The utility of modeling and simulation approaches to evaluate immunogenicity effect on the therapeutic protein pharmacokinetics

A Model-Based Approach to Evaluate Anti-Drug Antibody Impact on Drug Exposure With Biologics: A Case Example With the CD3 T-Cell Bispecific Cibisatamab

The administration of biologics can lead to immunogenic responses that trigger anti-drug antibody (ADA) formation. ADAs can decrease drug exposure. A population pharmacokinetic (popPK) model was developed to describe clinical PK data with and without ADA-driven exposure loss with CEA-directed T-cell bispecific antibody cibisatamab. The PK of cibisatamab was evaluated in two clinical studies (as a single agent and in combination with the checkpoint inhibitor atezolizumab) in patients. The popPK model was developed on cibisatamab clinical PK data using the Stochastic Approximation -Expectation Maximization (SAEM) algorithm implemented in Monolix. Cibisatamab's PK followed a two-compartment model with linear clearance decreasing over time and ADA-associated exposure loss. ADA-driven exposure loss was implemented in the model by accounting for ADA formation, reversible binding to cibisatamab, and elimination of both free ADA and the ADA-cibisatamab complex from the central compartment. The impact of ADAs on PK exposure was time-dependent in the model, with the ADA formation described as a function of time (increasing from zero, reaching its estimated maximum value, and possibly decreasing down to 94% of this maximum value in some patients). The final model included a mixture component differentiating patients with and without exposure loss due to ADA formation (75% and 25% of patients, respectively). The investigated patient demographics, dose or dosing schedule, or atezolizumab coadministration were not identified as factors influencing exposure loss due to ADAs. The developed model can be used to differentiate patients with and without ADA-driven exposure loss, as well as for a precise PK characterization in patients even with ADA formation.

An overview of immunotoxicity in drug discovery and development

The immune system is one of the common targets of drugs' toxicity (Immunotoxicity) and/or efficacy (Immunotherapy). Immunotoxicity leads to adverse effects on human health, which raises serious concerns for the regulatory agencies. Currently, immunotoxicity assessment is conducted using different in vitro and in vivo assays. In silico and in vitro human cell-based immunotoxicity assays should also be explored for screening purposes as these are time and cost effective as well as for ethical reasons. For in vivo studies, tier 1-3 assessments (Tier 1: hematology, serum globulin levels, lymphoid organ's weight and histopathology; Tier 2: immunophenotyping, TDAR and cell mediated immunity; and Tier 3: host resistance) should be used. These non-clinical in vivo assessments are useful to select immunological endpoints for clinical trials as well as for precautionary labeling. As per regulatory guidelines, adverse immunogenicity information of drug should be included in product's labeling to make health care practitioner aware of safety concerns before prescribing medicines and patient management (USFDA, 2022a, 2022b). This review mainly focuses on the importance of immunotoxicity assessment during drug discovery and development.

Mathematical Models to Characterize the Absorption, Distribution, Metabolism, and Excretion of Protein Therapeutics

Therapeutic proteins (TPs) have ranked among the most important and fastest-growing classes of drugs in the clinic, yet the development of successful TPs is often limited by unsatisfactory efficacy. Understanding pharmacokinetic (PK) characteristics of TPs is key to achieving sufficient and prolonged exposure at the site of action, which is a prerequisite for eliciting desired pharmacological effects. PK modeling represents a powerful tool to investigate factors governing in vivo disposition of TPs. In this mini-review, we discuss many state-of-the-art models that recapitulate critical processes in each of the absorption, distribution, metabolism/catabolism, and excretion pathways of TPs, which can be integrated into the physiologically-based pharmacokinetic framework. Additionally, we provide our perspectives on current opportunities and challenges for evolving the PK models to accelerate the discovery and development of safe and efficacious TPs. SIGNIFICANCE STATEMENT: This minireview provides an overview of mechanistic pharmacokinetic (PK) models developed to characterize absorption, distribution, metabolism, and elimination (ADME) properties of therapeutic proteins (TPs), which can support model-informed discovery and development of TPs. As the next-generation of TPs with diverse physicochemical properties and mechanism-of-action are being developed rapidly, there is an urgent need to better understand the determinants for the ADME of TPs and evolve existing platform PK models to facilitate successful bench-to-bedside translation of these promising drug molecules.

