How to Calculate the Inhibition Constant (Ki)

Calculating the inhibition constant, or Ki, requires you to match your math to the type of inhibition at work, and using the wrong approach is one of the most common errors in enzyme kinetics. Ki represents the equilibrium dissociation constant of the enzyme-inhibitor complex: the lower the value, the tighter the inhibitor binds. While many researchers default to converting an IC50 value using a single equation, that shortcut only works under specific conditions, and the path to an accurate Ki can look very different depending on whether you’re dealing with a competitive inhibitor, a slow-binding compound, or a molecule that never lets go of the enzyme at all.

Why Ki Matters More Than IC50

If you run an inhibition assay, the number you get most easily is the IC50, the concentration of inhibitor that cuts enzyme activity in half under a particular set of conditions. The trouble is that IC50 shifts depending on how much substrate is in the reaction. Double the substrate concentration and a competitive inhibitor’s IC50 doubles too, even though the inhibitor itself hasn’t changed. Ki, by contrast, is an intrinsic property of the inhibitor-enzyme pair. It doesn’t depend on how much substrate you happened to use. That makes Ki far more useful for comparing inhibitors tested in different labs, optimizing drug candidates, or predicting how an inhibitor will perform at the substrate concentrations found inside a living cell.

The practical consequence is straightforward: if you report only an IC50 without converting to Ki, anyone trying to reproduce or build on your work needs to know your exact assay conditions to interpret the number. Ki strips away that dependence and gives a value that travels between experiments.

The Cheng-Prusoff Equation

The most widely used route from IC50 to Ki is the relationship published by Yung-Chi Cheng and William Prusoff in 1973. For competitive inhibition, the equation adjusts the measured IC50 by accounting for how much substrate is present relative to the enzyme’s affinity for that substrate (expressed as the Michaelis constant, Km). In plain terms, you divide the IC50 by a correction factor that reflects how hard the substrate is competing with the inhibitor for the active site.

A key finding of Cheng and Prusoff’s analysis is that Ki does not equal IC50 when competitive inhibition applies; however, Ki is equal to IC50 under conditions of noncompetitive or uncompetitive inhibition.¹ That distinction trips people up constantly. If your inhibitor is noncompetitive, the IC50 you measured already is the Ki, and applying the competitive correction factor would give the wrong answer. The equation you need depends entirely on the mechanism of inhibition, which means identifying the inhibition type comes first.

There’s another caveat worth knowing. The Cheng-Prusoff equation was derived for classical enzyme-substrate reactions. When applied to competitive binding assays, such as fluorescence polarization assays commonly used in drug discovery, the standard equation can give incorrect Ki values because the assumptions about free ligand concentrations break down.² If you’re working with a binding assay rather than an enzymatic activity assay, check whether a modified equation has been validated for your specific format before plugging numbers in.

Figuring Out the Inhibition Type

Before you can calculate Ki properly, you need to know whether the inhibitor is competitive, uncompetitive, noncompetitive, or mixed. The standard approach is to collect enzyme velocity data at several substrate concentrations and several inhibitor concentrations, then look at how the data behave on diagnostic plots.

One useful graphical method plots the fractional change in velocity against inhibitor concentration. In this kind of plot, competitive inhibition produces straight lines that converge on the horizontal axis at a point equal to negative Ki. Uncompetitive inhibition produces parallel lines whose slope gives you the uncompetitive inhibition constant. Noncompetitive inhibition, a special case of mixed inhibition, produces lines that intersect in a characteristic pattern that also directly reveals Ki.³ The patterns are distinct enough that you can usually tell the inhibition type by visual inspection before doing any curve fitting.

If you skip this step and assume competitive inhibition by default, you risk using the wrong conversion and reporting a Ki that is systematically off. A noncompetitive inhibitor forced through a competitive model won’t give you a clean fit, but the resulting number can still look plausible enough to pass casual inspection. That’s what makes the error dangerous: it’s silent.

Fitting the Data

Once you know the inhibition type, you fit your data to the appropriate kinetic model. Historically, researchers linearized their data using double-reciprocal (Lineweaver-Burk) or similar transformations and then drew straight lines through the points. Those methods are still taught in textbooks, but they have a well-documented problem: linearization distorts the error structure of the data. Points measured at low substrate concentrations, which tend to be the noisiest, get the most weight in the fit, and the resulting parameter estimates can be significantly off.

