Epitaxial Relationships between Uric Acid Crystals and Mineral

In physiological deposits, crystalline uric acid is most frequently found either in a protonated state ... Ryan E. Sours, Amanuel Z. Zellelow, and Jen...
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Langmuir 2004, 20, 6524-6529

Epitaxial Relationships between Uric Acid Crystals and Mineral Surfaces: A Factor in Urinary Stone Formation M. Crina Frincu, Caitlin E. Fogarty, and Jennifer A. Swift* Department of Chemistry, Georgetown University, 37th and “O” Streets NW, Washington, D.C. 20057-1227 Received April 9, 2004. In Final Form: June 11, 2004 Uric acid (C5H4N4O3) is one of the final products of purine metabolism. Its concentration balance is maintained in the kidneys, but compromised kidney function can result in its crystallization either in the renal tract or in the interstitial fluid of joints. In physiological deposits, crystalline uric acid is most frequently found either in a protonated state (anhydrous or dihydrate phases) or as a deprotonated urate ion (sodium or ammonium salts). Often these precipitates are found in association with a number of mineral phases (e.g., calcium oxalates, calcium phosphates, and magnesium phosphates). Their frequent and common coexistence suggests that synergistic relationships between these crystalline phases may exist. A comprehensive list of different heterogeneous uric acid/uric acid and uric acid/mineral interfaces that are epitaxially matched was generated with the lattice-matching program EpiCalc. Two hundred twenty-five coincident epitaxial matches and four commensurate epitaxial matches were identified using this screening procedure.

Urinary stones are heterogeneous deposits, which often consist of mixtures of organic and inorganic crystalline phases. The compositional analysis of statistically significant numbers of human urinary stones collected in different regions throughout the world reveals which constituents are the most common.1-7 Uric acid is by far the most abundant organic material found in urinary stones. In the crystalline state, it is observed in either its protonated acid form (anhydrous or dihydrate phases) or as a wide variety of salts in a deprotonated urate form. The most abundant mineral species identified include calcium oxalates (whewellite, weddelite), calcium phosphates (hydroxyapatite, brushite, octacalcium phosphate, whitlockite), and magnesium phosphates (struvite, newberyite). The common coexistence of these crystalline species in physiological deposits and the observation that the nucleus of a stone is often chemically different than the material in subsequent layers led Lonsdale8 to suggest in 1968 that epitaxial relationships between these crystalline phases may be an important factor contributing to their formation. 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 lattice-matched “seeds” are present in solution, the barrier to nucleation can be significantly reduced, such that crystallization occurs in environments that have otherwise not met critical supersaturation conditions. Epitaxy is usually assessed computationally in two ways - either by simple geometric lattice-matching or by more rigorous potential energy (PE) calculations. Though * To whom correspondence should be addressed. E-mail: jas2@ georgetown.edu. (1) Herring, L. J. Urol. 1962, 88, 545-562. (2) Lonsdale, K.; Mason, P. Science 1966, 152, 1511-1512. (3) Lonsdale, K.; Sutor, J.; Wooley, S. E. Br. J. Urol. 1968, 402-411. (4) Lonsdale, K.; Sutor, D. J. Sov. Phys. Crystallogr. 1972, 16, 10601068. (5) Sutor, D. J.; Wooley, S. E.; Illingworth, J. J. Br. J. Urol. 1974, 46, 393-407. (6) Berg, W.; Schanz, H.; Eisenwinter, B.; Schorch, P. Urologe-Ausgabe A 1992, 31, 98-102. (7) Takasaki, E.; Suzuki, T.; Honda, M.; Imai, T.; Maeda, S.; Hosoya, Y. Urol. Int. 1995, 54, 89-94. (8) Lonsdale, K. Nature 1968, 217, 56-58.

