense, A. S.; van Helden, S. P.; Janssen, L. H. M. J . Cornput.Aided Mol. Des. 1991, 5 , 525-543. 10. Tabushi, I.; Kiyosuke, Y.-0.; Sugimoto, U.; Yamamura, K. J . Am. Chem. SOC.1978,100 (3), 916-919. 11. Matsui, Y. Bull. Chem. SOC.Jpn. 1982, 55 (4), 1246-1249. 12. Armstrong, D. W.; Ward, T. J.;Armstrong, R. D.; Beesley, T. E. Science 1986,232, 1132-1135. 13. Tabushi, I.; Mizutani, T. Tetrahedron 1987,43 (71,1439-1447. 14. Menger, F. M.; Sherrod, M. J. J . Am. Chem. SOC.1988, 110, 8606-8611. 15. Thiem, H . 4 . ; Brandl, M.; Breslow, R. J . Am. Chem. SOC.1988, 110, 8612-8616. 16. Venanzi, C. A.; Canzius, P. M.; Zhang, Z.; Bunce, J. D. J . Cornput. Chem. 1989,lO (8), 1038-1052. 17. Sherrod, M. J. Carbohydr. Res. 1989,192, 17-32. 18. deNamor, A. F. D.; Traboulssi, R.; Lewis, D. F. V. J . Chem. SOC., Chem. Commun. 1990, 751-753. 19. Ohashi, M.; Kasatani, K.; Shinohara, H.; Sato, H. J . Am. Chem. SOC.1990,112, 5824-5830. 20. Lipkowitz, K. B. J . Org. Chem. 1991,56, 6357-6367. 21. Kitagawa, M.; Hoshi, H.; Sakurai, M.; Inoue, Y.; Chujo, R. Carbohydr. Res. 1987, 163, Cl-C3. 22. Sakurai, M.; Kitagawa, M.; Hoshi, H. Chem. Lett. 1988,895898. 23. Kitagawa, M.;Hoshi, H.; Sakurai, M.; Inoue, Y.; Chujo, R. Bull. Chem. s o c . JDn. 1988.61.4225-4229. 24. Sakurai, M.; ktagawa, M:; Hoshi, H.; Inoue, Y.; Chujo, R. Bull. Chem. SOC.Jpn. 1989, 62, 2067-2069. 25. Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. F.: Stewart. J. J. P. J . Am. Chem. SOC.1985,107, 3902-3909. 26. Lindner, K.; Saenger, W. Acta Cryst. 1982, B38, 203-210. 27. Klar, B.; Hingerty, B.; Saenger, W. Acta Crystallogr. 1980, B36, 1154-1165. 28. Betzel, C.; Saenger, W.; Hingerty, B. E.; Brown, G. M. J. Am. Chem. SOC.1984,106, 7545-7557. 29. Li, S.; Purdy, W. C. Chem. Rev. 1992,92, 1457-1470. 30. Szejtli, J. In Cyclodextrin and Their Inclusion Complexes; Akademiai Kiado: Budapest, 1982. 31. Saenger, W. Angew. Chem. Int. Ed. Engl. 1980, 19, 344-362. 32. Brewster, M. E.; Huang, M . J . ; Pop, E.; Pitha, J.; Dewar, M. J. S.;Kaminski, J. J.; Bodor, N. Curbohydr. Res. 1993,242,53-67. JS940490R
Gainesville, FL 32610-0497, and Quantum Theory Project, P.0. Box 118435, 362 Williamson Hall, University of Florida, Accepted for publication December 14, 1994@. Gainesville, FL 3261 1-8435. Abstract 0 A series of semiempirical molecular orbital calculations using the AM1 method have been performed on isolated natural and alkylated a and p-cyclodextrins. For natural cyclodextrins, three geometries were considered: (i) molecular mechanics (MM2); (ii) AM1 fully optimized geometry; (iii) X-ray structures based on the experimental coordinates for heavy atoms with positions of hydrogen atoms optimized by AMI. Large differences between AM1 calculated properties of geometries i-iii were found. The differences between ii and iii are smaller and reflect the intermolecular%crystal packing forces. Comparisons are made between ii and iii and properties determined therefrom, such as cavity diameter, outer diameter, and height. In addition, AM1 semiempirical (hydroxypropyl)-/3calculations were performed on the mixed (2,3,6) cyclodextrin, 2,6-dimethyl-p-cyclodextrin,and 2,6-bis(hydroxypropyl)-/?cyclodextrin. The results were compared with the substituent effects on monoglucose. It was found that the alkylation and methyl and 2-(hydroxypropyl) functions on bcyclodextrin does not introduce significant steric hindrance.
