JoŽef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia.
Soft Matter. 2018 Feb 14;14(7):1149-1161. doi: 10.1039/c7sm02207g.
The importance of electrostatic interactions in soft matter and biological systems can often be traced to non-uniform charge effects, which are commonly described using a multipole expansion of the corresponding charge distribution. The standard approach when extracting the charge distribution of a given system is to treat the constituent charges as points. This can, however, lead to an overestimation of multipole moments of high order, such as dipole, quadrupole, and higher moments. Focusing on distributions of charges located on a spherical surface - characteristic of numerous biological macromolecules, such as globular proteins and viral capsids, as well as of inverse patchy colloids - we develop a novel way of representing spherical surface charge distributions based on the von Mises-Fisher distribution. This approach takes into account the finite spatial extension of individual charges, and leads to a simple yet powerful way of describing surface charge distributions and their multipole expansions. In this manner, we analyze charge distributions and the derived multipole moments of a number of different spherical configurations of identical charges with various degrees of symmetry. We show how the number of charges, their size, and the geometry of their configuration influence the behavior and relative importance of multipole magnitudes of different order. Importantly, we clearly demonstrate how neglecting the effect of charge size leads to an overestimation of high-order multipoles. The results of our work can be applied to construct analytical models of electrostatic interactions and multipole expansion of charged particles in diverse soft matter and biological systems.
静电相互作用在软物质和生物系统中的重要性通常可以追溯到非均匀电荷效应，这些效应通常可以用相应电荷分布的多极展开来描述。从给定系统中提取电荷分布的标准方法是将组成电荷视为点。然而，这可能导致高阶多极矩（如偶极矩、四极矩和更高阶矩）的高估。本研究关注位于球形表面上的电荷分布 - 这是许多生物大分子（如球状蛋白质和病毒衣壳）以及反向镶嵌胶体的特征 - 我们开发了一种基于冯·米塞斯-费歇尔分布（von Mises-Fisher distribution）的表示球形表面电荷分布的新方法。这种方法考虑了单个电荷的有限空间延伸，并为描述表面电荷分布及其多极展开提供了一种简单而强大的方法。通过这种方式，我们分析了许多具有不同对称性的相同电荷的不同球形构型的电荷分布和导出的多极矩。我们展示了电荷数量、大小以及它们的配置几何形状如何影响不同阶次多极矩的行为和相对重要性。重要的是，我们清楚地表明，忽略电荷大小的影响会导致高阶多极矩的高估。我们工作的结果可应用于构建不同软物质和生物系统中带电粒子的静电相互作用和多极展开的分析模型。
