An enzyme inhibitor can have IC50 values of 1.25, 2.00 and 5.00 micromolar without its intrinsic inhibition constant changing. The apparent contradiction disappears when the assay’s substrate concentration is included: IC50 and Ki are not interchangeable under simple competitive inhibition.
This Gold Standard guide derives the Cheng–Prusoff relationship from an explicit rate law, checks a synthetic competitive-inhibition experiment, and shows where the correction fails for tight-binding, time-dependent or more complex assay systems.
eduKateSG · The Gold Standard of Biochemistry
Choose your reading route
Define and calculate · Chapters 1–3: IC50, Ki and substrate dependence.
Challenge the model · Chapters 4–6: rate rescue, mechanism and reproducibility.
Check and connect · Chapters 7–8: FAQs, related biochemistry and primary sources.
Chapter index
Rate and concentration · Chapters 1–3
Mechanism and design · Chapters 4–6
Questions and sources · Chapters 7–8
An enzyme inhibitor is commonly tested by adding a range of inhibitor concentrations to an assay and observing how rapidly the enzyme produces its product. An experimental report may identify the inhibitor concentration that reduces the measured rate by half. This value is called IC50, the half-maximal inhibitory concentration under that experiment’s defined conditions.
Ki is a different parameter. In an appropriately specified inhibition model, it describes an inhibition constant related to the inhibitor’s interaction with the enzyme. It is not a generic synonym for the concentration that happens to cause a 50% rate decrease in one particular assay.
For simple, reversible, competitive inhibition, the observed IC50 depends on how much substrate was present relative to the substrate’s Michaelis constant Km. As substrate concentration rises, more inhibitor may be needed to achieve the same fractional reduction, even though the underlying Ki in the model is unchanged.
Cheng and Prusoff’s 1973 paper established a widely used relationship between Ki and experimentally measured IC50. Modern methodological analyses stress that its assumptions matter and that different inhibition mechanisms or assay formats require different interpretation.
This article uses a single-substrate steady-state teaching enzyme with invented Vmax, Km and Ki. We calculate its uninhibited velocity and velocity after adding inhibitor, then test how the apparent IC50 moves when the assay substrate concentration changes. The goal is to avoid comparing two headline IC50 values as though both were intrinsic binding constants.
In research, even Ki is meaningful only with its specified mechanism, conditions and appropriate uncertainty. Enzyme identity, preparation, temperature, pH, ionic strength, readout chemistry and substrate identity all matter.
Use the familiar steady-state Michaelis–Menten rate v₀=Vmax[S]/(Km+[S]) for the selected enzyme and substrate concentration [S]. Here Vmax and Km describe the enzyme under the chosen assay conditions and v₀ is the initial uninhibited rate.
For an ideal rapidly reversible competitive inhibitor binding the same free-enzyme form as the substrate, the model becomes vI=Vmax[S]/(Km(1+[I]/Ki)+[S]). The factor α=1+[I]/Ki increases the apparent Km while the limiting Vmax remains the same in this model.
Choose invented values Vmax=100 micromoles of product per minute, Km=2 µM and Ki=1 µM. Let the substrate concentration be [S]=2 µM. With no inhibitor, v₀=100×2/(2+2)=50 µmol/min.
Add [I]=1 µM. Then α=1+1/1=2, and the inhibited velocity is vI=100×2/(2×2+2)=200/6≈33.33 µmol/min. The fractional inhibition is (50−33.33)/50≈33.3%, not 50%.
The fact that [I] equals Ki did not force a 50% rate decrease. A substrate concentration equal to Km competes with the inhibitor for the available enzyme, so the assay’s half-inhibition point occurs at a different concentration.
Now double the inhibitor to [I]=2 µM. The apparent multiplier is α=1+2/1=3 and vI=200/(6+2)=25 µmol/min, exactly half the original uninhibited 50. Under these conditions IC50 is therefore 2 µM, although the assumed Ki is only 1 µM.
Keep the units explicit: Ki, Km and both concentrations in this example are micromolar, whereas velocity is micromoles of product per minute for the amount of enzyme in the assay. Equating these merely because they contain the word ‘micro’ is an error.
| At [S]=2 µM | Inhibitor [I] | Predicted rate | Relative inhibition |
|---|---|---|---|
| Uninhibited | 0 µM | 50.00 µmol/min | 0% |
| [I]=Ki | 1 µM | ≈33.33 µmol/min | ≈33.3% |
| Half-rate condition | 2 µM | 25.00 µmol/min | 50% |
| Higher dose | 4 µM | ≈16.67 µmol/min | ≈66.7% |
The special-case Cheng–Prusoff relation is Ki=IC50/(1+[S]/Km), or equivalently IC50=Ki(1+[S]/Km). This follows from setting the competitive-inhibition rate at the IC50 dose equal to half of the uninhibited rate, with all other model assumptions held fixed.
