Probing function in ligand-gated ion channels without measuring ion transport

Regardless of structural differences between superfamilies, all neurotransmitter-gated ion channels (NGICs) are integral membrane proteins formed by, essentially, two modules: an extracellular domain (ECD) that harbors the neurotransmitter-binding (orthosteric) sites, and a transmembrane domain (TMD) that forms the transmembrane aqueous pore. Conformational changes in the ECD result in different affinities for the neurotransmitter (low and high), whereas conformational changes in the TMD result in pores that either conduct (open) or do not conduct (closed and desensitized) ions. These conformational changes are not independent of each other, but rather, are thought to be strictly correlated (“coupled”) in such a way that conformations of the receptor-channel that bind neurotransmitter with low affinity have nonconductive closed pores, whereas conformations that bind neurotransmitters with high affinity have either ion-conductive open pores or nonconductive desensitized pores (Chang and Weiss, 1999; Grosman and Auerbach, 2001; Jackson, 1989). Thus, the interconversion of these ligand-gated ion channels between the closed, open, and desensitized states (hereafter referred to as “gating”) can be inferred by measuring the transport of ions through their pores or by estimating the extent of ligand binding, that is, by following the operation of one module or the other.

The higher sensitivity and time resolution of methods that measure ion transport—particularly, those that measure the associated ion currents—easily explain their dominance over ligand-binding studies as experimental approaches to probe function in NGICs. However, one can imagine a variety of circumstances under which the measurement of currents or ion fluxes is not possible: (1) mutations may render an ion channel electrically silent by stabilizing nonconductive conformations or by greatly reducing the single-channel conductance; (2) an agonist may desensitize a channel too quickly; (3) studies of the interaction between ion permeation and gating (“permeation–gating coupling”) may require that function also be studied in the absence of ion flow; (4) maneuvers that modify the lipid composition of the plasma membrane may render the formation of high-resistance patch-clamp seals unlikely, and vesicles for ion-flux assays leaky; (5) studies of the effects of the lipid environment on function may require that a channel be solubilized in detergent micelles so as to establish a baseline behavior; and (6) comparative studies of the effects of different types of membrane mimetic in the context of structural-biology efforts may require that channel function be studied in lipid nanodiscs. Furthermore, even if current measurements were possible, low single-channel conductance, poor expression levels, and/or hard-to-control time-dependent changes in channel activity upon patch-clamp seal formation or excision (usually referred to as “run-down” or “run-up”) may render electrophysiological studies highly impractical; in these cases, ligand-binding assays can provide a robust alternative.

Ligand-binding experiments often take the form of concentration–response assays in which some direct or indirect measure of binding is recorded and plotted against the concentration of ligand. The resulting curves are fitted with empirical functions—most commonly a Hill equation—and the values of the estimated parameters (that is, a half-effective concentration and a Hill coefficient) are used to characterize the receptor–ligand complex under different experimental conditions. Although, with some exceptions, these empirical parameters cannot be expressed easily in terms of the underlying equilibrium constants of state interconversions, their use is favored because they are convenient. Fitting the observations with more realistic, mechanism-based equations (having many more parameters) would likely be impossible (e.g., Hines et al. [2014]).

In the context of NGICs, ligand-binding studies have been mostly applied to the members of the pentameric ligand-gated ion channel (pLGIC) superfamily (also known as Cys-loop receptors), and within these, to the muscle-type nicotinic acetylcholine receptor (AChR; Blount and Merlie, 1988, 1989; Covarrubias et al, 1986; Franklin and Potter, 1972; Fulpius et al, 1972; Maelicke et al, 1977; Quast et al, 1978; Sine and Taylor, 1979; Weber and Changeux, 1974a, 1974b, 1974c; Weiland and Taylor, 1979) and the α7 AChR (Corringer et al., 1995; Gopalakrishnan et al., 1995; Peng et al., 1994). Undoubtedly, this is because of the availability of a powerful tool: α-bungarotoxin (α-BgTx; Lee, 1970), a 74-amino-acid snake toxin that binds to muscle-type and α7 AChRs competitively with orthosteric ligands (that is, ACh, nicotine, and their analogs) and dissociates from the complex slowly enough to allow the effective physical separation of bound from unbound label. However, although these assays have been in use since the 1970s, we have noticed a lack of uniformity in published protocols, as well as large discrepancies in the values of parameters estimated from even the simplest type of experiments. For example, for the chicken α7-AChR (in the context of an ECD–TMD chimera having the rat serotonin-receptor type 3A’s [5-HT_3AR’s] TMD), values of the α-BgTx dissociation equilibrium constant (K_D) from the closed-channel conformation of 70 pM (Rangwala et al., 1997) and 4.2 nM (Pittel et al., 2010) have been reported for receptors on resuspended cells. Similarly, for the wild-type human α7-AChR, values of this K_D have been reported to be 0.8 nM (Peng et al., 1994) and 4 nM (Tillman et al., 2016) in detergent-solubilized receptors; 0.7 nM (Gopalakrishnan et al., 1995) and 7 nM (Peng et al., 2005) in resuspended membrane homogenates; and 1.2 nM (Shabbir et al., 2021), 2.7 nM (daCosta et al., 2015), and 26 nM (Sine et al., 2019) in resuspended cells. Moreover, values of the Hill coefficient of small-molecule ligands reported in the literature of these ion channels often run counter to theoretical expectations, with values significantly different from unity for antagonists and values significantly lower than unity for agonists.

