Department of Chemistry, Center for Cell and Virus Theory, Indiana University, Bloomington, Indiana 47405, USA.
J Chem Phys. 2010 May 7;132(17):174112. doi: 10.1063/1.3424771.
Electrostatic effects in nanosystems are understood via a physical picture built on their multiscale character and the distinct behavior of mobile ions versus charge groups fixed to the nanostructure. The Poisson-Boltzmann equation is nondimensionalized to introduce a factor lambda that measures the density of mobile ion charge versus that due to fixed charges; the diffusive smearing and volume exclusion effects of the former tend to diminish its value relative to that from the fixed charges. We introduce the ratio sigma of the average nearest-neighbor atom distance to the characteristic size of the features of the nanostructure of interest (e.g., a viral capsomer). We show that a unified treatment (i.e., lambda proportional to sigma) and a perturbation expansion around sigma=0 yields, through analytic continuation, an approximation to the electrostatic potential of high accuracy and computational efficiency. The approach was analyzed via Padé approximants and demonstrated on viral system electrostatics; it can be generalized to accommodate extended Poisson-Boltzmann models, and has wider applicability to nonequilibrium electrodiffusion and many-particle quantum systems.
通过基于多尺度特征和可移动离子与固定在纳米结构上的电荷基团的不同行为的物理图像，可以理解纳米系统中的静电效应。泊松-玻尔兹曼方程被无量纲化，引入一个因子 lambda，它测量可移动离子电荷的密度与固定电荷的密度之比；前者的扩散模糊和体积排斥效应往往会使其相对于固定电荷的密度减小。我们引入平均最近邻原子距离与感兴趣的纳米结构特征（例如病毒衣壳）的特征尺寸的比值 sigma。我们表明，通过解析延拓，统一处理（即 lambda 与 sigma 成正比）和围绕 sigma=0 的微扰展开，可以以高精度和计算效率得到静电势的近似值。该方法通过 Padé 逼近进行了分析，并在病毒系统静电学中进行了演示；它可以推广到扩展的泊松-玻尔兹曼模型，并具有更广泛的适用性，适用于非平衡电扩散和多粒子量子系统。
