Concise theory of chiral lipid membranes

Abstract

A theory of chiral lipid membranes is proposed on the basis of a concise free energy density which includes the contributions of the bending and the surface tension of membranes, as well as the chirality and orientational variation of tilting molecules. This theory is consistent with the previous experiments [J.M. Schnur \textit{et al.}, Science \textbf{264}, 945 (1994); M.S. Spector \textit{et al.}, Langmuir \textbf{14}, 3493 (1998); Y. Zhao, \textit{et al.}, Proc. Natl. Acad. Sci. USA \textbf{102}, 7438 (2005)] on self-assembled chiral lipid membranes of DC${}_{8,9}$PC. A torus with the ratio between its two generated radii larger than $\sqrt{2}$ is predicted from the Euler-Lagrange equations. It is found that tubules with helically modulated tilting state are not admitted by the Euler-Lagrange equations, and that they are less energetically favorable than helical ripples in tubules. The pitch angles of helical ripples are theoretically estimated to be about 0${}^{\circ }$ and 35${}^{\circ }$, which are close to the most frequent values 5${}^{\circ }$ and 28${}^{\circ }$ observed in the experiment [N. Mahajan \textit{et al.}, Langmuir \textbf{22}, 1973 (2006)]. Additionally, the present theory can explain twisted ribbons of achiral cationic amphiphiles interacting with chiral tartrate counterions. The ratio between the width and pitch of twisted ribbons is predicted to be 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 [R. Oda \textit{et al.}, Nature (London) \textbf{399}, 566 (1999)].

14 pages, 7 figures

References in corpus (10)

• Nematic textures in spherical shells
• Theory of Cylindrical Tubules and Helical Ribbons of Chiral Lipid Membranes
• Geometric theory on the elasticity of bio-membranes
• Lipid membranes with free edges
• Lipid membranes with an edge
• The Role of Bilayer Tilt Difference in Equilibrium Membrane Shapes
• Rigid Chiral Membranes
• Microscopic membrane elasticity and interactions among membrane inclusions: Interplay between the shape, dilation, tilt and tilt-difference modes
• Stability of Texture and Shape of Circular Domains of Langmuir Monolayers
• Tilt Texture Domains on a Membrane and Chirality induced Budding

Cited by in corpus (8)

• Monte Carlo simulations of fluid vesicles with in plane orientational ordering
• Surface free energies for nematic shells
• Recent theoretical advances in elasticity of membranes following Helfrich's spontaneous curvature model
• Active morphogenesis of patterned epithelial shells
• Chiral edge fluctuations of colloidal membranes
• Possible effects of tilt order on phase transitions of a fixed connectivity surface model
• Chiral fluid membranes with orientational order and multiple edges
• Spherical surface models with directors