Trapping Crystal Nucleation of Cholesterol.H2O: Relevance to Pathological Crystallization

I Solomonov*, M.J. Weygand†, K. Kjaer†, H. Rapaport‡, and L. Leiserowitz*

*Dept. of Materials and Interfaces, The Weizmann Institute of Science, 76100 Rehovot, Israel; †Materials Research Dept, Riso National Research Laboratory, 4000 Roskilde, Denmark; ‡Dept. of Biotechnology Engineering, Ben-Gurion University of the Negev, 84105 Beer-Sheva, Israel.

Supplemental Material

Grazing Incidence X-ray Diffraction (GIXD)

For a detailed description of GIXD on liquid surfaces and schematic views of the liquid surface diffractometer and differences between diffraction from monolayer films on water and three-dimensional crystals see two references (Als-Nielsen and Kjaer, 1989) and (Kuzmenko et al, 2001) cited in the main article.

The GIXD experiments were performed on the liquid surface diffractometer at the undulator BW1 beam line at the HASYLAB synchrotron source, Desy (Hamburg, Germany). The films were spread at room temperature and diffraction measurements thereon were performed at 5°C. A monochromatic X-ray beam (=1.304 Å) was adjusted to strike the liquid surface at an incident angle i < 0.85c where c is the critical angle for total external reflection; this maximizes surface sensitivity. The dimensions of the footprint of the incoming X-ray beam on the liquid surface were approximately 2 by 50 mm. GIXD signals were obtained from mono- bi- and multilayer crystallites randomly oriented about the water surface normal in the form of a two-dimensional (2-D) “powder”. The scattered intensity was collected by means of a position-sensitive detector (PSD), which intercepts photons over the range 0.0 < qz< 1.1 Å-1, qz being the out-of-plane component of the scattering vector. Measurements were performed by scanning the horizontal component, qxy 4sinxy/ of the scattering vector, where xy is the angle between the incident and diffracted beam projected onto the horizontal plane. The diffraction data are represented in two ways: (1) The GIXD pattern I(qxy), obtained by integrating over the whole qz window of the PSD, shows Bragg ‘peaks’; (2) Bragg rod intensity profiles are the scattered intensity I(qz) recorded in channels along the PSD but integrated across the qxyrange of each Bragg peak.The full width at half maximum (FWHM) of the Bragg peaks yields the lateral 2D crystalline coherence length Lxy 0.9(2)/FWHM(qxy). The qxy positions of the Bragg ‘peaks’ yield the lattice repeat distances d = 2/qxy, which may be indexed by the two Miller indices h,k to yield the unit cell dimensions parallel to the water surface.

For vertically homogenous monolayers or for thick and thus, again, vertically homogenous multilayers (say, more than ten layers), the width of the Bragg rod profile along qz similarly gives a measure of the thickness of the crystalline film Lz 0.9(2)/FWHM(qz). For the few-layer films encountered in this work, Lz thus calculated may be used as a first guide. Generally, the intensity at a particular value of qz in a Bragg rod is proportional to the square of the unit cell structure factor, |Fhk(qz)|2. The structure factor Fhk(qz)|is given by the equation:

Fhk(qz) = jfojexpi(qhk.rj+qzzj)*exp(–0.5Ujq2), where foj is the scattering factor of the atom j at rest,rj = xja + yjb is the vector specifying the (x,y) position of the atom j in the unit cell of dimensions a, b,qhk = 2(ha* + kb*), zj is the atomic coordinate in Angstroms along the vertical direction and Ujis the isotropic temperature factor (in Å2) of atom j, as in Table 4.

In the event of crystalline multilayer formation of cholesterol the Bragg rods were found to exhibit distinct intensity maxima that could be assigned (h,k,l) indices, as would arise from a 3D crystal. This behavior was found to occur both for the multilayer obtained from compression of pure cholesterol and the 5:1 mixture of cholesterol and phospholipid DPPC. The 3D crystalline unit cell dimensions of cholesterol from the mixture with DPPC were determined by a least-squares procedure. The magnitude of qh,k,l for the intensity maxima with indices h,k,l may be derived from the sum of the vector components qx,y+qz = 2π(haxy*+kbxy*)+2π(haz*+kbz*+lc*), where axy*, bxy*, az* and bz* are the in-plane (x,y) and out-of-plane (z) components of the reciprocal lattice vectors a* and b*.