geometric matching alone does not provide information about the interfacial energetics, when the objective is to screen and identify potential epitaxial relationships from hundreds of pairs of surfaces, it can serve as a very efficient screening tool. A number of examples have shown that geometric-matching protocols and PE calculations can yield similar predictions.9,10 In previous work, we used the program EpiCalc11 to identify lattice matches between the surfaces of crystalline cholesterol phases and the calcium carbonate and phosphate phases with which they are typically associated in arterial plaque deposits and gallstones.12 The best theoretical match identified by the screening procedure was later confirmed experimentally.13 In the present study, we apply the EpiCalc screening techniques to kidney stone constituents as a means to generate a comprehensive list of lattice matches between (a) various known uric acid phases and (b) various uric acid and mineral phases. EpiCalc calculations are based on a simple analytic function that measures the geometric “fit” between two chemically different surfaces. The program rotates an overlayer with lattice parameters b1, b2, and β with respect to a substrate with lattice parameters a1, a2, and R, through a series of azimuthal angles (θ). Surfaces with hexagonal cell dimensions were first converted to nonhexagonal cells before running the EpiCalc screening protocol. The degree of matching is given as a dimensionless figure of merit, V/V0, which ranges from 0 to 1. The smaller the value of V/V0, the better the geometric “fit”. Incommensurate surfaces do not match at any θ angle (V/V0 ) 1). Coincident surfaces (V/V0 ∼ 0.5 or less) have a subset of geometrically matched lattice positions at a given θ. Commensurate surfaces (V/V0 ) 0) are perfectly matched at a particular θ angle. Interfacial molecular structures can be sensitive to competition between energy-lowering overlayer-sub(9) Hooks, D. E.; Fritz, T.; Ward, M. D. Adv. Mater. 2001, 13, 227241. (10) Last, J. A.; Hooks, D. E.; Hillier, A. C.; Ward, M. D. J. Phys. Chem. B 1999, 103, 6723-6733. (11) Hillier, A.; Ward, M. D. Phys. Rev. B 1996, 54, 14037-14051. (12) Frincu, M. C.; Sharpe, R. E.; Swift, J. A. Cryst. Growth Des. 2004, 4, 223-226. (13) Frincu, M. C.; Fleming, S. D.; Rohl, A. L.; Swift, J. A. J. Am. Chem. Soc. 2004, 126, 7915-7924.

10.1021/la049091u CCC: $27.50 © 2004 American Chemical Society Published on Web 06/26/2004

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Langmuir, Vol. 20, No. 16, 2004 6525 Table 1. Coincident Epitaxial Matches (V/V0 e 0.5) between Anhydrous UA, UAD, AAU, and MSU Surfaces

Figure 1. Schematic of typical anhydrous UA, UAD, and MSU growth morphologies.

strate interactions and energetic penalties associated with even minor lattice reconstruction. Because the interactions that hold molecular layers together are comparatively weaker than the bonds in minerals, EpiCalc calculations restricted the systematic variation of organic overlayer lattice parameters to no more than (5.0% of the unit cell dimensions. For organic/organic interfaces, only the overlayer surface is allowed to vary. For organic/mineral interfaces, the inorganic lattice parameters are held strictly fixed while the organic overlayer can vary. This screening method is mechanistically different from other kidney stone epitaxy searches,8,14 which typically examine the percentage of misfit (up to 15%) of heterogeneous interfacial lattice alignments without varying the cell parameters. Crystalline uric acid deposited under low-pH conditions typically exists either in an anhydrous phase (UA) or as a dihydrate (UAD). UA crystals are monoclinic [P21/a: a ) 14.464(3), b ) 7.403(2), c ) 6.208(1) Å, and β ) 65.10(5)°].15 Synthetic crystals of UA deposit as clear rectangular plates, with large (100) faces bounded by (210), (201), (001), and sometimes (121) (Figure 1).16,17 UAD crystals are also monoclinic [P21/c: a ) 7.237(3), b ) 6.363(4), c ) 17.449(11), and β ) 90.51(1)°]18 and adopt a rectangular morphology. Synthetic UAD crystals typically exhibit large (001) faces bounded by (011) and (102) and infrequently (210) faces.17 At pHs higher than the pKa ) 5.4 of uric acid, the predominant species in solution is the deprotonated urate. A number of different urate salts are known to crystallize in physiologic environments. The two forms most frequently observed in human deposits are monosodium urate monohydrate (MSU) and ammonium acid urate (AAU). In addition to being a urinary stone component, MSU crystal precipitates are also found in the joints of persons afflicted with gouty arthritis. MSU crystals have a triclinic structure (P1 h : a ) 10.888, b ) 9.534, c ) 3.567, R ) 95.06°, (14) Mandel, N. S.; Mandel, G. S. In Urolithiasis: Clinical and Basic Research; Smith, L. H., Robertson, W. G., Finlayson, B., Ed.; Plenum Press: New York, 1981; pp 469-480. (15) Ringertz, H. Acta Crystallogr. 1966, 20, 397-403. (16) Rinaudo, C.; Boistelle, R. J. Cryst. Growth 1980, 49, 569-579. (17) Sours, R. E.; Fink, D. A.; Swift, J. A. J. Am. Chem. Soc. 2002, 124, 8630-8636. (18) Parkin, S.; Hope, H. Acta Crystallogr., Sect. B 1998, 54, 339344.

