Anal. Chem. 2008, 80, 2426-2438
Molecular Dynamics Study of Chiral Recognition for the Whelk-O1 Chiral Stationary Phase C. F. Zhao and N. M. Cann*
Department of Chemistry, Queen’s University, Kingston, Ontario, Canada K7L 3N6
In this article, we examine the docking of 10 analytes on the Whelk-O1 stationary phase. A proper representation of analyte flexibility is essential in the docking analysis, and analyte force fields have been developed from a series of B3LYP calculations. Molecular dynamics simulations of a representative Whelk-O1 interface, in the presence of racemic analyte and solvent, form the basis of the analysis of chiral selectivity. The most probable docking arrangements are identified, the energy changes upon docking are evaluated, and separation factors are predicted. From comparisons between the analytes, the mechanism of chiral selectivity is divided into contributions from hydrogen bonding, ring-ring interactions, steric hindrance, and molecular flexibility. We find that both hydrogen bonding and ring-ring interactions are necessary to localize the analyte within the Whelk-O1 cleft region. We also identify one docking mechanism that is often dominant and analyze the conditions that lead to alternate docking modes. Enantiomers have distinct interactions with other chiral molecules, including the amino acids that are the building blocks for proteins. In recognition of this, the U.S. Food and Drug Administration issued a policy statement, in 1992, in regard to single-enantiomer pharmaceuticals.1 However, the isolation of single enantiomers is a challenging problem in chemistry. A range of synthetic approaches have been devised to obtain only one enantiomer,2,3 but resolution techniques are ubiquitous for several reasons: they provide a simple, general, and rapid means of separating mirror-image molecules.4 High-performance liquid chromatography (HPLC) resolutions are based on a range of selectors5 including cyclodextrins, polysaccharides, antibiotics, proteins, and organic molecules with functional groups chosen for enhanced selectivity. * To whom correspondence should be addressed. Telephone: 613-533-2651. Fax: 613-533-6669. E-mail:
[email protected]. (1) [Anon] Chirality 1992, 4, 338-340. (2) Katsuki, T.; Sharpless, K. B. J. Am. Chem. Soc. 1980, 102, 5974-5976. (3) Noyori, R.; Ohkuma, T.; Kitamura, M.; Takaya, H.; Sayo, N.; Kumobayashi, H.; Akutagawa, S. J. Am. Chem. Soc. 1987, 109, 5856-5858. (4) Francotte, E. R. J. Chromatogr., A 2001, 906, 379-397. (5) Consult the following for details on these classes of CSPs: Han, S. M. Biomed. Chromatogr. 1997, 11, 259-271. Okamoto, Y.; Kaida, Y. J. Chromatogr., A 1994, 666, 403-419. Armstrong, D. W.; Tang, Y. B.; Chen, S. S.; Zhou, Y. W.; Bagwill, C.; Chen, J. R. Anal. Chem. 1994, 66, 14731484. Haginaka, J. J. Chromatogr., A 2001, 906, 253-273. Davankov, V. A. J. Chromatogr., A 2003, 1000, 891-915. Oi, N.; Kitahara, H. J. Liq. Chromatogr. 1986, 9, 511-517. Welch, C. J. J. Chromatogr., A 1994, 666, 3-26.
