Proc. Nati. Acad. Sci. USA Vol. 89, pp. 1822-1826, March 1992 Biophysics

Molecular interactions in binary solids: Crystal structure of a cholesteryl ester solid solution (x-ray crysalography/neutral lipids/molecular copaddug)

DOUGLAS L. DORSET AND WALTER A. PANGBORN Medical Foundation of Buffalo, Inc., 73 High Street, Buffalo, NY 14203

Communicated by Herbert A. Hauptman, November 21, 1991 (received for review July 29, 1991)

The x-ray crystal structure analysis of a choABSTRACT lesteryl ester solid solution, cholesteryl undecanoate/cholesteryl laurate in a molar ratio 0.52/0.48, is described. The unit cell is monoclinic with a = 13.005(2) A, b = 9.005(1) A, c = 31.421(3) A, and 18 = 90.82(1)° and the space group P21 with Z = 4 (two molecules per asymmetric unit). Thus, the d4,j spacing is almost the value predicted by Vegard's law from the values for the pure compounds. The room-temperature crystal structure is very much like that of cholesteryl laurate monolayer I packing, in the form where the esterifled fatty acid chains are fully extended, with no salient sign of conformational disorder seen in this binary solid. The final R factor for 6571 observed reflections is 0.097.

Table 1. Unit cell dimensions Solid Cholesteryl Parameter solution undecanoate (10) 13.009 (6) a, A 13.005 (2) 9.005 (1) 9.006 (7) b, A c, A 31.421 (3) 31.063 (9) 90.82 (1) 90.60 (4) 3, 0 1.013 1.013 Pcalc' g-cm3 Numbers in parentheses are standard deviations.

Cholesteryl laurate (11) 12.989 (8) 9.008 (5) 32.020 (14)

91.36 (5) 1.009

compensate for the chain-length difference in a fashion which is very similar to the copacking in binary n-alkane lamellae (9), since the methylene chain regions are sequestered. Stabilization of such a solution in the monolayer I structure was more difficult to interpret in terms of a crystal structure, on the other hand, because the polymethylene chains pack next to sterol rings and thus do not form a methylene subcell. Nevertheless, superposition of crystal structures for two esters (10, 11) in the monolayer I structure, which differ by one methylene group, also reveals them to occupy very similar molecular volumes (5). Recently, considerable progress has been made toward understanding how molecular volume differences can cause phase separation in relatively simple layer structures such as the n-alkanes (9, 12), leading to the discovery of solid-state diffusion processes which can be described by subtle sequences of changing crystal structure (including epitaxial relationships across grain boundaries in phase-separated mixtures). A similar understanding of such phase separation in more complicated cholesteryl ester layers would be expected to require a starting packing model for a solid solution that is more exact than the cartoon obtained by merely superimposing the crystal structures of the pure components. This paper describes the quantitative x-ray crystal structure analysis of a nearly 1:1 solid solution of cholesteryl undecanoate with cholesteryl laurate (dodecanoate), where it is shown that the room temperature crystal structure of the longest chain component is closely preserved.

Because of their importance as components of immobilized lipid masses in diseases such as atherosclerosis, cholesteryl esters have been extensively studied in recent years in terms of their solid-state and liquid-crystalline behavior (1). From the extensive crystallographic work of Craven and his coworkers (ref. 2, for example), it is now known that many of these neutral lipids often crystallize in one of three preferred layer packing arrays, each of which has a unique expression of sterol-sterol, chain-chain, and chain-sterol interactions. Geometric parameters obtained from these crystal structures have been very important for postulating which molecular conformations and pairwise clusterings are most important in the liquid-crystalline state expressed by such lipid masses in vivo (1). No less important is how molecular geometry will influence the stability of a solid solution or a solution in the liquidcrystalline state, since natural accumulations of cholesteryl esters are a polydisperse combination of chain lengths. In the last several years, extensive studies of cholesteryl ester binary solids (3-7) have shown that the parameters which govern the formation of a stable solid solution are essentially the ones postulated originally for molecular crystals by Kitaigorodskii (8). Hence, for a solid solution to occur, the molecular components must be able to pack, first of all, in the same layer structure (4). Two esters with nearly the same molecular volume, therefore, will not be able to form a solid solution, if each will prefer its own unique crystal structure. However, within a layer packing common to a chain-length series, relative molecular volumes are the single factor that influences the stability of the crystalline-solid solution (4, 5). In an initial study of solid solutions within a given layer packing motif, it was found that an acyl chain-length difference of just one carbon atom resulted in melting behavior close to that predicted from Roautlt's law (5). For one of the crystal structure types studied, solid solutions in the bilayer form [using Craven's nomenclature (2)] could be imagined to

