Target-mediated Drug Disposition Model Research Articles

Population pharmacokinetics and pharmacodynamics of a novel vascular adhesion protein-1 inhibitor using a multiple-target mediated drug disposition model

ASP8232 is a novel inhibitor of vascular adhesion protein-1 that was under evaluation for reducing residual albuminuria in patients with diabetic kidney disease. To characterize the pharmacokinetics (PK) of ASP8232 and its effect on vascular adhesion protein 1 (VAP-1) plasma activity and VAP-1 concentrations (pharmacodynamics, PD) in an integrated and quantitative manner, a target mediated drug disposition model was developed based on pooled data from four completed clinical trials with ASP8232 in healthy volunteers, and in patients with diabetic kidney disease and diabetic macular edema, respectively. In this model, the binding of ASP8232 to its soluble and membrane-bound target in the central and peripheral compartments were included. The model was able to adequately describe the non-linear PK and PD of ASP8232. The observed difference in PK between healthy volunteers and renally impaired patients could be explained by an effect of baseline estimated glomerular filtration rate on ASP8232 clearance and relative bioavailability. The relationship between ASP8232 concentration and VAP-1 inhibition was successfully established and can be applied to simulate drug exposure and degree of VAP-1 inhibition for any given dose of ASP8232 across the spectrum of renal function.

Target-mediated exposure enhancement: a previously unexplored limit of TMDD.

Target-mediated drug disposition (TMDD) is often observed for targeted therapeutics, and manifests as decreases in clearance and volume of distribution with increasing dose as a result of saturable, high affinity target binding. In the present work, we demonstrate that classically defined TMDD is just one of the characteristic features of the system. In fact, for molecules with rapid non-specific elimination relative to target-mediated elimination, binding to target may actually lead to improved exposure at sub-saturating doses. This feature, which we refer to as target-mediated exposure enhancement (TMEE), produces the opposite trend to classical TMDD, i.e., with increasing dose levels, clearance and volume of distribution will also increase. The general model of TMDD was able to well-characterize the pharmacokinetics of two molecules that display TMEE, ALX-0081 and linagliptin. Additional fittings using the commonly reported TMDD model approximations revealed that both the quasi-equilibrium and quasi-steady-state approximations were able to well-describe TMEE; however, the Michaelis-Menten approximation was unable to describe this behavior. With the development of next-generation therapeutics with high affinity for target and rapid non-specific elimination, such as antibody fragments and peptides, this previously unexplored limit of TMDD is anticipated to become increasingly relevant for describing pharmacokinetics of investigational therapeutics.

Simultaneous Target-Mediated Drug Disposition Model for Two Small-Molecule Compounds Competing for Their Pharmacological Target: Soluble Epoxide Hydrolase.

1-(1-propanoylpiperidin-4-yl)-3-[4-(trifluoromethoxy)phenyl]urea (TPPU) and 1-(4-trifluoro-methoxy-phenyl)-3-(1-cyclopropanecarbonyl-piperidin-4-yl)-urea (TCPU) are potent inhibitors of soluble epoxide hydrolase (sEH) that have much better efficacy in relieving nociceptive response than the Food and Drug Administration-approved drug gabapentin in a rodent model of diabetic neuropathy. Experiments conducted in sEH knockout mice or with coadministration of a potent sEH displacer demonstrated that the pharmacokinetics of TPPU and TCPU were influenced by the specific binding to their pharmacologic target sEH, a phenomenon known as target-mediated drug disposition (TMDD). To quantitatively characterize the complex pharmacokinetics of TPPU and TCPU and gain better understanding on their target occupancy, population pharmacokinetics analysis using a nonlinear mixed-effect modeling approach was performed in the current study. The final model was a novel simultaneous TMDD interaction model, in which TPPU and TCPU compete for sEH, with TCPU binding to an additional unknown target pool with larger capacity that we refer to as a refractory pool. The total amount of sEH enzyme in mice was predicted to be 16.2 nmol, which is consistent with the experimental value of 10 nmol. The dissociate rate constants of TPPU and TCPU were predicted to be 2.24 and 2.67 hours-1, respectively, which is close to the values obtained from in vitro experiments. Our simulation result predicted that 90% of the sEH will be occupied shortly after a low dose of 0.3 mg/kg TPPU administration, with ≥40% of sEH remaining to be bound with TPPU for at least 7 days. Further efficacy experiments are warranted to confirm the predicted target occupancy. SIGNIFICANCE STATEMENT: Although target-mediated drug disposition (TMDD) models have been well documented, most of them were established in a single compound scenario. Our novel model represents the first TMDD interaction model for two small-molecule compounds competing for the same pharmacological target.

