nature publishing group
`
`development
`
`Development of Translational
`Pharmacokinetic–Pharmacodynamic Models
`DE Mager1 and WJ Jusko1
`
`Contemporary models in the field of pharmacokinetic–
`pharmacodynamic (PK–PD) modeling often incorporate
`the fundamental principles of capacity limitation and
`operation of turnover processes to describe the time course of
`pharmacological effects in mechanistic terms. This permits
`the identification of drug- and system-specific factors that
`govern drug responses. There is considerable interest in
`utilizing mechanism-based PK–PD models in translational
`pharmacology, whereby in silico, in vitro, and preclinical
`data may be effectively coupled with relevant models to
`streamline the discovery and development of new therapeutic
`agents. These translational PK–PD models form the subject
`of this review.
`
`Basic TeneTs of Pharmacodynamics
`The basic principles of pharmacokinetics, pharmacology,
`and physiology form the foundation of mechanism-based
`pharmacokinetic–pharmacodynamic (PK–PD) modeling.
`A summary of these components is shown as a diagram in
`Figure 1. Pharmacokinetics encompasses the factors affecting
`the time course of drug/metabolite concentrations in relevant
`biological fluids and tissues after various routes of adminis-
`tration and represents the driving force for pharmacological
`and most toxicological effects. Noncompartmental (i.e., area/
`moment analysis) and mammillary plasma-clearance mod-
`els that quantitatively assess pharmacokinetic processes (i.e.,
`absorption, distribution, metabolism, and excretion) are the
`most common methods used for PK data analysis. At the very
`minimum, the primary parameters of drug distribution and
`elimination should be identified (volume of distribution and
`clearance). Despite the widespread use of these assessment
`techniques in studies using various animal species, the rela-
`tively empirical and hybrid nature of the parameters derived
`from such techniques do not readily allow for extrapolation
`of the PK properties across species and compounds, a highly
`desirable feature of translational models. In contrast, physiol-
`ogy-based PK (PBPK) models seek to emulate physiological
`pathways and processes that control plasma and tissue drug
`
`concentrations, and this approach is regarded as the state-of-
`the-art technique in advanced PK systems analysis.1,2 As stated
`by Dedrick, “Physiologic modeling enables us to examine the
`joint effect of a number of complex interrelated processes and
`assess the relative significance of each.”3 The compartments in
`PBPK models represent organs and tissues of interest and are
`arranged and connected according to anatomical and physi-
`ological relationships (Figure 1, top left). A series of mass-
`balance differential equations that extend from Fick’s law of
`perfusion/diffusion describe the rate of change of drug con-
`centrations within each tissue. Other major processes may be
`incorporated, including drug metabolism and/or excretion,
`partitioning, binding, and transport. Most PK–PD models
`utilize the values of either free or total drug concentrations in
`plasma for driving PD, but there are increasing efforts to use
`techniques applicable across species, such as microdialysis and
`imaging, to capture the drug at or closer to its sites of action,
`that is, in the biophase.4
`The law of mass action and the relatively low concentra-
`tion of pharmacological receptors or targets impart capacity
`limitation in most drug responses. This concept is reflected
`in the traditional Hill function or sigmoidal Emax model of
`drug effects:5
`
`E
`
`=
`
`E
`max
`EC
`g
`50
`
`g
`
`C
`·
`+
`C
`
`g
`
` (1)
`
`where capacity or efficacy (Emax) and sensitivity or potency
`(EC50) parameters define the nonlinear relationship between
`drug effect (E) and concentration in plasma or at a biophase (C).
`Several curves defined by Equation 1 are shown in Figure 1
`(top right) for three different values of the Hill coefficient (γ).
`Whereas Equation 1 represents a linear transduction of Clark’s
`receptor occupancy theory, more complex functions of receptor
`occupancy, including the operational model of agonism,6 can
`be used for characterizing many pharmacological effects.