MATERIALS AND METHODS Cholesteryl undecanoate and cholesteryl dodecanoate (laurate), obtained from Nu Chek Prep (Elysian, MN) and stated to be >99% pure, was weighed into a vial in a molar ratio 0.52/0.48, and this mixture was dissolved in warm amyl alcohol. After this solution was poured into a beaker, evap-

oration was allowed to occur at room temperature for several weeks to form narrow lath crystals [major crystal face (001)], elongated along [010]. A crystal suitable for diffraction measurements (0.12 x 0.45 x 0.55 mm) was chosen by inspection of oscillation and Weissenberg photographs. Approximate unit cell constants were measured from these films. This crystal was mounted on an Enraf Nonius CAD-4 diffractometer for x-ray intensity data collection with Ni-filtered Cu Ka radiation. Accurate

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Biophysics: Dorset and Pangbom

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FIG. 1. Numbering scheme for the cholesteryl ester structure. The symbol for carbon is omitted.

unit cell parameters were determined by a least-squares fit to 25 reflections measured within the angular limits 21.090 < 20 < 29.37°. Intensity data collection at room temperature was monitored by periodic measurement of intensity values for six standard reflections to detect the occurrence of radiation damage to the crystal. In all, 8056 unique reflections were measured, of which 1478 were judged to be unobserved, based on the criterion that 1Fol < 3.0olFoI.

STRUCTURE ANALYSIS The unit cell is found to be monoclinic with dimensions comparable to those measured for the pure components at

FIG. 2. Molecular packing of the cholesteryl undecanoate/ cholesteryl laurate solid solution in a projection down the unit cell b axis. The two molecules of the asymmetric unit are labeled A and B.

room temperature (Table 1). The noncentrosymmetric space group for all these examples is P21 (13) with two molecules in the asymmetric unit. The unit cell parameters are intermediate between the ones found for the pure compounds. Indeed, the measured doo, = c sin (3 = 31.418 A value for the solid solution can be compared to the expected value 31.517 A [or 31.503 A if the length measured by Dahldn (14) for cholesteryl laurate is used], assuming Vegard's law (15) and an assumed laurate mole fraction X12 = 0.48. (Although the actual molar composition of this crystal is unknown, it should be near this value if the solidus and liquidus curves are close to one another.) Heating the solid-solution single crystals on a hot stage (87.70C -. 88.20C) indicates the melting point to be below that of the pure components (4) and that there may be slight differences in crystalline composition in the batch. Assuming the structure of the solid solution to be related to that of its pure components, a trial model was constructed from previously determined atomic coordinates (10, 11). (The atomic numbering scheme is represented in Fig. 1.) At first, only the cholesteryl nuclei were included, then initial segments of the esterfied acyl chains were added. Additional chain atom positions were then sought from electron density maps based on the phases estimated initially from the molecular fragments. All acyl chain carbon atoms were located for the A chain but only eight were found for the B chain, with an unresolved positive density region extending beyond these latter peak positions. The last four carbon positions were then added as suggested by the crystal structure of the laurate (11). Full matrix least-squares refinement was carried out on the increasingly large segments of the molecule with anisotropic thermal parameters used for atoms within the steroid nucleus and those immediately attached to it. Outer segments of the isoprenoid and acyl chains, when located in the map, were refined, assuming isotropic mean-square atomic displacements. After the last refinement cycle, hydrogen atom positions were added to the atoms with the smallest thermal motion, generated at theoretical positions. The final R factor for all atoms refined against 6571 reflections (rejecting 7 low-angle measurements on the basis of a normal probability distribution) is 0.097. The weighted R = 0.129 and the unweighted R including all unobserved reflections is 0.106.

