A Quantitative Model of the GIRK1/2 Channel Reveals That Its Basal and Evoked Activities Are Controlled by Unequal Stoichiometry of Gα and Gβγ

G protein-gated K⁺ channels (GIRK; Kir3), activated by Gβγ subunits derived from G_i/o proteins, regulate heartbeat and neuronal excitability and plasticity. Both neurotransmitter-evoked (I_evoked) and neurotransmitter-independent basal (I_basal) GIRK activities are physiologically important, but mechanisms of I_basal and its relation to I_evoked are unclear. We have previously shown for heterologously expressed neuronal GIRK1/2, and now show for native GIRK in hippocampal neurons, that I_basal and I_evoked are interrelated: the extent of activation by neurotransmitter (activation index, R_a) is inversely related to I_basal. To unveil the underlying mechanisms, we have developed a quantitative model of GIRK1/2 function. We characterized single-channel and macroscopic GIRK1/2 currents, and surface densities of GIRK1/2 and Gβγ expressed in Xenopus oocytes. Based on experimental results, we constructed a mathematical model of GIRK1/2 activity under steady-state conditions before and after activation by neurotransmitter. Our model accurately recapitulates I_basal and I_evoked in Xenopus oocytes, HEK293 cells and hippocampal neurons; correctly predicts the dose-dependent activation of GIRK1/2 by coexpressed Gβγ and fully accounts for the inverse I_basal-R_a correlation. Modeling indicates that, under all conditions and at different channel expression levels, between 3 and 4 Gβγ dimers are available for each GIRK1/2 channel. In contrast, available Gα_i/o decreases from ~2 to less than one Gα per channel as GIRK1/2's density increases. The persistent Gβγ/channel (but not Gα/channel) ratio support a strong association of GIRK1/2 with Gβγ, consistent with recruitment to the cell surface of Gβγ, but not Gα, by GIRK1/2. Our analysis suggests a maximal stoichiometry of 4 Gβγ but only 2 Gα_i/o per one GIRK1/2 channel. The unique, unequal association of GIRK1/2 with G protein subunits, and the cooperative nature of GIRK gating by Gβγ, underlie the complex pattern of basal and agonist-evoked activities and allow GIRK1/2 to act as a sensitive bidirectional detector of both Gβγ and Gα.