substrate surface

overlaye surface

UA (100) (201) (001) (100) (201) (100) (001) (001) (201) (100) (121) (121) (210) UAD (001) (011) (001) (011) (001) (011) UAD (001) (001) (001) (001) (001) (011) (011) (102) (102) AAU (001) (100) (001) (100) (100) AAU (100) (001) (010) (100) AAU (001) (100) (001) (100)

MSU (001) (001) (101) (101) (101) (011) (011) (011) (011) (11 h 0) (11 h 0) (11 h 0) (11 h 1) MSU (001) (001) (101) (101) (011) (011) UA (201) (210) (121) (001) (100) (201) (210) (201) (210) UA (121) (121) (201) (201) (210) UAD (011) (210) (210) (210) MSU (001) (001) (011) (111)

θ (supercell dimensions) 48° (1 × 1), 35° (1 × 1) 48° (1 × 1) 55° (1 × 1) 0° (7 × 2), 39° (1 × 1) 39° (1 × 1) 49° (1 × 1) 42° (1 × 1) 42° (1 × 1) 49° (1 × 1) 0° (1 × 1) 0° (1 × 3) 0° (1 × 3) 45° (1 × 1) 36° (1 × 1) 47° (1 × 1) 37° (1 × 1) 41° (1 × 2) 47° (5 × 5) 51° (1 × 1) 0° (1 × 2) 0° (1 × 1) 55° (4 × 2), 0° (4 × 1) 27° (1 × 1) 0° (1 × 1) V/V0 ) 0.04 1° (1 × 1) 0° (1 × 1) 25° (1 × 4) 4° (1 × 1) 21°(3 × 4), 48°(6 × 4), 7°(1 × 4) 42° (6 × 5) 0° (9 × 1) 17° (1 × 6) 57° (3 × 2) 6° (2 × 1) 5° (1 × 8) 48° (4 × 3) 39° (1 × 1) 39° (2 × 2) 16° (1 × 3) 20° (1 × 3) 20° (2 × 4)

β ) 99.47°, and γ ) 97.17°)19 and usually exhibit a needlelike morphology. Synthetic crystals are elongated along the c axis and are bounded by (100), (010), (11 h 0), and (001) faces. Four additional theoretical MSU faces have been predicted by Rinaudo and Boistelle20 on the basis of PBC theory: (011), (101), (11h 1), and (111). The single-crystal structure of AAU has yet to be determined; however, powder diffraction and thermogravimetric analysis data suggests an anhydrous monoclinic phase (a ) 17.356, b ) 3.528, c ) 11.285, and β ) 94.23°).21 Though the growth morphology has not been reported, crystals are likely to exhibit faces with low Miller indices such as (100), (010), and (001). When all possible pairs of the various natural and theoretical faces of UA, UAD, MSU, and AAU were subjected to EpiCalc screening, 46 epitaxial relationships were identified. A complete list of all matches with V/V0 e 0.5 and relatively small supercell dimensions appears in Table 1. All but one of the matches in Table 1 are (19) Mandel, N. S.; Mandel, G. S. J. Am. Chem. Soc. 1976, 98, 23192323. (20) Rinaudo, C.; Boistelle, R. J. Cryst. Growth 1982, 57, 432-442. (21) Tettenhorst, R. T.; Gerkin, R. E. Powder Diffr. 1999, 14, 305307.

