U. S. Schwarz and G. Gompper
Bending frustration of lipid-water mesophases based on cubic minimal surfaces
Langmuir 17 (7): 2084 -2096 (2001)

Inverse bicontinuous cubic phases are ubiquitous in lipid-water
mixtures and consist of a lipid bilayer forming a cubic minimal
surface, thereby dividing space into two cubic networks of water
channels. For small hydrocarbon chain lengths, the monolayers can be 
modeled as parallel surfaces to a minimal midsurface.  The bending
energy of the cubic phases is determined by the
distribution of Gaussian curvature over the minimal midsurfaces
which we calculate for seven different structures (G, D, P, I-WP,
C(P), S and F-RD). We show that the free-energy densities of the
structures G, D and P are considerably lower than those of the other
investigated structures due to their narrow distribution of Gaussian
curvature.  The Bonnet transformation between G, D, and P implies that
these phases coexist along a triple line, which also includes an 
excess water phase.  Our model includes thermal membrane undulations. 
Our qualitative predictions remain unchanged when higher order terms in 
the curvature energy are included. Calculated phase diagrams agree 
well with the experimental results for 2:1 lauric acid/dilauroyl 
phosphatidylcholine and water.