The model was refined to the resulting distinct (h,k,l) intensities by X-ray structure-factor least squares as a 3D crystal, but with constraints imposed upon the molecular structure, given the limited amount of observed diffraction data. The intensities of reflections (2,k,l) and (-2,k,l+2) were heavily overlapped and thus each pair was treated by adjusting their ‘observed’ |F|2values to have the same ratio as those calculated from the refinement program, but constrained to have their sum kept constant at the measured intensity. The CERIUS2 computational package (Accelrys, San Diego. CA) was used for the construction of the molecular models.

Table 1: Monolayer, multilayer and three-dimensional crystals of cholesterol and derivatives thereof that adopt the 10x7.5Å2 bilayer motif, as well as crystals of the triclinic anhydrous and monohydrate forms of cholesterol that incorporate different bilayer motifs: Unit cell dimensions (Å, °), space- or plane-group (SG, PG) and bilayer symmetry (BS) of the cholesterol moieties (twofold screw 21, twofold 2, or no crystallographic symmetry 1)

Crystal /

SG.

PG. / a b c
 / BS
Anhydrous cholesterol
C8H16C19H28-OH (Shieh et al., 1977) /

P1

/ 10.5 14.2 34.2
96.3 94.6 90.7 / 1
Cholesterol monohydrate
C8H16C19H28-OH.H2O (Craven, 1976) /

P1

/ 12.39 12.41 34.36
91.9 98.1 100.8 / 1
aCholesterol monohydrate
C8H16C19H28-OH.H2O (Present study) /

A2

/ 10.15 7.57 68.2
94.8 / 2
Stigmasterol.hemihydrate
C10H18C19H28-OH.0.5H2O (Rapaport et al.,2001) / P21 / 
 / 21
bCholestanol dihydrate
C8H16C19H29-OH.2H2O (Bernal et al., 1940) / P1 / 
 / 1
Cholesterol bilayer
C8H16C19H28-OH (Rapaport et al., 2001) / p21 / 10.07 7.57
90 / 21
Stigmasterol trilayer hydrate
cC10H18C19H28-OH.nH2O (Rapaport et al., 2001) / p21 / 10.2 7.7
90 / 21
Cholesteryl acetate monolayer
C8H16C19H28-O2CCH3 (Rapaport et al., 2001) / p1 / 10.1 7.6
92.2 / -
Cholesteryl L-glutamate monolayer
C8H16C19H28-O2C4H5(NH2)CO2H (Alonso et al 2001a) / p1 / 10.2 7.6
92.8 / -
Cholesteryl tridecanoate (80° C)
C8H16C19H28-O2C13H25 (Craven, 1986) / P21 / 10.0 7.6 57.5
96 / 21
Cholesteryl myristate
C8H16C19H28-O2C14H27 (Craven and de Titta, 1976) / A2 / 10.3 7.6 101.4
94.4 / 2
Cholesteryl palmitate (78° C)
C8H16C19H28-O2C16H31 (Craven, 1986) / A2 / 10.2 7.6 105.5
95.6 / 2
Cholesteryl 17-bromoheptadecanoate
C8H16C19H28-O2C17H32Br (Abrahamsson and Dahlen, 1977) / P21 / 7.7 10.3 56.0
103.1 / 21
Cholesteryl stearate
C8H16C19H28-O2C18H35 (Barnard and Lydon. 1974) / P21 / 10.2 7.6 101.8
93.4 / 21
dCholesteryl tridecanoate bilayer
C8H16C19H28-O2C13H25 (Alonso et al, 2001b) / p21 / 10.0 7.6
90
dCholesteryl palmitate bilayer
C8H16C19H28-O2C16H31 (Alonso et al, 2001b) / p21 / 10.2 7.6
90
dCholesteryl stearate bilayer
C8H16C19H28-O2C18H35 (Alonso et al, 2001b) / p21 / 10.3 7.5
90

aThis unit cell corresponds to that of the monoclinic phase described in the text.

