Elastic deformations in hexagonal phases studied by small-angle X-ray diffraction and simulations

In this study we present experimental and theoretical results which concern the deviations from circularity of the pivotal plane in the inverse hexagonal phases (H-II) of phospholipid self-assemblies. Due to packing constraints, the cross-section of the polar/apolar interface deviates from a circle, which we studied in minute detail by analysing small-angle X-ray diffraction data of dioleoyl-phosphatidylethanolamine (DOPE) and stearoyl-oleoyl-phosphatidylethanolamine (SOPE), respectively. On this structural basis, Monte Carlo (MC) simulated annealing variations of the free energy were carried out, both on the formation of the H-II-phase and on the particular shape of the cross-section in the H-II-phase. The equilibrium of the H-II-phase pivotal plane contour and the corresponding values of the mean intrinsic curvature, H-m, and the hydrocarbon chain stiffness, tau, were determined from MC calculations. The results of these calculations were tested by solving the corresponding system of non-linear differential equations derived using variational calculus. Here our main aim is to predict the range of possible values of H-m and tau. Comparing the measured structural data with predictions from MC calculations including lipid anisotropy, and accounting for the elastic deformations of the pivotal plane allowed us to determine a relationship between the bending deformation and stretching of hydrocarbon chains.