Mediterranean Institute for Life Sciences, Split, Croatia.
Biophys J. 2010 Mar 3;98(5):861-71. doi: 10.1016/j.bpj.2009.11.011.
Root mean-square deviation (RMSD) after roto-translational least-squares fitting is a measure of global structural similarity of macromolecules used commonly. On the other hand, experimental x-ray B-factors are used frequently to study local structural heterogeneity and dynamics in macromolecules by providing direct information about root mean-square fluctuations (RMSF) that can also be calculated from molecular dynamics simulations. We provide a mathematical derivation showing that, given a set of conservative assumptions, a root mean-square ensemble-average of an all-against-all distribution of pairwise RMSD for a single molecular species, <RMSD(2)>(1/2), is directly related to average B-factors () and <RMSF(2)>(1/2). We show this relationship and explore its limits of validity on a heterogeneous ensemble of structures taken from molecular dynamics simulations of villin headpiece generated using distributed-computing techniques and the Folding@Home cluster. Our results provide a basis for quantifying global structural diversity of macromolecules in crystals directly from x-ray experiments, and we show this on a large set of structures taken from the Protein Data Bank. In particular, we show that the ensemble-average pairwise backbone RMSD for a microscopic ensemble underlying a typical protein x-ray structure is approximately 1.1 A, under the assumption that the principal contribution to experimental B-factors is conformational variability.
均方根偏差（RMSD）经过旋转变换最小二乘法拟合后，是一种常用于衡量大分子整体结构相似性的方法。另一方面，实验 X 射线 B 因子常用于通过提供关于均方根波动（RMSF）的直接信息来研究大分子中的局部结构异质性和动力学，这些信息也可以从分子动力学模拟中计算出来。我们提供了一个数学推导，表明在一组保守假设下，对于单个分子物种的所有两两 RMSD 分布的均方根集合平均值 <RMSD(2)>(1/2)，与平均 B 因子 ()和 <RMSF(2)>(1/2)直接相关。我们展示了这种关系，并在使用分布式计算技术和 Folding@Home 集群生成的 villin 头片段的分子动力学模拟的异构结构集合上探索了其有效性的限制。我们的结果为直接从 X 射线实验定量衡量晶体中大分子的整体结构多样性提供了基础，我们在来自蛋白质数据库的大量结构上展示了这一点。具体来说，我们假设实验 B 因子的主要贡献是构象变异性，表明典型蛋白质 X 射线结构下微观集合的骨架均方根对 RMSD 约为 1.1 A。
