| IC50 |
Inhibitor concentration that reduces a response or activity by half |
Enzyme activity, displacement binding or cell assay across an inhibitor dilution series |
Yes: substrate or tracer concentration, enzyme concentration, time, cell context |
| EC50 |
Concentration of an agonist or activator that gives half its maximal effect |
Functional or cell response across an agonist dilution series |
Yes: receptor density, signal amplification, readout |
| Ki |
Dissociation constant of the enzyme-inhibitor or receptor-inhibitor complex |
Derived from IC50 values or from kinetics at several substrate concentrations |
No, for a given protein, buffer and temperature |
| Kd |
Dissociation constant of any complex: [A][B]/[AB] at equilibrium, or koff/kon |
Direct binding: ITC, SPR, saturation binding, fluorescence |
No, for a given protein, buffer and temperature |
EC50 is the activating counterpart of IC50. It describes how much agonist it takes to reach half the maximum response, and like IC50 it reflects the system as well as the molecule: a cell line with more receptors or a more amplified readout gives a lower EC50 for the same agonist.
## What IC50 measures
An IC50 comes from a concentration-response curve. Activity is measured at a series of inhibitor concentrations, plotted against the logarithm of concentration, and fitted with a sigmoid, usually the four-parameter logistic equation. The IC50 is the midpoint of that fit, and the fitted slope, the Hill coefficient, should be close to 1 for an inhibitor that binds one site on one protein.
The curve answers a practical question: how much compound does this assay need to lose half its signal? Everything else in the assay feeds into the answer. More substrate competes harder with a competitive inhibitor. More enzyme soaks up more inhibitor. A longer preincubation lets a slow-binding or covalent inhibitor look more potent. In cells, membrane permeability, protein binding and the cell's own substrate concentrations all add their effect.
So an IC50 is a property of a compound in an assay. Two IC50 values can be compared directly only when they were measured in the same assay, which is why medicinal chemistry teams rank a series in one standard assay and why IC50 values pulled from different papers disagree.
## Ki and Kd are equilibrium constants
Kd is the concentration of free ligand at which half the protein is bound. For a simple complex of protein P and ligand L, it is the ratio of free to bound concentrations at equilibrium, and kinetically it is the dissociation rate constant divided by the association rate constant:
$$
K_d = \frac{[\text{P}][\text{L}]}{[\text{PL}]} = \frac{k_\text{off}}{k_\text{on}}
$$
Ki is the same quantity for an inhibitor bound to an enzyme or receptor. Calling it Ki says how it was measured, through inhibition of activity or of tracer binding, not that it is a different kind of constant.
For one-site reversible binding, a Ki and a Kd measured for the same complex under the same conditions are the same number. In practice they often differ by a few-fold, because the Ki route goes through a Km or tracer Kd that carries its own error, and because buffers, temperatures and protein constructs differ between labs.
Because Kd is an equilibrium constant, it maps onto a [binding free energy](/guides/mm-pbsa-vs-mm-gbsa), $\Delta G = RT \ln K_d$. At 25 °C each tenfold change in Kd is 1.36 kcal/mol, and a 10 nM binder has ΔG of about −10.9 kcal/mol. That conversion is what docking scores borrow when they are quoted in kcal/mol; the [Vina score](/guides/vina-score) guide shows how far that resemblance goes.
## Why IC50 depends on substrate concentration
A competitive inhibitor and the substrate bind the same site on the free enzyme. Raising the substrate concentration shifts that competition toward the substrate, so more inhibitor is needed to reach the same 50% inhibition. Yung-Chi Cheng and William Prusoff worked out the exact relationship for each classic mechanism of a single-substrate enzyme in 1973:
$$
\begin{aligned}
\text{competitive:} \quad & K_i = \frac{IC_{50}}{1 + [S]/K_m} \\[4pt]
\text{noncompetitive:} \quad & K_i = IC_{50} \\[4pt]
\text{uncompetitive:} \quad & K_i = \frac{IC_{50}}{1 + K_m/[S]}
\end{aligned}
$$
The competitive form is the one usually meant by the Cheng-Prusoff equation. At $[S] = K_m$, Ki is exactly half the IC50. At $[S] = 10\,K_m$, the IC50 is 11 times Ki. A pure noncompetitive inhibitor binds the free enzyme and the enzyme-substrate complex equally well, so its IC50 equals Ki whatever the substrate level. An uncompetitive inhibitor binds only the enzyme-substrate complex and does the opposite of a competitive one: it looks more potent as substrate rises.
The same algebra applies to a radioligand displacement assay, with the radioligand concentration in place of [S] and its Kd in place of Km. A competitor with an IC50 of 45 nM against 2 nM of a radioligand whose Kd is 0.5 nM has a Ki of $\frac{45}{1 + 2/0.5} = 9$ nM.
## Worked example: one inhibitor, four IC50 values
Take a hypothetical ATP-competitive kinase inhibitor with a true Ki of 10 nM, and a kinase whose Km for ATP is 10 µM. Biochemical kinase assays are often run near the ATP Km, but cells contain far more ATP: across about 600 published measurements, mostly from mammalian cells, Traut found an average of 3,152 µM. That gap is a large part of why kinase inhibitors usually lose potency between enzyme and cell assays.