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We present a general theory for the equilibrium structure of cylindricaltubules and helical ribbons of chiral lipid membranes. This theory is based ona continuum elastic free energy that permits variations in the direction ofmolecular tilt and in the curvature of the membrane. The theory shows that theformation of tubules and helical ribbons is driven by the chirality of themembrane. Tubules have a first-order transition from a uniform state to ahelically modulated state, with periodic stripes in the tilt direction andripples in the curvature. Helical ribbons can be stable structures, or they canbe unstable intermediate states in the formation of tubules.Comment: 43 pages, including 12 postscript figures, uses REVTeX 3.0 and  epsf.st

Theory of cylindrical tubules and helical ribbons of chiral lipid membranes