Calculator
Pick a mode, enter concentrations, then describe ionizable groups if needed.
Example data table
Sample scenario showing how apparent affinity can change with pH.
| Scenario | Inputs | Representative outputs |
|---|---|---|
| Weak at low pH |
Kd0 50 nM, P 1.0 µM, L 0.5 µM Ligand group: pKa 7.0, binds deprotonated |
At pH 5.5: low active ligand fraction Apparent Kd increases, percent bound decreases |
| Stronger near neutral |
Same Kd0 and concentrations Same ligand group settings |
At pH 7.4: higher active fraction Apparent Kd drops, percent bound increases |
| Very strong at high pH |
Same Kd0 and concentrations Ligand binds deprotonated |
At pH 9.0: active fraction near one Apparent Kd approaches Kd0, binding peaks |
Formula used
- Protonated fraction: fH = 1 / (1 + 10^(pH − pKa))
- Deprotonated fraction: 1 − fH
- Active fraction: product of required-state fractions across enabled groups.
- Apparent affinity: Kdapp = Kd0 / (fL · fR)
- 1:1 binding: [PL] = 0.5·((P+L+Kd) − √((P+L+Kd)² − 4PL))
This model assumes only the specified protonation states contribute to binding.
How to use this calculator
- Select Single pH or a pH sweep.
- Enter Kd0, total protein, and total ligand with units.
- Enable any ligand or receptor groups that control binding.
- Set each group’s pKa and the state that binds.
- Click Calculate to view results above the form.
- Use Download CSV or Download PDF to export.
FAQs
1) What does Kd0 represent here?
Kd0 is the intrinsic affinity when both partners are in the binding‑competent protonation states. The calculator converts pH effects into an apparent Kd that reflects how much of each partner is actually active.
2) What if I have no ionizable groups to enter?
Leave all groups disabled. The active fractions become one, so Kdapp equals Kd0 at every pH. You still get binding percentages from the concentration inputs.
3) How do I choose “protonated” vs “deprotonated” binds?
Select the protonation state you believe participates in binding. For example, a salt bridge may require a protonated base, while a metal‑chelating carboxylate may require a deprotonated acid.
4) Why does the calculator multiply fractions across groups?
If binding requires several independent states at once, the probability of all being satisfied is the product of their individual probabilities. This yields a combined active fraction used to scale the apparent affinity.
5) Why can apparent Kd become very large?
When the active fraction becomes tiny, only a small portion can bind, so the observed affinity weakens. The minimum active fraction input prevents division by zero while still reflecting strong pH sensitivity.
6) Does this include cooperativity or multiple binding sites?
No. It uses a single 1:1 equilibrium model. For multiple sites, you can approximate by analyzing one site at a time or exporting a sweep and fitting a custom model separately.
7) Should I use protein‑bound percent or ligand‑bound percent?
Use protein‑bound percent when protein is the limiting component, and ligand‑bound percent when ligand is limiting. The complex concentration is the same; the percentage reference changes with the denominator.
8) What is the best way to compare buffer conditions?
Run a pH sweep for each condition, then export CSV files. Compare the pH range where Kdapp is lowest and binding percent is highest. This is often the most practical experiment‑planning view.