A Quantitative Model of the GIRK1/2 Channel Reveals That Its Basal and Evoked Activities Are Controlled by Unequal Stoichiometry of G[alpha] and G[Beta][gamma]

G protein-gated K+ channels (GIRK; Kir3), activated by G[Beta][gamma] subunits derived from Gi/o proteins, regulate heartbeat and neuronal excitability and plasticity. Both neurotransmitter-evoked (Ievoked) and neurotransmitter-independent basal (Ibasal) GIRK activities are physiologically important, but mechanisms of Ibasal and its relation to Ievoked are unclear. We have previously shown for heterologously expressed neuronal GIRK1/2, and now show for native GIRK in hippocampal neurons, that Ibasal and Ievoked are interrelated: the extent of activation by neurotransmitter (activation index, Ra) is inversely related to Ibasal. 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 G[Beta][gamma] 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 Ibasal and Ievoked in Xenopus oocytes, HEK293 cells and hippocampal neurons; correctly predicts the dose-dependent activation of GIRK1/2 by coexpressed G[Beta][gamma] and fully accounts for the inverse Ibasal-Ra correlation. Modeling indicates that, under all conditions and at different channel expression levels, between 3 and 4 G[Beta][gamma] dimers are available for each GIRK1/2 channel. In contrast, available G[alpha] i/o decreases from ~2 to less than one G[alpha] per channel as GIRK1/2's density increases. The persistent G[Beta][gamma]/channel (but not G[alpha] /channel) ratio support a strong association of GIRK1/2 with G[Beta][gamma], consistent with recruitment to the cell surface of G[Beta][gamma], but not G[alpha] , by GIRK1/2. Our analysis suggests a maximal stoichiometry of 4 G[Beta][gamma] but only 2 G[alpha] 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 G[Beta][gamma], underlie the complex pattern of basal and agonist-evoked activities and allow GIRK1/2 to act as a sensitive bidirectional detector of both G[Beta][gamma] and G[alpha] .