Nonlinear regression, where you fit the untransformed data directly to the rate equation, avoids this distortion and generally gives more accurate Ki values.⁴ Modern software handles this easily, and there’s no practical reason to rely on linearized plots for parameter estimation anymore. Linear plots are still useful as diagnostic tools for identifying inhibition type, but the final numbers should come from a nonlinear fit.

An even more powerful approach is global fitting, where you simultaneously fit all of your data from multiple substrate and inhibitor concentrations to a single kinetic model. Global progress curve analysis, which fits the full time-course of product formation across doses, can extract more information from the same amount of data and reduce the influence of random noise on the final Ki estimate.⁵ This approach is particularly valuable for drug discovery, where you want reliable numbers from the fewest possible experiments.

Tight-Binding Inhibitors Need a Different Equation

Standard Michaelis-Menten-based methods assume that the inhibitor concentration far exceeds the enzyme concentration, so binding the inhibitor doesn’t meaningfully deplete the free inhibitor pool. For most screening-level assays, that assumption holds. But when the inhibitor binds so tightly that its Ki approaches or drops below the enzyme concentration in the assay, a meaningful fraction of the added inhibitor gets tied up in the enzyme-inhibitor complex, and the free inhibitor concentration is no longer close to the total inhibitor concentration.

Under these conditions, the standard equations systematically overestimate Ki because they assume more free inhibitor is present than actually exists. The solution is to fit the data using the Morrison equation, a quadratic relationship that explicitly accounts for depletion of free inhibitor. This approach has been shown to yield more accurate Ki values for tight-binding compounds.⁶ In practice, you’ll know you need it when your dose-response curve is unusually steep or when the fitted Ki comes out close to or below half your enzyme concentration. If either of those signs appears, switch to the Morrison equation rather than forcing the data through a standard model.

Assay design also matters here more than usual. With tight-binding inhibitors, small errors in your enzyme concentration estimate propagate directly into the Ki, because the Morrison equation uses enzyme concentration as an explicit parameter. If your enzyme is partially inactive or your concentration measurement is off by twofold, the Ki you calculate will be off by a similar margin. Careful enzyme titration before the inhibition experiment is worth the extra effort.

Slow-Binding Inhibitors and Progress Curves

Most Ki calculations assume the enzyme, substrate, and inhibitor reach equilibrium quickly relative to the timescale of your measurement. Slow-binding inhibitors violate that assumption. Instead of an immediate drop in activity, you see the reaction rate decrease gradually over minutes to hours as the inhibitor slowly engages the enzyme. If you measure velocity only at a single early time point, you’ll underestimate inhibition; if you measure only late, you may miss the kinetics entirely.

Two basic mechanisms account for slow-binding behavior. In one, the inhibitor simply binds and releases slowly, taking time to reach equilibrium. In the other, the inhibitor binds rapidly to form an initial loose complex, which then slowly rearranges into a tighter complex through a conformational change.⁷ The two mechanisms require different mathematical treatments, and distinguishing between them matters because the tighter complex in the two-step mechanism can have a dramatically lower effective Ki than the initial encounter complex.

The standard approach to analyzing slow-binding inhibition is to collect full progress curves, plotting product formation over time at several inhibitor concentrations. The curvature of each progress curve contains information about both the initial and final rates, which in turn allow you to extract the relevant rate constants and compute the overall Ki.⁸ This is a case where progress curve analysis isn’t just better than endpoint measurements; it’s essentially the only way to get the right answer. An example from the literature: the tissue transglutaminase inhibitor LDN-27219 was characterized as a reversible, slow-binding inhibitor only through careful kinetic analysis of its time-dependent behavior, which further revealed that the compound binds at a regulatory site rather than the active site.⁹

Irreversible Inhibitors Play by Different Rules

If an inhibitor forms a permanent covalent bond with the enzyme, the concept of an equilibrium dissociation constant stops making sense. The inhibitor never lets go, so there’s no equilibrium to describe. For these compounds, the meaningful potency metric is not Ki alone but the ratio of the inactivation rate constant (kinact) to the inhibitor’s initial binding constant (KI). This ratio, kinact/KI, captures both how quickly the inhibitor finds and binds the enzyme and how efficiently it forms the irreversible covalent bond.¹⁰

Reporting an IC50 for an irreversible inhibitor is particularly misleading because the IC50 keeps dropping the longer you incubate. Given enough time, even a weak covalent inhibitor will inactivate all the enzyme. The kinact/KI ratio, by contrast, is time-independent and gives a fair comparison between compounds.