RESULTS The molecular packing of the binary solid solution is very much like that expected for cholesteryl laurate (11) (Fig. 2) or any other representative monolayer I-type cholesteryl ester crystal structure (2). For the molecular pair in the asymmetric unit, one, designated A in Fig. 2, many atoms have reasonably small thermal vibrational amplitudes. The largest motion is found at the end of the C17 isoprenoid side chain (Fig. 3a). This is contrasted with molecule B (Fig. 2), for which the acyl chain has very large thermal displacements, particularly at

W;V

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Biophysics: Dorset and Pangborn

1824 a

occupancy 0.48

1. b

03

found by Sawzik for the laurate at room temperature (16). Therefore, the regions of relatively small thermal motion in the crystal are found to form a tightly packed layer, whereas the segments with larger vibrational amplitude are located at molecular interfaces (Fig. 2). As has been often noted, this is characteristic of the monolayer I crystal structures (10, 16).

2

s

E

028

FIG. 3. Two molecules of the asymmetric unit viewed onto the plane of the cholesterol ring. Thermal motion is represented by 50% probability ellipsoids. (a) Molecule A. (b) Molecule B. In this study, the partial occupancy of the terminal methyl group is assumed to be identical for both molecules of the asymmetric unit.

the chain end (Fig. 3b), whereas the isoprenoid side chain for this molecule has relatively small vibrational motion. The thermal parameters (Table 2) are quite similar to the values

In general, bond distances and angles calculated from the final atomic coordinates (Table 2) are consistent with the values expected for such structures. Because of the large mean-square atomic displacements at the molecular interfaces, some bond distances in the outer part of the acyl chain of molecule B and the isoprenoid chain of molecule A are somewhat unreliable, as was also found for the cholesteryl laurate structure at room temperature (11). Molecular conformations are consistent with earlier determined structures (16). Both isoprenoid side chains are fully extended with torsion angles very similar to the values found for the higher-temperature laurate structure. In addition, within the uncertainty of diffuse electron density distribution for the B chain, both acyl chains are fuilly extended with approximate trans

