Accounting for inter-correlation between enzyme abundance: a simulation study to assess implications on global sensitivity analysis within physiologically-based pharmacokinetics

A two-stages global sensitivity analysis by using the δ sensitivity index in presence of correlated inputs: application on a tumor growth inhibition model based on the dynamic energy budget theory

Global sensitivity analysis (GSA) evaluates the impact of variability and/or uncertainty of the model parameters on given model outputs. GSA is useful for assessing the quality of Pharmacometric model inference. Indeed, model parameters can be affected by high (estimation) uncertainty due to the sparsity of data. Independence between model parameters is a common assumption of GSA methods. However, ignoring (known) correlations between parameters may alter model predictions and, then, GSA results. To address this issue, a novel two-stages GSA technique based on the δ index, which is well-defined also in presence of correlated parameters, is here proposed. In the first step, statistical dependencies are neglected to identify parameters exerting causal effects. Correlations are introduced in the second step to consider the real distribution of the model output and investigate also the 'indirect' effects due to the correlation structure. The proposed two-stages GSA strategy was applied, as case study, to a preclinical tumor-in-host-growth inhibition model based on the Dynamic Energy Budget theory. The aim is to evaluate the impact of the model parameter estimate uncertainty (including correlations) on key model-derived metrics: the drug threshold concentration for tumor eradication, the tumor volume doubling time and a new index evaluating the drug efficacy-toxicity trade-off. This approach allowed to rank parameters according to their impact on the output, discerning whether a parameter mainly exerts a causal or 'indirect' effect. Thus, it was possible to identify uncertainties that should be necessarily reduced to obtain robust predictions for the outputs of interest.

mvLognCorrEst: an R package for sampling from multivariate lognormal distributions and estimating correlations from uncomplete correlation matrix

BACKGROUND AND OBJECTIVE

Pharmacometrics (PMX) is a quantitative discipline which supports decision-making processes in all stages of drug development. PMX leverages Modeling and Simulations (M&S), which represents a powerful tool to characterize and predict the behavior and the effect of a drug. M&S-based methods, such as Sensitivity Analysis (SA) and Global Sensitivity Analysis (GSA), are gaining interest in PMX as they allow the evaluation of model-informed inference quality. Simulations should be correctly designed to obtain reliable results. Neglecting correlations between model parameters can significantly alter the results of simulations. However, the introduction of a correlation structure between model parameters can cause some issues. Sampling from a multivariate lognormal distribution, which is the typically distribution assumed for PMX model parameters, is not straightforward when a correlation structure is introduced. Indeed, correlations need to respect some constraints which depend by the CVs (i.e., coefficients of variation) of lognormal variables. In addition, when correlation matrices have some unspecified values, they should be properly fixed preserving the positive semi-definiteness of the correlation structure. In this paper, we present mvLognCorrEst, an R package developed to address these issues.

METHODS

The proposed sampling strategy was based on reconducting the extraction from the multivariate lognormal distribution of interest to the underlying Normal distribution. However, with high lognormal CVs, a positive semi-definite Normal covariance matrix cannot be obtained due to the violation of some theoretical constraints. In these cases, the Normal covariance matrix was approximated to its nearest positive definite matrix using Frobenius norm as matrix distance. For the estimation of unknown correlations terms, the graph theory was used to represent the correlation structure as weighed undirected graph. Plausible value ranges for the unspecified correlations were derived considering the paths between variables. Then, their estimation was performed by solving a constrained optimization problem.

RESULTS

Package functions are presented and applied on a real case study, that is the GSA of a PMX model that has been recently developed to support preclinical oncological studies.

CONCLUSIONS

mvLognCorrEst package is an R tool to support simulation-based analysis for which sampling from multivariate lognormal distributions with correlated variables and/or estimation of partially defined correlation matrix are required.

