Kuyucak S, Hoyles M, Chung S H
Department of Theoretical Physics, Research School of Physical Sciences, Australian National University, Canberra, ACT.
Biophys J. 1998 Jan;74(1):22-36. doi: 10.1016/S0006-3495(98)77763-X.
Analytical solutions of Poisson's equations satisfying the Dirichlet boundary conditions for a toroidal dielectric boundary are presented. The electric potential computed anywhere in the toroidal conduit by the analytical method agrees with the value derived from an iterative numerical method. We show that three different channel geometries, namely, bicone, catenary, and toroid, give similar potential profiles as an ion traverses along their central axis. We then examine the effects of dipoles in the toroidal channel wall on the potential profile of ions passing through the channel. The presence of dipoles eliminates the barrier for one polarity of ion, while raising the barrier for ions of the opposite polarity. We also examine how a uniform electric field from an external source is affected by the protein boundary and a mobile charge. The channel distorts the field, reducing it in the vestibules, and enhancing it in the constricted segment. The presence of an ion in one vestibule effectively excludes ions of the same polarity from that vestibule, but has little effect in the other vestibule. Finally, we discuss how the solutions we provide here may be utilized to simulate a system containing a channel and many interacting ions.
给出了满足环形电介质边界狄利克雷边界条件的泊松方程的解析解。通过解析方法计算出的环形管道内任意位置的电势与通过迭代数值方法得出的值一致。我们表明，三种不同的通道几何形状，即双锥、悬链线和环形，在离子沿其中心轴移动时具有相似的电势分布。然后，我们研究了环形通道壁中的偶极子对通过通道的离子电势分布的影响。偶极子的存在消除了一种极性离子的势垒，同时提高了相反极性离子的势垒。我们还研究了来自外部源的均匀电场如何受到蛋白质边界和移动电荷的影响。通道使电场发生畸变，在前庭区域减弱电场，而在收缩段增强电场。一个前庭中存在离子有效地排除了该前庭中相同极性的离子，但对另一个前庭影响很小。最后，我们讨论了如何利用我们这里提供的解来模拟包含一个通道和许多相互作用离子的系统。
