Steady-state activation of the high-affinity isoform of the α4β2δ GABAA receptor

Activation of GABAA receptors consisting of α4, β2 (or β3), and δ subunits is a major contributor to tonic inhibition in several brain regions. The goal of this study was to analyze the function of the α4β2δ receptor in the presence of GABA and other endogenous and clinical activators and modulators under steady-state conditions. We show that the receptor has a high constitutive open probability (~0.1), but is only weakly activated by GABA that has a maximal peak open probability (POpen,peak) of 0.4, taurine (maximal POpen,peak = 0.4), or the endogenous steroid allopregnanolone (maximal POpen,peak = 0.2). The intravenous anesthetic propofol is a full agonist (maximal POpen,peak = 0.99). Analysis of currents using a cyclic three-state Resting-Active-Desensitized model indicates that the maximal steady-state open probability of the α4β2δ receptor is ~0.45. Steady-state open probability in the presence of combinations of GABA, taurine, propofol, allopregnanolone and/or the inhibitory steroid pregnenolone sulfate closely matched predicted open probability calculated assuming energetic additivity. The results suggest that the receptor is active in the presence of physiological concentrations of GABA and taurine, but, surprisingly, that receptor activity is only weakly potentiated by propofol.

expressing α4β2δ GABA A receptors respond to application of GABA with inward current. Concentrationresponse measurements carried out in the presence of 0.3-1000 nM GABA yielded an EC 50 of 20 ± 10 nM and a Hill coefficient of 0.80 ± 0.09 (mean ± S.D.; n = 6 cells). Sample current traces in the presence of GABA are shown in Fig. 2A.
To convert the raw current amplitudes to units of open probability (P Open ), we compared the response to saturating GABA (0.3 μM) to the response to 300 μM picrotoxin (PTX) and the response to 10 μM GABA + 50 μM propofol. The details of this approach have been reported previously 6,7 . Blockade of activity from constitutively active receptors by PTX is expected to lead to zero GABAergic activity (P Open approaching 0), and receptor activation by the combination of saturating GABA and a high concentration of propofol is expected to generate a maximal possible peak response with a P Open indistinguishable from 1. Comparison of the holding current and peak responses to PTX, GABA, and GABA + propofol, yielded an estimate of 0. 13  where [X] is the concentration of agonist X (GABA in this experiment), K X is the equilibrium dissociation constant for agonist X of the resting receptor, c X is the ratio of the equilibrium dissociation constant for X of the open receptor to K X , and N X is the number of agonist binding sites. L expresses the level of background activity, and can be calculated from constitutive activity as: (1 − P Open,const )/P Open,const .
Curve-fitting of pooled data from 6 cells to Eq. (1) yielded a K GABA of 15.7 ± 2.3 nM (best-fit parameter ± S.E. of the fit) and a c GABA of 0.45 ± 0.01. The number of GABA binding sites was held at two 10 . The concentration-response relationship for peak currents is given in Fig. 2C.
The data indicate that GABA is a weak agonist of the α4β2δ receptor. The binding of two GABA molecules contributes only 0.94 kcal/mol ( × c N RT ln( ) Figure 1. The Resting-Active-Desensitized (RAD) model. The model is shown for agonist X (e.g., GABA) that has two binding sites on the receptor. The receptor can occupy a resting (R), active (A), or desensitized (D) state. The resting and desensitized states are non-conducting, and the active state is conducting (also called "open"). The active and desensitized states have higher affinity to the agonist than the resting state. The parameter L (=R/A) describes the equilibrium between the resting and active states, and the parameter Q (=A/D) describes the equilibrium between the active and desensitized states. K X is the equilibrium dissociation constant for agonist X of the resting receptor. K X c X is the equilibrium dissociation constant for agonist X of the active receptor, and K X c X d X is the equilibrium dissociation constant for X of the desensitized receptor. The inhibitory steroid PS has high affinity to the desensitized state and low affinity to the resting and active states. For the agonists studied, the ratio of affinities for the active and desensitized states (d) is close to 1 (see text for additional discussion). The behavior of the receptor in the RAD model is decribed by Eqs (1-3).
www.nature.com/scientificreports www.nature.com/scientificreports/ stabilization energy 11,12 . Thus, despite the relatively high constitutive open probability (i.e., low intrinsic energy barrier towards channel opening), the theoretical peak maximal open probability of the α4β2δ receptor in the presence of GABA, calculated as + c 1/(1 L ) GABA N GABA , is only 0.44. This is in agreement with previous estimates in single-channel and macroscopic studies demonstrating that GABA is a partial agonist of the α4βδ receptor [13][14][15][16][17] .
