  Random lateral translocation of lipids and proteins is a universal process on
membrane surfaces. Local aggregation or organization of lipids and proteins can
be induced when this lateral random diffusion is mediated by the electrostatic
interactions and membrane curvature. Though the lateral diffusion rates of
lipids on membrane of various compositions are measured and the electrostatic
free energies of predetermined protein-membrane-lipid systems can be computed,
the process of the aggregation and the evolution to the electrostatically
favorable states remain undetermined. Here we propose an electrodiffusion
model, based on the variational principle of free energy functional, for the
self-consistent lateral drift-diffusion of multiple species of charged lipids
on membrane surfaces. Finite sizes of lipids are modeled to enforce the
geometrical constraint of the lipid concentration on membrane surfaces. A
surface finite element method is developed to appropriate the Laplace-Beltrami
operators in the partial differential equations (PDEs) of the model. Our model
properly describes the saturation of lipids on membrane surface, and correctly
predicts that the MARCKS peptide can consistently sequester three multivalent
phosphatidylinositol 4,5-bisphosphate (\pip2) lipids through its basic amino
acid residues, even there is a large fraction of monovalent phosphatidylserine
(PS) in the membrane. Solutions of the PDEs also show the salt-dependence of
the lipid sequestration.
