The quest for balance between capturing data and model complexity: A quantitative clinical pharmacology approach applied to monoclonal antibodies.

The main objective of this tutorial is to provide the readers with a roadmap of how to establish increasingly complex target-mediated drug disposition (TMDD) models for monoclonal antibodies. To this end, we built mathematical models, each with a detailed visualization, starting from the basic TMDD model by Mager and Jusko to the well-established, physiologically based model by Li et al. in a step-wise fashion to highlight the relative importance of key physiological processes that impact mAb kinetics and system dynamics.

Impact of enzyme turnover on the dynamics of the Michaelis-Menten model.

Enzymatic (metabolic rate) processes are traditionally modelled by means of Michaelis-Menten type reactions. The experimental setup is usually performed in vitro also denoted as a 'closed system'. In this paper we explore the impact of enzyme turnover on the classical Michaelis-Menten model by modifying it to include enzyme turnover, specifically through zeroth-order synthesis and first-order degeneration of the enzyme.

An Extended Model Including Target Turnover, Ligand-Target Complex Kinetics, and Binding Properties to Describe Drug-Receptor Interactions.

Since the beginning of this century, target-mediated drug disposition has become a central concept in modeling drug action in drug development. It combines a range of processes, such as turnover, protein binding, internalization, and non-specific elimination, and often serves as a nucleus of more complex pharmacokinetic models. It is simple enough to comprehend but complex enough to be able to describe a wide range of phenomena and data sets.

Comparisons of basic target-mediated drug disposition (TMDD) and ligand facilitated target removal (LFTR).

In the well-known model for basic Target-Mediated Drug Disposition (TMDD), drug binds to the target and the resulting drug-target complex is removed by a first order process, leading to loss of both drug and target. In the present note we study what happens when, instead, drug is returned to the free drug pool so that it can a new target molecule. What results is a mechanism in which the drug, here referred to as the ligand, facilitates the removal of the target,and then returns to the free ligand pool.

Revisit ligand-receptor interaction at the human vasopressin V receptor: A kinetic perspective.

The vasopressin V receptor belongs to the superfamily of G protein-coupled receptors (GPCRs) and is a potential drug target for water balance disorders such as polycystic kidney disease. Traditionally, the discovery of novel agents for the vasopressin V receptor has been guided by evaluating their receptor affinity, largely ignoring the binding kinetics. However, the latter is receiving increasing attention in the drug research community and has been proved to be a more complete descriptor of the dynamic process of ligand-receptor interaction.

Mathematical Modelling of Alternative Pathway of Complement System.

The complement system (CS) is an integral part of innate immunity and can be activated via three different pathways. The alternative pathway (AP) has a central role in the function of the CS. The AP of complement system is implicated in several human disease pathologies.

Mathematical modeling of the glucagon challenge test.

A model for the homeostasis of glucose through the regulating hormones glucagon and insulin is described. It contains a subsystem that models the internalization of the glucagon receptor. Internalization is a mechanism in cell signaling, through which G-protein coupled receptors are taken from the surface of the cell to the endosome.

Michaelis-Menten from an In Vivo Perspective: Open Versus Closed Systems.

After a century of applications of the seminal Michaelis-Menten equation since its advent it is timely to scrutinise its principal parts from an in vivo point of view. Thus, the Michaelis-Menten system was revisited in which enzymatic turnover, i.e.

Predicting the Onset of Nonlinear Pharmacokinetics.

When analyzing the pharmacokinetics (PK) of drugs, one is often faced with concentration C vs. time curves, which display a sharp transition at a critical concentration C . For C > C , the curve displays linear clearance and for C < C clearance increases in a nonlinear manner as C decreases.

Correction to: Modelling the delay between pharmacokinetics and EEG effects of morphine in rats: binding kinetic versus effect compartment models.

The original version of this article was published open access. Unfortunately, due to a technical issue, the copyright holder name in the online version (HTML and XML) is incorrectly published as "Springer Science+Business Media, LLC, part of Springer Nature 2018". Instead, it should be "The Author(s) 2018".

Lost in translation: What's in an EC? Innovative PK/PD reasoning in the drug development context.

Translation across species and from in vitro to in vivo is a central tenet in drug discovery pharmacology. Successful implementation requires proper assessment of both in vivo potency and efficacy. This notwithstanding, in vivo data is typically defined mostly in terms of ligand-to-target binding affinity, similar to in vitro studies.

Modelling the delay between pharmacokinetics and EEG effects of morphine in rats: binding kinetic versus effect compartment models.

Drug-target binding kinetics (as determined by association and dissociation rate constants, k and k) can be an important determinant of the kinetics of drug action. However, the effect compartment model is used most frequently instead of a target binding model to describe hysteresis. Here we investigate when the drug-target binding model should be used in lieu of the effect compartment model.

New Equilibrium Models of Drug-Receptor Interactions Derived from Target-Mediated Drug Disposition.

In vivo analyses of pharmacological data are traditionally based on a closed system approach not incorporating turnover of target and ligand-target kinetics, but mainly focussing on ligand-target binding properties. This study incorporates information about target and ligand-target kinetics parallel to binding. In a previous paper, steady-state relationships between target- and ligand-target complex versus ligand exposure were derived and a new expression of in vivo potency was derived for a circulating target.

A two-state model for the kinetics of competitive radioligand binding.