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Table 2. Mineral Parameters Calcium Oxalate Monohydrate [Ca(C2O4)‚H2O]22 (Whewellite) P21/n: a) 9.976, b) 14.588, c) 6.291, β) 107.05° faces: (101 h ), (120), (110), (010), (011), (100), (120), (021) Calcium Oxalate Dihydrate [Ca(C2O4)‚2H2O]23 (Weddellite) I4/m: a ) b ) 12.33, c ) 7.353 faces: (100), (010), (101) Hydroxyapatite [Ca5(PO4)3OH] P63/m, a ) 9.418, c ) 6.875 faces: (0001), (101 h 0), (112 h 0), (112 h 2), (101 h 1), (101 h 2), (202 h 1) Brushite (CaHPO4‚2H2O) I2/a, a ) 5.88, b ) 15.15, c ) 6.37, β ) 117.46° faces: (010), (001), (1 h 01), (120), (1 h 11), (11 h 0) Whitlockite [β form Ca3(PO4)2] R3c, a ) 10.33, c ) 37.103 faces: (0001), (112 h 0), (011 h 2), (011 h 3), (1014 h) Octacalcium Phosphate [Ca8H2(PO4)6‚5H2O] P1, a ) 19.87, b ) 9.63, c ) 6.88, R ) 89.3°, β ) 92.2°, γ ) 108.9° faces: (100), (010), (001) Struvite (MgNH4PO4‚6H2O)25 Pmn21, a ) 6.955, b ) 6.142, c ) 11.218 faces: (011), (102), (100), (001) Newberyite (MgHPO4‚3H2O)26 Pbca: a ) 10.215, b ) 10.681, c ) 10.014 faces: (100), (010), (102), (021), (111), (001)

coincident with V/V0 values ranging between 0.45 and 0.50. The match between UAD (001) and UA (100) at an azimuthal angle of θ ) 0° stands out as significantly better than the rest (V/V0 ) 0.04) and can be considered a near perfect commensurate relationship. A schematic of this epitaxial relationship is shown in Figure 2. We next sought to examine potential epitaxial relationships between the surface lattices of uric acid phases and those of the minerals: calcium oxalates, calcium phosphates, and magnesium phosphates, species that are often found in association with uric acid in pathological samples. Table 2 lists the chemical composition, crystallographic cell parameters, space group, and naturally occurring faces of the minerals surveyed in this screening protocol. We note that the Miller indices and lattice parameters for calcium oxalate monohydrate (whewellite) used in this

θ (supercell dimensions)

Calcium Oxalate Monohydrate (Whewellite) (201) 27° (1 × 4) (121) 28° (1 × 1) (001) 0° (1 × 1) (121) 5° (1 × 7) (121) 16° (1 × 1) (210) 0° (1 × 4) (210) 37° (1 × 3) (210) 0° (1 × 3)

(010) (010) (010) (010) (101) (101)

Figure 2. Schematic of the commensurate epitaxial match between a (1 × 1) overlayer of UA (100) and a UAD (001) substrate at θ ) 0°. The uric acid molecules in the UAD substrate are shown, along with cell vectors a1, a2, and R (solid arrows). The orientation of the overlayer UA cell (b1, b2, and β) is indicated with dashed lines and arrows.

