Slow-Equilibration Approximation in Macroscopic Approach to Studying Kinetics at Equilibrium
Bibliographic record
Abstract
Macroscopic approach to studying kinetics at equilibrium (MASKE) facilitates measurements of rate constants of formation (k(+)) and dissociation (k(-)) of affinity complexes in the state of chemical equilibrium. MASKE relies on "informational nonequilibrium" created by a nonuniform initial spatial distribution of a label on one of the reactants. In general, finding k(+) and k(-) by MASKE requires fitting experimental label-propagation patterns-dependencies of label concentrations on a coordinate or time-with the simulated label-propagation patterns. Here we introduce a simple fitting-free approach for finding the rate constants in the case of slow equilibration. Slow equilibration means that the characteristic equilibration time of the labeled reactant and labeled complex, t(eq), is much greater than the characteristic separation time of the labeled reactant and labeled complex, t(sep). We developed the mathematics for this approach by solving the differential equations of mass transfer using the assumption of slow equilibration. The approach was then tested and its accuracy was studied by applying it to label-propagation patterns created with the earlier-developed exact solution of the mass-transfer equations. The results proved that the approximate solution was correct. They also showed that k(+) and k(-) can be found with this fitting-free approach with a relative error less than 20% if t(sep) < 0.6t(eq). The practical limitations of our slow-equilibration approximation are discussed.
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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".