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, τ, 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 τ. 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.