bTransformation of the primitive cell (a,b,c) of cholestanol dihydrate to an A-centered cell (a1, b1, c1), where c1= 2c-b, yields a1 = 9.8Å, b1=7.8Å, c1=73.8Å, 1= 89.1°, 1= 106.1°, 1= 88.5°.

cThe number of water molecules per steroid, n = 2-3 according to the structure refinement.

dIn these three crystalline films on water, the bilayer is formed via the interdigitated hydrocarbon chains. Thus the cholesterol moieties are not in contact with each other.

References

Abrahamsson, S. and B. Dahlen. 1977. The crystal structure of cholesteryl 17-bromoheptadecanoate. Chem. Phys. Lipids 20: 43-56.

Alonso, C., R. Eliash, T. R. Jensen, K. Kjaer, M. Lahav and L. Leiserowitz. 2001a. Guest intercalation at corrugated surface of host monolayer crystal on water. Cholesteryl-L-glutamate and water-soluble amino acids. J. Am. Chem. Soc. 123:10105-10106.

Alonso, C., I. Kuzmenko, T. Jensen, K. Kjaer, M. Lahav, and L. Leiserowitz. Self-assembly of crystalline films of interdigitated long-chain cholesteryl esters at the air-water interface. 2001b. J. Phys. Chem. B, 105:8563-8568.

Barnard, J. A. W. and J. E. Lydon. 1974. A Crystallographic Examination of 14 Straight Chain Alkyl Esters of Cholesterol Mol. Cryst. Liq. Cryst., 26:285-294.

Bernal, J.D., D. Crowfoot and I. Fankuchen. 1940. X-ray Crystallography and the Chemistry of the Steroids Philos. Trans. R. Soc. London Ser A. 239:135-182.

Craven, B. M. 1976. Cholesterol Monohydrate. Nature 260:727-729.

Craven, B. M. 1986. Cholesterol crystal structures: adducts and esters. In Handbook of Lipid Research, Vol. 4, The Physical Chemistry of Lipids. D. M. Small, editor. Plenum Press, New York. 149–182.

Craven, B. M. and G. T. de Titta. 1976. Cholesteryl Myristate: Structure of the Crystalline Solids and Mesophases. J.C.S. Perkin II: 814-822.

Rapaport, H., I. Kuzmenko, S. Lafont, K. Kjaer, P. B. Howes, J. Als-Nielsen, M. Lahav, L. Leiserowitz. 2001. Cholesterol Monohydrate Nucleation in Ultrathin Films on Water. Biophys. J. 81:2729-2736.

Shieh, H. S., L. G. Hoard and C.E. Nordman. 1977. Crystal Structure of Anhydrous Cholesterol. Nature267:287-289.

Table 2. Crystal unit cell data of the monoclinic cholesterol monohydrate phase appearing in multilayer form on the water surface, as determined by least squares from grazing incidence X-ray diffraction data measured at T=5 °C, making use of 37 reflections.

C27H46OxH2O

Fw=404.6 refinement h,k,l

Monoclinic

A121 (=A2)

a=10.15(2) Å

b=7.57(2) Å

c=68.2(3) Å

= 94.8(5)°

V=5222 Å3

Z= 8

Dx= 1.029 g/mL

Table 3. Measured and calculated X-ray structure factors |F(hkl)|2. The pairs of overlapping reflections (2,k,l) and (-2,k,l+2) are grouped together because the sum of each pair of |F|2 values was measured, so that their individual ‘measured’ intensities is model dependent. The list is in the same order of appearance as in Fig. 4, main text.