UA surface

Calcium Oxalate Dihydrate (Weddellite) (121) 0° (4 × 1) (121) 54° (2 × 1) V/V0 ) 0.40 (100) 5° (1 × 10) (001) 3° (1 × 10) (121) 29° (1 × 1) V/V0 ) 0.41 (201) 0° (7 × 1)

(202 h 1) (202 h 1) (101 h 0) (101 h 0) (101 h 0) (0001) (0001) (0001)

Hydroxyapatite (210) 29° (1 × 4) (100) 37° (1 × 1) (210) 27° (1 × 5) (121) 44° (3 × 2), 27° (2 × 2) (001) 29° (1 × 1) (210) 19° (1 × 8) (121) 8° (3 × 9) (100) 9° (1 × 6)

(001) (010) (010) (010) (1 h 11) (1 h 11) (11 h 1) (11 h 1) (1 h 01) (1 h 01) (120) (120) (120)

(201) (210) (201) (001) (121) (001) (121) (210) (201) (210) (201) (121) (210)

(0001) (0001) (011 h 2)

(001) (210) (121)

(010) (010) (100) (001) (010)

Brushite 0° (7 × 1) 0° (1 × 1) V/V0 ) 0.38 46° (1 × 2) 46° (2 × 1) 57° (4 × 2) 25° (1 × 1) 17° (3 × 6) 0° (1 × 4) 0° (6 × 1), 31° (1 × 4) 3° (1 × 1) 14° (1 × 8) 37° (1 × 1) 0° (1 × 2) V/V0 ) 0.23

Whitlockite 15° (2 × 4) 25° (1 × 5) 50° (5 × 3)

Octacalcium Phosphate (001) 59° (3 × 1) (201) 25° (1 × 4) (201) 27° (1 × 4) (210) 0° (1 × 2) (210) 0° (1 × 1) Struvite 0° (4 × 1), 58° (4 × 2) 56° (2 × 1), 0° (4 × 1) 4° (1 × 7), 51° (10 × 6) 4° (1 × 7), 51° (5 × 3) 0° (1 × 1) V/V0 ) 0.43 16° (1 × 9) 1° (1 × 1)

(001) (011) (100) (102) (001) (100) (102)

(121) (121) (121) (121) (100) (210) (210)

(111) (111)

Newberyite (121) 0° (1 × 1) V/V0 ) 0.20 (121) 57° (2 × 1)

study correspond to the P21/n cell of Deganello and Piro.22 An alternative P21/c space group setting has been proposed,23 and a list of Miller indices relating these two different notation systems can be found in ref 24. For each of the uric acid phases, EpiCalc was able to identify a number of epitaxially matched mineral substrates. A complete list of matches is found in Tables 3-6. Of the 58 matches identified between UA surfaces and (22) Deganello, S.; Piro, O. Neues Jahrb. Mineral., Monatsh. 1981, 2, 81-88. (23) Tazzoli, V.; Domeneghetti, C. Am. Mineral. 1980, 65, 327-334. (24) Millan, A. Cryst. Growth Des. 2001, 1, 245-254.

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Table 4. Coincident Epitaxial Matches (V/V0 e 0.5) between UAD and Mineral Substrates mineral surface (100) (100) (010) (110) (110) (120) (120) (021)

UAD surface

θ (supercell dimensions)

Calcium Oxalate Monohydrate (Whewellite) (011) 24° (1 × 1) (102) 17° (1 × 1) (102) 0° (1 × 1) (011) 47° (1 × 2) (102) 30° (1 × 6) (102) 33° (1 × 6) (011) 51° (1 × 2) (210) 52° (7 × 5)

(010) (0001) (0001) (101 h 0) (101 h 0) (101 h 1) (202 h 1)

Calcium Oxalate Dihydrate (Weddellite) (001) 5° (1 × 10) Hydroxyapatite (001) 9° (1 × 3) (210) 26° 21 × 1) (102) 22° (1 × 9) (210) 23° (1 × 2) (210) 27° (2 × 4), 37° (1 × 1) (210) 20° (1 × 2), 59° (2 × 1) Brushite

35° (1 × 3) 19° (1 × 1) 0° (3 × 1) V/V0 ) 0.37 53° (2 × 5) 6° (1 × 9) 25° (1 × 5) 17° (1 × 1) 0° (8 × 1) 0° (1 × 1) 1° (1 × 1)

