Note on importance of correct stoichiometric assumptions for modeling of monoclonal antibodies.

Pharmacokinetic modeling of monoclonal antibodies (mAbs) with non-linear binding is based on equations of the target-mediated drug disposition (Mager and Jusko, J Pharmacokinet Pharmacodyn 28:507-532, 2001). These equations demonstrated their utility in countless examples and drug development programs. The model assumes that the mAb drug and the target have only one binding site each while, in reality, most antibodies have two binding sites. Thus, the currently used model does not correspond to the biological process that it aims to describe. The correct mechanistic model should take into account both binding sites. We investigated, using simulations, whether this discrepancy is important and when it is advisable to use a model with correct stoichiometric 2-to-1 ratio. We show that for soluble targets when elimination rate of the drug-target complex is comparable with the elimination rate of the drug or lower, and when measurements of both total drug and total target concentrations are available, the model with 1-to-1 (monovalent) binding cannot describe data simulated from the model with 2-to-1 (bivalent) binding. In these cases, models with correct stoichiometric assumptions may be necessary for an adequate description of the observed data. Also, a model with allosteric binding that encompasses both 2-to-1 and 1-to-1 binding models as particular cases was proposed and applied. It was shown to be identifiable given the detailed concentration data of total drug and total target.

Target-mediated drug disposition model for drugs with N > 2 binding sites that bind to a target with one binding site.

The paper extended the TMDD model to drugs with more than two (N > 2) identical binding sites (N-to-one TMDD). The quasi-steady-state (N-to-one QSS), quasi-equilibrium (N-to-one QE), irreversible binding (N-to-one IB), and Michaelis-Menten (N-to-one MM) approximations of the model were derived. To illustrate properties of new equations and approximations, N = 4 case was investigated numerically. Using simulations, the N-to-one QSS approximation was compared with the full N-to-one TMDD model. As expected, and similarly to the standard TMDD for monoclonal antibodies (mAb), N-to-one QSS predictions were nearly identical to N-to-one TMDD predictions, except for times of fast changes following initiation of dosing, when equilibrium has not yet been reached. Predictions for mAbs with soluble targets (slow elimination of the complex) were simulated from the full 4-to-one TMDD model and were fitted to the 4-to-one TMDD model and to its QSS approximation. It was demonstrated that the 4-to-one QSS model provided nearly identical description of not only the observed (simulated) total drug and total target concentrations, but also unobserved concentrations of the free drug, free target, and drug-target complexes. For mAb with a membrane-bound target, the 4-to-one MM approximation adequately described the data. The 4-to-one QSS approximation converged 8 times faster than the full 4-to-one TMDD.

Individual Components of Polymyxin B Modeled via Population Pharmacokinetics to Design Humanized Dosage Regimens for a Bloodstream and Lung Infection Model in Immune-Competent Mice.

Polymyxin B is a "last-line-of-defense" antibiotic approved in the 1960s. However, the population pharmacokinetics (PK) of its four main components has not been reported in infected mice. We aimed to determine the PK of polymyxin B1, B1-Ile, B2, and B3 in a murine bloodstream and lung infection model of Acinetobacter baumannii and develop humanized dosage regimens. A linear 1-compartment model, plus an epithelial lining fluid (ELF) compartment for the lung model, best described the PK. Clearance and volume of distribution were similar among the four components. The bioavailability fractions were 72.6% for polymyxin B1, 12.0% for B1-Ile, 11.5% for B2, and 3.81% for B3 for the lung model and were similar for the bloodstream model. While the volume of distribution was comparable between both models (17.3 mL for the lung and ~27 mL for the bloodstream model), clearance was considerably smaller for the lung (2.85 mL/h) compared to that of the bloodstream model (5.59 mL/h). The total drug exposure (AUC) in ELF was high due to the saturable binding of polymyxin B presumably to bacterial lipopolysaccharides. However, the modeled unbound AUC in ELF was ~16.7% compared to the total drug AUC in plasma. The long elimination half-life (~4 h) of polymyxin B enabled humanized dosage regimens with every 12 h dosing in mice. Daily doses that optimally matched the range of drug concentrations observed in patients were 21 mg/kg for the bloodstream and 13 mg/kg for the lung model. These dosage regimens and population PK models support translational studies for polymyxin B at clinically relevant drug exposures.

Is CD25 blockade optimal in kidney transplant patients treated with basiliximab? A target-mediated drug disposition model.

