A Practical Approach to Quantitatively Assessing Equilibrium-Constant Accuracy from a Single Binding Isotherm
Bibliographic record
Abstract
High Resolution Image Download MS PowerPoint Slide Equilibrium constants are essential for understanding and predicting the behavior of chemical systems across various scientific disciplines. Traditionally, these constants are computed via nonlinear regression of reaction isotherms, which show the dependence of the unreacted fraction of one reactant on the total concentration of another reactant. However, while these equilibrium constants can be precise (with small random errors), they may also be grossly inaccurate (with large systematic errors), leading to potential misinterpretations. Although some statistical methods exist for assessing the accuracy of nonlinear regression, their limited practicality for molecular scientists has resulted in their neglect by this research community. The objective of this work is to develop a practical method for quantitatively assessing the accuracy of equilibrium constants that could be easily understood and immediately adopted by researchers routinely determining these constants. Our approach integrates error-propagation and regression-stability analyses to establish the accuracy confidence interval (ACI)─a range within which the true value of the computed parameter lies with a defined probability. In a proof-of-principle study, we applied this approach to develop a workflow for determining the ACI of the equilibrium dissociation constant ( K d ) of affinity complexes from a single binding isotherm. We clearly explained how the input parameters for this workflow can be determined, and finally, we have implemented this workflow in a user-friendly web application ( https://aci.sci.yorku.ca ) to facilitate its immediate adoption by molecular scientists, regardless of their mathematical and computer proficiency. We further conducted three case studies exemplifying the use of the ACI in the context of simultaneous assessment of precision and accuracy of determined K d values. By understanding the ACI of equilibrium constants and other parameters computed through nonlinear regression, researchers can avoid misconceptions that arise from relying solely on precision.
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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 | 0.026 | 0.072 |
| Meta-epidemiology (narrow) | 0.003 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.006 | 0.003 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.004 | 0.003 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.003 | 0.002 |
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".