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The Whelk-O1 chiral stationary phase (CSP) was designed6,7 in the 1990s to isolate S-naproxen, a nonsteroidal anti-inflammatory drug. As it turns out, this stationary phase is selective for a broad range of racemates8,9 and can be used in various solvent environments.8,10,11 Today, the Whelk-O1 stationary phase is the most successful12 charge-transfer CSP. The overall shape of the selective molecule is a cleft, and this shape is viewed as key to its selectivity.13-16 As a general rule, enantiomers with a hydrogen bond acceptor and an aromatic group close to a chiral center tend to be well resolved on the Whelk-O1 CSP.9 Experimental evidence for CSP selection mechanisms can be obtained from NMR,17,18 X-ray crystallography,19,20 spectroscopic methods,21-23 and calorimetry.24 Such studies are very instructive but only available for a few analytes and selectors. However, NMR has been employed for studies of Whelk-O1.14,25 Chemical shifts indicate that the replacement of the hydroxyl group in naproxen with an amine leads to a change in docking mechanism.25 A comprehensive 1H NMR study of 22 analytes in the presence of a modified Whelk-O1 selector14 found that most of the analytes show nonequivalent chemical shifts, and these were interpreted as evidence that the favored enantiomer docks inside the cleft (6) Pirkle, W. H.; Welch, C. J. J. Liq. Chromatogr. 1992, 15, 1947-1955. (7) Pirkle, W. H.; Welch, C. J.; Lamm, B. J. Org. Chem. 1992, 57, 3854-3860. (8) Pirkle, W. H.; Welch, C. J. Tetrahedron: Asymmetry 1994, 5, 777-780. (9) Welch, C. J.; Szczerba, T.; Perrin, S. R. J. Chromatogr., A 1997, 758, 9398. (10) Pirkle, W. H.; Brice, L. J.; Terfloth, G. J. J. Chromatogr., A 1996, 753, 109119. (11) Dungelova, J.; Lehotay, J.; Cizmarik, J.; Armstrong, D. W. J. Liq. Chromatogr. Relat. Technol. 2003, 26, 2331-2350. (12) Berthod, A. Anal. Chem. 2006, 78, 2093-2099. (13) Koscho, M. E.; Spence, P. L.; Pirkle, W. H. Tetrahedron: Asymmetry 2005, 16, 3147-3153. (14) Koscho, M. E.; Pirkle, W. H. Tetrahedron: Asymmetry 2005, 16, 33453351. (15) Wolf, C.; Pirkle, W. H. Tetrahedron 2002, 58, 3597-3603. (16) Pirkle, W. H.; Gan, K. Z. J. Chromatogr., A 1997, 790, 65-71. (17) Feibush, B.; Figueroa, A.; Charles, R.; Onan, K. D.; Feibush, P.; Karger, B. L. J. Am. Chem. Soc. 1986, 108, 3310-3318. (18) Yashima, E.; Yamamoto, C.; Okamoto, Y. J. Am. Chem. Soc. 1996, 118, 4036-4048. (19) Armstrong, D. W.; Ward, T. J.; Armstrong, R. D.; Beesley, T. E. Science 1986, 232, 1132-1135. (20) Hamilton, J. A.; Chen, L. Y. J. Am. Chem. Soc. 1988, 110, 4379-4391. (21) Horvath, E.; Kristof, J.; Frost, R. L.; Rintoul, L.; Redey, A.; Forsling, W. J. Chromatogr., A 2000,893, 37-46. (22) Czerwenka, C.; Zhang, M. M.; Kahlig, H.; Maier, N. M.; Lipkowitz, K. B.; Lindner, W. J. Org. Chem. 2003, 68, 8315-8327. (23) Xu, Y. F.; McCarroll, M. E. J. Phys. Chem. B 2005, 109, 8144-8152. (24) Lah, J.; Maier, N. M.; Lindner, W.; Vesnaver, G. J. Phys. Chem. B 2001, 105, 1670-1678. (25) Pirkle, W. H.; Welch, C. J. J. Chromatogr., A 1994, 683, 347-353. 10.1021/ac702126y CCC: $40.75
© 2008 American Chemical Society Published on Web 03/06/2008