To analyze the desensitization properties of the α4β2δ receptor, we fitted the concentration-response relationship for steady-state currents to Eq. (2) 5 : The parameter Q (=A/D) reflects the equilibrium between the active and desensitized states (Fig. 1). The other terms are as described for Eq. (1). Curve fitting of steady-state responses, using K GABA and c GABA constrained to the values determined for peak currents in the same set of cells, yielded an estimate of 0.78 ± 0.08 for Q. Thus, under steady-state conditions, the ratio of open/active vs. desensitized receptors is ~4:5.
Taurine, an endogenous sulfonic acid and a structural analog of GABA, can activate the GABA A receptor [18][19][20][21] . Its effects are likely mediated through interactions with the transmitter binding sites, as suggested by molecular modeling 22 and the finding that the β2(Y205S) mutation in the transmitter binding site that abolishes receptor activation by GABA 10 also eliminates activation of the α1β2γ2L and α4β2δ receptors by taurine (<0.2% of the response to GABA + propofol; data not shown).
Taurine concentration-response measurements on oocytes expressing the α4β2δ GABA A receptor yielded an EC 50 of 9.8 ± 4.8 μM and a Hill coefficient of 0.70 ± 0.08 (n = 6 cells) for peak currents. Fitting the concentration-response data to Eq.  Curve-fitting the peak response data recorded in the presence of 0.01-3 μM 3α5αP yielded an EC 50 of 0.23 ± 0.10 μM and a Hill coefficient of 1.17 ± 0.30 (n = 6 cells). Analysis of the peak currents using Eq. (1) gave a K 3α5αP of 0.21 ± 0.04 μM and a c 3α5αP of 0.68 ± 0.01 with the number of binding sites for 3α5αP held at 2. Sample current responses and the concentration-response relationships are shown in Fig. 4.
To determine receptor desensitization properties in the presence of propofol or 3α5αP, we analyzed the steady-state currents using Eq. (2). With the K and c values constrained to the values estimated by analyzing peak responses, we obtained the estimates for Q of 1.29 ± 0.14 in the presence of propofol, and 0.89 ± 0.33 in the presence of 3α5αP. A higher value of Q is associated with reduced desensitization, i.e., a higher steady-state to peak ratio.
We recently showed that propofol enhances steady-state activity elicited by saturating GABA in the α1β2γ2L receptor 23 . The effect, which is observed as an increase in the apparent value of Q, was attributed to propofol having a higher affinity to the open vs. desensitized state. To determine whether an analogous mechanism underlies the higher value of Q in the α4β2δ receptor activated by propofol, we compared the potentiating effect of propofol on peak and steady-state currents elicited by saturating GABA. We reasoned that if propofol potentiates the responses by enhancing receptor open probability then the potentiating effect will be similar for peak and steady-state activity. On the other hand, if propofol additionally reduces receptor desensitization, then the potentiating effect of propofol on steady-state current should exceed that on the peak response. In five cells, coapplication of 1 μM propofol enhanced the peak response to 0.3 μM GABA to 151 ± 12% of control. Application of 1 μM propofol on steady-state response elicited by 0.3 μM GABA augmented the response to 145 ± 14% of control (n = 5 cells). We infer that within the limits of our experimental precision, propofol does not modify the equilibrium between active and desensitized states.
Modulation of steady-state current by PS. The endogenous steroid PS promotes desensitization of the synaptic-type αβγ GABA A receptor 5,24,25 . Here, we determined the effect of PS on the α4β2δ receptor.
The receptors were activated by a prolonged application of 0.3 μM GABA. Once steady-state response was reached, the flow was switched to GABA + PS. The concentration of PS ranged from 0.1 to 10 μM. Curve-fitting (B) Propofol concentration-response relationship. The data points show mean ± S.D. from at least five cells per concentration. The curve for peak currents was fitted using Eq. (1). The best-fit parameters are: K propofol = 55.1 ± 6.6 μM, c propofol = 0.16 ± 0.01. The number of propofol binding sites was held at 4. The curve for steady-state currents was fitted using Eq. (2) with the K propofol and c propofol values constrained to those determined in fitting the peak currents. The best-fit value for Q was 1.29 ± 0.14. Curve-fitting was carried out using Origin v. In the framework of the RAD model, PS inhibits receptor activity by binding with high affinity to the desensitized state and with low affinity to the resting and active states. For receptors activated by GABA, the open probability in the presence of PS is: where K PS is the equilibrium dissociation constant of the resting and active receptors to PS, and d PS is the ratio of the equilibrium dissociation constant of the desensitized receptor to K PS . The number of sites for PS was assumed to be 1. Other terms are as described above for Eqs (1,2). In this model, PS does not modify the intrinsic properties of the receptor (i.e., L or Q) or the parameters of receptor activation by GABA (i.e., K GABA or c GABA ). Fitting the PS concentration-response data to Eq.
