Biomolecular network motif counting and discovery by color coding
Bibliographic record
Abstract
Protein-protein interaction (PPI) networks of many organisms share global topological features such as degree distribution, k-hop reachability, betweenness and closeness. Yet, some of these networks can differ significantly from the others in terms of local structures: e.g. the number of specific network motifs can vary significantly among PPI networks. Counting the number of network motifs provides a major challenge to compare biomolecular networks. Recently developed algorithms have been able to count the number of induced occurrences of subgraphs with k < or = 7 vertices. Yet no practical algorithm exists for counting non-induced occurrences, or counting subgraphs with k > or = 8 vertices. Counting non-induced occurrences of network motifs is not only challenging but also quite desirable as available PPI networks include several false interactions and miss many others. In this article, we show how to apply the 'color coding' technique for counting non-induced occurrences of subgraph topologies in the form of trees and bounded treewidth subgraphs. Our algorithm can count all occurrences of motif G' with k vertices in a network G with n vertices in time polynomial with n, provided k = O(log n). We use our algorithm to obtain 'treelet' distributions for k < or = 10 of available PPI networks of unicellular organisms (Saccharomyces cerevisiae Escherichia coli and Helicobacter Pyloris), which are all quite similar, and a multicellular organism (Caenorhabditis elegans) which is significantly different. Furthermore, the treelet distribution of the unicellular organisms are similar to that obtained by the 'duplication model' but are quite different from that of the 'preferential attachment model'. The treelet distribution is robust w.r.t. sparsification with bait/edge coverage of 70% but differences can be observed when bait/edge coverage drops to 50%.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".