Cooperative regulation by G proteins and Na+ of neuronal GIRK2 K+ channels

G protein gated inward rectifier K+ (GIRK) channels open and thereby silence cellular electrical activity when inhibitory G protein coupled receptors (GPCRs) are stimulated. Here we describe an assay to measure neuronal GIRK2 activity as a function of membrane-anchored G protein concentration. Using this assay we show that four Gβγ subunits bind cooperatively to open GIRK2, and that intracellular Na+ – which enters neurons during action potentials – further amplifies opening mostly by increasing Gβγ affinity. A Na+ amplification function is characterized and used to estimate the concentration of Gβγ subunits that appear in the membrane of mouse dopamine neurons when GABAB receptors are stimulated. We conclude that GIRK2, through its dual responsiveness to Gβγ and Na+, mediates a form of neuronal inhibition that is amplifiable in the setting of excess electrical activity. DOI: http://dx.doi.org/10.7554/eLife.15751.001


Introduction
Potassium channels oppose membrane electrical excitability by driving the membrane voltage towards the K + reversal potential, near -90 mV in mammalian neurons. In the nervous system many inhibitory neurotransmitters act through G protein coupled receptors (GPCRs), which regulate a G protein gated inward rectifier K + (GIRK) channel (Pfaffinger et al., 1985;Lesage et al., 1994;Lesage et al., 1995;Wang et al., 2014). In this form of signaling G proteins are released by stimulated GPCRs and diffuse on the cytosolic surface of the membrane to a site on the K + channel. A tight complex of the b and g G protein subunits (known as the 'Gbg subunit') binds to GIRK, favors the open conformation, and drives the membrane potential towards the K + reversal potential (Pfaffinger et al., 1985;Logothetis et al., 1987;Reuveny et al., 1994;Krapivinsky et al., 1995) ( Figure 1A).
Extensive research on GIRK channels in both neurons and cardiac cells has identified three important regulators of GIRK channel gating: Gbg subunits, the signaling lipid PIP 2 and intracellular sodium (Logothetis et al., 1987;Wickman et al., 1994;Huang et al., 1998;Sui et al., 1998;Ho and Murrell-Lagnado, 1999a;Petit-Jacques et al., 1999). Many aspects of how these ligands interact with the channel, whether they are absolutely required for channel opening, and how they interact with each other through their respective interactions with the channel have remained unclear. Some studies supported an absolute requirement for Gbg subunits (Logothetis et al., 1987;Wickman et al., 1994;Krapivinsky et al., 1995), while others concluded that Mg 2+ -ATP with Na + (Petit-Jacques et al., 1999) or PIP 2 (Huang et al., 1998) were by themselves sufficient to open GIRK channels in the absence of Gbg subunits. Furthermore, attempts to determine Gbg affinity for GIRK channels in cell membranes, assessed by applying detergent-solubilized Gbg to membrane patches, yielded values ranging from 3 nM to 125 nM (Wickman et al., 1994;Krapivinsky et al., 1995). The problem with these studies is the membrane partition coefficient for detergent-solubilized Gbg is not known and therefore the membrane concentration is not known. Isothermal titration calorimetry (ITC) measurements with a soluble form of Gbg (lipid anchor-removed) and a soluble cytoplasmic domain of a GIRK channel (removed from the transmembrane pore) measured the affinity to be 250 mM (Yokogawa et al., 2011). These experiments can only report binding affinity in the absence of energetic coupling to a gated pore, which was absent in the experiment.
Given the difficulty in knowing accurately the composition and quantity of components in living cell membranes -the experimental system in which the majority of studies had been carried outwe developed a total reconstitution assay to investigate the regulation of neuronal GIRK2 channel gating (Wang et al., 2014). Using planar lipid bilayers in which purified GIRK2 channels, G protein subunits and PIP 2 were reconstituted, we found that Gbg subunits and PIP 2 are simultaneously required to open GIRK2 channels (each alone is insufficient) and that Na + is not required for opening, but modulates GIRK2 channel opening. Because planar bilayers allow quantitative control of lipid concentrations, the reconstitution study also permitted a detailed characterization of channel opening as a function of the PIP 2 concentration.
