Stability of Inverse Bicontinuous Cubic Phases in Lipid-Water Mixtures

Abstract

We investigate the stability of seven inverse bicontinuous cubic phases [G, D, P, C͑P͒, S, I-WP, F-RD] in lipid-water mixtures based on a curvature model of membranes. Lipid monolayers are described by parallel surfaces to triply periodic minimal surfaces. The phase behavior is determined by the distribution of the Gaussian curvature on the minimal surface and the porosity of each structure. Only G, D, and P are found to be stable, and to coexist along a triple line. The calculated phase diagram agrees very well with experimental results for 2:1 lauric acid͞DLPC. 61.30.Cz, 87.16.Dg Most of the many mesomorphic phases formed by lipid-water mixtures are of the inverse type, with the selfassembled lipid monolayers curving towards the aqueous regions [1]. In inverse bicontinuous cubic phases, a single lipid bilayer extends throughout the whole sample, dividing it into two percolating water labyrinths. Until now, the structures G, D, and P have been identified. The only known lipid-water system in which G, D, and P coexist is 2:1 lauric acid͞DLPC and water [2]. The property of cubic lipid bilayer phases to divide space into interwoven polar and apolar compartments is utilized for biological function, e.g., in mitochondria and the endoplasmic reticulum [3]. Recently, they have also been used as artificial matrices which enable membrane proteins such as bacteriorhodopsin to crystallize in a three-dimensional array [4].It was shown by Luzzati and co-workers [5] that the midsurfaces of the lipid bilayers are very close to cubic minimal surfaces, which have zero mean curvature everywhere. These surfaces occur in lipid-water systems due to the local symmetry of the lipid bilayer, which implies that the surface should curve to both sides in the same way. However, it is well known [6] that many more cubic minimal surfaces exist than the structures G, D, and P identified in lipid-water mixtures. What might be the reason why these other phases have not been observed thus far? Helfrich and Rennschuh [7] argued that, based on the curvature model for fluid membranes [8], structures with a narrow distribution of Gaussian curvature over the minimal midsurface should be most favorable. However, the relevant data was known to them only for G, D, and P, which are degenerate in this respect due to the existence of a Bonnet transformation. Recently, we obtained numerical representations for a large number of cubic minimal surfaces in the framework of a simple Ginzburg-Landau model [9]. In this Letter we use this data to investigate seven inverse bicontinuous cubic phases (G, D, P, C͑P͒, S, I-WP, F-RD). For an illustration of the G and S surfaces, see Fig. 1. We find that the width of the different distributions of Gaussian curvature is indeed smallest for G, D, and P and larger for all other structures considered.This proves for the first time why only G, D, and P should be observed experimentally.Our detailed investigation of the stability of bicontinuous cubic phases shows that the existence of the Bonnet transformation implies...

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