Epitaxial Relationships between Cholesterol Crystals and Mineral Phases: Implication for Human Disease M. Crina Frincu, Richard E. Sharpe, and Jennifer A. Swift* Department of Chemistry, Georgetown University, 37th and “O” Streets NW, Washington, DC 20057-1227
CRYSTAL GROWTH & DESIGN 2004 VOL. 4, NO. 2 223-226
Received September 26, 2003
ABSTRACT: Human gallstones and atherosclerotic plaques are heterogeneous materials that consist of a variety of components, including crystalline cholesterol and assorted mineral phases. EpiCalc, a modeling algorithm that uses a simple geometric lattice matching protocol, was used as a screening tool to identify those surfaces of calcium carbonate and calcium phosphate that could potentially serve as epitaxial substrates for the nucleation and growth of anhydrous cholesterol (Ch) and cholesterol monohydrate (ChM) crystals. A surprisingly large number of coincident epitaxial relationships were identified, with the best match found between calcite (101 h 4) and ChM (001). The deposition of cholesterol crystals in vivo is an undesirable crystallization process that is implicated in a variety of human diseases including the formation of gallstones and atherosclerotic plaques. Although a detailed step-by-step formation of these complex biomaterials is not yet fully understood, the nucleation of cholesterol crystals is regarded as an important step in their formation. While homogeneous nucleation of cholesterol is possible under high supersaturation conditions, heterogeneous nucleation is generally regarded as a more energetically favorable process. In fact, a number of soluble species have been identified as possible cholesterol nucleators.1 The influence of insoluble impurities in solution on cholesterol precipitation has been given somewhat less attention to date, although it is well-known that epitaxial relationships between the surfaces of inorganic and bioorganic crystals can be an important factor in crystal nucleation and growth processes under a variety of biological environments.2-4 Crystalline cholesterol deposited under model bile or other aqueous conditions is typically in the form of cholesterol monohydrate (ChM), although there is evidence that the deposition of metastable intermediates including anhydrous cholesterol (Ch)5,6 and/or polymorphs of unknown structure7 may precede monohydrate formation. ChM is known to adopt a bilayer-type structure (P1: a ) 12.39, b ) 12.41, c ) 34.36, R ) 91.9°, β ) 98.1°, γ ) 100.8°)8 in which bilayers measuring 33.9 Å in height are stacked along c. The long axes of the molecules are nearly parallel and are tilted by ∼17° from the normal to the (001) plane. At the bilayer interface, the C3 hydroxyl groups and water molecules form a slightly puckered 2-dimensional hydrogen bonded network. ChM crystals adopt a platelike morphology when grown from bile9 and/or aqueous organic solutions.10 The largest plate face is always (001), with smaller low index (100), (010), (011), and (101) side faces. The plate morphology is consistent with faster growth within the bilayer plane (stronger intermolecular interactions). Anhydrous cholesterol crystals (Ch) also have a known structure (P1: a ) 14.17, b ) 34.21, c ) 10.48, R ) 94.64°, β ) 90.67°, and γ ) 96.32°).5 Their crystal packing consists of infinite one-dimensional hydrogen bonded chains along c (the fast growth direction), which align in parallel to form a corrugated sheet in the ac plane. Ch crystals adopt a characteristic needle or filament-type habit in which the * To whom correspondence should be addressed. E-mail: georgetown.edu.
jas2@
Figure 1. Schematic of a generic molecular overlayer with lattice parameters (a1, a2, R) on a rigid substrate with lattice constants (b1, b2, β). EpiCalc calculations rotate the two surfaces relative to one another through all azimuthal angles (θ). When the two surfaces come into registry at some value of (θ), they are said to be epitaxially matched.