(3) yielded a K PS of 2.6 ± 0.6 μM, and a d PS of 0.14 ± 0.02. The K PS and d PS estimates are similar to the values previously determined for the α1β2γ2L receptor (1.9 μM and 0.11, respectively) 23 . Sample current traces, the concentration-response data, and the fitted curve are shown in Fig. 5.
Steady-state activation in the presence of combinations of GABA, taurine, propofol, 3α5αp and/or PS. We previously showed for the α1β2γ2L GABA A receptor that steady-state activity in the presence of multiple active agents is determined by energetic additivity 5,23 . To verify that the same mechanism determines steady-state activity of the α4β2δ receptor, and to gain insight into receptor function in the presence of multiple endogenous and clinical activators and modulators, we measured steady-state responses in the presence of combinations of orthosteric (GABA, taurine) and allosteric activators (propofol, 3α5αP) and inhibitors (PS). The experimentally observed P Open,S.S. was compared with the predicted P Open,S.S. . The latter can be calculated using Eq. (4): [propofol] [3 5 P] where Γ propofol is: [propofol] propofol propofol propofol N propofol and Γ 3α5αP is: In practice, however, the predicted P Open,S.S. was calculated using Eq. (7) where Π Sum is a measure of peak activation by the mixture of agonists and is related to the peak open probability as: Open,peak Equations (7) and (8)  In total, 8 combinations of drugs and drug concentrations were tested. The concentration of GABA ranged from 10 nM to 10 μM, taurine from 10 to 100 μM, propofol from 1 to 50 μM, 3α5αP from 10 to 30 nM, and PS www.nature.com/scientificreports www.nature.com/scientificreports/ from 0.1 to 1 μM. Not all combinations included all 5 compounds. The data from 53 cells are shown in Fig. 6. A linear fit to all data points yielded an R 2 of 0.82 (P < 0.0001) with a regression slope of 0.99 ± 0.10.

Discussion
Receptors consisting of α4, β2 or β3, and δ subunits are a major extrasynaptic type of GABA A receptors in several brain regions such as the hippocampus and the thalamus [26][27][28][29] . Prior studies have indicated that the α4βδ receptor has a high affinity to GABA, and is only moderately desensitized during prolonged application of agonist [30][31][32][33] . Both properties support its presumed function to mediate tonic Cl − conductance in response to ambient GABA, and the concentration profile of ambient GABA in the brain. The α4βδ receptor is also activated by taurine, endogenous potentiating steroids, and various GABAergic sedative and anesthetic agents 3,14,20,30 . The overall goal of this study was to analyze the function of the α4β2δ receptor in the presence of one or more activators and modulators under steady-state conditions. Previous work has provided evidence for two types or isoforms of receptors resulting from the expression of α4, β (β2 or β3), and δ subunits. In electrophysiological recordings, this manifests as widely different sensitivities to the agonist. The high-affinity type has a GABA EC 50 at <100 nM whereas the low-affinity type has a GABA EC 50 at >1 μM. In some cases, concentration-response relationships show two components in a single cell indicating that both types of the receptor can express concurrently 31 . The underlying reason for differing sensitivity to the agonist is not fully established. Several studies have suggested that it is due to the "promiscuous" nature of the δ subunit that allows for variability in the assembly order of subunits and stoichiometry of the surface receptor. For example, Hartiadi et al. 34 showed that reduction in the ratio of α4 to β2 cRNAs tends to generate receptors with high affinity to GABA whereas changes in δ have no effect. We previously showed that linking individual subunits to concatemeric constructs enables selective generation of low-or high-affinity receptors 32 . In contrast, for receptors activated by the conformationally constrained analog of GABA, THIP, Meera et al. 35 proposed that the two types of behavior are simply due to a mixture of low-affinity αβ and high-affinity αβδ receptors, i.e., incomplete incorporation of δ in all surface receptors. We note that our study was conducted on the "high-affinity" isoform of the α4β2δ receptor.