Measuring kinact and KI separately usually requires collecting time-dependent inactivation data at multiple inhibitor concentrations and fitting the curves to extract both parameters. A newer approach, called EPIC-Fit, allows you to determine kinact and KI from pre-incubation IC50 data collected at multiple time points, using global fitting that can be implemented in a standard spreadsheet.¹¹ That makes the measurement more accessible to labs that don’t have specialized kinetics software.

Artifacts That Corrupt Your Ki

Even with the right equation and the right fitting method, you can still get a wrong Ki if something in the assay is behaving badly. One of the most common culprits in early-stage drug screening is colloidal aggregation. At micromolar concentrations, many small organic molecules clump together into tiny particles that stick to enzyme surfaces and block activity through a nonspecific physical mechanism rather than a genuine binding interaction.¹² The result looks like inhibition in your assay, and you can fit a beautiful dose-response curve and calculate a perfectly reasonable-looking Ki that is completely meaningless.

The telltale sign of aggregation-based inhibition is that it largely disappears when you add a small amount of nonionic detergent to the assay buffer. A simple counter-screen comparing inhibition with and without detergent can catch the vast majority of these false positives.¹³ If you’re working with a compound that shows potent inhibition but hasn’t been tested for aggregation, treat the Ki with suspicion until you’ve ruled this out.

Other artifacts to watch for include compound fluorescence or absorbance interfering with your detection method, enzyme inactivation over the course of the assay unrelated to the inhibitor, and substrate depletion at low substrate concentrations. None of these are exotic problems; they’re everyday realities of running enzyme assays, and each can silently bias Ki in one direction or another. Building in controls for these failure modes is as important as choosing the right kinetic model.

Alternative Measurement Approaches

Activity-based assays, where you measure how the inhibitor affects the rate of an enzymatic reaction, are the workhorse for Ki determination. But they aren’t the only option. Biophysical methods that directly measure binding, independent of catalytic activity, can provide complementary or sometimes superior information.

Isothermal titration calorimetry (ITC) measures the heat released or absorbed when an inhibitor binds to an enzyme, giving you the binding affinity and the thermodynamic driving forces behind it in a single experiment.¹⁴ The advantage is that ITC doesn’t require a functional assay, so it works for targets where good activity assays are hard to develop. The disadvantage is throughput: ITC experiments use relatively large amounts of protein and measure one compound at a time, making it impractical for screening hundreds of molecules.

On the computational side, methods like free energy perturbation (FEP) calculations attempt to predict binding affinities from molecular simulations. These approaches can estimate the relative Ki values of related compounds by simulating how small chemical changes affect binding.¹⁵ The accuracy of FEP and related methods has improved considerably, but they still work best for comparing closely related molecules rather than predicting absolute Ki values from scratch. They’re most useful as a complement to experimental data, helping prioritize which compounds to synthesize and test next rather than replacing the measurement entirely.

Choosing the Right Method for Your Situation

The method you use to calculate Ki should be driven by what kind of inhibitor you’re studying, not by habit or convenience. For a reversible inhibitor at concentrations well above the enzyme level, the Cheng-Prusoff equation applied to steady-state IC50 data works fine, provided you’ve correctly identified the inhibition type and your Km is well characterized. For tight binders, switch to the Morrison equation. For slow-binding compounds, collect progress curves and fit the time-dependent data. For covalent irreversible inhibitors, report kinact/KI, not Ki or IC50.

In all cases, nonlinear regression should be your default fitting method. Reserve linear transformations for visual diagnosis of the inhibition mechanism but don’t rely on them for parameter values. And regardless of the sophistication of your math, always run the basic controls that catch aggregation artifacts, enzyme instability, and detection interference. A carefully measured Ki from a well-controlled assay is worth more than a precisely fitted number from a flawed one. The goal isn’t mathematical elegance; it’s a number that faithfully represents how your inhibitor interacts with its target under conditions relevant to the question you’re trying to answer.