`Nevertheless, capacity limitation is a hallmark feature of quan-
`titative pharmacology and, as a consequence, a wide range of
`
`1Department of Pharmaceutical Sciences, University at Buffalo, State University of New York, Buffalo, New York, USA. Correspondence: DE Mager (dmager@buffalo.edu)
`Received 18 January 2008; accepted 13 February 2008; advance online publication 26 March 2008. doi:10.1038/clpt.2008.52
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`909
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`Apotex v. Novartis
`IPR2017-00854
`NOVARTIS 2058
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`development
`
`Pharmacokinetics
`
`Pharmacology
`
`Stimulus
`
`Log concentration
`
`Arterial
`
`GI
`
`Lung
`
`Heart
`
`Liver
`
`Kidney
`
`Other
`
`Venous
`
`Mechanism-based
`PK–PD modeling
`
`Physiology
`
`Production
`
`Outflow
`
`R
`
`figure 1 Major components contributing to assembly of mechanism-based
`pharmacokinetic–pharmacodynamic (PK–PD) models. GI, gastrointestinal.
`
`k × R, R(0)
`
`
`out
`
`0
`
`= R
`
`(2)
`
`Structure/function
`
`Time frame
`
`10–6
`
`Electrical signals
`Neurotransmitters
`Chemical signals
`Mediators
`Hormones
`Enzymes
`Electrolytes
`mRNA
`Proteins
`Cells
`Tissues
`Organs
`108
`Humans
`Seconds
`
`104
`
`EEG, ms
`Epinephrine, 1–4 min
`Calcium, 0.7 min
`cAMP, 1–6 min
`Cortisol, 1 h
`AChE (liver), 7 h
`Sodium, 15 h
`Many, 6–12 h
`IgG, 20 Da
`T cells, 3–4 wk
`Muscle, 2 wk
`Bone, 10 y
`Life span, 100 y
`
`figure 2 Time frames of turnover, life span, and half-life of various
`physiological materials, structures, and functions in humans. AChE,
`acetylcholinesterase; cAMP, adenosine 3’,5’-monophosphate; EEG,
`electroencephalogram; IgG, immunoglobulin G.
`
`indirect response model to capture the induction of neopterin
`(a classic biomarker of interferon-β receptor agonism) in concor-
`dance with known mechanisms. Two feedback signals account for
`altered drug and neopterin concentrations after multiple dosing,
`based on adaptation processes for receptor downregulation and
`reduced neopterin production. Relatively complex models are
`appearing with increasing frequency, fueled by advanced analyti-
`cal methods for measuring biomarkers, intermediary biosignals,
`and system components with high specificity and sensitivity, as
`well as by increased industrial, regulatory, and academic interest
`in using these models for drug development and pharmacologi-
`cal studies. The mechanistic assessment of the biological systems
`(e.g., calcium/bone metabolism) also offers the opportunity to
`extrapolate knowledge from one drug class to another and more
`quickly address new therapeutic targets.
`
`TranslaTional PK/Pd modeling
`Translational PK–PD modeling, shown in Figure 3, is the inte-
`gration of in silico, in vitro, and in vivo preclinical data with
`mechanism-based models to anticipate the effects of new drugs in
`humans and across levels of biological organization. Translational
`models hold promise to facilitate design and/or selection of lead
`compounds, selection of the first-in-human dose, early clinical
`trial design, and proof-of-concept studies of experimental drugs
`and drug combinations.10,11 This discussion will be limited to the
`scaling-up of PK–PD models developed in animals for applica-
`tion in humans. A recent review of quantitative structure–PK/PD
`relationships (QSPRs) describes approaches to predicting PK/PD
`profiles from in silico and in vitro experiments.12 Incidentally,
`considerable progress has been made in the field of toxicology,
`with QSPR models being combined with PBPK and PBPK–PD
`models to predict the exposure and dynamics of toxic chemicals
`in animals and humans.13,14 Implementing translational PK–PD
`methodology in the discovery and development of biotherapeu-
`tics has also been reviewed.15
`In any modeling endeavor, one begins by defining the goals
`and objectives of the analysis. These benchmarks will guide
`
`suitable dose levels is typically required to characterize the drug-
`specific parameters of the system.