Table 2. Atomic coordinates and isotropic thermal parameters for cholesteryl undecanoate/laurate solid solution Molecule A Molecule B y/b x/a y/b Atom x/a Biso, A2 Atom z/c z/c Biso, A2 0.2257 0.1616 Cl -0.2810 0.0984 6.8* Cl -0.4844 -0.0485 6.3* 0.1844 7.2* -0.5428 0.1217 C2 -0.3260 0.0742 C2 -0.0930 7.3* C3 -0.2424 6.7* -0.5165 0.0278 0.1085 7.2* 0.0803 -0.1250 C3 7.2* -0.0801 0.1429 C4 -0.1613 -0.0401 C4 -0.5403 -0.1158 7.3* -0.1206 6.5* -0.4885 -0.0380 0.1844 6.0* C5 -0.0273 -0.0712 CS C6 -0.0182 -0.0249 8.0* -0.1389 0.2065 6.3* -0.0638 C6 -0.4346 C7 0.0311 -0.0149 8.3* -0.1100 0.2482 6.5* -0.0213 C7 -0.3797 5.6* C8 -0.0419 -0.0388 7.0* -0.4120 0.0358 0.2685 0.0159 C8 C9 -0.1445 0.0390 0.0062 6.5* -0.4223 0.1578 0.2355 5.5* C9 -0.1979 -0.0169 6.6* 0.1215 0.1999 5.9* C10 -0.0351 -0.5018 C10 6.7* ClH -0.2169 0.0362 0.0446 8.2* 0.3125 0.2558 ClH -0.4390 6.6* -0.1655 0.0891 C12 0.0864 9.0* 0.3520 0.2912 C12 -0.3611 5.8* -0.0664 0.0029 0.2266 C13 0.0963 8.3* -0.3565 0.3261 C13 5.8* C14 0.0021 0.0191 0.0569 8.2* 0.0814 0.3034 -0.3340 C14 6.5* -0.0405 C15 0.1073 0.0730 10.4* -0.0264 0.3384 -0.3091 C15 6.8* C16 0.1142 0.0124 0.1187 11.9* 0.0683 0.3714 -0.2572 C16 6.3* C17 0.0053 0.0684 0.1313 9.4* 0.2343 0.3570 C17 -0.2668 7.0* -0.1625 C18 -0.0899 0.1066 10.1* 0.2248 -0.4586 0.3502 C18 6.8* -0.1711 C19 -0.2482 -0.0299 8.0* -0.6118 0.1378 0.2160 C19 6.8* 0.0429 0.1786 12.2* C20 -0.0180 0.3492 0.3948 C20 -0.2702 7.8 0.1906 C21 -0.1275 0.0817 14.3* 0.5125 0.3799 -0.2846 C21 8.1 0.1284 0.2066 12.2 C22 0.0590 0.3213 0.4200 C22 -0.1665 10.0 0.2528 0.0552 0.0929 16.6 0.4662 C23 0.3822 C23 -0.1717 11.1 0.1807 0.2785 C24 0.1359 17.1 0.4925 0.3485 C24 -0.0678 15.8 0.1351 0.3260 C25 0.1467 25.9 0.4332 0.5315 C25 -0.0763 19.8 0.2183 0.3443 C26 0.2338 31.5 0.5519 0.4193 C26 -0.1669 19.7 0.1842 0.3487 0.0536 C27 30.3 0.4094 0.5465 C27 0.0210 8.6* 0.1350 -0.1990 C28 -0.2630 6.8* 0.0301 0.0334 C28 -0.5515 10.0 -0.2380 0.0957 C29 -0.3200 6.6* -0.02% -0.0015 -0.6205 C29 11.0 0.2063 -0.2739 -0.3118 C30 6.7* -0.0444 -0.6074 0.0392 C30 12.0 -0.3732 0.1616 -0.3130 C31 7.2* -0.0769 -0.6839 -0.0176 C31 14.2 0.2740 -0.3494 C32 -0.3702 6.7* -0.1197 -0.6796 0.0577 C32 15.8 -0.3885 -0.4369 0.2163 C33 7.3 0.0068 -0.1487 -0.7674 C33 23.3 -0.4241 -0.4343 0.3403 C34 7.6 0.0898 -0.1913 -0.7736 C34 26.8 0.2868 -0.4599 C35 -0.5121 9.4 0.0523 -0.2169 C35 -0.8697 29.9 0.4090 -0.4760 C36 -0.5197 10.9 0.1417 -0.8801 -0.2584 C36 35.3 0.3403 -0.5170 C37 -0.6180 14.9 C37 -0.9740 0.0921 -0.2847 52.6 -0.5262 -0.65% 0.4282 C38 14.9 0.2028 -0.3233 C38 -0.9906 57.9 0.4188 -0.5560 C39t -0.7742 19.3 C39t -1.0737 0.1449 -0.3521 8.2* -0.1667 0.0527 03 -0.2889 6.9* -0.0190 0.0715 03 -0.5782 17.4* 0.2218 -0.1958 028 -0.1937 0.1179 0.0281 8.5* -0.4801 028 *Atom refined anisotropically; equivalent isotropic thermal parameter (B1s.) listed. tAtom refined with occupancy of 0.48.

