Anderson D M, Gruner S M, Leibler S
Department of Mathematics, University of Massachusetts, Amherst 01003.
Proc Natl Acad Sci U S A. 1988 Aug;85(15):5364-8. doi: 10.1073/pnas.85.15.5364.
Bicontinuous cubic phases, composed of bilayers arranged in the geometries of periodic minimal surfaces, are found in a variety of different lipid/water systems. It has been suggested recently that these cubic structures arrive as the result of competition between two free-energy terms: the curvature energy of each monolayer and the stretching energy of the lipid chains. This scenario, closely analogous to the one that explains the origin of the hexagonal phases, is investigated here by means of simple geometrical calculations. It is first assumed that the lipid bilayer is of constant thickness and the distribution of the (local) mean curvature of the phospholipid-water interfaces is calculated. Then, assuming the mean curvature of these interfaces is constant, the distribution of the bilayer's thickness is calculated. Both calculations quantify the fact that the two energy terms are frustrated and cannot be satisfied simultaneously. However, the amount of the frustration can be smaller for the cubic phase than for the lamellar and hexagonal structures. Therefore, this phase can appear in the phase diagram between the other two, as observed in many recent experiments.
双连续立方相由排列在周期性极小曲面几何结构中的双层组成，在多种不同的脂质/水体系中都能找到。最近有人提出，这些立方结构是两个自由能项之间竞争的结果：每个单层的曲率能和脂质链的拉伸能。这种情况与解释六方相起源的情况非常相似，本文通过简单的几何计算对其进行了研究。首先假设脂质双层厚度恒定，并计算磷脂 - 水界面（局部）平均曲率的分布。然后，假设这些界面的平均曲率恒定，计算双层厚度的分布。这两个计算都量化了这样一个事实，即这两个能量项相互矛盾，不能同时满足。然而，立方相的矛盾程度可能比层状和六方结构的要小。因此，正如最近许多实验所观察到的那样，这个相可以出现在其他两个相之间的相图中。