terminal crystal faces are likely a combination of (010), (100), and (001). Cholesterol gallstones are heterogeneous polycrystalline composites that consist primarily of cholesterol (∼85 wt %), but also contain significant concentrations of bile pigments, calcium salts, and phosphates. Many of the mineral phases present in gallstones have been previously identified, through analysis of stone microstructure using light microscopy, infrared spectroscopy,11 X-ray diffraction studies,12 and scanning electron microscopy after plasma etching.13 Among the most common minerals found are the three polymorphs of calcium carbonate (i.e., calcite, aragonite, and vaterite) as well as calcium phosphates such as hydroxyapatite.13 These minerals are often present in the core (nidius) of the stone, as well as radially distributed in the in the successive outer rings and/or shell of the stones.14 The common coexistence of minerals and crystalline cholesterol phases led Lonsdale15 as early as 1968 to suggest that epitaxial relationships between organic and inorganic phases may be important factors contributing to the formation of human stones. Epitaxy is defined as the growth of one crystal on the substrate of another, such that there is at least one preferred orientation and a near geometrical fit between the contacting surface lattices. When a lattice-matched “seed” is present in solution, the barrier to nucleation can be significantly reduced, such that crystal nucleation occurs
10.1021/cg034180a CCC: $27.50 © 2004 American Chemical Society Published on Web 11/14/2003
224
Crystal Growth & Design, Vol. 4, No. 2, 2004
Communications
Table 1. Coincident Epitaxial Matches (V/Vo E 0.5) between Cholesterol Monohydrate (ChM) and Calcium Carbonate Substrates
Table 2. Coincident Epitaxial Matches (V/Vo E 0.5) between Cholesterol Monohydrate (ChM) and Calcium Phosphate Substrates
mineral surface
mineral surface
ChM surface
θ (supercell dimensions)
(010) (001) (011) (021) (110) (010) (001) (011) (021) (110) (010) (001) (011) (021) (010) (001) (011) (110) (021) (110) (001)
Aragonitea (001) (001) (001) (001) (010) (010) (010) (010) (010) (100) (100) (100) (100) (100) (011) (011) (011) (101) (101) (011) (101)
(101 h 4) (0001) (011 h 2) (101 h 0) (101 h 1) (112 h 0) (0001)
Calciteb (001) (001) (001) (001) (001) (010) (010)
(101 h 1) (011 h 2) (101 h 0) (0001)
(010) (010) (010) (100)
(011 h 2) (101 h 0) (101 h 1) (0001) (011 h 2) (101 h 1) (0001) (101 h 0) (101 h 1)
(100) (100) (100) (011) (011) (011) (101) (101) (101)
39° (2 × 2)* 58° (5 × 4), 38° (3 × 1) 25° (2 × 2) 39° (2 × 2) 31° (2 × 2) 5° (3 × 2), 45° (2 × 7) 32° (3 × 1), 9° (5 × 4), 57° (3 × 5) 0° (5 × 3), 26° (2 × 5) 52° (1 × 7) 0° (5 × 3) 19° (3 × 2), 42° (3 × 2), 56° (3 × 4) 23° (2 × 5), 54° (1′7) 0° (3 × 1) 0° (3 × 2), 30° (2 × 4) 0° (7 × 2), 42° (9 × 1) 33° (5 × 2) 38° (5 × 2) 10° (3 × 6), 51° (7 × 2) 25° (7 × 1) 43° (5 × 2)
(0001) (0001) (101 h 0) (0001) (101 h 0) (0001)
Vateritec (001) (010) (010) (100) (011) (011)
48° (2 × 1) 0° (2 × 1) 38° (2 × 2) 55° (1 × 4) 26° (4 × 1), 39° (2 × 1) 3° (6 × 1), 56° (1 × 2) 0° (5 × 1), 58° (5 × 1)
13° (2 × 1) 51° (2 × 3) 13° (2 × 1) 52° (2 × 3) 51° (2 × 6) 15° (2 × 2), 23° (4 × 7) 23° (3 × 5) 15° (2 × 2), 49° (3 × 9) 56° (1 × 4) 50° (2 × 6) 26° (2 × 3) 57° (1 × 4) 62° (1 × 5) 55° (1 × 4) 26° (6 × 1) 33° (4′ × 1) 26° (6 × 1) 19° (7 × 1) 32° (5 × 1) 33° (6 × 2) 37° (4 × 1)
a Aragonite (CaCO ): orthorhombic space group Pmcn, a ) 3 4.959, b ) 7.968, c ) 5.741. b Calcite (CaCO3): trigonal space group R3c, a ) 4.989, c ) 17.062. c Vaterite (CaCO3): hexagonal space group P63/mmc, a ) 7.135, c ) 16.98.
