Xiao Zhu, David B Finlay, Michelle Glass, Stephen B Duffull

Functional selectivity describes the ability of ligands to differentially regulate multiple signalling pathways when coupled to a single receptor and the operational model is commonly used to analyse these data. Here, we assess the mathematical properties of the operational model and evaluate the impact of fixing parameters on model performance. The operational model was evaluated using both a mathematical identifiability analysis and simulation. Mathematical analysis revealed that the parameters R0and KE, were not independently identifiable which can be solved by considering their ratio, τ. The ratio parameter, τ, was often imprecisely estimated when only functional assay data were available and generally only the transduction coefficient R (τ/KA) could be estimated precisely. The general operational model (that includes baseline and the Hill coefficient) required either the parameters Emor KAto be fixed. The normalisation process largely cancelled out the mean error of the calculated ∆ log (R) caused by fixing these parameters. From this analysis it was determined that we can avoid the need for a full agonist ligand to be included in an experiment to determine ∆ log (R). This analysis has provided a ready-to-use understanding of current methods for quantifying functional selectivity. It was determined that current methods are generally tolerant to fixing parameters. A new method was proposed that removes the need for including a high efficacy ligand in any given experiment, which allows application to large-scale screening to identify compounds with desirable features of functional selectivity.