AFM force-data Kd calculator
Enter event counts or a force-value list. Values meeting the threshold are counted as binding events.
Formula used
This calculator estimates a single-site equilibrium dissociation constant from corrected binding occupancy. It treats threshold-qualified force events as bound interactions.
For the optional kinetic comparison, the calculator applies a Bell-Evans approximation: koff0 = (r × xβ / kBT) × exp[−F × xβ / kBT], then Kd = koff0 / kon. This uses a representative rupture force and should be interpreted cautiously.
How to use this calculator
- Set a force threshold using trace quality checks and negative controls.
- Enter total retraction cycles and specific events, or paste force values.
- Enter control cycles and control events using the same threshold.
- Enter the free ligand concentration at equilibrium.
- Calculate the corrected probability and equilibrium Kd.
- Add kinetic inputs only when they come from compatible measurements.
- Repeat across several ligand concentrations before reporting a final affinity.
Example data
| Input or result | Example value | Purpose |
|---|---|---|
| Total AFM cycles | 1,200 | All attempted retraction measurements. |
| Threshold-qualified events | 330 | Rupture events at or above 28 pN. |
| Negative-control cycles / events | 600 / 18 | Estimates non-specific event probability. |
| Free ligand concentration | 75 nM | Equilibrium concentration used in the occupancy model. |
| Corrected specific probability | 0.253 | Background-adjusted fraction of specific interactions. |
| Estimated equilibrium Kd | About 222 nM | Affinity estimate for this one concentration point. |
Interpreting AFM binding measurements
AFM spectroscopy detects molecular unbinding events. Each trace may contain no event, one event, or complex features. Careful analysis begins by defining a reproducible event rule. The rule may include force, extension, and contour length. This calculator uses a force threshold because it is transparent. It should not replace trace inspection. Remove unstable baselines, tip contamination, and instrument artifacts before counting events. Keep the selection rule identical for samples and controls. Consistent filtering protects the binding probability from subjective changes.
Correcting non-specific interactions
Raw event frequency is not a specific binding probability. Tips, surfaces, linkers, and contaminants may produce rupture-like signals. Negative controls measure this background. A blocked receptor, an inactive ligand, or a no-ligand surface can serve as a control. The correction used here removes the expected background fraction from observed events. It also scales the remaining probability by the unoccupied control fraction. A high control rate weakens confidence. Improve passivation or revise the event rule before trusting the affinity.
Linking occupancy to Kd
For a one-site equilibrium, binding occupancy rises as free ligand concentration increases. The relationship is P = [L] / ([L] + Kd). Rearranging this expression gives the estimate. Lower Kd means stronger affinity. A single concentration gives one estimate. It does not prove a complete binding model. Run several concentrations that span low, middle, and high occupancy. Fit all corrected probabilities to an isotherm. Compare the fitted curve with the individual estimates. This helps reveal saturation, cooperativity, or inconsistent samples.
Using force data wisely
Rupture force depends on loading rate and energy landscape shape. A larger rupture force does not always mean lower equilibrium Kd. The calculator uses force values to classify events. Its optional kinetic cross-check estimates zero-force dissociation from Bell-Evans assumptions. This step requires representative force, loading rate, transition-state distance, and association rate. These values must describe one interaction and buffer condition. Treat disagreement between occupancy and kinetic Kd as an investigation point, not automatic failure.
Designing reliable experiments
Collect cycles at each concentration. Small event counts create wide uncertainty ranges. Randomize order when drift is possible. Monitor tip condition regularly. Use fresh controls after changes. Report the threshold, control design, cycle counts, concentration units, and temperature. Record whether the ligand concentration is free or total. Free concentration is preferred for equilibrium calculations. Describe how multiple rupture events were treated. Clear records make the calculation easy to reproduce. They help others judge whether the one-site approximation is appropriate.
Reporting an affinity estimate
Report Kd with an uncertainty interval and context. State that the interval is an approximate propagation of binomial event uncertainty. It does not capture each source of error. Surface density, receptor orientation, drift, threshold choice, and molecular heterogeneity can matter. Use replicate tips and preparations when possible. Summarize replicate-level estimates before making biological claims. When a fitted concentration series and kinetic analysis agree, confidence increases. When they differ, examine equilibrium timing, model assumptions, and the force-loading protocol.
Frequently asked questions
1. What does Kd mean?
Kd is the dissociation constant. It is the free ligand concentration that gives about half occupancy in a simple one-site equilibrium model. Lower values indicate stronger apparent binding under the measured conditions.
2. Can I calculate Kd from one AFM concentration?
You can obtain a local estimate, but several ligand concentrations are stronger evidence. A concentration series can reveal saturation, poor equilibrium, unusual binding behavior, or a threshold that changes the apparent event frequency.
3. Why is a negative control necessary?
It estimates events caused by non-specific adhesion, surface defects, or noise. Without it, the observed event rate may overstate specific binding and produce an artificially low Kd.
4. What force threshold should I use?
Use a threshold supported by control distributions and trace inspection. Apply the same threshold to samples and controls. A threshold chosen after viewing only sample traces can bias the result.
5. Does a higher rupture force always mean stronger affinity?
No. Rupture force depends strongly on loading rate and molecular pathway. Equilibrium affinity depends on binding thermodynamics. Use force magnitudes to characterize mechanics, not as a direct substitute for Kd.
6. Why does the raw force list override manual events?
The list lets the calculator apply one visible threshold rule. It counts qualifying values and uses their median as a representative force. Remove the list to use your manual event total instead.
7. What is the optional kinetic calculation?
It estimates a zero-force dissociation rate using a Bell-Evans approximation. Dividing that rate by an independently measured association rate gives a kinetic Kd comparison. It is sensitive to model assumptions.
8. Which concentration should I enter?
Enter the free ligand concentration at equilibrium. Total added concentration can be misleading when depletion, surface capture, or competing binding materially changes the free concentration.
9. What happens when corrected probability is zero?
The observed signal is at or below the estimated background. The calculator cannot return a finite equilibrium Kd. Improve sensitivity, collect more cycles, or reduce background before interpreting affinity.
10. Are the reported confidence limits complete?
No. They reflect approximate binomial uncertainty from event counts and controls. They do not include systematic effects such as tip drift, threshold selection, surface heterogeneity, or concentration uncertainty.
11. When is this model unsuitable?
A simple occupancy model may be unsuitable for multivalent binding, irreversible events, slow equilibration, changing receptor density, or several force populations. In those cases, fit an experimental model tailored to the mechanism.