While it is possible to specify lipid (e.g. PIP 2 ) concentrations in a planar bilayer membrane, it is not possible to specify protein concentrations by simply mixing components during the bilayer membrane synthesis. For this reason, the reconstitution study described above did not permit accurate control of membrane Gbg concentration. In the current study we present a method to specify Gbg subunit concentration in planar lipid membranes and use the method to determine the Gbg-GIRK2 channel activity relationship. We then show that intracellular Na + regulates GIRK2 channel gating mostly by increasing the GIRK2 affinity for Gbg. Finally, we use the newly defined quantitative relationship between Gbg, Na + , and GIRK2 channel activity to estimate the membrane concentration of Gbg subunits that appear in mouse dopamine neuron membranes upon stimulation of GABA B receptors. eLife digest Signals from outside of a cell can alter the activity inside the cell. This process often involves members of a large family of proteins called G protein-coupled receptors (GPCRs) that are found on the surface of many cells in the body. When these receptors are activated they release a G protein on the inside of the cell that then splits into two parts. One of these parts -called the Gbg subunit -can directly bind to, and open, a protein channel called a GIRK channel in the cell membrane. Once opened, these channels allow potassium ions to flow into the cell.
GIRK channels are involved in a number of processes in the body. For example, GIRK2 is a major type of GIRK channel found in nerve cells. When this channel is activated the flow of potassium ions into the cell inhibits the nerve cell's activity and makes it less likely to send electrical impulses. However, it was not clear how many Gbg subunits are required to activate a GIRK2 channel. Now, Wang et al. report that four Gbg subunits must bind to a GIRK2 channel and then work together to open it. This means that a GIRK2 channel will switch between a closed and an open state whenever the density of Gbg subunits released onto the cell membrane reaches a certain threshold.
Wang et al. also found that a high concentration of sodium ions in the cell causes the Gbg subunits to bind more strongly to the GIRK2 channel; this makes that channel more likely to open and inhibit the nerve cell's activity. This action serves to dampen down the activity of the most active neurons, because highly active nerve cells contain more sodium. Also, in a related study, Touhara et al. -who include many of the same researchers -discovered that sodium ions affect GIRK4 channels from heart cells in a similar way.
These findings shed new light on G protein signaling, but there is still more that is not yet completely understood. Wang et al.'s findings suggest that the concentration of Gbg subunits in certain nerve cells is much higher than previously expected, and further work is now needed to explore how this might be achieved.

Results and discussion
Controlling membrane G protein concentration A method to control the concentration of G proteins on the surface of a lipid bilayer membrane is illustrated ( Figure 1B, Figure 1-figure supplement 1). GIRK2 channels were reconstituted into planar lipid membranes formed with known mole fractions of Ni-NTA lipid, doped into otherwise biological phospholipids (Nye and Groves, 2008;Knecht et al., 2009;Platt et al., 2010;Masek et al., 2011). Modified Gbg subunits with a His-tag replacing the lipid anchor on the g subunit were then  added at known concentrations to the solution on one side of the membrane with the idea that these would anchor to the membrane via the Ni-NTA lipid (Kubalek et al., 1994;Schmitt et al., 1994;Knecht et al., 2009;Platt et al., 2010). All experiments were carried out in the presence of a fixed concentration of 32 mM C8-PIP 2 to ensure high occupation of PIP 2 sites on the channel: 32 mM C8-PIP 2 , based on channel activity measurements, corresponds to 0.02 mol fraction (2%) membrane PIP 2 (Wang et al., 2014). Example data using this assay are shown ( Figure 1C). In the absence of Ni-NTA lipid, addition of soluble Gbg with a His-10 tag (sGbg-His10) to a solution concentration of 2 mM failed to activate the channel. The presence of channels in the membrane was subsequently confirmed by addition of a maximally effective (but unknown) concentration of lipid-anchored Gbg through vesicle fusion with the membrane. In another experiment, when the same concentration of sGbg-His10 was added to a membrane formed with 0.0019 mol fraction Ni-NTA (19 out of 10,000 lipid molecules in the membrane containing the Ni-NTA head group), channels were activated ( Figure 1C). Subsequent addition of excess lipid-anchored Gbg to the same membrane showed that about 60% of the GIRK channels had been activated by the Ni-NTA lipid-anchored Gbg. All further experiments were performed in the manner described, ending with saturation of the membrane with Gbg to achieve maximal activation of the GIRK channels present. This normalization step enables comparison of currents measured in different membranes with different numbers of GIRK channels by placing them on a common scale (normalized current).
