Model-free and kinetic modelling approaches for characterising non-equilibrium pharmacological pathway activity: Internalisation of cannabinoid CB1 receptors.

BACKGROUND AND
PURPOSE: Receptor internalisation is by nature kinetic. Application of a standard equilibrium dose response model to describe the properties of a ligand inducing internalisation, while commonly used, are therefore problematic. Here, we propose two quantitative approaches to address this issue-(a) a model-free method and (b) a kinetic modelling approach-and systematically evaluate the performance of these methods against traditional equilibrium methods to characterise the internalisation profiles of cannabinoid CB1 receptor agonists. EXPERIMENTAL APPROACH: Kinetic internalisation assays were conducted using a concentration series of six CB1 receptor ligands. Internalisation rate analysis and snapshot equilibrium analysis were performed. A model-free method was developed based on the mean residence time of internalisation. A kinetic internalisation model was developed under the quasi-steady state assumption. KEY
RESULTS: Rates of receptor internalisation depended on both agonist and concentration. Agonist potencies from snapshot equilibrium analysis increased with stimulation time, and there was no single time point at which internalisation profiles could infer agonist properties in a comparative manner. The model-free method yielded a time-invariant measure of potency/efficacy for internalisation. The kinetic model adequately described the internalisation of CB1 receptors over time and provided robust estimates of both potency and efficacy. CONCLUSION AND IMPLICATIONS: Applying equilibrium analysis to a non-equilibrium pathway cannot provide a reliable estimate of agonist potency. Both the model-free and kinetic modelling approaches characterised the internalisation profiles of CB1 receptor agonists. The kinetic model provides additional advantages as a method to capture changes in receptor number during other functional assays.