Helical structures of tilted chiral lipid bilayers viewed as cholesteric liquid crystals

We have derived the tilt and surface shape-equilibrium equations for tilted chiral lipid bilayers (TCLB's) in analogy with cholesteric liquid crystals. On a cylindrical surface the field of tilt directions of TCLB molecules forms a right-handed helix with 45^∘{} gradient angle for k₂>0 or a left-handed helix with -45^∘{} angle for k₂0, where k₂ is the cholesteric chiral curvature modulus. In addition, there exists another type of helical structure that looks like twisted strips or helicoids. We also show that on a spherical surface the tilt field has at least two singular points. These results explain the observed succession of transitions from a vesicular dispersion to a phase involving helical structures and then to tubes.