  We studied the adsorption of a charged protein onto an oppositely charged
membrane, composed of mobile phospholipids of differing valence, using a
statistical-thermodynamical approach. A two-block model was employed, one block
corresponding to the protein-affected region on the membrane, referred to as
the adsorption domain, and the other to the unaffected remainder of the
membrane. We calculated the protein-induced lipid rearrangement in the
adsorption domain as arising from the interplay between the electrostatic
interactions in the system and the mixing entropy of the lipids. Equating the
electrochemical potentials of the lipids in the two blocks yields an expression
for the relations among the various lipid fractions in the adsorption domain,
indicating a sensitive dependence of lipid fraction on valence. This expression
is a result of the two-block picture but does not depend on further details of
the protein-membrane interaction. We subsequently calculated the lipid
fractions themselves using the Poisson-Boltzmann theory. We examined the
dependence of lipid enrichment, i.e., the ratio between the lipid fractions
inside and outside the adsorption domain, on various parameters such as ionic
strength and lipid valence. Maximum enrichment was found for lipid valence of
about (-3) to (-4) in physiological conditions. Our results are in qualitative
agreement with recent experimental studies on the interactions between peptides
having a domain of basic residues and membranes containing a small fraction of
the polyvalent phosphatidylinositol 4,5-bisphosphate (PIP2). This study
provides theoretical support for the suggestion that proteins adsorbed onto
membranes through a cluster of basic residues may sequester PIP2 and other
polyvalent lipids.