In the assay two equilibrium reactions occur, as depicted ( Figure 1B). First, sGbg-His10 binds from solution to the Ni-NTA lipid, and second, the sGbg-His10-Ni-NTA lipid complex binds to the channel. We are ultimately interested in the second reaction as this determines channel activation as a function of Gbg concentration on the membrane (Gbg density in 2 dimensions). In Figure 2A the black symbols and curve show the normalized GIRK current level as a function of sGbg-His10 solution concentration with a membrane containing Ni-NTA lipid at a mole fraction 0.0019. Normalized currents under these conditions reach a maximum value around 0.6 (60% of current that is reached when the same membranes are saturated with lipid-anchored Gbg). A maximum, saturated value below 1.0 can be explained if 2 mM sGbg-His10 is sufficient to occupy all Ni-NTA lipid molecules in the membrane, but the concentration of Ni-NTA lipid in the membrane is too low to occupy all sites on the channel. This explanation is supported by the graph on the right ( Figure 2B) in which normalized current is plotted as a function of Ni-NTA lipid mole fraction in the presence of 2 mM sGbg-His10 (i.e. a concentration that is sufficient to occupy all Ni-NTA lipid molecules). This graph is asymptotic to~1 at higher values of Ni-NTA lipid mole fraction, and, as one would expect, 0.6 on the Y-axis corresponds to 0.0019 on the X-axis. A third graph ( Figure 2C) of values from the X-axis in Figure 2B, plotted as a function of corresponding values (dashed lines) from the X-axis in Figure 2A, isolates the binding reaction of sGbg-His10 to Ni-NTA lipid. The curve is a rectangular hyperbola (binding isotherm) with a K d of 150 nM ( Figure 2C, black curve). A similar binding curve and affinity were determined for fluorescent sGbg-His10 adsorption onto giant unilamellar vesicles (GUVs) containing Ni-NTA lipid at a mole fraction of 0.03 (Figure 2-figure supplement 1).
The blue data points and curve in Figure 2A show a similar set of experiments using sGbg-His4, that is, a soluble form of Gbg with 4 instead of 10 histidine residues in its tag. The normalized current level is asymptotic to a value higher than 0.6 (blue curve). The explanation for this becomes evident when the (apparent) Ni-NTA lipid mole fraction is plotted against the corresponding (blue dashed lines) sGbg-His concentration ( Figure 2C, blue symbols and curve): in this binding isotherm the affinity is lower and the maximum apparent Ni-NTA lipid mole fraction is~3 times higher. This result follows if sGbg-His4 binds to a single Ni-NTA lipid and sGbg-His10 binds to 3 Ni-NTA lipids. This stoichiometric difference is consistent with known structures of Ni-NTA-polyhistidine complexes, which show that a single Ni-NTA group is coordinated by 2 histidine residues separated by at least one histidine residue (Knecht et al., 2009). Thus, sGbg-His4 can only attach to a single Ni-NTA lipid while sGbg-His10 can -and does -attach to three.
All further experiments were carried out using sGbg-His10 at 2 mM concentration to fully occupy the Ni-NTA lipid binding sites in the membrane and thus ensure that the concentration of Gbg in the membrane would be controlled solely by the Ni-NTA lipid mole fraction. In other words, this approach isolates the reaction of interest -channel activity (related to occupancy in a manner to be determined) as a function of known membrane Gbg concentration. The graphs report Gbg concentration as Ni-NTA lipid mole fraction, while keeping in mind that the molar density of Gbg in the membrane is one third that of the Ni-NTA lipid density.