N / h / k / l / |Fcalc(hkl)|2 / |Fmeas(hkl)|2
1 / 1 / 0 / 0 / 1586 / 899
2 / -1 / 0 / 2 / 1372 / 1104
3 / 1 / 0 / 2 / 1050 / 3270
4 / -1 / 0 / 4 / 1692 / 1226
5 / 1 / 0 / 4 / 1134 / 1022
6 / -1 / 0 / 6 / 828 / 491
7 / 0 / 1 / 1 / 1281 / 4006
8 / 1 / 0 / 6 / 57 / 245
9 / 0 / 1 / 3 / 56547 / 35930
10 / 0 / 1 / 5 / 1909 / 1839
11 / -1 / 1 / 1 / 1513 / 1022
12 / 1 / 1 / 1 / 165758 / 172087
13 / 0 / 1 / 7 / 4898 / 4374
14 / -1 / 1 / 3 / 2423 / 2044
15 / 1 / 1 / 3 / 19409 / 16391
16 / -1 / 1 / 5 / 1330 / 1839
17 / 1 / 1 / 5 / 89036 / 78481
18 / 0 / 1 / 9 / 7068 / 5804
19 / -1 / 1 / 7 / 3771 / 3066
20 / 2 / 0 / 0 / 45988 / 36788
21 / -2 / 0 / 2 / 1111 / 899
22 / 1 / 1 / 7 / 4329 / 4456
23 / 2 / 0 / 2 / 231919 / 262667
24 / -2 / 0 / 4 / 23189 / 26283
25 / -1 / 1 / 9 / 8025 / 7358
26 / 2 / 0 / 4 / 38933 / 36257
27 / -2 / 0 / 6 / 299 / 286
28 / 1 / 1 / 9 / 14676 / 17168
29 / 2 / 0 / 6 / 327657 / 364734
30 / -2 / 0 / 8 / 2081 / 2330
31 / -2 / 1 / 1 / 6834 / 8238
32 / 2 / 0 / 8 / 21918 / 13980
33 / -2 / 0 / 10 / 2444 / 1553
34 / 2 / 1 / 1 / 3758 / 5764
35 / -2 / 1 / 3 / 2317 / 3556
36 / 2 / 1 / 3 / 39478 / 32292
37 / -2 / 1 / 5 / 733 / 613
38 / 2 / 1 / 5 / 20799 / 39200
39 / -2 / 1 / 7 / 6102 / 11486
40 / 0 / 2 / 0 / 11030 / 10546
41 / 2 / 1 / 7 / 1 / 0
42 / -2 / 1 / 9 / 5769 / 4496
43 / 0 / 2 / 2 / 488 / 5191
44 / 0 / 2 / 4 / 1183 / 4742
45 / 0 / 2 / 6 / 556 / 3107
46 / 2 / 1 / 9 / 9570 / 13693
47 / -2 / 1 / 11 / 3481 / 3147
48 / 0 / 2 / 8 / 1994 / 3393

Table 4. Fractional coordinates x,y,z and isotropic thermal parameters U (in Å2) of the C and O atoms of cholesterol monohydrate in the monoclinic (space group A2) multilayer phase.

