Mathematical modeling of SARS-CoV-2 viral dynamics and treatment with monoclonal antibodies.

The novel coronavirus (SARS-CoV-2) affects primarily the respiratory tract, and if left unchecked can cause a spectrum of pathological manifestations such as pneumonia, acute respiratory distress syndrome, myocardial injury, thromboembolism, and acute kidney injury. Medication strategies have involved minimizing the spread of the virus through antiviral medications (monoclonal antibodies or nucleotide reverse transcriptase inhibitors). Here, we develop a mathematical model that simulates viral dynamics in an untreated individual, and the evaluate the impact that a monoclonal antibody can have on slowing viral replication. Drug pharmacokinetics (PK) was informed by a typical two-compartment PK model with parameters typical of a monoclonal antibody, with a third compartment for the lung included as the drug site of action. The viral dynamics were captured using a simplified model describing uninfected target cells, infected target cells, and viral load in the body. The mechanism of action of the simulated antiviral is based on binding to the virus, thereby preventing it from infecting healthy cells. The model is used to project dosages needed to prevent severe disease under a variety of simulated conditions and subject to realistic constraints. The proposed model can capture a variety of scenarios of longitudinal viral dynamics and assess the impact of antiviral therapy on disease severity and duration. The described approach can be easily adapted to rapidly assess the dosages needed to affect duration and outcome of other viral infections and can serve as part of a fast and efficient scientific and modeling response strategy in the future as needed.

Bispecific antibodies: A guide to model informed drug discovery and development.

Affinity (KD) optimization of monoclonal antibodies is one of the factors that impacts the stoichiometric binding and the corresponding efficacy of a drug. This impacts the dose and the dosing regimen, making the optimum KD a critical component of drug discovery and development. Its importance is further enhanced for bispecific antibodies, where affinity of the drug needs to be optimized with respect to two targets. Mathematical modeling can have critical impact on lead compound optimization. Here we build on previous work of using mathematical models to facilitate lead compound selection, expanding analysis from two membrane bound targets to soluble targets as well. Our analysis reveals the importance of three factors for lead compound optimization: drug affinity to both targets, target turnover rates, and target distribution throughout the body. We describe a method that leverages this information to help make early stage decisions on whether to optimize affinity, and if so, which arm of the bispecific should be optimized. We apply the proposed approach to a variety of scenarios and illustrate the ability to make improved decisions in each case. We integrate results to develop a bispecific antibody KD optimization guide that can be used to improve resource allocation for lead compound selection, accelerating advancement of better compounds. We conclude with a discussion of possible ways to assess the necessary levels of target engagement for affecting disease as part of an integrative approach for model-informed drug discovery and development.

Identifying Safety Thresholds for Immunosuppressive Drugs: Applying Insights from Primary Antibody Deficiencies to Mitigate Adverse Events in Secondary Antibody Deficiencies Using Mathematical Modeling of Preclinical and Early Clinical Data.

Immunosuppressive drugs can alleviate debilitating symptoms of autoimmune diseases, but, by the same token, excessive immune suppression can result in an increased risk of infection. Despite the dangers of a compromised immune system, clear definitions of what constitutes excessive suppression remain elusive. Here we review the most common infections associated with primary antibody deficiencies (PADs), such as agammaglobulinemia, common variable immunodeficiency (CVID), and IgA deficiency, as well as infections that are associated with drug-induced or secondary antibody immunodeficiencies (SADs). We identify a number of bacterial, viral, and fungal infections (e.g., Listeria monocytogenes, Staphylococcus sp., Salmonella spp., Escherichia coli, influenza, varicella zoster virus, and herpes simplex virus) associated with both PADs and SADs, and suggest that diagnostic criteria for PADs could be used as a first-line measure to identify potentially unsafe levels of immune suppression in SADs. Specifically, we suggest that, based on PAD diagnostic criteria, IgG levels should remain above 2-3 g/L, IgA levels should not fall below 0.07 g/L, and IgM levels should remain above 0.4 g/L to prevent immunosuppressive drugs from inducing mimicking PAD-like effects. We suggest that these criteria could be used in the early stages of drug development, and that pharmacokinetic and pharmacodynamic modeling could help guide patient selection to potentially improve drug safety. We illustrate the proposed approach using atacicept as an example and conclude with a discussion of the applicability of this approach for other drugs that may induce excessive immune suppression.

Radiolabelling and preclinical characterization of 89Zr-Df-radiolabelled bispecific anti-PD-L1/TGF-ßRII fusion protein bintrafusp alfa.

