Abstract
A restricted version of the ternary complex model for receptorG protein complex formation has recently been proposed. Known as the twostate model, this model proposes that in the context of agonist and G protein interactions, only two thermodynamic states exist for the receptor: active (R*) and inactive (R). One form of this model suggests that only the R* state of the receptor is capable of interacting with and subsequently activating G proteins. We directly tested the kinetic aspects of a strict twostate receptor model in a cell line containing the native β_{2}adrenergic receptor that is capable of inducing G_{s} expression. We examined adenylyl cyclase activity in the presence of limiting GTP levels and concluded that there exists a different rate of heterotrimer dissociation (i.e., HR*G yields HR* + G*) for different β_{2}agonists. This finding is inconsistent with a strict twostate model in which R* is a characteristic of the receptor that is independent of the identity of the agonist. It implies that agonist activation of adenylyl cyclase is more complicated than a simple twostate model.
The concept of agonistinduced receptor conformation has been the subject of much debate. Although the order of the interaction between agonists, receptors, and G proteins is relatively undisputed, the stoichiometry and nature of the proteins during activation remain very much in question. One model in particular that seems to be gathering widespread acceptance for G proteincoupled receptors is the twostate model for receptor activation (13). The twostate model is a restricted version of the ternary complex model (4) and has been extremely useful for explaining the experimental observations involving β_{2}adrenergic receptor activation of adenylyl cyclase. Moreover, its stark simplicity makes it easy to set up arguments that attempt to predict the behavior of other features of the system.
In physicochemical terms, the twostate model cannot be exactly true. Molecules exist in a very large number of conformational states, and trying to describe the thermodynamic properties of a receptor with just two conformational states must be an approximation. That given, the usefulness of the model depends on just how reliable its predictions are. In terms of receptorG protein interactions, a strict twostate model is as shown here: Equation 1where G is the G protein, R is receptor, and H is agonist. It is supposed that the receptor must exist in one of two conformations (R and R*), with both H and G binding with greater affinity to the R* form. Given this condition, there automatically is cooperativity in binding of the G and H to the R (which explains the GTP shift). Moreover, the different efficiencies of different agonists to promote adenylyl cyclase activation is easily explained by supposing that stronger agonists favor binding to the R* form to a greater extent than do weaker agonists and hence more readily form the HR*G ternary complex. In addition, inverse agonists tend to stabilize the inactive R state (5, 6). It must be emphasized that in a strict twostate model, the affinity of G for R is identical to that for HR and its affinity for R* is identical to that for HR* because R and R* represent unique defined conformational states (or collection of states). Given the above setup, it is possible to develop the thermodynamics of the system in terms of the relative concentrations of the two conformations: when free and when bound to G protein, to agonist or to both.
The classic development of the thermodynamics of the H, R, and G interactions in terms of the ternary complex model (4) shown below is not a onestate but rather a multistate approach. The use of a different dissociation constants for the binding of G to HR than for the binding to R is an acknowledgment that the receptor in HR is in a different conformational state than in R Equation 2In this equation, therefore, unlike that for the twostate model, R, HR, and so on represent the totality of possible conformations and not a single conformation or a defined group of conformations in a constant proportion. Thus, although it is superficially simpler than Eq. 1, Eq. 2 is thermodynamically complete and, unlike Eq. 1, it is guaranteed to be correct if the ternary complex model is correct as drawn. Eq. 2 may be compared to a true onestate model shown below in Eq. 3. In this equation, because the receptor can exist in only one conformation, there can be no cooperativity of binding between G protein and agonist. Equation 3The scheme proposed by Samama et al. (1) (shown below in Eq. 4), although described in that publication as a twostate scheme, is in fact a multistate model. The fact that different affinities are used for the binding of H to the R* and the R*G state means that a different conformation is assumed for R* when bound and when not bound to G protein. In other words, there are at least three states. The use of this scheme enables one to be completely accurate with the thermodynamics, but it prevents one from making the simplistic twostate arguments, which are the attraction of the model. Equation 4For the twostate model to be useful in successfully making predictions not possible by the classic thermodynamic approach, additional assumptions beyond the schemes discussed above are necessary. If the assumptions are limited to proposing that agonists bind more strongly to the conformation that also more strongly binds G protein, then no argument can be drawn beyond those already possible for the classic thermodynamic scheme. Similarly, negative agonists that reduce the amount of adenylyl cyclase activity below the basal level found in the absence of ligand can be equally well explained (and predicted) by the classic thermodynamic approach. Where the strict twostate model potentially offers advantages is in quantification of predictions and as a potential for a quantitative relationship between thermodynamic properties (e.g., GTP shifts) and kinetic features (e.g., efficiencies of agonists in adenylyl cyclase activation).