(001) (001) (001) (010) (010) (1 h 01) (1 h 01) (1 h 11) (120) (120)

(011) (102) (210) (102) (210) (011) (102) (001) (011) (102)

(0001)

Whitlockite (210) 35° (2 × 3), 9° (1 × 6)

(010) (100) (010) (100)

Octacalcium Phosphate (001) 0° (3 × 1) (001) 0° (4 × 3) (011) 0° (1 × 1), 22° (1 × 6) (011) 19° (1 × 7) Struvite

0° (1 × 1) V/V0 ) 0.05 0° (2 × 1) 1° (1 × 3), 19° (1 × 8) 19° (1 × 7) 18° (1 × 10) 0° (1 × 2) V/V0 ) 0.44 38° (1 × 1)

(001) (011) (001) (011) (100) (100) (100)

(001) (001) (011) (011) (102) (102) (210)

(021) (102) (001) (021)

Newberyite (102) 0° (2 × 3) (102) 0° (1 × 2) (210) 38° (1 × 1), 52° (6 × 4) (210) 52° (3 × 2)

those of the assorted minerals (Table 3), only six of these matches were found to have V/V0 < 0.45. These are identified in the table in bold. Of the six, only two have V/V0 < 0.25. These are the matches between UA (210) and brushite (120) (V/V0 ) 0.23) and UA (121) and newberyite (111) (V/V0 ) 0.20). While the degree of misfit remains too high to consider the relationships between these surface pairs as commensurate, these two matches can certainly be regarded as better coincident fits than the other pairs of surfaces. There were 47 epitaxial matches found between UAD and mineral surfaces (Table 4). Only two have V/V0 values significantly less than 0.5. A better coincident match was found for brushite (001)/UAD (210) (V/V0 ) 0.37), and a near perfect commensurate match was found between struvite (001) and UAD (001) (V/V0 ) 0.05). A molecular model of the latter commensurate match appears in Figure 3. The most probable charge-neutral (001) surface of struvite is highly corrugated. Though the hydration state

Figure 3. Schematic of the commensurate epitaxial match between a (1 × 1) overlayer of UAD (001) and a struvite (001) substrate at θ ) 0°. The substrate struvite ions are shown, along with cell vectors a1, a2, and R (solid arrows). The orientation of the overlayer UAD cell (b1, b2, and β) is indicated with dashed lines and arrows.

of the interface is uncertain, the presence of oriented water molecules at the struvite/UAD interface may help to mediate the electrostatic differences between the ionic mineral substrate and the neutral organic overlayer. When the four natural and four theoretical faces of MSU were screened against the various mineral surfaces, 56 epitaxial relationships were identified (Table 5). Only nine of the matches occurred on natural faces of synthetic crystals while the remaining 47 matches were based on theoretical faces. The two best near-commensurate matches occurred with MSU (011), a theoretical face, and either (202 h 1) hydroxyapatite (V/V0 ) 0.08) or (100) newberyite (V/V0 ) 0.12). These matches are depicted in Figure 4. All other coincident relationships identified in Table 5 have V/V0 values ranging between 0.45 and 0.50. Only 22 coincident epitaxial matches were identified between AAU and mineral substrates (Table 6), none of which have V/V0 < 0.45. Additional epitaxial relationships with AAU surfaces may be identified if the number of faces examined is expanded. The morphology of AAU is not known with certainty at this time, and, consequently, a potentially incomplete list of presumed faces (001), (010), and (001) were examined in this survey. Most of the experimental studies examining the possibility for epitaxial growth in these systems have sought evidence for heterogeneous nucleation by introducing seeds of one material phase (most often MSU or UA) into supersaturated inorganic solutions of another constituent.27-33 The examination of this seeding effect has also (25) Ferraris, G.; Fuess, H.; Joswig, W. Acta Crystallogr., Sect. B 1986, 42, 253-258. (26) Abbona, F.; Boistelle, R.; Haser, R. Acta Crystallogr., Sect. B 1989, 2514-2518. (27) Pak, C. Y. C.; Arnold, L. H. Proc. Soc. Exp. Biol. Med. 1975, 149, 930-932. (28) Coe, F. L.; Lawton, R. N.; Goldstein, R. B.; Tembe, V. Proc. Soc. Exp. Biol. Med. 1975, 149, 926-929. (29) Pak, C. Y. C.; Hyashi, Y.; Arnold, L. H. Proc. Soc. Exp. Biol. Med. 1976, 153, 83-87. (30) Meyer, J. L.; Bergert, J. H.; Smith, L. H. Invest. Urol. 1976, 14, 115-119. (31) Hartung, R.; Laskovar, P.; Kratzer, M. Croat. Chem. Acta 1981, 53, 381-388. (32) Koutsoukos, P. G.; Lam-Erwin, C. Y.; Nancollas, G. H. Invest. Urol. 1980, 18, 178-184. (33) Grases, F.; Conte, A.; Gil, J. Br. J. Urol. 1988, 61, 468-473.

