Choose Ki, IC50, free ligand concentration, or K0 to solve the Cheng-Prusoff equation, then enter the three known quantities. Results are available in pM, nM, ฮผM, or mM.
Related Calculators
- 10 Fold Dilution Calculator
- Percent Viability Calculator
- Log Reduction Calculator
- Bacterial Concentration Calculator
- All Biology Calculators
Cheng-Prusoff Equation Formula
For reversible competitive equilibrium binding with a single binding-site class and negligible ligand depletion, the Cheng-Prusoff equation estimates Ki from IC50, free ligand concentration and ligand dissociation constant Kd (called K0 here). The enzyme version uses substrate concentration and Km instead; Km and ligand Kd are not interchangeable.
Rearranged forms used to solve for the other missing values are:
- 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 |
| ฮผM | 1 ฮผM = 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 | Free concentration of the labeled ligand in the binding 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.
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.
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?
Inconsistent inputs can imply a negative value, which this calculator rejects. L may be zero when IC50 equals Ki. A positive K0 requires positive L and IC50 greater than Ki. When L is zero and IC50 equals Ki, K0 is undetermined. Zero ligand is an algebraic limit, not an experimentally measurable zero-tracer IC50 assay.