In the current study, we investigated the specific hypothesis that the fraction of ternary complex in the activating conformation (i.e., in the HR*G form) determines the rate at which GDP/GTP exchange occurs. In the strict twostate model, the HR*G conformation is the same for all agonists, which differ only in the ratio of HR*G to HRG_{total} [where HRG_{total} = HRG (inactive R) + HR*G (active R)]. The rationale for the test of this hypothesis is to determine the rate of breakdown of the ternary complex for four different β_{2} agonists. It will be shown that in all the cases the thermodynamics requires that >85% of the ternary complex must be in the HR*G rather than the HRG form. Proportionality of the rate of breakdown for the ternary complex with the fraction of ternary complex that is HR*G would therefore require that all the rates be similar. This did not occur. We will therefore conclude that the twostate model in its strictest form cannot be applied in all cases.
Experimental Procedures
Materials.
Molecular biology reagents, Dulbecco’s modified Eagle’s medium, and geneticin were obtained from GIBCO BRL (Gaithersburg, MD). Tris Base, GTP, and guanosine5′O(3thio)triphosphate were from BoehringerMannheim Biochemicals (Indianapolis, IN). [α^{32}P]ATP, Na^{125}I, and [2,8^{3}H]cAMP were from DuPontNew England Nuclear (Boston, MA). Dexamethasone and the remaining reagents from Sigma Chemical (St. Louis, MO).
Cell culture of an inducible G_{sα} cell line.
The establishment and characterization of a stably transfected murine S49 cyc^{−} T cell lymphoma capable of inducing G_{s} protein after dexamethasone treatment have been previously described (7). Briefly, the S49 cyc^{−} cell line, lacking G_{sα} mRNA and protein (8), was electroporated with the 7.7kb pMMTV · G_{sα} neo vector (a generous gift from J. Gonzales; described in detail in Ref. 9). The vector contains the cDNA encoding rat G_{sαlong} linked downstream of the dexamethasoneinducible mouse mammary tumor virus long terminal repeat promoter. The vector also contains the selection marker for neomycin resistance, neomycin phosphotransferase, constitutively driven by the human βglobin promoter.
Transfected drugresistant cell lines (S49*cyc^{−}) were maintained in stock tissue culture flasks (Corning Glassworks, Corning, NY) at 37° in HEPESbuffered Dulbecco’s modified Eagle’s medium supplemented with penicillin, streptomycin, 10% heattreated horse serum, and 200 μg/ml geneticin to maintain selective pressure. Cells were expanded for G_{sα} gene induction experiments into eight individual preconditioned 2liter roller bottles (Corning) from a single stock source. The final cell density was 1 × 10^{6} cells/ml when the volume was made up to 2 liters with fresh Dulbecco’s modified Eagle’s medium plus 10% horse serum media. G_{sα} protein induction was initiated when the S49*cyc^{−} cells were incubated with 5 μmdexamethasone (final, added from a 10 mg/ml stock prepared in 95% ethanol) for times of 1–24 hr. Transfected control cells underwent no treatment.
Membrane preparations.
Cell membranes were prepared and isolated as follows. Cells were washed twice with an excess of buffer A (137 mm NaCl, 5.36 mm KCl, 1.1 mmKH_{2}PO_{4}, and 1.08 mmNa_{2}HPO_{4}, pH 7.2) by centrifugation at 600 × g. The cells were then resuspended in icecold cell lysis buffer B (20 mm HEPES, 150 mm NaCl, 5 mm NaH_{2}PO_{4}, 1 mm EDTA, and 1 mm benzamidine, pH 7.4; buffer B also contained 10 μg/ml trypsin inhibitor and 10 μg/ml leupeptin to protect G_{sα} from possible proteolysis) and placed in a Parr bomb (at 500 p.s.i.) for 25 min. The disrupted cells were centrifuged for 5 min at 600 × g to pellet nuclear debris. The supernatant was layered onto a 23% and 43% sucrose step gradient in HE buffer (20 mm HEPES and 1 mm EDTA, pH 8.0) and centrifuged at 25,000 rpm in a Beckman Instruments (Columbia, MD) SW 28 rotor for 45 min at 4°. The membrane fraction was collected as a band at the sucrose interface. The membranes were immediately frozen in liquid N_{2} and stored at −80°. Membrane concentrations were determined using the BioRad (Hercules, CA) assay (10).