x y z U

Molecule A

O(1) -0.35983 -0.51022 0.23285 0.05

C(1) -0.30845 -0.30885 0.18407 0.05

C(2) -0.32196 -0.31456 0.20597 0.05

C(3) -0.36288 -0.50269 0.21161 0.05

C(4) -0.26328 -0.63412 0.20536 0.05

C(5) -0.23249 -0.62051 0.18549 0.05

C(6) -0.23774 -0.76373 0.17378 0.05

C(7) -0.19920 -0.77058 0.15351 0.05

C(8) -0.14015 -0.59760 0.14623 0.05

C(9) -0.21382 -0.44123 0.15527 0.05

C(10) -0.20361 -0.43861 0.17696 0.05

C(11) -0.17348 -0.26315 0.14564 0.05

C(12) -0.16861 -0.26648 0.12369 0.05

C(13) -0.08255 -0.41537 0.11676 0.05

C(14) -0.14215 -0.58533 0.12470 0.05

C(15) -0.07458 -0.72937 0.11446 0.05

C(16) -0.05715 -0.65296 0.09431 0.05

C(17) -0.09822 -0.45876 0.09507 0.05

C(18) -0.06786 -0.38300 0.18604 0.05

C(19) 0.05703 -0.38702 0.12495 0.05

C(20) -0.01010 -0.35086 0.08098 0.05

C(21) -0.03521 -0.15029 0.08267 0.05

C(22) -0.03775 -0.42702 0.06092 0.15

C(23) 0.05670 -0.30272 0.05120 0.15

C(24) 0.18347 -0.35182 0.05265 0.15

C(25) 0.27531 -0.19407 0.04143 0.15

C(26) 0.39635 -0.30649 0.04242 0.15

C(27) 0.23319 -0.21458 0.02796 0.15

Molecule B

O(1) 0.18946 0.16322 0.23574 0.05

C(1) 0.33866 -0.01627 0.19149 0.05

C(2) 0.26937 -0.02209 0.21023 0.05

C(3) 0.26171 0.16824 0.21805 0.05

C(4) 0.19462 0.28731 0.20328 0.05

C(5) 0.18390 0.28315 0.25154 0.05

C(6) 0.28458 0.43157 0.17531 0.05

C(7) 0.33719 0.44507 0.15612 0.05

C(8) 0.32254 0.27162 0.14437 0.05

C(9) 0.36170 0.11211 0.15794 0.05

C(10) 0.26725 0.10521 0.17505 0.05

C(11) 0.37155 -0.06331 0.14657 0.05

C(12) 0.43503 -0.04296 0.12907 0.05

C(13) 0.40228 0.09955 0.11489 0.05

C(14) 0.40833 0.27188 0.12781 0.05

C(15) 0.39104 0.42176 0.11178 0.05

C(16) 0.45808 0.34460 0.09500 0.05

C(17) 0.49253 0.15343 0.09961 0.05

C(18) 0.13596 0.03042 0.16826 0.05

C(19) 0.26638 0.05748 0.10618 0.05

C(20) 0.49777 0.03983 0.08120 0.05

C(21) 0.52658 -0.15857 0.08492 0.05

C(22) 0.59712 0.10284 0.06586 0.15

C(23) 0.60438 0.03072 0.04352 0.15

C(24) 0.71842 0.10421 0.03353 0.15

C(25) 0.73636 -0.02646 0.01683 0.15

C(26) 0.86785 -0.02686 0.01443 0.15

C(27) 0.69055 0.09298 0.00529 0.15

Water molecules

O(1) 0.37248 0.43317 0.25964 0.25

O(2) 0.22170 0.71429 0.24038 0.25

Figure 9. View along the b axis of the four structural models 1-4, of the cholesterol bilayer arrangement in the monoclinic phase, space group A2, tested by X-ray structure-factor computations. The intralayer arrangement, containing symmetry-independent cholesterol molecules A and B, is the same in all the models. Note that space group A2 contains rows parallel to the a-axis of twofold (2) and twofold screw axes (21) parallel to b, which alternate along the c–axis.

(a, b) Molecules A1 and A2, and B1 and B2, are related by twofold and twofold screw symmetry in (a) and (b) respectively, yielding corresponding models 1 and 2. The 2- or 21-axis generating the cholesterol bilayer, lies at the unit cell origin x, z = 0,0 (and at x, z = 0.5,0). (c, d) In these two schemes the symmetry axis generating the bilayer lies at x,z = 0.25, 0 (as well as x,z = 0.75, 0) yielding models 3 and 4.

The intralayer arrangement of molecules A and B is such that the two models in each of the pairs 1 and 3, and 2 and 4, are similar.

Figure 10. Hydrogen-bonding arrangement in the crystal structure of the triclinic phase of cholesterol monohydrate (Craven, B. M. In Handbook of Lipid Research. The Physical Chemistry of Lipids; D. M. Small, Ed.; Plenum Press: New York, 1986; Vol. 4; pp 149-182). Open and filled circles are water and sterol O atoms respectively. (Reproduced with permission of Craven, 1976.)

1