Analytical Solutions for the Time-Dependent Dynamics of Stochastic Gene Expression with mRNA-sRNA Interactions
Bibliographic record
Abstract
The antagonistic interaction between small RNAs (sRNAs) and messenger RNAs (mRNAs) constitutes a fundamental regulatory mechanism of gene expression in both prokaryotic and eukaryotic cells. However, the stochastic nature of transcription renders mean-field approximations inadequate for quantitative analysis of such systems. In the regime of strong sRNA-mRNA antagonism, we generalize the conventional probability-generating-function (PGF) framework and derive a novel approximate solution in the form of a generalized PGF, which can be analytically transformed into the time-dependent joint distribution of sRNA and mRNA via Laurent series expansion. The proposed approximation accurately captures the full stochastic dynamics across diverse systems exhibiting strong antagonism, while incorporating key biological features such as transcriptional burstiness, translation and sRNA recycling over the entire temporal range. Building on this analytical foundation, we further develop a generalized-PGF-based parameter-inference method that enables efficient and precise estimation of kinetic parameters, achieving inference speeds up to three orders of magnitude faster than traditional maximum-likelihood estimation approaches.
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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 | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".