β_{2} Agonist competition binding: GTP shift analysis.
GTP shift binding analyses were used to analyze the total amount of ternary complex (HRG_{total}) present in the S49*cyc^{−} membrane preparations containing different G_{s} levels as [GTP] → 0. Binding analyses were carried out in 500μl reactions with a single 80 pm concentration of the radiolabeled β_{2} antagonist ^{125}ICYP [prepared according to the protocol of Barovsky et al. (11) with modifications by Hoyer et al. (12)] in the presence of increasing β_{2} agonist concentrations and the following final concentrations of the reagents: 1 mm EDTA, pH 7.4, 20 mm HEPES, pH 7.4, 10 μm phentolamine, 0.3 mm MgCl_{2}, and 20–50 μg of cell membranes (diluted with HE, pH 8.0). The binding reaction was conducted in the presence and absence of 10 μmguanosine5′O(3thio)triphosphate for 55 min at 30°. In some experiments, binding was conducted under adenylyl cyclase assay conditions (see below) to examine the effect of varied GTP concentrations on the area of the GTP shift. In all experiments, the nonspecific ^{125}ICYP binding was determined in the presence of 10 μm alprenolol. Reactions were terminated with the addition of 2.5 ml of icecold stop buffer (50 mm TrisCl, pH 7.4, 10 mm MgCl_{2}) followed by the immediate filtration of the solution [with the use of a Millipore (Bedford, MA) 1225 vacuum filtration apparatus] onto Whatman (Clifton, NJ) GF/C filters. The reaction tubes were rinsed with an additional 2.5 ml of icecold stop buffer. The GF/C filters were washed four or five times with 2.5 ml of stop buffer, dried, and removed to scintillation vials, in which ^{125}ICYP activity was counted on a Beckman Gamma 4000 System Counter for 1 min. Activity, measured as counts per minute, was converted into units of fmol/mg with the aid of a spreadsheet program using Lotus 123. The specific binding of ^{125}ICYP for each concentration was determined as mean values of triplicate measurements for total binding less the mean values of triplicate measurements for nonspecific binding. Data were plotted as log [agonist] versus the normalized fraction of agonist bound and were subsequently analyzed using our recently developed Scatchard method (15) to generate agonist affinity constants (to R and RG, respectively) and [G_{s}]_{total} and HRG_{total}levels. The use of twocomponent nonlinear regression analyses (GraphPAD) to analyze the −GTP curve for HRG_{total} levels resulted in values similar to those obtained according to the Scatchard method (±2.5%). The area for the GTP shifts were determined by the trapezoid method. Comparisons of data ± standard deviations were performed using singlefactor analysis of variance (p < 0.05).
Adenylyl cyclase assays.
Adenylyl cyclase assays, conducted with saturating agonist levels and decreasing GTP concentrations, were used to compare the rate of the ternary complex breakdown for different agonists. The premise for using these assays is described in greater detail below and in Discussion. Briefly, it is known experimentally that at normal (high) GTP concentration, the formation of the heterotrimer complex (HRG_{total}) is rate limiting, and once formed, it interacts with GTP extremely rapidly (13). For a strict twostate model, the rate at which the HR*G complex dissociates should be independent of the agonist used to stabilize the R* conformation; therefore, the rate of HRG_{total} breakdown should be proportional to the fraction of HR*G formed by each agonist. The rate of HR*G dissociation was made rate limiting by reducing GTP and allowing the HRG_{total} complex to accumulate.
Adenylyl cyclase activity was examined in S49*cyc^{−}membranes containing different G_{s} levels using the conditions for adenylyl cyclase assays as described by Clark et al. (14), with some modifications. Briefly, adenylyl cyclase activity in plasma membranes (∼0.2 μg/μl, final) was brought to steady state for 3 min at 30° in a 1800μl volume in a 15 × 100 mm borosilicate glass tube with the following reagents (given as final concentrations): 40 mm HEPES, pH 7.7, 1 mm EDTA, 0.3 mm MgCl_{2}, 8 mm creatine phosphate, 16 units/ml creatine phosphokinase, 0.05 mm ATP, and 0.1 mm3isobutyl1methylxanthine. The preincubation period was necessary to bring the HRG_{total} levels for each agonist to equilibrium. [For any agonist to be effective, the t _{1/2} of HRG_{total} formation cannot be less than thet _{1/2} for adenylyl cyclase inactivation (t _{1/2} = 15 sec for k _{−1}in S49 cells (16)]. Each assay tube consisted of a different GTP concentration (0, 10, 30, 100, and 300 nm, and 1, 3, and 10 μm), so that for a single agonist, a series of eight independent time courses was required to produce a single GTP doseresponse curve. The final concentrations of agonist required to saturate the β_{2}adrenergic receptors (i.e., occupy >90% of receptor sites with agonist) were 10 μm for epinephrine (K_{d} = 1100 nm), 2.2 μm for isoproterenol (K_{d} = 188 nm), 2.8 μm for fenoterol (K_{d} = 400 nm), and 13 μm for dobutamine (K_{d} = 1400 nm).