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Table 5. Coincident Epitaxial Matches (V/V0 e 0.5) between MSU and Mineral Substrates mineral surface

MSU surface

θ (supercell dimensions)

(010) (010) (1 h 01) (1 h 01) (011) (011) (011) (011)

Calcium Oxalate Monohydrate (Whewellite) (100) 15° (1 × 2) (101) 0° (2 × 1), 24° (2 × 6) (011) 0° (13 × 1) (111) 41° (1 × 1) (001) 0° (1 × 1), 34° (1 × 1) (011) 0° (1 × 1) (111) 41° (1 × 1) (11 h 1) 45° (1 × 1)

(010) (010) (010) (101)

Calcium Oxalate Dihydrate (Weddellite) (101) 0° (4 × 1), 39° (2 × 3) (011) 48° (3 × 3) (001) 50° (4 × 2) (111) 39° (3 × 3)

(0001) (0001) (0001) (0001) (0001) (101 h 0) (101 h 0) (101 h 0) (101 h 1) (101 h 1) (101 h 1) (202 h 1) (202 h 1) (202 h 1) (202 h 1) (202 h 1) (202 h 1)

Hydroxyapatite (001) 26° (1 × 2) (101) 55° (1 × 1) (011) 46° (1 × 1) (111) 35° (1 × 1), 0° (7 × 5) (11 h 1) 0° (3 × 2), 60° (3 × 2) (001) 39° (1 × 1) (101) 5° (1 × 13) (11h 0) 0° (2 × 1) (010) 0° (1 × 2) (011) 0° (4 × 1) (111) 45° (1 × 1) (001) 48° (2 × 1) (100) 12° (1 × 2) (101) 4° (4 × 1), 54° (1 × 1) (111) 0° (3 × 1) (11h 1) 0° (6 × 1) (011) 49° (1 × 1) V/V0 ) 0.08

(010) (010) (11 h 1) (11 h 1) (11 h 1)

(011) (111) (011) (111) (11h 1)

(0001) (0001) (011 h 2) (0001) (011 h 2)

Whitlockite (101) 39° (3 × 6) (111) 15° (2 × 5) (111) 12° (1 × 3) (11 h 1) 0° (4 × 3) (11h 1) 46° (1 × 1)

(100) (100)

Octacalcium Phosphate (101) 42° (2 × 3) (11 h 1) 44° (1 × 1)

Brushite 0° (2 × 1), 31° (1 × 2) 20° (1 × 2), 41° (2 × 2) 0° (1 × 1) 43° (1 × 1) 46° (1 × 1)

Struvite (001) (011) (001)

(001) (011) (001)

(001) (011) (001)

(100) (001) (010) (100)

Newberyite (011) 0° (1 × 1) V/V0 ) 0.12 (111) 44° (1 × 1) (111) 45° (1 × 1) (11 h 1) 46° (1 × 1)

