Orthosteric- versus allosteric-dependent activation of the GABAA receptor requires numerically distinct subunit level rearrangements

Anaesthetic molecules act on synaptic transmission via the allosteric modulation of ligand-gated chloride channels, such as hetero-oligomeric α1β2γ2 GABAA receptors. To elucidate the overall activation paradigm via allosteric versus orthosteric sites, we used highly homologous, but homo-oligomeric, ρ1 receptors that are contrastingly insensitive to anaesthetics and respond partially to several full GABA α1β2γ2 receptor agonists. Here, we coexpressed varying ratios of RNAs encoding the wild-type and the mutated ρ1 subunits, which are anaesthetic-sensitive and respond with full efficacy to partial GABA agonists, to generate distinct ensembles of receptors containing five, four, three, two, one, or zero mutated subunits. Using these experiments, we then demonstrate that, in the pentamer, three anaesthetic-sensitive ρ1 subunits are needed to impart full efficacy to the partial GABA agonists. By contrast, five anaesthetic-sensitive subunits are required for direct activation by anaesthetics alone, and only one anaesthetic-sensitive subunit is sufficient to confer the anaesthetic-dependent potentiation to the GABA current. In conclusion, our data indicate that GABA and anaesthetics holistically activate the GABAA ρ1 receptor through distinct subunit level rearrangements and suggest that in contrast to the global impact of GABA via orthosteric sites, the force of anaesthetics through allosteric sites may not propagate to the neighbouring subunits and, thus, may have only a local and limited effect on the ρ1 GABAA receptor model system.


Results
Imparting sensitivity to intravenous anaesthetics to the ρ 1 receptor. The homo-oligomeric GABA A ρ 1 receptor is insensitive to the intravenous anaesthetics etomidate, propofol, ketamine, midazolam, and pentobarbital 56,57 . To impart sensitivity to these structurally diverse classes of anaesthetics to the ρ 1 receptor, we mutated the ρ 1 subunit in TM 2 /TM 3 at positions 307(Ile)/328(Trp). We then examined the responses of the resulting mutants to different concentrations of anaesthetics in the presence of their respective EC 4 GABA (for EC 50 values, see Table 1). Figure 1 shows the potentiating action of the GABA-evoked current from ρ 1 307/328 mutants in response to these structurally diverse intravenous anaesthetics. Several 307/328 double mutations of the ρ 1 receptor conferred striking sensitivity to all the aforementioned anaesthetics (Fig. 1). The double mutants containing substitutions of Ile307 with Asn and Trp328 with Met or Ala exhibited a marked sensitivity to etomidate and propofol. Etomidate evoked 130 to 1700% potentiation at 10 to 50 µM of the ρ I307N/W328M receptor (see Fig. 1b and Table 2 for the potentiation values). Propofol also markedly increased the GABA currents, resulting in approximately 50 to 500% potentiation of the ρ I307N/W328M and ρ I307N/W328A receptors (2 to 20 µM, Fig. 1c). We also assessed the sensitivity of a number of ρ 1 307/328 mutants to ketamine, which is a dissociative anaesthetic that acts mainly as an NMDA blocker and shows a positive modulatory action on the α 6 β 2/3 δ GABA A receptor subtype 58,59 . Regarding ρ I307N/W328A , ketamine at 50, 100, and 200 µM potentiated the GABA currents by approximately 30-200% (Fig. 1d). The benzodiazepine (midazolam and diazepam) and barbiturate (pentobarbital) classes of intravenous anaesthetics also significantly increased the GABA-induced currents in the 307/328 mutants (2 to 20 µM). The substitutions of Ile307 with Ser and then Ile307 with Asn produced the highest levels of potentiation with midazolam and pentobarbital, respectively ( Fig. 1e and f). Overall, the propofol-, etomidate-, midazolam-, and pentobarbital-dependent modulation of the ρ 1 307/328 mutants occurred at clinically relevant concentrations. Thus, the 307/328 mutations conferred marked sensitivity to several classes of diverse anaesthetics including midazolam, pentobarbital, ketamine, propofol, and etomidate.
Pentobarbital and benzodiazepine diazepam were capable of directly activating the ρ 1 307/328 mutants at relatively higher concentrations. Figure 2a and d depict the current traces and the concentration-response relationships for pentobarbital and diazepam in the ρ 1 , ρ I307S/W328I , and ρ I307S/W328V receptors. The wild-type ρ 1 receptor was found to be insensitive to the direct action of these anaesthetics (Fig. 2). By contrast, both pentobarbital and diazepam directly activated the ρ 1 307/328 mutants in µM concentrations. Pentobarbital activated ρ I307S/W328I with an EC 50 of 181 ± 19 µM and a slope of 2.19 ± 0.09, while the corresponding numbers for the action of diazepam on ρ I307S/W328V were 102.3 ± 5.9 µM and 5 ± 1. The maximum current amplitudes that were elicited by pentobarbital and diazepam relative to those elicited by GABA were approximately 0.94 in the ρ I307S/W328I receptors and 0.68 in the ρ I307S/W328V receptors (see Table 3 for the relative maximum amplitudes).