Time course assays, spanning a 3min period, were initiated with the addition of 40 × 10^{6} cpm [α^{32}P]ATP in a 200μl aliquot containing the concentration of reagents described above. Time course assays were selected over a typical 10min adenylyl cyclase assay to examine the linearity of the response at low GTP concentrations. The reactions were quenched every 18 sec by removing 100μl aliquots into 500 μl of icecold stop buffer. The isolation and determination of [^{32}P]cAMP activity were performed as described by Salomon et al. (15). GTPdependent adenylyl cyclase doseresponse curves were produced using linear regression analysis (GraphPAD, San Diego, CA) to generate the slopes (i.e., cyclase activity) from the linear cAMP accumulation versus time plots. These data were subsequently transformed to EadieHofstee plots to examine the rate of HRG_{total} breakdown (see below). All comparisons of data were performed using singlefactor analysis of variance (p < 0.05, Excel).
Calculating the limiting HRG_{total} and minimum HR*G levels.
The limiting levels of HRG_{total}, as [GTP] → 0, were calculated from the G_{s}:R ratios obtained from GTP shift analyses for each β_{2} agonist. The G_{s}:R ratios, representing the maximum level of receptorG protein interaction in the presence of saturating agonist, were obtained for each S49*cyc^{−} membrane preparation containing variable G_{s} levels using a newly developed Scatchard method (16, and data not shown); however, analysis of HR versus HRG_{total} plots for the −GTP curves with a rectangular hyperbola will yield similar results (±2.5%). With the G_{s}:R level for an agonist, one can determine the limiting HRG_{total} levels by using the following relationship (16):
Equation 5where K
_{RG} represents the dissociation constant between HR and G. The values used forK
_{RG} (unitless when [R]_{total} is set to unity and all concentrations are expressed as fractions or multiples of [R]_{total}) were 0.007 ± 0.002 for epinephrine, 0.011 ± 0.006 for isoproterenol, 0.007 ± 0.003 for fenoterol, and 0.029 ± 0.016 for dobutamine, and [G_{s}]_{total}:R ranged from 0.246 to 0.692 when epinephrine was used in GTP shift studies (16). Under saturating agonist conditions, [HR] ≅ [R]_{total}, and the limiting values for HRG_{total} are determined by solving the following quadratic equation:
Determination of the rate of HRG_{total} breakdown.
In a strict twostate model, the rate of HRG_{total} breakdown should be proportional to the fraction of HR*G formed by each agonist (i.e., once HR*G is formed the rate of breakdown should be agonist independent). The experimental rate of HRG_{total} breakdown was determined by fitting the EadieHofstee plots (with reversed axes so that the xaxis represented υ and the yaxis represented v/s) for cyclase activity to a quartic solution that kinetically describes the GTPdependent activation of adenylyl cyclase (Appendix ). A formal derivation reveals that the yaxis in the present case is
Results
Examination of adenylyl cyclase response with varying GTP concentrations.
The kinetics of adenylyl cyclase activity, under reduced GTP concentrations, were examined in S49*cyc^{−}membranes containing variable G_{s} protein levels as described in Experimental Procedures. At low GTP levels, the system allows heterotrimeric (HRG_{total}) complexes to accumulate, which results in a change in the ratelimiting step of adenylyl cyclase activation from the rate of heterotrimer formation to the rate of active heterotrimer dissociation. The buildup of heterotrimer complexes at low GTP concentrations was confirmed by conducting GTP shift binding analyses with subsaturating GTP levels (4) using adenylyl cyclase assay conditions and demonstrating that the area of the GTP shift was proportional to the level of GTP in the assay (data not shown).
