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

We consider the possibility of free receptor (antigen/cytokine) levels rebounding to higher than the baseline level after the application of an antibody drug using a target-mediated drug disposition model. It is assumed that the receptor synthesis rate experiences homeostatic feedback from the receptor levels. It is shown for a very fast feedback response, that the occurrence of rebound is determined by the ratio of the elimination rates, in a very similar way as for no feedback. However, for a slow feedback response, there will always be rebound. This result is illustrated with an example involving the drug efalizumab for patients with psoriasis. It is shown that slow feedback can be a plausible explanation for the observed rebound in this example.

A mathematical analysis of rebound in a target-mediated drug disposition model: I.without feedback.

We consider the possibility of free receptor (antigen/cytokine) levels rebounding to higher than the baseline level after one or more applications of an antibody drug using a target-mediated drug disposition model. Using geometry and dynamical systems analysis, we show that rebound will occur if and only if the elimination rate of the drug-receptor product is slower than the elimination rates of the drug and of the receptor. We also analyse the magnitude of rebound through approximations and simulations and demonstrate that it increases if the drug dose increases or if the difference between the elimination rate of the drug-receptor product and the minimum of the elimination rates of the drug and of the receptor increases.

Integration not isolation: arguing the case for quantitative and systems pharmacology in drug discovery and development.

Quantitative and systems pharmacology (QSP) is an emerging modelling technique that combines the flexibility of systems biology and tractability of compartmental pharmacokinetic-pharmacodynamic modelling techniques. Historically, there has been extensive use of QSP within the field of pharmacokinetics to optimise drug biopharmaceutical properties. However, application to target and biomarker selection, and design of preclinical and clinical studies is limited, but growing rapidly. In this article we highlight the impact of QSP within drug discovery and development by citing examples from within the field of pharmacology and we argue for a more systematic integration of QSP within the drug discovery and development paradigm.

Mathematical analysis of the pharmacokinetic-pharmacodynamic (PKPD) behaviour of monoclonal antibodies: predicting in vivo potency.

We consider the relationship between the target affinity of a monoclonal antibody and its in vivo potency. The dynamics of the system is described mathematically by a target-mediated drug disposition model. As a measure of potency, we consider the minimum level of the free receptor following a single bolus injection of the ligand into the plasma compartment. From the differential equations, we derive two expressions for this minimum level in terms of the parameters of the problem, one of which is valid over the full range of values of the equilibrium dissociation constant K(D) and the other which is valid only for a large drug dose or for a small value of K(D). Both of these formulae show that the potency achieved by increasing the association constant k(on) can be very different from the potency achieved by decreasing the dissociation constant k(off). In particular, there is a saturation effect when decreasing k(off) where the increase in potency that can be achieved is limited, whereas there is no such effect when increasing k(on). Thus, for certain monoclonal antibodies, an increase in potency may be better achieved by increasing k(on) than by decreasing k(off).

Use of pharmacokinetic/ pharmacodynamic modelling for starting dose selection in first-in-human trials of high-risk biologics.

WHAT IS ALREADY KNOWN ABOUT THIS SUBJECT: Recent regulatory guidance has highlighted the importance of using pharmacokinetic-pharmacodynamic (PK-PD) modelling in the selection of starting doses in first-in-human trials of high-risk biologics. However, limited examples exist in literature illustrating this procedure. WHAT THIS STUDY ADDS: An interpretation of the recommended dose-selection methodology and the minimum anticipated biological effect level (MABEL) principle, contained in the updated European Medicines Agency guidance on risk-mitigation strategies for first-in-human studies, is presented. Some literature and simulation-based examples of the application of PK-PD modelling principles to starting dose selection using in vitro and in vivo data under the MABEL paradigm are highlighted, along with the advantages and limitations of this approach. AIMS: To illustrate the use of pharmacokinetic-pharmacodynamic (PK-PD) models to select rational starting doses in clinical trials within the minimum anticipated biological effect level (MABEL) principle using literature data and through simulations. METHODS: The new European Medicines Agency guidance on starting dose selection of high-risk biologics was analysed considering the basic pharmacological properties and preclinical testing limitations of many biologics. The MABEL approach to dose selection was illustrated through simulations and through literature-reported examples on the selection of starting doses for biologics such as antibodies based on in vitro biomarker data, in vivo PK and PK-PD data. RESULTS: Literature reports indicating the use of preclinical pharmacological and toxicological data to select successfully safe starting doses in line with the MABEL principle are summarized. PK-PD model-based simulations of receptor occupancy for an anti-IgE antibody system indicate that the relative abundance of IgE in animal models and patients and the turnover rate of the IgE-antibody complex relative to the off-rate of the antibody from IgE are important determinants of in vivo receptor occupancy. CONCLUSIONS: Mechanistic PK-PD models are capable of integrating preclinical in vitro and in vivo data to select starting doses rationally in first-in-human trials. Biological drug-receptor interaction dynamics is complex and multiple factors affect the dose-receptor occupancy relationship. Thus, these factors should be taken into account when selecting starting doses.

A non-parametric method to analyse time-course of effect in the absence of pharmacokinetic data: application to inhaled bronchodilators.

In spite of the extensive use of long-acting beta(2)-agonist (LABA) bronchodilators in asthma, the actual mechanism of their in vivo duration of action is not well understood, primarily due to limitations of standard pharmacokinetic-pharmacodynamic (PKPD) analysis methodologies. We have developed a novel method of analysing lung efficacy vs. time profiles for LABAs that can be used to provide comparative information on the lung PK. We hypothesised that for compounds that do not differ in their PK at the site of PD action, but differ in their in vivo potencies, the relationship between the area under the effect curve (AUEC) and the observed maximum effect (OME) at different doses is described by the same sigmoid curve. We have illustrated this property for standard PKPD models by obtaining analytical solution and through simulations. Anaesthetised dog in vivo effect vs. time profiles were gathered for six inhaled LABA candidates that differ in their in vitro potencies. Neither lung nor systemic PK was available for any compound. Analysis of the AUEC vs. OME data, derived from the efficacy profiles, using nonlinear mixed effects modelling indicated that for four compounds, the observed differences in in vivo duration of action was due to differences in their in vivo potencies and not because of lung PK differences. Therefore, it was concluded that for these compounds, characterisation of lung PK was unlikely to differentiate their PKPD characteristics. Thus, the proposed approach helped focus resources during translational research leading to lead candidate selection.

The role of mechanism-based pharmacokinetic-pharmacodynamic (PK-PD) modelling in translational research of biologics.

Lack of predictability of clinical efficacy and safety is an important problem facing pharmaceutical research today. Translational PK-PD has the ability to integrate data generated from diverse test platforms during discovery and development in a mechanistic framework. Therefore, successful implementation of translational PK-PD modelling and simulation early in the development cycle could have a substantial impact on overall efficiency and success of pharmaceutical research. Three case studies are presented, which outline successful implementation of the translational PK-PD methodology in the rational development of biotherapeutics across various stages of discovery and development. Emerging developments within the field are also discussed.