while the other docks outside of the cleft. An X-ray cocrystallization study13 of a modified Whelk-O1 selector with N-(1-(4bromophenyl)ethyl)pivalamide indicates that the favored enantiomer docks inside the cleft, while the least retained enantiomer is positioned outside of the cleft region. While these studies provide invaluable information on analyte docking on Whelk-O1, neither method investigates recognition for the tethered selector and the underlying surface may sterically prevent certain docking arrangements. Recent NOESY NMR studies26-28 have addressed this concern by focusing on silica-bonded chiral selectors, but tethered Whelk-O1 has not yet been studied with this approach. A second concern is that HPLC solvents are different from those employed in NMR and the solvent may affect the mechanism of selectivity. For instance, separation factors for naproxen derivatives on Whelk-O1 are quite different in deuterochloroform25 than in n-hexane/2-propanol, the binary solvent usually employed for separations on Whelk-O1.8 In this article, we examine analyte docking on Whelk-O1 via molecular dynamics (MD) simulations of the chiral interface in the presence of racemate and n-hexane solvent. These simulations provide atomic details of docking at the chiral interface. Three-point interaction models are generally invoked to explain the selectivity of CSPs.12 The idea is simply that one enantiomer can simultaneously form all three interactions with the selector while the other cannot. This leads to an energy difference in the diastereoisomeric complexes, which gives rise to different retention times within the column. For Whelk-O1, two three-point mechanisms have been proposed and both agree on the first two interactions: a hydrogen bond forms between the amide hydrogen and a hydrogen-bonding acceptor in the analyte, and a π-π stack forms between the dinitrophenyl group and an aromatic ring in the analyte. For the third point, Pirkle et al.8,25 proposed this to be an edge-face π-π interaction formed by the phenanthryl moiety of the Whelk and an aromatic ring in the analyte. In contrast, Del Rio et al.29 proposed that side-chain CH-π interaction accounts for the third interaction. Theoretical studies of separations30 can be divided into three categories: force field exploration of isolated docked complexes; selectivity predictions via structure-function relationships; and simulations. Docked complexes between the Whelk-O1 selector and 1-(4-halogenophenyl)-1-ethylamine derivatives were explored by Del Rio et al.29 They found that calculated enthalpy differences between the docked complexes were generally consistent with measured separation factors. Statistical modeling, via structurefunction relationships, was undertaken for Whelk-O1 separations in 80:20 n-hexane/2-propanol.31 An analysis of analyte attributes led to a statistical model for the separation factor. Simulations of stationary-phase interfaces are relatively recent, by virtue of the (26) Skogsberg, U.; Handel, H.; Gesele, E.; Sokoliess, T.; Menyes, U.; Jira, T.; Roth, U.; Albert, K. J. Sep. Sci. 2003, 26, 1119-1124. (27) Hellriegel, C.; Skogsberg, U.; Albert, K.; Lammerhofer, M.; Maier, N. M.; Lindner, W. J. Am. Chem. Soc. 2004, 126, 3809-3816. (28) Ye, Y. K.; Bai, S.; Vyas, S.; Wirth, M. J. J. Phys. Chem. B 2007, 111, 11891198. (29) Del Rio, A.; Hayes, J. M.; Stein, M.; Piras, P.; Roussel, C. Chirality 2004, 16, S1-S11. (30) Consult the following for details on theoretical studies on enantioselectivity of CSPs: (a) Booth, T. D.; Azzaoui, K.; Wainer, I. W. Anal. Chem. 1997, 69, 3879-3883. (b) Lipkowitz, K. B. J. Chromatogr., A 2001, 906, 417442. (c) Dodziuk, H. J. Mol. Struct. 2002, 614, 33-45. (31) Del Rio, A.; Piras, P.; Roussel, C. Chirality 2006, 18, 498-508.