from solutions with lower supersaturation levels. Epitaxy is usually assessed computationally in two ways, either by potential energy (PE) calculations or by using a simpler modeling algorithm based on geometric lattice matching. For molecular crystal systems, which contain many different types of atoms and multiple molecules per unit cell, PE calculations can be computationally intensive. Simple geometric matching can be performed in a much shorter amount of time, and has been shown in many cases to give similar predictions as PE calculations.16,17 Although geometric matching alone does not provide information about the energetics of the interface, it is still a very useful predictive tool for identifying possible epitaxial relationships, especially for molecular crystal systems.
(0001) (202 h 1) (101 h 1) (0001) (202 h 1) (202 h 1) (0001) (101 h 1) (101 h 1) (010) (1 h 11) (001) (010) (11 h 1) (120) (1 h 01) (001) (010) (11 h 1) (1 h 11) (120) (1 h 01) (1 h 11) (010) (100)
ChM surface
θ (supercell dimensions)
Hydroxyapatitea (001) 39° (3 × 1) (001) 39° (3 × 5) (100) 21° (1 × 3) (100) 0° (1 × 2), 44° (1 × 1) (101) 36° (5 × 2) (010) 39° (2 × 6) (010) 39° (3 × 2) (011) 20° (3 × 1) (010) 22° (1 × 3) Brushiteb (001) (001) (001) (100) (100) (100) (100) (101) (011) (011) (011) (010) (010) (010) (010)
35° (1 × 2) 0° (3 × 1) 0° (5 × 1) 58° (2 × 3) 54° (1 × 7) 56° (1 × 2) 12° (2 × 1) 31° (1 × 4) 3° (6 × 1) 56° (1 × 2) 34° (1 × 6) 60° (1 × 1) 0° (1 × 7) 59° (1′ × 5) 2° (2 × 1) 31° (1 × 3) 57° (2 × 3)
Octacalcium Phosphatec (101) 29° (5 × 1)
a Hydroxyapatite (Ca (PO ) OH): hexagonal space group P6 / 5 4 3 3 m, a ) 9.418, c ) 6.875. b Brushite (CaHPO4‚2H2O): monoclinic space group I2/a, a ) 5.88, b ) 15.15, c ) 6.37, β ) 117.46°. c Octacalcium phosphate (Ca H (PO ) ‚5H O): triclinic space group 8 2 4 6 2 P1, a ) 19.87, b ) 9.63, c ) 6.88, R ) 89.3°, β ) 92.2°, γ ) 108.9°.
In the present study, the program EpiCalc18 was utilized as a screening tool to identify those naturally occurring faces of calcium carbonate and calcium phosphate which are lattice-matched with ChM and Ch surfaces. This software is available as a free download from the web.19 EpiCalc calculations are based on a simple analytic function that measures the degree of geometric “fit” between two chemically different surfaces. The program rotates the organic overlayer (b1, b2, β) with respect to a mineral substrate (a1, a2, R) through a series of azimuthal angles (θ) (See Figure 1). The degree of epitaxy is given as a dimensionless figure of merit, V/Vo, which ranges from 0 to 1. Commensurate surfaces (V/Vo ) 0) are those in which a perfect geometric match exists between every overlayer and substrate lattice position at a given θ angle. A subset of geometrically matched lattice positions exists for coincident surfaces (V/Vo ∼ 0.5) at a given θ. Incommensurate surfaces do not match at any θ angle (V/Vo ) 1). Therefore, the smaller the value of V/Vo, the better the geometric match. Because the intermolecular interactions that hold molecular overlayers together are comparatively weaker than the covalent bonds in minerals, overlayer structures can be particularly sensitive to competition between energy lowering overlayer-substrate interactions and energetic penalties associated