Determination of ensemble-average pairwise root mean-square deviation from experimental B-factors.
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 (<B>) 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.
Kuzmanic
Antonija
A
Mediterranean Institute for Life Sciences, Split, Croatia.
Zagrovic
Bojan
B
D018360:Crystallography, X-Ray; D008840:Microfilament Proteins / Q000737:chemistry* / Q000378:metabolism; D011487:Protein Conformation; D017510:Protein Folding; D017434:Protein Structure, Tertiary
D008840:Microfilament Proteins; C026615:villin