complexity involved. Efforts have typically focused on achiral interfaces,32-35 such as the n-octadecane stationary phase.34,35 Recently, we have carried out MD simulations36,37 to explore the solvation of the Whelk-O1 CSP and its selectivity for epoxides. We found that hydrogen bonding with the amide hydrogen, and ring-ring stacking were common elements in the docked complexes. These are expected based on the proposed three-point interaction models,8,25 but other factors, such as torsional strain, were also identified as contributors to the overall selectivity. In addition, competition between multiple inside-the-cleft docked complexes was observed and this is not consistent with the idea that only one enantiomer enters the cleft to form three specific interactions with the Whelk-O1. These studies highlight the need for a comprehensive exploration of the factors that contribute to the chiral selectivity of Whelk-O1. In this article, the docking of 10 analytes is explored, with each analyte chosen to highlight the various aspects of the docking process. This article begins with a brief description of the model of the (3R,4S)-Whelk-O1 selector and the chiral interface. Details of the molecular dynamics simulations are provided in Theoretical Details. The simulation results will be presented in Results and Discussion. The article concludes with a brief discussion of the results. THEORETICAL DETAILS The Whelk-O1 CSP is formed when 1-(3,5-dinitrobenzamido)1,2,3,4-tetrahydrophenanthrene is attached to a surface by a short alkyl tether and a siloxyl group. In this article, “phenanthryl group” refers to 1,2,3,4-tetrahydrophenanthrene and “DNP” refers to the dinitrophenyl group. The Whelk-O1 selector is shown in Figure 1b. The amide linkage is somewhat flexible, and this is relevant to docking since flexibility in this region changes the cleft. Ab initio studies37 show that torsion about the C(27)-C(29) bond is particularly flexible with a (45° range within 2.5 kJ/mol of the minimum. In this way, the dinitrophenyl ring can twist, with little energy penalty, to form a ring-ring interaction with the analyte. Limited torsion, of roughly (15°, about the C(10)-N(25) bond may also occur so that the amide hydrogen can reorient somewhat to accommodate the analyte. A suitable semiflexible model for the selector, based on extensive ab initio calculations, was developed previously.36,37 Figure 2 illustrates the rationale for the model chiral interface. Experimentally, porous silica beads are coated with the chiral selector. The exposed surface of the bead is dominated by the pores,38 with widths typically between 50 and 100 Å. The model Whelk-O1 interface is representative of the pore surface: the interface includes 16 (3R,4S)-Whelk-O1 selectors, 48 trimethylsilyl end caps, and 64 silanol groups corresponding to coverages of 1.07, 3.20, and 4.26 µmol/m2, respectively, within the range of experimental values.6,39,40 An underlying layer of 128 Si atoms, to (32) Klatte, S. J.; Beck, T. L. J. Phys. Chem. 1993, 97, 5727-5734. (33) Slusher, J. T.; Mountain, R. D. J. Phys. Chem. B 1999, 103, 1354-1362. (34) Zhang, L.; Sun, L.; Siepmann, J. I.; Schure, M. R. J. Chromatogr., A 2005, 1079, 127-135. (35) Rafferty, J. L. Z. L.; Siepmann, J. I.; Shure M. R. Anal. Chem. In press. (36) Zhao, C. F.; Cann, N. M. J. Chromatogr., A 2007, 1149, 197-218. (37) Zhao, C.; Cann, N. M. J. Chromatogr., A 2006, 1131, 110-129. (38) Berthod, A. J. Chromatogr. 1991, 549, 1-28. (39) Szczerba, T. Regis Technologies, Inc., personal communication, 2004. (40) Nawrocki, J. J. Chromatogr., A 1997, 779, 29-71.
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Figure 1. Structures of the Whelk-O1 selector and the 10 analytes. In (a), a schematic showing the interactions proposed in existing threepoint binding models8,25,29 is given. In (b), the semiflexible representation of the selector, with rigid units identified by shaded areas, is shown along with the atom numbering used throughout. In (c), the B3LYP/6-311++G** optimized structures are provided for: (S)styrene oxide (S-STYO); (S,S)-stilbene oxide (S,S-STBO); (S)-2methyloxirane (S-MOXR); (R,R)-1,2-diphenylcyclopropane (R,RDPCP); (R)-1-phenylethanol (R-PEOL); (S)-1-phenylethanamine (SPEAM); (S)-1-phenylethane-1,2-diol (S-PEDO); (S,S)-1,2-diphenylethane-1,2-diol (S,S-DPED); (S)-2-hydroxy-1,2- diphenylethanone (SDPEO); (S)-N-(1-(4-bromophenyl)ethyl)pivalamide (S-PAMD). The shaded areas are treated as rigid units in the simulations.