Introduction Cyclodextrins (CDs) or cycloamyloses comprise a family of cyclic oligosaccharides obtained from starch by enzymatic degradation. Up to now, a-, /?-,y-, and 8-cyclodextrins,which are composed of six (a-CD), seven (B-CD),eight (y-CD), and nine (6-CD)a-1,4-linked a-D-glucopyranosylresidues, respectively, have been isolated by selective precipitation with appropriate organic compounds. Cyclodextrins with 10-13 a-D-gluCOpyranOSyl residues have also been identified by chromatographic methods. Cyclodextrins composed of less than six glucose units are not known to exist due to steric hindrance. The number of glucose units determines the dimension and size of the cavity. The cavity is lined by the hydrogen atoms and the glycosidic oxygen bridges. The nonbonding electron pairs of the glycosidic oxygen bridges are directed toward the inside of the cavity, producing a high electron density and lending it some Lewis base character. As a result of this special arrangement of the functional groups in the cyclodextrin molecules, the cavity is relatively hydrophobic compared t o water, while the external faces are hydrophilic. Because of these properties, cyclodextrins are able to bind a large number of guest molecules. In cyclodextrin molecules, a ring of hydrogen bonds is also formed intramolecularly between the 2-hydroxyl and the 3-hydroxyl groups of adjacent glucose units. This hydrogen bonding ring gives the cyclodextrins a remarkably rigid structure. Investigations of cyclodextrin chemistry have been on the increase for several decades. The reasons for the enormous effort in the study of cyclodextrins are (a) such molecules have inherent interest, that is, their physical and chemical properties merit study; (b) they are the first and probably the most
* This paper was presented in part at The 7th International Cyclodextrins Symposium, April 25-28, 1994, Tokyo, Japan. Abstract published in Advance ACS Abstracts, February 1, 1995. @
330 / Journal of Pharmaceutical Sciences Vol. 84, No. 3, March 1995
Table 1-Comparison of X-ray vs Optimized a-and /3-Cyclodextrins
(kcal/mol)
dipole (D)
HOMO (eV)
LUMO-HOMO
Compound
(a) a-cyclodextrin (X-rayPb (a)a-cyclodextrin (X-ray)".," (b) a-cyclodextrin (MM2) (d) a-cyclodextrin (AMI) (a)j3-cyclodextrin(X-ray)"," (b) j3-cyclodextrin(MM2) (c)j3-cyclodextrin(SYM) (d) /?-cyclodextrin(AMI)
-1 368.7 -1374.1 -1361.6 -1414.0 -1613.4 -1592.5 -1 644.8 -1647.5
13.3 14.3 13.8 10.4 8.8 11.7 8.5 7.5
-10.27 -10.19 -9.99 -10.21 -10.36 -9.96 -10.30 -10.35
11.32 11.19 11.42 11.55 11.53 11.40 11.77 11.79
AH
(ev)
a The experimental heavy atom X-ray frame was kept rigid, but all 0-H and C H bond lengths and bond angles were optimized using AM1 . The experimental heavy atom X-ray frame is from ref 26. ,"Theexperimental heavy atom X-ray frames are from refs 27 and 28.
important example of inclusion complex formation with other organic molecules; (c) they are excellent models of enzymes, which has led to their use as catalysts, both in enzymatic and nonenzymatic reactions; and (d) they are natural products and readily available t o most researchers. Pharmaceutical applications of cyclodextrins as additive and drug-complexing agents have been rapidly growing. Many drug molecules are capable of residing partially within the central cavity of a CD molecule, thus forming an inclusion complex. The interaction of guest molecules with CDs may induce useful modification of the chemical and physical properties of the guest molecule, which may lead to improved stability, solubility in the aqueous medium, and bioavailability. Poorly water soluble drugs can be orally administered in the complex form by taking advantage of the well-established low toxicity of CDs by the oral route. Therefore, experimental and theoretical information on the geometry and structural features of the CD inclusion complexes, as well as on the topology of the host-guest interactions, is increasingly important. Modern computers with graphical capabilities are valuable new tools for obtaining information on the structure and geometry of the inclusion compounds. A previous theoretical study of the conformational differences between a-cyclodextrin in aqueous solution and in crystalline form was performed using molecular dynamics simulation by Koehler et a1.l In additim, several molecular dynamics studies of cyclodextrins have been reported.2-6 A molecular modeling study of structural effects on the binding of m i n e drugs with the diphenylmethyl functionality to cyclodextrins has been reported by Tong et al.' A molecular modeling study of ,&cyclodextrin complexes with nootropic drugs with the MM2 molecular mechanics force field method in the MacroModel program for energy minimization of geometries and conformations of the isolated host and guest molecules has been presented by Amato et al.8 Conformational analysis of 8-cyclodextrin complexes using the MM2 force field in the MacroModel program has been performed by Kostense et al.9 Some other molecular mechanical studies of cyclodextrins have also been reported.10-20 These studies have all used potential energy functions which are based on a classical "balls and springs" model of a molecule and do not
0022-3549/95/3184-0330$09.00/0
0 1995, American Chemical Society and American Pharmaceutical Association
Table 2-X-ray and AM1 Conformers of aCyclodextrin
Table 3-X-ray and AM1 Conformers of pCyclodextrin 0
0
0 ‘0
‘O
7
H
.