Modeling approaches for reducing safety-related attrition in drug discovery and development: a review on myelotoxicity, immunotoxicity, cardiovascular toxicity, and liver toxicity

Introduction:Safety and tolerability is a critical area where improvements are needed to decrease the attrition rates during development of new drug candidates. Modeling approaches, when smartly implemented, can contribute to this aim.Areas covered:The focus of this review was on modeling approaches applied to four kinds of drug-induced toxicities: hematological, immunological, cardiovascular (CV) and liver toxicity. Papers, mainly published in the last 10 years, reporting models in three main methodological categories - computational models (e.g., quantitative structure-property relationships, machine learning approaches, neural networks, etc.), pharmacokinetic-pharmacodynamic (PK-PD) models, and quantitative system pharmacology (QSP) models - have been considered.Expert opinion:The picture observed in the four examined toxicity areas appears heterogeneous. Computational models are typically used in all areas as screening tools in the early stages of development for hematological, cardiovascular and liver toxicity, with accuracies in the range of 70-90%. A limited number of computational models, based on the analysis of drug protein sequence, was instead proposed for immunotoxicity. In the later stages of development, toxicities are quantitatively predicted with reasonably good accuracy using either semi-mechanistic PK-PD models (hematological and cardiovascular toxicity), or fully exploited QSP models (immuno-toxicity and liver toxicity).

Population Pharmacokinetics of the Interleukin-23 Inhibitor Risankizumab in Subjects with Psoriasis and Crohn's Disease: Analyses of Phase I and II Trials

Background and Objectives

Risankizumab is a humanized anti-interleukin-23 monoclonal antibody in development for the treatment of several inflammatory diseases. This work characterized the pharmacokinetics of risankizumab and evaluated covariates that may affect its exposures using phase I and II trial data in subjects with psoriasis and Crohn’s disease.

Methods

Plasma concentration measurements from a phase I study and a phase II study in subjects with psoriasis (n = 157; single doses of 0.01–5 mg/kg intravenously, 0.25–1 mg/kg subcutaneously, and 18 mg subcutaneously, and multiple doses of 90 and 180 mg subcutaneously), and a phase II study in subjects with Crohn’s disease (n = 115; doses of 200 or 600 mg intravenously every 4 weeks followed by 180 mg subcutaneously every 8 weeks) were analyzed using non-linear mixed-effects modeling. The model was qualified using bootstrap and simulation-based diagnostics.

Results

A two-compartment model with first-order absorption and elimination described the pharmacokinetics of risankizumab. Considering the body weight and baseline albumin central tendency differences between disease populations, risankizumab clearance, steady-state volume of distribution, and terminal-phase elimination half-life were estimated to be approximately 0.35 L/day, 11.7 L, and 27 days, respectively, for a typical 90-kg subject with psoriasis with an albumin level of 42 g/L, and 0.31 L/day, 8.45 L, and 22 days, respectively, for a typical 65-kg subject with Crohn’s disease with an albumin level of 37 g/L. Risankizumab absolute subcutaneous bioavailability and absorption rate constant were 72% and 0.18 day⁻¹, respectively. Inter-individual variability for clearance was 37%.

Conclusions

Risankizumab displayed pharmacokinetic characteristics typical for an IgG1 monoclonal antibody with no apparent target-mediated disposition. Accounting for the effects of body weight and baseline albumin explained the small differences in the pharmacokinetics of risankizumab between psoriasis and Crohn’s disease, with no further differences between the patient populations.

Electronic supplementary material

The online version of this article (10.1007/s40262-018-0704-z) contains supplementary material, which is available to authorized users.

Evaluating a Multiscale Mechanistic Model of the Immune System to Predict Human Immunogenicity for a Biotherapeutic in Phase 1

A mechanistic model of the immune response was evaluated for its ability to predict anti-drug antibody (ADA) and their impact on pharmacokinetics (PK) and pharmacodynamics (PD) for a biotherapeutic in a phase 1 clinical trial. Observed ADA incidence ranged from 33 to 67% after single doses and 27-50% after multiple doses. The model captured the single dose incidence well; however, there was overprediction after multiple dosing. The model was updated to include a T-regulatory (Treg) cell mediated tolerance, which reduced the overprediction (relative decrease in predicted incidence rate of 21.5-59.3% across multidose panels) without compromising the single dose predictions (relative decrease in predicted incidence rate of 0.6-13%). The Treg-adjusted model predicted no ADA impact on PK or PD, consistent with the observed data. A prospective phase 2 trial was simulated, including co-medication effects in the form of corticosteroid-induced immunosuppression. Predicted ADA incidences were 0-10%, depending on co-medication dosage. This work demonstrates the utility in applying an integrated, iterative modeling approach to predict ADA during different stages of clinical development.

