Why Convert an IC50?
An enzyme inhibition assay often reports an IC50: the inhibitor concentration that reduces the measured enzyme activity to 50% of its uninhibited value under the assay conditions. This is useful for describing a particular experiment, but it is not generally an intrinsic measure of inhibitor binding. In a competitive assay, the measured IC50 depends on the substrate concentration as well as on inhibitor affinity.
The Cheng–Prusoff relationship adjusts a competitive-inhibition IC50 for the substrate concentration used in the assay. Its use is conditional: the inhibition mechanism and assay conditions must support the model from which the relationship is derived. A numerical conversion is not a substitute for checking those conditions.
The equation predicts that, for the same inhibitor and enzyme system, increasing substrate concentration raises the IC50 needed to halve the rate. The substrate competes with inhibitor for free enzyme, so more inhibitor is required to produce the same reduction in activity. The calculated \(K_i\), in contrast, should be approximately independent of \([S]\) when the model and measurements are appropriate.
Deriving the Cheng–Prusoff Relationship
Assume a reversible competitive inhibitor at equilibrium, a single substrate, initial-rate measurement, and Michaelis–Menten behavior. Let \(v_0\) be the uninhibited rate and \(v_I\) the rate in the presence of inhibitor concentration \([I]\). In the competitive model, inhibitor increases the apparent substrate term from \(K_m\) to \(K_m(1+[I]/K_i)\), without changing \(V_{\max}\):
Divide the inhibited rate by the uninhibited rate at the same substrate concentration. At the IC50, the activity ratio is 0.5. Substituting \([I]=IC_{50}\) and solving gives the conversion:
Subtracting \(K_m+[S]\) from both sides gives \(K_m IC_{50}/K_i=K_m+[S]\). Dividing by \(K_m\) and rearranging yields:
The ratio \([S]/K_m\) is dimensionless, so \(IC_{50}\) and \(K_i\) have the same concentration units. This derivation also shows why the relationship is specific to the assumed competitive model: a different rate equation need not produce this activity ratio or this conversion.
Applying the Conversion
Worked Example: Converting an IC50 at the Assay Substrate Concentration
In a hypothetical initial-rate assay, a reversible inhibitor has an IC50 of 12.0 μM. The substrate concentration is 20.0 μM, and the measured \(K_m\) under these assay conditions is 10.0 μM. Assume the assay supports the single-substrate competitive model and that inhibitor depletion is negligible. Estimate \(K_i\).
The Cheng–Prusoff equation is \(K_i=IC_{50}/(1+[S]/K_m)\). Substitute the values, keeping the concentration units consistent:
The estimated competitive-inhibition \(K_i\) is 4.00 μM. The IC50 is three times this value because the assay substrate concentration is twice \(K_m\), making the correction factor \(1+2=3\).
Worked Example: Comparing Two Substrate Concentrations
Suppose a hypothetical inhibitor has a true competitive \(K_i\) of 2.00 μM and the enzyme has \(K_m=15.0\) μM. Predict the IC50 at substrate concentrations of 15.0 μM and 45.0 μM. Assume all other assay conditions remain suitable and unchanged.
Rearrange the relationship as \(IC_{50}=K_i(1+[S]/K_m)\). At 15.0 μM substrate:
At 45.0 μM substrate:
The predicted IC50 doubles as substrate rises from one to three times \(K_m\), while \(K_i\) remains 2.00 μM. Thus, IC50 values from assays run at different substrate concentrations should not be compared as if they were condition-independent affinity measures.
Conditions Required for a Meaningful Conversion
The calculation is only as reliable as its inputs and assumptions. Before applying it, check that the IC50 represents a 50% reduction relative to the uninhibited activity in the same assay, and that substrate concentration and \(K_m\) refer to the same enzyme system and conditions. In particular, \(K_m\) is a kinetic parameter; it should not be treated as a universal constant or automatically interpreted as a substrate binding affinity.
The relationship requires reversible competitive inhibition of the substrate reaction. If inhibition does not follow this mechanism, the derived activity ratio may not apply.
Use an initial-rate assay with substrate concentration effectively constant during measurement. Substantial substrate depletion or an endpoint signal that does not track initial rate can undermine the model.
Inhibitor binding should be reversible and sufficiently close to equilibrium. The conversion also assumes that free inhibitor concentration is represented adequately by the concentration used in the calculation; appreciable inhibitor binding to the enzyme or other assay components can violate that assumption.
Use the substrate concentration in the reaction mixture and a \(K_m\) measured or justified for that enzyme under compatible conditions. Ensure that \([S]\), \(K_m\), and IC50 use consistent concentration units.
Other features can also make a simple conversion inappropriate. For example, time-dependent loss of enzyme activity, substrate inhibition, multiple interacting substrates, or an assay signal affected directly by the inhibitor may produce an apparent IC50 that is not the value assumed in the derivation. If an enzyme uses multiple substrates, the relevant kinetic behavior may depend on the concentrations of the other substrates as well. A single-substrate correction should not be applied automatically.