Fig. 1 compares the GTP dependence for adenylyl cyclase activity in the presence of saturating concentrations of four different β_{2} agonists. In the absence of GTP, there was a small but detectable adenylyl cyclase activity, which increased from 1.4 ± 0.4 pmol/min/mg for control membranes with minimal G_{s}expression to 6.73 ± 2.2 pmol/min/mg at high G_{s}levels. This increase in spontaneous activity presumably reflects the increased G_{s} levels and the presence of endogenous guanine nucleotides associated with the membrane preparation. Under saturating agonist conditions, the presence of GTP resulted in increased response until the response became saturated at ∼3–10 μm GTP. Linear regression analysis of the curves indicated that adenylyl cyclase activity was always linear with time (r > 0.9), even under low GTP conditions, during the 3min course of the assay.
The magnitude of the adenylyl cyclase response was dependent on the increasing G_{s} levels in the membrane and the type of agonist used to stimulate activity. The rank order of efficacy (epinephrine ≥ isoproterenol > fenoterol > dobutamine) can be seen clearly in a comparison of the normalized adenylyl cyclase activity with respect to increasing GTP concentrations (Fig. 2). Fig. 2 was generated by computing the slopes of the individual linear responses shown in Fig. 1 using linear regression analysis for each GTP concentration. Sigmoid nonlinear regression curve analysis of the GTP response curves also revealed some agonist dependency of the EC_{50} value for GTP, but in most cases the EC_{50} value for GTP was ∼100–150 nm. The data shown in Fig. 2 were transformed to EadieHofstee plots to analyze the rate of HRG_{total}breakdown (see below).
Determination of the limiting HRG_{total}, HR*G, and rate of HRG breakdown for each agonist.
The test of a true twostate model for receptor activation lies in the assumption that the experimental rate of HRG_{total} dissociation should be proportional to the fraction of activated HR*G complexes. This is predicted to be so if the R* conformation is independent of the type of agonist. Fig. 3 compares the relative levels of HRG_{total}, the minimum HR*G, and rate of ternary complex breakdown for different β_{2} agonists.
The limiting level of heterotrimer complex (HRG_{total}) formed in the absence of GTP was calculated for each agonist using GTP shift binding assays (Ref. 16 and data not shown) as described in Experimental Procedures. With a value of 1.0 for epinephrine, the normalized HRG_{total} values (± standard error) for isoproterenol, fenoterol, and dobutamine are 0.92 ± 0.04, 0.92 ± 0.04, and 0.82 ± 0.09, respectively. The HRG_{total} calculated levels for isoproterenol, fenoterol, and dobutamine were consistently less than that for epinephrine regardless of the G_{s} protein level in the plasma membrane (data not shown). An analysis of variance yielded no statistical difference for the effects of G_{s} protein levels on the measured differences in HRG_{total} levels between the agonists and epinephrine. These data demonstrate that the HRG_{total} levels formed in the absence of GTP seem to be relatively similar from the strong agonist epinephrine to the weak agonist dobutamine.
The values for the minimum HR*G level for each of the agonists were calculated as described in Appendix and Experimental Procedures. Fig. 3 demonstrates that the minimum fraction of active HR*G heterotrimer complexes makes up a significant proportion (>85%) of the HRG_{total} pool. The HR*G levels for each agonist were normalized relative to the HR*G levels for epinephrine. The relative minimum HR*G values (± standard error) for isoproterenol, fenoterol, and dobutamine are 0.920 ± 0.001, 0.915 ± 0.002, and 0.764 ± 0.006, respectively. The 15% difference between HR*G and HRG_{total} for dobutamine is thought to be due to the difficulty in measuring K _{d2}, the high agonist affinity component; it is highly dependent on the HRG 171 HR*G distribution (in the HRG_{total} pool) in that even a small contribution of HRG (complex with inactive R) leads to a substantial affect on the measured K _{d2}. The use of a twocomponent nonlinear curve regression analysis to obtain a value for the high affinity binding component (data not shown) revealed that the difference between K _{d1}, the low affinity component, and K _{d2} averaged 28 ± 21fold for dobutamine (16 experiments), 215 ± 70fold for fenoterol (16 experiments), 232 ± 82fold for isoproterenol (eight experiments), and 400 ± 144fold for epinephrine (24 experiments). The K _{d2} values determined in this fashion also seemed to decrease with increasing G_{s} levels (r = −0.94), which may reflect a complicated receptorG protein stoichiometry or the difficulty in determining the high agonist affinity using a twocomponent curvefitting analysis.
A comparison between the minimum HR*G levels and the relative rate of ternary complex breakdown is also illustrated in Fig. 3. The rate of ternary complex breakdown was determined from theyintercept value of EadieHofstee plots representing GTPdependent adenylyl cyclase activity for each agonist (see above). The EadieHofstee plots were used to fit a quartic solution describing receptorG protein/adenylyl cyclase interactions in the presence of decreasing GTP (Appendix ). Using the conditions for fitting as described in Experimental Procedures, the xaxis represented the number of active G^{*} _{s}C complexes, a number that is limited by C in this system (16). Therefore in practice, when G_{s} ≤ C, the plots were linear; when G_{s} ≥ C, the plot tails downward as it approaches the xaxis.