0
0’ ~
X-ray
n’l
OH
AM1 Ave
Bond Length (A) 1.541 1.542 1.520 1.535 1.515 1.540 1.534 1.537 1.509 1.533 1.432 1.432 1.411 1.411 1.407 1.415 1.427 1.414 1.441 1.417 Bond Angle (deg) 107.9 110.0 109.7 110.7 111.4 111.1 112.5 111.8 109.9 111.2 111.9 111.6 109.3 110.2 110.3 109.1 Dihedral Angle (deg) -55.8 -51.5 54.8 50.5 -54.6 -51.7 59.9 57.2 -63.7 -58.8 59.7 54.8 -175.7 -1 72.0 175.4 169.1
Range [1.536,1.544] [1.533, 1.5371 ]1.538,1.542] [I ,536, 1.5381 [I ,531, 1.5361 [ 1.429, 1.4341 [I ,405, 1.4161 [1.411, 1.4211 [1.410, 1.4181 [1.416, 1.4181 [109.3, 111.61 [109.1, 112.7 [109.8, 112.71 [111.2, 112.81 [109.8,112.9] [110.3,112.3] [105.8, 111.7 [106.3,111.5] [-56.0, -43.21 [45.0,54.8] [-56.2, -44.01 [51.4,60.7] [-60.4, -57.61 [48.4,58.4] [-175.6, -165.61 [163.8,173.6]
explicitly consider the electrons. A series of fixed-geometry quantum chemical studies of cyclodextrins have been performed with the semiempirical CNDO or CND012 We now report a series of quantum mechanical calculations on cyclodextrins using the most advanced semiempirical molecular orbital method, namely AMl.25 In contrast to the CNDO studies, in these calculations we have performed complete and unrestricted geometry optimization and conformational analysis. The aim of this study is to (a)compare the X-ray crystalline structure, the MM2-optimized structure, and the AM1optimized conformers of a-and P-cyclodextrins; (b) understand substituent effects on B-cyclodextrin by performing AM1 calculations on the mixed (2,3,6) (hydroxypropy1)-p-cyclodextrin, 2,6-dimethyl-~-cyclodext~n, and 2,6-bis(hydroxypro-
0 ~~~
X-ray c1-c2 c2&3
crc4 C4-C5 cSc6
csos osci c1-01
Cz-On c3-03
cl-C2&
Cz-CrC4 c3-c4-c5
c4-c5-c6
O&-C2
oscscs
OrCrCs orC3-c~
C,-Cz-c3-C4 Cz-C3-C4-C5 C3-C4-C5-05
C4-C5-05-C1
c5-05-c1-c2
05-c,-c2-c3
OrCrCrC4 03-C3-C4-C5
~
AM1 Ave
Bond Length (A) 1.532 1.542 1.51I 1.535 1.524 1.538 1.536 1.537 1.514 1.533 1.450 1.432 1.410 1.411 1.432 1.418 1.426 1.413 1.434 1.417 Bond Angle (deg) 109.5 109.7 108.1 109.4 110.3 110.5 112.3 111.6 110.4 111.6 110.8 111.6 110.8 111.4 107.7 110.6 DihedralAngle (deg) -58.6 -54.9 57.4 54.3 -55.0 -53.2 56.4 55.3 -58.2 -56.5 58.8 55.4 -179.1 -175.1 177.8 172.2
~
~~
Range [I .538,1.545] [I .534,1.535] [I ,536, 1.5391 11.535, 1.5391 [1.530,1.535] [1.429,1.434] [1.405,1.418] [1.413,1.424] [1.407,1.416] [I ,416, 1.4181 [108.1, 110.31 [107.7,110.4] [109.0, Ill.8] [110.4, 113.6] [110.7, 113.1 [108.2, 113.9j [110.5, 112.31 [107.3, 112.21 [-59.7, -51.61 [51.O, 60.11 [-57.4, -48.71 [51.2,59.6] [-58.2, -53.91 [52.6,57.8] [-179.1, -171.7 [168.2, 177.81
py1)-B-cyclodextrin and comparing the results with the substituent effects on mono-glucose. Our present calculations are performed on isolated, uncomplexed molecules and therefore pertain to the gas phase. Information on the free species is essential for the understanding the differences between crystalline structure and free species structure and substituent effects.
