Traveling Waves in a Simplified Model of Calcium Dynamics
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Bibliographic record
Abstract
We analyze traveling wave propagation in a simplified model of intracellular calcium dynamics. Despite its simplicity, the model is thought to capture fundamental features of wave propagation in calcium models. We explore aspects of the dynamics of traveling front, pulse, and periodic wave solutions as $J$, a parameter in our model, is varied. We focus on the closed-cell version of the model, which corresponds to a singular limit of the full (open-cell) model. We use our results about the closed-cell model to make conjectures about the nature of wave solutions in the open-cell version of the model. A comparison between the properties of wave solutions of the calcium model and wave solutions of the FitzHugh--Nagumo equations reveals that the calcium model is an excitable system essentially different from the FitzHugh--Nagumo equations. Our analysis suggests that there are two regimes in which the closed-cell model has traveling fronts. In the regime with lower values of $J$ there are two families of traveling fronts, each parametrized by $J$: one with wave speed $s_F(J)$ and one with wave speed $s_B(J)$. For $J$ such that $s_F(J)>s_B(J)$, there is a unique (up to a translation) traveling pulse with wave speed $s_P(J)\in(s_B(J),s_F(J))$, while for $J$ such that $s_F(J)\leq s_B(J)$ there is no traveling pulse. In the regime with higher values of $J$ there are analogous families of traveling fronts and pulses, but in this case the traveling pulses exist when $s_F(J)<s_B(J)$. The stability of the traveling fronts and pulses identified is investigated using the Evans function. The traveling front with wave speed $s_F(J)$ is always stable, while for the traveling front with wave speed $s_B(J)$, we can find numerically a Hopf bifurcation at $s=s_B(J_{\mathrm{HP}})$ dividing the curve $s=s_B(J)$ into stable and unstable sections. The traveling pulse is unstable when it exists. The existence of periodic waves is also investigated.
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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 | 0.001 | 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 | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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