标题： 手性脂质膜的简明理论 显示英文标题

标题： Concise theory of chiral lipid membranes

摘要： 一种手性脂质膜的理论是基于一个简洁的自由能密度提出的，该密度包括了膜的弯曲和表面张力的贡献，以及倾斜分子的手性和取向变化。 该理论与之前的实验一致 [J.M. Schnur \textit{等.}, Science \textbf{264}, 945 (1994); M.S. Spector \textit{等.}, Langmuir \textbf{14}, 3493 (1998); Y. Zhao, \textit{等.}, Proc. Natl. Acad. Sci. USA \textbf{102}, 7438 (2005)] 关于DC$_{8,9}$PC自组装手性脂质膜的实验。 如果其两个生成半径的比值大于$\sqrt{2}$，则从欧拉-拉格朗日方程可以预测一个环面。 发现具有螺旋调制倾斜状态的管状结构不被欧拉-拉格朗日方程所允许，并且它们的能量不如管状结构中的螺旋波纹更有利。 螺旋波纹的倾角理论上估计约为 0$^\circ$和 35$^\circ$，这与实验中观察到的最常见值 5$^\circ$和 28$^\circ$非常接近 [N. Mahajan\textit{等.}, Langmuir\textbf{22}, 1973 (2006)]。 此外，该理论还可以解释非手性阳离子两亲分子与手性酒石酸反离子相互作用形成的扭曲条带。 扭曲条带的宽度与间距之比在低相对浓度差区域被预测与左旋和右旋对映体的相对浓度差成正比，这与实验结果[R. Oda \textit{等.}，Nature (London) \textbf{399}，566 (1999)]有很好的一致性。 显示英文摘要

摘要： 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)].