Here, we set out to optimize the values of the different experimental variables in otherwise classic concentration–response assays at equilibrium. To this end, we used radio-iodinated α-BgTx, small-molecule cholinergic ligands, and the full-length homomeric α7-AChR expressed in HEK-293 cells. Furthermore, using a realistic five-binding-site reaction scheme, we investigated the quantitative relationships between the empirical parameters estimated from equilibrium concentration–response curves and the underlying equilibrium constants of ligand-binding and ion-channel gating. Finally, we end the paper with examples of the practical application of this method to tackle two longstanding questions in the field: whether the ligand-binding affinity for any of the orthosteric sites is sensitive to the occupancy of the other orthosteric sites, and whether mutations to amino-acid residues in the TMD can affect the channel’s affinities for ligands that bind to the ECD.

cDNA coding the human α7-AChR (UniProt accession no. P36544) in pcDNA3.1 was purchased from Addgene (#62276); cDNA coding isoform 1 of human RIC-3 (UniProt accession no. Q7Z5B4; Treinin, 2008) in pcDNA3.1 was provided by W.N. Green (University of Chicago, Chicago, IL); cDNA coding human NACHO (TMEM35A; UniProt accession no. Q53FP2; Gu et al., 2016) in pCMV6-XL5 was purchased from OriGene Technologies (#SC112910); cDNA coding the cut-and-splice (CS) chimera between the ECD of the α7-AChR from chicken and the TMD of β-GluCl from Caenorhabditis elegans in pMT3 (Cymes and Grosman, 2021) was obtained by mutagenesis of a related clone provided by Y. Paas (Bar-Ilan University, Tel Aviv, Israel; Sunesen et al., 2006); cDNA coding the human–C. elegans counterpart of the chicken–C. elegans CS α7-AChR–β-GluCl chimera was obtained by mutating the latter (the mutations were L34V, T56S, M60L, Y81S, N99T, L106Q, K163H, N165K, T172S, S192P, T206S, S208R, and I220V); cDNA coding the human acid-sensing ion channel subunit 1 (ASIC1; UniProt accession no. P78348) in pCR-BluntII-TOPO was purchased from Horizon (#MHS6278-211689646) and was subcloned in pcDNA3.1; and cDNAs coding the mouse β1, δ, and ε subunits of the (muscle) AChR (UniProt accession nos. P09690, P02716, and P20782, respectively) in pRBG4 were provided by S.M. Sine (Mayo Clinic, Rochester, MN). Mutations were engineered using the QuikChange kit (Agilent Technologies), and the sequences of the resulting cDNAs were verified by dideoxy sequencing of the entire coding region (ACGT). Wild-type and mutant channels were heterologously expressed in transiently transfected adherent HEK-293 cells grown at 37°C and 5% CO₂. cDNAs coding the human α7-AChR, human RIC-3, and human NACHO were cotransfected using 125, 687.5, and 687.5 ng cDNA/cm², respectively; cDNAs coding the chicken–C. elegans α7-AChR–β-GluCl chimera, the human–C. elegans α7-AChR–β-GluCl chimera, or human ASIC1 were transfected using 187.5 ng cDNA/cm²; and cDNAs coding the mouse β1-, δ-, and ε-AChR subunits were cotransfected using 62.5 ng cDNA/cm² each. Transfections were performed using a calcium-phosphate-precipitation method; they proceeded for 16–18 h, after which the cell-culture medium (DMEM; Gibco) containing the DNA precipitate was replaced with fresh medium. As a control of the nonspecific binding of α-BgTx to cells, HEK-293 cells were transiently transfected with cDNA coding the human ASIC1 or the mouse β1-, δ-, and ε-AChR subunits. These cells were incubated with [¹²⁵I]-α-BgTx (in the absence of unlabeled competitive ligand) under the same conditions as were the cells expressing wild-type or mutant α7-AChRs. The resulting nonspecific binding values were used to calculate specific binding for the saturation curves and for the subset of competition curves in which the highest concentrations of unlabeled ligand were unable to displace the specifically bound [¹²⁵I]-α-BgTx completely.

