Ki to IC50 converter
Cheng–Prusoff conversion for competitive inhibition, from substrate concentration and Km.
Cheng–Prusoff conversion for competitive inhibition, from substrate concentration and Km.
The inhibition constant Ki is the dissociation constant of the enzyme–inhibitor complex, a property of the inhibitor alone. The IC50 is the inhibitor concentration that halves enzyme activity in a particular assay, and for a competitive inhibitor it depends on how much substrate was present. Cheng and Prusoff (1973) showed that the two are related through the substrate concentration [S] and the Michaelis constant Km:
The factor (1 + [S]/Km) is how many times more inhibitor is needed to overcome substrate competition. With no substrate it is 1 and IC50 equals Ki; at [S] = Km it is 2; at [S] = 10 × Km it is 11.
Choose Ki → IC50, enter Ki, the substrate concentration used in the assay and the substrate's Km, and read the IC50 in the same unit as Ki. [S] and Km share one unit because only their ratio matters. Worked example: Ki = 1 nM, [S] = 5 µM, Km = 10 µM gives 1 nM × (1 + 0.5) = 1.5 nM.
Choose IC50 → Ki and enter the IC50 measured under known [S] and Km. This is the usual direction when comparing inhibitors from papers that used different substrate concentrations: Ki values are comparable, IC50 values are not. To obtain the IC50 itself from a dose–response curve, use the IC50 calculator.
The conversion above is for classic competitive inhibition. For other mechanisms the relationship changes, and this page's numbers should not be used:
| Mechanism | IC50 in terms of Ki |
|---|---|
| Competitive | Ki × (1 + [S]/Km) |
| Noncompetitive | Ki |
| Uncompetitive | Ki × (1 + Km/[S]) |
| Receptor binding (radioligand) | Ki × (1 + [L]/Kd) |
For receptor binding assays the same form applies with the radioligand concentration [L] and its dissociation constant Kd in place of [S] and Km. Tight-binding inhibitors, where the inhibitor concentration is comparable to the enzyme concentration, need the Morrison equation.
For competitive inhibition, IC50 = Ki × (1 + [S]/Km), where [S] is the substrate concentration in the assay and Km is the Michaelis constant of the substrate. It links the measured IC50 to the substrate-independent inhibition constant Ki.
Multiply Ki by (1 + [S]/Km). With Ki = 1 nM, [S] = 5 µM and Km = 10 µM the factor is 1.5, so IC50 = 1.5 nM.
Divide IC50 by (1 + [S]/Km). An IC50 of 1.5 nM measured at [S] = 5 µM with Km = 10 µM gives Ki = 1.0 nM.
A competitive inhibitor competes with substrate for the same site, so more inhibitor is needed to reach 50% inhibition when substrate is present. The factor (1 + [S]/Km) grows with substrate concentration; at [S] = Km the IC50 is twice the Ki.
It assumes classic competitive, reversible inhibition with [S] and [E] well below the inhibitor concentration. Noncompetitive, uncompetitive, mixed and tight-binding inhibitors follow different IC50–Ki relationships, and receptor binding assays use the radioligand form with [L] and Kd instead of [S] and Km.