Physiologically-Based Pharmacokinetic Modeling to Support Determination of Bioequivalence for Dermatological Drug Products: Scientific and Regulatory Considerations

Physiologically-based pharmacokinetic (PBPK) modeling and simulation provides mechanism-based predictions of the pharmacokinetics of an active ingredient following its administration in humans. Dermal PBPK models describe the skin permeation and disposition of the active ingredient following the application of a dermatological product on the skin of virtual healthy and diseased human subjects. These models take into account information on product quality attributes, physicochemical properties of the active ingredient and skin (patho)physiology, and their interplay with each other. Regulatory and product development decision makers can leverage these quantitative tools to identify factors impacting local and systemic exposure. In the realm of generic drug products, the number of US Food and Drug Administratioin (FDA) interactions that use dermal PBPK modeling to support alternative bioequivalence (BE) approaches is increasing. In this report, we share scientific considerations on the development, verification and validation (V&V), and application of PBPK models within the context of a virtual BE assessment for dermatological drug products. We discuss the challenges associated with model V&V for these drug products stemming from the fact that target-site active ingredient concentrations are typically not measurable. Additionally, there are no established relationships between local and systemic PK profiles, when the latter are quantifiable. To that end, we detail a multilevel model V&V approach involving validation for the model of the drug product of interest coupled with the overall assessment of the modeling platform in use while leveraging in vitro and in vivo data related to local and systemic bioavailability.

In Silico Modeling and Simulation to Guide Bioequivalence Testing for Oral Drugs in a Virtual Population

Model-informed drug discovery and development (MID3) shows great advantages in facilitating drug development. A physiologically based pharmacokinetic model is one of the powerful computational approaches of MID3, and the emerging field of virtual bioequivalence is well recognized to be the future of the physiologically based pharmacokinetic model. Based on the translational link between in vitro, in silico, and in vivo, virtual bioequivalence study can evaluate the similarity and potential difference of pharmacokinetic and clinical performance between test and reference formulations. With the aid of virtual bioequivalence study, the pivotal information of clinical trials can be provided to streamline the development for both new and generic drugs. However, a regulatory framework of virtual bioequivalence study has not reached its full maturity. Therefore, this article aims to present an overview of the current status of bioequivalence study, identify the framework of virtual bioequivalence studies for oral drugs, and also discuss the future opportunities of virtual bioequivalence in supporting the waiver and optimization of in vivo clinical trials.

A latent variable approach to account for correlated inputs in global sensitivity analysis

In drug development decision-making is often supported through model-based methods, such as physiologically-based pharmacokinetics (PBPK). Global sensitivity analysis (GSA) is gaining use for quality assessment of model-informed inference. However, the inclusion and interpretation of correlated factors in GSA has proven an issue. Here we developed and evaluated a latent variable approach for dealing with correlated factors in GSA. An approach was developed that describes the correlation between two model inputs through the causal relationship of three independent factors: the latent variable and the unique variances of the two correlated parameters. The latent variable approach was applied to a set of algebraic models and a case from PBPK. Then, this method was compared to Sobol’s GSA assuming no correlations, Sobol’s GSA with groups and the Kucherenko approach. For the latent variable approach, GSA was performed with Sobol’s method. By using the latent variable approach, it is possible to devise a unique and easy interpretation of the sensitivity indices while maintaining the correlation between the factors. Compared methods either consider the parameters independent, group the dependent variables into one unique factor or present difficulties in the interpretation of the sensitivity indices. In situations where GSA is called upon to support model-informed decision-making, the latent variable approach offers a practical method, in terms of ease of implementation and interpretability, for applying GSA to models with correlated inputs that does not violate the independence assumption. Prerequisites and limitations of the approach are discussed.

Role of Glucuronidation Pathway in Quetiapine Metabolism: An In vivo Drug-Drug Interaction Study between Quetiapine and Probenecid

Background:

Uridine 5'-diphospho-glucuronosyltransferase (UGT) enzymes play a significant role in the metabolism of quetiapine, and coadministration with a UGT inhibitor/inducer drug may change its pharmacokinetic profile.

Objective:

The objective of this study was to assess the impact of probenecid, a UGT enzyme inhibitor, on the pharmacokinetic profile of quetiapine.

Materials and Methods:

Twelve treatment-naïve, 7-week-old male Sprague–Dawley rats (weighting 161 ± 22 g) were randomly and equally divided into control, quetiapine-alone and quetiapine plus probenecid groups. The quetiapine plus probenecid group received a single oral dose of probenecid (50 mg/kg) followed by 50 mg/kg of quetiapine; the quetiapine-alone group only received 50 mg/kg of quetiapine. Blood samples (0.2 ml) were collected from all rats after 0, 0.25, 0.5, 1, 2, 4, 6, 8, 10, 12 and 24 h of the drug administration in heparinized tubes. The pre-established liquid chromatography–mass spectrometry method was utilized to ascertain the plasma concentration of quetiapine and the control group was used to prepare the controlled standard.