AIMS: Basiliximab, an anti-CD25 chimeric monoclonal antibody, is approved in prevention of acute kidney transplant rejection. This study aims at investigating target-mediated pharmacokinetics of basiliximab. METHODS: Data from the IDEALE study, where 16 kidney transplant patients were treated with 2 40- or 80-mg basiliximab injections, were reanalysed. Basiliximab pharmacokinetics was described using a population 2-compartment target-mediated drug disposition model with the quasi-steady-state approximation. RESULTS: Volume of distribution was significantly higher in males (P = .029). Estimated baseline target antigen (CD25) level was lower is patients cotreated with cyclosporine (P = .026). CONCLUSION: This analysis allows the first description of the target-mediated nonlinear elimination of basiliximab. Our results suggest that cyclosporine cotreatment is associated with decreased target level and that an optimized dosing regimen may improve basiliximab effects.

Estimating drug potency in the competitive target mediated drug disposition (TMDD) system when the endogenous ligand is included.

Predictions for target engagement are often used to guide drug development. In particular, when selecting the recommended phase 2 dose of a drug that is very safe, and where good biomarkers for response may not exist (e.g. in immuno-oncology), a receptor occupancy prediction could even be the main determinant in justifying the approved dose, as was the case for atezolizumab. The underlying assumption in these models is that when the drug binds its target, it disrupts the interaction between the target and its endogenous ligand, thereby disrupting downstream signaling. However, the interaction between the target and its endogenous binding partner is almost never included in the model. In this work, we take a deeper look at the in vivo system where a drug binds to its target and disrupts the target's interaction with an endogenous ligand. We derive two simple steady state inhibition metrics (SSIMs) for the system, which provides intuition for when the competition between drug and endogenous ligand should be taken into account for guiding drug development.

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.

Population pharmacokinetics and covariate analysis of Sym004, an antibody mixture against the epidermal growth factor receptor, in subjects with metastatic colorectal cancer and other solid tumors.

Sym004 is an equimolar mixture of two monoclonal antibodies, futuximab and modotuximab, which non-competitively block the epidermal growth factor receptor (EGFR). Sym004 has been clinically tested for treatment of solid tumors. The present work characterizes the non-linear pharmacokinetics (PK) of Sym004 and its constituent antibodies and investigates two types of covariate models for interpreting the interindividual variability of Sym004 exposure. Sym004 serum concentration data from 330 cancer patients participating in four Phase 1 and 2 trials (n = 247 metastatic colorectal cancer, n = 87 various types advanced solid tumors) were pooled for non-linear mixed effects modeling. Dose regimens of 0.4-18 mg/kg Sym004 dosed by i.v. infusion weekly or every 2nd week were explored. The PK profiles for futuximab and modotuximab were parallel, and the parameter values for their population PK models were similar. The PK of Sym004 using the sum of the serum concentrations of futuximab and modotuximab was well captured by a 2-compartment model with parallel linear and saturable, Michaelis-Menten-type elimination. The full covariate model including all plausible covariates included in a single step showed no impact on Sym004 exposure of age, Asian race, renal and hepatic function, tumor type and previous anti-EGFR treatments. The reduced covariate model contained statistically and potentially clinically significant influences of body weight, albumin, sex and baseline tumor size. Population PK modeling and covariate analysis of Sym004 were feasible using the sum of the serum concentrations of the two constituent antibodies. Full and reduced covariate models provided insights into which covariates may be clinically relevant for dose modifications and thus may need further exploration.

Nonlinear pharmacokinetics of rituximab in non-Hodgkin lymphomas: A pilot study.

AIMS: Rituximab is an anti-CD20 monoclonal antibody approved in non-Hodgkin lymphoma (NHL). This study aimed to assess the relationship between antigen mass and nonlinear pharmacokinetics of rituximab in NHL patients. METHODS: In a retrospective cohort of 25 NHL patients treated with rituximab, antigen mass was assessed at baseline by measuring metabolic tumour volume (MTV) by positron emission tomography. Rituximab pharmacokinetics was described using a semimechanistic 2-compartment model including a latent target antigen. Rituximab target-mediated elimination was described as irreversible binding between rituximab and it target. Histology (follicular or diffuse large B-cell lymphomas), initial MTV and body weight were tested as covariates on pharmacokinetic parameters. RESULTS: The model allowed a satisfactory description of rituximab serum concentrations. Target-mediated elimination was maximum at the beginning of treatment and became negligible towards the end of follow-up. The second-order elimination of rituximab due to target binding and complex elimination increased with baseline MTV. Central volume of distribution increased with body weight (P = .022) and baseline MTV (P = .005). CONCLUSIONS: This study quantified for the first time the target-mediated elimination of rituximab in NHL patients and confirmed rituximab retention by antigen mass.

