Impact of Genetic Polymorphism on Drug-Drug Interactions Mediated by Cytochromes: A General Approach

Abstract

Currently, quantitative prediction of the impact of genetic polymorphism and drug-drug interactions mediated by cytochromes, based on in vivo data, is made by two separate methods and restricted to a single cytochrome. We propose a unified approach for describing the combined impact of drug-drug interactions and genetic polymorphism on drug exposure. It relies on in vivo data and uses the following three characteristic parameters: one for the victim drug, one for the interacting drug, and another for the genotype. These parameters are known for a wide range of drugs and genotypes. The metrics of interest are the ratio of victim drug area under the curve (AUC) in patients with genetic variants taking both drugs, to the AUC in patients with either variant or wild-type genotype taking the victim drug alone. The approach was evaluated by external validation, comparing predicted and observed AUC ratios found in the literature. Data were found for 22 substrates, 30 interacting drugs, and 38 substrate-interacting drug couples. The mean prediction error of AUC ratios was 0.02, and the mean prediction absolute error was 0.38 and 1.34, respectively. The model may be used to predict the variations in exposure resulting from a number of drug-drug–genotype combinations. The proposed approach will help (1) to identify comedications and population at risk, (2) to adapt dosing regimens, and (3) to prioritize the clinical pharmacokinetic studies to be done.

Appendix: derivation of Eq. 11

In vitro, according to Hisaka (67), in case of reversible inhibition of a cytochrome, the ratio of victim drug intrinsic clearances is related to the inhibitor concentration, I_u, and the inhibition constant Ki as follows:

$$ \frac{\mathrm{CL}{\mathrm{i}}^{\mathrm{XM}}}{\mathrm{CL}{\mathrm{i}}^{\mathrm{XM}*}}=1+\frac{{\mathrm{I}}_{\mathrm{u}}}{{\mathrm{K}}_{\mathrm{i}}} $$

In case of mechanism-based inhibition, the ratio of intrinsic clearances depends on k_inact, k_deg, and K_I which are the maximum inactivation rate constant, degeneration constant, and inhibitor concentration when the rate constant of inactivation reaches half k_inact, respectively (68):

$$ \frac{\mathrm{CL}{\mathrm{i}}^{\mathrm{XM}}}{\mathrm{CL}{\mathrm{i}}^{\mathrm{XM}*}}=1+\frac{{\mathrm{k}}_{\mathrm{i}\mathrm{nact}}.{\mathrm{I}}_{\mathrm{u}}}{{\mathrm{k}}_{\deg }.\left({\mathrm{I}}_{\mathrm{u}}+{\mathrm{K}}_{\mathrm{i}}\right)} $$

In vivo, using the following assumptions: (1) the metabolic clearance of the victim drug is assumed to be close to total clearance, (2) metabolism is assumed to occur for a small part in the gut wall and for the main part in the liver, (3) hepatic clearance is related to intrinsic clearance by the well-stirred model, and (4) the kinetics of victim drug is linear, i.e., clearance is independent of time and dose, then the ratio of oral clearances is approximately equal to the ratio of intrinsic clearances. Replacing I_u by the time-averaged unbound concentration of interacting drug at the target site, I_u,av:

$$ \begin{array}{ccc}\hfill \frac{\mathrm{CLora}{\mathrm{l}}^{\mathrm{XM}}}{\mathrm{CLora}{\mathrm{l}}^{\mathrm{XM}*}}=1+\frac{{\mathrm{I}}_{\mathrm{u},\mathrm{av}}}{{\mathrm{K}}_{\mathrm{i}}}\hfill & \hfill \mathrm{and}\hfill & \hfill \frac{\mathrm{CLora}{\mathrm{l}}^{\mathrm{XM}}}{\mathrm{CLora}{\mathrm{l}}^{\mathrm{XM}*}}=1+\frac{{\mathrm{k}}_{\mathrm{i}\mathrm{nact}}.{\mathrm{I}}_{\mathrm{u},\mathrm{av}}}{{\mathrm{k}}_{\deg }.\left({\mathrm{I}}_{\mathrm{u},\mathrm{av}}+{\mathrm{K}}_{\mathrm{i}}\right)}\hfill \end{array} $$

Defining the in vivo potency of an inhibitor as follows:

$$ \mathrm{IX}=-\left(1-\frac{\mathrm{CLora}{\mathrm{l}}^{\mathrm{XM}*}}{\mathrm{CLora}{\mathrm{l}}^{\mathrm{XM}}}\right) $$

It comes

$$ \mathrm{IX}=-\left(1-\frac{1}{1+\frac{{\mathrm{I}}_{\mathrm{u},\mathrm{av}}}{{\mathrm{K}}_{\mathrm{i}}}}\right)=-\frac{{\mathrm{I}}_{\mathrm{u},\mathrm{av}}}{{\mathrm{K}}_{\mathrm{i}}+{\mathrm{I}}_{\mathrm{u},\mathrm{av}}} $$

