Enter Binding and Thermodynamic Inputs
Formula Used
This page combines a one-site binding model, a Hill adjustment, and thermodynamic relationships to estimate fit quality and equilibrium behavior.
Fraction bound (θ) = [L]^n / (Kd^n + [L]^n)
Predicted signal = Baseline + θ × (Maximum signal − Baseline)
Residual = Observed signal − Predicted signal
Association constant Ka = 1 / Kd
ΔG = −RT ln(Ka)
ΔG = ΔH − TΔS
ln(Ka) = −ΔH / RT + ΔS / R
R is 8.314462618 J·mol⁻¹·K⁻¹, temperature is converted to Kelvin, and all concentrations are normalized to molar units before calculation.
How to Use This Calculator
- Enter assay temperature in Celsius.
- Provide ligand and receptor concentrations using the correct units.
- Enter Kd and the Hill coefficient for the selected model.
- Fill baseline, maximum, and observed signal values from your assay.
- Optionally add enthalpy and entropy for thermodynamic cross-checking.
- Choose replicate count and confidence level, then submit.
- Review affinity, occupancy, ΔG, residual, and fit score above the form.
- Use the CSV or PDF buttons to save and share outputs.
Example Data Table
| Sample | Temperature (°C) | Ligand | Receptor | Kd | Observed Signal | ΔH (kJ/mol) | ΔS (J/mol·K) |
|---|---|---|---|---|---|---|---|
| A1 | 25 | 2.5 uM | 1.0 uM | 0.85 uM | 103 | -42 | -68 |
| A2 | 30 | 4.0 uM | 1.0 uM | 0.75 uM | 124 | -40 | -61 |
| A3 | 20 | 1.5 uM | 0.8 uM | 1.10 uM | 88 | -38 | -57 |
Frequently Asked Questions
1. What does this calculator estimate?
It estimates binding occupancy, predicted signal, residual error, association strength, Gibbs free energy, and optional thermodynamic agreement using enthalpy and entropy values.
2. Why is Kd important?
Kd describes how much ligand is needed to occupy half the binding sites. Lower Kd values indicate stronger binding under the same assay conditions.
3. What does the Hill coefficient change?
The Hill coefficient adjusts curve steepness. Values above one suggest positive cooperativity, while values below one can indicate weaker cooperative behavior or system heterogeneity.
4. Why include observed signal?
Observed signal lets the page compare measured output with model prediction. That difference produces the residual, approximate RMSE, and fit score.
5. What is the meaning of ΔG?
ΔG shows the energetic favorability of binding. More negative values generally indicate a more spontaneous association at the selected temperature.
6. When should I enter ΔH and ΔS?
Enter them when calorimetry or literature values are available. The calculator then computes a second free-energy estimate and a van’t Hoff association constant.
7. Is the fit score a formal statistical metric?
No. It is a practical normalized score based on residual size relative to signal span. Use it for screening, not as a substitute for full regression analysis.
8. Can I use this for publication-grade fitting?
It is excellent for rapid interpretation and teaching. For publication work, confirm results with dedicated nonlinear regression, residual diagnostics, and replicate-rich datasets.