A mathematical analysis of rebound in a target-mediated drug disposition model: II. With feedback

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.

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“…The parameters that affected rebound were also mathematically analyzed by Aston et al . (see Figure ).…”

Section: One‐compartment Modelmentioning

confidence: 99%

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

Dua

Hawkins

Graaf

2015

CPT Pharmacometrics Syst. Pharmacol.

108

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“…Towards this goal, assays have been established to study inhibition reversibility [9]. It is generally accepted that response to irreversible inhibitors are time-dependent.…”

Section: Discussionmentioning

confidence: 99%

“…They can be served as a useful theoretical framework. Model-based analysis revealed that the necessary and sufficient condition for receptor rebound in a single dose animal experiment is that elimination rate of the drug-receptor product being slower than the elimination rates of the drug and of the receptor [9]. A time-scale analysis was also performed to provide accurate approximations of the temporal evolution under the assumption of high drug binding affinity [10].…”

Section: Discussionmentioning

confidence: 99%

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Time scale analysis of receptor enzyme activity: Irreversible inhibition sometimes exhibits incubation-time independence

You

Yue

2014

2014 IEEE International Conference on Bioinformatics and Biomedicine (BIBM)

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At early drug discovery, purified protein-based assays are often used to characterise compound potency. As far as dose response is concerned, it is often thought that a timeindependent inhibitor is reversible and a time-dependent inhibitor is irreversible. Using a simple kinetics model, we investigate the legitimacy of this. Our model-based analytical analysis and numerical studies reveal that dose response of an irreversible inhibitor may appear time-independent under certain parametric conditions. Hence, time-independence cannot be used as evidence for inhibitor reversibility. Furthermore, we also analysed how the synthesis and degradation of a target receptor affect drug inhibition in an in vitro cell-based assay setting. Indeed, these processes may also influence dose response of an irreversible inhibitor in such a way that it appears timeindependent under certain conditions. Hence, time-independent dose response in a cell assay also needs careful considerations. It is necessary to formulate a suitable model for analysis of proteinbased assay and in vitro cell assay data to ensure a consistent understanding. Keywords-irreversible inhibition; model of receptor turnover; fast drug process; slow drug process; timescale analysis I.

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

Gibiansky¹,

Gibiansky²

2017

J Pharmacokinet Pharmacodyn

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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.

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A mathematical analysis of rebound in a target-mediated drug disposition model: II. With feedback

Cited by 3 publications

References 10 publications

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

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

Time scale analysis of receptor enzyme activity: Irreversible inhibition sometimes exhibits incubation-time independence

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

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