Target-Mediated Population Pharmacokinetic Modeling of Endothelin Receptor Antagonists.

PURPOSE: 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. METHODS: 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. RESULTS: 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. CONCLUSION: 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.

Pharmacokinetics of the Monocarboxylate Transporter 1 Inhibitor AZD3965 in Mice: Potential Enterohepatic Circulation and Target-Mediated Disposition.

PURPOSE: To evaluate the pharmacokinetics (PK) of the monocarboxylate transporter 1 (MCT1) inhibitor AZD3965 in mice after IV and oral administration and to develop mechanistic PK models to assess the potential enterohepatic circulation (EHC) and target-mediated drug disposition (TMDD) of AZD3965. METHODS: Female BALB/c mice were administered AZD3965 by IV injection (10, 50 and 100 mg/kg) or oral gavage (100 mg/kg). Plasma samples were analyzed using LC/MS/MS, and PK parameters determined by compartmental and non-compartmental analyses. RESULTS: AZD3965 exhibited a large volume of distribution and rapid oral absorption, with a high oral bioavailability. Prominent reentry peaks were observed after both oral and IV administration, suggesting potential EHC of AZD3965 or of a potential glucuronide conjugate. The dose-dependent studies indicated greater than proportional increases in exposure, an increase in the terminal half-life, and decrease in clearance and volume of distribution with increasing IV doses, indicating nonlinear pharmacokinetics and potential TMDD of AZD3965. Mechanistic compartmental models were developed to characterize the complex pharmacokinetics of AZD3965. CONCLUSIONS: The current study represents the first comprehensive report of the pharmacokinetics of AZD3965 in mice, indicating the potential contribution of EHC and TMDD in the disposition of AZD3965.

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.

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.

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.

Mathematical modeling of antibody drug conjugates with the target and tubulin dynamics to predict AUC.

Antibody drug conjugates (ADCs)are one of the most recently developed chemotherapeutics to treat some types of tumor cells. They consist of monoclonal antibodies (mAbs), linkers, and potent cytotoxic drugs. Unlike common chemotherapies, ADCs combine selectively with a target at the surface of the tumor cell, and a potent cytotoxic drug (payload) effectively prevents microtubule polymerization. In this work, we construct an ADC model that considers both the target of antibodies and the receptor (tubulin) of the cytotoxic payloads. The model is simulated with brentuximab vedotin, one of ADCs, and used to investigate the pharmacokinetic (PK) characteristics of ADCs in vivo. It also predicts area under the curve (AUC) of ADCs and the payloads by identifying the half-life. The results show that dynamical behaviors fairly coincide with the observed data and half-life and capture AUC. Thus, the model can be used for estimating some parameters, fitting experimental observations, predicting AUC, and exploring various dynamical behaviors of the target and the receptor.

Absorption, metabolism and excretion of [14C]omarigliptin, a once-weekly DPP-4 inhibitor, in humans.

1. Omarigliptin (MARIZEV®) is a once-weekly DPP-4 inhibitor approved in Japan for the treatment of type 2 diabetes. The objective of this study was to investigate the absorption, metabolism and excretion of omarigliptin in humans. 2. Six healthy subjects received a single oral dose of 25 mg (2.1 µCi) [14 C]omarigliptin. Blood, plasma, urine and fecal samples were collected at various intervals for up to 20 days post-dose. Radioactivity levels in excreta and plasma/blood samples were determined by accelerator mass spectrometry (AMS). 3. [14 C]Omarigliptin was rapidly absorbed, with peak plasma concentrations observed at 0.5-2 h post-dose. The majority of the radioactivity was recovered in urine (∼74.4% of the dose), with less recovered in feces (∼3.4%), suggesting the compound was well absorbed. 4. Omarigliptin was the major component in urine (∼89% of the urinary radioactivity), indicating renal excretion of the unchanged drug as the primary clearance mechanism. Omarigliptin accounted for almost all the circulating radioactivity in plasma, with no major metabolites detected. 5. The predominantly renal elimination pathway, combined with the fact that omarigliptin is not a substrate of key drug transporters, suggest omarigliptin is unlikely to be subject to pharmacokinetic drug-drug interactions with other commonly prescribed agents.