Worked Example: Recognizing When the Conversion Is Unreliable
A hypothetical assay reports an IC50 of 0.50 μM. The enzyme concentration in the assay is 0.80 μM. A researcher proposes to use \([S]=K_m\) and report \(K_i=0.25\) μM.
The arithmetic would be \(0.50\ \mu\mathrm{M}/(1+1)=0.25\ \mu\mathrm{M}\), but the required concentration assumption is not credible: the enzyme concentration is greater than the reported IC50. The calculation assumes that the concentration used for inhibitor can represent free inhibitor concentration. When enzyme and inhibitor concentrations are comparable, appreciable inhibitor can be bound, so free and total inhibitor concentrations may differ substantially. The reported IC50 may also be shaped by inhibitor depletion.
Therefore, 0.25 μM is not justified as a Cheng–Prusoff \(K_i\) from these data. The assay should be redesigned or analyzed with an approach that accounts for inhibitor depletion and binding; simply substituting the reported values does not fix the violated assumption.
Interpreting Results and Choosing an Approach
A Cheng–Prusoff value is a model-based estimate, not a direct measurement of affinity that is guaranteed to be correct. Report the measured IC50 together with substrate concentration, \(K_m\), and the converted \(K_i\), and state that the conversion assumes reversible competitive inhibition under the assay conditions. If the IC50 was determined using nominal rather than free inhibitor concentrations, describe it accordingly.
There are three practical alternatives when the assumptions are uncertain. First, report the IC50 as an assay-specific result without converting it; this avoids presenting a conditional estimate as an intrinsic quantity. Second, measure inhibition across multiple substrate concentrations and fit a kinetic model to the rate data, which tests whether a competitive model describes the data more adequately than a single IC50 correction. Third, use a suitable direct binding or equilibrium method when the experimental question is binding affinity rather than inhibition under a particular substrate condition. Each approach answers a somewhat different question, and model complexity should be supported by informative data.
| Approach | What it reports | Main caution |
|---|---|---|
| Report IC50 alone | Concentration giving half activity in the specified assay | Depends on assay conditions, including substrate concentration |
| Cheng–Prusoff conversion | Model-based competitive \(K_i\) estimate | Requires the assumptions and compatible \(K_m\) described above |
| Fit rates across substrate concentrations | Kinetic parameters under the fitted model | Needs suitable rate data and a model that describes them |
| Direct binding or equilibrium method | Binding measure for the method's defined system | May not represent functional inhibition in the enzyme assay |
A useful diagnostic is consistency across conditions. If IC50 rises with substrate concentration in the direction predicted by \(IC_{50}=K_i(1+[S]/K_m)\), and the resulting \(K_i\) estimates are similar, that supports—but does not prove—the competitive model. Strong disagreement can signal inaccurate \(K_m\) or concentration inputs, assay artifacts, or a mechanism outside the model. It is a reason to investigate, not to average the converted values without explanation.
Common Mistakes
- Using the correction in the wrong direction. For competitive inhibition, \(IC_{50}=K_i(1+[S]/K_m)\); therefore divide IC50 by the correction factor to estimate \(K_i\).
- Ignoring substrate concentration. An IC50 measured at high \([S]/K_m\) can be much larger than \(K_i\). The IC50 should not be treated as a condition-independent affinity constant.
- Using a mismatched \(K_m\). A \(K_m\) from different conditions may not be appropriate for the assay being converted. Verify its relevance rather than assuming it is universal.
- Converting every IC50. The equation follows from a specific reversible competitive model. If assay design or inhibition behavior contradicts its assumptions, the arithmetic may be correct while the interpretation is not.
Check Your Understanding
Try each question, then compare your reasoning with the solutions.
- A hypothetical assay has IC50 = 9.00 μM, \([S]=K_m\), and satisfies the conversion assumptions. What is \(K_i\)?
- For a fixed competitive inhibitor and enzyme, what happens to IC50 when \([S]/K_m\) increases from 0.5 to 2.0? Explain using the equation.
- A researcher uses a \(K_m\) measured in a different enzyme preparation and at different assay conditions. What should be checked before converting the IC50?
- Why is a competitive Cheng–Prusoff conversion not justified merely because an assay reports a numerical IC50?
Solutions. (1) \(K_i=9.00\ \mu\mathrm{M}/(1+1)=4.50\ \mu\mathrm{M}\). (2) The correction factor increases from 1.5 to 3.0, so predicted IC50 doubles for the same \(K_i\): \(IC_{50}=1.5K_i\) becomes \(3.0K_i\). (3) Confirm that the \(K_m\) represents the same enzyme system and compatible conditions, and that the measured \([S]\) and concentration units are appropriate. (4) IC50 alone does not establish reversible competitive inhibition, initial-rate conditions, equilibrium, negligible depletion, or the other assumptions required by the derivation.