The Effect of Electrostatics on the Line Tension at the Edge of a Bilayer

Abstract

For bilayers composed of charged lipids placed in an aqueous medium, Betterton and Brenner (Phys Rev. Lett., 2000) showed that the line tension λ at the bilayer edge comprises two contributions: a positive hydrophobic line tension, λh, corresponding to the elastic deformation of lipids in the line, and a negative electrostatic line tension, λe, corresponding to the capacitive energy of double layer charging. They showed that λe depends on a single dimensionless parameter, P, which is the ratio of λh and a characteristic scaling of λe. For values of P below a critical value of 2, the net line tension becomes negative, implying that fluid bilayers with high surface charge densities should be unable to close up to form vesicles, and that vesicles should be unstable structures. However, we have prepared and imaged stable vesicles with surface charge densities and pH/salt conditions corresponding to P<<2; this is inconsistent with the above prediction.To understand this discrepancy, we revisit the calculations of Betterton and Brenner, with the new, key inclusion of details of the geometry of the bilayer. This results in two additional dimensionless parameters in the problem: α, the ratio of the bilayer thickness to the Debye length, and f, the surface charge density in the edge of the bilayer relative to the planar region of the bilayer. If the surface charge density is uniform over the entire bilayer (f=1) and α is O(1) or higher, we show that λh can be positive, i.e. even electrostatics would favor a decrease in the perimeter of an open hole in the bilayer! We delineate conditions under which the net line tension becomes positive, and show that this can happen even when P<<2, in agreement with our experimental observations.