In our simulations of fitting the quartic solution to adenylyl cyclase response data (data not shown), only a change ink _{2} levels could result in differentyintercepts for agonists of different efficacy (i.e., different k _{1} values). Using the quartic solution to analyze experimental data revealed that the rates of breakdown (normalized average ± standard error) for isoproterenol, fenoterol, and dobutamine were 0.906 ± 0.005, 0.738 ± 0.015, and 0.505 ± 0.011, respectively. No statistical significance could be demonstrated for the effects of G_{s}protein levels on the measured differences in the rates of heterotrimer dissociation between the agonists and epinephrine. In addition, no significant difference could be demonstrated between the minimum HR*G levels and the rate of heterotrimer breakdown for either epinephrine or isoproterenol. However, a significant difference could be demonstrated for fenoterol (p = 4 × 10^{−3}, eight experiments) and dobutamine (p = 1.5 × 10^{−4}; eight experiments). These data demonstrate that the rate of breakdown is not similar for different β_{2}agonists (even when corrected for disparities in HR*G levels between the agonists), implying that agonist activation of receptors is more complicated than a simple twostate model.
Discussion
Twostate receptor activation model and the rate of HRG_{total} breakdown.
The extended ternary complex model has provided an extremely useful thermodynamic description of agonist/receptorG protein interactions (13). This model proposes that the receptor exists in one of two conformations: an inactive state, R, which displays low agonist affinity and presumably does not couple to G (2), and an active state, R*, which displays high agonist affinity and couples to the G protein. The inactive state, R, can isomerize into the active state R*, either spontaneously or with the presence of an agonist. The agonist then stabilizes the R* form, and in general it is accepted that stronger agonists have a greater ability to stabilize the active state.
The twostate model of receptor conformation offers advantages over the more general classic ternary complex model only if it can make verifiable predictions that the latter cannot. There are no qualitative predictions that can be made by the twostate model that are not also obvious from the classic model. The advantage, if there is one, is to use the twostate system to make quantitative predictions based on the amounts of the active form (R*, HR*, or HR*G) present in the system. Essentially, this devolves to relating the quantities (or the relative quantities) of these forms to effector activation or to the steady state of effector activation under conditions in which the nature of the agonist or antagonist is changed.
The scheme for the twostate ternary complex model as illustrated by Samama et al. (1), in fact, depicts a multistate model in which
1) We give measurements that show the actual accumulation of ternary complex at [GTP] → 0 for all the agonists used. In combination with 2) below, we can therefore calculate the maximum differences between the agonists for the steady state concentrations of [HR*G].
2) If the twostate model is an adequate description of the thermodynamics of ternary complex formation, then all of the agonists used are primarily in the HR*G state rather than in the HRG (R inactive) state in the ternary complex (HRG_{total}).
3) We measure the adenylyl cyclase activity for all agonists as [GTP] → 0. As [GTP] → 0, the rate of breakdown of the ternary complex is the ratedetermining step in adenylyl cyclase activation. Measurement of adenylyl cyclase activity under these conditions therefore gives estimates for the relative rates of ternary complex conversion to active G^{*} _{s}.
4) The strict twostate model requires proportionality between the amount of HR*G in the system at steady state and the rate of conversion to active G^{*} _{s}.
It is known experimentally that at low values of [GTP], the ternary complex accumulates. This is the basis for the theory of the GTP shift for agonist binding (4). In any process involving more than a single step, the intermediate species before the ratedetermining step accumulates; therefore, it can reasonably be supposed that when GTP levels are very low, the rate at which adenylyl cyclase is activated becomes directly dependent on the rate at which the ternary complex breaks down. In the current report, however, we performed a complete kinetic analysis over the full range of GTP concentrations from very low to saturating concentrations of GTP. A complete theoretical analysis for the relationship between GTP concentration and adenylyl cyclase activity is given for the shuttle model of cyclase activation (Appendix ). However, although the overall equation is somewhat different when developed for a precoupled model (18), the conclusion that the rate of breakdown of the ternary complex can be inferred from the adenylyl cyclase activity is the same in both cases. It should be pointed out that the exact form of the relationship between adenylyl cyclase activity and GTP concentration is not crucial to the test of the twostate model performed in this report. The solution for that relationship was derived using a G_{s}toC shuttle model as the primary mechanism for adenylyl cyclase activation because it is interesting in its own right and because it allows the mathematical demonstration that as [GTP] → 0, the adenylyl cyclase activity is directly proportional to the rate of ternary complex breakdown (Appendix ).
