Structure of cholesterol helical ribbons and self-assembling biological springs

Abstract

We report the results of x-ray-scattering studies of individual helical ribbons formed in multicomponent solutions of cholesterol solubilized by various surfactants. The solutions were chemically defined lipid concentrate (CDLC) and model bile. In these and many analogous multicomponent surfactant-cholesterol solutions, helical ribbons of two well defined pitch angles, namely 11°and 54°, are formed. We have suggested previously that this remarkable stability results from an underlying crystalline structure of the sterol ribbon strips. Using a synchrotron x-ray source, we have indeed observed Bragg reflections from individual ribbons having 11°pitch angle. We have been able to deduce the parameters of the unit cell. The crystal structure of these ribbons is similar to that of cholesterol monohydrate, with the important difference that the length of the unit cell perpendicular to the cholesterol layers is tripled. We discuss possible origins for this triplication as well as the connection between the crystalline structure and the geometrical form of the helical ribbons.crystal structure ͉ x-ray diffraction ͉ crystallization ͉ surfactants S elf assembly of helical ribbons in complex fluids is an interesting phenomenon, which poses fundamental questions about the molecular structure, elastic properties, and kinetic evolution of these objects. In particular, quaternary solutions, which contain cholesterol, nonionic surfactants, and lipids, spontaneously form helical ribbons with characteristic pitch angles of 11°and 54°. These helical ribbons are long rectangular strips, which curl along a cylindrical surface. These objects were discovered in human gallbladder bile, where they form spontaneously upon the dilution of bile. This dilution produces a solution supersaturated with respect to cholesterol (1). Formation of similar helical ribbons has been later reported in Ͼ20 different solutions with various sterols analogous to cholesterol, surfactants, and phospholipids or fatty acids (2). These helical ribbons form in a variety of axial lengths, widths, and radii. Remarkably, however, almost all have pitch angles of either 11°o r 54°. Several theoretical models have been proposed to explain the formation and properties of helical ribbons, which sometimes form in complex fluids containing chiral amphiphilic molecules (3-10). These theories were designed to describe the helical ribbons in solutions containing a single species of phospholipids, which can form bilayers. Therefore, the ribbons were modeled theoretically as fluid bilayers, where hydrophobic carbon chains are sandwiched between hydrophilic head groups. Calculations of the properties of such membranes are usually based on the curvature elasticity model (11), which is founded on general physical arguments about the dependence of the fluid membrane elastic free energy on its curvature. Based on this model, subsequent theories attempted to explain the geometrical and elastic properties of the helical ribbons. For example, the formation of helices is attributed to b...

Concise theory of chiral lipid membranes

“…(vii) Twisted ribbons satisfy Euler-Lagrange equations (33), (34) and boundary conditions (35)- (38). The ratio between the width and pitch of the ribbons is proportional to the relative concentration difference of left-and right-handed enantiomers in the low relative concentration difference region, which is in good agreement with the experiment [9].…”

“…It has recently been found that the cholesterol helical stripes have good crystal structure [38], which is out of the range of our theory. There might be two possible ramifications based on the present theory: One would be to include anisotropic bending effects [39] in the free energy density (8); Another one would be to consider a line tension γ depending on the angle between the directions of the tilting and the free edges [40] in the free energy (32).…”

“…Thus δF = 0 will give the Euler-Lagrange equation (34) and boundary conditions (37) and (38). For a cylindrical surface, take a frame such that e 1 , e 2 and e 3 are along the circumferential, axial and radial directions, respectively.…”

Anisotropic surface effects on the formation of chiral morphologies of nanomaterials

“…Therefore, they concluded that molecular chirality is not the determining factor in helix formation. Recently, Khaykovich et al (2007) further examined the structure of cholesterol helical ribbons and self-assembled biological springs at the molecular and granular levels.…”

Neutron and X-ray scattering for biophysics and biotechnology: examples of self-assembled lipid systems

“…For example, surfactant-lipid-sterol systems form unusually thick helical ribbons, despite the absence of a bilayer structure and the predominance of sterol in their composition. 71 …”