Formula Used
The calculation of the inhibition constant ($Ki$) from protein thermal shift assays (Differential Scanning Fluorimetry, DSF) is derived from thermodynamic relationships governing ligand-induced stabilization of proteins. The fundamental equation links the melting temperature shift ($\Delta Tm$) to the ligand concentration and unfolding thermodynamics:
$$K_i = \frac{[L]}{\exp\left(\frac{\Delta H_m}{R} \left(\frac{1}{Tm_0} - \frac{1}{Tm}\right)\right) - 1}$$
Where:
- $[L]$ = Total or free ligand concentration
- $\Delta H_m$ = Enthalpy of protein unfolding at melting temperature
- $R$ = Universal gas constant ($8.314 \text{ J}\cdot\text{mol}^{-1}\cdot\text{K}^{-1}$)
- $Tm_0$ = Melting temperature of the free protein in Kelvin
- $Tm$ = Melting temperature of the protein-ligand complex in Kelvin
How to Use This Calculator
- Input Thermal Data: Enter the baseline melting temperature of your free protein and the shifted melting temperature after adding the ligand. Provide the unfolding enthalpy ($\Delta H$).
- Specify Concentrations: Enter your working ligand concentration and protein concentration in micromolar ($\mu\text{M}$) units.
- Configure Buffer Settings: Input the assay buffer pH and ionic strength to ensure precise modeling adjustments.
- Execute Calculation: Click the Calculate Ki Value button to instantly analyze your binding affinity results displayed above the form.
Understanding Protein Thermal Shift Assays and Ki Estimation
Protein thermal shift assays, frequently referred to as Differential Scanning Fluorimetry (DSF) or thermal shift binding assays, serve as a cornerstone technique in modern drug discovery, structural biology, and high-throughput screening campaigns. By monitoring the thermal denaturation of a protein in the presence of fluorescent probes, researchers can rapidly evaluate how small molecules, fragments, or peptides interact with and stabilize target macromolecules. When a ligand binds preferentially to the native, folded state of a protein over its unfolded conformation, it shifts the thermal denaturation profile toward higher temperatures, a phenomenon quantified as $\Delta Tm$.
Translating this thermal stabilization into quantitative thermodynamic metrics like the inhibition constant ($Ki$) is critical for lead optimization. Traditional biophysical methods like Isothermal Titration Calorimetry (ITC) or Surface Plasmon Resonance (SPR) yield direct binding constants, but thermal shift assays offer a high-throughput, low-consumption alternative. The mathematical model implemented in our calculator leverages the van't Hoff equation combined with ligand-binding equilibria to bridge the gap between qualitative thermal shifts and rigorous affinity constants. Researchers can accurately estimate dissociation or inhibition constants without complex curve-fitting across multiple dilution series, provided the unfolding enthalpy is known or estimated reliably.