A stochastic model for circadian rhythms from coupled ultradian oscillators
Bibliographic record
Abstract
BACKGROUND: Circadian rhythms with varying components exist in organisms ranging from humans to cyanobacteria. A simple evolutionarily plausible mechanism for the origin of such a variety of circadian oscillators, proposed in earlier work, involves the non-disruptive coupling of pre-existing ultradian transcriptional-translational oscillators (TTOs), producing "beats," in individual cells. However, like other TTO models of circadian rhythms, it is important to establish that the inherent stochasticity of the protein binding and unbinding does not invalidate the finding of clear oscillations with circadian period. RESULTS: The TTOs of our model are described in two versions: 1) a version in which the activation or inhibition of genes is regulated stochastically, where the 'unoccupied" (or "free") time of the site under consideration depends on the concentration of a protein complex produced by another site, and 2) a deterministic, "time-averaged" version in which the switching between the "free" and "occupied" states of the sites occurs so rapidly that the stochastic effects average out. The second case is proved to emerge from the first in a mathematically rigorous way. Numerical results for both scenarios are presented and compared. CONCLUSION: Our model proves to be robust to the stochasticity of protein binding/unbinding at experimentally determined rates and even at rates several orders of magnitude slower. We have not only confirmed this by numerical simulation, but have shown in a mathematically rigorous way that the time-averaged deterministic system is indeed the fast-binding-rate limit of the full stochastic model.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".