with (even minor) overlayer lattice reconstruction. Therefore, all EpiCalc calculations allowed for the organic overlayer lattice parameters to be systematically varied by a modest amount, typically up to (5.0% of the unit cell dimensions. From the outset, coincident epitaxial matches were believed to be more probable than commensurate matches, since the unit cell dimensions of molecular crystals are significantly larger than those of minerals. Unit cell parameters of each of the three polymorphs of calcium
Communications
Crystal Growth & Design, Vol. 4, No. 2, 2004 225
Table 3. Coincident Epitaxial Matches (V/Vo E 0.5) between Anhydrous Cholesterol (Ch) and Calcium Carbonate Substrates mineral surface
Ch surface
θ (supercell dimensions)
(021) (012) (011) (010) (001) (010) (110) (012) (021) (001) (010) (110) (011)
(010) (010) (010) (010) (010) (100) (100) (100) (100) (100) (001) (001) (001)
Aragonitea 58° (1 × 1) 37° (1 × 1) 32° (2 × 1) 21° (5 × 1), 35° (2 × 1) 21° (3 × 1), 55° (1 × 1) 25° (5 × 1) 17° (7 × 1) 28° (3 × 1) 34° (4 × 1) 47° (3 × 1) 39° (2 × 4) 45° (2 × 6) 39° (2 × 4)
(101 h 4) (011 h 2) (112 h 0) (0001) (011 h 2) (101 h 1) (112 h 0) (101 h 0) (0001) (0001) (101 h 0) (112 h 0) (101 h 1)
(010) (010) (010) (010) (100) (100) (100) (100) (100) (001) (001) (001) (001)
Calciteb 37° (2 × 1) 55° (1′ × 2) 27° (3 × 1) 55° (3 × 1) 16° (6 × 1), 50° (3 × 2) 56° (3 × 2) 58° (4 × 2) 27° (6 × 1) 30° (4 × 2)* 5° (3 × 3), 55° (3 × 4) 7° (3 × 1), 46° (2 × 5) 0° (6 × 1), 44° (2 × 6) 38° (2 × 5), 0° (3 × 2)
(0001) (0001) (0001) (101 h 0)
(010) (100) (001) (001)
Vateritec 56° (2′1) 50° (5 × 1) 2° (2 × 2), 20° (2 × 1) 43° (3 × 7), 4° (2 × 1), 14° (2 × 2)
a Aragonite (CaCO ): orthorhombic space group Pmcn, a ) 3 4.959, b ) 7.968, c ) 5.741. b Calcite (CaCO3): trigonal space group R3c, a ) 4.989, c ) 17.062. c Vaterite (CaCO3): hexagonal space group P63/mmc, a ) 7.135, c ) 16.98.
carbonate (calcite, vaterite, aragonite) and a number of calcium phosphate phases (hydroxyapatite, brushite, octacalcium phosphate, and whitlockite) were retrieved from known X-ray data. When the naturally occurring faces20 of these minerals were screened against the common surfaces of ChM and Ch, EpiCalc calculations identified 186 coincident matches with (V/Vo e 0.5) and relatively small supercell dimensions. Tables 1 and 2 list the epitaxial matches identified between ChM and calcium carbonates (64 matches) and calcium phosphates (28 matches), respectively. Table 3 (40 matches) and Table 4 (54 matches) are analogous lists based on matches found for Ch and the same mineral substrates. All but two of the matches in Tables 1-4 have V/Vo values between 0.45-0.50. The match between a ChM (001) overlayer and a calcite (101h 4) substrate stands out as significantly better than the rest (V/Vo ) 0.26). At a rotation angle of θ ) 39°, a (2 × 2) supercell formed at the interface has a total area of 161.87 Å2 (See Figure 2). Though epitaxy calculations are based solely on geometry, this pair of faces also makes intuitive chemical sense. Calcite crystallizes with alternating planes of calcium and carbonate ions stacked along the crystallographic 3-fold c axis. The (101 h 4) surface of calcite contains an equal number of calcium and carbonate ions and is charge neutral. It is also the primary cleavage face of the mineral, and likely one of the largest and most abundant faces present. The (001) face of ChM is also the largest plate face of the crystal. A second match with a good figure of merit (V/Vo ) 0.26) was found between a Ch (100) overlayer and a calcite (0001)
