Some shortest paths in the two 8 Å C-alpha ubiquitin majority graphs without added consecutive-residue edges occur in less than half the coordinate models.

This study counts how often all edges of each shortest path in a majority contact graph occur together in the deposited coordinate models. It uses all 116 models from PDB entry 2K39 and all 176 models from 6V5D, with C-alpha contacts below 8 Å between residues more than two positions apart. In 2K39, 2,344 of 15,146 shortest paths (15.48%) occur in fewer than half the models; in 6V5D, 917 of 13,436 (6.82%) do. Every shortest path occurs in at least one model in these primary graphs, and in all 12 tested graph settings. For example, each edge of one 2K39 path is a majority contact, but only 19 of 116 models contain the full path. Counts describe these two related coordinate ensembles under the stated graph rules. They are not biological probabilities, estimates for other coordinate sets, or tests of protein function.

ubiquitin · protein contact graphs · shortest paths · coordinate ensembles · C-alpha contacts · model membership · exact counting