  Using integral equation theory of liquids to a binary mixed fluid lipid
membrane, we study the membrane-mediated interactions between the macroions and
the redistribution of neutral and charged lipids due to binding macroions. We
find that when the concentration of binding macroions is infinitely dilute, the
main contribution to the attractive potential between macroions is the line
tension between neutral and charged lipids of the membrane, and the bridging
effect also contributes to the attraction. As the relative concentration of
charged lipids is increased, we observe a repulsive - attractive - repulsive
potential transition due to the competition between the line tension of lipids
and screened electrostatic macroion-macroion interactions. For the finite
concentration of macroions, the main feature of the attraction is similar to
the infinite dilution case. However, due to the interplay of formation of
charged lipid - macroion complexes, the line tension of redistributed binary
lipids induced by single macroion is lowered in this case, and the maximum of
attractive potential will shift toward the higher values of the charged lipid
concentration.
