Mathematical Model of Basal and Agonist-Dependent GIRK Channel Activity
We developed a model of GIRK channel activity. The channel activation scheme was based on sequential non-cooperative binding of 4 Gβγ molecules to channel protein (generating 5 closed states) and Gβγ independent channel opening. The kinetics of Gβγ interaction with subsequent change of channel conformation were adjusted to generate activation time of ∼ 1 s for a step rise in Gβγ concentration. The kinetics of switch from closed to open conformation were derived from single-channel analysis of GIRK1/2 recordings in Xenopus leaves oocytes. For simulation of agonist-dependent channel activation we incorporated the above scheme into a general model of G-protein cycle. This model was derived from that of Thomsen-Jaquez-Neubig. Several features were added: a) receptor was allowed to couple to G-protein in agonist-bound and in free state; b) finite affinity of Gα to Gβγ was assumed in GTP- and GDP-bound states; c) microscopic reversibility was obeyed in cyclic schemes containing reversible reactions; d) the assumption that G-protein concentration exceeded the receptor concentration was relaxed in order to enable simulation of titration experiments. We simulated the time-course of channel activation induced by step change in agonist concentration in presence and in absence of Gβγ-scavenging protein. We also simulated receptor-titration experiments. The results of simulations were compared to whole-cell experiments in Xenopus leaves oocytes. Our model produced realistic time course of channel activation and also demonstrated decremental dependence of activation time on receptor concentration. Comparing the simulation results with those expected from binary shuttle model of channel activation based on considerations of free diffusion of membrane proteins lead to the conclusion that G-protein activation by receptor is probably of catalytic collision-coupling type, while the channel and G protein were either in a tight complex or diffused in a restricted membrane domain.