Kumaran V
Department of Chemical Engineering, Indian Institute of Science, Bangalore 560 012, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Nov;64(5 Pt 1):051922. doi: 10.1103/PhysRevE.64.051922. Epub 2001 Oct 30.
The modification of the curvature moduli due to surface charges in lipid bilayers 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 the 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 constant values. The total energy of curvature for a symmetrically charged membrane becomes negative when the charge density is increased beyond a critical value, indicating that the membrane spontaneously forms vesicles. An asymmetry in the charge densities on the two monolayers that form the bilayer results in a spontaneous curvature, and the radius of curvature could be large compared to the Debye length when the asymmetry is small. The case of adsorbed charges is also considered, where there is a reduction in the chemical 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 Gaussian curvature approach values identical to that for a surface with fixed charges. Numerical calculations of the change in the curvature moduli with realistic parameter values indicate that these effects are likely to be of importance in the spontaneous formation of vesicles.
利用电荷密度与表面电势之间关系的非线性泊松 - 玻尔兹曼方程，分析了脂质双层中表面电荷对曲率模量的影响。采用了一个小参数ε（即德拜长度与曲率半径之比）进行展开。在低电荷密度下，恢复了从德拜 - 休克尔近似得到的先前结果。在高电荷密度下，对平均曲率和高斯曲率的修正趋近于恒定值。当电荷密度增加超过临界值时，对称带电膜的总曲率能变为负值，这表明膜会自发形成囊泡。形成双层的两个单分子层上电荷密度的不对称会导致自发曲率，当不对称性较小时，曲率半径可能比德拜长度大。还考虑了吸附电荷的情况，即电荷吸附在表面时化学能会降低。在低电荷密度下，平均曲率和高斯曲率的大小与固定电荷的情况相等但符号相反，而在高电荷密度下，平均曲率和高斯曲率趋近于与固定电荷表面相同的值。用实际参数值对曲率模量变化进行的数值计算表明，这些效应在囊泡的自发形成中可能很重要。