`The third major component of pharmacodynamics is
` physiological turnover and homeostasis. For a simple open
` system (as shown at the bottom of Figure 1), the turnover of a
`substance, R, can be described by:
`R = k
`d
`in
`t
`d
`where the rate of change of R is determined by a zero-order pro-
`duction rate (kin) and a first-order removal rate constant (kout),
`and R0 is the initial value (kin/kout, assuming the steady-state
`value is time invariant). Indirect response models reflect inhi-
`bition or stimulation of either kin or kout.7 Biological materials,
`structures, or functions, many of which are used as biomark-
`ers of drug effects and disease processes, exhibit turnover rates
`over a large range of temporal scales (Figure 2). A knowledge
`of the turnover rates for physiological system components at
`the desired level of organization is important for identifying
`the rate-limiting steps for specific pharmacological responses
`and for assisting in the design of studies. Such information
`might also impact the characterization of feedback mechanisms
`which are abundant in physiology, given that both drugs and
`diseases often interfere with the normal biological cascades that
`are responsible for regulating the homeostasis of physiological
`systems. Time-dependent transduction steps can be factored
`into models; these are often a series of turnover processes that
`assemble into systems biology models.7
`Mechanism-based PD models, therefore, frequently reflect an
`integration of the basic components to describe and understand
`the complex interplay between the pharmacology of drug action
`and the (patho-)physiological control systems.7,8 One example is
`the target-mediated PK–PD model developed for interferon-β1a
`in monkeys.9 This model includes receptor binding as a key factor
`in both PK and PD processes and utilizes a precursor-dependent
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`development
`
`on the fractal nature of biological systems and energy balance.23
`In order to improve the translational potential of empirical PK
`models, nonlinear mixed-effects modeling has been coupled
`with allometric relationships24 and in vitro metabolism experi-
`ments as well.25
`The basic expectation for allometry in pharmacodynamics is
`that biological turnover rates in mechanistic models for most
`general structures and functions should be predictable among
`species on the basis of allometric principles, whereas intrinsic
`capacity (Emax) and sensitivity (EC50) to drugs tend to be similar
`across species. However, many genetic differences are also found.
`Brodie and colleagues were the first to examine some PK–PD
`properties across species, demonstrating interspecies differences
`in global terms such as duration of action and half-life, but simi-
`larities in plasma concentration on awakening following hexo-
`barbital administration.26 There has long been a case made for
`the usefulness of studying drug effects in preclinical models, and
`a general belief that the plasma drug concentration required for
`eliciting a certain (intensity of) action (e.g., EC50) is often similar
`in experimental animals and humans.27 While interspecies dif-
`ferences in relative receptor affinity and plasma protein binding
`often exist,28 several examples show reasonable concordance of
`such properties between rats and humans for congeneric series
`of drugs. Ito and colleagues demonstrated a linear correlation
`between the logarithm of equilibrium dissociation constants of
`benzodiazepines in the cerebral cortex tissue of rats and humans,
`of more than four orders of magnitude.29 Cox and co-workers
`also showed a similar relationship for the EC50 values of four syn-
`thetic opioids between these same two species.30 A retrospective
`analysis of S(+)-ketoprofen PK–PD parameters obtained from
`mechanistic modeling for two response biomarkers supports
`these basic expectations. Allometric scaling showed that PK
`parameters changed proportionally to body weight (albeit with
`unusual power coefficients) and PD parameters exhibited limited
`ranges in essentially a weight-independent manner.31
`Interspecies scaling has been applied to complex PK–PD
`models, including the hypothermic and cortisol responses to
`buspirone and flesinoxan (two 5-HT1A receptor agonists)32 and
`the effects of erythropoietin on reticulocytes, red blood cells, and
`hemoglobin levels in humans.33 Despite the relative complexity
`of the models, their diverse structural components, and the dif-
`ferences in the molecular sizes of the drugs, the prevailing obser-
`vations were that: (i) PK and physiological turnover parameters
`obeyed allometric principles, and (ii) pharmacological capacity
`and sensitivity parameters were essentially species-independent.
`Clinical trial simulations using the scaled models for buspirone
`and flesinoxan32 also suggest that such an approach may be
` useful for predicting responses in humans.
