Mathematical analysis and numerical simulations of a Rho-GEF-H1-Myosin reaction-diffusion model
Bibliographic record
Abstract
Spatial patterns in reaction–diffusion (RD) systems appear in many settings, from chemistry to cell biology. This thesis studies a small RD model for the RhoA–GEF-H1–Myosin signaling module, which helps control cell contractility. The work has two parts. First, we analyse the well-mixed system (no space). We show solutions stay non-negative and bounded, and we map out the main behaviors of the ordinary differential equations: a single stable state, sustained oscillations (limit cycles), and bistability (two stable states). Second, we add diffusion in one spatial dimension only (an interval with no-flux boundaries) and ask what patterns form. Linearising the RD model gives a curve (the dispersion relation) that predicts which spatial wavelengths can grow. From this we choose values of a control parameter so that only one wavelength is unstable (“single-mode windows”). We then run time-dependent simulations in MATLAB (pdepe). To keep the diagnostics simple, we plot u(x, t) and v(x, t) and track the size of their time-derivatives; a single spike followed by decay indicates growth and then saturation to a steady pattern. The results are clear and consistent. (i) In the Turing-admissible stable regime, diffusion creates stationary spatial patterns whose wavelength matches the one predicted by the single-mode window. (ii) In the non-Turing stable regime, diffusion smooths out perturbations: the system returns to a uniform state. (iii) In oscillatory regimes, diffusion produces standing or traveling waves rather than steady patterns; the time-derivative diagnostic does not decay to zero. (iv) In bistable regimes, diffusion allows traveling fronts between the two states; we track their position and estimate their speed. Overall, the thesis provides a compact, reproducible workflow that links the well-mixed analysis to one-dimensional RD simulations: use the dispersion prediction to pick parameters, simulate with pdepe, and confirm outcomes with a simple diagnostic. The approach offers a clear baseline for future studies of richer networks and for extensions to two and three spatial dimensions.
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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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.003 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".