A mathematical model of CB1 receptor allosteric modulation

Introduction: The type 1 cannabinoid receptor (CB1) is among the most abundant G-protein coupled receptors in the central nervous system.  CB1 modulates neurotransmission, and plays a vital role in both physiology and pathology.  Allosteric ligands bind to a different site on the receptor to the endogenous (orthosteric) ligand and can have effects that are unique to the allosteric ligand as well as modulating endogenous ligands. ORG27569 (ORG) is an allosteric modulator, which increases the binding of the orthosteric agonist CP55940 (CP), inhibiting CP’s effect on cAMP production and CP mediated receptor internalisation. ORG itself does not affect internalisation and has only a slight effect on increasing cAMP production. Simple concepts like ‘upregulate’ or ‘downregulate’ mislabel the complicated time and concentration related interactions of these ligand combinations on CB1 function, which actually shows a delay prior to ORG impacting on receptor function. We propose a unified mathematical model to describe the above phenomena, explore the underlying mechanism and predict some behaviours, which have not yet been observed in experiments.


Objectives: The aim of this work is to establish a mathematical model of allosteric modulation of CB1 and explore currently observed phenomenon, and predict future experimental responses.



Methods:  Data were available from experiments of receptor binding, cAMP and internalization associated with CP in the presence and absence of ORG. A 6-state model was proposed, including unbound receptor, CP-receptor complex, ORG-receptor complex, CP-receptor-ORG complex, and two proposed inactive states of CP-ORG receptor complex and ORG-receptor complex. This full model was reduced through quasi-equilibrium state assumptions and model lumping and the model parameters were estimated using NONMEM. New experimental data were predicted by simulating from this reduced model with global sensitivity confidence bands around the predictions (based on the standard error matrix of parameter estimates). The reduced model was then applied to explore delayed onset effects of ORG in a cAMP experiment and propose possible experiments to test underlying model assumptions.



Results: The 6-state mathematical model of allosteric modulation provided a good fit to the CP, ORG and CP & ORG data from binding, internalisation and cAMP signaling experiments. The model was reduced from 6 states with 24 parameters to 5 states with 16 parameters.  The performance of the reduced model was equivalent to the full model and the reduced model performed well for estimation and described the existing data well. Predictions using global sensitivity confidence bands predicted by the reduced model well described new (external) data. When used to quantify the delayed onset of the action of ORG, the model indicated that the CB1-CP complex dominates inhibition of cAMP in first few minutes due to receptor reserve (this means achieving the maximal effect at a concentration of CP that does not bind all of the receptors), which causes a delay in ORG activity. The reduced model has now been used to predict future experimental outcomes for validation of the above proposed mechanism – this work is ongoing.



Conclusion: A mathematical model for CB1 allosteric modulation was developed and reduced. The reduced model performed well for predicting external data. New mechanisms were proposed that underpin the notable delayed onset of activity of ORG.


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