G protein and Na + regulation of the GIRK2 channel
Having established an assay to control the concentration of Gbg in the membrane, we measured the activity of GIRK2 as a function of membrane Gbg concentration as well as solution Na + concentration ( Figure 3A). At each Na + concentration, normalized current increases as a steep sigmoidal function of membrane Gbg concentration ( Figure 3B). The slope of these functions on a log-log plot at sufficiently low Gbg concentrations (achieved in these experiments for the Gbg titrations at lower Na + concentrations) are consistent with four Gbg subunits being required to open a GIRK2 channel (see methods) ( Figure 3C). A strong effect of Na + on the functional relationship is clear and noteworthy because in cells Na + is known to regulate GIRK currents, but by a mechanism that is unknown (Sui et al., 1996;Ho and Murrell-Lagnado, 1999b;Petit-Jacques et al., 1999). The titrations show that Gbg activates the channel to a greater extent, especially at lower Gbg concentrations, as Na + is increased ( Figure 3B). To further understand how these two ligands interact with the channel to regulate its gating we constructed an equilibrium model. This model was guided by atomic structures, which show that a tetramer GIRK2 channel has 4 structurally identical Gbg binding sites and 4 Na + Figure 3. GIRK activity as a function of Gbg and Na + concentration. 2 mM sGbg-His10 was included in the solution on the intracellular side of GIRK. (A) Normalized GIRK current (red spheres, mean ± SEM, n = 3-5 membranes) is graphed as a function of Gbg and Na + concentration. Surface mesh shows predictions of a model for ligand activation (Figure 3-figure supplement 1). (B) Data points in (A) are graphed as a family of curves (surface intersections) corresponding to each Na + concentration. (C) Log-log plot of normalized current against NTA lipid mole fraction. Data points corresponding to 0.0001 NTA lipid mole fraction were excluded because the current levels (<0.02 normalized current) were much smaller than background noise. Other data points are connected with solid lines. Dashed lines show the slope of the line connecting the first two graphed data points. (D) A schematic of the ligand activation model fit to the data. i and j are integers between 0 and 4. The fitted parameters are: equilibrium dissociation constant for the first Na + to bind in the absence of Gbg, K dn = 60 ± 20 mM, equilibrium dissociation constant for the first Gbg in the absence of Na + , K db = 0.019 ± 0.007, cooperativity factor for each successive Gbg binding b = 0.30 ± 0.06, cross-cooperativity factor between Gbg and Na + binding h = 0.63 ± 0.04 and an activity term as described in Figure 3-figure supplement 1. A comparison of fits to the data using cooperative and non cooperative models is shown in Figure 3  binding sites (Whorton and MacKinnon, 2013). The model contains 25 states, corresponding to an order-independent occupation number 0 to 4 for each ligand ( Figure 3D and Figure 3-figure supplement 1). Fitted parameters in the model include a dissociation constant and cooperativity factor for each ligand, a cross cooperativity factor between Gbg and Na + and a parameter relating ligand occupancy to channel activity (see Figure 3-figure supplement 1). The data and modeling support the following conclusions. First, all four Gbg binding sites must be occupied on the channel before it opens, consistent with the limiting slope analysis ( Figure 3C). Second, Gbg binding is cooperative with a factor of 0.30, which means the fourth Gbg subunit binds with an affinity 37 times higher than the first. Attempts to fit the data imposing no cooperativity (b = 1) yields higher residuals (0.126 compared to 0.064 when allowing cooperativity) and fail to replicate the steep rise in channel activity as a function of Gbg concentration (Figure 3-figure supplement 2). The strong cooperative binding of four Gbg subunits accounts for the steep sigmoidal dependence of GIRK current on membrane Gbg concentration ( Figure 3A,B). Third, Gbg binds with a Na + cross cooperativity factor (h) of 0.63, which means Gbg binds with 6-fold higher affinity when four Na + sites are occupied compared to when the Na + sites are not occupied. This effect of Na + on Gbg affinity accounts for channel opening at lower membrane Gbg concentrations as Na + concentration increases ( Figure 3B).
The ability of Na + to increase the affinity of Gbg is demonstrable in another way, through a simple, intuitive analysis. The family of data points ( Figure 3B) conform well to the Hill equation with a single global Hill coefficient (n » 3) but variable, Na + -dependent equilibrium constant for Gbg binding ( Figure 4A). The Gbg equilibrium constant decreases (i.e. the affinity for Gbg increases) as Na + concentration increases according to a rectangular hyperbola, with a~6-fold difference between maximum and minimum values ( Figure 4B). The apparent equilibrium constant for the effect of Na + on Gbg activation is~5 mM, which is very close to the physiological Na + concentration in the cytoplasm of a resting neuron (Rose and Ransom, 1997). Thus, the GIRK2 channel's response to Gbg should be sensitive to changes in Na + concentration right in the physiological range.

Structural basis of Gbg cooperativity and Na + activation
The atomic structures of the GIRK2 channel and its complex with ligands offers clues to the mechanistic underpinnings of Gbg and Na + regulation of GIRK2 beyond the 4:1 stoichiometry of ligand binding ( Figure 5A). When four Gbg subunits bind to the cytoplasmic domain of GIRK2, which forms a ring made by the four channel subunits, they cause the ring to rotate as a rigid body with respect to the pore, which twists open the helical bundle that forms the pore's gate (Whorton et al., 2013).
