For example, I have a paper that says: "the atomic RMS distribution about the mean coordinate positions is 0.41 +/- 0.04 A for the backbone atoms and 0.82 +/- 0.04 A for all atoms" And I have no idea what any of this means, I found several papers with this kind of information but none of them explain why this is relevant in order to understand the structure of a protein and I haven't learned anything about NMR yet so I'm very confused and curious haha.
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The RMSD measures how similar two conformations of a protein are, for example a model and the native structure. See https://en.wikipedia.org/wiki/Root-mean-square_deviation_of_atomic_positions.
After superimposing the two structures, the RMSD is 0 Angstrom if the conformations are identical or higher if the paired atoms are further apart.
It can be used for many things, such as assessing the quality of a model or monitoring conformational change during a molecular dynamics simulation.
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The ELI5 for this would be: big RMSD bad, low RMSD good.