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\subsection{Comparison to experimental chemical shifts using NMR-derived ensembles}  Table \ref{table:ensembles} lists the RMSD and $r$ values computed for ubiquitin using the x-ray structure 1UBQ ubiquitin  and five NMR-derived structural ensembles with between 10 and 640 structures. For ProCS15 the average chemical shift is obtained by computing the average chemical shielding for each nucleus followed by the linear regression fit to experimental chemical shift values (cf. Eq \ref{eqn:scaling}) to obtain the predicted average chemical shifts. The procedure is the same for the remaining methods except that chemical shifts are used instead of chemical shieldings. For ProCS15 use of ensemble structures lowers the RMSD values for all atom types, with decreases in the range 0.2 - 0.7 ppm for heavy atoms and 0.1 ppm hydrogen atoms. Simmilar improvements are observed for C$\alpha$ and C$\beta$ for CheShift-2, except that the improvement in RMSD (0.5 ppm) is larger compared to ProCS15 (0.3 ppm). This improvement is expected if the NMR-derived ensembles are a more accurate representation of the protein structure in solution than the single x-ray structure. 
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