24 h after changing the cell-culture medium, transfected cells were resuspended in a HEPES-buffered sodium-saline solution (in mM: 142 NaCl, 5.4 KCl, 1.8 CaCl₂, 1.7 MgCl₂, and 10 HEPES/NaOH, pH 7.4) by gentle agitation and divided in 1-ml aliquots in 1.7-ml plastic tubes. Ligand binding-reaction mixtures were incubated at the indicated temperature and for the indicated duration with constant rotation. Upon completion, cell-bound label was separated from unbound label by centrifugation at 16,000 g for 3 min at room temperature. To reduce the amount of nonspecifically bound label, the pellets were resuspended in 1 ml Dulbecco’s PBS (pH 7.4; Gibco), vortexed for 30 s, and pelleted again at 16,000 g for 3 min at room temperature; this resuspension–pelleting procedure was repeated twice. Finally, the washed pellets were resuspended in a solution containing 0.1 N NaOH and 1% (wt/vol) SDS and incubated at 65–70°C for 30 min. The radioactivity and protein content of each solubilized pellet were estimated: ¹²⁵I radioactivity was measured using a Wiper 100 γ-counter (Laboratory Technologies) that we calibrated (efficiency = 0.826) using a QCI-501 standard (Reflex Industries), and the amount of protein was measured using the bicinchoninic acid assay (Thermo Fisher Scientific) and a freshly prepared BSA (Thermo Fisher Scientific) calibration curve.

The number of transfected cells contained in each reaction tube of any given curve was adjusted, by trial and error, to minimize the depletion of labeled and unlabeled ligands while ensuring a sufficiently high signal. For some constructs, the expression of receptors was so high that the amount of transfected cells that satisfied this criterion resulted in pellets that were too small to handle reliably. In these cases, to increase the size of the pellets, transfected cells were mixed with nontransfected cells. Most experiments were repeated several times, each one using two replicates per concentration of [¹²⁵I]-α-BgTx (in saturation experiments) or unlabeled ligand (in competition experiments). [¹²⁵I]-α-BgTx was purchased from PerkinElmer (initial specific activity ≅ 80–140 Ci/mmol); methyllycaconitine (MLA) and dihydro-β-erythroidine (DHβE) from Tocris Bioscience; and carbamylcholine, choline, and nicotine from MilliporeSigma.

All curves corresponding to a given set of conditions were fitted globally with a Hill equation using SigmaPlot 14 (Systat Software Products). For display purposes, these data points were normalized using the globally fitted parameters, averaged, and plotted as mean ± 1 SEM of the several replicates. For all fits, the reciprocal of the y-axis variable was used as weight, and parameter standard errors were computed using the reduced χ² statistic.

Fig. S1 shows concentration–response curves and various ligand-binding probabilities calculated on the basis of the reaction scheme in Fig. 1. Fig. S2 shows calculated competition concentration–response curves for several hypothetical scenarios involving perturbations that affect the affinities of the receptor for the unlabeled and labeled ligands. Fig. S3 shows the predicted effects of changes in the unliganded-gating equilibrium constant on competition concentration–response curves for an inverse-agonist labeled ligand. Fig. S4 illustrates the process of global curve fitting followed in this paper. Fig. S5 shows a structural model of the human α7-AChR bound to the orthosteric agonist epibatidine and the positive allosteric modulator PNU-120596.

Ligand-binding assays often entail the use of labeled ligands that allow the direct estimation of the number of ligand-molecules bound. When the characterization of the interaction between a labeled ligand and its receptor is of interest, the experiment takes its simplest form: receptor and ligand are incubated in mixtures containing an approximately constant concentration of receptors and a variable concentration of ligand ranging from zero (or very small, if the curves are displayed on a logarithmic x axis) to saturating. The binding reactions are allowed to proceed until equilibrium is attained, and then the label associated with ligand–receptor complexes is measured. Here, we refer to these assays as saturation assays. However, it may also be of interest to characterize the interaction between the receptor in question and other ligands that may not be readily available in labeled form but that may bind to the receptor in a manner that is mutually exclusive with the binding of the available labeled ligand. In this case, two alternative (seemingly similar, but conceptually very different) approaches can be taken (Weber and Changeux, 1974a). In one of them, mixtures containing a fixed concentration of receptor and a range of concentrations of unlabeled ligand are incubated until equilibrium between the two is reached. Then, in a second step, a fixed concentration of the labeled ligand is added to each reaction, and the amount of binding is recorded as a function of time. The extent to which the initial rate of labeled-ligand binding is slowed down with increasing concentrations of unlabeled ligand is then plotted and analyzed. In this method, the purpose of the labeled ligand is to act as a mere reporter of the number of sites left unoccupied by the equilibrated mixture of unlabeled ligand and receptor. The binding of the labeled ligand is analyzed over very short times, much shorter than needed for equilibrium to be attained by the three components of the mixture. These kinetic studies are typically referred to as protection assays.