Transitioning from Basic toward Systems Pharmacodynamic Models: Lessons from Corticosteroids.

Technology in bioanalysis, -omics, and computation have evolved over the past half century to allow for comprehensive assessments of the molecular to whole body pharmacology of diverse corticosteroids. Such studies have advanced pharmacokinetic and pharmacodynamic (PK/PD) concepts and models that often generalize across various classes of drugs. These models encompass the "pillars" of pharmacology, namely PK and target drug exposure, the mass-law interactions of drugs with receptors/targets, and the consequent turnover and homeostatic control of genes, biomarkers, physiologic responses, and disease symptoms. Pharmacokinetic methodology utilizes noncompartmental, compartmental, reversible, physiologic [full physiologically based pharmacokinetic (PBPK) and minimal PBPK], and target-mediated drug disposition models using a growing array of pharmacometric considerations and software. Basic PK/PD models have emerged (simple direct, biophase, slow receptor binding, indirect response, irreversible, turnover with inactivation, and transduction models) that place emphasis on parsimony, are mechanistic in nature, and serve as highly useful "top-down" methods of quantitating the actions of diverse drugs. These are often components of more complex quantitative systems pharmacology (QSP) models that explain the array of responses to various drugs, including corticosteroids. Progressively deeper mechanistic appreciation of PBPK, drug-target interactions, and systems physiology from the molecular (genomic, proteomic, metabolomic) to cellular to whole body levels provides the foundation for enhanced PK/PD to comprehensive QSP models. Our research based on cell, animal, clinical, and theoretical studies with corticosteroids have provided ideas and quantitative methods that have broadly advanced the fields of PK/PD and QSP modeling and illustrates the transition toward a global, systems understanding of actions of diverse drugs. SIGNIFICANCE STATEMENT: Over the past half century, pharmacokinetics (PK) and pharmacokinetics/pharmacodynamics (PK/PD) have evolved to provide an array of mechanism-based models that help quantitate the disposition and actions of most drugs. We describe how many basic PK and PK/PD model components were identified and often applied to the diverse properties of corticosteroids (CS). The CS have complications in disposition and a wide array of simple receptor-to complex gene-mediated actions in multiple organs. Continued assessments of such complexities have offered opportunities to develop models ranging from simple PK to enhanced PK/PD to quantitative systems pharmacology (QSP) that help explain therapeutic and adverse CS effects. Concurrent development of state-of-the-art PK, PK/PD, and QSP models are described alongside experimental studies that revealed diverse CS actions.

GQSPSim: A SimBiology-Based GUI for Standardized QSP Model Development and Application.

Quantitative systems pharmacology (QSP) models are often implemented using a wide variety of technical workflows and methodologies. To facilitate reproducibility, transparency, portability, and reuse for QSP models, we have developed gQSPSim, a graphical user interface–based MATLAB application that performs key steps in QSP model development and analyses. The capabilities of gQSPSim include (i) model calibration using global and local optimization methods, (ii) development of virtual subjects to explore variability and uncertainty in the represented biology, and (iii) simulations of virtual populations for different interventions. gQSPSim works with SimBiology‐built models using components such as species, doses, variants, and rules. All functionalities are equipped with an interactive visualization interface and the ability to generate presentation‐ready figures. In addition, standardized gQSPSim sessions can be shared and saved for future extension and reuse. In this work, we demonstrate gQSPSim’s capabilities with a standard target‐mediated drug disposition model and a published model of anti‐proprotein convertase subtilisin/kexin type 9 (PCSK9) treatment of hypercholesterolemia.

