On a stochastic approach to model the double phosphorylation/dephosphorylation cycle
Bibliographic record
Abstract
Because of the unavoidable intrinsic noise affecting biochemical processes, a stochastic approach is usually preferred whenever a deterministic model gives too rough information or, worse, may lead to erroneous qualitative behaviors and/or quantitatively wrong results. In this work we focus on the chemical master equation (CME)-based method which provides an accurate stochastic description of complex biochemical reaction networks in terms of the probability distribution of the underlying chemical populations. Indeed, deterministic models can be dealt with as first-order approximations of the average-value dynamics coming from the stochastic CME approach. Here we investigate the double phosphorylation/dephosphorylation cycle, a well-studied enzymatic reaction network where the inherent double time scale requires one to exploit quasisteady state approximation (QSSA) approaches to infer qualitative and quantitative information. Within the deterministic realm, several researchers have deeply investigated the use of the proper QSSA, agreeing to highlight that only one type of QSSA (the total QSSA) is able to faithfully replicate the qualitative behavior of bistability occurrences, as well as the correct assessment of the equilibrium points, accordingly to the not approximated (full) model. Based on recent results providing CME solutions that do not resort to Monte Carlo simulations, the proposed stochastic approach shows some counterintuitive facts arising when trying to straightforwardly transfer bistability deterministic results into the stochastic realm, and suggests how to handle such cases according to both theoretical and numerical results.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| 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 | 0.001 | 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".