The alternative approach consists of the incubation of receptor (at a fixed concentration), labeled ligand (also, at a fixed concentration), and unlabeled ligand (at a range of concentrations) until equilibrium between all three components of the ternary mixture is reached; only then is the amount of receptor-bound label measured. We refer to this method as the equilibrium binding-competition approach. This is the method we chose to study here as a probe for pLGIC function when ion transport is not measured.

In the presence of two ligands that bind in a mutually exclusive manner (such as the labeled and unlabeled ligands), a homopentameric pLGIC with five identical binding sites can exist in several different ligation and conformational states. These states are indicated in the reaction scheme in Fig. 1, which (in keeping with experimental observations [Grosman and Auerbach, 2001, 2000a, 2000b; Jackson, 1984]), is built around the concepts of unliganded gating and binding–gating thermodynamic cycles (Jackson, 1989). For the sake of clarity of display and simplicity of calculation, the open and desensitized conformations—that is, the conformations of the channel that bind agonists with higher affinity—were grouped together and are denoted, collectively, as “O” or open.

A variety of methods have been developed to study the binding of ligands to macromolecules, including several that do not make use of labeled ligands, such as isothermal-titration calorimetry (e.g., Wöhri et al., 2013), surface plasmon resonance (e.g., Seeger et al., 2012), and microscale thermophoresis (e.g., Bernhard and Laube, 2020). One of the key advantages of methods that do use labeled ligands, however, is that the relationship between the observed signal and the ligand-binding phenomenon under study is most straightforward. Indeed, upon subtraction of nonspecific binding, the signal is directly proportional to the mean number of binding sites per receptor occupied by the labeled ligand. In turn, the expected value of the latter quantity as a function of the concentration of ligand (whether labeled or unlabeled) in concentration–response curves can be calculated for any set of equilibrium constants. Fig. S1 shows some examples of these calculations for a variety of parameters in a hypothetical competition assay in the context of the reaction scheme in Fig. 1.

In equilibrium binding-competition assays, the experimenter is usually interested in elucidating properties of the receptor as it interacts with the unlabeled ligand—the labeled ligand acts as a probe. However, because the binding of both types of ligand is expected to have reached equilibrium before the signal is recorded, the (fixed) concentration of unbound labeled ligand and its affinities for the different conformational states of the receptor-channel contribute to the steepness and displacement along the x axis of competition concentration–response curves. In other words, rather than being a mere reporter, the labeled ligand is an integral part of the binding reactions with potentially confounding effects on the results.

Labeled ligands used in competition assays are often antagonists (that is, molecules that bind with indistinguishable affinities to the different conformations of the receptor-channel; e.g., Colquhoun, 1998) or inverse agonists (molecules that bind with higher affinity to the “resting,” closed conformation; e.g., Colquhoun, 1998), such as α-BgTx, in the case of AChRs, and strychnine, in the case of glycine receptors. Moreover, most wild-type pLGICs almost exclusively populate the low-affinity closed conformation when unliganded. Quite conveniently, it can be shown that, under these conditions, competition curves remain essentially unaffected by the properties of the labeled ligand as long as the ratio between its fixed (unbound) concentration used in the assays and the concentration that half-saturates the receptor remains constant. This concept becomes important, for example, when binding-competition assays are performed to assess the effects of mutations on channel function (because mutations may affect the channel’s affinities for the labeled ligand). Another example would be when having to switch from one labeled ligand to another one (because of, say, changes in their commercial availability) in the middle of a large comparative study. Fig. S2 illustrates these ideas in detail with calculated curves.

Although some authors have used labeled agonists in competition assays (such as radiolabeled epibatidine in studies of the ACh-binding protein; Kaczanowska et al., 2014), in this paper, we restricted our analysis to labeled ligands that act as antagonists or inverse agonists.