Methods AM1 calculations on a-cyclodextrin and @-cyclodextrinand their derivatives were performed using a modified version of the AhPAC program from QCPE.25 The monomers and dimers of glucose and
Journal of Pharmaceutical Sciences / 331 Vol. 84, No. 3, March 1995
Table 4-Selected Geometric Parameters for AMl-Optimized Structures 4 CH2OH
i
Table 5-Molecular Dimensions for AM1-Optimized and X-ray Structure of a-Cyclodextrin Inner Diameter (A)
1,4 2s 3,6 Ave
X-ray
AM1
5.835 5.873 7.326 6.345
5.389 5.986 7.065 6.147
Outer Diameter (A) A a-D-Glucose in CD 1,4 2,5 3,6 Ave
Bond Length (Ap 1.542 1.542 1.537 1.535 1.533 1.540 1.536 1.537 1.531 1.533 1.432 1.432 1.412 1.411 1.408 1.415 Bond Angle (deg) 109.3 110.0 108.5 110.7 108.7 111.1 111.1 111.8 113.8 111.2 111.2 111.6 112.4 110.2 111.9 109.1
ct-c2 c2-c3 c3-c4
c4-CS
cSc6 c5-05
oscc ct-01
c1-c2-c3
cz-crc4 C344-G C4-c&6 OSCI-CZ
oSc6-cS
OTCZ-C~
or&-&
1.542 1.535 1.538 1.537 1.533 1.432 1.41 1 1.418 109.7 109.4 110.5 111.6 111.6 111.6 111.4 110.6
C1-Cz-CrC4 CrCpCrCs CrCrCsOs C~-CS-OS-C~ cd5-c142
05-Ci-c& a
-55.7 59.9 -58.7 55.4 -52.4 51.8
Range
Dihedral Angle (deg) -51.5 [-56.0, -43.21 50.5 [45.0,54.8] -51.7 [-56.2,44.0] 57.2 [51.4,60.7] -58.8 [-60.4, -57.61 54.8 [48.4,58.4]
Ave
Ranqe
-54.9 54.3 -53.2 55.3 -56.5 55.4
[-59.7, -51.61 [51.0,60.1] [-57.4, -48.71 [51.2,59.6] [-58.2, -53.91 [52.6,57.8]
No significant change in bond lengths and bond angles.
related compounds were studied using the MM2 and MOPACZ5 programs on t h e Tektronix CAChe (Computer Assisted Chemistry) workstation. In all cases, the default Broyden-Fletcher-GoldfarbShanno geometry search method was employed to get fully optimized geometries. The X-ray structures for a-cyclodextrin are those of the inclusion complexes a - C N H z 0 given by Lindner and Saenger26for form I and by Klar et al.27 for form 11. The X-ray structure for B-cyclodextrin is that of the inclusion complex j3-CD.llHzO given by Betzel e t al.2s It is anticipated that the water molecules will have only a moderate influence on the structure and conformation, so the X-ray data should be a reasonable model of solid phase CD. Four sets of AM1 calculations were performed on a- and B-CD and the results compared (a) since the X-ray structures for a-and 8-CD only give the coordinates of the C and 0 atoms, we first ran AM1 calculations with the X-ray frame of the C and 0 atoms futed and fully optimized all 0-H and C-H bond lengths and bond angles; (b) we ran single point AM1 calculations on a- and 8-CD at the MM2 (CAChe version) optimized geometry; (c) AM1-optimized geometries were obtained within C, symmetry constraints; (d) fully optimized AM1 geometries with no symmetry constraints or other restrictions were calculated.
332 /Journal of Pharmaceutical Sciences Vol. 84, No. 3, March 1995
X-ray
AM1
X-ray
AM1
X-ray
AM1
12.782 11.300 11.265 11.782
12.472 11.441 10.282 11.398
9.324 7.428 12.763 9.838
8.167 7.794 12.350 9.437
10.341 10.392 9.635 10.123
11.065 11.132 10.170 10.789
1 2 3 4 5 6 Ave
X-ray
AM1
(6.194, 6.812; 6.797) (6.701, 6.642; 6.250) (6.107, 6.549; 7.810) (6.687, 6.61 1; 6.877) (6.135, 6.320; 6.362) (6.270,6.683; 5.431) (6.476; 6.588)
(6.771,6.169; 6.499) (6.677,6.711; 6.040) (6.631,6.154; 6.758) (6.708,6.624; 5.989) (6.222,6.067; 6.312) (6.494,6.160; 5.927) (6.449; 6.254)
Table 6-Molecular Dimensions for AM1-Optimized and X-ray Structure of /?-Cyclodextrin Inner Diameter (A)
1,4 15 23 2,6 3,6 3,7 4,7 Ave
P
a
ave
C
Height (A)
a-D-Glucosein CD
a-D-Glucose
B
X-ray
AM1
7.821 7.821 7.818 7.821 7.821 7.821 7.822 7.821 Outer Diameter (A)
7.766 7.169 7.556 7.786 7.265 7.797 8.391 7.676
B
A