Modeling and Simulation of the Pharmacokinetics and Target Engagement of an Antagonist Monoclonal Antibody to Interferon-γ-Induced Protein 10, BMS-986184, in Healthy Participants to Guide Therapeutic Dosing.

BMS‐986184 is a human, second‐generation, anti–interferon‐γ–induced protein 10 (IP‐10) monoclonal antibody. In this study the pharmacokinetics and target engagement (TE) of BMS‐986184 in healthy participants were characterized using population‐based target‐mediated drug disposition (TMDD) modeling and data from a first‐in‐human study (NCT02864264). The results of the first‐in‐human study and the model generated were used to conduct stochastic simulations of a virtual population of healthy participants to predict pharmacokinetic exposures and TE responses for different dosage regimens. A 2‐compartment, 2‐target, TMDD structural model, assuming quasi‐steady‐state and stimulated production on treatment, was developed by simultaneous fitting of the total drug, serum‐free IP‐10, and serum total IP‐10 concentration data, with the second unobservable target contribution to drug elimination described by the Michaelis‐Menten elimination term. Model evaluation confirmed agreement between model predictions and observed data. Simulation of a virtual population of healthy individuals demonstrated that steady state was reached at the eighth dosing interval, and that around 150 mg subcutaneously every other week could be a suitable target dosage regimen for future clinical trials. Integrated modeling strategies such as this can be used to help guide rational clinical trial development of drugs with TMDD, leading to improved dose selection and greater patient benefits.

Pharmacokinetics and pharmacodynamic effect of crenezumab on plasma and cerebrospinal fluid beta-amyloid in patients with mild-to-moderate Alzheimer\u2019s disease

BackgroundCrenezumab, a fully humanized anti-beta-amyloid (Aβ) immunoglobulin G4 (IgG4) monoclonal antibody, binds to both monomeric and aggregated forms of Aβ. We assessed the pharmacokinetics (PK)/pharmacodynamics (PD) of crenezumab and its interaction with monomeric Aβ(1–40) and Aβ(1–42) peptides in serum/plasma and cerebrospinal fluid (CSF) samples from the phase II ABBY and BLAZE studies and the phase Ib GN29632 study.MethodsIn ABBY, BLAZE, and GN29632 studies, patients with mild-to-moderate AD were treated with either placebo or crenezumab (300 mg subcutaneously every 2 weeks [q2w], or 15 mg/kg, 30 mg/kg, 45 mg/kg, 60 mg/kg, or 120 mg/kg intravenously q4w). Serum/plasma PK/PD analyses included samples from 131 patients who received crenezumab in all three studies. CSF PK/PD analyses included samples from 76 patients who received crenezumab in ABBY or BLAZE. The impact of baseline patient factors on Aβ profiles was also evaluated.ResultsThe serum concentration of crenezumab increased in a dose-proportional manner between 15 and 120 mg/kg q4w. Total monomeric plasma Aβ(1–40) and Aβ(1–42) levels significantly increased after crenezumab administration. The mean crenezumab CSF to serum ratio was ~ 0.3% and was similar across dosing cohorts/routes of administration. No clear correlation was observed between crenezumab concentration and Aβ(1–42) increase in CSF at week 69. The target-mediated drug disposition (TMDD) model described the observed plasma concentration–time profiles of crenezumab and Aβ well. Elimination clearance (CLel) and central volume of distribution (Vcent) of crenezumab were estimated at 0.159 L/day and 2.89 L, respectively, corresponding to a half-life of ~ 20 days. Subcutaneous bioavailability was estimated at 66.2%.ConclusionsCrenezumab PK was dose proportional up to 120 mg/kg, with a half-life consistent with IgG monoclonal antibodies. Our findings provide evidence for peripheral target engagement in patients with mild-to-moderate AD. The study also showed that a model-based approach is useful in making inference on PK/PD relationship with unmeasured species such as free plasma Aβ levels.Trial registrationsABBY: ClinicalTrials.gov, NCT01343966. Registered April 28, 2011. BLAZE: ClinicalTrials.gov, NCT01397578. Registered July 19, 2011. GN29632: ClinicalTrials.gov, NCT02353598. Registered February 3, 2015.