Thus, in competition experiments in which the K_D,B/[B] ratio is equal to 1 (Eq. 4), N decreases from n/2 (at [A] = 0) to 0, as [A] increases, and the value of [A] that displaces one-half of the bound labeled ligand (and thus, leaves one-fourth of the binding sites bound to the label) is numerically equal to 2 × K_D,A. More generally, the half-competition concentration is equal to K_D,A × (1 + [B]/K_D,B). It should be emphasized that these simple mathematical relationships are accurate only for antagonists competing against antagonists. In many cases, however, the unlabeled ligand is an agonist, and the counterparts of Eqs. 2, 3, 4, and 5 become more complicated because the various gating equilibrium constants no longer cancel. In these cases, neither ligand-dissociation nor gating equilibrium constants can be estimated directly from fits to ligand-binding curves.

As can be appreciated from a comparison of empirical Eqs. 1 and 2 with mechanism-based Eqs. 4 and 5, Hill equations (with n_H = 1) provide an accurate description of concentration–response curves only when the ligands involved are antagonists, regardless of the number of binding sites on the receptor (or, for all types of ligand, in the trivial case of receptors with a single binding site). In all other cases, Hill equations are only convenient approximations.

We propose, here, the use of ligand-binding assays to answer questions about how LGICs operate. Probing mechanisms often involves the use of perturbations (such as mutations) that change the equilibrium constants of the different binding and gating steps, but these changes are not readily observable. Instead, using ligand-binding assays, we only have access to the resulting concentration–response curves. Thus, to learn about the relationship between the values of the empirical parameters of such curves and the values of the equilibrium constants of ligand binding and gating, we calculated four hypothetical scenarios in the context of the reaction scheme in Fig. 1 (Figs. 2, 3, 4, and 5). These calculations show the limits of what can be learned from this type of assay (even in the complete absence of experimental errors) and allow the identification of “impossible” results that would otherwise be accepted as valid.

Fig. 2 shows the effects of changes in the unliganded-gating equilibrium constant (without concomitant changes in ligand affinities) for the case in which the labeled ligand is an “ideal” antagonist (that is, a ligand with identical affinities for all conformations), and the unlabeled ligand is an agonist. From Eq. 6, as the unliganded-gating equilibrium constant increases, so do the gating equilibrium constants of the receptor in its different ligation states. As a result, competition concentration–response curves shift to lower concentrations (Fig. 2 A), as expected from the higher affinity of agonists for the open-channel conformation. The displacement of these curves along the concentration axis is bounded by two limits: the half-competition concentration cannot be >2 × K_D,closed or <2 × K_D,open (where the K_D values are those of the unlabeled ligand; Fig. 2 B). The Hill coefficient, on the other hand, approaches unity at very low and very high values of the unliganded-gating equilibrium constant, going through a maximum somewhere in between (Fig. 2 C). It could be argued, however, that an inverse agonist is a better model of labeled ligand in the particular context of AChRs. Indeed, electrophysiological studies of the wild-type muscle AChR (Jackson, 1984) and gain-of-function mutants of the α7-AChR (Bertrand et al., 1997) have revealed that the binding of αBgTx reduces the spontaneous open probability (that is, it favors a nonconductive conformation), and structural models of the αBgTx-bound (Noviello et al., 2021) and unliganded α7-AChRs (Zhao et al., 2021) suggest that this nonconductive conformation is the closed (rather than the desensitized) state. Thus, we explored the behavior of competition curves for inverse-agonist labeled ligands. Fig. S3 shows that, in this case, the half-competition concentration also goes from 2 × K_D,closed to 2 × K_D,open but passes through a minimum that becomes increasingly pronounced as the inverse agonism of the labeled ligand increases. The behavior of the Hill coefficient, on the other hand, is very similar to that observed in the case of an antagonist labeled ligand, but the peak is higher and displaced to higher concentrations.

Fig. 3 shows the effects of variable closed- and open-state affinities for an agonist unlabeled ligand in the idealized case when these affinities change in such a way that the ratio between them remains constant. From Eq. 6, when this ratio and the unliganded-gating equilibrium constant remain unchanged, so do the liganded-gating equilibrium constants. Under these conditions, as the dissociation equilibrium constants increase (that is, as the affinities decrease), competition curves shift to higher concentrations (Fig. 3 A). Half-competition concentrations increase linearly as the dissociation equilibrium constants do (Fig. 3 B), irrespective of whether the labeled ligand is an antagonist or an inverse agonist. The Hill coefficient, on the other hand, remains unchanged (Fig. 3 C), thus showing its dependence on the channel’s gating equilibrium constants rather than ligand affinities.