which end caps, silanol groups, and selectors are attached, is stationary and represents the solid substrate. The end cap and silanol models have been discussed elsewhere.36 Figure 1 shows the 10 analytes under consideration. Racemates of n-(1-(4-bromophenyl)ethyl)pivalamide (PAMD) are very well resolved by Whelk-O1, while styrene oxide (STYO), stilbene oxide (STBO), 1,2-diphenylethane-1,2-diol (DPED), and 2-hydroxy-1,2diphenylethanone (DPEO) are well resolved, 1-phenylethane-1,2diol (PEDO) is poorly resolved, and 1,2-diphenylcyclopropane (DPCP), 2-methyloxirane (MOXR), and 1-phenylethanamine (PEAM) are not resolved at all, and conflicting results41,42 have been reported for 1-phenylethanol (PEOL). Comparisons among these analytes provide a direct assessment of the factors that influence selectivity. For instance, a comparison between STYO and MOXR highlights the impact of ring-ring interactions. In the simulations, the analyte potentials must accurately represent molecular flexibility. The models are based on an extensive series of ab initio calculations. Full details are provided in the Supporting Information. (41) Huang, J. M.; Zhang, P.; Chen, H.; Li, T. Y. Anal. Chem. 2005, 77, 33013308. (42) Moiteiro, C.; Fonseca, N.; Curto, M. J. M.; Tavares, R.; Lobo, A. M.; RibeiroClaro, P.; Felix, V.; Drew, M. G. B. Tetrahedron: Asymmetry 2006, 17, 3248-3264.
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Extensive MD simulations were performed for the Whelk-O1 interface. The simulation cell includes two chiral interfaces, with solvent and racemate in-between, as the side view in Figure 2 shows. In actual fact, the figure does not show the entire simulation cell: empty space is included above and below the two underlying Si layers and the full cell is 4.992 nm × 4.992 nm × 15.000 nm. This extra space is required43 to minimize interactions between pairs of surface-fluid-surface slabs when the simulation cell is replicated in three dimensions. All simulations are performed in the NVT ensemble at 273 K, with the temperature maintained by Nose´-Hoover thermostats.44,45 The equations of motion are integrated following the algorithm of Martyna et al.46 to preserve the Rattled47 positions and velocities. The time step in the simulations is 0.77 fs. The simulation temperature is somewhat lower than usual,8,9 although separation factors for Whelk-O1 have been measured at 273 K.48-50 At this temperature, the selectivity factor is slightly higher than for 298 K,49,50 but retention factors increase more significantly. The solvent consists of 450-470 n-hexane molecules, consistent with the experimental hexane density51 of 7.859 mol/L at 273 K. Each simulation cell also includes 16 analytes: 8 of each enantiomer. An n-hexane solvent has been chosen for the simulations by appeal to its ubiquitous use as the major solvent in normal-phase chromatography.8 In addition, several experimental studies50,52 report only small changes in separation factors with modest additions of 2-propanol. In accordance with solvation studies for Whelk-O1,37 the TraPPE-UA53 model for n-hexane has been selected. For each analyte, fifteen to forty 1 500 000-1 600 000 time step MD simulations have been performed; this corresponds to a total simulation time of 15-36 ns. The lower limit is appropriate for analytes with low retention times while the upper limit applies to strongly interacting analytes. In all cases, the racemate distribution is assessed over shorter time periods and simulations continue until satisfactory convergence is achieved. We have chosen to perform a large number of ∼1-ns simulations, rather than a small number of longer simulations, to improve statistical averaging over the various docking arrangements. This choice is based, in part, on a dynamical study of STYO,36 which showed that analytes typically visited several selectors during this time. Initial configurations are generated as discussed elsewhere.36,54 The first 50 000100 000 time steps are used for equilibration. Following this, distributions