Figure 4. Schematic of the near-commensurate epitaxial matches between MSU (011) and either hydroxylapatite (202h 1) or newberyite (100). The surface molecules of MSU are shown, along with cell vectors b1, b2, and β (solid black arrows). The orientation of the matching (202h 1) hydroxylapatite substrate at θ ) 49° (a1, a2, and R) is indicated with blue dashed lines and arrows. The orientation of the matching (100) newberyite substrate at θ ) 0° (a1, a2, and R) is indicated with black dashed lines and arrows. Hydrogen atoms are omitted for clarity. Table 6. Coincident Epitaxial Matches (V/V0 e 0.5) between AAU and Mineral Substrates mineral surface (001) (010) (100) (111 h)

AAU surface

θ (supercell dimensions)

Calcium Oxalate Monohydrate (Whewellite) (010) 56° (2 × 2) (010) 53° (6 × 8) (010) 59° (1 × 1) (010) 34° (3 × 8), 58° (1 × 1)

(101 h 2) (101 h 0) (202 h 1)

Hydroxyapatite (001) 25° (5 × 2), 32° (3 × 1) (010) 36° (1 × 2) (010) 55° (5 × 6), 19° (1 × 4)

(010) (1 h 01) (1 h 11) (120)

(010) (010) (010) (010)

(0001) (011 h 2)

Whitlockite (010) 44° (4 × 7) (010) 34° (2 × 5), 58° (1 × 1)

Brushite

(001) (100)

28° (1 × 3) 57° (2 × 2) 57° (1 × 1) 17° (1 × 5), 35° (2 × 5)

Octacalcium Phosphate (010) 20° (1 × 5) (010) 58° (1 × 1) Struvite

0° (2 × 1)

(102)

(010)

(100)

Newberyite (010) 59° (1 × 1)

been extended to urine solutions.34,35 These experiments provide strong indirect evidence for epitaxy and do support the concept of heterogeneous nucleation. A more limited number of experimental studies have examined the specifics of the epitaxial interfaces with molecular-level detail. For example, Boistelle and Rinaudo36 showed that UAD nucleates preferentially on UA substrates and vice versa. This has also been experimen-

tally observed in our laboratory.37 In both studies, the contacting UAD (001)/UA (100) planes are oriented in the same orientation predicted by the current EpiCalc calculations. Rinaudo et al.38 also examined solutions simultaneously supersaturated with respect to newberyite and uric acid. They reported a number of random overgrowths of UA and/or UAD and newberyite, as well as what appears to be three preferred orientations for UA crystals grown on the (010) surface of newberyite. Interestingly, the EpiCalc screening did not identify any matches for either UA or UAD and the newberyite (010) surface. Future experi-

(34) Grover, P. K.; Ryall, R. L. Clin. Sci. 1997, 205-213. (35) Grover, P. K.; Ryall, R. L. Mol. Med. 2002, 8, 525-535. (36) Boistelle, R.; Rinaudo, C. J. Cryst. Growth 1981, 53, 1-9.

(37) Sours, R. E.; Swift, J. A. Unpublished results. (38) Rinaudo, C.; Abbona, F.; Boistelle, R. J. Cryst. Growth 1984, 66, 607-615.

Letters

mental work may be able to reconcile the discrepancy between theoretical predictions and experimental observations. The systematic screening of geometric matches between organic and inorganic crystalline phases can serve as an efficient tool for identifying epitaxial relationships and is intended to guide future experimental efforts. This EpiCalc study has generated a comprehensive list of potential coincident and commensurate epitaxial matches between uric acid phases and the minerals often found associated with them in physiological deposits. While, in principle,

Langmuir, Vol. 20, No. 16, 2004 6529

any of the coincident matches listed in Tables 1 and 3-6 could serve as a viable means to initiate the nucleation of these constituents in vivo, some are likely to be more suitable than others when surface energetics are additionally considered. Acknowledgment. J.A.S. is grateful for the financial support provided by the Henry Luce Foundation. C.E.F. thanks Georgetown University for an undergraduate GUROP fellowship. LA049091U