Application of pharmacometric methods to quantify functional selectivity

Abstract

Interest has arisen in the ability of ligands to differentially regulate signalling pathways when coupled to a single receptor, a concept termed functional selectivity. The current approach used to quantify functional selectivity heavily relies on the application of equilibrium pharmacological models, despite the non-equilibrium nature of some functional assay data. The overall aim of this thesis was to apply pharmacometric techniques to provide a comprehensive understanding of the current methods for quantifying functional selectivity and to introduce a new perspective on the quantification of functional selectivity within a kinetic framework. The assumptions underpinning the classic Emax model were systematically assessed. By relaxing these assumptions, a unified framework for pharmacological models was developed to accommodate different experimental conditions and physiological behaviours of systems. The developed unified model is a mathematical representation of the widely recognised receptor theory and serves as a thinking framework to facilitate better application of the Emax model. The identifiability of the operational model and its variants was systematically evaluated. It was shown that current application of the operational model for quantifying functional selectivity is generally tolerant to misspecification of parameters set to fixed constants. The identifiability analyses also revealed that, with only functional assay data, the transduction coefficient was the minimal element that could be derived directly from the operational model. Furthermore, an objective method was proposed that removes the need for including a highly efficacious ligand in any given experiment, allowing for its application to large-scale screening to identify compounds with desirable features of functional selectivity. The intact operational model proposed allowed for receptor selectivity across all pathways simultaneously. Through power analyses and practical applications, it was demonstrated that in comparison to the commonly utilised operational model, the intact operational model was more sensitive to identify biased ligands and provided a more precise estimate of the ligand bias metric. Hence, the intact operational model may provide a valuable step to describe and improve the understanding of the underlying mechanisms of functional selectivity. The agonist-induced internalisation of the cannabinoid-1 (CB1) receptor was investigated for a mini-panel of CB1 agonists. It was clearly demonstrated that analysing kinetic internalisation data with an equilibrium pharmacological model was problematic and that the model was unable to provide a reliable estimate of potency. Both a model-free method and a kinetic modelling approach accurately characterised the internalisation activity profiles of the CB1 agonists. The developed kinetic internalisation model is unique in its ability to account for the influence of receptor internalisation in functional selectivity. The joint kinetic model of functional selectivity at the CB1 receptor was developed to simultaneously describe the time-dependent complex activities in three signalling pathways (i.e., internalisation, cyclic AMP, and phospho-ERK pathway), with the kinetics of ligand binding shared across the different pathways. Based on the insights from the kinetic model, fingerprint profiles of CB1 ligand bias were constructed and visualised. This renders the first kinetic assessment of functional selectivity at the G-protein coupled receptor (e.g., CB1 receptor) under non-equilibrium conditions. The work conducted in this thesis offered a new perspective on the quantification of functional selectivity. The next step would be to translate in vitro bias into in vivo therapeutic effects. This would require a preclinical pharmacokinetics/pharmacodynamics study of a mini-panel of CB1 agonists to examine the findings of ligand bias in this thesis. Furthermore, a unified framework for pharmacological models was proposed. An important future step would be to conduct a systematic identifiability assessment of the unified framework to facilitate better application of the Emax model towards various experimental conditions and physiological behaviours.