Knowledge of free drug intracellular concentration is necessary to predict the impacts of drugs on intracellular targets. The goal of this study was to develop models to predict free intracellular drug concentrations in the presence of apical efflux transporters. The apical efflux transporter P-glycoprotein (P-gp), encoded by human gene multidrug resistance 1 (MDR1), was studied. Apparent permeabilities for 10 compounds in Madin-Darby canine kidney (MDCK) and MDR1-MDCK cell monolayers were obtained experimentally. Six of these compounds were evaluated additionally in the presence of the P-gp inhibitor cyclosporine A. A three-compartment model was developed, and passive and apical efflux clearances (CL_d and CL_ae, respectively) were estimated. Endogenous canine transporters also were delineated. The three-compartment model was unable to simulate experimentally observed lag times and exhibited systematic bias across the simulations. Next, a five-compartment model with explicit membrane compartments was developed. This model resulted in lower systematic errors and simulated the lag time observed experimentally. Apical efflux was modeled out of the cell or out of the membrane. The five-compartment model with apical efflux out of the membrane predicted marked differences in unbound intracellular concentrations between the apical-to-basolateral and the basolateral-to-apical directions. Upon apical drug addition, large decreases in intracellular concentrations were observed with the efflux transporter. No such difference was predicted upon basolateral drug addition. This is consistent with experimental differences in the impact of P-gp on hepatic and brain distribution and supports the hypothesis that apical efflux occurs out of the apical membrane.

Drug distribution is a necessary component of models to predict human pharmacokinetics. A new membrane-based tissue-plasma partition coefficient (K_p) method (K_p,mem) to predict unbound tissue to plasma partition coefficients (K_pu) was developed using in vitro membrane partitioning [fraction unbound in microsomes (f_um)], plasma protein binding, and log P. The resulting K_p values were used in a physiologically based pharmacokinetic (PBPK) model to predict the steady-state volume of distribution (V_ss) and concentration-time (C-t) profiles for 19 drugs. These results were compared with K_p predictions using a standard method [the differential phospholipid K_p prediction method (K_p,dPL)], which differentiates between acidic and neutral phospholipids. The K_p,mem method was parameterized using published rat K_pu data and tissue lipid composition. The K_pu values were well predicted with R² = 0.8. When used in a PBPK model, the V_ss predictions were within 2-fold error for 12 of 19 drugs for K_p,mem versus 11 of 19 for K_p,dPL. With one outlier removed for K_p,mem and two for K_p,dPL, the V_ss predictions for R² were 0.80 and 0.79 for the K_p,mem and K_p,dPL methods, respectively. The C-t profiles were also predicted and compared. Overall, the K_p,mem method predicted the V_ss and C-t profiles equally or better than the K_p,dPL method. An advantage of using f_um to parameterize membrane partitioning is that f_um data are used for clearance prediction and are, therefore, generated early in the discovery/development process. Also, the method provides a mechanistically sound basis for membrane partitioning and permeability for further improving PBPK models. SIGNIFICANCE STATEMENT A new method to predict tissue-plasma partition coefficients was developed. The method provides a more mechanistic basis to model membrane partitioning.

Inhibition of cytochromes P450 by time-dependent inhibitors (TDI) is a major cause of clinical drug-drug interactions. It is often difficult to predict in vivo drug interactions based on in vitro TDI data. In part 1 of these manuscripts, we describe a numerical method that can directly estimate TDI parameters for a number of kinetic schemes. Datasets were simulated for Michaelis-Menten (MM) and several atypical kinetic schemes. Ordinary differential equations were solved directly to parameterize kinetic constants. For MM kinetics, much better estimates of K_I can be obtained with the numerical method, and even IC₅₀ shift data can provide meaningful estimates of TDI kinetic parameters. The standard replot method can be modified to fit non-MM data, but normal experimental error precludes this approach. Non-MM kinetic schemes can be easily incorporated into the numerical method, and the numerical method consistently predicts the correct model at errors of 10% or less. Quasi-irreversible inactivation and partial inactivation can be modeled easily with the numerical method. The utility of the numerical method for the analyses of experimental TDI data is provided in our companion manuscript in this issue of Drug Metabolism and Disposition (Korzekwa et al., 2014b).