Because the rigid body rotation involves all four subunits at once, conformational changes induced by the binding of Gbg to one site will favor binding at the neighboring sites (i.e. positive cooperativity). A cartoon illustrating this concept depicts Gbg binding more favorably to the channel's open conformation ( Figure 5B). Because opening involves a concerted rotation of the subunits, all four Gbg binding sites change to higher affinity at once, giving rise to strong positive cooperativity. In addition to increasing Gbg affinity, Na + also increases the GIRK2 current when the Gbg binding sites are fully occupied: at the highest (0.03) Ni-NTA lipid mole fraction Na + increases current approximately 2.5-fold when Na + is increased from 0 mM to 32 mM ( Figure 3A). This increase follows a rectangular hyperbola. The simplest physical explanation for this behavior, which is also consistent with the equilibrium model, is that Na + stabilizes the open, conductive state of the channel in direct proportion to its occupancy on the channel. In other words, four Gbg subunits bind to GIRK2 and permit opening to a probability that is higher in proportion to occupancy of the Na + sites. Thus, by thermodynamic linkage, Na + would increase the apparent affinity of Gbg for GIRK2 and it would also increase the maximum level of current reached when four Gbg subunits bind. This physical mechanism is consistent with the location of the Na + binding sites at the interface between the cytoplasmic domains and the transmembrane pore, where opening is transduced through the binding of Gbg ( Figure 5A) (Whorton et al., 2013). It is also consistent with the observations that Na + in the absence of Gbg does not open GIRK ( Figure 3A) and in crystal structures Na + binds to GIRK but does not cause a rotation of the cytoplasmic domain in the absence of Gbg (Whorton and MacKinnon, 2011). Thus, Na + facilitates Gbg-mediated pore opening.

Physiological role of Na + amplified Gbg activation
How might neuronal electrical signaling be affected by the GIRK2 channel's dual regulation by Gbg and Na + ? GIRK2 suppresses electrical activity in neurons when inhibitory neurotransmitters stimulate GPCRs on the cell surface, such as GABA B receptors, which release Gbg on the intracellular membrane surface to open GIRK2 channels. At the same time, the level of GIRK2 channel opening -and therefore the level of neuronal inhibition -brought about by the released Gbg potentially depends on the intracellular Na + concentration. This conclusion derives from the family of Gbg activation curves ( Figure 3B): at all Gbg concentrations, the level of GIRK2 current is increased as Na + is increased. We refer to this phenomenon as Na + -amplification of Gbg-activated current. Na + -amplification is clearly not constant but is instead a function of the Gbg concentration: at high Gbg concentrations (right side of graph) amplification is 2.5-fold (i.e. GIRK2 current increases 2.5-fold) when Na + is increased from 0 to 32 mM, while at lower Gbg concentrations (corresponding to the steep sigmoidal rise in current) amplification approaches ten fold. The potential importance of Na + amplification to neuronal electrical signaling lies in the fact that cytosolic Na + increases with higher levels of electrical activity due to Na + entry through both synaptic channels and voltage-dependent Na + channels (Lasser-Ross and Ross, 1992;Fleidervish et al., 2010, Rose andKonnerth, 2001). Thus, Na + amplification should, in principle, provide a mechanism for strengthening an inhibitory input to a more active neuron.