Results:

Significant pharmacokinetic differences were observed between the quetiapine-alone and quetiapine plus probenecid groups in terms of C_max (392 ± 209 vs. 1323 ± 343 ug/L, respectively, P = 0.004), AUC_0-∞ (P = 0.04) and T_max (P = 0.004). Further, in the combined drug group, there was a decrease in drug clearance (CL/F) (from 27 ± 11 to 16 ± 3 L/h/kg; P = 0.005) and an increase in the volume of distribution (Vd) (P = 0.01), but there was no significant difference between both groups in terms of half-lives (P = 0.27). No significant within-group variability of pharmacokinetic parameters was observed (P = 0.25).

Conclusion:

The results of this animal study suggest that glucuronidation by UGT enzyme system may also play an important role in quetiapine metabolism, which, if proven in future human studies, would imply that the bioavailability and pharmacokinetic parameters of quetiapine may require alterations when co-administered with probenecid to avoid development of quetiapine toxicity.

Inter-compound and Intra-compound Global Sensitivity Analysis of a Physiological Model for Pulmonary Absorption of Inhaled Compounds

In recent years, global sensitivity analysis (GSA) has gained interest in physiologically based pharmacokinetics (PBPK) modelling and simulation from pharmaceutical industry, regulatory authorities, and academia. With the case study of an in-house PBPK model for inhaled compounds in rats, the aim of this work is to show how GSA can contribute in PBPK model development and daily use. We identified two types of GSA that differ in the aims and, thus, in the parameter variability: inter-compound and intra-compound GSA. The inter-compound GSA aims to understand which are the parameters that mostly influence the variability of the metrics of interest in the whole space of the drugs' properties, and thus, it is useful during the model development. On the other hand, the intra-compound GSA aims to highlight how much the uncertainty associated with the parameters of a given drug impacts the uncertainty in the model prediction and so, it is useful during routine PBPK use. In this work, inter-compound GSA highlighted that dissolution- and formulation-related parameters were mostly important for the prediction of the fraction absorbed, while the permeability is the most important parameter for lung AUC and MRT. Intra-compound GSA highlighted that, for all the considered compounds, the permeability was one of the most important parameters for lung AUC, MRT and plasma MRT, while the extraction ratio and the dose for the plasma AUC. GSA is a crucial instrument for the quality assessment of model-based inference; for this reason, we suggest its use during both PBPK model development and use.

A Novel Physiologically Based Model of Creatinine Renal Disposition to Integrate Current Knowledge of Systems Parameters and Clinical Observations

Creatinine is the most common clinical biomarker of renal function. As a substrate for renal transporters, its secretion is susceptible to inhibition by drugs, resulting in transient increase in serum creatinine and false impression of damage to kidney. Novel physiologically based models for creatinine were developed here and (dis)qualified in a stepwise manner until consistency with clinical data. Data from a matrix of studies were integrated, including systems data (common to all models), proteomics-informed in vitro-in vivo extrapolation of all relevant transporter clearances, exogenous administration of creatinine (to estimate endogenous synthesis rate), and inhibition of different renal transporters (11 perpetrator drugs considered for qualification during creatinine model development and verification on independent data sets). The proteomics-informed bottom-up approach resulted in the underprediction of creatinine renal secretion. Subsequently, creatinine-trimethoprim clinical data were used to inform key model parameters in a reverse translation manner, highlighting best practices and challenges for middle-out optimization of mechanistic models.

A novel mass spectrometry method for the absolute quantification of several cytochrome P450 and uridine 5'-diphospho-glucuronosyltransferase enzymes in the human liver

