One three-dimensional coordinate set cannot give the mean C-alpha distances for residues 1–70 in 2K39 and 6V5D

For equal-weight models of chain A C-alpha atoms, arithmetic and root mean square (RMS) mean distances across residues 1–70 in PDB entries 2K39 and 6V5D cannot all be represented by one three-dimensional coordinate set. For both averaging rules, the fourth centered Gram eigenvalue remains positive after a deterministic bound for coordinate rounding to 0.001 Å. The same bound is inconclusive for 1D3Z residues 1–70. For residues 1–76, all three entries and both means have positive decision margins. The 2K39 full-range arithmetic mean also remains non-Euclidean in any dimension under the stated bound. These calculations use 302 deposited models from three selected ubiquitin entries; model counts are not independent biological samples. The result is geometric and does not establish biological dynamics, causal effects, or errors in the original models. The scope was selected after a pilot and is exploratory, not preregistered.

ubiquitin · distance geometry · C-alpha distances · NMR ensembles · Euclidean distance matrices · classical multidimensional scaling