1,4 1,5 2,5 2,6 3,6 3,7 4,7 Ave
C
X-ray
AM1
X-ray
AM1
X-ray
AM1
11.793 11.286 11.242 11.250 12.239 11.725 12.307 11.692
12.700 13.243 12.141 11.107 12.825 11553 10.100 11.953
13.571 14.023 13.991 13.558 14.299 13.554 14.302 13.900
13.919 12.333 12.929 13.957 12.851 12.742 15.322 13.436
11.017 11.684 11.923 12.634 12.895 12.557 11.679 12.056
11.150 12.382 11.890 11.465 12.717 10.051 9.050 11.244
Height (A) X-ray
AM 1 ~
1 2 3 4 5 6 7 Ave
(6.352,6.252; 5.950) (6.257, 6.352; 6.330) (6.702, 6.576; 6.159) (6.717, 6.598; 6.101) (6.240, 6.331; 7.122) (6.244,6.353; 5.921) (6.245,6.351; 5.918) (6.398; 6.214)
~~~
(6778,6578; 5.933) (6.680,6.630; 6.211) (6,779,6583; 6.464) (6.715,6.623; 5.987) (6.244,6.376; 7.086) (6.276,6.427; 5.854) (6.720,6.646; 6.090) (6.575; 6.232)
Results and Discussion Chemical environment (e.g. the nature of the guest and solvent) and phase (gas, solid, or liquid) influence the geom-
etry and conformation of CDs. These molecules may change geometry and conformation to accommodate a guest molecule. In the solid phase, intermolecular crystalline packing forces will also influence structure and reduce conformational flexibility. Free cyclodextrin molecules in the gas phase have fewer constraints and are expected to have greater conformational freedom. Differences between the structures and conformations of gas phase cyclodextrin molecules and those of their condensed phase, including inclusion complex structures, provide information about the nature of the homogeneous and heterogeneous intermolecular interactions. Cyclodextrins are traditionally depicted as symmetrical molecules of C,, symmetry (n = 6 and 7 for a- and B-CD). Of course, in any inclusion complex, rigorous symmetry will be destroyed, but for free cyclodextrins in the gas phase, symmetrical conformations may be anticipated. However, there is no a priori reason why the most symmetrical free cyclodextrin will be the most stable energetically, and at any finite temperature a free cyclodextrin molecule will sample all accessible regions of conformational space. The AM1 heats of formation, dipole moment, HOMO energy, and LUMO-HOMO gap for geometries a-d of a-and B-CD are shown in Table 1. In all cases, the AM1-optimized conformers (c and d) have the lowest heats of formation, while the MM2-optimized geometry (b) is the least stable. The differences between the heats of formation for geometries a (X-ray structure) and d (MI-optimized conformers) of the a-cyclodextrin and B-cyclodextrin are 45.3 and 35.2 kcal/mol, respectively. The AM1-optimized structures differ somewhat
0
0D,
0
= inner Diameter
DZa = Outer Diameter for group A
~ , =bOuter Diameter for group R DTC= Outer Diameter for group C D, = Height
Figure 1-The definition of the inner diameter, outer diameter, and height of P-cyclodextrin.
CH,OCH,
CHzOH
I
I
H
H
OH
OCH,
AH,= -287.5 kcaVmol
A€& = -302.9 kcaVrnol
M d g ) = AHr (2.6-dimethvl-a-glucose) - AHf (a-glucose)= 15.4 kcaVmol OCH.
0
H,CO
0
AH,= - 1647.5 kcaUmol
AH,= 1547.9 kcaUmol ~
M A c D ) = mf(2.6-dimethylP-cD)- AH, (p-CD) = 99.6 kcal/mol
-
SE = AAHACD) 7 x AAHAg) = -8.2 kcrUmol Figure 2-The stabilization energy for 2,6-dimethyl-8-cyclodextrin.
Journal of Pharmaceutical Sciences I 333 Vol. 84, No. 3, March 1995
OH
CH2OH
I
C H 2 0 4
I
J
H
OH AHf = -401.2kcaVmol
AHf= -302.9 kcaVrno1
)-
OH
AAHAg) = AHf (2,6-bis(hydroxypmpyl)-u-glucose) - AHf (a-glucose) = -98.3 kc3Urnol 0
O
J
0
AHf= -1647.5 k c a h o l
AHf= -2332.8 kcaUmol
AAHdCD) = AH~(2,6-bis(hydroxypropyl)p-CD) - AHf (p-CD) = -685.3 kcaVmol
SE = MHdCD) - 7 x MH&) = 2.8 kwl/mol Figure 3-The stabilization energy for the 2,6-bis(hydroxypropyl)-B-cyclodextrin.
