LSEC, National Center for Mathematics and Interdisciplinary Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China.
School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China.
Int J Mol Sci. 2018 Feb 28;19(3):695. doi: 10.3390/ijms19030695.
Membrane channel proteins control the diffusion of ions across biological membranes. They are closely related to the processes of various organizational mechanisms, such as: cardiac impulse, muscle contraction and hormone secretion. Introducing a membrane region into implicit solvation models extends the ability of the Poisson-Boltzmann (PB) equation to handle membrane proteins. The use of lateral periodic boundary conditions can properly simulate the discrete distribution of membrane proteins on the membrane plane and avoid boundary effects, which are caused by the finite box size in the traditional PB calculations. In this work, we: (1) develop a first finite element solver (FEPB) to solve the PB equation with a two-dimensional periodicity for membrane channel proteins, with different numerical treatments of the singular charges distributions in the channel protein; (2) add the membrane as a dielectric slab in the PB model, and use an improved mesh construction method to automatically identify the membrane channel/pore region even with a tilt angle relative to the -axis; and (3) add a non-polar solvation energy term to complete the estimation of the total solvation energy of a membrane protein. A mesh resolution of about 0.25 Å (cubic grid space)/0.36 Å (tetrahedron edge length) is found to be most accurate in linear finite element calculation of the PB solvation energy. Computational studies are performed on a few exemplary molecules. The results indicate that all factors, the membrane thickness, the length of periodic box, membrane dielectric constant, pore region dielectric constant, and ionic strength, have individually considerable influence on the solvation energy of a channel protein. This demonstrates the necessity to treat all of those effects in the PB model for membrane protein simulations.
膜通道蛋白控制着离子在生物膜上的扩散。它们与各种组织机制的过程密切相关，如心脏冲动、肌肉收缩和激素分泌。将膜区域引入隐式溶剂化模型扩展了泊松-玻尔兹曼（PB）方程处理膜蛋白的能力。使用横向周期性边界条件可以正确模拟膜蛋白在膜平面上的离散分布，并避免边界效应，这是传统 PB 计算中由于有限盒尺寸引起的。在这项工作中，我们：（1）开发了第一个有限元求解器（FEPB）来求解具有二维周期性的膜通道蛋白的 PB 方程，对通道蛋白中的奇异电荷分布采用不同的数值处理方法；（2）在 PB 模型中添加膜作为介电片，并使用改进的网格构造方法自动识别膜通道/孔区域，即使相对于 - 轴有倾斜角度；（3）添加非极性溶剂化能项来完成膜蛋白总溶剂化能的估计。发现大约 0.25 Å（立方网格空间）/0.36 Å（四面体边长）的网格分辨率在 PB 溶剂化能线性有限元计算中最为准确。对几个示例分子进行了计算研究。结果表明，所有因素，包括膜厚度、周期性盒的长度、膜介电常数、孔区介电常数和离子强度，都对通道蛋白的溶剂化能有相当大的影响。这表明在膜蛋白模拟中需要在 PB 模型中考虑所有这些效应。