Fig. 4 shows the effects of a variable closed-state affinity for the unlabeled ligand in the idealized case when this is the only affinity that changes; Fig. 5 shows these effects for the open-state affinity. From Eq. 6, as K_D,closed increases, so do the liganded-gating equilibrium constants, whereas as K_D,open increases, the liganded-gating equilibrium constants decrease. Despite these opposite changes in gating, the displacement of the curves along the concentration axis is qualitatively similar in both cases (Fig. 4, A and B; and Fig. 5, A and B). Hill-coefficient values, on the other hand (Figs. 4 C and 5 C), change in opposite directions—increasing in one case and decreasing in the other—as expected from the opposite effects of closed- and open-state affinities on the liganded-gating equilibrium constants (Eq. 6). The behavior of the competition curves illustrated in Figs. 4 and 5 is essentially the same irrespective of whether the labeled ligand used for the calculations is an antagonist or an inverse agonist.

The interpretation of Hill-coefficient values is often linked to the concept of cooperativity of ligand binding. In all the calculated competition curves shown above, in Figs. 2, 3, 4, and 5, the sites were assumed to be identical and independent of each other, and thus, binding-site affinities changed only as a result of the global closed ⇌ open state transition. In other words, ligand affinities did not change as a function of binding-site occupancy within a given end state (closed or open/desensitized) of the receptor-channel. Under these particular conditions, a Hill coefficient can be thought of as a measure of the extent to which the composition of the mixture of states populated by the channel (specifically, open or desensitized versus closed) changes between the ends of the competition curve, in going from zero to saturating concentrations of unlabeled ligand. In one of these ends, the receptor is bound only to labeled ligand (to a degree that depends on the latter’s fixed concentration), and in the other, it is fully bound to unlabeled ligand. As a result, in these assays, Hill-coefficient values depend not only on properties of the receptor and its interaction with the unlabeled ligand, but also on the concentration of labeled ligand and the properties of the labeled-ligand–receptor complex. This “intuitive” interpretation of the Hill coefficient nicely explains, for example, the value expected for the competition curve between two antagonists (n_H = 1; Eq. 3). Indeed, in this case, the probability of the receptor being open or desensitized (rather than closed) stays unchanged throughout the curve, whether it is the labeled or the unlabeled ligand that is bound, and thus, the coefficient takes its minimum possible number. On the other hand, changes in the open/desensitized probability are more pronounced for the competition between agonists and antagonists, and thus for these curves, 1 < n_H < n. Finally, these ideas also help us understand the behavior of the Hill coefficient in, for example, Figs. 2 C and S3 C. Here, n_H approaches unity at both very low and very high values of the unliganded-gating equilibrium constant, and 1 < n_H < n otherwise. This is because at sufficiently extreme values of this gating equilibrium constant, the channel remains essentially closed or essentially open/desensitized throughout the competition curve regardless of the types of ligand involved.

Although ligand-binding assays at equilibrium have been in use for several decades now, published protocols and reported results for α-BgTx-binding AChRs span a wide range. In particular, an analysis of the literature revealed that the critical distinction between the short incubations required for protection assays and the long incubations required for equilibrium assays is often blurred, and that the Hill coefficient is frequently reported to take values that lie outside the theoretically allowed bounds. Thus, we set out to identify the optimal conditions for equilibrium-binding assays.

Saturation and competition assays were performed on resuspended HEK-293 cells transiently expressing the wild-type human α7-AChR or some mutants thereof. The labeled ligand was [¹²⁵I]-α-BgTx, and its fixed, unbound concentration in competition assays was chosen to be equal to its half-saturation concentration, which in turn, was estimated from saturation-binding assays (Fig. 6). After an incubation period, the reactions were terminated by centrifugation, which separated cell-bound label from unbound, free label. To reduce nonspecifically bound toxin, the cell pellets were washed extensively with a sodium-saline solution, a crucial step made possible by the toxin’s slow dissociation from the α7-AChR. Inconveniently, however, the slow dissociation kinetics of α-BgTx also slowed down the approach to equilibrium.