We have shown that the α4β2δ receptor exhibits relatively high constitutive open probability (P Open,const = 0.1). In the cyclic MWC model, high background activity is associated with enhanced sensitivity to agonist because of a lower energy barrier that needs to be crossed during transition from closed/resting to open/active 9,36 . Despite the high P Open,const , the receptor is only weakly activated by the endogenous agonists GABA and taurine. The maximal peak open probabilities were ~0.4 for either agonist. However, both GABA and taurine are relatively potent agonists, and the equilibrium dissociation constants for GABA (~15 nM) and taurine (10 μM) are near their reported extracellular concentrations of 5-30 nM and 10-25 μM, respectively [37][38][39] . The receptor is weakly directly activated by the endogenous steroid 3α5αP (maximal peak P Open ~0.2), but the intravenous anesthetic propofol is a full agonist (P Open,max ~0.99). www.nature.com/scientificreports www.nature.com/scientificreports/ The estimate for Q (=A/D in Fig. 1) was 0.52 in the presence of taurine, 0.78 in the presence of GABA, 0.89 with 3α5αP, and 1.29 when the receptors were activated by propofol. Followup experiments showed that propofol similarly potentiates peak and steady-state currents from receptors activated by GABA. We infer that the observed difference in Q for GABA vs. propofol is a result of experimental imprecision rather than higher affinity of propofol to the open state as previously observed for the α1β2γ2L receptor 23 . In subsequent simulations, we used a value of Q of 0.87, averaged from the individual estimates in the presence of taurine, GABA, 3α5αP, or propofol.
We tested the independence of the actions of orthosteric and allosteric agents by coapplying various combinations of such agents, and comparing the observed P Open,S.S. with a predicted value calculated using Eq. (7), which assumes additive effects of each agonist and inhibitor. Overall there was a good agreement between predicted and observed data (Fig. 6). We infer that the actions GABA, taurine, propofol, 3α5αP, and PS on the α4β2δ receptor follow the basic rules of energetic additivity. We did not test energetic additivity of the drugs on peak responses.
The data indicate that taurine is a potent agonist of the α4β2δ receptor with an EC 50 (10 μM) near its extracellular concentration in the resting state in brain 37 . This is in agreement with a previous study that showed increased tonic current and reduced action potential firing in the presence of 10-100 μM taurine in the thalamus 20 . The reported EC 50 for taurine on recombinant α4β2δ receptors in HEK cells was, however, higher by several orders of magnitude 20 . We propose that this discrepancy arises from the HEK cells preferentially expressing the low-affinity isoform of the α4β2δ receptor 32 .
Taurine and GABA act additively rather than synergistically because both agonists interact with the same binding site. The calculated (Eq. (4)) steady-state P Open of the α4β2δ receptor is 0.24 in the presence of 30 nM GABA, 0.21 in the presence of 10 μM taurine, and 0.25 in the presence of GABA + taurine. The predicted P Open,S.S. in the simultaneous presence of physiological concentrations of major endogenous GABAergic agonists and modulators -30 nM GABA 39 , 10 μM taurine 37 , 30 nM 3α5αP 40 , and 0.1 μM PS 40 -is 0.24. The addition of 1 μM propofol 41 increases the P Open,S.S. to 0.28. Such a small potentiating effect may be expected given the low affinity of the receptor for propofol (K propofol > 50 μM). The full extent of physiological significance of these predictions is unclear, but the results tend to argue against the α4β2δ receptor being a significant target for propofol.
The overall predicted theoretical dynamic range of steady-state activity in the α4β2δ receptor is relatively small, ranging from ~0.10 (constitutive activity) to ~0.45 (maximal allowable steady-state activity with Q = 0.87). We speculate that the α4β2δ receptor acts to stabilize the membrane potential near the Cl − reversal potential, and that surface receptor turnover plays a relatively large role in regulation of its function.