from the crystalline X-ray forms, which may be due to the intramolecular hydrogen bonds between the 2-hydroxyl and the 3-hydroxyl groups of adjacent glucose units, but are more likely due to the crystalline intermolecular forces which give the X-ray structure a conformationally rigid form. The AM1 C , structures are a few kcavmol higher in energy than the unconstrained structures. This is in agreement with the MM studies of Lipkowitz.20 The large differences between heats of formation of AM1 and MM2 structures call into question the reliability of MM2 for structural optimization of these complex molecules. The difference in dipole moment between the symmetrical and unsymmetrical conformers has been suggested to have implications for the mechanism of incorporation of a guest molecule. Thus, while a large dipole moment will tend to stabilize a complex, it will tend t o create a larger barrier. Hence, a CD molecule may change t o a conformation with a lower dipole moment in order to accommodate a guest. Then, once the guest molecule has been incorporated, the stability of complex may be increased by changing to a high dipole moment conformation. Our AM1 dipole moments differ appreciably for the different conformers c and d, in accord with the suggestion of Kitagawa et al.23 Comparisons of geometric parameters of X-ray and AM1 conformers of a- and p-cyclodextrins are given in Tables 2 and 3. Since the lowest energy AM1 conformers of a- and /?-cyclodextrins are not completely symmetric, Tables 2 and 3
334 / Journal of fharmaceuticaf Sciences Vol. 84, No. 3, March 1995
represent the average values and corresponding range of the bond lengths, bond angles, and dihedral angles. The average C2-C3, C3-C4, and c5-C~bond lengths in the AM1 conformers for a- and P-cyclodextrins are slightly larger than the X-ray values. The average C2-02 and C3-O3 bond lengths in the AM1 conformers for a- and B-cyclodextrins are slightly smaller than the X-ray values. The average C1-C2-C3 bond angle in the AM1 conformer for a-cyclodextrin is larger than the X-ray values, and the average 03-C3-C4bond angle in the AM1 conformers for P-cyclodextrin is also larger than the X-ray value. The remaining average bond angles in the AM1 conformers €or a- and 8-cyclodextrins are very close to the X-ray values. All of the average dihedral angles in the AM1 conformers for a- and P-cyclodextrins are smaller than the X-ray values. The geometric parameters of AM1-optimized structures for a-D-glUCOSe, a-cyclodextrin, and #I-cyclodextrin are given in Table 4. It was found that the average bond lengths and average bond angles of a-D-glucose do not differ significantly from the respective values in a-cyclodextrin and B-cyclodextrin. The dihedral angles C1-C2-C3-Cd, C2-C3-C4-C5, and C3-C4-C5-05 in a- and B-cyclodextrins are smaller than the corresponding angles in a-D-glucose. Dihedral angles C5-05c1-C~and 05-C1-C2-C3 in a- and B-cyclodextrins are larger than those in a-D-glucose. For the dihedral angle C4-C505-C1, the #I-cyclodextrin value is very close to that of a-D-
4 HO
AHf = -302.9 kcaUmol
CHIOH I
CHIOH I
HO
OH
H
OH
CH2OR I
HO
OH H
OR
HO
OH
OH H
OH
R = CH*CH(OH)CH3 AHf = -353.0 kcaVmol
AHf = -347.9 kcaUmol
AHf = -349.4kcaVmol
S6 = AHr (6-hydroxypropyl-a-glucose)- AH[(a-glucose)= -50.1 kcaUmol S2 = AHf (2-hydmxypmpyl-a-glucosc)- AHf (a-glucose)= -46.5 kcaVmol (a-glucose)= -45.0 kcaUmol S, = AHf (3-hydmxypm~yl-a-glucose)-
S - unit substitution
s6 > s, > s,
0
0
0
0
- -(y)
UQ
(4*6 + 2.2 AHf = - 1995.1 kcaUmol
AHf = - 1647.5 kcaUmol MHQ)
= Al& (HP-p-CDmixed) - AHf (p-CD) = -347.6 kcaUmol 4 X S6 2 X S, * 1 X S, = -9.2kcaUmol
SE = MHACD)
-
-
Figure 4-The stabilization energy for the mixed (2,3,6)(hydroxypropy1)-p-cyclodextrin.