In summary, concomitant substitutions of ρ Ile307 with Asn or Ser and ρ Trp328 with Met or Ala imparted sensitivity to five structurally distinct anaesthetics to ρ 1 receptors. In the anaesthetic-sensitive hetero-oligomeric α 1 β 2 γ 2 GABA A receptor, Asn and Ser were found at the corresponding TM 2 , while Met and Ala were found at the equivalent TM 3 positions of the β 2 and α 1 subunits, respectively, thereby validating the use of the ρ 1 receptor as a model system to study the mechanism of action of anaesthetics.
Co-impartation of full efficacy to partial agonists. The GABA agonists imidazole 4-acetic acid (I4AA) and (Z)-3-[(aminoiminomethyl)thio] prop-2-enoic acid (ZAPA) are partial agonists of the ρ 1 receptor but act as full agonists at the α 1 β 2 γ 2 GABA A receptors 60,61 . We then examined the action of the GABA agonists I4AA and ZAPA in the ρ 1 307/328 mutants. Several 307/328 mutations, which have been shown here to confer sensitivity to anaesthetics to the ρ 1 receptor, also converted the partial agonists I4AA and ZAPA into full agonists. Figure 2b and d show the GABA-and I4AA-induced current traces and the concentration-response relationships in the ρ 1 , ρ I307S/W328I , and ρ I307S/W328V receptors. The maximal current amplitudes elicited by I4AA and ZAPA relative to those elicited by GABA in the wild-type ρ 1 receptor were approximately 0.04. In marked contrast, both I4AA and ZAPA were full agonists in ρ I307S/W328I or ρ I307S/W328V (Both I4AA and ZAPA elicited maximal currents relative to that of GABA that were greater than 0.95, Table 3, Fig. 2c). In conclusion, the 307/328 mutations not only conferred sensitivity to diverse classes of anaesthetics but also imparted full efficacy to the partial agonists I4AA and ZAPA in the ρ 1 receptor. Differential contributions of Ile307 and Trp328. We then asked whether the Ile307 and Trp328 mutations contribute differently to the conversion from partial to full GABA agonists and the impartation of anaesthetic sensitivity. To dissect the individual contribution of each mutation, the current maximal value of the I4AA relative to that of GABA was determined in the mutants ρ I307S (or N) and ρ W328M . The single substitution mutation of Ile307 with Ser (ρ I307S ) or Ile307 with Asn (ρ I307N ) conferred nearly full efficacy to I4AA (a maximum-induced current of ~70% with respect to that of GABA). By contrast, I4AA was a partial agonist of ρ W328M with an efficacy that was similar to that at the ρ 1 receptor (Table 3). It has been shown previously that ρ I307S displays a relatively low pentobarbital sensitivity at the potentiation level (with no apparent direct agonist action) 20 . By contrast, a substitution of Trp328 alone in the TM 3 with any hydrophobic residue (e.g., ρ W328M ) imparts a high sensitivity to pentobarbital to the ρ 1 receptor at both the potentiation and direct activation levels (with maxima relative to that mediated by GABA of 10 to 20%) 19 . Thus, in the double mutant (e.g., ρ I307S/W328I ), the Ile307 to Ser substitution contribute to the increasing efficacy, whereas the Trp328 mutation is key to conferring anaesthetic sensitivity to the ρ 1 receptor.

Distinct activation by GABA versus anaesthetics.
We utilized the capacity of the ρ 1 307/328 mutations, which collectively impart full efficacy to otherwise partial GABA agonists and anaesthetic sensitivity, to compare the mechanism of activation of GABA agonists to that of anaesthetics. Using co-injection of cRNAs for the wild-type and the mutated ρ 1 subunits at different ratios to express different ensembles of receptors containing five, four, three, two, one, or zero mutated subunits, we attempted to identify the number of mutated subunits that is sufficient 1) to confer full efficacy to otherwise partial GABA agonists and 2) impart anaesthetic sensitivity. Prior to the experiments, the maximal GABA-induced current amplitudes of the key mutants (ρ I307S/W328I and ρ I307S/W328V ) relative to that of wild-type were first examined following equivalent injections of each mutant versus wild-type cRNAs (see Materials and Methods). These experiments yielded maximal GABA-induced currents in ρ I307S/W328I and ρ I307S/W328V relative to that for wild-type ρ 1 of 0.93 and 0.43, respectively (Table 4). Thus, ρ I307S/ W328I exhibited a maximal GABA-induced current that was nearly equal to that of the ρ 1 receptor, while for the ρ I307S/W328V , this value was approximately half of that of the ρ 1 receptor. Then, the cRNAs of ρ 1 and ρ I307S/W328I or ρ 1 and ρ I307S/W328V at ratios of 1:6, 2:5, 3:4, 4:3, 5:2, and 6:1 (ρ 1 : ρ 307/328 mutants ) were co-injected to express distinct ensembles of the following six subpopulations of receptors: homo-oligomers of wild-type and mutant subunits and hetero-oligomers containing one, two, three, and four mutated subunit(s). For the controls, the cRNAs of ρ 1 , ρ I307S/W328I , or ρ I307S/W328V were also injected individually. In each injected oocyte, we then determined the maximal currents evoked by GABA, I4AA, ZAPA, and pentobarbital after injections of different ratios of ρ 1 : ρ I307S/W328I , ρ 1 and ρ I307S/W328I ; we further determined the maxima of GABA, I4AA, ZAPA, and diazepam with varying ratios of ρ 1 :ρ I307S/W328V , ρ 1 , and ρ I307S/W328V . The maximal currents that were evoked by I4AA, ZAPA, and the anaesthetics   Table 2. Potentiation values (% increase) of etomidate, propofol, midazolam, and pentobarbital in the presence of EC 4 GABA in the ρ 1 and ρ307/328 mutants. Pentobarbital-and diazepam-dependent potentiation of ~ EC 4 GABA arising from ρ 1 and different ratios of ρ 1 mutant to wild-type. All data are presented as the mean ± standard error (s.e.m.).
