Physiologically-Based Pharmacokinetic (PBPK) Modeling and Simulations E-Book

Sheila Annie Peters

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 591

Veröffentlichungsjahr: 2012

Beschreibung

The only book dedicated to physiologically-based pharmacokinetic modeling in pharmaceutical science

Physiologically-based pharmacokinetic (PBPK) modeling has become increasingly widespread within the pharmaceutical industry over the last decade, but without one dedicated book that provides the information researchers need to learn these new techniques, its applications are severely limited. Describing the principles, methods, and applications of PBPK modeling as used in pharmaceutics, Physiologically-Based Pharmacokinetic (PBPK) Modeling and Simulations fills this void.

Connecting theory with practice, the book explores the incredible potential of PBPK modeling for improving drug discovery and development. Comprised of two parts, the book first provides a detailed and systematic treatment of the principles behind physiological modeling of pharmacokinetic processes, inter-individual variability, and drug interactions for small molecule drugs and biologics. The second part looks in greater detail at the powerful applications of PBPK to drug research.

Designed for a wide audience encompassing readers looking for a brief overview of the field as well as those who need more detail, the book includes a range of important learning aids. Featuring end-of-chapter keywords for easy reference—a valuable asset for general or novice readers without a PBPK background—along with an extensive bibliography for those looking for further information, Physiologically- Based Pharmacokinetic (PBPK) Modeling and Simulations is the essential single-volume text on one of the hottest topics in the pharmaceutical sciences today.

Leseprobe

CONTENTS

Preface

Acknowledgments

Section I. Principles and Methods

Chapter 1: Modeling in the Pharmaceutical Industry

1.1 Introduction

1.2 Modeling Approaches

1.3 Steps Needed to Maximize Effective Integration of Models Into R&D Workflow

1.4 Scope of The Book

Keywords

References

Chapter 2: Physiologically-Based Modeling

2.1 Introduction

2.2 Examples of Physiological Modeling

2.3 Need For Physiological Models in The Pharmaceutical Industry

2.4 Organs As Compartments

2.5 Bottom-Up vs. Top-Down Modeling in Pharmacokinetics

References

Chapter 3: Review of Pharmacokinetic Principles

3.1 Introduction

3.2 Routes of Administration

3.3 Drug Disposition

3.4 Linear and Nonlinear Pharmacokinetics

3.5 Steady-State Pharmacokinetics

3.6 Dose Estimations

3.7 Successful PK Optimization in Drug Discovery

Keywords

References

Chapter 4: Physiological Model for Absorption

4.1 Introduction

4.2 Drug Absorption and Gut Bioavailability

4.3 Factors Affecting Drug Absorption and Gut Bioavailability

4.4 In Silico Predictions of Passive Permeability and Solubility

4.5 Measurement of Permeability, Solubility, Luminal Stability, Efflux, and Intestinal Metabolism

4.6 Absorption Modeling

Keywords

References

Chapter 5: PHYSIOLOGICAL MODEL FOR DISTRIBUTION

5.1 Introduction

5.2 Factors Affecting Tissue Distribution of Xenobiotics

5.3 In Silico Models of Tissue Partition Coefficients

5.4 Measurement of Parameters Representing Rate and Extent of Tissue Distribution

5.5 Physiological Model For Drug Distribution

5.6 Drug Concentrations At Site of Action

Keywords

References

Chapter 6: Physiological Models for Drug Metabolism and Excretion

6.1 Introduction

6.2 Factors Affecting Drug Metabolism and Excretion of Xenobiotics

6.3 Models For Hepatobiliary Elimination and Renal Excretion

6.4 Physiological Models

References

Chapter 7: Generic Whole-Body Physiologically-Based Pharmacokinetic Modeling

7.1 Introduction

7.2 Structure of A Generic Whole Body PBPK Model

7.3 Model Assumptions

7.4 Commercial PBPK Software

References

Chapter 8: Variability, Uncertainty, and Sensitivity Analysis

8.1 Introduction

8.2 Need For Uncertainty Analysis

8.3 Sources of Physiological, Anatomical, Enzymatic, and Transporter Variability

8.4 Modeling Uncertainty and Population Variability With Monte Carlo Simulations

8.5 Sensitivity Analysis

8.6 Conclusions

Keywords

References

Chapter 9: Evaluation of Drug–Drug Interaction Risk with PBPK Models

9.1 Introduction

9.2 Factors Affecting Drug–Drug Interactions

9.3 In Vitro Methods To Evaluate Drug–Drug Interactions

9.4 Static Models To Evaluate Drug–Drug Interactions

9.5 Pbpk Models To Evaluate Drug–Drug Interactions

9.6 Comparison of PBPK Models and Static Models For The Evaluation of Drug–Drug Interactions

Keywords

References

Chapter 10: Physiologically-Based Pharmacokinetics of Biotherapeutics

10.1 Introduction

10.2 Therapeutic Proteins

10.3 Pharmacokinetics of Therapeutic Proteins

10.4 PBPK/PD Modeling For Therapeutic Proteins

10.5 Antisense Oligonucleotides and RNA Interferance

Keywords

References

Section II. Applications in the Pharmaceutical Industry

Chapter 11: Data Integration and Sensitivity Analysis

11.1 Introduction

11.2 Examples of Data Integration With PBPK Modeling

11.3 Examples of Sensitivity Analysis With PBPK Modeling

References

Chapter 12: Hypothesis Generation and Pharmacokinetic Predictions

12.1 Introduction

12.2 PBPK Simulations of Pharmacokinetic Profiles For Hypothesis Generation and Testing

12.3 Pharmacokinetic Predictions

References

Chapter 13: Integration of PBPK and Pharmacodynamics

13.1 Introduction

13.2 Pharmacodynamic Principles

13.3 Pharmacodynamic Modeling

13.4 Pharmacokinetic Modeling: Compartmental PK and PBPK

13.5 Integration of PK or PBPK With PD Modeling

13.6 Reasons For Poor PK/PD Correlation

13.7 Applications of PK or PBPK/PD Modeling in Drug Discovery and Development

13.8 Regulatory Perspective

13.9 Conclusions

Keywords

References

Chapter 14: Physiologically-Based Pharmacokinetic Modeling of Populations

14.1 Introduction

14.2 Population Modeling With PBPK

14.3 Healthy to Target Patient Population: Impact of Disease On Pharmacokinetics

14.4 Modeling Subpopulations: Impact of Age, Gender, Co-Morbidities, and Genetics on Pharmacokinetics

14.5 Personalized Medicine With PBPK/PD

Keyword

References

Chapter 15: PBPK Models along the Drug Discovery and Development Value Chain

15.1 Summary of Applications of PBPK Models Along Value Chain

15.2 Obstacles and Future Directions For PBPK Modeling

Keyword

References

Appendices

Index

Copyright © 2012 by John Wiley & Sons. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey

Published simultaneously in Canada

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Library of Congress Cataloging-in-Publication Data:

Peters, Sheila Annie.

Physiologically-based pharmacokinetic (PBPK) modeling and simulations : principles, methods, and applications in the pharmaceutical industry / Sheila Annie Peters.

p. ; cm.

Includes bibliographical references and index.