How large is Na + -amplification in neurons? As noted above, the magnitude of amplification depends on the concentrations of Gbg generated inside a neuron when its GPCRs are stimulated. While the concentration of Gbg inside cells is unknown, the data in this study provide an approach to estimate its value. The rationale is as follows: the curves in Figure 3B characterize the amplification as a function of Gbg concentration, therefore we should be able to solve the inverse problem of deducing Gbg concentration by measuring the Na + amplification in a cell. Figure 6 shows this analysis applied to GIRK currents recorded in midbrain dopamine neurons when baclofen was used to stimulate GABA B receptors. A recording pipette was used to set the cytoplasmic Na + concentration to either 0 or 27 mM. Baclofen-activated currents had the strongly inwardly-rectifying current-voltage relationship expected from GIRK channel activation ( Figure 6A). Baclofen-activated GIRK current was much smaller in neurons recorded with 0 mM internal Na + compared with those recorded with 27 mM internal Na + ( Figure 6B,C). Currents measured with 27 mM internal Na + were amplified by an average of 8 fold compared to currents with 0 mM Na + . From the Gbg/Na + titration data ( Figure 3B), 8-fold amplification corresponds to a Gbg concentration of about 0.003 in NTA-lipid mole fraction units ( Figure 6D). In this concentration range the amplification curve becomes very steep, allowing relatively small cell-to-cell variations in Gbg concentration to translate into larger differences in current response ( Figure 6E). This property offers an explanation for the large spread of current values measured upon baclofen activation in the presence of 27 mM Na + . Most importantly, the estimated Gbg concentration stimulated by baclofen in dopamine neurons ( Figure 6D,E) is centered in the middle of the steep sigmoidal rising phase of the Gbg-activation curves ( Figure 3B). In this regime even modest changes in intracellular Na + concentration should amplify Gbg-mediated inhibition of neuronal electrical activity. The intracellular Na + concentration in neurons is subject to complex regulation by multiple channels and transporters and changes during neuronal activity (Rose and Ransom, 1997). Intracellular Na + in dendrites can double during synaptic activity (Rose and Konnerth, 2001), and high local increases also occur in cell bodies and axons during action potential firing (Lasser-Ross and Ross, 1992;Fleidervish et al., 2010). Thus, the Na + amplification of GIRK currents likely occurs during normal physiological activity. Even stronger amplification is likely during epileptiform activity, when intracellular Na + can likely reach 30 mM (Raimondo et al., 2015).

Gbg membrane density and channel affinity
Taking into account the surface area of a lipid head group and the stoichiometry of 3 Ni-NTA lipid molecules per sGbg-His10 subunit, a mole fraction value 0.003 (i.e. the concentration of Gbg subunits estimated in dopamine neurons) translates into approximately 1200 Gbg subunits per mm 2 of membrane. To place this 2-dimensional membrane density into more familiar concentration units we multiply the membrane surface area by the linear dimension of a Gbg subunit (about 70 Å ) to approximate a Gbg concentration in the solution layer adjacent to the membrane equal to 280 mM. At this Gbg concentration GIRK is between 10% and 80% activated, depending on the Na + concentration ( Figure 3B). Thus, the apparent affinity of Gbg for the GIRK channel is in this range.
This estimate is close to the affinity reported using ITC to study the interaction of lipid anchorremoved Gbg in solution with the soluble cytoplasmic domain of a GIRK channel (250 mM) (Yokogawa et al., 2011). A more careful comparison, however, reveals a fascinating difference. Removed from the pore, the cytoplasmic domain, even though it is a tetramer with four Gbg binding sites like the full channel, binds to Gbg according to a 1:1 binding isotherm. As we have shown here, the full GIRK2 channel by contrast exhibits strong cooperativity, the first Gbg subunit binding with very low affinity (equilibrium constant 0.019 mol fraction corresponding to 1.9 mM in the solution layer adjacent to the membrane) and the fourth binding with higher affinity (equilibrium constant (0.019) Â (0.3) 3 mol fraction corresponding to 50 mM in the solution layer adjacent to the membrane). This cooperativity, which gives rise to the steep dependence of GIRK channel activity on Gbg concentration, is completely lost when the transmembrane pore is removed. The mechanism proposed for coupling Gbg binding to pore opening, illustrated in Figure 5, offers an explanation: when the pore is removed, Gbg binding free energy is no longer utilized to twist open the pore's helical gate, and at the same time the rotational origin of cooperativity disappears. The ITC-determined affinity of 250 mM lies in between the affinities of the first (1.9 mM) and fourth (50 mM) Gbg subunits to bind to the intact, cooperative system.