`
`conclusions
`Major advances have been made in mechanism-based modeling
`of drug responses in animals and humans based on the integra-
`tion of fundamental pharmacokinetic, pharmacological, and
`physiological processes. At present, the most common approach
`for transforming mechanistic models into translational PK–PD
`models is to utilize allometric principles for PK and turnover
`
`PK/PD models
`
`In silico: QSPR, various software
`
`Bioassays, physicochemical measurements
`
`PK: allometric scaling, PBPK models
`
`In vitro binding, drug metabolism
`
`Pharmocology: assume similar to start
`
`Ex vivo receptor binding, functional assays
`
`Physiology: allometric scaling, systems biology
`
`Biomarkers; pharmacogenetic screens
`
`figure 3 Components of mechanism-based pharmacokinetic–
`pharmacodynamic (PK–PD) models for translation of animal data to
`human clinical pharmacology. Predictive techniques (top of arrows) can be
`augmented by selective measurements (bottom of arrows). PBPK, physiology-
`based PK; QSPR, quantitative structure–PK/PD relationship.
`
`model development, determine the appropriate level of preci-
`sion and model detail (parsimony), and reveal methods to be
`used to qualify or validate the model. In addition, the successful
`use of PK–PD modeling and biomarker data is predicated on:
`(i) selection of mechanism-based biomarkers and their link with
`clinical end points, (ii) quantification of drug and/or metabo-
`lites in biological fluids under Good Laboratory Practices (GLP)
`conditions, (iii) GLP-like assay methods for biomarkers, and
`(iv) mechanism-based PK–PD modeling and validation.16
`Ideally, measurements of responses to drugs should be sensitive,
`gradual, reproducible, objective, and meaningful. Measurements
`in animal models need to reflect relevant processes in humans,
`thereby facilitating “proof-of-concept” studies.
`In order to scale up PK–PD models to anticipate outcomes
`in humans, structural models developed on the basis of data
`obtained from lower species should be applicable in humans,
`and the likelihood of this condition being met may or may
`not be known a priori. For example, the model developed for
`interferon-β1a in monkeys was shown to characterize its PK–PD
`properties well in human male volunteers.9,17 This was not unex-
`pected, given that most of the mechanisms and processes emu-
`lated by the model appear to be largely conserved across species,
`a feature often shared for many macromolecules.15 Although the
`structural nature of PBPK models makes them uniquely suited
`for scaling and predicting human drug exposures, the extrapo-
`lation of PK–PD models from animals to humans is primarily
`based on classical allometric relationships. Notwithstanding the
`controversies surrounding the prospective use of allometry18,19
`or the rationale for allometric correction factors20 for predicting
`PK properties in humans, there are general expectations that
`many physiological processes and organ sizes (θ) tend to obey
`a power law:21
` (3)
`θ = a . Wb
`where W is body weight and a and b are drug/process coeffi-
`cients. The allometric exponent, b, tends to be around 0.75 for
`clearance processes, 1.0 for organ sizes or physiological volumes,
`and 0.25 for physiological times or the duration of physiological
`events (e.g., heartbeat and breath duration, cell life span, and
`turnover times of endogenous substances or processes).22 West
`and colleagues describe a theoretical basis for allometry founded
`
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`development
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`parameters, whereas pharmacological terms are often fixed
`across species. In addition to the assessment of drug metabo-
`lism rates, receptor binding or functional assays are needed in
`situations where genetic differences are expected. New theo-
`retical and experimental approaches will be needed in order to
`identify the conditions under which allometry is appropriate,
`to screen efficiently for key differences, and to provide tech-
`niques for scaling-up complex biological and pharmacological
`systems, analogous to the enabling QSPR–PBPK methodology
`for intermolecular and interspecies PK predictions. Research is
`also needed for testing whether inclusion of disease state and
`progression in preclinical models is able to facilitate the predic-
`tion of the disease-modifying properties of drugs in early human
`testing. In any event, translational PK–PD modeling has the
`potential to direct and integrate pharmaceutical sciences toward
`the efficient design and development of novel drugs based on
`first principles.
`
`acKnowledgmenT
`This work was supported by Grant GM 57980 from the National Institutes of
`Health.
`
`conflicT of inTeresT
`The authors declared no conflict of interest.
`
`© 2008 American Society for Clinical Pharmacology and Therapeutics
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