Theoretical Considerations for Direct Translation of Unbound Liver-to-Plasma Partition Coefficient from In Vitro to In Vivo

Utility of Minimal Physiologically Based Pharmacokinetic Models for Assessing Fractional Distribution, Oral Absorption, and Series-Compartment Models of Hepatic Clearance

Minimal physiologically based pharmacokinetic (mPBPK) models are physiologically relevant, require less information than full PBPK models, and offer flexibility in pharmacokinetics (PK). The well-stirred hepatic model (WSM) is commonly used in PBPK, whereas the more plausible dispersion model (DM) poses computational complexities. The series-compartment model (SCM) mimics the DM but is easier to operate. This work implements the SCM and mPBPK models for assessing fractional tissue distribution, oral absorption, and hepatic clearance using literature-reported blood and liver concentration-time data in rats for compounds mainly cleared by the liver. Further handled were various complexities, including nonlinear hepatic binding and metabolism, differing absorption kinetics, and sites of administration. The SCM containing one to five (n) liver subcompartments yields similar fittings and provides comparable estimates for hepatic extraction ratio (ER), prehepatic availability (Fg ), and first-order absorption rate constants (ka ). However, they produce decreased intrinsic clearances (CLint ) and liver-to-plasma partition coefficients (Kph ) with increasing n as expected. Model simulations demonstrated changes in intravenous and oral PK profiles with alterations in Kph and ka and with hepatic metabolic zonation. The permeability (PAMPA P) of the various compounds well explained the fitted fractional distribution (fd ) parameters. The SCM and mPBPK models offer advantages in distinguishing systemic, extrahepatic, and hepatic clearances. The SCM allows for incorporation of liver zonation and is useful in assessing changes in internal concentration gradients potentially masked by similar blood PK profiles. Improved assessment of intraorgan drug concentrations may offer insights into active moieties driving metabolism, biliary excretion, pharmacodynamics, and hepatic toxicity. SIGNIFICANCE STATEMENT: The minimal physiologically based pharmacokinetic model and the series-compartment model are useful in assessing oral absorption and hepatic clearance. They add flexibility in accounting for various drug- or system-specific complexities, including fractional distribution, nonlinear binding and saturable hepatic metabolism, and hepatic zonation. These models can offer improved insights into the intraorgan concentrations that reflect physiologically active moieties often driving disposition, pharmacodynamics, and toxicity.

Investigating the relevance of CYP2J2 inhibition for drugs known to cause intermediate to high risk torsades de pointes

Cardiac cytochrome P450 2J2 (CYP2J2) metabolizes endogenous polyunsaturated fatty acid, arachidonic acid (AA), to bioactive regioisomeric epoxyeicosatrienoic acid (EET) metabolites. This endogenous metabolic pathway has been postulated to play a homeostatic role in cardiac electrophysiology. However, it is unknown if drugs that cause intermediate to high risk torsades de pointes (TdP) exhibit inhibitory effects against CYP2J2 metabolism of AA to EETs. In this study, we demonstrated that 11 out of 16 drugs screened with intermediate to high risk of TdP as defined by the Comprehensive in vitro Proarrhythmia Assay (CiPA) initiative are concurrently reversible inhibitors of CYP2J2 metabolism of AA, with unbound inhibitory constant (K_i,AA,u) values ranging widely from 0.132 to 19.9 µM. To understand the physiological relevancy of K_i,AA,u, the in vivo unbound drug concentration within human heart tissue (C_u,heart) was calculated via experimental determination of in vitro unbound partition coefficient (K_puu) for 10 CYP2J2 inhibitors using AC16 human ventricular cardiomyocytes as well as literature-derived values of fraction unbound in plasma (f_u,p) and plasma drug concentrations in clinical scenarios leading to TdP. Notably, all CYP2J2 inhibitors screened belonging to the high TdP risk category, namely vandetanib and bepridil, exhibited highest K_puu values of 18.2 ± 1.39 and 7.48 ± 1.16 respectively although no clear relationship between C_u,heart and risk of TdP could eventually be determined. R values based on basic models of reversible inhibition as per FDA guidelines were calculated using unbound plasma drug concentrations (C_u,plasma) and adapted using C_u,heart which suggested that 4 out of 10 CYP2J2 inhibitors with intermediate to high risk of TdP demonstrate greatest potential for clinically relevant in vivo cardiac drug-AA interactions. Our results shed novel insights on the relevance of CYP2J2 inhibition in drugs with risk of TdP. Further studies ascertaining the role of CYP2J2 metabolism of AA in cardiac electrophysiology, characterizing inherent cardiac ion channel activities of drugs with risk of TdP as well as in vivo evidence of drug-AA interactions will be required prior to determining if CYP2J2 inhibition could be an alternative mechanism contributing to drug-induced TdP.

