Kinetic modeling of Na⁺-induced, Gβγ-dependent activation of G protein-gated K⁺ channels

G protein-activated K⁺ (GIRK) channels are activated by numerous neurotransmitters that act on G_i/o proteins, via a direct interaction with the Gβγ subunit of G proteins. In addition, GIRK channels are positively regulated by intracellular Na⁺ via a direct interaction (fast pathway) and via a Gβγ-dependent mechanism (slow pathway). The slow modulation has been proposed to arise from the recently described phenomenon of Na⁺-induced reduction of affinity of interaction between Gα_GDP and Gβγ subunits of G proteins. In this scenario, elevated Na⁺ enhances basal dissociation of G protein heterotrimers, elevating free cellular Gβγ and activating GIRK. However, it is not clear whether this hypothesis can account for the quantitative and kinetic aspects of the observed regulation. Here, we report the development of a quantitative model of slow, Na⁺- dependent, G protein-mediated activation of GIRK. Activity of GIRK1 _F137S channels, which are devoid of direct interaction with Na ⁺, was measured in excised membrane patches and used as an indicator of free Gβγ levels. The change in channel activity was used to calculate the Na⁺-dependent change in the affinity of G protein subunit interaction. Under a wide range of initial conditions, the model predicted that a relatively small decrease in the affinity of interaction of Gα_GDP and Gβγ (about twofold under most conditions) accounts for the twofold activation of GIRK induced by Na⁺, in agreement with biochemical data published previously. The model also correctly described the slow time course of Na⁺ effect and explained the previously observed enhancement of Na⁺-induced activation of GIRK by coexpressed Gα_i3. This is the first quantitative model that describes the basal equilibrium between free and bound G protein subunits and its consequences on regulation of a Gβγ effector.