In the context of other known protein complexes, the interaction of Gbg with GIRK2 is weak, consistent with a short lifetime for the complex. For example, two proteins with a diffusion-limited association rate constant of, say, 10 7 M -1 sec -1 , will remain in complex on average for less than 2 milliseconds if the equilibrium constant is 50 mM (i.e. affinity of the fourth Gbg subunit) and the lifetime of an activated channel (GIRK2 with 4 Gbg subunits, any one of which can dissociate) less than 0.5 milliseconds. Even if the association rate constant is smaller, the lifetime of an active channel will be brief compared to the duration of macroscopic GIRK current in a cell during GPCR stimulation (~1 s) (Ford et al., 2009). This means Gbg apparently associates and dissociates many times on and . The same scale is used for both recordings. Current was measured as the average current between -142 mV and -147 mV evoked by voltage ramps (1 mV/ms) from +8 to -147 mV delivered from a steady holding potential of -92 mV every 2 s. (C) Collected values for baclofen-induced GIRK current (mean ± SEM) in dopamine neurons equilibrated with 0 mM (n = 10) and 27 mM (n = 11) intracellular Na + . (D) Data and curves from Figure 3B are used to estimate the concentration of Gbg required to yield the 8-fold amplification of GIRK current observed in (C). (E) A Na + amplification curve is defined as the green curve (32 mM Na + , which is near 27 mM) divided by the black curve (0 mM Na + ) in (D). Amplification is a steep function of Gbg concentration near the stimulated levels of Gbg in dopamine neurons. DOI: 10.7554/eLife.15751.013 off the channel during a period of stimulation. Because Gbg binds to Ga(GDP) with greater than ten thousand times higher affinity (K d~1 nM Sarvazyan et al., 1998) than to the channel, whenever Ga (GTP) hydrolyses GTP to GDP it will rapidly bind free Gbg and remove it from the channel by mass action. Thus, the very weak binding of Gbg to the channel means that the duration of GIRK current activation during GPCR stimulation will be controlled by the lifetime of Ga(GTP).
The Gbg concentrations reported here represent the thermodynamic activity concentrations in equilibrium with the GIRK channel. In living cells it is distinctly possible that GIRK and GPCRs/G proteins reside in specialized regions of the cell membrane. In this case the relevant density of Gbg is the local density near GIRK channels, which would be much higher than that averaged over the entire membrane. Such specialized regions would promote locally high Gbg densities, in line with the relatively low affinity for GIRK subunits that allows rapid control of free Gbg by Ga.

Summary
A method to control the concentration (density) of G protein subunits in lipid membranes has let us reach the following conclusions. (1) Four Gbg subunits bind to the GIRK channel with high cooperativity to give rise to a steep dependence of channel activity on membrane Gbg concentration. (2) Intracellular Na + concentration increases Gbg affinity with an apparent K d-Na+ near the cytoplasmic Na + concentration of a resting neuron. (3) Inhibitory GPCR stimulation generates membrane Gbg concentrations corresponding to the steep regime of the Gbg-activation curve. (4) Properties (1) -(3) give rise to Na + amplification of Gbg-activation. Such amplification provides a mechanism for strengthening GPCR inhibition when Na + enters neurons during activity. (5) Gbg binds to GIRK with low affinity. Rapid equilibrium between Gbg and GIRK allows rapid signal termination when Ga hydrolyses GTP to GDP.

Protein expression and purification
Mouse GIRK2 (residues 52-380) was expressed in Pichia pastoris and purified as previously described (Whorton et al., 2011). High Five (Life Technologies, Grand Island, NY) insect cells were infected with baculovirus bearing Human G protein subunits b 1 and g 2 . The G protein Gbg subunit was then purified using an established protocol (Whorton et al., 2013;Wang et al., 2014). To produce non-lipid modified and His-tagged Gbg, baculovirus bearing a mutant Gg 2 DNA with a C68S mutation and a 4-or 10-His tag connected to the C-terminus by a GSSG linker was generated. This mutant virus and the virus bearing b 1 DNA were co-infected into High Five cells. The purification process of non-lipid modified and His-tagged Gbg is essentially the same as non-lipid modified Gbg (Wang et al., 2014) except that PreScission protease digestion was not necessary since no cleavable tag was used.

Fluorescent labeling of sGbg-His10 protein
Purified sGbg-His10 protein was exchanged into conjugation buffer (50 mM potassium phosphate pH 7.4, 100 mM NaCl, 0.1 mM TCEP) and diluted to~1 mg/ml. 5-fold molar excess of Alexa-Fluor 488 maleimide was mixed with the protein. The mixture was rotated at 4˚C overnight. Labeled protein was affinity purified using Ni 2+ -NTA (Qiagen, Valencia, CA) beads followed by size exclusion chromatography in a buffer containing 10 mM potassium phosphate pH 7.4 and 150 mM KCl. The labeling efficiency was approximately one dye per sGbg-His10 protein.
supported in part by NIHGM43949 and NIHNS036855. RM is an investigator in the Howard Hughes Medical Institute.