The adsorption free energy of charged proteins on mixed membranes, containing varying amounts of (oppositely) charged lipids, is calculated based on a mean-field free energy expression that accounts explicitly for the ability of the lipids to demix locally, and for lateral interactions between the adsorbed proteins. Minimization of this free energy functional yields the familiar nonlinear Poisson-Boltzmann equation and the boundary condition at the membrane surface that allows for lipid charge rearrangement. These two self-consistent equations are solved simultaneously. The proteins are modeled as uniformly charged spheres and the (bare) membrane as an ideal two-dimensional binary mixture of charged and neutral lipids. Substantial variations in the lipid charge density profiles are found when highly charged proteins adsorb on weakly charged membranes; the lipids, at a certain demixing entropy penalty, adjust their concentration in the vicinity of the adsorbed protein to achieve optimal charge matching. Lateral repulsive interactions between the adsorbed proteins affect the lipid modulation profile and, at high densities, result in substantial lowering of the binding energy. Adsorption isotherms demonstrating the importance of lipid mobility and protein-protein interactions are calculated using an adsorption equation with a coverage-dependent binding constant. Typically, at bulk-surface equilibrium (i.e., when the membrane surface is 'saturated' by adsorbed proteins), the membrane charges are 'overcompensated' by the protein charges, because only about half of the protein charges (those on the hemispheres facing the membrane) are involved in charge neutralization. Finally, it is argued that the formation of lipid-protein domains may be enhanced by electrostatic adsorption of proteins, but its origin (e.g., elastic deformations associated with lipid demixing) is not purely electrostatic.
Bibliographical noteFunding Information:
The financial support of the Israel Science Foundation (Excellence Center, Grant No. 8003/97) and the U.S.-Israel Binational Science Foundation (Grant No. 94/130) is gratefully acknowledged. S.M. thanks the DFG for support through SFB 197. D.H. thanks the Clore Foundation for a doctoral fellowship. The Fritz Haber research center is supported by the Minerva Foundation, Munich, Germany.