were then normalized to their respective GABA maximal current values (see Materials and Methods). The averages of the relative current maxima (to that elicited by GABA) with I4AA, ZAPA, or pentobarbital with ρ 1 ; ρ I307S/ W328I ; 1:6, 2:5, 3:4, 4:3, 5:2, and 6:1 cRNA ratios of ρ 1 : ρ I307S/W328I are presented in Fig. 3 whereas the averages of the relative current maxima (to that of GABA) with I4AA, ZAPA, or diazepam with ρ 1 ; ρ I307S/W328V ; and varying ratios of ρ 1 : ρ I307S/W328V are shown in Fig. 4. With increases in the ratio of the wild-type to mutated cRNAs, a progressive reduction in the relative current maxima (to that elicited by GABA) for I4AA, ZAPA, pentobarbital, or diazepam was discernible, but the degree of the overall decline at each ratio was markedly greater with the anaesthetics (diazepam or pentobarbital) than the GABA agonists (I4AA or ZAPA). For example, for the 1:6 ratio of ρ 1 : ρ I307S/ W328I cRNAs, the relative current maxima (to that mediated by GABA) decreased to approximately 0.87 with both GABA agonists, i.e., I4AA and ZAPA (from 0.98 in the homo-oligomeric ρ I307S/W328I ); the corresponding values of the 1:6 ratio of ρ 1 : ρ I307S/W328V declined to 0.79 and 0.82 with I4AA and ZAPA, respectively (from ~0.95 in ρ I307S/W328V , Supplementary Information-Datasets). By contrast, the relative current maxima of pentobarbital   or diazepam (to that elicited by GABA) at 1:6 (ρ 1 : ρ 307/328 mutants ) exhibited a significantly greater decline compared to that of I4AA or ZAPA, thereby diminishing the corresponding value of the 1:6 ratio of ρ 1 : ρ I307S/W328I to 0.47 with pentobarbital (from 0.94 in ρ I307S/W328I ) and of the 1:6 ratio of ρ 1 :ρ I307S/W328V to 0.23 with diazepam (from 0.68 in ρ I307S/W328V ). The differential reductions in the relative current maxima (with respect to that induced by GABA) between the GABA agonists and the anaesthetics continued after increasing the ratio of the wild-type  Table 4. The GABA-induced maximal current of key ρ 307/328 mutants (used in the mixing experiments) relative to that of ρ 1 at equivalent cRNA injections. All data are presented as the mean ± standard error (s.e.m.). to the mutated cRNAs, showing a greater prominence with diazepam. The decline in the relative current maximum (to that of GABA) with diazepam was markedly greater than that with pentobarbital across the different ratios, which may be due to 1) the lesser maximum current with diazepam (to that mediated by GABA) in the homo-oligomeric ρ I307S/W328V than that with pentobarbital in ρ I307S/W328I and 2) the lower GABA maximal current (based on maximal GABA-induced current for ρ I307S/W328V relative to that for wild-type, at equivalent cRNA injection) of ρ I307S/W328V compared to that of the wild-type (Table 3). We used a binomial equation to determine the relative quantities of the receptor sub-populations that contained five, four, three, two, one, or zero mutated subunits at each ratio and assumed an equivalent assembly of wild-type and mutated subunits (Fig. 3a, Supplementary Information-Datasets). Then, using an iterative process, we conducted simulation studies to determine the likelihood of contribution of each sub-population of receptor(s) in the ensemble toward the total response to I4AA, ZAPA, or the anaesthetics. In the subpopulation ensembles at each ratio, the experimentally determined values were utilized for the homo-oligomers of the wild-type or mutated receptors, while, depending on the model, all (homo-oligomeric mutant-like activity) or none of the weight (wild-type-like activity) was assigned to the hetero-oligomeric receptors that contained four, three, two, or one mutated subunits with unknown activity. Three different models were tested. In the first model, the contribution of only the subpopulation of homo-oligomeric mutant receptors with all the weight activity (homo-oligomeric mutant-like activity) given