Kleijn W B, Bruner L J
J Theor Biol. 1983 Jan 7;100(1):139-52. doi: 10.1016/0022-5193(83)90098-x.
To calculate the electric field inside a membrane the aqueous phase can be approximated by a conductor since the dielectric constant of water is much larger than that of the membrane. Then, using the method of image charges, ions adsorbed inside the membrane can be considered as dipoles and dipolar molecules adsorbed inside the membrane may similarly be regarded as sets of two similarly oriented dipoles. The microscopic interactions and, therefore, the spatial correlations of the adsorbed species can then be obtained. Together with the Gouy theory for the diffuse double layer these results allow the determination of the adsorbed phase--aqueous phase equilibrium. From the densities and spatial correlations of the adsorbed ions and dipolar species, their influence upon the electrostatic barrier as experienced by an ion translocating the membrane can be calculated. Changes observed in the relaxation time and initial conductance of translocating hydrophobic ions in voltage-pulse experiments on bilayer membranes are predicted using this model of the electrostatic barrier. In addition, an equation giving the surface tension as a function of the (non-ideal) adsorption of hydrophobic ions and dipoles is derived.
为了计算膜内的电场，由于水的介电常数远大于膜的介电常数，水相可近似为导体。然后，利用镜像电荷法，膜内吸附的离子可被视为偶极子，膜内吸附的偶极分子同样可被看作是两组同向偶极子。这样就可以得到吸附物质的微观相互作用以及空间相关性。结合扩散双层的古依理论，这些结果可用于确定吸附相 - 水相平衡。根据吸附离子和偶极物质的密度及空间相关性，可计算出它们对跨膜离子所经历的静电势垒的影响。利用这个静电势垒模型，可以预测在双层膜电压脉冲实验中，跨膜疏水离子的弛豫时间和初始电导率所观察到的变化。此外，还推导了一个将表面张力表示为疏水离子和偶极子（非理想）吸附函数的方程。