Target-Mediated Population Pharmacokinetic Modeling of Endothelin Receptor Antagonists.

Bosentan, clazosentan, and tezosentan are three small-molecule endothelin receptor antagonists (ERAs), displacing endothelin-1 (ET-1) from its binding site. A target-mediated drug disposition (TMDD) pharmacokinetic (PK) model described the non-linearity in the PK of bosentan caused by its high receptor binding affinity with time-dependent varying receptor expression or reappearance. The aim of this analysis was to investigate the presence of TMDD for clazosentan and tezosentan and to corroborate the hypothesis of a diurnal receptor synthesis. PK data from healthy subjects after intravenous (i.v.) administration of single ascending doses of bosentan, clazosentan, and tezosentan were analyzed. Frequent blood samples for PK measurements were collected. Population analyses, simulations, and evaluations were performed using a non-linear mixed-effects modeling approach. Two-compartment TMDD models were successfully developed describing the PK of all three ERAs with different receptor-complex internalization properties. The observed multiple peaks in the concentration-time profiles were captured with cosine functions on the receptor synthesis rate mimicking a diurnal receptor expression or reappearance. The results strongly suggest that TMDD is a class effect of ERAs. The developed TMDD PK models are a next step towards understanding the complex PK of ERAs and further support the hypothesis that TMDD is a class effect of ERAs.

Comparing Model Performance in Characterizing the PK/PD of the Anti‐Myostatin Antibody Domagrozumab

Modeling and simulation provides quantitative information on target coverage for dose selection. Optimal model selection often relies on fit criteria and is not necessarily mechanistically driven. One such case is discussed where healthy volunteer data of an anti‐myostatin monoclonal antibody domagrozumab were used to develop different target‐mediated drug disposition models; a quasi‐steady state (QSS) rapid binding approximation model, a Michaelis−Menten (MM)‐binding kinetics (MM‐BK) model, and an MM‐indirect response (MM‐IDR) model. Whereas the MM‐BK model was identified as optimal in fitting the data, with all parameters estimated with high precision, the QSS model also converged but was not able to capture the nonlinear decline. Although the least mechanistic model, MM‐IDR, had the lowest objective function value, the MM‐BK model was further developed as it provided a reasonable fit and allowed simulations regarding growth differentiation factor‐8 target coverage for phase II dose selection with sufficient certainty to allow for testing of the underlying mechanistic assumptions.

Tumor necrosis factor-mediated disposition of infliximab in ulcerative colitis patients

Ulcerative Colitis (UC) is an inflammatory bowel disease typically affecting the colon. Patients with active UC have elevated tumor necrosis factor (TNF) concentrations in serum and colonic tissue. Infliximab is a monoclonal antibody directed against TNF and binds with high affinity. Target-mediated drug disposition (TMDD) is reported for monoclonal antibodies meaning that their pharmacokinetics are affected by high target affinity. Here, a TMDD model is proposed to describe the interaction between infliximab and TNF in UC patients. Data from 20 patients with moderate to severe UC was used. Patients received standard infliximab induction therapy (5 mg kg−1) at week 0, followed by infusions at week 2 and 6. IFX, anti-drug antibodies and TNF serum concentrations were measured at day 0 (1 h after infusion), 1, 4, 7, 11, 14, 18, 21, 28 and 42. A binding model, TMDD model, and a quasi-steady state (QSS) approximation were evaluated using nonlinear mixed effects modeling (NONMEM). A two-compartment model best described the concentration–time profiles of infliximab. Typical clearance of infliximab was 0.404 L day−1 and increased with the presence of anti-drug antibodies and with lower albumin concentrations. The TMDD-QSS model best described the pharmacokinetic and pharmacodynamics data. Estimate for TNF baseline (Bmax was 19.8 pg mL−1 and the dissociation constant (Kss) was 13.6 nM. This model could eventually be used to investigate the relationship between suppression of TNF and the response to IFX therapy.