to the overall current was considered; the remainder of the sub-populations was speculated to have wild-type-like activity (close to zero). In the second model, two receptor sub-populations in the ensemble were simulated to have all the weight mutant-like activity, including the homo-oligomer of the mutant and the hetero-oligomer with the four mutated subunits. The remainder of the four subpopulations was presumed to have wild-type like activity. Finally, in the third model, three subpopulations of receptors containing five, four, and three mutated subunits were assumed to exhibit mutant-like activity, while the remaining three subpopulations were believed to exhibit wild-type-like activity. In the simulation of the total activity at each ratio, the known (homo-oligomer) values and the presumed (hetero-oligomer) values for each receptor sub-population were multiplied by the corresponding sub-population fraction that was present in the ensemble (determined using a binomial equation). The resulting values were then summed (For details regarding the simulation procedures, see Methods and Supplementary Information-Datasets). In comparison to the wild-type, all simulations were corrected for the lower maxima current (relative to that mediated by GABA) of diazepam or pentobarbital in the homo-oligomeric ρ I307S/W328V or ρ I307S/W328I , as well as the lower GABA maximal current of ρ I307S/W328V (based on maximal GABA-induced current for mutant relative to that for wild-type, at equivalent cRNA injection). The conclusions were unaffected even if no corrections for the differences in the GABA-induced maxima were included in the simulation steps for ρ I307S/W328V (see Supplementary  Information-Datasets). Figures 3 and 4 show the three simulations for the ρ 1 :ρ I307S/W328I and ρ 1 :ρ I307S/W328V co-expression studies (in the form of bars and different shades of grey). A comparison of the data points with the three different simulations at each ratio demonstrated that the summation of the contributions of the receptors containing three or more mutated subunits (i.e., the summation of the receptors containing five, four, and three mutated subunits) with mutant-like activity best matched the experimental data of the GABA agonists I4AA and ZAPA (denoted by a hash # on the bar , Figs 3c and 4b). In striking contrast, the model simulation that represented only the contribution of the homo-oligomer of the 307/328 mutant subunits with mutant-level activity (only the receptor sub-population of five mutated subunits) corresponded to the experimental data of pentobarbital (Fig. 3c, denoted by a hash #) and diazepam (Fig. 4b, denoted by a hash #).
Then, we constructed diazepam concentration-response relationships for the 1:6 and 2:5 ratios from the ρ 1 : ρ I307S/W328V experiments. These experiments were carried out to determine whether the diazepam-induced current arises solely from a single sub-population of receptors (ρ I307S/W328V ) or a mixture of homo-and hetero-oligomeric receptor-channels (with different EC 50 s and slopes) in the co-expressional experiments. The derived EC 50 and Hill coefficient in these experiments were nearly identical to the corresponding values in the ρ I307S/W328V receptor ( Table 1), indicating that the diazepam-induced current observed in the experiment using the 6:1 or 2:5 ratios of ρ 1 : ρ I307S/W328V cRNAs arose mainly from the sub-population of the homo-oligomeric ρ I307S/W328V .
In summary, our data indicate that GABA and anaesthetics act via distinct mechanisms in terms of the number of mutated subunits that are necessary for direct activation; three 307/328 mutated subunits are sufficient for the GABA-dependent action, while the corresponding mutations must be present in all five subunits for the anaesthetic-dependent activation to transpire.

A single mutated subunit confers anaesthetic-dependent potentiation of GABA currents.