PURPOSE: Τhis study aimed to optimize the 89Zr-radiolabelling of bintrafusp alfa investigational drug product and controls, and perform the in vitro and in vivo characterization of 89Zr-Df-bintrafusp alfa and 89Zr-Df-control radioconjugates. METHODS: Bintrafusp alfa (anti-PD-L1 human IgG1 antibody fused to TGF-ß receptor II (TGF-ßRII), avelumab (anti-PD-L1 human IgG1 control antibody), isotype control (mutated inactive anti-PD-L1 IgG1 control antibody), and trap control (mutated inactive anti-PD-L1 human IgG1 fused to active TGF-ßRII) were chelated with p-isothiocyanatobenzyl-desferrioxamine (Df). After radiolabelling with zirconium-89 (89Zr), radioconjugates were assessed for radiochemical purity, immunoreactivity, antigen binding affinity, and serum stability in vitro. In vivo biodistribution and imaging studies were performed with PET/CT to identify and quantitate 89Zr-Df-bintrafusp alfa tumour uptake in a PD-L1/TGF-ß-positive murine breast cancer model (EMT-6). Specificity of 89Zr-Df-bintrafusp alfa was assessed via a combined biodistribution and imaging experiment in the presence of competing cold bintrafusp alfa (1 mg/kg). RESULTS: Nanomolar affinities for PD-L1 were achieved with 89Zr-Df-bintrafusp alfa and 89Zr-avelumab. Biodistribution and imaging studies in PD-L1- and TGF-ß-positive EMT-6 tumour-bearing BALB/c mice demonstrated the biologic similarity of 89Zr-Df-bintrafusp alfa and 89Zr-avelumab indicating the in vivo distribution pattern of bintrafusp alfa is driven by its PD-L1 binding arm. Competition study with 1 mg of unlabelled bintrafusp alfa or avelumab co-administered with trace dose of 89Zr-labelled bintrafusp alfa demonstrated the impact of dose and specificity of PD-L1 targeting in vivo. CONCLUSION: Molecular imaging of 89Zr-Df-bintrafusp alfa biodistribution was achievable and allows non-invasive quantitation of tumour uptake of 89Zr-Df-bintrafusp alfa, suitable for use in bioimaging clinical trials in cancer patients.

Quantitative Systems Pharmacology Approaches for Immuno-Oncology: Adding Virtual Patients to the Development Paradigm.

Drug development in oncology commonly exploits the tools of molecular biology to gain therapeutic benefit through reprograming of cellular responses. In immuno-oncology (IO) the aim is to direct the patient's own immune system to fight cancer. After remarkable successes of antibodies targeting PD1/PD-L1 and CTLA4 receptors in targeted patient populations, the focus of further development has shifted toward combination therapies. However, the current drug-development approach of exploiting a vast number of possible combination targets and dosing regimens has proven to be challenging and is arguably inefficient. In particular, the unprecedented number of clinical trials testing different combinations may no longer be sustainable by the population of available patients. Further development in IO requires a step change in selection and validation of candidate therapies to decrease development attrition rate and limit the number of clinical trials. Quantitative systems pharmacology (QSP) proposes to tackle this challenge through mechanistic modeling and simulation. Compounds' pharmacokinetics, target binding, and mechanisms of action as well as existing knowledge on the underlying tumor and immune system biology are described by quantitative, dynamic models aiming to predict clinical results for novel combinations. Here, we review the current QSP approaches, the legacy of mathematical models available to quantitative clinical pharmacologists describing interaction between tumor and immune system, and the recent development of IO QSP platform models. We argue that QSP and virtual patients can be integrated as a new tool in existing IO drug development approaches to increase the efficiency and effectiveness of the search for novel combination therapies.

Guiding principles for mechanistic modeling of bispecific antibodies.

System based pharmacokinetic (PK) models can be used to study and predict the distribution of antibody based drugs into target tissues and assess the pharmacobinding (PB) of the drug to the target and the subsequent pharmacodynamic (PD) changes. In the absence of relevant PD readouts, compounded in cases of novel mechanisms, one can rely on binding between the drug and the target, computed as target occupancy (TO), as a relevant biomarker. This approach assumes that at maximum TO across the dosing interval, the drug-target interaction must demonstrate the intended pharmacology. Such analysis can help set laboratory objectives for protein engineers and chemists and guide them to the appropriate design and binding affinity of the molecule. Analysis of mechanistic models to guide affinity optimization against soluble and membrane-bound targets has been done for monoclonal antibodies (mAbs) (Tiwari et al., The AAPS Journal, 2017). However, comparable understanding of bispecific antibodies (BsAb; drugs with two targets, which are either soluble, membrane-bound, or a combination of the two) is still lacking. We propose to extend the work done by Tiwari et al. (2017) to BsAb. We focus on describing a generic BsAb with two membrane-bound targets, and explore the impact of various parameters on the TO of the BsAb to each target. Performed analysis can guide the optimization of dissociation constant (KD) of the BsAb, and can also help in identifying druggable targets. Proposed model can be modified and tailored to specific biologics as needed.