Reporting, Visualization, and Modeling of Immunogenicity Data to Assess Its Impact on Pharmacokinetics, Efficacy, and Safety of Monoclonal Antibodies

The rapidly increasing number of therapeutic biologics in development has led to a growing recognition of the need for improvements in immunogenicity assessment. Published data are often inadequate to assess the impact of an antidrug antibody (ADA) on pharmacokinetics, safety, and efficacy, and enable a fully informed decision about patient management in the event of ADA development. The recent introduction of detailed regulatory guidance for industry should help address many past inadequacies in immunogenicity assessment. Nonetheless, careful analysis of gathered data and clear reporting of results are critical to a full understanding of the clinical relevance of ADAs, but have not been widely considered in published literature to date. Here, we review visualization and modeling of immunogenicity data. We present several relatively simple visualization techniques that can provide preliminary information about the kinetics and magnitude of ADA responses, and their impact on pharmacokinetics and clinical endpoints for a given therapeutic protein. We focus on individual sample- and patient-level data, which can be used to build a picture of any trends, thereby guiding analysis of the overall study population. We also discuss methods for modeling ADA data to investigate the impact of immunogenicity on pharmacokinetics, efficacy, and safety.

Potential Sources of Inter-Subject Variability in Monoclonal Antibody Pharmacokinetics

Understanding inter-subject variability in drug pharmacokinetics and pharmacodynamics is important to ensure that all patients attain suitable drug exposure to achieve efficacy and avoid toxicity. Inter-subject variability in the pharmacokinetics of therapeutic monoclonal antibodies (mAbs) is generally moderate to high; however, the factors responsible for the high inter-subject variability have not been comprehensively reviewed. In this review, the extent of inter-subject variability for mAb pharmacokinetics is presented and potential factors contributing to this variability are explored and summarised. Disease status, age, sex, ethnicity, body size, genetic polymorphisms, concomitant medication, co-morbidities, immune status and multiple other patient-specific details have been considered. The inter-subject variability for mAb pharmacokinetics most likely depends on the complex interplay of multiple factors. However, studies aimed at investigating the reasons for the inter-subject variability are sparse. Population pharmacokinetic models and physiologically based pharmacokinetic models are useful tools to identify important covariates, aiding in the understanding of factors contributing to inter-subject variability. Further understanding of inter-subject variability in pharmacokinetics should aid in development of dosing regimens that are more appropriate.

Immunogenicity assessment during the development of protein therapeutics

Objective

Here we provide a critical review of the state of the art with respect to non-clinical assessments of immunogenicity for therapeutic proteins.

Key findings

The number of studies on immunogenicity published annually has more than doubled in the last 5 years. The science and technology, which have reached a critical mass, provide multiple of non-clinical approaches (computational, in vitro, ex vivo and animal models) to first predict and then to modify or eliminate T-cell or B-cell epitopes via de-immunization strategies. We discuss how these may be used in the context of drug development in assigning the immunogenicity risk of new and marketed therapeutic proteins.

Summary

Protein therapeutics represents a large share of the pharma market and provide medical interventions for some of the most complex and intractable diseases. Immunogenicity (the development of antibodies to therapeutic proteins) is an important concern for both the safety and efficacy of protein therapeutics as immune responses may neutralize the activity of life-saving and highly effective protein therapeutics and induce hypersensitivity responses including anaphylaxis. The non-clinical computational tools and experimental technologies that offer a comprehensive and increasingly accurate estimation of immunogenic potential are surveyed here. This critical review also discusses technologies which are promising but are not as yet ready for routine use.

Population pharmacokinetics of exenatide

AIM

The aim of the present analysis was to develop a core population pharmacokinetic model for the pharmacokinetic properties of immediate-release (IR) exenatide, which can be used in subsequent analyses of novel sustained-release formulations.

METHODS

Data from eight clinical trials, evaluating a wide range of doses and different administration routes, were available for analysis. All modelling and simulations were conducted using the nonlinear mixed-effect modelling program NONMEM. External model validation was performed using data from the phase III clinical trials programme through standard visual predictive checks.