Mathematical description of drug-target interactions: application to biologics that bind to targets with two binding sites.

The emerging discipline of mathematical pharmacology occupies the space between advanced pharmacometrics and systems biology. A characteristic feature of the approach is application of advance mathematical methods to study the behavior of biological systems as described by mathematical (most often differential) equations. One of the early application of mathematical pharmacology (that was not called this name at the time) was formulation and investigation of the target-mediated drug disposition (TMDD) model and its approximations. The model was shown to be remarkably successful, not only in describing the observed data for drug-target interactions, but also in advancing the qualitative and quantitative understanding of those interactions and their role in pharmacokinetic and pharmacodynamic properties of biologics. The TMDD model in its original formulation describes the interaction of the drug that has one binding site with the target that also has only one binding site. Following the framework developed earlier for drugs with one-to-one binding, this work aims to describe a rigorous approach for working with similar systems and to apply it to drugs that bind to targets with two binding sites. The quasi-steady-state, quasi-equilibrium, irreversible binding, and Michaelis-Menten approximations of the model are also derived. These equations can be used, in particular, to predict concentrations of the partially bound target (RC). This could be clinically important if RC remains active and has slow internalization rate. In this case, introduction of the drug aimed to suppress target activity may lead to the opposite effect due to RC accumulation.

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.

MPBPK-TMDD models for mAbs: alternative models, comparison, and identifiability issues.

The aim of the present study was to evaluate model identifiability when minimal physiologically-based pharmacokinetic (mPBPK) models are integrated with target mediated drug disposition (TMDD) models in the tissue compartment. Three quasi-steady-state (QSS) approximations of TMDD dynamics were explored: on (a) antibody-target complex, (b) free target, and (c) free antibody concentrations in tissue. The effects of the QSS approximations were assessed via simulations, taking as reference the mPBPK-TMDD model with no simplifications. Approximation (a) did not affect model-derived concentrations, while with the inclusion of approximation (b) or (c), target concentration profiles alone, or both drug and target concentration profiles respectively deviated from the reference model profiles. A local sensitivity analysis was performed, highlighting the potential importance of sampling in the terminal pharmacokinetic phase and of collecting target concentration data. The a priori and a posteriori identifiability of the mPBPK-TMDD models were investigated under different experimental scenarios and designs. The reference model and QSS approximation (a) on antibody-target complex were both found to be a priori identifiable in all scenarios, while under the further inclusion of QSS approximation (b) target concentration data were needed for a priori identifiability to be preserved. The property could not be assessed for the model including all three QSS approximations. A posteriori identifiability issues were detected for all models, although improvement was observed when appropriate sampling and dose range were selected. In conclusion, this work provides a theoretical framework for the assessment of key properties of mathematical models before their experimental application. Attention should be paid when applying integrated mPBPK-TMDD models, as identifiability issues do exist, especially when rich study designs are not feasible.

Target-mediated drug disposition with drug-drug interaction, Part I: single drug case in alternative formulations.

Target-mediated drug disposition (TMDD) describes drug binding with high affinity to a target such as a receptor. In application TMDD models are often over-parameterized and quasi-equilibrium (QE) or quasi-steady state (QSS) approximations are essential to reduce the number of parameters. However, implementation of such approximations becomes difficult for TMDD models with drug-drug interaction (DDI) mechanisms. Hence, alternative but equivalent formulations are necessary for QE or QSS approximations. To introduce and develop such formulations, the single drug case is reanalyzed. This work opens the route for straightforward implementation of QE or QSS approximations of DDI TMDD models. The manuscript is the first part to introduce DDI TMDD models with QE or QSS approximations.

Target mediated drug disposition with drug-drug interaction, Part II: competitive and uncompetitive cases.

We present competitive and uncompetitive drug-drug interaction (DDI) with target mediated drug disposition (TMDD) equations and investigate their pharmacokinetic DDI properties. For application of TMDD models, quasi-equilibrium (QE) or quasi-steady state (QSS) approximations are necessary to reduce the number of parameters. To realize those approximations of DDI TMDD models, we derive an ordinary differential equation (ODE) representation formulated in free concentration and free receptor variables. This ODE formulation can be straightforward implemented in typical PKPD software without solving any non-linear equation system arising from the QE or QSS approximation of the rapid binding assumptions. This manuscript is the second in a series to introduce and investigate DDI TMDD models and to apply the QE or QSS approximation.