Mechanical Engineering Department, School of Engineering, University of Connecticut, Storrs, CT, United States of America.
Pharmaceutical Sciences Department, School of Pharmacy, University of Connecticut, Storrs, CT, United States of America.
PLoS One. 2018 Apr 9;13(4):e0195618. doi: 10.1371/journal.pone.0195618. eCollection 2018.
Many physical simulations aim at evaluating the net interaction between two rigid bodies, resulting from the cumulative effect of pairwise interactions between their constituents. This is manifested particularly in biomolecular applications such as hierarchical protein folding instances where the interaction between almost rigid domains directly influences the folding pathway, the interaction between macromolecules for drug design purposes, self-assembly of nanoparticles for drug design and drug delivery, and design of smart materials and bio-sensors. In general, the brute force approach requires quadratic (in terms of the number of particles) number of pairwise evaluation operations for any relative pose of the two bodies, unless simplifying assumptions lead to a collapse of the computational complexity. We propose to approximate the pairwise interaction function using a linear predictor function, in which the basis functions have separated forms, i.e. the variables that describe local geometries of the two rigid bodies and the ones that reflect the relative pose between them are split in each basis function. Doing so replaces the quadratic number of interaction evaluations for each relative pose with a one-time quadratic computation of a set of characteristic parameters at a preprocessing step, plus constant number of pose function evaluations at each pose, where this constant is determined by the required accuracy of approximation as well as the efficiency of the used approximation method. We will show that the standard deviation of the error for the net interaction is linearly (in terms of number of particles) proportional to the regression error, if the regression errors are from a normal distribution. Our results show that proper balance of the tradeoff between accuracy and speed-up yields an approximation which is computationally superior to other existing methods while maintaining reasonable precision.
许多物理模拟旨在评估两个刚体之间的净相互作用，这是其组成部分之间的成对相互作用累积效应的结果。这在生物分子应用中表现得尤为明显，如层次蛋白质折叠实例，其中几乎刚性域之间的相互作用直接影响折叠途径、药物设计目的的大分子之间的相互作用、用于药物设计和药物输送的纳米粒子自组装以及智能材料和生物传感器的设计。通常，除非简化假设导致计算复杂性崩溃，否则蛮力方法需要对两个物体的任何相对姿势进行二次（以粒子数为单位）的成对评估操作。我们建议使用线性预测函数来近似成对相互作用函数，其中基函数具有分离的形式，即描述两个刚体局部几何形状的变量和反映它们之间相对姿势的变量在每个基函数中分开。这样，对于每个相对姿势，用一次二次计算一组特征参数来代替二次数量的相互作用评估，再加上在每个姿势处的常数数量的姿势函数评估，其中该常数由所需的逼近精度以及所使用的逼近方法的效率来确定。我们将表明，如果回归误差来自正态分布，则净相互作用的误差的标准偏差与回归误差成线性（以粒子数为单位）比例。我们的结果表明，在准确性和加速之间进行适当的权衡取舍，可以产生一种在保持合理精度的同时在计算上优于其他现有方法的逼近。