Exploring the Pharmacokinetic Mysteries of the Liver: Application of Series Compartment Models of Hepatic Elimination

Among the basic hepatic clearance models, the dispersion model (DM) is the most physiologically sound compared with the well-stirred model and the parallel tube model. However, its application in physiologically-based pharmacokinetic (PBPK) modeling has been limited due to computational complexities. The series compartment models (SCM) of hepatic elimination that treats the liver as a cascade of well-stirred compartments connected by hepatic blood flow exhibits some mathematical similarities to the DM but is easier to operate. This work assesses the quantitative correlation between the SCM and DM and demonstrates the operation of the SCM in PBPK with the published single-dose blood and liver concentration-time data of six flow-limited compounds. The predicted liver concentrations and the estimated intrinsic clearance (CLint ) and PBPK-operative tissue-to-plasma partition coefficient (Kp ) values were shown to depend on the number of liver sub-compartments (n) and hepatic enzyme zonation in the SCM. The CLint and Kp decreased with increasing n, with more remarkable differences for drugs with higher hepatic extraction ratios. Given the same total CLint , the SCM yields a higher Kp when the liver perivenous region exhibits a lower CLint as compared with a high CLint at this region. Overall, the SCM nicely approximates the DM in characterizing hepatic elimination and offers an alternative flexible approach as well as providing some insights regarding sequential drug concentrations in the liver. SIGNIFICANCE STATEMENT: The SCM nicely approximates the DM when applied in PBPK for characterizing hepatic elimination. The number of liver sub-compartments and hepatic enzyme zonation are influencing factors for the SCM resulting in model-dependent predictions of total/internal liver concentrations and estimates of CLint and the PBPK-operative Kp . Such model-dependency may have an impact when the SCM is used for in vitro-to-in vivo extrapolation (IVIVE) and may also be relevant for PK/PD/toxicological effects when it is the driving force for such responses.

Evolving approaches on measurements and applications of intracellular free drug concentration and Kpuu in drug discovery

Introduction: Intracellular-free drug concentration (C_u,cell) and unbound partition coefficient (Kp_uu) are two important parameters to develop pharmacokinetic and pharmacodynamic relationships, predict drug-drug interaction potentials and estimate therapeutic indices.Area covered: Methods on measurements of C_u,cell, Kp_uu, partition coefficient (Kp) and fraction unbound of cells (f_uc) are discussed. Advantages and limitations of several f_uc methods are reviewed. Applications highlighted here are bridging the potency gaps between biochemical and cell-based assays, in vitro hepatocyte assay to predict in vivo liver-to-plasma Kp_uu, the role of Kp_uu in prediction of hepatic clearance for enzyme- and transporter-mediated mechanisms using extended clearance equation, and structural attributes governing tissue Kp_uu.Expert opinion: C_u,cell and Kp_uu are of growing applications in drug discovery. Methods for measurements of these properties continue to evolve in order to achieve higher precision/accuracy and obtain more detailed information at the subcellular levels. Future directions of the field include the development of in vitro and in silico models to predict tissue Kp_uu, direct measurement of free drug concentration in subcellular organelles, and further investigations into the critical elements governing cell and tissue Kp_uu. Significant innovation is needed to advance this complex, but highly impactful and exciting area of science.

Consideration of the Unbound Drug Concentration in Enzyme Kinetics

The study of enzyme kinetics in drug metabolism involves assessment of rates of metabolism and inhibitory potencies over a suitable concentration range. In all but the very simplest in vitro system, these drug concentrations can be influenced by a variety of nonspecific binding reservoirs that can reduce the available concentration to the enzyme system(s) under investigation. As a consequence, the apparent kinetic parameters, such as K_m or K_i, that are derived can deviate from the true values. There are a number of sources of these nonspecific binding depots or barriers, including membrane permeation and partitioning, plasma or serum protein binding, and incubational binding. In the latter case, this includes binding to the assay apparatus as well as biological depots, depending on the characteristics of the in vitro matrix being used. Given the wide array of subcellular, cellular, and recombinant enzyme systems utilized in drug metabolism, each of these has different components which can influence the free drug concentration. The physicochemical properties of the test compound are also paramount in determining the influential factors in any deviation between true and apparent kinetic behavior. This chapter describes the underlying mechanisms determining the free drug concentration in vitro and how these factors can be accounted for in drug metabolism studies, illustrated with case studies from the literature.