For our chosen parameters Ki=1 µM, [S]=2 µM and Km=2 µM, the factor is 1+2/2=2. Thus IC50=1×2=2 µM, confirming the explicit rate calculation from the preceding chapter.
Now imagine the same inhibitor and the same enzyme measured at a lower substrate concentration [S]=0.5 µM. The factor becomes 1+0.5/2=1.25 and IC50=1.25 µM. At a higher substrate concentration [S]=8 µM, the factor is 1+8/2=5 and IC50=5 µM.
One hypothetical inhibitor has therefore generated three different IC50 figures: 1.25, 2.00 and 5.00 µM. Calling the 1.25 µM experiment evidence for a stronger inhibitor than the 5 µM experiment would be incorrect because the Ki was deliberately held identical.
The correct inference is that, for simple competitive inhibition, IC50 is a conditional readout at the assay’s substrate concentration. A meaningful comparison between studies requires either matching substrate conditions or a justified mechanism-specific correction with a reliably estimated Km.
The formula is not a universal conversion for time-dependent covalent inhibitors, tight-binding inhibitor concentrations approaching the enzyme concentration, mixed inhibition, multistep mechanisms or assays that report downstream cellular response instead of an initial enzyme rate.
| Substrate [S] | [S]/Km | Predicted IC50 | Uninhibited v₀ |
|---|---|---|---|
| 0.5 µM | 0.25 | 1.25 µM | 20 µmol/min |
| 2.0 µM | 1.00 | 2.00 µM | 50 µmol/min |
| 8.0 µM | 4.00 | 5.00 µM | 80 µmol/min |
In the competitive model the inhibitor’s effect on rate decreases, in fractional terms, as substrate concentration becomes large compared with Km. The active sites experience more competition from substrate, so a fixed inhibitor concentration suppresses a smaller proportion of the original velocity.
Keep inhibitor concentration [I]=2 µM, Ki=1 µM, Vmax=100 µmol/min and Km=2 µM. Its α is 3. At [S]=2 µM, the inhibited rate is 25 against uninhibited 50, so the inhibition fraction is 50%.
Now increase [S] to 8 µM. The uninhibited rate becomes v₀=100×8/(2+8)=80 µmol/min. With [I]=2 µM, the inhibited rate is vI=100×8/(2×3+8)=800/14≈57.14 µmol/min. The fractional inhibition is (80−57.14)/80≈28.6%.
The inhibitor itself has not become chemically weaker. Its Ki was held fixed by construction. The lower fraction inhibited follows from moving along a different substrate condition while comparing velocities to their own matched uninhibited controls.
In the very-high-substrate limit of this ideal model, both inhibited and uninhibited velocities approach the same Vmax. But high substrate may also cause substrate inhibition, solubility problems or altered assay signals. The mathematical limiting behaviour should not be presented as an instruction to add unlimited substrate to a real reaction.
This also separates IC50 from an inhibitor’s toxicological safety or therapeutic effectiveness. A micromolar biochemical assay result is not a validated effective dose in a person, nor does it establish cellular exposure or selectivity against other enzymes.
| Fixed [I]=2 µM | Uninhibited rate | Inhibited rate | Inhibition fraction |
|---|---|---|---|
| [S]=2 µM | 50.00 | 25.00 | 50.0% |
| [S]=8 µM | 80.00 | ≈57.14 | ≈28.6% |
An IC50 measurement belongs to a particular assay. The same label can appear in enzyme kinetics, receptor binding, cellular proliferation and fluorescence-based screening even though the observed response and underlying models differ.
Pure competitive inhibition under the simple model changes the apparent substrate Km without changing the theoretical Vmax. In uncompetitive, noncompetitive or mixed mechanisms, the rate law and substrate dependence of observed inhibition differ. A universal Ki=IC50/(1+[S]/Km) calculation would be invalid when those mechanisms are more appropriate.
Slow-binding or time-dependent inhibitors can produce IC50 values that change with pre-incubation duration or the time at which the signal was read. Covalent inhibition requires kinetic descriptions of binding and inactivation, often involving parameters other than a single equilibrium Ki.
Tight-binding inhibitors complicate mass balance because a substantial fraction of the inhibitor may be bound to enzyme. The concentration labelled ‘added inhibitor’ can differ importantly from free inhibitor; an ordinary nondepleting competitive model may fail.
Coupled assays can create another false comparison. If the measured fluorescence or absorbance is generated by a reporter enzyme, the inhibitor could affect the reporter rather than the primary target. A curve that looks like target-enzyme inhibition may actually reflect an optical or secondary-reaction problem.
The coupled-assays guide explains that measurement chain. The substrate-inhibition guide demonstrates another reason why assuming simple Michaelis–Menten kinetics can fail.
