We present a molecular-level theory for lipid-protein interaction and apply it to
the study of lipid-mediated interactions between proteins and the protein-induced
transition from the planar bilayer (Lalpha) to the inverse-hexagonal (HII) phase.
The proteins are treated as rigid, membrane-spanning, hydrophobic inclusions of different
size and shape, e.g., "cylinder-like," "barrel-like," or "vase-like." We assume strong
hydrophobic coupling between the protein and its neighbor lipids. This means that,
if necessary, the flexible lipid chains surrounding the protein will stretch, compress,
and/or tilt to bridge the hydrophobic thickness mismatch between the protein and the
unperturbed bilayer. The system free energy is expressed as an integral over local
molecular contributions, the latter accounting for interheadgroup repulsion, hydrocarbon-water
surface energy, and chain stretching-tilting effects. We show that the molecular interaction
constants are intimately related to familiar elastic (continuum) characteristics of
the membrane, such as the bending rigidity and spontaneous curvature, as well as to
the less familiar tilt modulus. The equilibrium configuration of the membrane is determined
by minimizing the free energy functional, subject to boundary conditions dictated
by the size, shape, and spatial distribution of inclusions. A similar procedure is
used to calculate the free energy and structure of peptide-free and peptide-rich hexagonal
phases. Two degrees of freedom are involved in the variational minimization procedure:
the local length and local tilt angle of the lipid chains. The inclusion of chain
tilt is particularly important for studying noncylindrical (for instance, barrel-like)
inclusions and analyzing the structure of the HII lipid phase; e.g., we find that
chain tilt relaxation implies strong faceting of the lipid monolayers in the hexagonal
phase. Consistent with experiment, we find that only short peptides (large negative
mismatch) can induce the Lalpha --> HII transition. At the transition, a peptide-poor
Lalpha phase coexists with a peptide-rich HII phase.