Calculate the missing Ki, IC50, ligand concentration, or K0 from the Cheng-Prusoff equation and show the result in pM, nM, μM, or mM.
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Cheng-Prusoff Equation Formula
The Cheng-Prusoff equation converts an observed IC50 value into an inhibition constant, Ki, by adjusting for ligand concentration and the ligand dissociation constant.
Ki = IC50 / (1 + (L / K0))
Rearranged forms used to solve for the other missing values are:
IC50 = Ki * (1 + (L / K0))
L = K0 * ((IC50 / Ki) - 1)
K0 = L / ((IC50 / Ki) - 1)
- Ki = inhibitor constant, the adjusted binding affinity of the inhibitor
- IC50 = half-maximal inhibitory concentration measured in the assay
- L = ligand concentration used in the assay
- K0 = dissociation constant of the ligand, often written as Kd in related references
To calculate Ki, enter IC50, ligand concentration, and K0. To calculate IC50, enter Ki, ligand concentration, and K0. To calculate L, enter Ki, IC50, and K0. To calculate K0, enter Ki, IC50, and ligand concentration. The values are converted internally to nM, then the result is converted back to your selected output unit.
Concentration Unit Conversions
The equation requires all concentration terms to use the same unit. The calculator normalizes inputs to nM before solving.
| Unit | Equivalent in nM | Use case |
|---|---|---|
| pM | 1 pM = 0.001 nM | Very high-affinity binding values |
| nM | 1 nM = 1 nM | Common biochemical assay range |
| μM | 1 μM = 1,000 nM | Moderate or weaker binding values |
| mM | 1 mM = 1,000,000 nM | High concentration assay components |
How to Interpret Cheng-Prusoff Inputs
| Quantity | What it represents | Effect on Ki calculation |
|---|---|---|
| IC50 | Observed concentration causing 50% inhibition | Higher IC50 gives higher Ki if L and K0 stay fixed |
| L | Concentration of labeled ligand or substrate in the assay | Higher L makes Ki lower relative to IC50 |
| K0 | Ligand dissociation constant | Higher K0 reduces the correction factor |
| Ki | Corrected inhibitor affinity estimate | Lower Ki generally means stronger inhibition |
Example
Example 1: Calculate Ki
You have an IC50 of 50 nM, a ligand concentration of 10 nM, and a K0 of 5 nM.
Ki = 50 / (1 + (10 / 5))
Ki = 50 / 3 = 16.6667 nM
The calculated Ki is 16.6667 nM.
Example 2: Calculate IC50
You have a Ki of 20 nM, a ligand concentration of 30 nM, and a K0 of 10 nM.
IC50 = 20 * (1 + (30 / 10))
IC50 = 20 * 4 = 80 nM
The calculated IC50 is 80 nM.
FAQ
What is the difference between IC50 and Ki?
IC50 is an assay-dependent measurement. It depends on the experimental ligand concentration and binding conditions. Ki is an adjusted inhibition constant that estimates inhibitor affinity after accounting for ligand concentration and the ligand dissociation constant.
Why is Ki usually lower than IC50 in the Cheng-Prusoff equation?
Ki is calculated by dividing IC50 by 1 + (L / K0). Since that correction factor is usually greater than 1, the resulting Ki is usually smaller than the IC50. If ligand concentration is very low compared with K0, Ki and IC50 become closer.
Can the equation produce a negative ligand concentration or K0?
Yes, if the entered values are not physically consistent. When solving for L or K0, the term (IC50 / Ki) – 1 must be positive. That means IC50 must be greater than Ki for a positive result.
