Mathematical modelling of signalling in a two-ligand G-protein coupled receptor system: Agonist–antagonist competition

A new mathematical model of cell signalling for a two-ligand G-protein coupled receptor (GPCR) system is presented. This model extends the single-ligand cubic ternary complex to account for the possibility of an agonist and an antagonist competing for receptor sites. The G-protein cycle is included, and signalling as far as the dissociated GαGα subunit is considered. Numerical simulations are performed, and the effects on the system dynamics, such as peak and plateau behaviour, of antagonist “stickiness”, and of the doses of agonist and antagonist, are discussed. Under certain parameter regimes, the plateau response is subject to surmountable antagonism, while the peak response is subject to insurmountable antagonism. The numerical results reveal responses evolving over a number of time-scales. An asymptotic analysis is presented which identifies dominant reactions and gives leading order solutions over these various time-scales, for a number of parameter regimes.