We then examined the mechanism underlying the anaesthetic-dependent modulation of the GABA current by deciphering the minimal number of mutated subunits that are necessary to confer potentiation. The co-expression of cRNAs for the wild-type with ρ I307S/W328Y or ρ I307S/W328A at different ratios were used to determine the mechanism underlying the anaesthetic-dependent potentiation at the subunit level. The ρ I307S/W328Y receptor showed a high sensitivity to diazepam, while the ρ I307S/W328A receptor exhibited a marked sensitivity to pentobarbital in potentiation action (see Tables 1, 3, and 4). At equivalent cRNA injection, ρ I307S/W328A exhibited a maximal GABA-induced current that was nearly equal to that of the ρ 1 receptor, while for the ρ I307S/W328Y , this value was approximately 0.6 of that of the wild-type ( Table 4). The GABA concentration-response relationship was constructed for ρ I307S/W328A and ρ I307S/W328Y . These experiments demonstrated that the ρ I307S/W328A and ρ I307S/W328Y mutants had GABA EC 50 s that were similar to those of the wildtype (~1 and 0.5, respectively, compared to 0.6 µM in the wild type). This finding was an important consideration since the degree of the potentiation magnitude is highly dependent on the relative GABA-induced activity of the receptor-channel 22 . To determine the minimal number of mutated subunits that are necessary to confer potentiation, the cRNAs of ρ 1 and ρ I307S/W328Y or ρ 1 and ρ I307S/W328A were co-injected at ratios of 22:1, 5:2, 4:3, 3:4, and 2:5 (ρ 1 : ρ 307/328 mutant ). In the presence of the approximate EC 4 GABA, the extents of the diazepam-(30 µM, for ρ I307S/W328Y ) and pentobarbital-(20 and 50 µM, for ρ I307S/W328A ) dependent potentiation were then determined at each ratio. Figure 5 shows the pentobarbital (ρ I307S/W328A )-and diazepam (ρ I307S/W328Y )-dependent potentiation levels of ρ 1 , ρ I307S/W328A , ρ I307S/W328Y , as well as of different ratios of ρ 1 : ρ I307S/W328A and ρ 1 : ρ I307S/W328Y . In the presence of the EC 4 GABA, pentobarbital (50 µM) caused only a minuscule change in the GABA currents arising from the ρ 1 receptor but increased the corresponding GABA current of ρ I307S/W328A by 870 ± 89% (Table 2). At the 22:1 ratio (wild-type:mutant), assuming an equal assembly of wild-type and mutant subunits, the binomial calculations predicted that 80% of the constituted receptors in the ensemble were wild-type, while the remainder were comprised of primarily hetero-oligomeric receptors with only a single mutated subunit (four wild-type, Fig. 5a). At the 22:1 ratio of ρ 1 : ρ I307S/W328A , pentobarbital (20, 50, 100, or 200 µM) produced a potentiation that was significantly greater than that in the wild-type ( Fig. 5c and d; statistically greater than wild-type, p < 0.05, Supplementary Information-Datasets). In the diazepam-dependent modulation, there was also a statistically greater potentiation compared to that in the wild-type in the experiments corresponding to the 22:1 ratio of ρ 1 : ρ I307S/W328Y ( Supplementary Information-Datasets). Thus, in contrast to the direct receptor activation by diazepam or pentobarbital, the modulatory properties of the anaesthetics can be imparted to the receptor sub-population containing a single mutated subunit.
To study the mechanism underlying the anaesthetic-dependent modulation, we constructed models to carry out potentiation simulations at each ratio. For these calculations, we used the experimentally determined potentiation values for the subpopulation of receptors corresponding to the homo-oligomers of the wild-type or mutant subunits. However, the values of the potentiation magnitude arising from hetero-oligomeric receptors containing one, two, three, or four mutated subunit(s) were unknown and were therefore estimated by reducing the known potentiation values of the mutated homo-oligomers by ~0.5 n (0.47 n , 0.5 n , and 0.53 n for pentobarbital; 0.57 n , 0.6 n , and 0.63 n for diazepam), where n represents the number of the wild-type subunits in the pentamer. The numbers (~0.5 n ) used in these simulations to estimate the potentiation values of the hetero-oligomeric channels at the tested concentrations of the anaesthetics were derived using an iterative process. The total potentiation simulations at each ratio, as shown in Fig. 5, were then calculated by multiplying the known (for homo-oligomers) and the presumed (for hetero-oligomers) potentiation values by the corresponding fraction of the subpopulations that were present in each ensemble (determined using the binomial equation) followed by summing the resulting values ( Supplementary Information-Datasets). Figure 5 depicts the three simulations for each co-expression at different ratios of wild-type:mutant experiments (in the form of horizontal lines, different shades of grey). For each ratio, the simulation numbers corresponded closely to the data points of the pentobarbital-or diazepam-dependent potentiation (Fig. 5c and e). An examination of the simulated potentiation values of each receptor sub-population reveals that the sequential replacement of each wild-type subunit with a mutant subunit in the pentamer did not appear to increase the potentiation levels synergistically in the tested concentration range of the anaesthetics. For example, a single hetero-oligomeric receptor with two mutated subunits (of ρ I307S/W328A ) generates a potentiation level (e.g., 0.5 3(# of wild-type subunits) *870%) that is nearly equal to the sum of the potentiation values of two receptors each having a single mutated subunit (e.g., 0.5 4(# of wild-type subunits) *870% + 0.5 4 *870% = 2*0.5 4 *870% = 1*0.5 3 *870%).
Collectively, these studies demonstrate that the magnitude of the potentiation declines sequentially along with the reduction in the number of mutated subunits in the pentamer. Importantly, receptors that contain even a single mutated subunit are sensitive to the potentiation action of the anaesthetics.

Discussion
Using coexpression of cRNAs for the wild-type and mutated (307/328) ρ 1 subunits at different ratios, we demonstrate that the number of anaesthetic-sensitive ρ 1 subunits crucial for imparting full efficacy to the partial GABA agonists in the pentamer is three, while the number needed to confer anaesthetic sensitivity at the level of direct activation is five. Importantly, the number of anaesthetic-sensitive ρ 1 subunits needed to convey potentiation by the anaesthetics is one.