ISBN 978-0-470-48406-7 (cloth)

1. Pharmacokinetics—Mathematical models. 2. Drugs—Design—Mathematical models. I. Title.

[DNLM: 1. Pharmacokinetics. 2. Drug Design. 3. Models, Biological. QV 38]

RM301.5.P48 2011

615′.7—dc23

2011019939

This book is dedicated to my parents, friends, and Alfred and Christina who have always believed in me.

Preface

Physiologically-based pharmacokinetic (PBPK) modeling has made rapid strides in the pharmaceutical industry in the last decade or so, thanks to an increasing awareness of the potential applications of this powerful tool. As pharmaceutical companies are working to integrate PBPK modeling into their lead selection cycle and clinical development, the availability of commercial software has played a key role in enabling even those without modeling expertise to come on board. However, this entails the risk of misuse, misinterpretation, or overinterpretation of modeling results, if the principles and underlying assumptions of PBPK modeling are not clearly understood by the users. Today, the challenge facing pharmaceutical companies is educating and training their staff to achieve an effective application of PBPK/pharmacodynamics (PD) in projects across the value chain. In the future, providers of education should take on the responsibility of making available, modelers with appropriate skills. Given the complexity of PBPK modeling, it is certainly not an easy task for a beginner with little or no background to understand the model structure and to be aware of its limitations. The lack of a textbook on PBPK has been a further deterrent. It is hoped that this book will serve as a primary source of information on the principles, methods, and applications of PBPK modeling, exposing the power of a largely hidden and unexplored tool. Applications in the pharma sector will be the main focus, as applications in environmental toxicology and human health risk assessment have already been the subject of a previous publication.

Target audiences for the book include students and researchers in academia, apart from scientists and modelers in the pharmaceutical industry. The book can also be a resource for R&D managers in the pharmaceutical industry, seeking a quick overview of the benefits of applying PBPK modeling along the drug discovery and development value chain. An understanding of the principles of PBPK modeling by R&D management would enhance their acceptance and appreciation, which in turn can translate to effective managerial support for PBPK modeling. This book is intended to serve the interests of both the general reader, who may only want an overview of the applications of PBPK modeling without wanting an in-depth understanding of the underlying methods, and the specialist reader, who may be interested to build new models. For the general reader, keywords appear in boldface and are explained at the end of the chapters. No particular expertise is assumed in order to keep the book accessible to a diverse audience. An extensive list of bibliographic references will help the specialist reader to build on the concepts developed in the book. A generous use of figures to illustrate concepts will help the reader gain valuable insights into this fascinating subject.

The book comprises two parts. The first part provides a detailed and systematic treatment of the principles behind physiological modeling of pharmacokinetic processes, interindividual variability, and drug interactions for small-molecule drugs and biologics. The second part exposes the reader to the powerful applications of PBPK modeling along the value chain in drug discovery and development.

Sheila Annie Peters

ACKNOWLEDGMENTS

I would like to thank Bernd Meibohm and several of my colleagues at AstraZeneca—Balaji Agoram, Ulf Bredberg, James Bird, Hugues Dolgos, Ulf Ericsson, Marcus Friden, Rasmus Jansson Löfmark, Martin Hayes, Sarah Kelly, Maria Learoyd, James Tucker, Pete Webborn, and Anna-Lena Ungell, who helped review the chapters. I would like to record my deep appreciation for the meticulous work of Tony Johansson, whose positive attitude and hard work has resulted in the excellent figures in this book. This work would not have been possible without the consistent support extended by my friends and family.

S. A. P.

SECTION I

PRINCIPLES AND METHODS

Chapter 1

MODELING IN THE PHARMACEUTICAL INDUSTRY

CONTENTS

1.1 Introduction1.2 Modeling Approaches1.3 Steps Needed to Maximize Effective Integration of Models into R&D Workflow1.4 Scope of the Book KeywordsReferences

1.1 INTRODUCTION

In an effort to reduce the attrition rates of drugs, pharmaceutical companies are constantly looking to improve and understand compound behavior through the use of novel tools. Modeling is one such tool that has gradually gained recognition in the pharmaceutical industry, over the last couple of decades, as a means of achieving quality, efficiency, and significant cost savings. Modeling and simulation methods have played a crucial role in the pharmaceutical industry in identifying and validating target, predicting the efficacy, absorption, distribution, metabolism, excretion, toxicity (ADMET), and safety of drug candidates, aiding a better understanding of data through effective integration and extraction of knowledge, predicting the human dose, developing new formulations, designing safety and efficacy trials, and guiding regulatory decisions. Most models are used in a build–validate–learn–refine cycle in which all available knowledge that can aid prediction of a property of interest is initially captured during model building. It is then used for predicting observations (validation phase), and any discrepancies of the predicted from observed is then understood on a scientific basis (learning phase) and appropriately incorporated in the model (refine phase). Once a model has been tested to provide satisfactory results, it can be used on a routine basis, reserving animal studies and other resource-intensive experiments for confirmation only. The use of in silico technologies can reduce the cost of drug development by up to 50% according to some analysts.1 The impact of integrating modeling into the research and development (R&D) workflow has been so encouraging that many companies have increased their investments in this sector. The Food and Drug Administration (FDA) “critical path” document2 recommends model-based drug development for improved knowledge management and decision making. The key elements of such a model-based drug development and how they fit together to aid strategy and decision making in drug development is outlined by Lalonde et al.3

1.2 MODELING APPROACHES

From understanding a disease to bringing a safe and effective new treatment to patients, it takes about 10–15 years for a pharmaceutical company to discover a potential drug (drug discovery) and to develop it as a final product (drug development). A schematic of a drug discovery and development pipeline is shown in Figure 1.1. Advances in genomics and proteomics and an increase in computational power have contributed to increasing our knowledge of disease at the level of genes, proteins, and cells. This understanding leads to the identification of proteins, which are involved in a disease of interest. A single protein/gene that has been validated to be relevant in a disease and to be druggable is chosen as the target. Hits to this target are identified through virtual screening and high-throughput screening (HTS) assays. Compounds that can best modulate the target are chosen as hits. Hits are classified into a small set of lead series (lead generation). The most promising series showing potential drug activity, reduced off-target toxicity, and with physicochemical and metabolic profiles that are compatible with acceptable in vivo bioavailability progress into the lead optimiztion stage. The objective at this stage is to select a candidate drug that meets predefined criteria with respect to efficacy, pharmacokinetics, and safety. The candidate drug is then developed to a final drug product, after sufficient testing in animals (preclinical development) and humans (clinical development) to confirm the efficacy and safety of the drug. The modeling methods along the drug discovery and development value chain are indicated in Figure 1.1.

Figure 1.1 Modeling at various stages of drug discovery and development.