It is not fully established which affinity isoform is the best recombinant model of the native, neuronally-expressed extrasynaptic receptor. Several lines of evidence support the idea that the "high-affinity" isoform is a better analog of the native receptor. Submicromolar concentrations of THIP activate tonic current in cerebellar granule cells that is missing in the cells from δ knockout mice 35 . The α4β3δ receptors expressed in oocytes produced THIP concentration-response curves with a high-affinity component at <100 nM (assumed to be analogous to high affinity to GABA) and a low-affinity component at >10 μM 35 . A low concentration (10-100 μM) of taurine elicits tonic inhibitory currents in thalamic neurons 20 . This agrees with our study of the high-affinity isoform in oocytes where we saw strong activation in the 1-100 μM range (see above), but not with concentration-response studies of the α4β2δ receptor expressed in HEK cells 20 , which preferentially express the low-affinity isoform 32 . The physiological relevance of the high-affinity isoform is indirectly supported by the finding that the steroid alfaxalone elicits large currents in the presence of picrotoxin in hippocampal neurons transfected with α4β2δ(T269Y) subunits 32 . Finally, we note that the high-affinity isoform of the α4β2δ receptor with a GABA EC 50 at 20 nM is expected to be responsive to extracellular (5-30 nM 38,39 ) GABA, unlike the low-affinity isoform with an EC 50 > 1 μM.

Methods
Receptors and expression. The human α4β2δ GABA A receptors were expressed in Xenopus laevis oocytes.
Harvesting of oocytes was conducted under the Guide for the Care and Use of Laboratory Animals as adopted and promulgated by the National Institutes of Health. The animal protocol was approved by the Animal Studies Committee of Washington University in St. Louis (Approval No. 20170071).
Prior studies have indicated that the α4βδ receptors in oocytes can assemble as isoforms characterized by high affinity to GABA (EC 50 at tens to hundreds of nM) or low affinity (EC 50 in the μM range) to GABA [32][33][34][35] . The high-affinity isoform has been shown to be directly activated by the δ-specific drug DS-2 whereas the low-affinity isoform is potentiated but not directly activated by DS2 34,42 . The underlying mechanism for this discrepancy is not fully understood, but distinct stoichiometries or subunit order in the two isoforms have been proposed as the cause [32][33][34] . The isoform investigated in the present study had a high affinity to the transmitter and was directly activated by DS-2.
Electrophysiology and analysis of current responses. The recordings were conducted at room temperature using standard two-electrode voltage clamp. The pipets were filled with 3 M KCl. The oocytes were clamped at −60 mV. The chamber (RC-1Z, Warner Instruments, Hamden, CT) was perfused with bath solution (see above) at 5-8 ml/min. Solutions were gravity-applied from 30-ml glass syringes with glass luer slips via Teflon tubing, and switched manually.
A typical experiment entailed recording of baseline current for 10-20 s, followed by application of a test compound or a combination of compounds for 60-270 s (1-4.5 min), and by application of bath solution to demonstrate recovery. Due to long exposure times, not all cells yielded a full range of concentration-response data. Thus, the concentration-response relationships shown may reflect mean responses from cells exposed to an incomplete range of agonist concentrations. In such cases, the number of cell provided is given as a range of cell numbers for each concentration point. The effects of the inhibitory steroid PS were determined by coapplying the steroid with 0.3 μM GABA. Each cell was tested with 1-3 concentrations of PS. Each cell was also tested with 10 μM GABA + 50 μM propofol to determine the maximal attainable peak response, which was assigned a P Open of 1, and to which the responses to test drugs were compared. This approach assumes that peak responses are not affected by desensitization, i.e., that desensitization develops slowly compared to activation, and that the combination of GABA + propofol activates all resting receptors. The level of constitutive activity was determined by exposing the cells to 100-300 μM picrotoxin.
The current traces were analyzed using Clampfit (Molecular Devices) to determine the amplitudes of peak and steady-state responses. If steady-state (defined as ΔI < 2% during the last 20 s of agonist application) was not reached by the end of the agonist application, an estimate was made by exponential fitting of the current decay. Fitting was done using pClamp, to a single exponential or sums of up to three exponentials. The constant offset is reported as the steady-state response. The estimated value of the offset was relatively insensitive to the number of exponentials used in fitting (up to ~10% variability in the fitted offset).

Materials and chemicals.
The salts and HEPES used to prepare the bath solution, GABA, and 3α5αP were purchased from Sigma-Aldrich (St. Louis, MO). Propofol was purchased from MP Biomedicals (Solon, OH). Pregnenolone sulfate (PS) was bought from Tocris (Bio-Techne, Minneapolis, MN).
The stock solution of GABA was made in the bath solution at 500 mM, stored in aliquots at −20 °C, and diluted on the day of experiment. Stock solution of propofol was made in DMSO at 200 mM and stored at room temperature. 3α5αP was dissolved in DMSO at 10-20 mM and stored at room temperature. PS was dissolved in DMSO at 50 mM and stored at 4 °C.

Data availability
The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.