  We derived free energy functional of a bilayer lipid membrane from the first
principles of elasticity theory. The model explicitly includes
position-dependent mutual slide of monolayers and bending deformation. Our free
energy functional of liquid-crystalline membrane allows for incompressibility
of the membrane and vanishing of the in-plane shear modulus and obeys
reflectional and rotational symmetries of the flat bilayer. Interlayer slide at
the mid-plane of the membrane results in local difference of surface densities
of the monolayers. The slide amplitude directly enters free energy via the
strain tensor. For small bending deformations the ratio between bending modulus
and area compression coefficient, Kb/KA, is proportional to the square of
monolayer thickness, h. Using the functional we performed self-consistent
calculation of steric potential acting on bilayer between parallel confining
walls separated by distance 2d. We found that temperature-dependent curvature
at the minimum of confining potential is enhanced four times for a bilayer with
slide as compared with a unit bilayer. We also calculate viscous modes of
bilayer membrane between confining walls. Pure bending of the membrane is
investigated, which is decoupled from area dilation at small amplitudes. Three
sources of viscous dissipation are considered: water and membrane viscosities
and interlayer drag. Dispersion has two branches. Confinement between the walls
modifies the bending mode with respect to membrane in bulk solution.
Simultaneously, inter-layer slipping mode, damped by viscous drag, remains
unchanged by confinement.