Models allow us to understand how complex interactions and processes work. Sometimes, modeling provides a unique way to understanding a system. Figure 1.2 summarizes the reasons for employing models in the pharmaceutical industry. It is important to be aware that all models are only approximations of the system they represent. Underlying assumptions should be carefully weighed to get the best benefits from a model. In addition, different modeling approaches differ in their strengths and limitations. Quantitative structure–activity relationships (QSAR) and quantitative structure property relationships (QSPR) models rely on combining appropriate descriptors for compounds in a training set. Their key strengths are simplicity and ease of use. However, the predictive power of these models is restricted to compounds within the same chemical space as that of the training set. Empirical or data-driven models are built and refined only after the experimental data is collected (cannot be prespecified) and its parameters lack physical/physiological/biochemical interpretation. They are best employed for exploratory data analysis. On the other hand, mechanistic models are prespecified and capture the underlying mechanisms of the system they represent to the extent known, with parameters corresponding to some physical entities of the system. These models can, therefore, be used to predict the next set of data. An example of this is physiologically-based models.

Figure 1.2 Need for modeling.

Pharmacokinetic (PK) modeling provides information about processes that affect the kinetics of a compound in a species, such as absorption, distribution, metabolism, and excretion using the concentration–time profile. Traditionally, this has been done with compartmental PK modeling, a data-driven approach in which the model structure is defined by the data (therefore empirical). The fall in concentration with respect to time is fitted to a series of exponential terms whose decay constants and pre-exponents are related to the rates of absorption, distribution, metabolism, and elimination. The model that best fits the in vivo PK data, according to some defined statistical criterion, is chosen as the final model. Empirical models are case specific and the potential for credible extrapolations using these models is limited. Since the pharmacodynamic response of a drug need not necessarily parallel its pharmacokinetics, PK models are combined with pharmacodynamic (PD) effect–concentration profiles at different doses. This data-driven, exploratory PK/PDmodeling4 has long been used in drug development, for getting a continuous description of the effect–time course resulting directly from the administration of a certain dose. Physiologically-based pharmacokinetic (PBPK) modeling offers a mechanistic approach to predicting the disposition of a drug, which can then be combined with a PD model (PBPK/PD). Although the principles behind a PBPK approach has long been known through the work of Teorell5 in 1937, the mathematical complexity of the model and the lack of physiological data needed for the model meant that the idea remained dormant until the 1960s.6 The tremendous increase in computational power at relatively low cost paved the way for complex PBPK models to be built. PBPK models help simulate the concentration–time profile of a drug in a species by integrating the physicochemical properties of the compound with the physiology of the species. Being mechanistic, PBPK models can be used to simulate and to predict the next set of data and to plan the next experiment.

1.3 STEPS NEEDED TO MAXIMIZE EFFECTIVE INTEGRATION OF MODELS INTO R&D WORKFLOW

Although PBPK models were developed for cancer drugs even during the 1960s and 1970s by Bischoff et al.7 and Bischoff and Dedrick,8 the pharma industry has been slow to exploit the power of PBPK. While the importance of integrating modeling, simulation, and other in silico technologies in the R&D workflow is clearly acknowledged by leaders in the industry and by regulatory authorities, practical implementation has been slow especially in some areas of modeling. A number of reasons have been identified. The lack of trained/skilled scientists, sceptical attitude from project teams, and lack of commitment on the part of leadership to implement are the most important among them.9 In all this, the role of management in driving the integration is seen as key to bringing about a change in the workflow and mindset of the scientists as well as to allocate resources for training scientists. Gaining acceptance among project teams is vital to ensure that modeling results are seriously considered and incorporated in decisions, thus paving the way for cost-effective and efficient drug discovery and development.

1.4 SCOPE OF THE BOOK

Physiologically-based pharmacokinetic modeling for the discovery and development of small-molecule and biological drugs will be the main focus of the book, as applications of PBPK in environmental toxicology and human health risk assessment have already been the subject of a previous publication.10 The chapters in the first section will cover the basics of PBPK modeling and simulation, while the second section will deal with its applications in drug discovery and development.

Chapters 2–6 will elaborate on the principles essential for integrating species physiology with compound-dependent properties. Chapter 7 will put together all of the absorption, distribution, metabolism, and excretion (ADME) physiological models for small-molecule drugs.

Physiologically-based PK modeling involves the use of a number of compound-dependent and physiology-dependent parameters. Being a parameter-intensive model, the predicted outcome could be associated with a high level of uncertainty. It is, therefore, important to consider the propagation of error arising from the uncertainties in input parameters. These uncertainties can be modeled using the Monte Carlo approach, which forms the subject of Chapter 8.

As late failures in the drug development process become more costly, the desire to evaluate the potential for risks earlier in the drug discovery process has become a growing industry trend. An early assessment of the potential for drug–drug interactions (DDI) with co-medications mediated by inhibition/induction of cytochrome P450 (CYP) enzymes or from transporters is, therefore, seen as imperative even in the lead optimization stage. PBPK models provide a mechanistic approach to integrating relevant information on a potential inhibitor and a substrate for the prediction of DDI risk. Chapter 9 details the differential equations that describe the mutually dependent kinetics of coadministered drugs and wraps up with a discussion on the advantages of physiological models over static models in the evaluation of drug–drug interactions.

Biologicals (or biologics) are fast emerging as alternative therapeutics to small molecules. Biologicals are proteins such as monoclonal antibodies, cytokines, growth factors, enzymes, and thrombolytics that can treat a variety of diseases. Since the launch of Eli Lilly’s recombinant human insulin in 1982, more than 100 biologicals have received marketing approval in the United States, highlighting their importance as a source of new drugs and new revenues. With an increasing fraction of pharmaceutical R&D devoted to biologicals, it is expected to have a significant role in drug development in the future. Chapter 10 is devoted to examining the differences between biologicals and small molecules with respect to PK behavior and how these differences can be accommodated within PBPK models.

Section II of the book will cover applications of PBPK modeling in drug discovery and development with examples. Applications in the pharmaceutical sector will be the main focus. PBPK modeling can be used as a prediction, simulation, or as an extrapolation tool. PK properties such as absorption, distribution, and elimination of compounds are influenced not only by compound properties but also by the physiology of the species in which they are observed. PBPK modeling attempts to integrate available structural, in silico or in vitro physicochemical, and human-specific biochemical compound data in a physiological context for the predictions of PK parameters such as absorption and distribution or time profiles of plasma concentrations of drugs. Chapter 11 describes how PBPK models provide an excellent framework for enabling data integration and human PK predictions. Chapter 11 also describes the applications of parameter sensitivity analysis for optimizing lead compounds during drug discovery. In the lead optimization stage, understanding the effects of modulating key ADME-determining compound-dependent properties on a desired PK outcome is often needed in order to optimize the physicochemical space. The PK outcome could be metabolic liability, absorption, distribution, or bioavailability of compounds. The effects of modulation depend very much on the physicochemical space chosen initially.

The value of a PBPK model as a prediction tool is sometimes limited by the lack of reliable input parameters especially for clearance, where the in vitro measurements for intrinsic clearance rarely match up to the in vivo. The mechanistic structure of PBPK models can be better exploited when it is used as a simulation tool. In a simulation, the focus is not on quantitative predictions. Instead, the emphasis is on gaining valuable insights into processes driving the pharmacokinetics of a compound, through hypothesis generation and testing. This neglected area, holding the promise of improving the quality of selected leads, reducing animal studies and cost, is the subject of Chapter 12. The mechanistic basis of PBPK models makes them ideal for extrapolation.