Fig. 7 shows the effects of duration and temperature of the incubations on the competition between [¹²⁵I]-α-BgTx and MLA (an inverse agonist; Bertrand et al., 1997) or the nonhydrolyzable, synthetic ACh analog carbamylcholine (an agonist), whereas Fig. 8 shows the effect of temperature on the competition between [¹²⁵I]-α-BgTx and choline (an agonist), nicotine (an agonist), or DHβE (an extremely weak agonist; Bertrand et al., 1997). For all five competing ligands (whose structures are shown in Fig. 9), the effects were qualitatively the same: as the temperature rose from 4°C to 37°C, and the duration increased from 4 h to 48–96 h, the Hill equations that best fitted the data switched from having two components to having only one, and the curves seemed to shift to the right. At 4°C, 24-h incubations were too short for equilibrium to be attained, but at 37°C, 24-h incubations seemed long enough. With these results in mind, we decided to adopt an incubation temperature of 37°C and a duration of 24–48 h for these assays. Also, we found that the binding-competition curves were more sensitive to the temperature of the incubations than were the saturation-binding curves (Fig. 6 A).

In addition to the need of measuring the amount of bound signal, the concentrations of unbound labeled and unlabeled ligands at equilibrium need to be known for all the individual points of the curve. Indeed, the concentration of unbound labeled ligand needs to remain constant, whereas the concentration of unbound unlabeled ligand is the independent variable plotted on the x axis. Although the concentration of unbound labeled ligand can be easily measured upon separating it from the bound form (in our case, in the supernatant; Fig. 10), measuring the concentration of unbound unlabeled ligand is often more cumbersome, and thus, we assumed its value to be equal to its total concentration (total = bound + unbound). Clearly, for the latter assumption to be valid, the concentration of receptors needs to be low enough to make the depletion of ligand negligible. This is a challenge because, at the same time, the amount of receptors needs to be large enough to generate a sizable bound signal. We addressed this issue by trial and error—adjusting the amount of cDNA used in the transfections and the number of transfected cells—so as to strike a balance. We deemed the concentration of ligand-binding receptor sites to be adequate when (1) the difference between the maximum and minimum values of the measured concentrations of unbound labeled toxin for any given competition curve (Fig. 10) was <0.2 nM and the mean was lower than the total concentration of added toxin by <0.2 nM (for the α7-AChR and its mutants, the desired concentration of unbound α-BgTx was in the ∼1–2 nM range); and (2) the specific cell-bound radioactivity in the absence of unlabeled ligand was higher than the nonspecifically bound radioactivity by a factor >10.

In our assays, these conditions were met when the concentration of orthosteric binding sites was in the 0.03–0.3 nM range. Owing to their different expression levels, different constructs required different conditions to hit these values (see Materials and methods), but once identified, they remained reproducibly valid for all subsequent assays. Therefore, with a concentration of binding sites of, at most, 0.3 nM, the difference between the total concentration of ligand (whether labeled or unlabeled) and the concentration of unbound ligand could not have been any higher than 0.3 nM. In the case of the unlabeled ligand (whose unbound concentrations we did not measure), this maximum depletion happened only at saturating concentrations, when all five binding sites of the receptor were occupied. For most unlabeled ligands, saturating concentrations were much higher than 0.3 nM, and thus, this low level of depletion was deemed acceptable.

At 37°C and with 24-h incubations, the α-BgTx saturation curve of the human α7-AChR in intact HEK-293 cells was best fitted with a one-component Hill equation with n_H = 1.03 ± 0.05 and a half-saturation concentration of 0.87 ± 0.08 nM (Fig. 6 and Table 1). The value of the Hill coefficient is consistent with the toxin’s inverse agonism on a receptor that displays a nearly undetectable unliganded channel activity and whose closed-state toxin-binding sites are identical and independent of each other’s occupancy. Moreover, under these particular conditions, Eq. 5 provides an excellent description of the ligand–receptor interaction, and thus, the toxin’s half-saturation concentration is a good estimate of its K_D from the closed state. Our estimate of the latter’s value agrees most closely with those of Oz and coworkers (1.18 nM; Shabbir et al., 2021), Sullivan and coworkers (0.71 nM; Gopalakrishnan et al., 1995), and Lindstrom and coworkers (0.81 nM; Peng et al., 1994) for the same heterologously expressed receptor in intact SH-EP1 cells, HEK-293 cell-membrane homogenates, and detergent micelles, respectively.