The lesson is not that IC50 is useless. It is an excellent operational comparison when assay conditions and analysis rules are sufficiently similar. It becomes misleading only when stripped of those conditions and promoted into an intrinsic constant without support.
Specify the enzyme identity, preparation, functioning enzyme amount, substrate, cofactor requirements and the reason the chosen inhibition mechanism is plausible. Record the temperature, buffer, pH, ionic environment and timing of mixing and measurement.
Determine Km under compatible conditions, with a substrate concentration series that tests the chosen kinetic model. A Km borrowed from a different buffer or temperature may not be appropriate for a Cheng–Prusoff correction applied to the present assay.
Collect inhibitor concentration-response measurements against a matched uninhibited control at each substrate concentration. Use independent replicates, appropriate baseline corrections and a valid readout proportional to primary reaction product formation over the selected initial-rate window.
Consider measuring more than one substrate concentration. For competitive inhibition in the simple model, an increase of observed IC50 with [S] is predicted. But observing that trend alone may not establish a unique mechanism if other assay components change across conditions.
A dose-response fit should identify whether the reported IC50 is based on half of the uninhibited rate, a fitted percentage of an assumed dynamic range or another normalisation. Arbitrarily forcing the top and bottom response plateaus can distort the midpoint.
For reversible inhibitors, check equilibration or pre-incubation effects; for high-affinity compounds, test whether free inhibitor depletion can be ignored. Where feasible, independent binding or orthogonal chemical measurements can strengthen a mechanism claim.
Preserve raw progress curves, substrate and inhibitor stock preparation, concentration uncertainty, plate layout, outlier decisions, software version and the exact fitted equation. STRENDA reporting principles offer a reproducible framework for enzyme-kinetics experiments.
A professional article should say ‘IC50 at [S]=2 µM under the chosen assay’ before quoting a number. If Ki is calculated, report the mechanism-specific formula and the independently supported Km, rather than implying the number came directly from the instrument.
Is IC50 the same as Ki? No. IC50 is an assay-dependent half-inhibition concentration; Ki belongs to a specified inhibition model and can be inferred under suitable conditions.
If inhibitor concentration equals Ki, should the enzyme rate always halve? No. In our competitive model at [S]=Km, [I]=Ki produces about one-third inhibition, not one-half.
Does lower IC50 always mean a stronger-binding inhibitor? Not across assays with different substrates, mechanisms, timing and detection; the conditions must be matched or modelled.
Why does increasing substrate raise IC50 for competitive inhibition? The substrate competes with the inhibitor, reducing its fractional effect at a fixed inhibitor concentration under the selected model.
Can I apply Cheng–Prusoff to irreversible inhibition? Not as the ordinary reversible competitive conversion. Time-dependent covalent processes require other models.
What happens if the enzyme amount is too high relative to inhibitor? Free inhibitor may be depleted by binding, invalidating a simple non-tight-binding calculation.
Does a biochemical IC50 tell me a patient’s dose? No. Cellular exposure, pharmacokinetics, safety and selectivity require separate evidence.
Does competitive inhibition always mean Vmax decreases? Under the ideal reversible competitive Michaelis–Menten model, Vmax is unchanged while apparent Km rises. Other mechanisms behave differently.
What does it mean if IC50 changes with assay time? It may reflect slow binding, irreversible inhibition, enzyme instability, reporter behaviour or other time-dependent effects needing investigation.
Can a fluorescence artifact produce a convincing inhibition curve? Yes. Signal quenching or direct interference with the reporter can imitate an enzymatic effect.
A model parameter should never be separated from the model that gives it meaning. In the simple competitive example Ki=1 µM remains constant while substrate levels of 0.5, 2 and 8 µM generate IC50 values of 1.25, 2 and 5 µM respectively. All three fit the same biochemical hypothesis.
Try changing Km from 2 to 4 µM while keeping Ki=1 µM and [S]=2 µM. The predicted IC50 falls from 2.0 to 1.5 µM. That is a model-based sensitivity exercise, not evidence that the inhibitor or enzyme physically changed in any particular sample.
Related eduKateSG reading: The Gold Standard of Biochemistry, Substrate Inhibition, Hill Coefficients and Site-Count Limits, Active Enzyme Fraction and Turnover, and Chemical Biology. For wider study see Learning Transfers into Life and How X Works.
Authoritative references reviewed on 23 October 2026: Cheng and Prusoff (1973): Ki and IC50 Relationship, Cheng (2001): Limits and Related Power Equations, Practical Substrate Concentrations for IC50 Assays (2025), and STRENDA Guidelines.
All kinetic constants, initial velocities and inhibitory concentrations used in the worked examples are fictional. The calculations assume rapidly reversible, single-substrate, non-tight-binding competitive inhibition and do not establish medical efficacy or safety.