The structure of PBPK models allows the prediction of tissue concentrations, which can be valuable in human health risk assessment or for linking with pharmacodynamic models. PBPK models when combined with PD models can be powerful in predicting the time-course of drug effects under physiological and pathological conditions. The integration of PBPK models with PD models aid a robust design of clinical trials and is covered in Chapter 13. PBPK–based predictions aid the optimal use of all available compound information within a physiological context, making experiments confirmatory rather than exploratory. These have a tremendous impact in reducing preclinical and clinical studies thereby reducing costs.

Applications of PBPK in population modeling form the subject of Chapter 14. Drug failures can sometimes result from considering only an average person and neglecting physiological and genomic variability that can lead to a spread in both plasma drug concentrations and drug response. Chapter 14 describes how targeted therapy and personalized medicine can be achieved with PBPK/PD modeling.

Chapter 15 aims to seamlessly integrate all the applications of PBPK along the drug discovery and development value chain.

KEYWORDS

Binding Site Analysis: Use of computational tools for the prediction of potential ligand-binding active sites in a target protein, given its three-dimensional structure. This is achieved through searching for surface features of the protein (geometry and functional groups) that provide the best shape complementarity and interactions with a set of known ligands.

Biological Systems Modeling: Involves computer simulations of biological systems to analyze and visualize the complex connections of cellular processes such as the networks of metabolites and enzymes that comprise metabolism, signal transduction pathways, and gene regulatory networks.

Clinical Trial Simulation: Combining structural and stochastic elements of pharmacokinetic and pharmacodynamic models to produce a data set that will resemble the results of an actual trial.

Compartmental PK Modeling: Uses kinetic models to describe the concentration–time profile. The compartments do not relate to meaningful physiologic spaces.

Druggable: A druggable target is a protein whose activity can be modulated by a small molecule drug. A druggable target is crucial in determining the progression of a drug discovery project to the lead generation stage.

hERG Modeling: The human ether-à-go-go related gene (hERG) codes for the potassium ion channel Kv11.1, a protein that mediates the repolarizing IKr current in the cardiac action potential. Drugs inhibiting the channel can cause a potentially fatal QT prolongation with a concomitant risk of sudden death. In computational drug design, there are 2 main approaches to hERG modeling. Pharmacophoric or ligand-based modeling relies on determining the physicochemical features associated with the channel block to predict the hERG blocking potential of compounds. Target-based partial homology models of the hERG channel have also been built to interpret electrophysiological and mutagenesis studies.

Homology Modeling: Involves taking a known sequence with an unknown structure and mapping it against a known structure of one or more homologous proteins in an effort to gain insights into three-dimensional structure of the protein.

Lead Generation: A phase in drug discovery in which the objective is to identify one or more chemical series with potential drug activity, reduced off-target toxicity, and with physicochemical and metabolic profile that are compatible with acceptable in vivo bioavailability.

Lead Optimization: Phase in drug discovery, following lead generation, in which the objectives are to optimize the PK and PD (efficacy, selectivity and safety) in the screening stage and to select for drug development, a high-quality candidate drug that satisfies a preset target profile in the drug candidate selection stage.

Model-Based Drug Development: Statistical and mathematical modeling that allows for quantitative and effective use of prior information (preclinical efficacy and safety models) and clinical data (information across drugs, end points, trials and doses) for improved data analysis, clinical study design, knowledge management and decision making in clinical drug development.

PBPK/PD Modeling: Linking a physiologically-based pharmacokinetic (PBPK) model, which relates a drug’s exposure to its dose with a pharmacodynamic (PD) model, which relates the pharmacological response to exposure.

Pharmacophore Modeling: A ligand-based approach to virtual screening, which makes use of two- or three-dimensional pharmacophores generated from a set of known active compounds to the selected target.

PK/PD Modeling: Linking a pharmacokinetic (PK) model, which relates a drug’s exposure to its dose with a pharmacodynamic (PD) model, which relates the pharmacological response to exposure.

Population Modeling: Seeks to identify and quantify the pathophysiological factors that cause changes in the dose–concentration relationship, so that any resulting clinically significant shifts in the therapeutic index can be addressed through appropriate dose adjustments.

Prediction of PK Properties: Generally QSPR models that employ the structure-dependent properties of a compound to arrive at pharmacokinetic properties such as fraction of drug unbound in plasma, volume of distribution, renal elimination, fraction of compound absorbed, or bioavailability. Physiological models are also used to predict PK properties.

Protein Modeling is the prediction of the three-dimensional (secondary, tertiary, and quaternary) structure of a protein from its amino acid sequence.

Reactive Metabolite Prediction: Using the chemical structure of a compound and a database of known reactive metabolites to predict the likelihood that a compound of interest might produce reactive metabolites.

QSAR and QSPR Models: Quantitative structure–activity relationships (QSAR) are mathematical equations relating pharmacological activity to chemical structure for a series of structurally related compounds. Quantitative structure–property relationships (QSPR) relate physicochemical properties of compounds to their structures. QSARs are derived using regression and pattern recognition techniques.

Scaffold Hopping: Computational approaches that use a set of known active compounds to find structurally novel compounds with chemically completely different core structures, and yet binding to the same receptor by modifying the central core structure of the molecule.

Site of Metabolism Prediction: Given the structure of a lead compound, to predict the sites that are prone to metabolic activity. Databases of known reactivity and/or principles of chemical reactivity are employed to predict sites of metabolism. If metabolizing enzyme is identified, then its protein structure is also used for getting poses of a compound of interest at the active site of the enzyme. Machine learning and semiempirical quantum chemical calculation can also be incorporated into prediction models.

Virtual Screening: A computational technique used in early drug discovery for rapid in silico assessment of large libraries of chemical structures against three-dimensional structure of a target protein in order to identify structures that are most likely to bind to a target protein.

REFERENCES

1. PricewaterhouseCoopers. Pharma 2005 Silicon Rally: The Race to e-R&D. Paraxel’s Pharmaceutical R&D statistical sourcebook, 2002/2003.

2. U.S. FDA. Critical path initiative. Available at: http://www.fda.gov/ScienceResearch/SpecialTopics/CriticalPathInitiative/default.htm.

3. Lalonde RL, et al. Model-based drug development. Clin Pharmacol Ther. 2007; 82(1):21–32.

4. Dingemanse J, Appel-Dingemanse S. Integrated pharmacokinetics and pharmacodynamics in drug development. Clin Pharmacokinet. 2007;46(9):713–737.

5. Teorell T. Kinetics of distribution of substances administered to the body. Archives Internationales de Pharmacodynamie et de Thérapie. 1937;57:205–240.

6. Rowland M, Balant L, Peck C. Physiologically-based pharmacokinetics in drug development and regulatory science: A workshop report (Georgetown University, Washington, DC, May 29–30, 2002). AAPS J. 2004;6(1):56–67.

7. Bischoff KB, Dedrick RL, Zaharko DS, Longstreth JA. Methotrexate pharmacokinetics. J Pharm Sci. 1971;60(8):1128–1133.

8. Bischoff KB, Dedrick RL. Thiopental pharmacokinetics. J Pharm Sci. 1968;57(8):1346–1351.

9. Edginton AN, Theil FP, Schmitt W, Willmann S. Whole body physiologically-based pharmacokinetic models: Their use in clinical drug development. Expert Opin Drug Metab Toxicol. 2008;4(9):1143–1152.

