Interplay between writhe and knotting for swollen and compact polymers
Bibliographic record
Abstract
The role of the topology and its relation with the geometry of biopolymers under different physical conditions is a nontrivial and interesting problem. Aiming at understanding this issue for a related simpler system, we use Monte Carlo methods to investigate the interplay between writhe and knotting of ring polymers in good and poor solvents. The model that we consider is interacting self-avoiding polygons on the simple cubic lattice. For polygons with fixed knot type, we find a writhe distribution whose average depends on the knot type but is insensitive to the length N of the polygon and to solvent conditions. This "topological contribution" to the writhe distribution has a value that is consistent with that of ideal knots. The standard deviation of the writhe increases approximately as square root(N) in both regimes, and this constitutes a geometrical contribution to the writhe. If the sum over all knot types is considered, the scaling of the standard deviation changes, for compact polygons, to approximately N(0.6). We argue that this difference between the two regimes can be ascribed to the topological contribution to the writhe that, for compact chains, overwhelms the geometrical one, thanks to the presence of a large population of complex knots at relatively small values of N. For polygons with fixed writhe, we find that the knot distribution depends on the chosen writhe, with the occurrence of achiral knots being considerably suppressed for large writhe. In general, the occurrence of a given knot thus depends on a nontrivial interplay between writhe, chain length, and solvent conditions.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".