Abstract 678: Drug-induced TMDD: a novel class of PK models relevant to Immune-stimulating therapies

Abstract Purpose: Many biologics exhibit target-mediated drug disposition (TMDD). That is, given the high affinity and low doses typical for antibody-based therapeutics, drug clearance is often mediated through target binding and endocytosis, in addition to 1st-order elimination processes. Accounting for the process of TMDD in pharmacokinetic (PK) models is thus necessary to describe and predict drug exposure. TMDD is typically characterized by dose-dependent clearance, wherein drug elimination is faster at lower doses. In standard TMDD-models, target concentration and turnover are assumed to be constant. While this is generally a good approximation, the assumption does not always hold. Immune-stimulating drugs are the largest class of agents currently being developed in oncology, including checkpoint inhibitors (PD-1/PD-L1, CTLA4), cytokines (IL-2, IL-15), and immune agonists (GITR, OX40, ICOS). For immune-stimulating agents, drug treatment may induce lymphocyte proliferation, expanding the pool of target along with the target-expressing cells. TMDD in such cases is thus induced by drug treatment, and thereby target burden is dynamic; both dose- and time- dependent. PK dose response profiles in such cases could exhibit very different characteristics from standard (static) TMDD. Methods: The goal of this work is to invest the role of target dynamics on drug pharmacokinetics (PK) and receptor occupancy (RO). To do so, we have developed a mathematical modelling construct termed ‘Drug-induced TMDD’, wherein drug-target binding induces increase of the target synthesis rate, subsequently target concentration, leading to enhanced TMDD. We incorporate this construct into a 2-compartment model typical of monoclonal antibodies. Simulations were then used to characterize how dose, drug-target affinity, and the amplitude and the delay in target up-regulation affect the PK and RO profiles, and compared static vs. drug-induced TMDD behavior. Results: For Drug-induced TMDD, target expression increases with increased target engagement. This creates a pseudo-negative-feedback circuit, wherein the rate of TMDD-mediated clearance is dependent upon drug concentration. As a result, drug clearance does not appear dose-proportional at low doses, as is typical of static-TMDD. The AUC of drug concentration for drug-induced TMDD can be higher than static TMDD at low doses, but lower at higher doses. Similar results are predicted for the AUC of RO as well with the nominal parameter set. Increasing target affinity (decreasing KD) however results in faster clearance, typical of both cases of TMDD. Conclusions: Dynamic-TMDD could lead to different dose-dependent PK and RO behaviors from a static TMDD. Based on these characteristic profiles presented, one can determine whether a static vs. drug-induced TMDD model may be required for PK modelling, particularly important consideration for immune-stimulating biologics. Citation Format: Fei Hua, David Flowers, Daniel C. Kirouac, John M. Burke, Joshua F. Apgar. Drug-induced TMDD: a novel class of PK models relevant to Immune-stimulating therapies [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2019; 2019 Mar 29-Apr 3; Atlanta, GA. Philadelphia (PA): AACR; Cancer Res 2019;79(13 Suppl):Abstract nr 678.

Guiding dose selection of monoclonal antibodies using a new parameter (AFTIR) for characterizing ligand binding systems.

Guiding the dose selection for monoclonal antibody oncology drugs is often done using methods for predicting the receptor occupancy of the drug in the tumor. In this manuscript, previous work on characterizing target inhibition at steady state using the AFIR metric (Stein and Ramakrishna in CPT Pharmacomet Syst Pharmacol 6(4):258-266, 2017) is extended to include a "target-tissue" compartment and the shedding of membrane-bound targets. A new potency metric average free tissue target to initial target ratio (AFTIR) at steady state is derived, and it depends on only four key quantities: the equilibrium binding constant, the fold-change in target expression at steady state after binding to drug, the biodistribution of target from circulation to target tissue, and the average drug concentration in circulation. The AFTIR metric is useful for guiding dose selection, for efficiently performing sensitivity analyses, and for building intuition for more complex target mediated drug disposition models. In particular, reducing the complex, physiological model to four key parameters needed to predict target inhibition helps to highlight specific parameters that are the most important to estimate in future experiments to guide drug development.

