Differential Binding Models for Isothermal Titration Calorimetry: Moving beyond the Wiseman Isotherm
Bibliographic record
Abstract
We present a set of model-independent differential equations to analyze isothermal titration calorimetry (ITC) experiments. In contrast with previous approaches that begin with specific assumptions about the number of binding sites and the interactions among them (e.g., sequential, independent, cooperative), our derivation makes more general assumptions, such that a receptor with multiple sites for one type of ligand species (homotropic binding) can be studied with the same analytical expression. Our approach is based on the binding polynomial formalism, and the resulting analytical expressions can be extended to account for any number of binding sites and any type of binding interaction among them. We refer to the set of model-independent differential equations to study ITC experiments as a differential binding model (DBM). To demonstrate the flexibility of our DBM, we present the analytical expressions to study receptors with one or two binding sites. The DBM for a receptor with one site is equivalent to the Wiseman isotherm but with a more intuitive representation that depends on the binding polynomial and the dimensionless parameter c = K·MT, where K is the binding constant and MT the total receptor concentration. In addition, we show how to constrain the general DBM for a receptor with two sites to represent sequential, independent, or cooperative binding interactions between the sites. We use the sequential binding model to study the binding interaction between Gd(III) and citrate anions. In addition, we simulate calorimetry titrations of receptors with positive, negative, and noncooperative interactions between the two binding sites. Finally, we derive a DBM for titrations of receptors with n-independent binding sites.
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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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.004 | 0.002 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".