Fluorescence Binding Fit Calculator

Example Data Table

Formula Used

The calculator fits fluorescence to a binding isotherm by minimizing the sum of squared residuals between observed and predicted signal.

• 1:1 binding: F = Fmin + (Fmax − Fmin) × ([L] / (Kd + [L]))
• Hill model: F = Fmin + (Fmax − Fmin) × ([L]^n / (Kd^n + [L]^n))
• Fit target: minimize Σ (w × (Fobs − Ffit))², with optional weighting rules.

How to Use This Calculator

1. Enter titration points as concentration and fluorescence pairs.
2. Select a model: 1:1 for simple binding, Hill for cooperativity.
3. Optionally enable baseline correction or choose a weighting scheme.
4. Click “Fit Binding Curve” to compute Kd, fitted values, and residuals.
5. Use CSV or PDF export to share tables and key metrics.

Why Fluorescence Binding Fits Matter

Fluorescence titrations translate binding into intensity changes. The calculator estimates Kd, the ligand concentration producing half of the fitted response. Using fitted parameters reduces bias from noisy endpoints and avoids over-interpreting single points. Reporting Fmin and Fmax helps detect drift, bleaching, or incomplete saturation. When multiple runs are compared, consistent fitting makes affinity trends clearer across conditions.

Model Selection and Practical Interpretations

Choose the 1:1 model when a single site and smooth saturation are expected. Select the Hill model when the transition is unusually steep or shallow, or when cooperativity is plausible. The Hill coefficient n adjusts curve steepness; n>1 suggests positive cooperativity or compressed dynamic range, while n<1 can reflect heterogeneity. Compare both models using RMSE, R², and residual plots rather than slope intuition alone. This comparison improves interpretability for reviewers.

Data Quality Signals You Can Quantify

Variance often increases with fluorescence intensity, so unweighted least squares may overfit high-signal points. Weighting options (1/|F|, 1/|F|², or 1/[L]) can balance influence across the curve and stabilize Kd when endpoints are noisy. Baseline correction subtracts the early mean to reduce offset drift, but it should complement blank subtraction and instrument checks. Inspect residuals for patterns indicating quenching or inner-filter effects. Replicate fits should agree within stated precision.

Using Kd Across Concentration Ranges

Robust Kd estimation requires concentrations that bracket the midpoint of the response. If all points lie far below Kd, the curve is nearly linear and Kd becomes weakly identifiable. If all points are far above Kd, saturation hides the midpoint and small Fmax errors dominate. A practical plan samples roughly 0.1×Kd to 10×Kd, with tighter spacing near the inflection. Prior knowledge from pilot runs improves efficiency and reduces reagent waste.

Exportable Outputs for Reporting and Audit

After fitting, the calculator outputs observed fluorescence, fitted values, and residuals in an audit-ready table. Exporting CSV supports plotting, aggregation, and statistical summaries in notebooks. PDF export provides a compact record for lab books and methods supplements. When comparing ligands or mutants, use the same model and weighting settings to keep estimates comparable. Document buffer composition, temperature, and instrument settings alongside Kd to avoid false trends consistently clearly.