Asymptotic analysis of equations for the buffered diffusion of intracellular Ca2
Bibliographic record
Abstract
The "domain" calcium (Ca2+) concentration near an open Ca2+ channel can be mod- eled as buffered diffusion from a point source. The concentration profiles can be well approximated by hemispherically symmetric steady-state solutions to a system of reaction-diffusion equations. After nondimensionalizing these equations and scaling space so that both reaction terms and the source amplitude are 0(1), we identify two dimensionless parameters, Cc and Eb, that correspond to the diffusion coefficients of dimensionless Ca2+ and buffer, respectively. Using perturbation methods, we derive approximations for the Ca2+ and buffer profiles in three asymptotic limits: (1) an "excess buffer approximation" (EBA), where the mobility of buffer exceeds that of Ca2+ (Eb > Ec) and the fast diffusion of buffer toward the Ca2+ channel prevents buffer saturation (cf. Neher [Calcium Electrogenesis and Neuronal Functioning, Exp. Brain Res. 14, Springer-Verlag, Berlin, 1986, pp. 80-96]); (2) a "rapid buffer approximation" (RBA), where the diffusive time-scale for Ca2+ and buffer are comparable, but slow compared to reaction (ec << 1, Eb reaction (ec << 1, Eb reaction (ec << 1, Eb
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How this classification was reachedexpand
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 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".