Introduction: Type 1 Cannabinoid Receptor (CB1) is the most abundant receptor in human brain and regulates multiple physiological activities via triggering downstream signalling network. CB1 internalisation is part of the signalling network, causing desensitization and this is a highly dynamic process. Orthosteric ligand (OL) could bind to endocannabinoids’ binding site and allosteric modulator (AM) could bind to different site, which also proved could affect CB1’s downstream signal collaborating with OM. While agonist-receptor model was established to describe the time-course signal of internalisation caused by orthosteric ligand, it’s not applicable when allosteric modulator is present. Therefore, establishing a kinetic model to quantity the time-course data of orthosteric and allosteric modulator to characterize ligands is critical for compound screening.
Aims: (1) To develop and validate a mathematical framework based on ternary complex theory to characterize receptor internalization kinetics. (2) To quantify and compare the modulatory effects of various AMs on both basal and agonist-stimulated internalization rates.
Method: Receptor internalisation was investigated using immunocytochemistry assays and antibody were deployed to track the time course of human CB1 receptor internalisation in HEK293 cells. Surface receptor inventory was monitored for 60 minutes following treatment with orthosteric cannabinoids (2-AG, AEA and AMB) alone or in combination with allosteric modulators (ZCZ011, GAT229 and ABD1236). These real time kinetic internalisation trajectories were then mathematically evaluated using differential equation and receptor theory. The total number of Receptor partitions into four distinct states, including free receptor (R), orthosteric agonist-receptor complex (OL-R), allosteric modulator-receptor complex (AM-R) and orthosteric agonist-receptor-allosteric modulator complex(OL-R-AM). The fraction occupancy (Ccc) for each state is derived from the respective dissociation constants (KA,KB) and the cooperativity factor as follows:
And the total normalized receptor number was written according to mass-balance:
Each receptor state internalized via its own specific internalisation rate. The final apparent internalisation rate of the whole system is defined by the sum of parallel pathways:
To map the theoretical receptor inventory to the observed fluorescence intensity, a scaling factor for receptor density was merged to initial fluorescence intensity due to parameter unidentifiable. Final equation for fluorescence intensity is:
Result: Five concentrations of each agonist were evaluated individually and cross-combined with two fixed concentrations of each allosteric modulator. The model was evaluated using SAEM algorithm, statistical error model is additive plus proportional error model. Final parameters RSE less than 30%. It successfully described the basal internalization effect of receptor itself and time-course internalisation process for different OLs under different agonists in concentration gradient manner. For model characterization, the ranking for efficacy is AMB>2AG>AEA>GAT229 = ABD>ZCZ011. ABD enhance the internalisation rate of AMB and AEA. GAT229 can enhance the internalisation rate of AEA but weak effect on AMB.
Conclusion: The dynamic framework successfully describes ternary system internalization kinetics(OL-CB1-AM). By decoupling ligand-specific parameters from binding affinity, this framework provides a mathematically rigorous approach for the quantitative evaluation of allosteric modulator caused modulatory effect under kinetic conditions.
Reference: 1. Green HM, et.al. Positive allosteric modulation of the cannabinoid CB1 receptor potentiates endocannabinoid signalling and changes ERK1/2 phosphorylation kinetics. BJP 2024 Oct;181(19):3642-62.