RESULTS

The pharmacokinetics of IR exenatide was described by a two-compartment model, and the absorption of subcutaneous exenatide was described with a sequential zero-order rate constant followed by a saturable nonlinear absorption process. Drug elimination was characterized by two parallel routes (linear and nonlinear), with significant relationships between renal function and the linear elimination route, and between body weight and volume of distribution. For a subject with normal renal function, the linear clearance was estimated to be 5.06 l hr^-1 . The nonlinear elimination was quantified with a Michaelis-Menten constant (K_m ) of 567 pg ml^-1 and a maximum rate of metabolism (V_max ) of 1.6 μg h^-1 . For subcutaneous administration, 37% of the subcutaneous dose is absorbed via the zero-order process, and the remaining 63% via the nonlinear pathway.

CONCLUSIONS

The present analysis provides a comprehensive population pharmacokinetic model for exenatide, expanding the elimination process to include both linear and nonlinear components, providing a suitable platform for a broad range of concentrations and patient conditions that can be leveraged in future modelling efforts of sustained-release exenatide formulations.

A cell-level model of pharmacodynamics-mediated drug disposition

We aimed to develop a cell-level pharmacodynamics-mediated drug disposition (PDMDD) model to analyze in vivo systems where the PD response to a drug has an appreciable effect on the pharmacokinetics (PK). An existing cellular level model of PD stimulation was combined with the standard target-mediated drug disposition (TMDD) model and the resulting model structure was parametrically identifiable from typical in vivo PK and PD data. The PD model of the cell population was controlled by the production rate k in and elimination rate k out which could be stimulated or inhibited by the number of bound receptors on a single cell. Simulations were performed to assess the impact of single and repeated dosing on the total drug clearance. The clinical utility of the cell-level PDMDD model was demonstrated by fitting published data on the stimulatory effects of filgrastim on absolute neutrophil counts in healthy subjects. We postulated repeated dosing as a means of detecting and quantifying PDMDD as a single dose might not be sufficient to elicit the cellular response capable of altering the receptor pool to visibly affect drug disposition. In the absence of any PD effect, the model reduces down to the standard TMDD model. The applications of this model can be readily extended to include chemotherapy-induced cytopenias affecting clearance of endogenous hematopoietic growth factors, different monoclonal antibodies and immunogenicity effects on PK.

Clinical Pharmacokinetics and Pharmacodynamics of Monoclonal Antibodies Approved to Treat Rheumatoid Arthritis

Monoclonal antibodies (mAbs) are increasingly used to treat rheumatoid arthritis (RA). At present, anti-tumor necrosis factor-α drugs (infliximab, adalimumab, certolizumab pegol, and golimumab), rituximab, and tocilizumab are approved for RA treatment. This review focuses on the pharmacokinetics and pharmacodynamics of mAbs approved in RA. Being large proteins, mAbs exhibit complex pharmacokinetic and pharmacodynamic properties. In particular, owing to the interactions of mAbs with their antigenic targets, the pharmacokinetics of mAbs depends on target turnover and exhibits non-specific (linear) and target-mediated (often nonlinear) clearances. Their volume of distribution is low (3-4 L) and their elimination half-life usually ranges from 2 to 3 weeks. The inter-individual pharmacokinetic variability of mAbs is usually large and is partly explained by differences in antigenic burden or by anti-drug antibodies, which accelerate mAb elimination. The inter-individual variability of clinical response is large and influenced by the pharmacokinetics. The analysis of mAbs concentration-effect relationship relies more and more often on pharmacokinetic-pharmacodynamic modeling; these models being suitable for dosing optimization. Even if adverse effects of mAbs used in RA are well known, the relationship between mAb concentration and adverse effects is poorly documented, especially for anti-tumor necrosis factor-α mAbs. Overall, RA patients treated with mAbs should benefit from individualized dosing strategies. Because of the complexity of their pharmacokinetics and mechanisms of action, the current dosing strategy of mAbs is not based on sound knowledge. New studies are needed to assess individual dosing regimen, adjusted notably to disease activity.