Mutations in the key residues ρ Ile307 and ρ Trp328 play distinctive roles in the co-impartation of the full efficacy to the partial GABA agonists (I4AA) and anaesthetic sensitivity to the ρ 1 receptor. Both Ile307 and Trp328 are located at the hydrophobic/hydrophilic interface in the upper leaflet of the membrane bilayer; however, the Trp side chain not only constitutes the largest volume among all amino acids, but it also has the potential to anchor the TM 3 polypeptide to the membrane interface. Mutations in ρ Trp328 could dislodge the TM 3 from the membrane interface and create a void, thus exposing the delicate gating components to anaesthetic action. However, the substitution of the highly hydrophobic ρ Ile307 with the hydrophilic Ser can shift the gating component, which is located in the TM 2 , closer to the hydrophilic upper leaflet, hence contributing to an increase in the efficacy of the GABA agonists (and allosteric agonists). Collectively, the double 307/328 mutations may create novel relaxed state(s) with relatively reduced free energy levels of activation 44 , in which access to or efficient alignment with the molecular actions of anaesthetics is probable.
Our key finding is that the activation of GABA A receptors by GABA via orthosteric sites compared to that by anaesthetics via allosteric sites requires numerically distinct subunit level rearrangements. In the GABA-dependent activation mode, the number of GABA binding steps (at the orthosteric sites) needed to open the channel differs between the homo-oligomeric ρ 1 and the hetero-oligomeric α 1 β 2 γ 2 receptors 3, 49-52, 62, 63 . It is currently well-established that for the ρ 1 receptor, the required number of GABA bindings to open the channel is three (one per subunit, with five total subunits) 50, 51 , while for the α 1 β 2 γ 2 receptor, the required number of GABA bindings is only two 49, 64 (one per β-α subunits; out of five). This raises the following question: what are the underlying structural and mechanical differences underlying the lower efficiency that is observed in the GABA-dependent activation of ρ 1 compared to that of α 1 β 2 γ 2 receptor? The α 1 β 2 γ 2 receptor exhibit fixed stoichiometry with two non-equivalent, but predetermined, GABA binding sites intermittingly positioned at the β-α interface of the pentamer (See Fig. 6), which is similar to the homologous hetero-oligomeric nicotinic acetylcholine receptor 65 . GABA agonists bind to the extracellular domain in the interface of the two subunits with an asymmetrical geometry, presumably via a strong electrostatic bonds 66,67 . Thus, the binding of GABA to the higher affinity site may impart structural perturbation to the two subunits, leading to a facilitation of subsequent secondary binding in the α 1 β 2 γ 2 receptor. Consequently, the sequential but intermittent bindings of two GABA molecules at the orthosteric sites have the capacity to impact four subunits, thus rendering them into the relaxed state. In comparison, for the ρ 1 receptor, the first binding can occur randomly at any of the five potential GABA binding sites at the interface, potentially transforming two subunits into their relaxed states. This first binding then cooperatively facilitates the second consecutive binding at the adjacent subunit. However, the perturbation (a) A model of the GABA-dependent activation of α 1 β 2 γ 2 compared to that of the ρ 1 GABA A receptors. T and R represent tense and relaxed states, respectively. Note that in this model, a single GABA binding can stabilize two subunits into a relaxed state and cast a more widespread effect on the overall structure. For the α 1 β 2 γ 2 receptor, the intermittent binding of two GABA molecules can stabilize four subunits into a relaxed state, while for the ρ 1 receptor, three consecutive GABA binding events (three GABA molecules) are needed to achieve the same task. (b) Represents the distinct model of the anaesthetic-dependent activation of the mutated ρ 1 receptors. In the presented model, the anaesthetics produce a local and limited effect on the state of the subunits.
(stabilization) caused by the secondary binding to the ρ 1 receptor may transmit to only three subunits. Therefore, to complete the stabilization of the four subunits into their relaxed states, GABA binding to a third consecutive site is needed (see the presented model in Fig. 6). Therefore, in a model where rendering four subunits into the relaxed state via the orthosteric sites dictates an open configuration, the number of GABA molecules required for the α 1 β 2 γ 2 receptor binding is two, while for the ρ 1 receptor, the number required is three. Thus, through efficient inter-subunit action (location) and the presumed strong nature of its binding force, GABA can exert a relatively global action on the structure of the receptor-channel 68 . In contrast to GABA action, our data support the notion that anaesthetics act locally and transmit a more limited force on the stabilization of the channel in the open configuration. The following three findings support the local effects of anaesthetics: 1) Anaesthetic molecules act allosterically in the channel in the transmembrane medium close to the gating component likely through a weak hydrophobic interaction. 2) The five-subunit (the entire pentamer) requirement to confer anaesthetic-dependent direct activation indicates the weak nature of the transduction in opening the channel. 3) A single anaesthetic-sensitive subunit, paradoxically, confers an anaesthetic-dependent potentiation, but the addition of each mutated subunit does not appear to increase the potentiation levels synergistically. How can one explain the differences in the requirement for activation versus modulation (all 5 subunits versus 1 subunit)? In the modulatory mode, in a model in which three sequential GABA binding events stabilize the channel in the open state, the anaesthetic-dependent activation of a single subunit needs to enhance the binding of GABA to the receptor only in the first binding step, thus increasing the efficiency of the subsequent GABA bindings and the eventual channel opening. Collectively, these findings indicate that, unlike GABA, the force of anaesthetics does not appear to propagate to the neighbouring subunits, is limited in its scope and poses only a local effect on the channel.
