  When the charge densities on the inner and outer surface of the vesicle
membrane are similar one may assume that the potential at a point closer to the
outer/inner surface is more affected by the charges located at the outer/inner
surface of the vesicle membrane. However, because of the curvature of the
vesicle and the screening effect of the electrolyte ions the situation is more
complicated. When the charge densities at the inner and outer surface of the
vesicle membrane are the same then at any finite distance Z from the center of
the vesicle the contribution of the charges, located at the outer membrane
surface, to the vesicle potential Vex is different from the contribution of the
charges, located at the inner membrane surface, to the vesicle potential Vin.
At low electrolyte ion concentrations (from C=0 to 0.00001 [Mol]) Vex/Vin>1 and
increases with increasing distance from the center of the vesicle until the
external surface of the vesicle membrane. With further increasing distance
Vex/Vin remains constant at C=0 [Mol], while at C>0 [Mol] it starts decreasing.
However, at high electrolyte ion concentrations (C>0.01 [Mol]) with increasing
distance from the center of the vesicle Vex/Vin reaches its maximum at the
internal surface of the vesicle membrane. With further increasing distance,
close to the outer surface of the vesicle Vex/Vin becomes less than 1 (i.e. the
charges at the inner surface of the membrane contribute to the potential more
than the charges at the outer surface). Further increasing the distance Vex/Vin
reaches its minimum and then increases to 1 (i.e. the charges at the inner
surface of the membrane contribute to the potential like the charges at the
outer surface of the membrane). With increasing electrolyte ion concentration
the minimum of Vex/Vin is getting deeper (approaching zero) and its location is
getting closer to the outer surface of the vesicle.