10. Reddy MB, Yang RSH, Clewell HJ, Eds. Physiologically-Based Pharmacokinetic Modeling Science and Applications. Hoboken, NJ: Wiley, 2005.

Chapter 2

PHYSIOLOGICALLY-BASED MODELING

CONTENTS

2.1 Introduction2.2 Examples of Physiological Modeling2.3 Need for Physiological Models in the Pharmaceutical Industry2.4 Organs as Compartments2.5 Bottom-Up vs. Top-Down Modeling in Pharmacokinetics References

2.1 INTRODUCTION

Physiological modeling or physiology-based mathematical modeling aims to integrate knowledge of physiological processes to the extent known with physicochemical attributes or other known/measured information about compounds in order to predict or simulate complex biological properties. The level of detail in a physiological model can vary depending on the nature of the property to be predicted or the process to be simulated, extent of knowledge available, and the level of complexity required to meet an acceptable degree of prediction/simulation accuracy. Physiological models of cells (focusing on cellular processes at molecular level), tissues, a system of organs, and whole organisms aid an increased mechanistic understanding of biological systems, and the potential benefits for a pharmaceutical company are very high. Despite the unique advantages that physiological models can provide, the sheer size and complexity of these models, as well as the problems of parameterization, have been deterrents to their widespread application for a long time. However, the tremendous progress in high-performance computing has removed the constraints in computing power, allowing for a dramatic increase in the comprehensiveness and complexity of physiological models. A steady growth in biological pathway information and genetic data, information on molecular mechanisms, and technological advances in biological measurements have made it possible to obtain the data needed for parameterization of models. Physiological models of today are, therefore, considerably more complex, seeking to answer more demanding questions and addressing the interdependence of component models.

2.2 EXAMPLES OF PHYSIOLOGICAL MODELING

A number of examples of physiological modeling can be found in the field of medicine. Mathematical models of the coupling between membrane ionic currents, energy metabolism [adenosine triphosphate (ATP) regeneration via phosphocreatine buffer effect, glycolysis, and mitochondrial respiration], blood–brain barrier exchanges, and hemodynamics in the brain, physiological model for liver or muscle metabolism, and tumor modeling to understand the signaling pathways leading to angiogenic activities of tumors are some of the examples of physiological organ modeling. Apart from these, physiological models of the cardiovascular system and respiratory system (including respiratory organs such as lung, respiratory muscles such as diaphragm, and peripheral organs such as nasal cavity and oral cavity) are commonly used as a useful way of monitoring conditions of a whole system. Physiological models that simulate human internal thermal physiological systems, including muscle and blood, predict thermoregulatory responses such as metabolic heat generation by computing heat flow by conduction, convection, and mass transport. Thus, physiological models aim to provide meaningful predictions based on a physical and biological understanding of the underlying processes. There is considerable scientific interest in modeling not just the various tissues or systems of organs but the entire human body. Physiological modeling of the human body, and to some extent the modeling of any animal body, provides very precise information that can help improve the well-being or healing time of individuals facing health issues. In addition, the growing complexity and accuracy of physiological modeling brings critical information to the pharma industry. The pathophysiological conditions of diseases can be modeled1 for the advancement of basic knowledge of a disease and the development of new disease diagnostics. Important whole-body parameters to be considered are volumes, blood flow rates, circulating pools of endogenours or exogenous proteins and nutrients, and other aggregate properties of the body such as cardiac output, body weight, and the like.

2.3 NEED FOR PHYSIOLOGICAL MODELS IN THE PHARMACEUTICAL INDUSTRY

Physiological modeling approaches are important for transitioning biology from a descriptive to a predictive science. Pharmaceutical companies identify molecular interventions that can lead to therapies. Physiological models that integrate an understanding of known biological mechanisms with all available compound information can greatly improve the efficiency of transforming targets into therapies. In the pharma industry, physiological models are used to predict pharmacokinetics, to simulate clinical outcomes and organ-level behavior, and to predict human response to drugs. Patel2 describes a single physiological model to explain the acute and chronic changes in sodium and water balance in the human body in response to changes in the physiological mechanisms regulating sodium. Noble3 describes a physiological model of the heart that provides a unified description of organ-level physiology in terms of protein-level biology. The model provides nonintuitive explanations for how antiarrhythmia drugs might work. An extensive knowledge of cell–cell organization, signaling pathways, and the tissue geometry of the heart were necessary to build the model. A similar attempt to integrate proteins to organ-level systems4 is also described in the literature. Physiological models of type II diabetes have been used for over a decade to understand key parameters, such as insulin sensitivity and β-cell function, pertaining to pathology in patients.5 Such models provide new insights into important biological processes, thus aiding the development of new medicines and treatment regimes. Physiological models also facilitate the incorporation of interindividual differences in enzymology and receptor densities, making it possible to apply pharmacogenomic principles.

2.4 ORGANS AS COMPARTMENTS

Compartments are areas of the body where muscle, nerves, and blood vessels are confined to relatively inflexible spaces bounded by skin, fascia, and bone. Many physiological models consider each organ in the body as one or more compartments. The contents within a compartment are expected to be homogenous. The complexity of the model is a function of the number of compartments. As such, this number should not exceed more than what is critical for characterizing the system.

2.5 BOTTOM-UP VS. TOP-DOWN MODELING IN PHARMACOKINETICS

In pharmacokinetics, compartmental PK models are widely used in the drug discovery stage. The compartments in these models do not have a physiological relevance. Parameters have no physical or biochemical meaning. These empirical models describe the data but are of little value in understanding the mechanisms underlying the observations and cannot be extended to the next set of data. They do not account for the sequential metabolism of a drug in different organs, do not consider metabolite kinetics, and cannot distinguish the effects of transporter barriers between drug and metabolites.

Population PK models are another class of empirical models that are used during clinical development to understand the sources of observed variability in the drug concentrations among the individuals of a target population through correlations of observed variability with demographical, pathophysiological, and therapeutical variations. These empirical models are useful in evaluating the need for dosage changes to the drug in the event of clinically significant shifts in the therapeutic index. Compartmental and population PK models are conventional approaches seeking to get to the system characteristics starting from the observed data. Contrary to this top-down modeling approach, PBPK models present the opportunity for bottom-up modeling, in which prior information on the system characteristics and other variables that may result in an observation are assembled together to predict an outcome. Any deviations from the predicted outcome can then provide insights into the mechanisms of the underlying processes. PBPK model structure is independent of any observed drug data. PBPK models and systems biology6 models are good examples of a bottom-up approach. In practice, a combination of these two approaches can be very valuable in understanding drug response in a population. Model parameters are extracted from one set of observations in a system and then used to predict possible outcomes in another.

REFERENCES

1. Butcher EC, Berg EL, Kunkel EJ. Systems biology in drug discovery. Nat Biotechnol. 2004;22(10):1253–1259.

2. Patel S. Sodium balance—an integrated physiological model and novel approach.Saudi J Kidney Dis Transpl. 2009;20(4):560–569.