are assessed every 20 iterations and a snapshot of (43) Yeh, I. C.; Berkowitz, M. L. J. Chem. Phys. 1999, 111, 3155-3162. (44) Nose, S. J. Chem. Phys. 1984, 81, 511-519. (45) Hoover, W. G. Phys. Rev. A 1985, 31, 1695-1697. (46) Martyna, G. J.; Tobias, D. J.; Klein, M. L. J. Chem. Phys. 1994, 101, 41774189. (47) Andersen, H. C. J. Comput. Phys. 1983, 52, 24-34. (48) Job, G. E.; Shvets, A.; Pirkle, W. H.; Kuwahara, S.; Kosaka, M.; Kasai, Y.; Taji, H.; Fujita, K.; Watanabe, M.; Harada, N. J. Chromatogr., A 2004, 1055, 41-53. (49) Dungelova, J.; Lehotay, J.; Krupcik, J.; Cizmarik, J.; Armstrong, D. W. J. Sep. Sci. 2004, 27, 983-990. (50) Liu, D. H.; Wang, P.; Zhou, W. F.; Gu, X.; Chen, Z. S.; Zhou, Z. Q. Anal. Chim. Acta 2006, 555, 210-216. (51) Smith, B. D.; Srivastava, R. Thermodynamic data for pure compounds; Elsevier: New York, 1986. (52) Magora, A.; Abu-Lafi, S.; Levin, S. J. Chromatogr., A 2000, 866, 183-194. (53) Chen, B.; Potoff, J. J.; Siepmann, J. I. J. Phys. Chem. B 2001, 105, 30933104. (54) Nita, S.; Cann, N. M.; Horton, J. H. J. Phys. Chem. B 2004, 108, 35123522.
Figure 2. Rational design of the simulation cell beginning with the chiral chromatography column and ending with the dimensions of a typical pore. The rightmost picture shows a snapshot of the simulation cell. In the snapshot, the Whelk-O1 selectors are identified by thick gray lines, the n-hexane solvent is represented with thin gray lines, and R- and S-PEOL are shown in purple and green, respectively.
the simulation cell is collected every 2000 iterations. All simulations are performed with the MDMC program.55 RESULTS AND DISCUSSION The simultaneous presence of a hydrogen bond (H-bond) and a face-to-face ring-ring interaction (“π-π stack”) brings the analyte into proximity with the Whelk-O1 selector, allowing other interactions to be discerned. A recent NMR study14 of analytes in the presence of a modified Whelk-O1 selector showed that analytes that lack an H-bond acceptor were not discriminated by the solvating agent while those without an aromatic ring only interacted weakly. A simulation study36 of chiral epoxides also revealed that the recognition process involved these two specific interactions. These results support the idea that H-bonding and π-π stacking are essential, and we begin with an analysis of analyte-selector interactions based on these two modes of interaction. Further justification for our emphasis on these interactions will be based on comparisons between the 10 analytes. Specifically, the necessity for hydrogen bonding will be evident in the comparison between STBO and DPCP below. Likewise, the comparison between STYO and MOXR presented below will illustrate the importance of π-π stacking. At this point, working definitions for a hydrogen bond and a π-π stack are required. A geometric criterion56,57 is used to define an H-bond: the distance between the hydrogen and the H-bond acceptor should be less than 2.6 Å and the donor-H-acceptor angle should be larger than 150°. This, or similar geometric criteria, have been used in many studies of H-bonding.58,59 A definition for a π-π stack is more problematic. The benzene dimer has been the subject of several recent ab initio studies.60,61 These studies reveal that the slipped parallel configuration is slightly more stable than a T-configuration. Within the simulations, the rings will have a broad range of relative orientations, but (55) Cressman, E.; Das, B. J. D.; Ghenea, R.; Huh, Y.; Nita, S.; Paci, I.; Wang, S.; Zhao, C.; Cann, N. M. Queen’s University, unpublished. (56) Luzar, A.; Chandler, D. Nature 1996, 379, 55-57. (57) Levitt, M.; Sharon, R. Proc. Natl. Acad. Sci. U.S.A. 1988, 85, 7557-7561. (58) Nieto-Draghi, C.; Hargreaves, R.; Bates, S. P. J. Phys. Condens. Matter 2005, 17, S3265-S3272. (59) Andoh, Y.; Yasuoka, K. J. Phys. Chem. B 2006, 110, 23264-23273. (60) Tsuzuki, S.; Honda, K.; Uchimaru, T.; Mikami, M.; Tanabe, K. J. Am. Chem. Soc. 2002, 124, 104-112. (61) Sinnokrot, M. O.; Sherrill, C. D. J. Phys. Chem. A 2006, 110, 1065610668.
