McLaughlin S, Mulrine N, Gresalfi T, Vaio G, McLaughlin A
J Gen Physiol. 1981 Apr;77(4):445-73. doi: 10.1085/jgp.77.4.445.
The Stern equation, a combination of the Langmuir adsorption isotherm, the Boltzmann relation, and the Grahame equation from the theory of the diffuse double layer, provides a simple theoretical framework for describing the adsorption of charged molecules to surfaces. The ability of this equation to describe the adsorption of divalent cations to membranes containing brain phosphatidylserine (PS) was tested in the following manner. Charge reversal measurements were first made to determine the intrinsic 1:1 association constants of the divalent cations with the anionic PS molecules: when the net charge of a PS vesicle is zero one-half of the available sites are occupied by divalent cations. The intrinsic association constant, therefore, is equal to the reciprocal of the divalent cation concentration at which the mobility of a PS vesicle reverses sign. The Stern equation with this association constant is capable of accurately describing both the zeta potential data obtained with PS vesicles at other concentrations of the divalent cations and the data obtained with with vesicles formed from mixtures of PS and zwitterionic phospholipids. Independent measurements of the number of ions adsorbed to sonicated PS vesicles were made with a calcium-sensitive electrode. The results agreed with the zeta potential results obtained with multilamellar vesicles. When membranes are formed at 20 degrees C in 0.1 M NaCl, the intrinsic 1:1 association constants of Ni, Co, Mn, Ba, Sr, Ca, and Mg with PS are 40, 28, 25, 20, 14, 12, and 8 M-1, respectively.
斯特恩方程结合了朗缪尔吸附等温线、玻尔兹曼关系式以及扩散双电层理论中的格雷厄姆方程,为描述带电分子在表面的吸附提供了一个简单的理论框架。该方程描述二价阳离子在含有脑磷脂酰丝氨酸(PS)的膜上吸附的能力通过以下方式进行了测试。首先进行电荷反转测量,以确定二价阳离子与阴离子PS分子的固有1:1缔合常数:当PS囊泡的净电荷为零时,一半的可用位点被二价阳离子占据。因此,固有缔合常数等于PS囊泡迁移率反转时二价阳离子浓度的倒数。具有此缔合常数的斯特恩方程能够准确描述在其他二价阳离子浓度下用PS囊泡获得的zeta电位数据以及用PS和两性离子磷脂混合物形成的囊泡获得的数据。用钙敏感电极对吸附到超声处理的PS囊泡上的离子数量进行了独立测量。结果与用多层囊泡获得的zeta电位结果一致。当在0.1 M NaCl中于20℃形成膜时,Ni、Co、Mn、Ba、Sr、Ca和Mg与PS的固有1:1缔合常数分别为40、28、25、20、14、12和8 M-1。