3. Noble D. Systems biology and the heart. BioSystems. 2006;83(2–3):75–80.

4. Hunter PJ, Borg TK. Integration from proteins to organs: The physiome project. Nat Rev Mol Cell Biol. 2003;4(3):237–243.

5. Kansal AR. Modeling approaches to type 2 diabetes. Diabetes Technol Ther. 2004;6(1):39–47.

6. Kohl P, Crampin EJ, Quinn TA, Noble D. Systems biology: An approach. Clin Pharmacol Ther. 2010;88(1):25–33.

Chapter 3

REVIEW OF PHARMACOKINETIC PRINCIPLES

CONTENTS

3.1 Introduction3.2 Routes of Administration3.3 Drug Disposition 3.3.1 Absorption3.3.2 Plasma Protein Binding, Blood–Plasma Ratio3.3.3 Distribution, Elimination, Half-Life, and Clearance3.3.4 Role of Transporters in ADME3.4 Linear and Nonlinear Pharmacokinetics3.5 Steady-State Pharmacokinetics3.6 Dose Estimations3.7 Successful PK Optimization in Drug Discovery KeywordsReferences

3.1 INTRODUCTION

Pharmacokinetics is the study of the rate and extent of drug transport in the body to the various tissues, right from the time of its administration to its elimination. The rate of drug transport to the target tissue of pharmacological action determines the rate of drug action. It is dependent on the rate of drug absorption from the site of administration into the capillaries and the blood flow rates to the organs of elimination and to target tissue. The extent of drug that reaches the site of drug action at any point in time is dependent on protein binding, extent of metabolism, or biotransformation and elimination. The absorption, distribution, metabolism and elimination (ADME) of a drug should be such that the drug is delivered at the target site at a rate and concentration consistent with a once or twice daily administration. To ensure this, the effective elimination half-life of a drug, determined by the rates and extent of ADME, should ideally be equal to the dosing interval. With successive administrations of a drug, the rate of its elimination tends to equal the rate of administration, at which point an equilibrium steady state is said to have been attained. The dosing frequency of a drug in humans is dictated by the half-life of the drug and by its unbound steady-state concentration, which should equal its pharmacologically effective concentration. The forthcoming chapters will draw heavily upon these concepts, and the reader is encouraged to use this chapter as a reference to basic pharmacokinetic principles.

3.2 ROUTES OF ADMINISTRATION

Common routes of drug administration include per oral (PO), intramuscular (IM), subcutaneous (SC), and intravenous (IV) injections and IV infusion. Other routes include buccal, sublingual, rectal, transdermal, inhalational, and topical. The oral route is the most preferred route, but it is not suitable for drugs that are not stable in the gut, such as for example, peptide and protein drugs.

3.3 DRUG DISPOSITION

3.3.1 Absorption

Other than the IV administrations, all other routes require the drug to be absorbed into the capillaries surrounding the site of administration. The rate of absorption from IM and SC routes depends on the type of tissue at the site of administration—the density, vascularity, and fat content. The IM route, for example, has a higher rate of absorption compared to the SC because of lesser fat and greater vascularity of the dense muscles. Oral drug absorption (Fig. 3.1) refers to the transport of drug molecules across the enterocytes lining the gastrointestinal (GI) tract into the venous capillaries along the gut wall. The rate of drug absorption is dependent upon a number of physiology-, drug-, and formulation-dependent factors such as the gastric emptying rate, intestinal motility, porosity of tight junctions, luminal and mucosal enzymology, carrier and efflux transporters, small intestinal secretions (bile and digestive enzymes), food interactions, regional differences in pH, permeability, solubility, dissolution rate and particle size, among others. An orally absorbed drug is subjected to first-pass metabolism in the liver before it is available in systemic circulation.

Figure 3.1 Orally administered drug disintegrates, dissolves, transits, and permeates the enterocytes. Along its way down the gastrointestinal tract, the drug may bind to luminal contents—food, bacteria, etc., which prevents its absorption. Transcellular drug absorption can result in transporter-mediated efflux or drug metabolism by intestinal enzymes such as cytochrome P450s (CYPs) and uridine 5′-diphospho-glucuronosyltransferases (UGTs). Small, hydrophilic drugs rely on the paracellular route, while large hydrophilic molecules rely on transcytosis and receptor-mediated endocytosis for absorption. Molecules possessing certain special groups such as peptide linkages are transported across the membrane by carrier transporters. Most drug molecules are sufficiently lipophilic for transcellular passive absorption.

3.3.2 Plasma Protein Binding, Blood–Plasma Ratio

Drugs reversibly bind to plasma proteins depending upon their lipophilicity and ionizability. In general, the greater the lipophilicity of a compound, the greater is its plasma protein binding. The binding equilibrium can be represented as

where [P] is the protein concentration, and Cu and Cb are the unbound and bound concentrations of the drug at equilibrium. The equilibrium constant, KA, also called the affinity constant, is given by

(3.1)

where n is the number of binding sites per mole of the binding protein. Since therapeutic concentrations of most drugs are low, [P] can be assumed to be the total protein concentration [P]Total. The fraction unbound drug in plasma (fup) can be obtained from equation 3.1 in terms of [P]Total or in terms of the concentrations of the plasma proteins α1-acidic glycoprotein (AGP), [P]AGP, and albumin [P]albumin:

(3.2)

The fraction unbound in plasma (fup) thus depends on the concentration of protein and the affinity of the drug to the protein. Albumin is the principal protein to which many drugs bind, followed by AGP. Other plasma proteins include lipoproteins and the globulins. The concentrations of various plasma proteins are shown in Table 3.1. Albumin is distributed in intravascular (plasma: 43 g/kg organ) and extravascular organs (muscle: 2.3 g/kg, skin: 7.7 g/kg, liver: 1.4 g/kg, gut: 5 g/kg, and other tissues: 3 g/kg). Albumin exists abundantly in the interstitial fluids.

TABLE 3.1 Plasma Proteins

Albumin has six distinct binding sites, two of which specifically bind to long-chain fatty acid, another selectively binds to bilirubin, and the remaining two bind to acidic and lipophilic drugs. One of these drug-binding sites binds to drugs such as warfarin and phenylbutazone, while the other to drugs such as diazepam and ibuprofen. Drugs binding to different binding sites do not compete with one another. When more than 20% of the sites are occupied, concentration dependence of binding begins to get appreciable, ultimately leading to saturation at higher concentrations. Saturation of albumin is rare and restricted to drugs (especially acids) with high therapeutic concentration. However, the binding sites of a few drugs such as tolbutamide and some sulfonamides are saturated even at therapeutic concentrations. AGP concentrations being much lower compared to albumin, saturation of AGP occurs at lower therapeutic concentrations. The concentrations of several plasma proteins can be altered by many factors including stress, surgery, liver or surgery dysfunction, and pregnancy. Most commonly, disease states increase AGP concentration while reducing albumin concentration. Higher levels of AGP have been reported in obese patients with nephrosis. Stress, cancer, and arthritis have been associated with lower AGP levels. Neonates have higher AGP levels. AGP has a higher degree of interindividual variability compared to albumin. Reduced levels of albumin have been reported in myalgia patients. Drugs that are highly bound to plasma proteins are confined to the vascular space and are not readily available for distribution to other tissues and organs. Many carboxylic acid drugs are not easily displaced from plasma proteins and have a low distribution volume. However, this is not true if the affinity of a drug to tissue proteins is higher than that to plasma proteins. Ultrafiltration and equilibrium dialysis are the two commonly employed methods for the determination of plasma protein binding1. Albumin is the principal drug-binding protein in tissues followed by ligandin. Measurement of tissue binding is not as straightforward as that in plasma, as the tissue must be disrupted and it is not readily accessible to sampling. Tissue proteins cannot be easily separated into their constituents and cannot easily be quantified.

