[Equilibrium surface charge distribution in phospholipid vesicles. I. Method of calculation]

This paper presents a method of calculation of the surface charge equilibrium distribution between the two surfaces of a spherically closed phospholipid bilayer suspended in aqueous electrolyte solution. The net surface charge is supposed to be provided by the ionized polar groups of the phospholipid molecules. Its equilibrium distribution is found by minimization of the free electrostatic energy. The procedure of minimization utilizes the solution of the Poisson-Boltzmann equation which describes the double electric layers of the membrane and an expression for the membrane potential derived under the assumption of absence of charges in the membrane phase. An analytical solution of the problem in the range of validity of the linearized Poisson-Boltzman equation is obtained. It is shown that in this case an equilibrium transmembrane potential exists, and the surface charge density is greater at the outer surface of the vesicle.