glucose and the a-cyclodextrin value is larger than for a-D-glucose. Molecular dimensions such as inner diameter, outer diameter, and height for the AM1 and X-ray structures of a- and P-cyclodextrins are given in Tables 5 and 6. The definitions of the inner diameter, outer diameter, and height are given in Figure 1. In Tables 5 and 6 the inner diameter is the distance between the hydrogen attached to the C5 of one glucose unit and the corresponding atom of another glucose unit. The outer diameter for group A is the distance between the hydrogen in the secondary alcohol which is attached t o the C2 of one glucose unit and the corresponding atom of another glucose unit. The outer diameter for group B is the distance between the hydrogen in the primary alcohol of one glucose unit and the corresponding atom of another glucose unit. The outer diameter for group C is the distance between the hydrogen in the secondary alcohol which is attached to the C3 of one glucose unit and the corresponding atom of another glucose unit. For height, the first two values in the same row of each glucose unit are the distances between the two hydrogens attached to Cs and the hydrogen in the
secondary alcohol of C2; the third value is the distance between the hydrogen in the primary alcohol and the hydrogen in the secondary alcohol of C2. We found that the average inner diameters for the X-ray structure are slightly greater than for the AM1 structure for a- and /3-cyclodextrins. The inner diameters fqr the AM1 structure of a- and /3-cyclodextrins are 6.1 and 7.7 A, respectively, which are quite close to the values (of unspecified origin) given in Figure 3 of Li and Purdy’s review29 and the approximate dimensions of cyclodextrins shown in Figures 1-9 of Szejtli30 (5.7 and 7.8 A for a- and /3-cyclodextrins,respectively), but quite different from those diameters measured with the aid of Corey-Pauling-Koltun (CPK) models and mpst popular citation reporting cavity diameters of 4.7-5.2 A for the a-cyclodextnn and 6.0-6.4 A for the ,%cyclodextrin,3l One of the reviewers quoted the estimates of 4.8-6.4 A for the cavity diameter for a-CD, a range that includes our result. The difference between CPK estimates emphasizes the value of more rigorous and unambiguous methods such as AM1 for estimating these parameters. If we substrac; twice the van der Wads radius of the hydrogen atom (1.2 A), then the cavity diameter will be 3.7 Journal of Pharmaceutical Sciences / 335 Vol. 84, No. 3, March 7995
and 5.3 A for a- and P-cyclodextrins,respectively. The largest outer diameter for the a-cyclodextrinis from group A of Table 5, which is the distance between the hydrogen in the secondary alcohol of Cz of one glucose unit and the corresponding atom of another glucose unit. The largest outer diameter for the b-cyclodextrin is from group B of Table 6, which is the distance between the hydrogen in the primary alcohol of one glucose unit and the corresponding atom of another glucose unit. The outer diameters for the AM$ structure of the aand B-cyclodextrins are 11.4 and 13.4 A, respectively. If we add twice the van der Waals radius of hydrogen, then the external diameters of the a- and B-cyclodextrins are 13.8and 15.8A, respectively, which are surprisingly close to the values of Li and Purdy’sZ9Figure 3 and the approximate dimensions of Szejtli’s3O Figures 1-9. None of our largest outer diameters are taken from the distance between the hydrogen in the secondary alcohol of C3 of one glucose unit and the corresponding atom of another glucose unit, as described by Saenger.31 For the height, the AM1 structure of a-cyclodextrin is slightly smaller than the X-ray structure, but the AM1 structure of the B-cyclodextrinis slightly higher than the X-ray structure. The largest diameters for the a- and j3-cyclodextrins are 6.4 and 6.6 A, respectively. If we add twice of the van der Waals radius of hydrogen, then the heights for the aand B-cycl2dextrins are 8.8 and 9.0 A, respectively, which are about 1.0 A higher than those of Li and Purdy’sZ9Figure 3. The heats of formation of 2,6-dimethyl-a-~-glucose and 2,6dimethyl-b-cyclodextrinare given in Figure 2. The calculated difference between the heats of formation of 2,6-dimethyl-aD-glUCOSe and a-D-ghCOSe is 15.4 kcdmol, and the difference between the heats of formation of 2,6-dimethyl-P-cyclodextrin and ,6-cyclodextrin is 99.6 kcaYmol. Thus, the “stabilization energy“ for the 2,6-dimethyl-~-cyclodextrin is 8.2 kcdmol. The and heats of formation of 2,6-bis(hydroxypropyl)-a-~-glucose 2,6-bis(hydroxypropyl)-~-cyclodextrinare shown in Figure 3. The differences between the heats of formation of 2,6-bis(hydroxypropy1)-a-D-glucose and a-D-glucose and between 2,6bis(hydroxypropyl)-j3-cyclodextrinand P-cyclodextrinare -98.3 and -685.3 kcaumol, respectively. The “stabilization energy” is -2.8 kcdmol. for the 2,6-bis(hydroxypropyl)-~-cyclodextrin The mixed (2,3,6) (hydroxypropy1)-P-cyclodextrinis built in such a way that there is only one hydroxypropyl substituent in each glucose unit: four glucose units have the hydroxypropyl substituent in the 6 position, two glucose units have the hydroxypropyl substituent in the 2 position, and one glucose unit has the hydroxypropyl substituent in the 3 position. The detailed structure of this mixed (2,3,6) (hydroxypropy1)-Bcyclodextrin is shown in Figure 4. Based on our previous the differences between the heats of formation of isomers with the hydroxypropyl substituent in the 6,2, and 3 positions of the a-D-glucose and the a-D-glucose are 50.1, 46.5, and 45.0kcdmol, respectively. The stabilization energy for the mixed (2,3,6)(hydroxypropy1)-b-cyclodextrinis 9.2 k c d mol. In conclusion, compared with X-ray results, AM1-optimized cyclodextrins have a somewhat distorted, less symmetrical structure, with a slightly smaller inner diameter or cavity
336 / Journal of Pharmaceutical Sciences Vol. 84, No. 3, March 1995
diameter. The stabilization energies for the 2,6-dimethyl-Pand mixed cyclodextrin, 2,6-bis(hydroxypropyl)-~-cyclodextrin, (2,3,6) (hydroxypropy1)-/3-cyclodextrinare 8.2, -2.8, and 9.2 kcal/mol, respectively. As a results of these calculations, we found that the alkylation and hydroxylalkylation of the cyclodextrins do not introduce significant steric hindrance.