Table 4. Coincident Epitaxial Matches (V/Vo E 0.5) between Anhydrous Cholesterol (Ch) and Calcium Phosphate Substrates mineral surface (202 h 1) (101 h 1) (101 h 2) (112 h 2) (112 h 0) (0001) (202 h 1) (101 h 2) (101 h 1) (112 h 2) (0001) (112 h 2) (101 h 1) (101 h 2) (202 h 1) (101 h 0) (101 h 0) (112 h 0) (120) (1 h 01) (010) (001) (11 h 1) (1 h 11) (120) (010) (010) (001) (1 h 01) (120) (100) (010) (001) (001) (010) (011 h 2) (112 h 0) (112 h 0) (011 h 3) (011 h 2) (1014 h) (0001) (011 h 2) (011 h 3)
Ch surface
θ (supercell dimensions)
Hydroxyapatitea (010) 36° (2 × 2), 5° (3 × 1) (010) 31° (1 × 1) (010) 26° (1 × 1) (010) 55° (1 × 1) (010) 36° (2 × 1) (010) 36° (2 × 1) (100) 6° (7 × 1) (100) 16° (3 × 1), 32° (2 × 1) (100) 35° (2 × 1) (100) 43° (3 × 1) (001) 35° (2 × 1) (001) 42° (4 × 9) 9° (3 × 3) (001) 50° (1 × 7) (001) 37° (1 × 4) 0° (3 × 5) (001) 5° (3 × 3) (100) 51° (2 × 1) (001) 50° (1 × 3) (001) 16° (2 × 2) 35° (3 × 7) Brushiteb (010) (010) (010) (010) (100) (100) (100) (100) (001) (001) (001) (001)
13° (1 × 2) 30° (2 × 1) 21° (2 × 1) 58° (1 × 1) 21° (1 × 1), 53° (1 × 1) 48° (2 × 1) 60° (4 × 2) 0° (5 × 1) 12° (2 × 4), 42° (1 × 6) 25° (1 × 1), 0° (3 × 1) 28° (2 × 3) 11° (1 × 7)
Octacalcium Phosphatec (100) 39° (4 × 1) (100) 36° (4 × 1) (100) 37° (2 × 1) (010) 32° (1 × 1) (001) 6° (2 × 1), 14° (2 × 2) Whitlockited (010) (010) (100) (100) (100) (100) (001) (001) (001)
0° (4 × 1) 38° (2 × 1) 32° (3 × 1) 17° (3 × 1) 18° (4 × 1) 16° (5 × 1) 38° (3 × 1), 0° (3 × 3) 48° (1 × 4) 44° (1 × 4)
a Hydroxyapatite (Ca (PO ) OH): hexagonal space group P6 / 5 4 3 3 m, a ) 9.418, c ) 6.875. b Brushite (CaHPO4‚2H2O): monoclinic space group I2/a, a ) 5.88, b ) 15.15, c ) 6.37, β ) 117.46°. c Octacalcium phosphate (Ca H (PO ) ‚5H O): triclinic space group 8 2 4 6 2 P1, a ) 19.87, b ) 9.63, c ) 6.88, R ) 89.3°, β ) 92.2°, γ ) 108.9°. d Whitlockite (β-form Ca (PO ) ): trigonal space group R3c, a ) 3 4 2 10.33, c ) 37.103.
substrate. The (4 × 2) supercell match found at θ ) 30°, has a total area of 344.02 Å2. The smoothest (0001) calcite surface is parallel to the ionic planes in the mineral and therefore carries a net charge, either positive or negative. It is not clear how geometry-based epitaxy findings hold up against the energetic penalties associated with an interface between a neutral organic layer and a charged mineral surface. This charge incompatibility plus the significantly larger supercell area make this a somewhat less likely choice than the first match, despite the notable V/Vo. This theoretical study has demonstrated that systematic screening of geometric matches between inorganic and organic surfaces can serve as an efficient tool for identifying
226
Crystal Growth & Design, Vol. 4, No. 2, 2004
Communications
References
Figure 2. Molecular model of the coincident epitaxial match at θ ) 37° between a (001) ChM overlayer (with cell parameters b1, b2, and β) on a (101h 4) calcite substrate (with cell parameters a1, a2, and R).