Utility of a Bayesian Mathematical Model to Predict the Impact of Immunogenicity on Pharmacokinetics of Therapeutic Proteins

The impact of an anti-drug antibody (ADA) response on pharmacokinetic (PK) of a therapeutic protein (TP) requires an in-depth understanding of both PK parameters and ADA characteristics. The ADA and PK bioanalytical assays have technical limitations due to high circulating levels of TP and ADA, respectively, hence, significantly hindering the interpretation of this assessment. The goal of this study was to develop a population-based modeling and simulation approach that can identify a more relevant PK parameter associated with ADA-mediated clearance. The concentration-time data from a single dose PK study using five monoclonal antibodies were modeled using a non-compartmental analysis (NCA), one-compartmental, and two-compartmental Michaelis-Menten kinetic model (MMK). A novel PK parameter termed change in clearance time of the TP (α) derived from the MMK model could predict variations in α much earlier than the time points when ADA could be bioanalytically detectable. The model could also identify subjects that might have been potentially identified as false negative due to interference of TP with ADA detection. While NCA and one-compartment models can estimate loss of exposures, and changes in clearance, the two-compartment model provides this additional ability to predict that loss of exposure by means of α. Modeling data from this study showed that the two-compartment model along with the conventional modeling approaches can help predict the impact of ADA response in the absence of relevant ADA data.

Standardizing terms, definitions and concepts for describing and interpreting unwanted immunogenicity of biopharmaceuticals: recommendations of the Innovative Medicines Initiative ABIRISK consortium

Biopharmaceuticals (BPs) represent a rapidly growing class of approved and investigational drug therapies that is contributing significantly to advancing treatment in multiple disease areas, including inflammatory and autoimmune diseases, genetic deficiencies and cancer. Unfortunately, unwanted immunogenic responses to BPs, in particular those affecting clinical safety or efficacy, remain among the most common negative effects associated with this important class of drugs. To manage and reduce risk of unwanted immunogenicity, diverse communities of clinicians, pharmaceutical industry and academic scientists are involved in: interpretation and management of clinical and biological outcomes of BP immunogenicity, improvement of methods for describing, predicting and mitigating immunogenicity risk and elucidation of underlying causes. Collaboration and alignment of efforts across these communities is made difficult due to lack of agreement on concepts, practices and standardized terms and definitions related to immunogenicity. The Innovative Medicines Initiative (IMI; http://www.imi-europe.org), ABIRISK consortium [Anti-Biopharmaceutical (BP) Immunization Prediction and Clinical Relevance to Reduce the Risk; http://www.abirisk.eu] was formed by leading clinicians, academic scientists and EFPIA (European Federation of Pharmaceutical Industries and Associations) members to elucidate underlying causes, improve methods for immunogenicity prediction and mitigation and establish common definitions around terms and concepts related to immunogenicity. These efforts are expected to facilitate broader collaborations and lead to new guidelines for managing immunogenicity. To support alignment, an overview of concepts behind the set of key terms and definitions adopted to date by ABIRISK is provided herein along with a link to access and download the ABIRISK terms and definitions and provide comments (http://www.abirisk.eu/index_t_and_d.asp).

A Tutorial on Target-Mediated Drug Disposition (TMDD) Models

Target-mediated drug disposition (TMDD) is the phenomenon in which a drug binds with high affinity to its pharmacological target site (such as a receptor) to such an extent that this affects its pharmacokinetic characteristics.1 The aim of this Tutorial is to provide an introductory guide to the mathematical aspects of TMDD models for pharmaceutical researchers. Examples of Berkeley Madonna2 code for some models discussed in this Tutorial are provided in the Supplementary Materials.

Review on modeling anti-antibody responses to monoclonal antibodies

Monoclonal antibodies (mAbs) represent a therapeutic strategy that has been increasingly used in different diseases. mAbs are highly specific for their targets leading to induce specific effector functions. Despite their therapeutic benefits, the presence of immunogenic reactions is of growing concern. The immunogenicity identified as anti-drug antibodies (ADA) production due to the continuous administration of mAbs may affect the pharmacokinetics (PK) and/or the pharmacodynamics (PD) of mAbs administered to patients. Therefore, the immunogenicity and its clinical impact have been studied by several authors using PK modeling approaches. In this review, the authors try to present all those models under a unique theoretical mechanism-based framework incorporating the main considerations related to ADA formation, and how ADA may affect the efficacy or toxicity profile of some therapeutic biomolecules.