References and Notes 1. Koehler, J. E. H.; Saenger, W.; van Gunsteren, W. F. J . Mol. Biol. 1988,203, 241-250. 2. Koehler, J. E. H.; Saenger, W.; van Gunsteren, W. F. Eur. Biophys. J . 1987, 15, 197-210. 3. Koehler, J. E. H.; Saenger, W.; van Gunsteren, W. F. Eur. Biophys. J . 1987,15, 211-224. 4. Prabhakaran, M.; Harvey, S. C. Biopolymers 1987,26, 10871096. 5. Koehler, J. E. H.; Saenger, W.; van Gunsteren, W. F. J. BiomoE. Struct. Dvn. 1988. 6 (1). 181-198. 6. Koehler, “J. E. H.’; Saenger, W.; van Gunsteren, W. F. Eur. Biophys. J . 1988,16, 153-168. 7. Tong, W.-Q.; Lach, J. L.; Chin, T.-F.; Guillory, J. K. Pharm. Res. 1991.8. 1307-1312. 8. Amatb, M.E.; Djedaini, F.; Pappalardo, G. C.; Perly, B.; Scarlata,
G. J . Pharm. Sci. 1992,81, 1157-1161. 9. Kostense, A. S.; van Helden, S. P.; Janssen, L. H. M. J . Cornput.Aided Mol. Des. 1991, 5 , 525-543. 10. Tabushi, I.; Kiyosuke, Y.-0.; Sugimoto, U.; Yamamura, K. J . Am. Chem. SOC.1978,100 (3), 916-919. 11. Matsui, Y. Bull. Chem. SOC.Jpn. 1982, 55 (4), 1246-1249. 12. Armstrong, D. W.; Ward, T. J.;Armstrong, R. D.; Beesley, T. E. Science 1986,232, 1132-1135. 13. Tabushi, I.; Mizutani, T. Tetrahedron 1987,43 (71,1439-1447. 14. Menger, F. M.; Sherrod, M. J. J . Am. Chem. SOC.1988, 110, 8606-8611. 15. Thiem, H . 4 . ; Brandl, M.; Breslow, R. J . Am. Chem. SOC.1988, 110, 8612-8616. 16. Venanzi, C. A.; Canzius, P. M.; Zhang, Z.; Bunce, J. D. J . Cornput. Chem. 1989,lO (8), 1038-1052. 17. Sherrod, M. J. Carbohydr. Res. 1989,192, 17-32. 18. deNamor, A. F. D.; Traboulssi, R.; Lewis, D. F. V. J . Chem. SOC., Chem. Commun. 1990, 751-753. 19. Ohashi, M.; Kasatani, K.; Shinohara, H.; Sato, H. J . Am. Chem. SOC.1990,112, 5824-5830. 20. Lipkowitz, K. B. J . Org. Chem. 1991,56, 6357-6367. 21. Kitagawa, M.; Hoshi, H.; Sakurai, M.; Inoue, Y.; Chujo, R. Carbohydr. Res. 1987, 163, Cl-C3. 22. Sakurai, M.; Kitagawa, M.; Hoshi, H. Chem. Lett. 1988,895898. 23. Kitagawa, M.;Hoshi, H.; Sakurai, M.; Inoue, Y.; Chujo, R. Bull. Chem. s o c . JDn. 1988.61.4225-4229. 24. Sakurai, M.; ktagawa, M:; Hoshi, H.; Inoue, Y.; Chujo, R. Bull. Chem. SOC.Jpn. 1989, 62, 2067-2069. 25. Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. F.: Stewart. J. J. P. J . Am. Chem. SOC.1985,107, 3902-3909. 26. Lindner, K.; Saenger, W. Acta Cryst. 1982, B38, 203-210. 27. Klar, B.; Hingerty, B.; Saenger, W. Acta Crystallogr. 1980, B36, 1154-1165. 28. Betzel, C.; Saenger, W.; Hingerty, B. E.; Brown, G. M. J. Am. Chem. SOC.1984,106, 7545-7557. 29. Li, S.; Purdy, W. C. Chem. Rev. 1992,92, 1457-1470. 30. Szejtli, J. In Cyclodextrin and Their Inclusion Complexes; Akademiai Kiado: Budapest, 1982. 31. Saenger, W. Angew. Chem. Int. Ed. Engl. 1980, 19, 344-362. 32. Brewster, M. E.; Huang, M . J . ; Pop, E.; Pitha, J.; Dewar, M. J. S.;Kaminski, J. J.; Bodor, N. Curbohydr. Res. 1993,242,53-67. JS940490R