A reduced mathematical model to explore Gi/Gs preferences of the CB1 receptor

Introduction: The cannabinoid type 1 receptor (CB1) induces both Gi and Gs (G-protein) pathways. The Gi pathway inhibits cyclic adenosine monophosphate (cAMP) production and Gs stimulates cAMP responses, the net cAMP response is therefore a mixture of the effects of the two pathways. CB1 shows a preference for the Gi protein and produces a net inhibition of cAMP under standard CB1 expression. However, CB1 switches its signalling from Gi preference to Gs preference to cause cAMP stimulation under high CB1 expression. Different CB1 agonists show different extents of cAMP response under the standard or high CB1 expression [1]. It is therefore difficult to predict the effects of any new agonist under these conditions. A QSP model was developed (previously) that accurately predicted the cAMP signalling switch in the presence of standard and high CB1 expression [2]. However, the QSP model was too complex to be used for estimation and hence cannot be re-used for different agonists easily. A reduced model is needed that supports parameter estimation in order to quantify Gi/Gs preference.

Objectives: The aim of this work was to develop a reduced mathematical model of the QSP model for CB1 Gi and Gs pathways in order to explore further CB1 agonists.

Methods:  Data were available from cAMP experiments for six CB1 agonists: CP55940 (CP),  anandamide (AEA), Δ9-tetrahydrocannabinol (THC), 2-arachidonoylglycerol (2-AG), WIN55212-2(WIN),  BAY593074 (BAY). A reduced model was derived by fast-equilibrium assumptions and lumping of species and could be represented by a set of algebraic equations with a single differential equation. The model was structurally identifiable. The model was applied to estimate the cAMP assays of the six CB1 agonists to quantify their Gi/Gs response properties on cAMP production. A two-stage method of estimation was applied. Firstly, the global search method (particle swarm, MATLAB 2020b) was used to determine the rough ranges of parameter initial values. Then a local search method (nlmefit, MATLAB 2020b) was applied to estimate the parameters and the between-experiment variation. The estimated parameters of the six agonists were compared to explore the agonist effects on cAMP.

Results: The reduced model showed similar predictive performance to the full model for the standard CB1 agonist CP used in full model development. The reduced mathematical model showed a good fit to the cAMP assays of the five new CB1 agonists. Two ligand-specific parameters Gi activation scale  KGiaRL and Gs activation scale KGsaRL, were estimated to have different values for different ligands. But the ratios of the two parameters KGiaRL and KGsaRL were similar for the six ligands. This result indicates that the six CB1 agonists only change the amounts of Gi/Gs activation but do not change the Gi/Gs preference. Full agonists such as CP have both large values of KGiaRL and KGsaRL, which show both high cAMP inhibition and high stimulation under standard or high CB1 levels, respectively. However, partial agonists such as  BAY have small values of KGiaRL and KGsaRL, which show low cAMP inhibition and low stimulation under standard or high CB1 levels, respectively. The model also indicates the ratio of Gi/Gs pathways is more likely to be a function of the system rather than the ligand.

Conclusion: A reduced mathematical model for CB1 Gi/Gs pathways was developed and applied to quantify the agonist preference. The reduced model performed well for estimation and yielded additional insights into the influence of different ligands on the system.


  1. Finlay DB et al (2017) British journal of pharmacology, 174(15): 2545-2562.
  2. Yang L et al (2021) PAGE 29 Abstr 9713 [www.page-meeting.org/?abstract=9713]