Splay and tilt energy of bipolar lipid membranes
  Archaea organisms are able to survive in extremely aggressive environment. It is thought that such resistance, at least, in part is sustained by unique properties of archaea membrane. The membrane consists of so called bolalipids, which has two polar heads joined by two hydrocarbon chains. Thus bolalipids can exist in two conformations: i) polar heads are located at different sides of bolalipid layer, so called, O-shape; ii) polar heads are located at the same side of the layer, so called, U-shape. Both polar heads and chains are chemically different from those for conventional lipids. In the present study we develop basis for theory of elasticity of bolalipid membranes. Deformations of splay, tilt and Gaussian curvature are considered. We show that energetic contributions of tilt deformation from two surfaces of bolalipid layer are additive, as well as Gaussian curvature, while splay deformations yield a cross-term. The presence of U-shapes is taken into account in terms of the layer spontaneous curvature. Estimation of tilt modulus and possible experiments allowing to measure splay moduli are described. 
Timur R. Galimzyanov, Peter I. Kuzmin, Peter Pohl, Sergey A. Akimov
cond-mat.soft