  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.
