Polymorphism, Structure, and Nucleation of Cholesterol·H2O at Aqueous Interfaces and in Pathological Media: Revisited from a Computational Perspective

We revisit the important issues of polymorphism, structure, and nucleation of cholesterol·H2O using first-principles calculations based on dispersion-augmented density functional theory. For the lesser known monoclinic polymorph, we obtain a fully extended H-bonded network in a structure akin to that of hexagonal ice. We show that the energy of the monoclinic and triclinic polymorphs is similar, strongly suggesting that kinetic and environmental effects play a significant role in determining polymorph nucleation. Furthermore, we find evidence in support of various O–H···O bonding motifs in both polymorphs that may result in hydroxyl disorder. We have been able to explain, via computation, why a single cholesterol bilayer in hydrated membranes always crystallizes in the monoclinic polymorph. We rationalize what we believe is a single-crystal to single-crystal transformation of the monoclinic form on increased interlayer growth beyond that of a single cholesterol bilayer, interleaved by a water bilayer. We show that the ice-like structure is also relevant to the related cholestanol·2H2O and stigmasterol·H2O crystals. The structure of stigmasterol hydrate both as a trilayer film at the air–water interface and as a macroscopic crystal further assists us in understanding the polymorphic and thermal behavior of cholesterol·H2O. Finally, we posit a possible role for one of the sterol esters in the crystallization of cholesterol·H2O in pathological environments, based on a composite of a crystalline bilayer of cholesteryl palmitate bound epitaxially as a nucleating agent to the monoclinic cholesterol·H2O form.

. The |F(h,k,l)| 2 values are displayed as a function of increasing q(h,k,l), = 2d*( h,k,l), equally separated for clarity of presentation. The bars marked with an asterisk, represent reflection pairs of the type (2,k,l) and (−2,k,l + 2), which are heavily overlapped in the GIXD pattern and thus are shown superimposed. Reprinted from our previous studies, ref. (3) . Copyright: 2005, Biophysical Journal.
The symmetry of this crystal structure of monoclinic monohydrate was assigned based on 48 reflections, the hkl indices of which obeyed the condition k + l = 2n. The cholesterol molecular packing was then generated by utilizing the cholesteryl myristate crystal structure (4) as an initial model. This is because the cholesteryl myristate crystal structure exhibits a bilayer motif with a,b axial dimensions and a  angle, very similar to those of monoclinic cholesterol.H2O and because its 32.9 Å bilayer thickness almost matches half the length of the c-axis of the monoclinic cholesterol (assuming the latter is a monohydrate phase with a 1.5 Å thick water layer). This was consistent with the calculated density of the monoclinic form (1.029 g/mL) which almost matched the density of the triclinic form of cholesterol (1.048 g/mL).
Even with this structural information some ambiguities still had to be resolved. Firstly, the cholesterol bilayer was generated via a twofold (2) axis as in the cholesteryl myristate crystal structure, with space group A2. However, because this monoclinic space group incorporates rows of twofold (2) and twofold screw (21) axes parallel to b and alternating along the c axis, the cholesterol bilayer could have been constructed across the 21 axes instead. Indeed, the latter arrangement occurs in the organization of a single cholesterol bilayer on the air-water interface, (5) and in the crystal structures of the tridecanoate and stearate derivatives of cholesterol. (6) The model crystal structure, constructed with a cholesterol bilayer whose two leaflets were related by twofold symmetry, was refined by least squares X-ray structure factor analysis. In this procedure, the two sterol molecules per asymmetric unit were treated as rigid bodles (corresponding to 11 parameters), which yielded a satisfactory fit between the observed and computed X-ray structure factors shown in Figure S1.2. The reliability index, , where F(hkl) is the X-ray structure factor of a particular diffraction peak and 'o' and 'c' refer to its observed and calculated values, proved to be as low as 13.5%, indicating an overall correct structure. §2. Eight H-bonding motifs of the triclinic cholesterol.H2O polymorph. Fig. S2. Eight H-bonding motifs of the triclinic cholesterol.H2O polymorph. The number before each dot refers to the configuration of the cholesterol molecules connected by hydrogen bonds between the two hydroxyl groups. In 1.1 to 1.4, one of the oxygens acts as a donor and the other one as an acceptor. In motifs 2.1 to 2.4, cholesterol oxygen molecules switch their roles. The number after the dot refers to the different orientations of the acceptor hydrogen atom, as shown with colored arrows. The donor hydrogen bonding orientation remains unchanged within each donor-acceptor configuration. 1.3 corresponds to the motif originally determined by Craven, (7,8) based on computational refinement of this structure by Frincu et al. (9)

Theoretical morphology simulations
Theoretical crystal morphologies were obtained using the Materials Studio Morphology module 6.1. (11) The crystal shape was simulated by use of the "growth morphology" approach. Attachment energies and surface energies were calculated using the Dreiding force field. (12) We note, however, that the morphology simulation method does not take into account solvent effects and possible surface reconstructions, which could have a profound influence on experimentally observed morphologies.
Cholesterol crystals were grown on supported lipid bilayers ( Fig. S8C and F1) following a procedure described in detail in our previous work . (13) The procedure for crystal growth from cell culture models (Fig. S8F2), following crystal characterization using cryo-transmission electron diffraction and cryo-soft X-ray tomography, is described in Varsano et al. (14) The theoretical growth morphologies of both the triclinic and monoclinic structures were Two cut-off edges expose minor {11 0} and {11 1 } side faces. This is in good agreement with the experimental morphology of triclinic cholesterol crystals grown from water solutions, which appear as thin quadrilateral plates (Fig. S8B, C), where a bi-axial growth along a and b, forming an angle of 101 o , is found. The crystals are so thin that accurate determination of the side faces is difficult to perform.
For the monoclinic structure, the growth analysis predicts a crystal habit with a rectangular shape (Fig. S8D) The very thin crystals develop diagonal end faces (11l) and (1 1l) with an angle between them of ~106°, rather than (010) end faces (Fig. S8E,F1). The long aspect ratio results in the monoclinic crystals having a needle shape (Fig. S8E,F1). Crystals grown from supported bilayers can also form tens of micrometer-long ribbons elongated in b (Fig. S8F2). It is noteworthy that the habit of cholestanol crystals reported by D. Hodgkin (Fig. 5D and S13) matches the transmission electron microscope image of a monoclinic crystal grown on a supported lipid bilayer (Fig. S8F1).     S15. The different stages of cholesterol formation, at the air-water interface, (3,5) or hydrated at both sides. (17,18)  Cross-section through a layer of cholesterol molecules.