Competitive Binding Calculator

The Competitive Binding Calculator converts an experimentally measured IC50 into a true inhibition constant (Ki) using the Cheng-Prusoff equation. In a radioligand competition assay, a labeled "hot" ligand and an unlabeled competitor fight for the same receptor binding site. The IC50 you read off a displacement curve is the competitor concentration that knocks off half of the specifically bound radioligand. Because IC50 depends on how much radioligand you used and how tightly that radioligand binds, it is not a pure measure of competitor affinity. This Ki from IC50 calculator removes that assay dependence so you can compare drug affinities across different experiments and laboratories.

Enter the radioligand concentration [L*], the radioligand dissociation constant Kd, the competitor IC50, the competitor concentration [I], and the receptor density Bmax. The competitive binding calculator instantly returns the Ki, the pKi (negative log of Ki), the apparent Kd of the radioligand in the presence of competitor, the fold shift in binding, the amount of receptor bound with and without competitor, and the percent inhibition. These outputs let pharmacologists, biochemists, and drug-discovery scientists characterize receptor-ligand interactions, rank candidate compounds, and design follow-up dose-response experiments.

The heart of this competitive binding calculator is the Cheng-Prusoff equation, derived by Yung-Chi Cheng and William Prusoff in 1973. It relates the measured IC50 to the intrinsic Ki, correcting for the radioligand concentration and affinity. The calculator also models the apparent shift in radioligand affinity caused by competition, and the resulting change in specific binding.

The relationships used by the page are:

• Ki = IC50 / (1 + [L*]/Kd)
• Apparent Kd = Kd × (1 + [I]/Ki)
• Bound (with competitor) = (Bmax × [L*]) / (Apparent Kd + [L*])
• Bound (no competitor) = (Bmax × [L*]) / (Kd + [L*])
• Percent inhibition = (Bound​_{no comp} − Bound​_comp) / Bound​_{no comp} × 100
• pKi = −log₃₀(Ki × 10⁻⁹)
• Fold shift = Apparent Kd / Kd

Notice that as the radioligand concentration [L*] approaches zero relative to Kd, the Cheng-Prusoff correction term shrinks and Ki approaches IC50. In practice this means that running an assay with a low radioligand concentration produces an IC50 that is already close to the true Ki, while using a high radioligand concentration inflates the IC50 and demands a larger correction.

Using the Ki from IC50 calculator takes only a few seconds once you have your assay numbers. Follow these steps:

1. Enter the radioligand concentration [L*] in nM. This is the free concentration of the labeled ligand actually used in the binding reaction.
2. Enter the radioligand Kd in nM, determined from a separate saturation binding (homologous) experiment.
3. Enter the competitor IC50 in nM, read from the midpoint of your displacement curve.
4. Enter the competitor concentration [I] in nM to model the apparent Kd shift and the bound receptor levels.
5. Enter Bmax in fmol/mg to scale the specific binding outputs.

The calculator then displays Ki and pKi prominently, followed by the apparent Kd, fold shift, bound radioligand with and without competitor, and the percent inhibition bar. Because every input is in consistent nanomolar units, you can mix and match values from any radioligand assay. A lower Ki means a tighter, higher-affinity competitor; a higher pKi (typically 7-10 for useful drug leads) indicates sub-nanomolar to low-nanomolar potency.

The inhibition constant Ki is the gold-standard affinity metric reported in receptor pharmacology because it is independent of the assay conditions. Two compounds tested in different labs with different radioligands can be compared directly through their Ki values, whereas raw IC50 values cannot. The table below shows how to read the calculator's outputs.

The fold shift equals the apparent Kd divided by the true Kd and tells you how much the competitor weakens radioligand binding at the chosen [I]. A fold shift near 1 means negligible competition, while a large fold shift signals strong displacement. The percent inhibition bar gives an at-a-glance read of how much specific binding the competitor removed under the exact conditions you entered.

The Cheng-Prusoff equation behind this competitive binding calculator rests on several assumptions that you should respect to get meaningful Ki values:

• Competitive, reversible inhibition. The competitor and radioligand must bind the same orthosteric site in a mutually exclusive, reversible way. The page even notes the equation is "valid for competitive inhibitors only." Allosteric or irreversible compounds break the model.
• Equilibrium. The assay must reach binding equilibrium before measurement; otherwise the IC50 is kinetically distorted.
• Single binding site. One homogeneous population of receptors with one Kd is assumed. Multiple affinity states require more complex two-site models.
• Negligible ligand depletion. The free radioligand concentration [L*] should approximate the added concentration, which holds when receptor density is low relative to ligand.
• Accurate Kd. The radioligand Kd must come from a reliable saturation experiment, because errors in Kd propagate directly into Ki.

When these conditions are met, the Ki from this calculator is a robust, transferable affinity constant. When they are violated, treat the result as an approximation and consider global nonlinear curve fitting of the full competition data instead. The calculator is intended for research, teaching, and assay design, not for clinical dosing decisions.