Background And Purpose: Ligand-receptor binding kinetics is receiving increasing attention in the drug research community. The Motulsky and Mahan model, a one-state model, offers a method for measuring the binding kinetics of an unlabelled ligand, with the assumption that the labelled ligand has no preference while binding to distinct states or conformations of a drug target. As such, the one-state model is not applicable if the radioligand displays biphasic binding kinetics to the receptor.

In vivo potency revisited - Keep the target in sight.

Potency is a central parameter in pharmacological and biochemical sciences, as well as in drug discovery and development endeavors. It is however typically defined in terms only of ligand to target binding affinity also in in vivo experimentation, thus in a manner analogous to in in vitro studies. As in vivo potency is in fact a conglomerate of events involving ligand, target, and target-ligand complex processes, overlooking some of the fundamental differences between in vivo and in vitro may result in serious mispredictions of in vivo efficacious dose and exposure.

Impact of mathematical pharmacology on practice and theory: four case studies.

Drug-discovery has become a complex discipline in which the amount of knowledge about human biology, physiology, and biochemistry have increased. In order to harness this complex body of knowledge mathematics can play a critical role, and has actually already been doing so. We demonstrate through four case studies, taken from previously published data and analyses, what we can gain from mathematical/analytical techniques when nonlinear concentration-time courses have to be transformed into their equilibrium concentration-response (target or complex) relationships and new structures of drug potency have to be deciphered; when pattern recognition needs to be carried out for an unconventional response-time dataset; when what-if? predictions beyond the observational concentration-time range need to be made; or when the behaviour of a semi-mechanistic model needs to be elucidated or challenged.

Use of mathematics to guide target selection in systems pharmacology; application to receptor tyrosine kinase (RTK) pathways.

A key element of the drug discovery process is target selection. Although the topic is subject to much discussion and experimental effort, there are no defined quantitative rules around optimal selection. Often 'rules of thumb', that have not been subject to rigorous exploration, are used.

Pharmacokinetic Steady-States Highlight Interesting Target-Mediated Disposition Properties.

In this paper, we derive explicit expressions for the concentrations of ligand L, target R and ligand-target complex RL at steady state for the classical model describing target-mediated drug disposition, in the presence of a constant-rate infusion of ligand. We demonstrate that graphing the steady-state values of ligand, target and ligand-target complex, we obtain striking and often singular patterns, which yield a great deal of insight and understanding about the underlying processes. Deriving explicit expressions for the dependence of L, R and RL on the infusion rate, and displaying graphs of the relations between L, R and RL, we give qualitative and quantitive information for the experimentalist about the processes involved.

Impact of saturable distribution in compartmental PK models: dynamics and practical use.

We explore the impact of saturable distribution over the central and the peripheral compartment in pharmacokinetic models, whilst assuming that back flow into the central compartiment is linear. Using simulations and analytical methods we demonstrate characteristic tell-tale differences in plasma concentration profiles of saturable versus linear distribution models, which can serve as a guide to their practical applicability. For two extreme cases, relating to (i) the size of the peripheral compartment with respect to the central compartment and (ii) the magnitude of the back flow as related to direct elimination from the central compartment, we derive explicit approximations which make it possible to give quantitative estimates of parameters.

Identifying clinically relevant sources of variability: The clopidogrel challenge.

High interindividual variability in clinical outcomes following clopidogrel's standard dosing regimen continues to be a challenge even two decades after its approval. CYP2C19 polymorphisms, obesity, older age, diabetes, and drug-drug interactions have been identified as risk factors for adverse events and treatment failure. We conducted a mechanism-based pharmacokinetic/pharmacodynamic analysis, where we integrated knowledge on in vitro enzyme kinetic, physiological, genetic, and demographic information to characterize changes in platelet reactivity from baseline following clopidogrel antiplatelet therapy.

Understanding the Behavior of Systems Pharmacology Models Using Mathematical Analysis of Differential Equations: Prolactin Modeling as a Case Study.

In this tutorial, we introduce basic concepts in dynamical systems analysis, such as phase-planes, stability, and bifurcation theory, useful for dissecting the behavior of complex and nonlinear models. A precursor-pool model with positive feedback is used to demonstrate the power of mathematical analysis. This model is nonlinear and exhibits multiple steady states, the stability of which is analyzed.

Mixture dynamics: Combination therapy in oncology.

In recent years combination therapies have become increasingly popular in most therapeutic areas. We present a qualitative and quantitative approach and elucidate some of the challenges and solutions to a more optimal therapy. For tumor growth this involves the study of semi-mechanistic cell-growth/kill models with multiple sites of action.

Modelling the dynamics of polar auxin transport in inflorescence stems of Arabidopsis thaliana.

The polar transport of the plant hormone auxin has been the subject of many studies, several involving mathematical modelling. Unfortunately, most of these models have not been experimentally verified. Here we present experimental measurements of long-distance polar auxin transport (PAT) in segments of inflorescence stems of Arabidopsis thaliana together with a descriptive mathematical model that was developed from these data.

Dose-response-time modelling: Second-generation turnover model with integral feedback control.

This study presents a dose-response-time (DRT) analysis based on a large preclinical biomarker dataset on the interaction between nicotinic acid (NiAc) and free fatty acids (FFA). Data were collected from studies that examined different rates, routes, and modes of NiAc provocations on the FFA time course. All information regarding the exposure to NiAc was excluded in order to demonstrate the utility of a DRT model.