A white paper--consensus and recommendations of a global harmonization team on assessing the impact of immunogenicity on pharmacokinetic measurements

The Global Bioanalysis Consortium (GBC) set up an international team to explore the impact of immunogenicity on pharmacokinetic (PK) assessments. The intent of this paper is to define the field and propose best practices when developing PK assays for biotherapeutics. We focus on the impact of anti-drug antibodies (ADA) on the performance of PK assay leading to the impact on the reported drug concentration and exposure. The manuscript describes strategies to assess whether the observed change in the drug concentration is due to the ADA impact on drug clearance rates or is a consequence of ADA interference in the bioanalytical method applied to measure drug concentration. This paper provides the bioanalytical scientist guidance for developing ADA-tolerant PK methods. It is essential that the data generated in the PK, ADA, pharmacodynamic and efficacy/toxicity evaluations are viewed together. Therefore, the extent for the investigation of the PK sensitivity to the presence of ADA should be driven by the project needs and risk based.

Immunogenicity and PK/PD evaluation in biotherapeutic drug development: scientific considerations for bioanalytical methods and data analysis

With the advent of novel technologies, considerable advances have been made in the evaluation of the relationship between PK and PD. Ligand-binding assays have been the primary assay format supporting PK and immunogenicity assessments. Critical and in-depth characterizations of the ligand-binding assay of interest can provide valuable understanding of the limitations, for interpreting PK/PD and immunogenicity results. This review illustrates key challenges with regard to understanding the relationship between anti-drug antibody and PK/PD, including confounding factors associated with the development and validation of ligand-binding assays, mechanisms by which anti-drug antibody impacts PK/PD, factors to consider during data analyses and interpretation, and a perspective on integrating immunogenicity data into the well-established quantitative modeling approach. Through recognizing these challenges, we propose some opportunities for improvements in the development and validation of fit-for-purpose bioanalytical methods.

Utility of population pharmacokinetic modeling in the assessment of therapeutic protein-drug interactions

Assessment of pharmacokinetic (PK) based drug-drug interactions (DDI) is essential for ensuring patient safety and drug efficacy. With the substantial increase in therapeutic proteins (TP) entering the market and drug development, evaluation of TP-drug interaction (TPDI) has become increasingly important. Unlike for small molecule (e.g., chemical-based) drugs, conducting TPDI studies often presents logistical challenges, while the population PK (PPK) modeling may be a viable approach dealing with the issues. A working group was formed with members from the pharmaceutical industry and the FDA to assess the utility of PPK-based TPDI assessment including study designs, data analysis methods, and implementation strategy. This paper summarizes key issues for consideration as well as a proposed strategy with focuses on (1) PPK approach for exploratory assessment; (2) PPK approach for confirmatory assessment; (3) importance of data quality; (4) implementation strategy; and (5) potential regulatory implications. Advantages and limitations of the approach are also discussed.

The use of pharmacometrics to optimize biosimilar development

Pharmacometric approaches can assist in biosimilar development by leveraging quantitative knowledge of the originator product characteristics such as dose-exposure and exposure-response information to support a targeted approach to clinical studies. The degree to which these approaches can be applied relies on the level of information known about the originator and information that supports application of the originator model to the biosimilar. A model-based approach testing the hypothesis that the biosimilar PK and/or PK/PD profile is similar to the originator in the target patient population is aligned with the central comparability exercise required for the biosimilar approval. This Commentary details the key opportunities in study design and study analysis where pharmacometrics approaches can aid biosimilar development.

A mathematical model of the effect of immunogenicity on therapeutic protein pharmacokinetics

A mathematical pharmacokinetic/anti-drug-antibody (PK/ADA) model was constructed for quantitatively assessing immunogenicity for therapeutic proteins. The model is inspired by traditional pharmacokinetic/pharmacodynamic (PK/PD) models, and is based on the observed impact of ADA on protein drug clearance. The hypothesis for this work is that altered drug PK contains information about the extent and timing of ADA generation. By fitting drug PK profiles while accounting for ADA-mediated drug clearance, the model provides an approach to characterize ADA generation during the study, including the maximum ADA response, sensitivity of ADA response to drug dose level, affinity maturation rate, time lag to observe an ADA response, and the elimination rate for ADA-drug complex. The model also provides a mean to estimate putative concentration-time profiles for ADA, ADA-drug complex, and ADA binding affinity-time profile. When simulating ADA responses to various drug dose levels, bell-shaped dose-response curves were generated. The model contains simultaneous quantitative modeling and provides estimation of the characteristics of therapeutic protein drug PK and ADA responses in vivo. With further experimental validation, the model may be applied to the simulation of ADA response to therapeutic protein drugs in silico, or be applied in subsequent PK/PD models.