Challenging the Relevance of Unbound Tissue-to-Blood Partition Coefficient (Kpuu) on Prediction of Drug-Drug Interactions

PURPOSE

To examine the theoretical/practical utility of the liver-to-blood partition coefficient (Kp_uu) for predicting drug-drug interactions (DDIs), and compare the Kp_uu-approach to the extended clearance concept AUC_R-approach.

METHODS

The Kp_uu relationship was derived from first principles. Theoretical simulations investigated the impact of changes in a single hepatic-disposition process on unbound systemic (AUC_B,u) and hepatic exposure (AUC_H,u) versus Kp_uu. Practical aspects regarding Kp_uu utilization were examined by predicting the magnitude of DDI between ketoconazole and midazolam employing published ketoconazole Kp_uu values.

RESULTS

The Kp_uu hepatic-disposition relationship is based on the well-stirred model. Simulations emphasize that changes in influx/efflux intrinsic clearances result in Kp_uu changes, however AUC_H,u remains unchanged. Although incorporation of Kp_uu is believed to improve DDI-predictions, utilizing published ketoconazole Kp_uu values resulted in prediction errors for a midazolam DDI.

CONCLUSIONS

There is limited benefit in using Kp_uu for DDI-predictions as the AUC_R-based approach can reasonably predict DDIs without measurement of intracellular drug concentrations, a difficult task hindered by experimental variability. Further, Kp_uu changes can mislead as they may not correlate with changes in AUC_B,u or AUC_H,u. The well-stirred model basis of Kp_uu when applied to hepatic-disposition implies that nuances of intracellular drug distribution are not considered by the Kp_uu model.

How Transporters Have Changed Basic Pharmacokinetic Understanding

The emergence and continued evolution of the transporter field has caused re-evaluation and refinement of the original principles surrounding drug disposition. In this paper, we emphasize the impact that transporters can have on volume of distribution and how this can affect the other major pharmacokinetic parameters. When metabolic drug-drug interactions or pharmacogenomic variance changes the metabolism of a drug, the volume of distribution appears to be unchanged while clearance, bioavailability, and half-life are changed. When transporters are involved in the drug-drug interactions or pharmacogenomic variance, the volume of distribution can be markedly affected causing counterintuitive changes in half-life. Cases are examined where a volume of distribution change is significant enough that although clearance decreases, half-life decreases. Thus, drug dosing decisions must be made based on CL/F changes, not half-life changes, as such volume of distribution alterations will also influence the half-life results.

Drug Concentration Asymmetry in Tissues and Plasma for Small Molecule-Related Therapeutic Modalities

The well accepted "free drug hypothesis" for small-molecule drugs assumes that only the free (unbound) drug concentration at the therapeutic target can elicit a pharmacologic effect. Unbound (free) drug concentrations in plasma are readily measurable and are often used as surrogates for the drug concentrations at the site of pharmacologic action in pharmacokinetic-pharmacodynamic analysis and clinical dose projection in drug discovery. Furthermore, for permeable compounds at pharmacokinetic steady state, the free drug concentration in tissue is likely a close approximation of that in plasma; however, several factors can create and maintain disequilibrium between the free drug concentration in plasma and tissue, leading to free drug concentration asymmetry. These factors include drug uptake and extrusion mechanisms involving the uptake and efflux drug transporters, intracellular biotransformation of prodrugs, membrane receptor-mediated uptake of antibody-drug conjugates, pH gradients, unique distribution properties (covalent binders, nanoparticles), and local drug delivery (e.g., inhalation). The impact of these factors on the free drug concentrations in tissues can be represented by K _p,uu, the ratio of free drug concentration between tissue and plasma at steady state. This review focuses on situations in which free drug concentrations in tissues may differ from those in plasma (e.g., K _p,uu > or <1) and discusses the limitations of the surrogate approach of using plasma-free drug concentration to predict free drug concentrations in tissue. This is an important consideration for novel therapeutic modalities since systemic exposure as a driver of pharmacologic effects may provide limited value in guiding compound optimization, selection, and advancement. Ultimately, a deeper understanding of the relationship between free drug concentrations in plasma and tissues is needed.