ΔG to Kd converter
Binding free energy and dissociation constant, either direction, at any temperature.
Binding free energy and dissociation constant, either direction, at any temperature.
The standard binding free energy and the dissociation constant describe the same equilibrium. For a complex AB ⇌ A + B, Kd is the concentration ratio at equilibrium and ΔG° is the free energy change of forming the complex from its parts at standard state:
R is the gas constant, 8.314 J/mol·K or 1.987 cal/mol·K, and T is the temperature in kelvin. Because Kd is a fraction of a mole per litre for any useful binder, ln Kd is negative and so is ΔG°. The converter accepts kcal/mol or kJ/mol and scales Kd automatically between pM and mM.
At 25 °C, RT = 1.987 cal/mol·K × 298.15 K = 592.5 cal/mol = 0.5925 kcal/mol. Then Kd = e^(−10 / 0.5925) = e^(−16.88) = 4.7 × 10⁻⁸ M, that is 47 nM. In the other direction, a Kd of 1 µM gives ΔG° = 0.5925 × ln(10⁻⁶) = −8.2 kcal/mol (−34.3 kJ/mol).
Since ΔG° = 2.303 RT log₁₀ Kd, each tenfold change in Kd is worth 2.303 RT: 1.36 kcal/molor 5.7 kJ/mol at 25 °C, and 1.42 kcal/mol at 37 °C. A medicinal-chemistry rule of thumb follows from this: gaining one log unit of affinity needs roughly 1.4 kcal/mol of extra binding energy, about one good hydrogen bond.
Yes, in two ways. The conversion itself uses RT, so the same ΔG° maps to a different Kd at 37 °C than at 25 °C. And ΔG° = ΔH° − TΔS° depends on temperature through the enthalpy and entropy of binding, so a Kd measured by ITC at 25 °C is not exactly the Kd in a cell at 37 °C. Always report the temperature the value belongs to. The default here is 25 °C, which is 298.15 K.
The association constant Ka is 1/Kd and is quoted in M⁻¹; pKd is −log₁₀ Kd. All three appear in the result. Typical ranges: pM Kd for antibodies and the tightest inhibitors, nM for good drugs and most protein–protein interactions, µM for fragments and weak enzymes–substrate complexes, mM for very weak or transient binding.
Kd is a direct equilibrium constant. Ki is the Kd of an inhibitor for an enzyme and can be used here unchanged. IC50 is not a thermodynamic quantity: it shifts with substrate concentration and assay format. Convert it to Ki first with theKi to IC50 converter, then convert Ki to ΔG.
ΔG° = RT ln Kd, where R is the gas constant (8.314 J/mol·K) and T the absolute temperature in kelvin. Rearranged, Kd = exp(ΔG° / RT). Kd must be in molar units for the equation to hold.
ΔG° is the free energy released when the complex forms. The more negative it is, the further the equilibrium lies toward the bound state, so the dissociation constant is smaller. Every 1.36 kcal/mol (5.7 kJ/mol) at 25 °C changes Kd by a factor of 10.
Yes. The same ΔG° gives a different Kd at 37 °C than at 25 °C, because RT changes. Strictly, ΔG° itself also varies with temperature through ΔH and ΔS, so quote the temperature with the value. The converter defaults to 25 °C (298.15 K).
Ka is the association constant, the reciprocal of Kd (Ka = 1/Kd, in M⁻¹). A Kd of 10 nM corresponds to a Ka of 10⁸ M⁻¹. pKd is −log10 Kd, so 10 nM is pKd 8.
Not directly. IC50 depends on assay conditions such as substrate concentration. Convert IC50 to Ki first with the Ki to IC50 converter, then treat Ki like Kd here.