unfortunately, few ab initio60 studies include any consideration of ring tilt. We have proceeded by evaluating the average angle between the analyte rings and the DNP group. Illustrative results are shown in Figure 3b. The average angle between the two rings increases sharply from less than 20° to nearly 70°, and the transition occurs when the ring centers are separated by roughly 4.6 Å. Based on this, we define the following: Two aromatic rings form a π-π stack when they have a center-to-center distance of less than 4.6 Å and a ring-ring tilt angle of less than 30°. This criterion, illustrated in Figure 3a, is more stringent than we adopted previously.36 An analyte is “docked” when it simultaneously forms an H-bond and a π-π stack, and the presence of these interactions is determined by the application of the geometric criteria described above. The Whelk-O1 selector has three potential H-bonding sites: the amide hydrogen [H(26)]; the amide oxygen [O(28)]; or one of the nitro oxygens [O(36), O(37), O(39), O(40)]. Likewise, two π-π stacking interactions are possible since the Whelk-O1 selector has two aromatic regions. The Pirkle8 and del Rio29 binding models consider only H-bonding to the H(26) and π-π stacking with the DNP ring, but we consider a total of six possible docking modes. The analysis of the selector-analyte interactions begins with an evaluation of the frequency of interactions. This analysis is summarized in the first four columns of Table 1. At any instant in time, roughly 60-80% of the analytes do not participate in either a π-π stack or an H-bond with a selector. However, 10-30% of the enantiomers form one of these interactions while 2-15% form two interactions. The latter category is dominated by docked analytes but also includes analytes that interact with multiple selectors or form multiple H-bonds or multiple π-π stacks. At first glance, the interaction frequencies in Table 1 suggest that most analytes are “far” from the selector. In fact, this is not the case. The H-bond and π-π stack definitions adopted here are stringent. By relaxing these conditions slightly, for example, by increasing the distance criteria for H-bonding and π-π stacking to 3.0 and 5.0 Å, respectively, the number of one- and two-point interactions increase by a few percent. Thus, a significant proportion of the analytes are in the general vicinity of a selector, but many are not quite close enough to the H-bonding sites and the Analytical Chemistry, Vol. 80, No. 7, April 1, 2008
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Figure 3. Definition of a π-π stack and docking arrangements (a). The distance between ring centers (R) must be less than 4.6 Å and the ring tilt angle (θ) is less than 30°. (b) The average ring tilt angle as a function of the center-to-center distance between the DNP ring of the Whelk-O1 selector and the aromatic ring of STYO (S, red solid; R, red dashed) and DPEO (S, blue solid; R, blue dashed). (c) The four docking arrangements (M1-M4) on Whelk-O1. Snapshots show S-PEOL, docked according to each mechanism. Red arrows identify hydrogen bonding and π-π stacking interactions. Note that other selectors, end caps, the solvent, etc., are omitted from the snapshots to highlight the docking arrangements.
