Mathematical Modeling of Exposure and Target Interaction in Pharmaceutical Development of Therapeutic Proteins

Thursday, June 17 at 04:15am (PDT)
Thursday, June 17 at 12:15pm (BST)
Thursday, June 17 08:15pm (KST)

SMB2021 SMB2021 Follow Wednesday (Thursday) during the "MS18" time block.
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Jeroen Elassaiss-Schaap (PD-value BV, Netherlands), Johannes Schropp (University of Konstanz, Germany)


The use of mathematical modeling in pharmaceutical sciences began more than 50 years ago with the use of differential equations to quantify plasma drug disposition (pharmacokinetics) and drug exposure effects (pharmacodynamics). Under increasing computing power and statistical advances, more complex models and methods have been developed to address challenging problems in this field. One of the applications is in the research on therapeutic proteins. Advances in bio-genetic engineering have amplified the industrial efforts spent on developing proteins as medicines. These therapeutics have their own demands on modeling approaches, such as feedback loops between pharmacokinetics and pharmacodynamics labeled target-mediated drug disposition and interesting dual pharmacology of bispecific antibodies. The pharmacokinetic properties of therapeutic proteins furthermore allow excellent predictions using physiology-based pharmacokinetic models. The organization of this mini-symposium is initiated by the Mathematical and Computational Sciences Special Interest Group of the International Society of Pharmacometrics. This group strives to strengthen the mathematical perspective in pharmacometrics: the interplay of pharmacology, biology and statistics, among else by seeking collaboration with related fields. This mini-symposium covers related mathematical topics in the pharmacology of antibodies, with the intent of seeking common grounds with the SMB community and initiate further collaboration between our disciplines.

Leonid Gibiansky

(QuantPharm LLC, North Potomac, MD, USA)
"Target-mediated drug disposition in the pharmacokinetics of monoclonal antibodies and its quasi-steady state solutions"
The term TMDD refers to the biological processes and models where drug-target binding significantly influences both pharmacodynamics (PD) and pharmacokinetics (PK). These are typical for the biologic drugs with high specificity to the intended target. The TMDD model describes the processes on the widely different time scales: fast drug-target binding and relatively slow drug distribution and elimination. Given the typical clinically relevant sampling, this model is rarely identifiable thus requiring use of approximations. Various TMDD approximations have been developed. Investigation of the TMDD equations identified distinct phases in the concentration time profiles. The initial fast phase reflects drug-target binding processes. This phase is followed by a slow phase where the drug, target, and drug-target complex are in a slowly changing equilibrium. Several approximations that differ by the underlying assumptions have been developed. The quasi-steady state (QSS) approximation describes the TMDD system where the elimination of the drug-target complex is much slower than the elimination of the free target. In this case, the drug-target complex contributes significantly to the drug kinetics. The QSS approximation was successful in describing PK and PD of monoclonal antibodies that target soluble receptors. When the drug-target complex is eliminated faster than the free target, the QSS equations can be simplified to result in the Michaelis-Menten (MM) approximation. The MM approximation was shown to describe PK of many monoclonal antibodies that target membrane receptors. For drugs that bind to both soluble and membrane receptors, the QSS approximation of the two-target TMDD equations can be used. TMDD modeling framework can be adapted to many different systems, e.g. drugs that bind to targets with two binding sites, drugs with two identical binding sites, antibody-drug conjugates, etc.

Wojciech Krzyzanski

(University at Buffalo, USA)
"Application of Quasi-equilibrium Approximation to Reduction of Complex Physiologically Based Pharmacokinetic Models of Monoclonal Antibodies"
Physiologically based pharmacokinetic (PBPK) models are commonly used to describe the time courses of plasma concentrations of monoclonal antibodies. These models use ordinary differential equations to quantify monoclonal antibodies disposition in compartments such as the plasma, lymph node, as well as major peripheral organs. In addition, each organ consists of vascular, interstitial, and endosomal sub-compartments. The drug molecules are distributed to all compartments, taken up by the organs, internalized to the cell cytoplasm, and degraded in the endosomes or recycled to the interstitial space. In result, a PBPK model becomes a high dimensional nonlinear system with many parameters. We present a model reduction technique that is based on the quasi-equilibrium assumptions about the rates of processes of the dynamical system that simplifies the PBPK model to a three-compartment linear model. The technique is applied to a previously published PBPK model for monoclonal antibodies.

Johannes Schropp

(University of Konstanz, Germany)
"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, i.e., promise as immune-oncology drugs. We present a general target-mediated drug disposition model for these BsAbs, which bind to two different targets on different cell membranes. In addition, a quasi-equilibrium approximation with less binding parameters and, if necessary, reduced internalization parameters is presented. The model is used to investigate the kinetics of BsAb and TC. The analysis shows that larger doses of BsAbs may delay the build-up of the TC. Consequently, an optimal dosing strategy of BsAbs, which immediately create and maintain maximal possible TC concentration, is presented.

Weirong Wang

(Janssen, USA)
"Target-mediated drug disposition of immuno-oncology drugs: mathematical models for exposure and pharmacodynamics, and its translation between animal and man"
The therapeutic effect of all biotherapeutics is driven by its interaction with the therapeutic target. These interactions are often called target engagement (TE) when the target is a soluble protein and receptor occupancy (RO) when the target is a cell surface receptor. TE and RO assessments play a central role in translational pharmacology. Although TE or RO itself does not guarantee efficacy, it reflects the dynamics of drug engagement and corresponding target modulation and provides a mechanism to extrapolate drug effects between preclinical species and humans, as well as between healthy and disease populations. Together with mechanism and physiologically based PK/PD modeling, TE and RO are commonly used to facilitate rational dose selection and clinical study design.

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