While the liver can extract high extraction drugs, even if they are highly bound to plasma proteins, the clearance (CL) of many low hepatic extraction drugs are limited by protein binding. Only the unbound drug is available for glomerular filtration and, therefore, for renal elimination. An increase in unbound drug concentration due to a reduced plasma protein binding will enable higher tissue distribution and higher CL. However, since the half-life of a drug is directly proportional to the distribution volume and inversely proportional to CL, there is no net effect on the half-life. Thus, changes in plasma protein binding of a drug are not likely to be clinically relevant2 except in the following cases:

1. The drug is >98% bound to plasma proteins. In this case even a small shift in plasma protein binding can have a substantial effect on the clearance but less so on the distribution volume, thus temporarily altering the unbound drug concentrations, until new equilibrium is attained.

2. The drug has a high hepatic extraction. The clearance of such drugs will be dependent only on the hepatic blood flow rate and not on the product of fup×CLint, where CLint is the intrinsic clearance of a comound in the liver. Thus an increase in distribution volume is not sufficiently compensated by an increase in CL, leading to a temporary increase in unbound drug concentrations.

3. The drug has a narrow therapeutic window/safety margin such that the differences in unbound drug concentrations discussed in case 1 or 2 will have a greater impact.

4. There is a rapid equilibrium (short pharmacological response time) between drug concentration and pharmacological response (e.g., lidocaine with a PK–PD equilibration time of 2 min) compared to the time required for the body to regain equilibrium (about 30 min). Many antiarrhythmic drugs and anesthetics require only a short time for a change in concentration to cause a change in drug effect. In these cases, the response is sensitive to small transient changes in unbound drug concentrations.

5. The pharmacological response sensitive to changes in drug concentration.

Scaling of PK parameters such as clearance or volume of distribution or pharmacodynamc properties3 from preclinical species to humans should always be done with the unbound parameters. Any comparisons/correlations of PK parameters should also be done with unbound values.

Some drugs also bind to and distribute into erythrocytes, the main drivers being lipophilicity, pKa, and active uptake into the erythrocytes. Binding sites within erythrocytes are proteins such as hemoglobin, carbonic anhydrase, as well as plasma membrane. Blood–plasma concentration ratio4 (R) of a drug is a measure of its binding and distribution to erythrocytes relative to plasma. A compound having similar extent of binding to constituents of erythrocytes and plasma has a blood–plasma ratio of 1. Acids tend to have R values around 0.55 and never exceed 1, and bases tend to have higher range of values, often exceeding 1, while neutrals and ampholytes have values around 1.5 Uchimura et al.4 describe several methods to determine R. The minimum value of R can be only 0.55, corresponding to no distribution into erythrocytes. However, there is no upper limit. For tacrolimus, R is as high as 55 and exhibits concentration dependence.6R is determined by measuring the concentrations of 14C-labeled drug in erythrocytes (Ce) and plasma (Cp) in freshly collected blood. Then, knowing the hematocrit, H (the relative volume of blood occupied by erythrocytes), R is obtained as follows:

(3.3)

R can also be predicted.7 Partitioning into erythrocytes can be fast for some drugs, and distribution equilibrium is reached within a few seconds to minutes. However, many drugs with primary amine groups show delayed equilibrium probably due to formation of Schiff bases with membrane fatty acids and aldehydes. While the displacement of the plasma-protein-bound drug to the unbound is rapid except for protein molecules, displacement of erythrocyte-bound drug is relatively slow. For acids with high plasma protein binding, distribution into erythrocytes can significantly affect its distribution volume, as other tissue compartments are not as significant. If blood to plasma ratios exceed 1, as for lipophilic bases, the plasma clearance significantly overestimates blood clearance and could even exceed hepatic blood flow. This is because the concentrations measured in plasma will always be much smaller compared to that measured in whole blood due to the higher distribution into the erythrocytes, when R is > 1. Thus, if Cb is the concentration of the drug in blood, CLp is the plasma clearance and CLb is the blood clearance of the drug, the following relation holds:

3.3.3 Distribution, Elimination, Half-Life, and Clearance

The following derivations will aid an appreciation for the relationship between distribution, elimination, and half-life. The rate of change of drug concentrations in the blood (C) can be given by the first-order rate equation

(3.4)

where A is the amount of drug in the body at any time, t, kel is the first-order elimination rate constant, and V is the volume of distribution of the drug. The higher the lipophilicity and unbound fraction of the drug, the greater is the V. Tissue partition coefficient (KT, P) is the ratio of concentration of the drug in a tissue and plasma at steady state and is, therefore, a measure of distribution into that tissue. Tissue partition coefficients are different for different tissues depending on the composition of the tissue and the nature of the compound (Fig. 3.2). The product of kel and V is defined as the total clearance, CL, of the drug from blood. Integrating the equation − dA/dt = kel×A yields

Figure 3.2 Both the blood plasma and the tissues are composed of water, lipid, and proteins. The proportion of the constituents varies in different tissues. A drug equilibrates between the different constituents of plasma and tissues, depending on its lipophilicity.

(3.5)

where A0 is the initial amount of drug in the body. A0 is simply the dose administered for an IV bolus, but for all other non-IV routes, it is F ×dose, where F is the systemic bioavailability of the drug. The F of an oral dose is

(3.6)

where fabs is the fraction of dose absorbed, fgut is the fraction escaping gut extraction, and fhep is the fraction escaping hepatic extraction. The oral bioavailability of a drug can be estimated from the areas under the PK curves (AUC) of intravenous and oral doses (AUCIV and AUCoral), assuming that the clearance does not vary between the IV and oral routes:

(3.7)

Bringing A0 to the left-hand side of equation 3.5, taking the natural logarithms on both sides of the resulting equation, and defining the half-life (t1/2) of a drug to be the time taken for half of the drug amount to get eliminated from the body (i.e., A becomes A0/2), the half-life is given by

(3.8)

Integrating the equation −dA =CL×C dt yields

(3.9)

Recognizing that the integral dA over time is the dose, equation 3.9 becomes Dose = CL×AUC, where AUC is the area under the concentration–time profile. The total clearance, CL, is the sum of clearance from every eliminating organ but mainly hepatic (CLH), renal (CLR), and biliary (CLB):

(3.10)

where CLorgan is the clearance from an eliminating organ, Qorgan is the blood flow rate to that organ, and CART and CVEN are the arterial and venous concentrations. Qorgan×CART− Qorgan×CVEN is the rate of elimination from that organ.