aromatic rings of the selector. The snapshot in Figure 2 illustrates this point: most PEOL enantiomers are near the interface but only 2 of the 16 enantiomers are docked at that instant. From Table 1, the frequency of docked interactions varies greatly among the analytes. R-PAMD is the least likely to dock with, on average, only 1.4% of the molecules simultaneously forming an H-bond and a π-π stack at any given time. In contrast, an average of 14.1% of the S,S-DPED enantiomers will be docked at any point in time. Although six docked arrangements are possible, snapshot analysis reveals that only four are probable and these are shown in Figure 3 for S-PEOL. The final four columns in Table 1 identify the relative probabilities for these four docking arrangements. Note that the M1 docking arrangement is consistent with the Pirkle8 and del Rio29 interaction models. M2 was 2430
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identified as an important docking mode for STYO and STBO,36 but to our knowledge, this is the first evidence for M3 and M4 docking. For all analytes, the most frequently docked enantiomer has a preference for the M1 mechanism. In contrast, the other enantiomer adopts multiple docking arrangements. A similar result29 has been observed from the molecular mechanics optimization of docked 1-(4-halogenophenyl)-1-ethylamines on WhelkO1, where the binding of the most retained enantiomer was highly specific, while the other showed multiple low-energy conformations. Similar trends have been noted for other CSPs.22,27 From a thermodynamic perspective, the docking process can be summarized by two equilibria:
R-enantiomer + selector T R-selector (docked)
K1
Figure 4. Comparison of DPCP and STBO. Radial distributions (a) between H(26) and either the epoxide oxygen of STBO (S,S, blue solid; R,R, blue dashed) or the unsubstituted carbon of the DPCP cyclopropane ring (S,S, red solid; R,R, red dashed). Snapshots of R,R-DPCP with Whelk-O1 are shown in (b). The dominant docking modes for S,S-STBO (c) and R,R-STBO (d) are shown for comparison. For clarity, analyte carbons are yellow.
S-enantiomer + selector T S-selector (docked) K2
(1)
where K1 and K2 are equilibrium constants for the docking process. The separation factor is
R)
Ka ) Kb [most retained]docked/[most retained]undocked [least retained]docked/[least retained]undocked
(2)
where R is unity or larger. Theoretical estimates of the separation factor, Rcalc, can be obtained from eq 2 via the docking frequencies since they reflect the equilibria in eq 1. The agreement between theory and experiment in Table 1 is outstanding, considering that the experiments were performed with a range of cosolvents, in different proportions. The only exception is PAMD, where the
simulations significantly underestimate the separation factor. To confirm that docking modes have been well explored, several 3-5 ns simulations were carried out for PAMD and these also underestimate the separation factor. Since PAMD is flexible and branched, relative to the other analytes, some docking modes may require even longer times and may not be sampled sufficiently in the simulations. On the other hand, PAMD is particularly complex since the enantiomers have very distinct docking preferences and these involve analyte and selector torsion: docking probabilities may be sensitive to details of the potential. Regardless, simulations correctly predict a PAMD separation factor that is much larger than for the other analytes (Table 1). Absolute elution orders have been determined from experiment for STYO62 and PAMD63 and the most retained enantiomers are S-STYO and S-PAMD. Elution orders can be extracted from the simulations by identifying the enantiomer that interacts most frequently with the Whelk-O1. Table 1 reveals that the docking Analytical Chemistry, Vol. 80, No. 7, April 1, 2008
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Table 1. Interaction Summary for the 10 Analytes on Whelk-O1 Extracted from MD Snapshot Analysisa analyte
STYO STBO DPCP MOXR PEOL PEAM PEDO DPED DPEO PAMD
interaction frequency
S R S,S R,R S,S R,R S R S R S R S R S,S R,R S R S R
docking arrangement
0
1
2
3
docked
63.6 66.8 62.5 65.6 66.6 69.0 88.0 88.2 63.8 63.7 66.4 69.0 65.7 64.0 56.7 59.1 66.6 62.8 79.7 82.7
26.3 25.4 23.5 24.7 30.1 28.7 12.0 11.8 26.5 25.8 22.7 20.7 23.0 25.0 25.3 24.6 23.8 23.2 14.8 14.7
10.1 7.8 13.0 9.1 3.3 2.3 0 0 9.0 9.9 9.9 9.0 10.0 9.3 15.1 13.3 8.9 13.2 5.4 2.5