For a reversible inhibitor, and

$$ \mathrm{IX}=-\frac{\left({\mathrm{k}}_{\mathrm{i}\mathrm{nact}}/{\mathrm{k}}_{\deg}\right).{\mathrm{I}}_{\mathrm{u},\mathrm{av}}}{{\mathrm{K}}_{\mathrm{i}}+\left(1+\frac{{\mathrm{k}}_{\mathrm{i}\mathrm{nact}}}{{\mathrm{k}}_{\deg }}\right).{\mathrm{I}}_{\mathrm{u},\mathrm{av}}} $$

For a mechanism-based inhibitor. Because k_inact is much greater than k_deg (69), we have k_inact/k_deg >> 1. Therefore,

$$ \mathrm{IX}=-\frac{{\mathrm{k}}_{\mathrm{i}\mathrm{nact}}.{\mathrm{I}}_{\mathrm{u},\mathrm{av}}}{{\mathrm{K}}_{\mathrm{i}}.{\mathrm{k}}_{\deg }+{\mathrm{k}}_{\mathrm{i}\mathrm{nact}}.{\mathrm{I}}_{\mathrm{u},\mathrm{av}}} $$

Assuming linear kinetics of the inhibitor, its concentration I_u,av is proportional to its dose or dosing rate:

$$ {\mathrm{I}}_{\mathrm{u},\mathrm{av}}=\upalpha .\mathrm{Dose} $$

Hence,

$$ \mathrm{IX}=-\frac{\upalpha .\mathrm{Dose}}{{\mathrm{K}}_{\mathrm{i}}+\upalpha .\mathrm{Dose}}=-\frac{\mathrm{D}\mathrm{ose}}{\left({\mathrm{K}}_{\mathrm{i}}/\upalpha \right)+\mathrm{Dose}}=-\frac{\mathrm{D}\mathrm{ose}}{{\mathrm{D}}_{50}+\mathrm{Dose}} $$

for a reversible inhibitor, and

$$ \mathrm{IX}=-\frac{{\mathrm{k}}_{\mathrm{i}\mathrm{nact}}.\upalpha .\mathrm{Dose}}{{\mathrm{K}}_{\mathrm{i}}.{\mathrm{k}}_{\deg }+{\mathrm{k}}_{\mathrm{i}\mathrm{nact}}.\upalpha .\mathrm{Dose}}=-\frac{\mathrm{D}\mathrm{ose}}{\frac{{\mathrm{K}}_{\mathrm{i}}.{\mathrm{k}}_{\deg }}{\upalpha .{\mathrm{k}}_{\mathrm{i}\mathrm{nact}}}+\mathrm{Dose}}=-\frac{\mathrm{D}\mathrm{ose}}{{\mathrm{D}}_{50}+\mathrm{Dose}} $$

for a mechanism-based inhibitor. The final expression is the same for both types of inhibitor, but the expression of D₅₀ is different.

Similarly, the inductive effect may be determined in vitro on hepatocyte cell cultures and modeled as (3) follows:

$$ \frac{\mathrm{CL}{\mathrm{i}}^{\mathrm{XM}*}}{\mathrm{CL}{\mathrm{i}}^{\mathrm{XM}}}=1+\frac{{\mathrm{E}}_{\max }.{\mathrm{I}}_{\mathrm{u}}}{{\mathrm{I}}_{50}+{\mathrm{I}}_{\mathrm{u}}} $$

Where E_max is the maximal induction effect and I₅₀ is the inducer unbound concentration resulting in a half maximal induction.

Defining the in vivo potency of an inducer as follows:

$$ \mathrm{IX}=\frac{\mathrm{CL}{\mathrm{o}}^{\mathrm{XM}*}}{\mathrm{CL}{\mathrm{o}}^{\mathrm{XM}}}-1 $$

We have, by combining the last two equations:

$$ \mathrm{IX}=\frac{\mathrm{I}{\mathrm{X}}_{\max }.{\mathrm{I}}_{\mathrm{u},\mathrm{av}}}{{\mathrm{I}}_{50}+{\mathrm{I}}_{\mathrm{u},\mathrm{av}}} $$

Where E_max has been replaced by IX_max for consistency. Using I _u,av = α.Dose, we find:

$$ \mathrm{IX}=\frac{\mathrm{I}{\mathrm{X}}_{\max }.\upalpha .\mathrm{Dose}}{{\mathrm{I}}_{50}+\upalpha .\mathrm{Dose}}=\frac{\mathrm{I}{\mathrm{X}}_{\max }.\mathrm{Dose}}{\left({\mathrm{I}}_{50}/\upalpha \right)+\mathrm{Dose}}=\frac{\mathrm{I}{\mathrm{X}}_{\max }.\mathrm{Dose}}{{\mathrm{D}}_{50}+\mathrm{Dose}} $$