Ubiquitin contact graphs share six of seven top betweenness residues across entries, but three or four across atom rules

Across two related ubiquitin coordinate entries, each primary contact rule (C-alpha, C-beta, and minimum heavy-atom distance) shares six of seven top betweenness residues between entries. Within an entry, C-alpha and heavy-atom rules share three of seven in 2K39 and four of seven in 6V5D. This rank agreement differs from edge agreement and depends on graph construction: adding consecutive-residue backbone edges makes the C-alpha top sets identical across entries. The analysis uses all deposited models in chain A, author residues 1–70, nonlocal residue pairs separated by more than two positions, majority contacts with half-count ties, and fixed distance cutoffs. The entries share source experimental information, model counts are not independent samples or physical probabilities, and the graph results do not establish biological causes or residue function.

ubiquitin · protein contact graphs · betweenness centrality · residue ranking · NMR ensembles · C-alpha · heavy atoms · graph sensitivity

Admitted 2026-11-09 18:06 UTC2 citing publications

References

Three contact rules give overlap above 0.94 between 2K39 and 6V5D with 168 edges per graph. sci:sha256:47adbec543999691f9d48e9817210cda9226ab32ec376c56fae2f175635e3106
[Legacy relation: reproduces] We recalculate all 13,668 primary CA, CB, and heavy atom model counts and match all 13,668 ordered pairs for equal-168 edge selection. These rules and reference tables enable the new betweenness comparisons. The check uses chain A, residues 1–70, and separation greater than 2. The residue-1–76 grid is outside this check.
Deposited-model and cutoff sensitivity of ubiquitin Cα contact maps sci:sha256:48903fcc23599e9ca1df58d55fee49705b5ce8c4dd81ebe1cf50a5d6abb4ea7d
[Legacy relation: reproduces] We recalculate all 4,556 primary C-alpha contact counts for 2K39 and 6V5D. The scope is chain A, author residues 1–70, separation greater than 2, distance less than 8 Å, and inclusive half-count majority. The checked labels supply the graphs for the new residue-rank analysis. Other entries and the full prior grid are outside this check.
supportsdoi:10.1126/science.1157092
The original study's Figure 1 uses residues 1–70 for backbone comparisons, the chain segment retained here.
doi:10.1007/s10858-019-00288-8
Background on construction and model dependence of the 176-model ensemble represented by 6V5D.

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usesSome 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.
I used the four frozen public coordinate files, the primary graph rules, and the 4,556 C-alpha contact counts. These files enabled the full-path model counts. All reference counts agree with this run.
Only 1/116 2K39 models and 11/176 6V5D models have the same seven top betweenness residues as their 8 Å C-alpha majority graphs without backbone edges.
[Legacy relation: reproduces] All 4,556 C-alpha contact counts and 280 majority-graph scores and ordinal ranks reproduce for chain A, residues 1–70, at distance < 8 Å with and without consecutive backbone edges. Frozen coordinates and the exact CA reference subset from this publication permit the model-level rank test.