Optimal Affinity of a Monoclonal Antibody: Guiding Principles Using Mechanistic Modeling.

Affinity optimization of monoclonal antibodies (mAbs) is essential for developing drug candidates with the highest likelihood of clinical success; however, a quantitative approach for setting affinity requirements is often lacking. In this study, we computationally analyzed the in vivo mAb-target binding kinetics to delineate general principles for defining optimal equilibrium dissociation constant ([Formula: see text]) of mAbs against soluble and membrane-bound targets. Our analysis shows that in general [Formula: see text] to achieve 90% coverage for a soluble target is one tenth of its baseline concentration ([Formula: see text]), and is independent of the dosing interval, target turnover rate or the presence of competing ligands. For membrane-bound internalizing targets, it is equal to the ratio of internalization rate of mAb-target complex and association rate constant ([Formula: see text]). In cases where soluble and membrane-bound forms of the target co-exist, [Formula: see text] lies within a range determined by the internalization rate ([Formula: see text]) of the mAb-membrane target complex and the ratio of baseline concentrations of soluble and membrane-bound forms ([Formula: see text]). Finally, to demonstrate practical application of these general rules, we collected target expression and turnover data to project [Formula: see text] for a number of marketed mAbs against soluble (TNFα, RANKL, and VEGF) and membrane-bound targets (CD20, EGFR, and HER2).

Simulations of site-specific target-mediated pharmacokinetic models for guiding the development of bispecific antibodies.

Bispecific antibodies (BAbs) are novel constructs that are under development and show promise as new therapeutic modalities for cancer and autoimmune disorders. The aim of this study is to develop a semi-mechanistic modeling approach to elucidate the disposition of BAbs in plasma and possible sites of action in humans. Here we present two case studies that showcase the use of modeling to guide BAb development. In case one, a BAb is directed against a soluble and a membrane-bound ligand for treating systemic lupus erythematosus, and in case two, a BAb targets two soluble ligands as a potential treatment for ulcerative colitis and asthma. Model simulations revealed important differences between plasma and tissues, when evaluated for drug disposition and target suppression. Target concentrations at tissue sites and type (soluble vs membrane-bound), tissue-site binding, and binding affinity are all major determinants of BAb disposition and subsequently target suppression. For the presented case studies, higher doses and/or frequent dosing regimens are required to achieve 80 % target suppression in site specific tissue (the more relevant matrix) as compared to plasma. Site-specific target-mediated models may serve to guide the selection of first-in-human doses for new BAbs.

Quantitative prediction of human pharmacokinetics for mAbs exhibiting target-mediated disposition.

Prediction of human pharmacokinetics (PK) can be challenging for monoclonal antibodies (mAbs) exhibiting target-mediated drug disposition (TMDD). In this study, we performed a quantitative analysis of a diverse set of six mAbs exhibiting TMDD to explore translational rules that can be utilized to predict human PK. A TMDD model with rapid-binding approximation was utilized to fit PK and PD (i.e., free and/or total target levels) data, and average absolute fold error (AAFE) was calculated for each model parameter. Based on the comparative analysis, translational rules were developed and applied to a test antibody not included in the original analysis. AAFE of less than two-fold was observed between monkey and human for baseline target levels (R 0), body-weight (BW) normalized central elimination rate (K el/BW(-0.25)) and central volume (V c/BW(1.0)). AAFE of less than three-fold was estimated for the binding affinity constant (K D). The other four parameters, i.e., complex turnover rate (K int), target turnover rate (K deg), central to peripheral distribution rate constant (K pt) and peripheral to central rate constant (K tp) were poorly correlated between monkey and human. The projected human PK of test antibody based on the translation rules was in good agreement with the observed nonlinear PK. In conclusion, we recommend a TMDD model-based prediction approach that integrates in vitro human biomeasures and in vivo preclinical data using translation rules developed in this study.

A mechanistic pharmacodynamic model of IRAK-4 drug inhibition in the Toll-like receptor pathway.

