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Determination of Ensemble-Average Pairwise Root Mean-Square Deviation from Experimental B-Factors

2010; Elsevier BV; Volume: 98; Issue: 5 Linguagem: Inglês

10.1016/j.bpj.2009.11.011

1542-0086

Antonija Kuzmanic, Bojan Žagrović,

Probabilistic and Robust Engineering Design

Abstract 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 ∼1.1 Å, under the assumption that the principal contribution to experimental B-factors is conformational variability.