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Protein Binding Affinity (Kd) Calculator

Calculate Kd and Bmax from a saturation binding experiment, the fraction of sites bound at a ligand concentration, or Kd from a measured fraction bound, with ΔG°.

Formula

bound=Bmax⁡ [L]Kd+[L]\text{bound} = \dfrac{B_{\max}\,[L]}{K_{\mathrm{d}} + [L]}
θ=[L]Kd+[L]\theta = \dfrac{[L]}{K_{\mathrm{d}} + [L]}
Kd=[L] (1−θ)θK_{\mathrm{d}} = \dfrac{[L]\,(1 - \theta)}{\theta}
ΔG∘=RTln⁡Kd\Delta G^\circ = RT\ln K_{\mathrm{d}}
KdK_{\mathrm{d}}
the free ligand concentration at which half of the sites are occupied
Bmax⁡B_{\max}
the maximum binding, when all sites are occupied
[L][L]
free ligand concentration

How it works

When a ligand binds a single kind of site, the amount bound rises with the free ligand concentration as a hyperbola, the same form as the Michaelis-Menten equation. The dissociation constant Kd is the concentration at which half the sites are occupied; a smaller Kd means tighter binding. Fitting the saturation data gives Kd and Bmax.

The standard free energy of binding follows from the Kd in mol/L as ΔG° = RT ln Kd, which is negative for Kd below 1 M. The fit assumes that the free ligand is about equal to the total, so that binding does not deplete it; if the binding sites are present at a concentration comparable to the Kd, that assumption fails and a quadratic binding model is needed.

Worked example

Specific binding of a ligand at seven concentrations from 1 to 1,000 nM (illustrative data).

  1. The fit gives Kd = 18.26 ± 2.48 nM and Bmax = 164 ± 4.8.
  2. ΔG° = RT ln(18.26 × 10⁻⁹) = −44.2 kJ/mol at 25 °C.

Kd about 18 nM, a fairly tight interaction with a binding free energy of about −44 kJ/mol.

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

  • One class of independent binding sites, at equilibrium.
  • The free ligand concentration is known and is not depleted by binding.
  • Non-specific binding has been subtracted.

Common mistakes

  • Using the total ligand concentration when a large fraction is bound.
  • Not reaching saturation, so that Bmax and Kd are not separately determined.
  • Reporting Kd without the temperature, buffer and salt, which affect it.

Related tools

Michaelis-Menten CalculatorRate at a given [S], or [S] for a target rate, with the curveOpen calculatorGibbs Free Energy CalculatorΔG from K, from ΔH and ΔS, and under non-standard conditionsOpen calculatorEquilibrium Constant CalculatorK from concentrations, Ka ⇄ Kd ⇄ pKd, and K at another temperatureOpen calculatorIC50 CalculatorFour-parameter logistic fit, with Ki by Cheng-PrusoffOpen calculator

Related equipment

Service documentation, failure modes and parts for the instruments this calculation is used with.