Curve Fitting

The first stage of the pipeline converts raw CETSA dose–response measurements into quantitative biophysical parameters.

Model

Each protein is modeled using a 4-parameter logistic function:

• Baseline response (E0)
• Maximum response (Emax)
• EC50 (half-maximal concentration)
• Hill coefficient (cooperativity)

This captures the characteristic sigmoidal response of protein stability under ligand perturbation.

Key implementation details

• Fitting is performed in log-dose space for numerical stability.
• Monotonic smoothing is applied using isotonic regression to reduce noise.
• Parameter bounds are enforced to avoid unrealistic solutions.
• A mild Hill regularization is used to prevent extreme cooperativity.

Quality control

Fits are discarded if they fail basic biological or statistical criteria:

• Low variance in signal
• Poor fit quality (low R²)
• Insufficient effect size (Δmax)

Output

For each protein (and condition), the model returns:

• EC50 and logEC50
• Hill coefficient
• R² (goodness of fit)
• Δmax (effect size)

Interpretation

• Low EC50 indicates high sensitivity to NADPH.
• High Δmax reflects strong stabilization or destabilization.
• R² provides confidence in the estimated parameters.

This stage transforms raw experimental data into interpretable biochemical quantities.