Experimental conditions were chosen such that similar levels of HRG_{total} were used to stimulate adenylyl cyclase activity for four different β_{2}adrenergic agonists: the strong agonists epinephrine and isoproterenol, the moderate agonist fenoterol, and the weak agonist dobutamine. If a strict twostate model were manifest for receptor conformation, then similar levels of HR*G are predicted for each agonist when examining adenylyl cyclase activity under limiting GTP concentrations. Appendix provides the formal thermodynamic justification of the statement above by showing that it is possible to use GTP shift binding data to calculate the minimum percentage of HRG_{total} that must be in the HR*G state. Fig.3 reveals the similarity in the HR*G levels between the agonists and shows that the weak agonist dobutamine is capable of producing >80% of the HR*G complexes as epinephrine under saturating agonist conditions. Because the percentage is very high even for the weak agonist dobutamine, the subsequent arguments are facilitated.
If the properties of the ternary complex depended proportionately only on the fraction in the active HR*G form, then there should be little difference between the ternary complex that included the weak agonist dobutamine, the stronger agonist fenoterol, and the very strong agonists epinephrine and isoproterenol. It would then be expected that the rate of HRG_{total} breakdown would be similar for all of the agonists. Significant differences in the rates of breakdown would demonstrate that a simple twostate model is inappropriate for this process. Fig. 3 demonstrates that the relative rates of heterotrimer breakdown for fenoterol and dobutamine are significantly different from the minimum HR*G levels determined for each of the two agonists. This suggests that the rate of HRG_{total} breakdown is dependent on the type of agonist, a finding that is inconsistent with a single conformation for the activated state of the receptor.
It is unlikely that the agonistdependent differences in the rate of heterotrimer breakdown are due to 1) the ability of a particular agonist to form the ternary complex or 2) the agonistdependent variation in the rates of agonist association and dissociation to the β_{2}adrenergic receptor. Our experiments were designed to minimize the effects described above by bringing adenylyl cyclase activity to steady state during a 3min incubation period before the addition of labeled ATP and subsequent data collection. Therefore, problems resulting from the delay in reaching full activity on the addition of stimulating agonist do not arise. Similarly, the preincubation ensures that agonist binding has also attained a steady state before measurements are taken. Thus, the rates at which agonist binds and dissociates from the receptor should also not be a significant factor.
A possible explanation for these data that would preserve a strict twostate model requires the selective activation of the inhibitory heterotrimeric G protein, G_{i}. If G_{i} were preferentially activated by dobutamine and fenoterol, then the reduced adenylyl cyclase activity at low GTP, under stimulation by those agonists, would be the result of G_{i}mediated inhibition rather than a slower rate of breakdown of the ternary complex. In the current circumstances, this is unlikely because G_{i}coupled αadrenergic receptors have not been demonstrated in these cells. In addition, the low level of βadrenergic receptors makes it unlikely that a lowefficiency interaction between the βadrenergic receptor and G_{i} could have a significant effect.
Our data therefore are not consistent with a strict twostate model as described by Samama et al. (1). Our data do not, however, invalidate the classic ternary complex model (4), but they do suggest that receptor activation of G_{s} is more complicated than agonist stabilization of an active R* state. Indeed, other investigators have suggested that each agonist stabilizes a unique set of receptor conformations (known as the multistate model) with a range of G proteinactivating abilities (17, 18). However, caution should be taken in extrapolating data from solubilized receptor systems and mutant receptors to biological systems. It should also be noted that although other models for receptor activation are possible, it may be that a more realistic model of agonist/receptor/G protein interactions might only complicate matters while only marginally improving the resolution of the twostate model. In any case, these findings have important implications not only in the study of the mechanisms involved in hormoneactivated receptors but also for future studies involving the search pharmaceutical agents that may selectively activate different forms of a receptor.
