Dynamics and stability of a three-dimensional model of cell signal transduction with delay
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Bibliographic record
Abstract
In this paper, we consider a three-dimensional model of cell signal transduction with delay. The deactivation of signalling proteins occurs throughout the cytosol and activation is localized to specific sites in the cell. The enzyme kinetic functions employ a constant delay to model the time lapse during reactions and also the recovery times associated with conformational changes. We use matched asymptotic expansions to construct the dynamic solutions of signalling protein concentrations. The result of the asymptotic analysis is a system of delayed differential algebraic equations. This reduced system is compared to numerical simulations of the full three-dimensional system. As well, we consider the stability of equilibrium solutions. We find that the systems under consideration may undergo Hopf bifurcations for certain delay values. In these cases sustained oscillations are observed. The Poincaré–Lindstedt3 method is used to improve upon the asymptotic approximations. The simulations of the full three-dimensional system correspond well with simulations of the reduced delayed differential algebraic equations.
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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 it