Why Assay Results Need Translation
A transporter inhibition assay reports an effect under particular experimental conditions: a specified probe substrate concentration, incubation medium, and measured endpoint. A PBPK model, by contrast, needs an inhibition parameter that can be combined with inhibitor exposure and substrate conditions at a modeled site. The assay’s IC50 is therefore not automatically a transferable measure of inhibitor potency. It depends, among other things, on the substrate concentration used in the assay.
The key task is to preserve the meaning of the measurement while translating it into the parameterization used by the model. For reversible competitive inhibition, this usually means converting an assay IC50 to a Ki, with corrections for substrate concentration and, when justified by the data, nonspecific binding in the assay. These corrections are conditional: they are not universal adjustments for every inhibition mechanism or assay format.
Competitive Inhibition and the IC50-to-Ki Relationship
Consider a transporter assay measuring initial transport rate for one substrate. Under a simple competitive model, substrate and inhibitor compete reversibly for the same binding site. Assume Michaelis–Menten substrate kinetics, a single relevant substrate and inhibitor, negligible substrate depletion, and no time-dependent loss of transporter activity. Let \(S\) denote substrate concentration, \(I\) inhibitor concentration, \(K_m\) the substrate concentration giving half-maximal transport rate, and \(K_i\) the competitive inhibition constant. All concentrations and kinetic parameters must use a consistent concentration basis.
Here \(v_0\) is the transport rate without inhibitor and \(v_I\) is the rate with inhibitor. Divide the second rate by the first. This gives the remaining fraction of the control transport response, \(v_I/v_0\); the fraction inhibited is \(1-v_I/v_0\).
At the assay IC50, half of the control response remains, so \(v_I/v_0=0.5\). Substituting 0.5 into the ratio and solving for \(I\) gives the competitive-inhibition correction.
This result shows why IC50 is assay-condition dependent: increasing substrate concentration raises the IC50 for a competitive inhibitor, even if the inhibitor’s Ki is unchanged. The formula is justified only when the assay response follows the stated competitive model and the substrate concentration and Km describe the same assay conditions on the same concentration scale.
Worked Example: Correcting a Competitive IC50 for Substrate Concentration
Suppose a hypothetical transporter assay reports an unbound IC50 of 2.00 µM. The unbound substrate concentration was 2.00 µM, and the applicable unbound Km was 4.00 µM. Assume reversible competitive inhibition, initial-rate measurements, and negligible substrate depletion.
The substrate correction factor is \(1+S/K_m=1+(2.00/4.00)=1.50\). Therefore:
The model input is a competitive Ki of 1.33 µM on an unbound concentration basis. It is not appropriate to enter the assay IC50 of 2.00 µM as though it were the substrate-independent Ki. To check the conversion, using this Ki at the assay substrate concentration predicts \(IC_{50}=1.33(1+2.00/4.00)=2.00\) µM, up to rounding.
Accounting for Unbound Fractions
Inhibitor may bind to proteins, plastic, or other components of an assay system. If the assay’s IC50 is reported as a nominal concentration, the concentration available to interact with the transporter may be lower. When the unbound fraction of inhibitor in the assay, \(f_{u,I}\), is measured and approximately constant across the relevant concentration range, the unbound inhibitor concentration at the IC50 is:
The subscript \(u\) denotes unbound and “nom” denotes nominal. Under the competitive assumptions above, the resulting Ki is \(IC_{50,u}/(1+S_u/K_{m,u})\), where \(S_u\) and \(K_{m,u}\) are expressed on a consistent unbound basis. Alternatively, if the assay’s substrate concentration and Km are both represented on the same nominal scale, their ratio can be used on that scale, provided that the apparent Km appropriately reflects the assay’s substrate binding. Do not combine an unbound substrate concentration with a nominal-scale Km, or vice versa.
A measured unbound fraction is not a generic correction factor. The fraction should correspond to the assay matrix and conditions used to obtain the IC50. If binding is concentration-dependent, equilibration is incomplete, or the fraction is unavailable, multiplying by an assumed value can create false precision. In those cases, preserve the reported assay value with its units and conditions, obtain better binding information, or represent the uncertainty explicitly in the model-development analysis.
Worked Example: Correcting Nominal IC50 for Assay Binding
In a hypothetical assay, the nominal inhibitor IC50 is 8.00 µM and the measured inhibitor unbound fraction is 0.25. The assay substrate concentration is 2.00 µM and its applicable Km is 4.00 µM, both expressed on a consistent basis. Assume the inhibition is reversible and competitive.
First calculate the unbound IC50: \(IC_{50,u}=0.25(8.00\ \mu\mathrm{M})=2.00\ \mu\mathrm{M}\). Then account for the substrate concentration:
The converted input is Ki = 1.33 µM on an unbound basis. The arithmetic relies on the stated unbound fraction being applicable at the measured IC50 and on substrate concentration and Km being comparable in the correction. If those conditions are not supported, this point estimate is not warranted.
Choosing the Input to Match the Model
A model may accept a mechanistic Ki or an assay-specific IC50. These are not interchangeable labels for the same number. If the model uses a competitive Ki, provide a Ki converted under the competitive assumptions and use inhibitor concentration and substrate kinetics on compatible bases. If the model instead uses an IC50-based inhibition function, the IC50 must correspond to the defined assay or be adjusted to the conditions represented by that function. Record whether the parameter is nominal or unbound, and document the substrate concentration and kinetic basis used for any conversion.