The interaction between the GABA agonist and the orthosteric sites required to open the channel has been evolutionarily optimized through precise/specific positioning of the GABA binding sites, the tuning of the inter-subunit dynamics, and the facilitation of the transduction/stabilization processes. Anaesthetic effects, by contrast, appear to be more generic, their site of action is not as fine-tuned, and their transduction/stabilization is not as enhanced. In the evolutionary ladder of ligand-gated ion channels, the hetero-oligomeric receptors (e.g., α 1 β 2 γ 2 ) evolved more recently 69 . The fact that two versus three GABA molecules are needed to bind the receptor to open the hetero-versus homo-oligomer of GABA A receptors suggests that the optimization in terms of the tuning of the inter-subunit dynamic and the facilitation of the transduction/stabilization processes has resulted in a binding/opening process in the hetero-oligomeric α 1 β 2 γ 2 that is more efficient than that in the ρ 1 receptor. Thus, the difference in the α 1 β 2 γ 2 receptor versus the ρ 1 receptor predicts that in the allosteric-dependent activation by anaesthetics, the number of subunits required to bind (sense) the anaesthetic may be lower in the α 1 β 2 γ 2 receptors relative to that in the ρ 1 GABA A receptors.
Our findings demonstrate that, in comparison to GABA, anaesthetic molecules not only use a different site of action but also exhibit a different activation paradigm to maintain the channel in the open state. Thus, allosteric molecules such as anaesthetics can modulate GABA-gated ion channels in a dynamically distinct fashion.

Methods
Oocyte preparation and electrophysiology. The oocyte isolation, site-directed mutagenesis, complementary RNA (cRNA) synthesis, cRNA injection into the oocyte, the drug perfusion system, and the oocyte electrophysiology have been previously described 22,58 . The quality of the cRNAs was determined by electrophoresis of set dilutions of the cRNA on a 1% formaldehyde-containing agarose gel. The amount of cRNA was first determined and matched by interpolation of lanes containing different dilutions of the cRNA and then quantified spectrophotometrically. Following the injection, the oocytes were incubated in a solution containing the following (in mM): 5 HEPES, 82.5 NaCl, 2.5 KCl, 1 CaCl 2 , 1 MgCl 2 , 1 Na 2 HPO 4 , and 2.5 Na pyruvate, with the pH adjusted to 7.5 with NaOH. This mixture was supplemented with 50 U/ml penicillin, 50 µg/ml streptomycin, and 2% horse serum. The oocytes were maintained at 14 °C. The recording solution (OR 2 ) contained the following (in mM): 5 HEPES, 92.5 NaCl, 2.5 KCl, 1 CaCl 2 , and 1 MgCl 2 , with the pH adjusted to 7.5 with NaOH. All methods relating to animal procedures were approved by Animal Care and Use Committee of University of South Florida, and were carried out in accordance with Guidelines of the National Institute of Health for the Use of Laboratory Animals.

Comparison of the wild-type and mutant expression levels.
To measure the expression levels of the key mutant subunits (ρ I307S/W328I , ρ I307S/W328V , ρ I307S/W328Y , and ρ I307S/W328A ) relative to those of the wild-type subunits, the cRNAs of the wild-type or mutant ρ 1 subunit were injected individually into sets of oocytes at equal quantities. The same needle was used for the injections of the wild-type and the mutant cRNA to ensure equal quantities of the cRNA injection. The needle was washed several times between injections to avoid cross contamination. The maximal GABA-induced currents were then determined 4 days post-injection (see Supplementary  Information-Datasets). To evoke the maximal GABA current in the wild-type and mutant subunits, concentrations of GABA equivalent to 20 to 100 times the corresponding EC 50 values were used. The average and SEM of the maximal elicited GABA current were first determined for each injection set of the wild-type and mutant subunits. To calculate the relative expression levels of the key mutants, the average of the maximal GABA current in the mutant was divided by the average of the maximal GABA current in the wild-type ( Table 4).