The TLR pathway has been implicated in the pathogenesis of numerous diseases. IRAK-4 is integral to this pathway, making it a viable target for therapeutic intervention. This paper describes the application of a mechanistic pharmacodynamic model to assess the impact of IRAK-4 inhibition on the TLR-4 pathway. The model uses a minimal number of rate equations, molecular species, and parameters to characterize TLR signal transduction biology, including ligand-receptor interaction, protein complex formation, protein phosphorylation, negative regulation, and cytokine production. The model successfully reproduces the dynamic responses of TNFα to LPS stimulation, the tolerance to sequential LPS bolus dosing, the burst following a LPS bolus or infusion, and the modulation of pathway biomarkers following administration of an IRAK-4 inhibitor. Drug dosing schemes are evaluated for simulated disease states. The results emphasize the significance of LPS kinetics on response dynamics and the utility of a mechanistic model to help translate drug efficacy.

Discovery of an Oral Potent Selective Inhibitor of Hematopoietic Prostaglandin D Synthase (HPGDS).

Hematopoietic prostaglandin D synthase (HPGDS) is primarly expressed in mast cells, antigen-presenting cells, and Th-2 cells. HPGDS converts PGH2 into PGD2, a mediator thought to play a pivotal role in airway allergy and inflammatory processes. In this letter, we report the discovery of an orally potent and selective inhibitor of HPGDS that reduces the antigen-induced response in allergic sheep.

Saturation of multidrug-resistant protein 2 (mrp2/abcc2)-mediated hepatobiliary secretion: nonlinear pharmacokinetics of a heterocyclic compound in rats after intravenous bolus administration.

Multidrug-resistant protein 2 (MRP2/ABCC2), expressed on the canalicular membrane of hepatocytes, mediates the secretion of conjugated or nonconjugated compounds into bile and plays an important role in physiology and drug elimination. A heterocyclic compound, BPCPU [1-(1-(4-bromophenyl)-3-carbamoyl-1H-pyrazol-4-yl) urea], which was metabolically stable in vitro in rat liver microsomes and freshly isolated rat hepatocytes, demonstrated a saturable nonlinear pharmacokinetic profile in the rat. Polarized efflux was observed for this compound in Caco-2 cells, with a low K(m) = 1.06 +/- 0.06 microM. The Caco-2 efflux was dose-dependent and saturable. Coadministration of 25 microM MK571 ([3-[[3-[2-(7-chloroquinolin-2-yl)vinyl]phenyl]-(2-dimethylcarbamoylethylsulfanyl)methylsulfanyl] propionic acid]), an MRP inhibitor, blocked the polarized efflux in Caco-2 cells. In contrast, this compound did not inhibit calcein efflux in MRP2 gene-transfected Madin-Darby canine kidney cells, suggesting that it is a substrate, not an inhibitor, of the MRP2/ABCC2 transporter. To investigate the mechanism for the nonlinear pharmacokinetics, bile duct-cannulated rats were used to obtain time profiles of plasma concentration, biliary, and urinary excretion after intravenous administration at various doses. The plasma clearance increased remarkably with decreased dose, from 1.5 ml/min/kg at 5 mg/kg to 14.9 ml/min/kg at 0.05 mg/kg. A dose-dependent biliary excretion also was observed. The results revealed that saturation of hepatobiliary secretion played a role in the dose-dependent changes in total body clearance and biliary clearance. Saturating concentrations of the Mrp2/Abcc2 substrate, BPCPU, causing decreased hepatobiliary clearance could be the major cause for the nonlinear pharmacokinetics observed in rats.

Toxicokinetics of 2-methylimidazole in male and female F344 rats.

The toxicokinetics of 2-methylimidazole (2-MI) were studied in male and female Fischer 344 rats after a single iv dose of 10 mg/kg or gavage dose of 25, 50, or 100 mg/kg. The 2-MI was formulated in 0.05 M phosphate-buffered saline (pH 7.4). The iv profiles could be best described by a two-compartment model with first-order elimination. The terminal elimination half-life, volume of distribution at steady state, and clearance values were 0.78 and 0.85 h(-1), 1.5 and 1.9 L, and 4.97 and 12.0 L/h/kg for males and females, respectively. After a gavage dose, the plasma concentration time profiles could be best described by a one-compartment model, no lag phase, and first-order absorption and elimination. The peak 2-MI plasma concentrations increased proportionately with dose and were reached within 35 to 50 min (T(max)) for all groups. The estimated half-life value for 2-MI was about 1 h for the iv group and the male 25-, 50-, or 100-mg/kg groups and female 25-mg/kg groups. Clearance increased for the male 100- and female 50- and 100- mg/kg groups. For a given dose group, clearance was also two to three times greater for female rats when compared to male rats. Absolute bioavailability for 2-MI was estimated to approach 97%. The results of this study indicated that 2-MI was (1) rapidly and completely absorbed, (2) quickly eliminated, (3) cleared differently for females than for males, (4) affected somewhat by dose for females, and (5) unlikely to undergo tissue accumulation following repeated exposure.