For example, under the competitive model, the fraction of transport activity remaining at a modeled site is:
Here \(I_u\) is the unbound inhibitor concentration at the transporter site, and \(S\) and \(K_m\) must be consistent with the model’s substrate formulation. This expression illustrates why a Ki is not by itself a predicted interaction magnitude: the modeled inhibitor exposure and substrate conditions also matter. Estimating inhibitor concentrations at transporter sites is a separate modeling task.
Worked Example: Checking a Converted Ki at a Second Substrate Concentration
Use the hypothetical Ki of 1.33 µM from the first example. Suppose a second assay condition has unbound substrate concentration 1.00 µM and unbound Km 4.00 µM. Assume the same reversible competitive mechanism and unchanged Ki.
The expected unbound IC50 under this condition is:
Using the unrounded Ki \(2.00/1.50=1.333\ldots\) µM gives 1.667 µM, or 1.67 µM to three significant figures. Thus the assay IC50 is expected to be lower at the lower substrate concentration. A substantial departure from this relationship across well-controlled conditions would prompt review of the mechanism, assay quality, or parameter consistency rather than an automatic averaging of the IC50 values.
When the Simple Conversion Does Not Apply
The Cheng–Prusoff-type relationship above is specifically derived for competitive inhibition in the stated kinetic model. It should not be applied merely because an assay reports an IC50. For a pure noncompetitive model, inhibitor reduces the effective transport capacity without changing the substrate’s apparent affinity; its response does not have the same substrate correction. Mixed inhibition can affect both apparent capacity and apparent substrate affinity. Irreversible or time-dependent inhibition, multiple binding sites, cooperative effects, and complex transporter processes may also require different models or direct fitting of richer data.
Likewise, an assay-reported Ki may already be obtained by fitting a mechanistic model or applying a substrate correction. Applying the correction a second time would bias the potency estimate. Check what the reported term means, which substrate and inhibitor concentrations were used, and whether concentrations are nominal or unbound. A fitted Ki is only as defensible as the model and data that produced it.
Transporter assay endpoints also matter. Inhibition of probe-substrate uptake in a cell system is not automatically equivalent to inhibition of net transport in a tissue, and a parameter determined with one probe substrate may not fully characterize another substrate. The assay evidence should identify the transporter, probe substrate, endpoint, and experimental conditions. The earlier material on selecting transporter substrates and inhibitors from evidence provides the context for evaluating whether the assay is relevant to the modeled pathway.
Diagnostics, Alternatives, and Limitations
When several assay conditions are available, inspect whether the data support a common mechanism-based parameter. For competitive inhibition, unbound IC50 should increase with substrate concentration in the pattern \(IC_{50,u}=K_i(1+S_u/K_{m,u})\), when Km and substrate concentrations are compatible and other conditions remain comparable. Fit or calculate the implied Ki for each condition and compare them. Large systematic differences suggest that assumptions or measurements may be inconsistent; they are not proof of a particular alternative mechanism.
Review concentration-response curves for incomplete inhibition, non-unit slopes, unusual curve shapes, or inconsistent replicate responses. These features can indicate assay limitations or a mechanism not represented by the simple model. Confirm that transport rates are measured in an appropriate initial-rate range, controls are valid, and depletion or accumulation has not distorted the nominal substrate concentration. Check that the inhibitor remains soluble and that the measured unbound fraction is suitable for the tested concentration range.
The main alternatives are to retain an assay-specific IC50 with its assay conditions, fit a richer mechanistic model to concentration-response data collected at multiple substrate concentrations, or use a separately reported mechanistic Ki when its derivation and assumptions are documented. Retaining an unadjusted IC50 avoids an unsupported conversion but does not make the value independent of assay conditions. More elaborate fitting can distinguish mechanisms only when the data are informative enough; a complex model cannot rescue sparse or poorly controlled measurements. In all cases, preserve the underlying experimental result and the rationale for the selected PBPK input.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions below.
- A hypothetical competitive assay gives an unbound IC50 of 3.00 µM at \(S_u=2.00\) µM and \(K_{m,u}=2.00\) µM. What is Ki?
- A nominal IC50 is 10.0 µM and the measured inhibitor unbound fraction is 0.30. What is the unbound IC50, assuming the fraction is constant and applicable?
- Why should a competitive IC50 measured at high substrate concentration not automatically be used as a substrate-independent Ki?
- An assay reports Ki after fitting a competitive model that already accounts for substrate concentration. Should the IC50-to-Ki correction be applied again?
- What does a substantial change in calculated Ki across substrate concentrations suggest, and what does it not establish by itself?
Solutions. (1) \(K_i=3.00/[1+(2.00/2.00)]=3.00/2.00=1.50\) µM. (2) \(IC_{50,u}=0.30(10.0\ \mu\mathrm{M})=3.00\) µM. This is the unbound IC50; a substrate correction would still be needed to obtain a competitive Ki. (3) Competitive inhibition raises IC50 with increasing substrate concentration according to \(IC_{50}=K_i(1+S/K_m)\), so the measured IC50 includes an assay-condition effect. (4) No. Applying the correction again would double-correct the value; first confirm the reported Ki’s definition and fitting method. (5) It suggests that the simple model assumptions, assay measurements, or concentration bases may not be consistent across conditions. The change alone does not identify which mechanism is correct; further evidence and suitable data are needed.