Parameter estimation in rational models of molecular biological systems
Bibliographic record
Abstract
Based on statistical thermodynamics or Michaelis -Menten kinetics, molecular biological systems can be modeled by a system of nonlinear differential equations. The nonlinearity in the model stems from rational reaction rates whose numerator and denominator are linear in parameters. It is a nonlinear problem to estimate the parameters in such rational models of molecular biological systems. In principle, any nonlinear optimization methods such as Newton-Gauss method and its variants can be used to estimate parameters in the rational models. However, these methods may converge to a local minimum and be sensitive to the initial values. In this study, we propose a new method to estimate the parameters in the rational models of molecular biological systems. In the proposed method, the cost function in all parameters is first reduced to a cost function only in the parameters in the denominator by a separable theorem. Then the parameters in the denominator are estimated by minimizing this cost function using our proposed new iteration method. Finally, the parameters in the numerator are estimated by a well defined linear least squares formula. A simple gene regulatory system is used as an example to illustrate the performance of the proposed method. Simulation results show that the proposed method performs better than the general nonlinear optimization methods in terms of the running time, robustness (insensitivity) to the initial values, and the accuracy of estimates.
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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 | 0.000 |
| 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 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".