a number of epitaxial relationships that may be important in crystallization under biological conditions. While in principle, any of the matches listed in Tables 1-4 could serve as a viable means to initiate the nucleation of cholesterol phases in vivo, some are likely to be more suitable than others when surface energetics are additionally considered. Ongoing in situ atomic force microscopy experiments in our laboratory suggest that epitaxial growth can also be observed experimentally for at least some of the orientations predicted by EpiCalc.21
Acknowledgment. J.A.S. is grateful for the financial support provided by the Henry Luce Foundation and the National Science Foundation (DMR-0093069). R.E.S. thanks Georgetown University for an undergraduate summer GUROP fellowship.
(1) Whiting, M. J.; Watts, J. M. Clin. Sci. 1985, 68, 589-596. (2) Addadi, L.; Weiner, S. Stereochemical and Structural Relations Between Macromolecules and Crystals in Biomineralization; Mann, S., Webb, J., Williams, R. J. P., Eds.; VCH: New York, 1989; pp 133-156. (3) Mann, S. Biomineralization: Principles and Concepts in Bioinorganic Materials Chemistry; Oxford University Press: New York, 2002. (4) Lowenstam, H. A.; Weiner, S. On Biomineralization; Oxford University Press: New York, 1989. (5) Shieh, H. S.; Hoard, L. G.; Nordman, C. E. Nature 1977, 267, 287-289. (6) Frincu, M. C.; Swift, J. A., unpublished results. (7) Konikoff, F. M.; Chung, D. S.; Donovan, J. M.; Small, D. M.; Carey, M. C. J. Clin. Invest. 1992, 90, 1155-1160. (8) Craven, B. M. Nature 1976, 260, 727-729. (9) Konikoff, F. M.; Danino, D.; Weihs, D.; Rubin, M.; Talmon, Y. Hepatology 2000, 31, 261-268. (10) Abendan, R. S.; Swift, J. A. Langmuir 2001, 18, 4847-4853. (11) Malet, P. F.; Dabezies, M. A.; Huang, G.; Long, W. B.; Gadacz, T. R.; Soloway, R. D. Gastroenterology 1988, 94, 1217-21. (12) Nagpal, K. C.; Ghori, T. A.; Ali, S. Z. Curr. Sci. 1982, 51, 814-815. (13) Bogren, H. G.; Mutvei, H.; Renberg, G. Ultrastruct. Pathol. 1995, 19, 447-453. (14) van der Berg, A. A.; van Buul, J. D.; Tytgat, G. N. J.; Groen, A. K.; Ostrow, J. D. J. Lipid. Res. 1998, 39, 1744-1751. (15) Lonsdale, K. Nature 1968, 217, 56-58. (16) Hooks, D. E.; Fritz, T.; Ward, M. D. Adv. Mater. 2001, 13, 227-241. (17) Last, J. A.; Hooks, D. E.; Hillier, A. C.; Ward, M. D. J. Phys. Chem. 1999, 103, 6723-6733. (18) Hillier, A.; Ward, M. D. Phys. Rev. B 1996, 54, 14037-14051. (19) http://www1.cems.umn.edu/research/ward/Software/Software.html. (20) Aragonite: (001), (010), (110), (011), (012), (021); calcite: (0001), (101 h 4), (101 h 0), (112 h 0), (101 h 1), (011 h 2); vaterite: (0001), (101 h 0); hydroxyapatite: (0001), (101 h 0), (112 h 0), (112 h 2), (101 h 1), (101 h 2), (202 h 1); brushite: (010), (001), (1h 01), (120), (1h 11), (11 h 0); octacalcium phosphate: (100), (010), (001); whitlockite: (0001), (112 h 0), (011 h 2), (011 h 3), (1014 h ). (21) Frincu, M. C.; Fleming, S. D.; Rohl, A. L.; Swift, J. A., manuscript in preparation.
CG034180A