Geometric singular perturbation analysis of a dynamical target mediated drug disposition model.

In this paper we present a mathematical analysis of a pharmacological ODE model for target mediated drug disposition (TMDD). It is known that solutions of this model undergo four qualitatively different phases. In this paper we provide a mathematical identification of these separate phases by viewing the TMDD model as a singular perturbed system. Our analysis is based on geometric singular perturbation theory and we believe that this approach systemizes-and sheds further light on-the scalings arguments used by previous authors. In particular, we present a novel description of the third phase through a distinguished solution of a nonlinear differential equation. We also describe the solution curve for large values of initial drug doses and recover, en route, a result by Aston et al. (J Math Biol 68(6):1453-1478, 2014) on rebounding using our alternative perturbation approach. Finally, from our main result we derive a new method for estimating the parameters of the system in the event that detailed data is available. Ideally our approach to the TMDD model should stimulate further research into applications of these methods to more complicated models in pharmacology.

Target-Mediated Drug Disposition Model for Bispecific Antibodies: Properties, Approximation, and Optimal Dosing Strategy.

Bispecific antibodies (BsAbs) bind to two different targets, and create two binary and one ternary complex (TC). These molecules have shown promise as immuno‐oncology drugs, and the TC is considered the pharmacologically active species that drives their pharmacodynamic effect. Here, we have presented a general target‐mediated drug disposition (TMDD) model for these BsAbs, which bind to two different targets on different cell membranes. The model includes four different binding events for BsAbs, turnover of the targets, and internalization of the complexes. In addition, a quasi‐equilibrium (QE) approximation with decreased number of binding parameters and, if necessary, reduced internalization parameters is presented. The model is further used to investigate the kinetics of BsAb and TC concentrations. Our analysis shows that larger doses of BsAbs may delay the build‐up of the TC. Consequently, a method to compute the optimal dosing strategy of BsAbs, which will immediately create and maintain maximal possible TC concentration, is presented.

Simulation-based simplification of target-mediated drug disposition model of denosumab

Simulation-based simplification of target-mediated drug disposition model of denosumab

General Pharmacokinetic Features of Small-Molecule Compounds Exhibiting Target-Mediated Drug Disposition (TMDD): A Simulation-Based Study.

Although target-mediated drug disposition (TMDD) can occur in both large- and small-molecule compounds, TMDD in small-molecule compounds has received much less attention due to its lower prevalence. To facilitate the identification of nonlinear pharmacokinetics of small-molecule compounds caused by TMDD, a comprehensive simulation was conducted in the current study to provide the general pharmacokinetic features of small-molecule compounds exhibiting TMDD. Various conditions, including single escalating intravenous bolus doses, multiple escalating intravenous bolus doses, and intravenous infusion, were simulated for small-molecule compounds with saturable binding to (1) targets located in tissues and (2) targets located in plasma. Sobol global sensitivity analysis was performed to evaluate the impact of key parameters (Rmax , kon and koff ) in a small-molecule TMDD model on the apparent volume of distribution and apparent clearance. Our simulation data indicated that small-molecule compounds with saturable binding to targets in plasma demonstrate distinctly different TMDD behavior compared with those with binding to targets in tissue. Sobol global sensitivity analysis results showed that, in general, koff is much more influential than kon and Rmax on apparent clearance and apparent volume of distribution. The TMDD features predicted in various situations in the current work could serve as a valuable reference to help quickly recognize TMDD when it does happen in a small-molecule compound. The TMDD principals summarized based on our simulation could be used to aid pharmacokinetic data interpretation, dose regimen optimization, and clinical trial design of small-molecule drugs exhibiting TMDD.

Lack of ethnic differences in the pharmacokinetics and pharmacodynamics of evolocumab between Caucasian and Asian populations.