Biophysics: Dorset and Pangbom conformations for all bonds, contrasting with the conformational disorder found at a cholesteryl laurate chain end by Dahldn (14). [The laurate structure determined by Sawzik and Craven (11), on the other hand, has fully extended B-acyl chains at room temperature, including the chain termini. Note, however, that an isotropic B = 58 A2 reported for the partially occupied C39 in molecule B (Table 2) corresponds to an rms displacement of 0.86 A.]

DISCUSSION Given the difference in measured average molecular volumes for cholesteryl undecanoate (10) and cholesteryl laurate (11) at room temperature-i.e., A = 26.6 A3-it is not surprising that the two molecules form continuous solid solutions at all concentrations. The degree of similarity defined by Kitaigorodskii (8), E = 1 - (Air) = 0.97, where r = 909.7 A3, is the overlap volume for the two pure molecules, is certainly well within allowable range for such cosolubility. What is surprising from the crystal structure analysis is that there is no salient conformational disorder detected at the molecular layer interface, despite the reported observation of such disorder in one crystal structure determination of pure cholesteryl laurate (14). [Of course, the high thermal motion of chain atoms at this interface may obscure the fact that the two room-temperature crystal structures could be identical, even though a possible solvent effect on the crystallization of this structure has been mentioned (16).] The prospect for interfacial packing disorder is more likely for rapidly crystallized samples. Electron diffraction measurements of binary solids of this ester pair epitaxially oriented by cooling a comelt with benzoic acid (4) show that the lamellar spacing is nearly constant for large concentration domains, with solids containing less than 45 mol% cholesteryl laurate crystallizing as cholesteryl undecanoate and those with a larger concentration crystallizing as the laurate structure. Similar steplike increases of lamellar spacing have been noted for the n-paraffins (12). In terms of crystal density, the binary solids crystallizing as the undecanoate structure would start with a value of 1.013 g cm-3 at 0 laurate concentration and increase to 1.024 at X12 = 0.45. Those solids in the laurate structure would decrease from 1.009 g-cm-3 to 0.996 g cm-3 at X12 = 0.5. Thus, since a twisted acyl chain is found for the high-density cholesteryl laurate structure (p = 1.036 gcm-3) at 198 K (17), it is likely that the laurate-rich solids in the undecanoate structure may also contain this sort of interfacial disorder. The near adherence to Vegard's law found in this slowly crystallized solid solution is expressed by a crystal which has the same calculated density as pure cholesteryl undecanoate (10). Molecular lengths including the fractional atomic position-i.e., 31.6 A for molecule A and 30.4 A for molecule B-are identical to the values found for the laurate structure (16), but the projected molecular lengths along doo1 are somewhat shorter than the values for laurate-i.e., 28.2 A and 28.4 A, respectively, vs. 28.6 A and 28.8 A (16). Hence, if the terminal atom positions on the acyl chains had unit occupancy, the structure would be somewhat more crowded, since the molecular tilt is unchanged. This effect can be demonstrated further by a listing of intermolecular packing distances for some atoms near the layer interface (Table 3). In general, these distances are smaller than comparable values calculated from the room temperature laurate crystal structure (11). The observed unit cell shortening is the most obvious consequence of the solid solution formation, because otherwise there is no sign of increased molecular disorder or atomic thermal motion to fill a "void." These interesting results point to further experiments. For many solid solutions, there is a theoretical critical temperature below which phase separation occurs (12). When the

Proc. Natl. Acad. Sci. USA 89 (1992)