The liver is the most important eliminating organ, where phase I and phase II metabolism of the small-molecule drugs convert them into more hydrophilic compounds, which can then be renally eliminated. About 40 human CYP genes have been cloned and classified according to sequence homology. Of these, only 3 CYP families and less than 12 unique enzymes play a substantial role in the hepatic metabolism of drugs in humans. The rate of such an enzyme-driven biotransformation reaction, v, depends on the concentration of the drug according to the Michaelis–Menten equation:

(3.11)

CLint is the intrinsic clearance of the drug, dependent only on the intrinsic chemical nature of the drug; vmax is the maximum velocity of the reaction; and KM is the Michaelis–Menten constant (Fig. 3.3). The therapeutic concentration ranges of most drugs are very low compared to their KM, and equation 3.11 then becomes

Figure 3.3 Rate of an enzyme-catalyzed reaction as a function of substrate concentration.

(3.12)

Equation 3.12 suggests that the rate of a metabolic reaction varies linearly with the drug concentration at concentrations not exceeding KM. CLint then equals the ratio of vmax to KM, and it is independent of the drug concentration. However, when drug concentrations are comparable with or exceeds KM, which can be the case with high doses of drugs, CLint is dependent on C (see equation 3.11). The greater the drug concentration, the greater the extent of enzyme saturation and smaller the CLint. The maximal rate of metabolism is reached. Under these conditions, zero-order kinetics is said to prevail, and a constant amount of drug is eliminated per unit time, independent of the amount of drug in the body. Well-known examples of drugs exhibiting nonlinear clearance include phenytoin, ethanol, methyl salicylate, and theophylline (in some individuals). Apart from CLint, the hepatic clearance CLH is dependent on how fast the drug is delivered to the enzymes in the hepatocytes, which is basically governed by the total blood flow rate to the liver. A basic tenet of pharmacokinetics is that only the fraction of drug that is not bound to the plasma proteins is available for distribution into tissues and for hepatic, biliary, or renal clearance. These dependencies of CLH are encapsulated in the well-stirred model in which the liver is considered to be a well-stirred compartment. According to this model, the hepatic clearance from blood, CLH, is given by

(3.13)

where fub is the fraction unbound in blood. Since the unbound concentrations in plasma and blood are expected to be the same, fub, fup, and R are related as follows:

(3.14)

Equation 3.13 shows that when the product fup×CLint is high compared to QLI, then CLH is simply determined by the blood flow rate to the liver. The drug clearance is limited by the rate at which it is delivered to the drug-metabolizing enzymes. On the other hand, when the product fup×CLint is low compared to QLI, then the hepatic clearance linearly varies with the product of fraction unbound in plasma and the intrinsic clearance. For high CLint compounds, the displacement of the drug from plasma proteins is rapid and equilibrium cannot be established between concentrations of the bound and unbound drug in blood (Cb, Cu, b) and in liver (Cu, liver). This can be represented as

The liver is capable of extracting even the bound drug. For low CLint compounds, there is equilibrium between the bound drug and unbound drug in blood and liver and only the Cu, liver is available to the drug-metabolizing enzymes. The equilibrium between the different drug concentrations is shown below:

The hepatic extraction ratio of a drug is obtained from equation 3.13, by taking the QLI to the left-hand side:

(3.15)

For hydrophilic drugs, the parent compound can get eliminated in the urine, unchanged. For example, the renal route is the predominant route of elimination for about 60% of anti-infection compounds.8 The fraction of the dose excreted in the urine unchanged (fe) is

(3.16)

where Ae, unchanged is the amount of drug excreted in the urine unchanged. Therefore, CLR is

and CLR = fub×GFR, where GFR is the glomerular filtration rate for a drug for which there is no tubular active secretion or tubular reabsorption (Fig. 3.4). Active tubular secretion is evident if CLR > fub×GFR and tubular reabsorption is apparent when CLR < fub×GFR. Reported values of GFR are measured with endogenous filtration markers such as creatinine, which is freely filtered and secreted (15%) in the proximal tubule. However, since the synthesis and blood concentration of creatinine are influenced by several factors, including age, sex, ethnicity, muscle mass, and chronic illness, other markers such as serum cystatin C, 51CrEDTA, or inulin are employed. Since the maximum renal clearance can be about 1.8 mL/min/kg, (the GFR in humans) in the absence of active secretion, drugs cleared exclusively in the kidney (hydrophilic acids and bases with high polar surface area (PSA) and rotatable bond count) generally tend to have low clearances. Apart from low clearances, these compounds are also unaffected by CYP-related issues such as polymorphisms, drug-drug interactions (DDI), and reactive metabolites.

Figure 3.4 Renal elimination of a drug: glomerular filtration, active tubular secretion, and tubular reabsorption. Lipophilic drugs are readily reabsorbed, making renal elimination an important route only for hydrophilic drugs.

Amphiphilic compounds (compounds with both acidic and basic groups) with molecular weights >350 also have the possibility of being actively transported into the bile and excreted via feces. Biliary clearance can be estimated by determining the concentration of a drug in the bile (Cbile) collected from a bile-duct-cannulated preclinical species:

(3.17)

The parent drug in bile is emptied into the duodenal section of the small intestinal tract and may be reabsorbed back into the portal vein as it transits down the small intestine. This is called the enterohepatic recirculation (EHR) of a parent drug. A metabolite of the drug can also be emptied into bile and into the duodenum (Fig. 3.5). Certain phase II metabolites such as glucuronides are then reconverted to the parent drug by the gut microflora and reabsorbed and recirculated. Although the pharmacokinetic profile is very similar to that associated with parent EHR, the measured Cbile for the parent drug in this case would be low, allowing one to distinguish between parent and metabolite EHR.

Figure 3.5 Entero-hepatic recirculation of a parent drug or a metabolite.

Absorption, distribution, renal elimination, and biliary elimination are all dependent on physicochemical properties of the drug, particularly lipophilicity and acid/base/neutral characteristics and physiology of the species such as blood flow, organ volumes, transit rates, and the like. The chemical structure of a drug dictates its rate and extent of biotransformation as well as affinity to transporters.

3.3.4 Role of Transporters in ADME

Transporters (Fig. 3.6a in plasma, target issue, as well as in the blood–brain barrier,10 as shown in Table 3.2 and the ATP-binding cassette, or ABC, transporters of 49 proteins in 7 subfamilies. The SLC transporters mediate cellular influx of substrates either by facilitated diffusion or by secondary active transport, driven by co-transport (symport or antiport) of endogenous organic ions.12–15 ABC transporters mediate the primary active transport of unidirectional efflux of drugs often against a steep diffusion gradient, deriving energy from ATP hydrolysis.16–18 The transporters that play an important role in human drug disposition are the active SLC transporters OATP1B1, 1B3 and 2B1, SLC transporters that mediate facilitated diffusion OCTs 1 and 2, SLC antiport transporters MATE1 and MATE2K, and the ABC efflux transporters P-gp (MDR1), MRP2 (important in the transport of glucuronide and glutathione conjugates), BCRP, and BSEP. ATP-independent secondary efflux transporters are probably meant to be an additional mechanism for toxin extrusion even if cells are energy deprived. The different types of transporters are shown in Figure 3.6b.

Figure 3.6