Calculator
Formula Used
Fraction bound from polarization:
Fbound = (mPobs - mPfree) / (mPbound - mPfree)
Single point direct binding:
Kd = Xfree × (1 - Fbound) / Fbound
Direct curve model:
mP = Bottom + (Top - Bottom) × X / (Kd + X)
Tracer depletion model:
Complex = ((Rtotal + Ftotal + Kd) - sqrt((Rtotal + Ftotal + Kd)^2 - 4RtotalFtotal)) / 2
Fraction bound = Complex / Ftotal
mP = Bottom + (Top - Bottom) × Fraction bound
How to Use This Calculator
- Select curve fit or single point mode.
- Enter free tracer and fully bound polarization controls.
- Choose the direct model for dilute tracer assays.
- Choose depletion mode when tracer concentration affects binding.
- Paste concentration and observed mP data in matching order.
- Set optional Kd search limits when you know the range.
- Press Calculate and review the result above the form.
- Download CSV or PDF for your records.
Example Data Table
| Point | Partner Concentration | Observed mP | Expected Use |
|---|---|---|---|
| 1 | 0 nM | 37 | Baseline check |
| 2 | 1 nM | 43 | Low response |
| 3 | 3 nM | 58 | Early binding |
| 4 | 10 nM | 88 | Curve rise |
| 5 | 30 nM | 136 | Near midpoint |
| 6 | 100 nM | 181 | Upper region |
| 7 | 300 nM | 207 | Near plateau |
| 8 | 1000 nM | 217 | Saturation check |
Understanding Fluorescence Polarization Kd
Fluorescence polarization measures molecular rotation during excited state lifetime. A small labeled tracer rotates faster, so its emitted light becomes less polarized. When the tracer binds a larger partner, rotation slows. The measured millipolarization value rises. This change can estimate binding strength.
What This Calculator Does
This calculator converts polarization readings into a dissociation constant, called Kd. A lower Kd means tighter binding. You can run a single point estimate when free and bound controls are known. You can also fit a full titration series. Full curve fitting is preferred, because it uses all points and reports residual error.
Important Inputs
Enter the low signal for free tracer. Enter the high signal for fully bound tracer. Add ligand or receptor concentrations in increasing order. Add matching observed polarization values. Choose the direct model when the x value is treated as free binding partner. Choose the depletion model when the fluorescent tracer concentration is significant compared with Kd.
Why Model Choice Matters
Simple binding assumes the free partner concentration is close to the total concentration. This is common when tracer is very dilute. Tight binding assays can break that assumption. The quadratic depletion model corrects for ligand removal by bound complex. It is useful when receptor total, tracer total, and Kd are similar.
Reading The Output
The result section reports Kd, fitted bottom, fitted top, span, mean residual, root mean squared error, and R squared. Residuals show how far each point sits from the fitted curve. Random small residuals are a good sign. Large patterned residuals suggest aggregation, wrong controls, inner filter effects, or mixed binding modes.
Good Assay Practice
Use enough concentrations around the expected Kd. Include points below and above saturation. Keep temperature, buffer, plate type, and incubation time consistent. Run replicates when possible. Avoid using only the steep middle of the curve. A stable upper plateau and lower baseline improve confidence.
Limitations
This tool is for planning and routine analysis. It does not replace full laboratory validation. Complex systems may need competition binding, Hill models, global fitting, or replicate weighting. Always review plots, controls, and raw fluorescence intensity before reporting a final Kd.
Exported tables help document assumptions, inputs, fitted values, and calculation notes.
FAQs
What is Kd in fluorescence polarization?
Kd is the dissociation constant. It describes binding strength between the labeled tracer and binding partner. Lower Kd values usually mean tighter binding under the tested conditions.
What does mP mean?
mP means millipolarization. It is the common unit used for fluorescence polarization assay output. Binding usually increases mP because the labeled molecule rotates more slowly.
Should I use single point or curve fit mode?
Use curve fit mode when you have a titration series. Use single point mode only for quick estimates with trusted free and bound controls.
When should I use depletion mode?
Use depletion mode when tracer concentration is not negligible compared with Kd. This helps correct tight binding experiments where total and free concentrations differ.
Why is my fraction bound above one?
It can happen when observed mP is higher than the bound control. Check controls, gain settings, background subtraction, aggregation, and plate artifacts.
What is a good R squared value?
A high R squared suggests the model follows the data. Still review residuals and controls. A high value does not prove the assay is valid.
Can this handle competition assays?
This page focuses on direct binding Kd. Competition assays need extra equations, competitor concentration, tracer Kd, and often Cheng-Prusoff style analysis.
Why do residuals matter?
Residuals reveal pattern and fit quality. Random small residuals support the selected model. Curved or systematic residuals suggest a model or assay problem.