Thickness–radius relationship and spring constants of cholesterol helical ribbons

Abstract

Using quantitative phase microscopy, we have discovered a quadratic relationship between the radius R and the thickness t of helical ribbons that form spontaneously in multicomponent cholesterol-surfactant mixtures. These helical ribbons may serve as mesoscopic springs to measure or to exert forces on nanoscale biological objects. The spring constants of these helices depend on their submicroscopic thickness. The quadratic relationship (R ؔ t 2 ) between radius and thickness is a consequence of the crystal structure of the ribbons and enables a determination of the spring constant of any of our helices solely in terms of its observable geometrical dimensions.biological force spectroscopy ͉ elasticity of thin films ͉ phase-contrast microscopy in biophysics T he elastic properties of meso-and nanoscale thin elastic strips forming helical ribbons or tubules, have been the focus of active recent research in both biophysics and nanoscience communities (1-7). We have discovered that in a number of complex aqueous solutions containing a sterol (cholesterol in particular) and a mixture of surfactants, the sterol molecules may self-assemble into ribbons of helical shape (8). The geometry of the helical ribbons is characterized by the radius, width, thickness, contour length, and pitch angle, see figure 1a in ref. 9. Remarkably, the pitch angle is always either 11°or 54°, whereas axial length, width, and radius vary by two orders of magnitude in the range from 1 to Ϸ100 m. These helical ribbons are fascinating objects for fundamental studies (2,(8)(9)(10). Furthermore, because low-pitch helical ribbons have spring constants in the range of 0.5 to 500 pN/m (2), and the elongation of these springs from 1 m up to 100 m can easily be observed microscopically, it follows that they can be used as mesoscopic spring scales to measure forces between nanoscale biological objects in the range from 0.5 pN to 50 nN. For this and other applications, the ability to readily determine the spring constants of individual helixes is of crucial importance. In this article, we establish the relationship between the spring constant of the low-pitch cholesterol helical ribbons and its readily observable dimensions: width, radius, and length.Originally, it had been thought that cholesterol helical ribbons formed in surfactant mixtures had liquid crystalline structure and that their shape was governed by elastic properties of liquid crystalline layer (9,11,12). Recently, we have shown by X-ray diffraction that these helical ribbons are, in fact, single crystals with structure closely resembling that of cholesterol monohydrate (10). Having in mind the single-crystal nature of our ribbons, we have proposed that their helical shape is determined by a balance between two terms in the free energy of deformation of the cholesterol crystalline strip (2). The first term, the spontaneous bending energy, favors curling toward one of the two faces of the ribbon and is linear in curvature, ϪK s /R. The second term is the elastic energy of bending a strip. Thi...

Nanotubes Self-Assembled from Amphiphilic Molecules via Helical Intermediates

“…Zastavker et al., who have experimented with diverse helix forming systems based on the crystallization of cholesterol in bile, found it unlikely that all of these systems, involving diverse molecular species, would have precisely the same two angles of molecular packing and consequently sought other explanations. Indeed, researchers in investigating the crystallization of cholesterol tend to believe that the helical assemblies that they work on are distinct from the others discussed in this Review and provide good evidence to this effect. , …”

“…It seems that crystallinity has often been used to describe the phase of tubules, and crystallization as the tubule forming process, simply for want of better terms to characterize the prevailing high degree of order. Nevertheless, some researchers argue that the tubule phase is crystalline. ,− Evidence to support this argument includes X-ray and electron diffraction studies on diacetylenic lipid tubules, which have shown chain packing with crystalline character over the length scales probed by these techniques. − Such experiments have so far produced insufficient resolution to examine the extent of the correlation length, and the large number of higher harmonics is only really indicative of a highly defined lamellar order. , Part of the argument for the crystalline nature of tubes is based on the X-ray diffraction (XRD) analysis of dried tube samples, where it has been suggested that the hydration of the bilayer does not significantly affect lipid packing, although this is a dangerous assumption to make . Indeed, Thomas et al found that dry tubes showed 3-D crystallinity, while a suspension in a water/ethanol solution had no evident interlayer correlations.…”

“…Such a polymerization requires specific alignment and spacing of diacetylenic groups, and this, it is argued, is indicative of the crystallinity within the self-assembled tubes. , Similarly, Fuhrhop postulates that the regular nature of the helices that form tubes (long ribbons with constant width) provides sufficient evidence for crystallinity. Likewise, researchers working on helically based tubes of cholesterol ,, suggest that the organization of cholesterol into tubules is crystalline, as these tubules are the precursor for cholesterol monohydrate crystals. These arguments that are based on apparent amphiphile organization, however, are equally well sustained by a tubule existing in highly correlated hexatic phases; a hypothesis that is supported by the majority of theoretical argument and the weight of experimental evidence …”

Cholesterol – a biological compound as a building block in bionanotechnology

“…The quadratic relationship (R f t 2 ) between radius and thickness is a consequence of the crystal structure of the ribbons and enables the determination of the spring constant of any helices solely in terms of its observable geometrical dimensions. 111 Choi et al used high-speed synthetic aperture microscopy to image helical cholesterol ribbons in surfactant mixtures, as well as to measure the thickness of a nanoscale cholesterol helical ribbon ( Fig. 3b) which was determined to be 68 nm.…”

High-speed synthetic aperture microscopy for live cell imaging

“…Many applications of the quantitatively recorded phase information have been reported in studying biological specimens [1,2]. For samples with a homogeneous refractive index, quantified phase information can be used to determine the height of samples with nanometer accuracy [3]. Another important use of phase information is that it enables high-speed three-dimensional (3D) imaging of a sample without scanning an objective lens via numerical propagation along the axial direction [4].…”