Effect of surface charges on the curvature moduli of a membrane - art. no.051922

The modificatior, of the curvature moduli due to surface charges in lipid b ilayers is analyzed using the nonlinear Poisson-Boltzmann equation for the relationship between the charge density and surface potential. An expansion in a small parameter epsilon, which is the ratio of the Debye length and t he radius of curvature, is used. At low charge densities, previous results obtained from the Debye-Huckel approximation are recovered. At high charge densities, the corrections to the mean and Gaussian curvature approach cons tant values. The total energy of curvature for a symmetrically charged memb rane becomes negative when the charge density is increased beyond a critica l value, indicating that the membrane spontaneously forms vesicles. An asym metry in the charge densities on the two monolayers that form the bilayer r esults in a spontaneous curvature, and the radius of curvature could be lar ge compared to the Debye length when the asymmetry is small. The case of ad sorbed charges is also considered, where there is a reduction in the chemic al energy when a charge is adsorbed on the surface. At low charge density, the mean and Gaussian curvature are equal in magnitude and opposite in sign to that for fixed charges, while at high charge density, the mean and Gaus sian curvature approach values identical to that for a surface with fixed c harges. Numerical calculations of the change in the curvature moduli with r ealistic parameter values indicate that these effects are likely to be of i mportance in the spontaneous formation of vesicles.