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Table 3. Selected intermolecular atomic distances for the cholesteryl esters at sites near the layer interface Intermolecular distance, A Cholesteryl Cholesteryl undecanoate laurate Solid (298 K) (298 K) solution Atoms 3.95 4.07 3.96 BC35-BC38 4.03 3.62 BC39-BC26 4.34 4.16 AC39-BC27 4.78 4.51 4.39 AC38-BC25 4.66 4.72 4.61 AC34-BC21 Note that C26 and C27 positions in the crystal structures of the pure compounds (10, 11) are relabeled to correspond to the orientation found in the solid-solution structure (Table 2).

low-temperature structure analysis of cholesteryl laurate (17) is used as a guide, it is clear that a similar analysis of this solid solution at 198 K would enable us to investigate packing constraints for a denser structure. This may lead to ideas about fractionation mechanisms, particularly since the smaller atomic motion found at this temperature (17) will permit a more precise determination of acyl chain geometry. It will also be interesting to investigate the structure of solid solutions formed from esters with greater molecular volume differences-e.g., the calculated degree of similarity for cholesteryl caprate/cholesteryl laurate (a difference of two methylene groups in the acyl chains) is E = 0.94, again well within the range of continuous cosolubilization, as verified by our experimental phase diagram (5). An x-ray data set for a near-1:1 solid solution of these esters again results in a c sin p value (31.13 A) that is between the values determined for the pure caprate (30.2 A) (18) or laurate (32.0 A). The space group remains the same and the a and b values are again nearly the same as those found for the pure compounds. Additionally, the copacking of other crystalline forms should be investigated, and crystals of a nearly 1:1 molecular composition in the bilayer structure (2)-i.e., cholesteryl myristate/cholesteryl pentadecanoate-have been grown for this purpose. Appreciation of the molecular packing constraints in such binary solids will therefore enable us to propose more accurate models for polydisperse smectic layers relevant to neutral lipid accumulation in vivo. The research described in this paper was funded in part by grants from the Baird Foundation and the Cummings Foundation. 1. Ginsburg, G. S., Atkinson, D. & Small, D. M. (1984) Prog. Lipid Res. 23, 135-167. 2. Craven, B. M. (1986) in Handbook of Lipid Research, ed. Small, D. M. (Plenum, New York), Vol. 4, pp. 149-182. 3. Small, D. M., ed. (1986) in Handbook of Lipid Research (Plenum, New York), Vol. 4, pp. 450-466. 4. Dorset, D. L. (1987) J. Lipid Res. 28, 993-1005. 5. Dorset, D. L. (1988) Biochim. Biophys. Acta 963, 88-97. 6. Dorset, D. L. (1990) Biochim. Biophys. Acta 1046, 57-63. 7. Dorset, D. L. (1990) Biochim. Biophys. Acta 1046, 195-201. 8. Kitaigorodskii, A. I. (1961) Organic Chemical Crystallography (Consultant's Bureau, New York), pp. 231-240. 9. Dorset, D. L. (1990) Proc. Natl. Acad. Sci. USA 87, 85418544. 10. Sawzik, P. & Craven, B. M. (1980) Acta Crystallogr. Sect. B 36, 215-218. 11. Sawzik, P. & Craven, B. M. (1979) Acta Crystallogr. Sect. B 35, 789-791. 12. Dorset, D. L. (1990) Macromolecules 23, 623-633. 13. Henry, N. F. M. & Lonsdale, K., eds (1969) International Tables for X-Ray Crystallography (Kynoch, Birmingham, U.K.), Vol. 1, 3rd Ed. 14. Dahldn, B. (1979) Chem. Phys. Lipids 23, 179-188.

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15. Azaroff, L. V. (1975) Introduction to Solids (Krieger, Huntington, NY), p. 290. 16. Sawzik, P. (1984) Ph.D. thesis (University of Pittsburgh, PA).

Proc. NatL. Acad. Sci. USA 89 (1992) 17. Sawzik, P. & Craven, B. M. (1980) Acta Crystallogr. Sect. B 36, 3027-3033. 18. Pattabhi, V. & Craven, B. M. (1979) J. Lipid Res. 20, 753-759.