Appendix
This section describes the derivation of a complete kinetic analysis of steady state adenylyl cyclase activity with respect to varying GTP concentrations in terms of the CasselSelinger cycle (19). The scheme shown below shows the cycle of G_{s} activation and inactivation after receptor activation. In this version, a shuttle model for G^{*} _{s} to adenylyl cyclase catalytic unit is assumed, although an analysis of the process in terms of a precoupled model for G_{s} and adenylyl cyclase would give almost identical values for the estimates of the rate of breakdown from experimental data. The description of active adenylyl cyclase is given as the solution of a quartic equation; however, the quartic itself can be factored into two quadratic equations, which simplifies matters somewhat. Equation 9In the scheme above, HR is the agonistoccupied receptor, G_{s} is the inactivated stimulatory G protein, G^{*} _{s} is activated G protein, C is inactive adenylyl cyclase, and G^{*} _{s}C is the active adenylyl cyclase complex. The kinetic constants governing the cycle are represented byk _{1}, the rate of heterotrimer (HRG) formation;k _{10}, the rate of dissociation of an inactive heterotrimer; k _{2}, the rate of active heterotrimer (HRG) dissociation; k _{3}, the rate of adenylyl cyclase activation by activated G^{*} _{s}, andk _{−1}, the rate of G^{*} _{s} and G^{*} _{s}C inactivation via the intrinsic GTPase mechanism [because adenylyl cyclase does not seem to act as a GAP for G^{*} _{s} (20) k _{−1}, the rates for G^{*} _{s} and G^{*} _{s}C are identical].
In the presence of GTP, we want to determine the steady state rate of adenylyl cyclase, G^{*}
_{s}C activity. From the conservation of mass, the levels of R, G_{s}, and C are defined as
Relating the rate of heterotrimer breakdown to theyintercept of the EadieHofstee plot.
From eq. 27, we find that
The thermodynamics of receptor/G protein/agonist interactions in terms of the twostate model.
In this section, we use the twostate model to calculate the minimum fraction of receptors that must be in the R* state in the ternary complex to achieve the measured GTP shifts. If a receptor exists in two distinct conformational states that have different affinities for a ligand (K_{a} for state A and K_{b} for state B), then the measured dissociation constant (K_{d} ) for the ligand is given by K_{d} =K_{afa} + K_{bfb} , wherefa is the fraction of receptor in state A in the receptor/ligand complex, and fb is the fraction of receptor in state B in the ligand/receptor complex. Because this is a twostate model, fa plus fb is equal to unity. The above equations is derived from the first principles in Appendix .
If we adhere strictly to the twostate model, then when a ligand binds to a given receptor with increased affinity as a result of a change in conditions, according to the above equation, which is completely general, all changes in K_{d} must be interpreted in terms of changes in fa and fb, becauseK_{a} and K_{b} refer to the binding to the two defined states.
In the absence of GTP, the βadrenergic receptor forms a ternary complex with G_{s} and agonist (4). In this ternary complex, the affinity of the agonist for the receptor is increased relative to its binding in the presence of GTP when ternary complex does not accumulate. If B is the high affinity form of the receptor, thenK_{b} < K_{a} , and the greater measured affinity for ligand in the absence of GTP requires there be a greater contribution of the B form to the ternary complex. In fact, the measured greater affinity places limits on the fraction of each conformation that is thermodynamically allowable.
If K
_{d1} is the dissociation constant of ligand from the receptor alone and K
_{d2} is the dissociation constant from the ternary complex, then we may writeK
_{d1} = K
_{afa1} +K
_{bfb1} and K
_{d2} =K
_{afa2} + K
_{bfb2}. Noting that fa1 = 1 − fb1 andfa2 = 1 − fb2, these two equations may be combined and rearranged to give
It can be seen by inspection that any significant difference inK _{d1} and K _{d2} must lead to large proportion of receptors (>0.9) in the fb2 state. In the specific case of this report, even the rather weak agonist dobutamine requires that ≥80% (based on the differences in affinity obtained using a nonlinear twocomponent curve fit with the high and low values of the curve constant in addition to the low affinity portion of the curve) of the ternary complex be in the HR*G form (i.e., the active form) in terms of the twostate model.
Appendix
In the following system, only a single dissociation constant is observed provided the conversion time between the different state of the receptor R ↔ R* is rapid compared with the time allowed for equilibration of ligand binding.
Equation 44In this scheme, the dissociation for agonist bindingK_{D}
is given as
Footnotes
 Received December 26, 1996.
 Accepted April 4, 1997.

Send reprint requests to: Roger Barber, Ph.D., The University of TexasHouston Medical School, Department of Integrative Biology, Pharmacology, and Physiology, 6431 Fannin, P.O. Box 20708, Houston, TX 772250334. Email:rbarber{at}farmr1.med.uth.tmc.edu

This work was supported by National Institutes of Health Grant RR07710.
 The American Society for Pharmacology and Experimental Therapeutics