Cytochrome P450 (CYP450) and 5'-diphosphate glucuronosyltransferases (UGT) are the two major families of drug-metabolizing enzymes in the human liver microsome (HLM). As a result of their frequent abundance fluctuation among populations, the accurate quantification of these enzymes in different individuals is important for designing patient-specific dosage regimens in the framework of precision medicine. The preparation and quantification of internal standards is an essential step for the quantitative analysis of enzymes. However, the commonly employed stable isotope labeling-based strategy (QconCAT) suffers from requiring very expensive isotopic reagents, tedious experimental procedures, and long labeling times. Furthermore, arginine-to-proline conversion during metabolic isotopic labeling compromises the quantification accuracy. Therefore, we present a new strategy that replaces stable isotope-labeled amino acids with lanthanide labeling for the preparation and quantification of QconCAT internal standard peptides, which leads to a threefold reduction in the reagent costs and a fivefold reduction in the time consumed. The absolute amount of trypsin-digested QconCAT peptides can be obtained by lanthanide labeling and inductively coupled plasma-optical emission spectrometry (ICP-OES) analysis with a high quantification accuracy (%RE < 20%). By taking advantage of the highly selective and facile ICP-OES procedure and multiplexed large-scale absolute target protein quantification using biological mass spectrometry, this strategy was successfully used for the absolute quantification of drug-metabolizing enzymes. We obtained good linearity (correlation coefficient > 0.95) over concentrations spanning 2.5 orders of magnitude with improved sensitivity (limit of quantification = 2 fmol) in nine HLM samples, indicating the potential of this method for large-scale absolute target protein quantification in clinical samples. Graphical abstract.

Global Sensitivity Analysis of the Rodgers and Rowland Model for Prediction of Tissue: Plasma Partitioning Coefficients: Assessment of the Key Physiological and Physicochemical Factors That Determine Small-Molecule Tissue Distribution

In physiologically based pharmacokinetic (PBPK) modelling, the large number of input parameters, limited amount of available data and the structural model complexity generally hinder simultaneous estimation of uncertain and/or unknown parameters. These parameters are generally subject to estimation. However, the approaches taken for parameter estimation vary widely. Global sensitivity analyses are proposed as a method to systematically determine the most influential parameters that can be subject to estimation. Herein, a global sensitivity analysis was conducted to identify the key drug and physiological parameters influencing drug disposition in PBPK models and to potentially reduce the PBPK model dimensionality. The impact of these parameters was evaluated on the tissue-to-unbound plasma partition coefficients (Kpus) predicted by the Rodgers and Rowland model using Latin hypercube sampling combined to partial rank correlation coefficients (PRCC). For most drug classes, PRCC showed that LogP and fraction unbound in plasma (fu_p) were generally the most influential parameters for Kpu predictions. For strong bases, blood:plasma partitioning was one of the most influential parameter. Uncertainty in tissue composition parameters had a large impact on Kpu and Vss predictions for all classes. Among tissue composition parameters, changes in Kpu outputs were especially attributed to changes in tissue acidic phospholipid concentrations and extracellular protein tissue:plasma ratio values. In conclusion, this work demonstrates that for parameter estimation involving PBPK models and dimensionality reduction purposes, less influential parameters might be assigned fixed values depending on the parameter space, while influential parameters could be subject to parameters estimation.

Quantitative Proteomics of Clinically Relevant Drug-Metabolizing Enzymes and Drug Transporters and Their Intercorrelations in the Human Small Intestine

The levels of drug-metabolizing enzymes (DMEs) and transporter proteins in the human intestine are pertinent to determine oral drug bioavailability. Despite the paucity of reports on such measurements, it is well recognized that these values are essential for translating in vitro data on drug metabolism and transport to predict drug disposition in gut wall. In the current study, clinically relevant DMEs [cytochrome P450 (P450) and uridine 5′-diphospho-glucuronosyltransferase (UGT)] and drug transporters were quantified in total mucosal protein preparations from the human jejunum (n = 4) and ileum (n = 12) using quantification concatemer–based targeted proteomics. In contrast to previous reports, UGT2B15 and organic anion-transporting polypeptide 1 (OATP1A2) were quantifiable in all our samples. Overall, no significant disparities in protein expression were observed between jejunum and ileum. Relative mRNA expression for drug transporters did not correlate with the abundance of their cognate protein, except for P-glycoprotein 1 (P-gp) and organic solute transporter subunit alpha (OST-α), highlighting the limitations of RNA as a surrogate for protein expression in dynamic tissues with high turnover. Intercorrelations were found within P450 [2C9-2C19 (P = 0.002, R² = 0.63), 2C9–2J2 (P = 0.004, R² = 0.40), 2D6-2J2 (P = 0.002, R² = 0.50)] and UGT [1A1-2B7 (P = 0.02, R² = 0.87)] family of enzymes. There were also correlations between P-gp and several other proteins [OST-α (P < 0.0001, R² = 0.77), UGT1A6 (P = 0.009, R² = 0.38), and CYP3A4 (P = 0.007, R² = 0.30)]. Incorporating such correlations into building virtual populations is crucial for obtaining plausible characteristics of simulated individuals.