Determination of the maximal current in the co-expressional studies. To evoke the maximal current for the wild-type, mutant, and different wild-type:mutant ratios, concentrations of agonists equivalent to 3 to 100 times the corresponding EC 50 values were used. To determine the maximal-induced current of the different agonists, each oocyte injected with cRNA of ρ 1 , ρ I307S/W328I , ρ I307S/W328V , different ratios of ρ 1 : ρ I307S/W328I , or that of ρ 1 : ρ I307S/W328V was tested with two applications of GABA, followed by applications of two GABA agonists (I4AA and then ZAPA), anaesthetics, and finally GABA again. Washes of several minutes each were conducted between applications. To determine the relative maxima, the maximal current values for each I4AA, ZAPA, or anaesthetic were then normalized to their respective maximal GABA current values. The current values used in the calculations were limited to those with a magnitude that was less than 1 µA. Data fitting and binomial calculations. The data points for the concentration-response relationships were fitted to the following logistic equation: where I is the peak current at a given concentration of agonist A, and I max is the maximum current. EC 50 is the concentration of the agonist yielding a half-maximal current, and n is the slope. The EC 4 values were determined based on the concentration-response relationships. The extrapolated values were tested and then adjusted empirically.
The fraction of each sub-population of receptors (containing five, four, three, two, one, or zero mutated subunits) at each ratio was determined using the binomial equation based on the following assumptions: (1) the receptor is a pentamer, (2) the efficiency of the assembly was not affected by the mutations, and (3) the two different stoichiometries present in the receptor chimaeras containing two or three mutated subunits are equivalent in function. The binomial equation is as follows: n r r where for a given ratio, r is the number of wild-type subunits incorporated at a given time (e.g., 3); n is the number of subunits in the receptor complex (5); P(r) is the sub-population fraction of the receptor comprising the r wild-type subunits; and p and q are the probabilities of the wild-type and the mutant subunit assimilation, respectively. For example, for the 6:1 ratio of the wild-type to mutant injection, p is equal to 6/7, while q is equal to 1/7.
The percent increases in the GABA currents induced by the anaesthetic (% potentiation) were calculated using the following equation: where I GABA is the current value elicited by a given concentration of GABA, and I GABA+Anaesthetic is the evoked current induced by the same concentration of GABA plus the anaesthetic.

Mathematical simulations.
To determine the number of mutated subunits that are required for the activation by the GABA agonist compared to that required for the activation by the anaesthetics, simulations were carried out by assigning experimentally determined values to the sub-population of the homo-oligomers of the wild-type (wild-type-like, close to zero activity) or mutated receptors (mutant-like, close to 100% activity). For the hetero-oligomer receptors containing four, three, two, or one mutated subunits (with unknown activity), depending on the model, either all (homo-oligomeric mutant-like activity) or none weight (wild-type-like activity) was assigned to each receptor sub-population. Three models were considered as follows: 1) The contribution from only the subpopulation of the homo-oligomeric mutant receptors with all weight activity (homo-oligomeric mutant-like activity, ~100%) on the overall current was considered; the remainder of the sub-populations was then speculated to have wild-type-like activity (close to zero). 2) Two receptor sub-populations in the ensemble were simulated to have mutant-like activity. These included the homo-oligomer of the mutated subunit and the hetero-oligomer with four mutated subunits. The remaining four subpopulations were presumed to have wild-type-like activity. 3) Finally, three subpopulations of receptors containing five, four, and three mutated subunits were assumed to exhibit mutant-like activity, while the remaining three subpopulations were instead assumed to have wild-type-like activity (Figs 3 and 4; see Supplementary Information-Datasets for the simulation steps).
To derive the final value of each ratio, the known (homo-oligomers) and the presumed values (hetero-oligomers) of each receptor sub-population were multiplied by the corresponding sub-population fraction present in the ensemble (determined using binomial equation), and the resulting numbers were then summed.
To correct for the differences in the expression levels (determined based on maximal GABA-induced current for mutant relative to that for wild-type, at equivalent cRNA injection), between the wild-type ρ 1 and ρ I307S/W328V and the ρ 1 and ρ I307S/W328Y in the simulations, the relative sub-population (fraction) of the receptors containing five, four, three, two, one and zero mutated subunit(s) at each ratio was first estimated using the binomial equation, which assumed the equal assembly of wild-type and mutated subunits. Each subpopulation of receptors was then corrected for the difference in GABA maximal using the following procedure. First, the determined fraction (binomial calculation) of each receptor subpopulation containing 3 or more mutated subunits in each ensemble was multiplied by the relative GABA maximal determined for the mutant (e.g., ~0.5 for ρ I307S/W328V , mutant-like expression), while the expression of the receptor subpopulations containing 3, 4 and 5 wild-type subunits was corrected by the wild-type-like expression in terms of GABA maximal (~1). Second, the products from the first step were summed. Finally, each receptor sub-population, corrected for its GABA maximal levels, was normalized to the derived sum in the second step ( Supplementary Information-Datasets). Notably, the number of required mutated subunits for the GABA agonist-dependent versus the anaesthetic-dependent activation and the number of mutated subunits needed for potentiation were unaffected if the lower maxima of ρ I307S/W328V or ρ I307S/W328Y were not considered in the calculations of the simulation studies ( Supplementary Information-Datasets).