Parameterizing Reversible CYP Inhibition from In Vitro Data

From an Assay Measurement to a PBPK Parameter

An in vitro inhibition result is not automatically the inhibition parameter a PBPK model needs. An assay may report an IC50 measured at a particular substrate concentration and based on the inhibitor concentration added to the incubation. The model, by contrast, needs an inhibition constant that can be used with the inhibitor concentration at the enzyme site. Substrate concentration and inhibitor binding in the assay can therefore change the translation.

This tutorial develops that translation for reversible competitive inhibition. The derivation assumes a competitive model is appropriate for the data; it does not establish which inhibition mechanism applies to a particular CYP assay. The distinction matters because an IC50 is conditional on assay conditions, whereas Ki is a model parameter for the specified inhibition mechanism.

The subscript \(u\) emphasizes that inhibitor concentration and inhibition constant must use compatible unbound-concentration conventions. Concentrations must also use the same units: for example, \(I_u\) and \(K_{i,u}\) can both be expressed in micromoles per litre. If a reported Ki has already been corrected to unbound concentration, applying an additional binding correction would be inappropriate.

Competitive Inhibition and the Substrate Effect

For a single substrate under the Michaelis–Menten competitive-inhibition model, the reaction rate in the presence of inhibitor is

Here \(V_{\max}\) is the maximum reaction rate in the absence of inhibitor. Competitive inhibition increases the apparent \(K_m\) by the factor \(1+I_u/K_{i,u}\), while leaving \(V_{\max}\) unchanged in this model. The corresponding rate without inhibitor is \(v_0=V_{\max}S/(K_m+S)\). Dividing the inhibited rate by the uninhibited rate gives the fraction of activity remaining:

This ratio is the competitive-inhibition multiplier for the CYP reaction at that substrate and inhibitor concentration. The fraction of activity inhibited is \(1-v_I/v_0\). When \(S\) is small relative to \(K_m\), the multiplier approaches \(1/(1+I_u/K_{i,u})\). At appreciable substrate concentrations, substrate competes with inhibitor, so the same \(I_u\) produces a smaller fractional reduction in rate.

Deriving the Ki–IC50 Relationship

An IC50 is defined by the condition \(v_I/v_0=0.5\). Applying that condition to the rate ratio shows how the measured value depends on substrate concentration.

In many assays, the concentration used to label the IC50 is the nominal amount added, \(I_{\text{nom}}\), rather than the unbound concentration. If the unbound fraction in the incubation is \(f_{u,\text{inc}}\), assume \(I_u=f_{u,\text{inc}}I_{\text{nom}}\) over the relevant concentration range. Substitution gives the nominal-concentration relationship and its rearrangement:

This correction is appropriate only when the reported IC50 is based on nominal inhibitor concentrations and the stated \(f_{u,\text{inc}}\) represents the unbound fraction under the assay conditions. If the assay reports an IC50 already expressed as unbound concentration, omit the factor \(f_{u,\text{inc}}\). Similarly, if a Ki was fitted using nominal concentrations, the fitted value must be interpreted according to how binding was handled in that fit.

Using the Corrected Parameter in a PBPK Model

Once \(K_{i,u}\) has been established, it is used with an unbound inhibitor concentration appropriate to the enzyme site represented by the model. A concentration from a different basis cannot be inserted without a justified conversion. The detailed prediction of enzyme-site concentration is a separate modeling task; the parameterization step here is to keep the concentration basis of \(I\) compatible with \(K_{i,u}\).

For the competitive model, the multiplier on the CYP reaction rate is

Apply this factor to the relevant CYP-mediated reaction, or implement the inhibited rate equation directly. Do not automatically apply it to all victim-drug clearance: clearance through other enzymes, renal excretion, and other pathways is not inhibited by this CYP parameter. If the PBPK reaction is implemented with its substrate dependence, evaluate inhibition at the modeled substrate concentration rather than assuming a single constant effect across all conditions.

Assumptions, Diagnostics, and Alternatives

The equations above are useful only when their assumptions are plausible. The derivation treats inhibition as reversible and competitive, assumes rapid equilibrium for the modeled rate, and uses a single-substrate Michaelis–Menten description. It also assumes that rates are measured over an appropriate initial-rate interval, that the inhibitor is not substantially depleted by binding to enzyme or other assay components, and that the unbound fraction used in the correction represents the assay conditions. These assumptions are not guaranteed merely because an assay reports an IC50.

Check the assay record before parameterizing: identify the substrate and its concentration, obtain the relevant \(K_m\) measured under compatible conditions, determine whether inhibitor concentrations are nominal or unbound, and confirm how the reported Ki or IC50 was fitted. Where several substrate concentrations are available, the competitive model predicts that IC50 increases in proportion to \(1+S/K_m\), provided other conditions are comparable. A failure of this relationship, inconsistent fitted parameters, or a concentration-response curve that cannot be described adequately by the model is a warning not to force the conversion.

A direct fit of the full competitive rate equation to assay data can use more information than converting one IC50 value, particularly when rates are available across multiple substrate and inhibitor concentrations. An IC50-based conversion is a practical alternative when the assay conditions and mechanism are sufficiently characterized. A reported Ki is another possible input, but its concentration basis and fitting assumptions still need to be checked. These approaches are not interchangeable when their assumptions differ.

A common pitfall is to use \(IC_{50,\text{nom}}\) directly as \(K_{i,u}\). That reasoning ignores both substrate competition and incubation binding. Under the assumptions here, the correction is \(K_{i,u}=IC_{50,\text{nom}}f_{u,\text{inc}}/(1+S/K_m)\); omitting the corrections generally overstates the unbound Ki and can understate inhibition when the PBPK model uses unbound inhibitor concentrations.

A second failure mode is scaling total clearance by the CYP reaction multiplier. The multiplier describes the modeled inhibited reaction, not every route of elimination. Apply it to the CYP pathway represented by the assay and model; the total disposition response depends on the contribution of that pathway. Finally, do not use this competitive conversion if the assay evidence does not support competitive inhibition. Other inhibition patterns require a different rate model and parameter interpretation.