Thermal Shift DSF Melt Curve and Boltzmann Apparent Tm
Estimate apparent protein melting temperatures from differential scanning fluorimetry melt traces using both Boltzmann sigmoid fitting within a chosen temperature window and the first-derivative extremum. This reference explains why post-peak aggregation requires explicit windowing and why apparent Tm is not an equilibrium thermodynamic calorimetric constant.
The thermal-shift worked example: synthetic fluorescence melts from a dye whose signal rises on unfolding, generated with apparent Tm 52.0 and 56.3 °C and fixed noise over 25 to 95 °C. The interval engine is compared with an eleven-case SciPy fixture; the R cross-check that fixture names was not run.
Isolate the unfolding transition from baseline drift and aggregation
In an extrinsic dye thermal shift assay, an environmentally sensitive fluorophore remains quenched in aqueous buffer while the protein is folded, then binds exposed hydrophobic cores as thermal unfolding progresses. Once the protein unfolds completely, exposed hydrophobic patches often aggregate and exclude the dye, while elevated temperature increases collisional quenching. The raw trace therefore rises through the unfolding transition and falls sharply at higher temperatures.
Fitting a monotone Boltzmann equation to the entire temperature ramp fails unless the post-peak aggregation descent is excluded. Select a lower boundary on the pre-transition baseline and an upper boundary near the fluorescence maximum before running the nonlinear solver, and compare the sigmoid midpoint against the smoothed first-derivative extremum as a consistency check.
Control buffer pKa shifts and DMSO vehicle effects
Because buffer ionization enthalpies vary widely, the actual pH inside a well can shift by more than half a unit between twenty-five degrees and seventy degrees Celsius, especially in Tris buffers. Always include matched DMSO vehicle wells on the same plate and report the heating ramp rate, protein concentration, dye concentration and buffer composition alongside every ΔTm summary.
Equations and variables
Boltzmann two-state melt sigmoid
F(T) = Fmin + (Fmax − Fmin) / (1 + exp((Tm − T) / a))
- F(T)
- Measured dye fluorescence at temperature T inside the selected transition window (RFU)
- Fmin, Fmax
- Lower pre-transition and upper post-transition fluorescence plateaus (RFU)
- Tm
- Apparent midpoint temperature of the unfolding transition (°C)
- a
- Slope factor describing the steepness of the thermal transition (°C)
Thermal shift relative to vehicle control
ΔTm = Tm,ligand − μTm,reference
- ΔTm
- Apparent melting temperature shift in the presence of test compound (°C)
- Tm,ligand
- Estimated melting midpoint for the ligand-treated condition (°C)
- μTm,reference
- Mean melting midpoint of the matched vehicle reference wells (°C)
Scope and limitations
- A single-well temperature ramp collects sequential readings from the same physical well, producing strongly autocorrelated residuals that invalidate naive single-curve confidence intervals.
- Irreversible post-unfolding aggregation and temperature-dependent dye quenching cause fluorescence to drop after the peak, requiring careful upper-window truncation before fitting a monotone Boltzmann sigmoid.
- A positive or negative ΔTm depends on heating rate, dye concentration, buffer pH temperature dependence and binding enthalpy; it does not directly yield an isothermal dissociation constant.
Sources and provenance
- Published numerical verification inputs and independent referencesOriginal synthetic inputs; see individual fixture notices
The generated inputs are demonstrations, not experimental measurements. Existing versioned fixtures are retained unchanged.
- Independent thermal-shift Tm intervals verification fixtureMIT; SciPy reference
The fixture records that its R cross-check was not run.
- Niesen, Berglund and Vedadi: the use of differential scanning fluorimetry to detect ligand interactions that promote protein stabilityCited method; no reproduced article data
Technical questions
Why do the Boltzmann midpoint and the derivative peak sometimes disagree?
For a symmetric four-parameter Boltzmann curve with flat baselines, the inflection point where the first derivative reaches its maximum coincides with the halfway midpoint Tm. Sloping native or unfolded baselines, asymmetric multi-domain unfolding or truncation near the aggregation downturn shift the empirical derivative peak away from the fitted sigmoid midpoint.
Why are confidence intervals calculated across replicate wells rather than from one melt trace?
One melt trace contains dozens of temperature readings from a single well, so its residuals exhibit high lag-one autocorrelation. Treating those sequential points as independent observations produces deceptively narrow intervals; true experimental uncertainty must be estimated from independent replicate wells.
Does a larger ΔTm always mean higher binding affinity?
Not across different protein targets or unrelated chemotypes. The magnitude of a thermal shift depends on the enthalpy and heat capacity of unfolding, the enthalpy of ligand binding and the free ligand concentration at the melting temperature. Compare ΔTm rankings cautiously within a closely related series under identical buffer and dye conditions.
Connected workflows
- EC50 and Hill slope fitting
Compare rising sigmoidal transition parameterisations and slope factors.
- EGFR sequence and structure inspection
Inspect domain boundaries and structural constructs of the target protein.
- Protein A280 concentration calculation
Verify purified protein stock concentration before setting up thermal melt plates.