Six ubiquitin tables on a 10⁻⁹ Å grid have minimum metric changes equal to one third of their largest triangle violations.

For six selected distance tables from ubiquitin NMR model ensembles, the exact minimum maximum-entry change to obtain a metric equals one third of the largest triangle violation in each table on a 10⁻⁹ Å grid. Shortest-path certificates show that these bounds are sufficient for all 10, 116, or 176 models in each table. The changes range from 396397/3000000000 Å to 244361733/250000000 Å. This metric repair gives a lower bound on the maximum distance error of any common Euclidean coordinate representation; it does not construct such a representation or measure biological variation. The six residues were selected because earlier scans found large violations, so the results do not estimate their frequency in proteins.

metric nearness · ubiquitin · distance tables · triangle inequalities · NMR ensembles · shortest paths · exact certificates