To evaluate the potential ethnic differences in the pharmacokinetics (PK) and pharmacodynamics (PD) of evolocumab in Caucasian and Asian populations using population PK/PD modelling analysis. Data from different ethnic groups in 5 Phase I clinical trials, including two American studies, one Japanese study and two Chinese studies, were chosen for model building and evaluation. A target-mediated drug disposition model together with an indirect response model best captured evolocumab binding and the removal of unbound proprotein convertase subtilisin/kexin type 9 (PCSK9) as well as a reduction in circulating low-density lipoprotein cholesterol (LDL-C). Ethnicity and other related factors (body weight, target expression level etc.) were analysed as potential covariates. The estimated linear clearance and volume of evolocumab were 0.24lday-1 and 2.75l, respectively, which was consistent with the previous modelling results from the American trials. The time course of the LDL-C reduction was described by an indirect response model with the elimination rate of LDL-C being modulated by unbound PCSK9. The concentration of unbound PCSK9 associated with the half-maximal inhibition of LDL-C elimination was 1.28nmoll-1 . Both the PK and PD characteristics were consistent between the Caucasian and Asian populations. The target-mediated drug disposition model successfully described the PK and PD characteristics of evolocumab, and this analysis found no significant differences in the PK/PD relationship for its LDL-C lowering effects between Caucasians and Asians.

Predicting the Onset of Nonlinear Pharmacokinetics.

When analyzing the pharmacokinetics (PK) of drugs, one is often faced with concentration C vs. time curves, which display a sharp transition at a critical concentration C crit. For C > C crit, the curve displays linear clearance and for C < C crit clearance increases in a nonlinear manner as C decreases. Often, it is important to choose a high enough dose such that PK remains linear in order to help ensure that continuous target engagement is achieved throughout the duration of therapy. In this article, we derive a simple expression for C crit for models involving linear and nonlinear (saturable) clearance, such as Michaelis‐Menten and target‐mediated drug disposition (TMDD) models.Study Highlights

Reduced and optimized trial designs for drugs described by a target mediated drug disposition model

Monoclonal antibodies against soluble targets are often rich and include the sampling of multiple analytes over a lengthy period of time. Predictive models built on data obtained in such studies can be useful in all drug development phases. If adequate model predictions can be maintained with a reduced design (e.g. fewer samples or shorter duration) the use of such designs may be advocated. The effect of reducing and optimizing a rich design based on a published study for Omalizumab (OMA) was evaluated as an example. OMA pharmacokinetics were characterized using a target-mediated drug disposition model considering the binding of OMA to free IgE and the subsequent formation of an OMA–IgE complex. The performance of the reduced and optimized designs was evaluated with respect to: efficiency, parameter uncertainty and predictions of free target. It was possible to reduce the number of samples in the study by 30% while still maintaining an efficiency of almost 90%. A reduction in sampling duration by two-thirds resulted in an efficiency of 75%. Omission of any analyte measurement or a reduction of the number of dose levels was detrimental to the efficiency of the designs (efficiency ≤ 51%). However, other metrics were, in some cases, relatively unaffected, showing that multiple metrics may be needed to obtain balanced assessments of design performance.

Asymptotic analysis of a TMDD model: when a reaction contributes to the destruction of its product.

The multi-scale dynamics of a two-compartment with first order absorption Target-Mediated Drug Disposition (TMDD) pharmacokinetics model is analysed, using the Computational Singular Perturbation (CSP) algorithm. It is shown that the process evolves along two Slow Invariant Manifolds (SIMs), on which the most intense components of the model are equilibrated, so that the less intensive are the driving ones. The CSP tools allow for the identification of the components of the TMDD model that (i) constrain the evolution of the process on the SIMs, (ii) drive the system along the SIMs and (iii) generate the fast time scales. Among others, such diagnostics identify (i) the factors that determine the start and the duration of the period in which the ligand-receptor complex acts and (ii) the processes that determine its degradation rate. The counterintuitive influence of the process that transfers the ligand from the tissue to the main compartment, as it is manifested during the final stage of the process, is studied in detail.