2017 - Budapest - Hungary

PAGE 2017: Methodology - New Modelling Approaches
Johannes Schropp

Target-mediated drug disposition model for a bispecific antibody: development of full model and quasi-equilibrium like approximation

Johannes Schropp (1), Gilbert Koch (2)

(1) Department of Mathematics and Statistics, University of Konstanz, Germany (2) Paediatric Pharmacology and Pharmacometrics, University of Basel, Children’s Hospital (UKBB), Basel, Switzerland

Objectives: Bispecific monoclonal antibodies (BsMAb) are created from two different MAbs that bind simultaneously to two different types of targets. First, we construct a full BsMAb target-mediated drug disposition (TMDD) model based on binding kinetics presented in [1]. Second, a quasi-equilibrium (QE) like method is applied to construct an approximation of the full model with a reduced the number of the parameters and less ordinary differential equations (ODE).

Methods: Model from [1] was extended (i) by typical TMDD properties such as synthesis and degradation behaviour of the two receptors [2], and (ii) inclusion of a first-order elimination process for the BsMAb concentration. This model consists of 6 ordinary ODEs, one for the free BsMAb concentration C, one for each receptor RA and RB, and one for each binary RCA, RCB and ternary RCAB complex. First, a QE like approximation method was applied to reduce the number of parameters by substituting the eight kon and koff binding parameters with its ratio the dissociation constant. Additionally, we use an affinity ratio parameter [2] between C and RCB for receptor RA, and C and RCA for receptor RB so that number of binding related parameters can be reduced from eight to three. Second the approximation is formulated in free BsMAb C and free receptor RA and RB concentration by three ODEs. Further reductions of parameters can be achieved in case of constant total target concentrations.

Results: Similar to single [3] or competitive TMDD [4] a QE like method can be used to reduce the number of parameters in the full BsMAb model by a QE like approximation written in free variables. The reduced QE model could reasonably well approximate the free BsMAb concentration from the full model.

Conclusions: A general full BsMAb TMDD model was developed and the QE like method could be applied to develop a useful approximation. This shows the way to design approximations with less parameter and equations being better suited for data fitting.



References:
[1] Doldan-Martelli V et al. (2013) A mathematical model for the rational design of chimeric ligands in selective drug therapies, CPT: Pharmacometrics & Systems Pharmacology doi:0.1038/psp.2013.2
[2] Li L et al. (2014) Modeling the binding kinetics of bispecific antibodies under the framework of a minimal human PBPK model, AAPS meeting 2014
[3] Koch G et al. (2017) Target -mediated drug disposition with drug-drug interaction, Part I: single drug case in alternative formulations J Pharmacokinet Pharmacodyn doi:10.1007/s10928-016-9501-1
[4] Koch G et al. (2017) Target mediated drug disposition with drug-drug interaction, Part II: competitive and uncompetitive cases, J Pharmacokinet Pharmacodyn doi:10.1007/s10928-016-9502-0


Reference: PAGE 26 (2017) Abstr 7169 [www.page-meeting.org/?abstract=7169]
Poster: Methodology - New Modelling Approaches
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