The competition between α-BgTx and MLA or DHβE for binding to the wild-type α7-AChR (at 37°C for 24 or 48 h) gave rise to concentration–response curves that are best fitted with a single Hill-equation component of n_H ≅ 1 (Figs. 7 C and 8 C, and Table 1). This is further experimental evidence for the notion that the five closed-state ligand-binding sites (the open state is hardly visited in competitions between these ligands) have indistinguishable affinities and are independent of each other’s occupancy. Certainly, even a small degree of positive cooperativity among sites—only strong enough to make the affinity of the tetra-liganded channel for the fifth molecule of antagonist/inverse-agonist ligand appreciably higher—would be expected to increase the Hill coefficient above unity (Fig. 11). Similarly, even a small degree of negative cooperativity would have been detected as a competition curve that requires a lower-than-unity Hill coefficient, or even a second Hill-equation component, to be best fitted (Fig. 11). Conversely, as elaborated in the sections above, the larger-than-unity Hill-coefficient values required to fit the competition curves between [¹²⁵I]-α-BgTx and carbamylcholine, choline, or nicotine (at 37°C for 24 or 48 h; Fig. 7 D; Fig. 8, A and B; and Table 1) do not necessarily imply the occurrence of positive cooperativity among sites; instead, they may simply reflect that these unlabeled ligands are agonists. Fig. S4 illustrates the curve-fitting procedure followed in this paper using the nicotine–[¹²⁵I]-α-BgTx competition curves as an example.

When binding reactions are not allowed to reach equilibrium, competition curves often display features that are theoretically inconsistent with the notion of identical and independent binding sites. Indeed, out-of-equilibrium concentration–response curves often require two (or more) Hill-equation components or one component with n_H < 1 to be best fitted (Figs. 7, 8, and 12). Quite notably, these theoretically nonsensical features would be expected at equilibrium from ligand-binding proteins whose binding-site affinities display various degrees of interdependence in the form of “negative cooperativity” (Fig. 13) and, therefore, could be misinterpreted as genuine signs of interactions between sites. For proteins with identical and independent binding sites, however, these anomalous features indicate only that the binding reactions were terminated too soon.

A longstanding question in the field of NGICs is whether side-chain mutations to the TMD can affect the ligand affinities of the rather distant neurotransmitter-binding sites, in the ECD (the distance between bound orthosteric ligands and the center of the ion channel pore is ∼50 Å). This is an example of the more general question as to how far structural perturbations can travel through a protein. In the context of the muscle AChR and its naturally occurring agonist, ACh, efforts to tackle this question with the kinetic analysis of single-channel recordings have led to diametrically opposed answers (Hatton et al., 2003; Purohit et al., 2015; Wang et al., 1997).

Here, to eliminate the complications associated with ligand affinities that change upon opening and desensitization, we estimated the closed-state K_D values of the wild-type α7-AChR and some mutants for the inverse agonist MLA. Furthermore, to avoid the use of such an indirect approach to the estimation of ligand affinities as the kinetic modeling of single-channel open and shut dwell times, we performed binding-competition assays against [¹²⁵I]-α-BgTx following the procedures and concepts elaborated above. In addition to the wild-type human α7-AChR, we studied two other constructs: (1) a chimera that combines the human α7-AChR’s ECD with the TMD of the β subunit of the glutamate-gated Cl⁻ channel (β-GluCl) from C. elegans, as an extreme example of a human α7-AChR bearing extensive mutations in the TMD; and (2) a chimera that combines the chicken α7-AChR’s ECD with the TMD of C. elegans β-GluCl, as an example of a chimera with multiple mutations in the ECD. More precisely, the human and chicken α7-AChR ECDs differ at 13 positions (see Materials and methods), none of which approaches the agonists epibatidine or EVP-6124 (Fig. 9) closer than 3.0 Å in existing atomic models of the ligand-bound receptor (Noviello et al., 2021; Zhao et al., 2021; Fig. S5). As for the TMDs, those of the human α7-AChR and C. elegans β-GluCl are identical at only ∼40 positions out of a total of 273 (∼15%) in α7-AChR and 190 in β-GluCl (∼21%).

Toxin-saturation curves for the three constructs displayed similar α-BgTx half-saturation concentrations (∼1–2 nM) and Hill-coefficient values (∼1; Fig. 6 and Table 1). Also, the MLA–toxin competition curves for the two constructs having a human α7-AChR ECD and highly divergent TMDs were very similar, whereas those for the two constructs having the same β-GluCl TMD and slightly different α7-AChR ECDs were clearly different (Fig. 14 A and Table 1). Under the conditions of these assays—that is, receptor-channels that barely open when unliganded, unlabeled and labeled ligands that favor the closed state, and a ratio between the fixed and half-saturation concentrations of labeled ligand equal to 1—Eq. 4 provides an excellent description of the ligand–receptor interaction. Thus, the half-competition concentration values are approximately equal to 2 × K_D,closed, that is, direct estimates of (true) MLA affinities. Therefore, the obtained curves support the idea that small structural perturbations to the TMD do not reach the neurotransmitter binding sites (because large perturbations barely have an effect), whereas small structural perturbations introduced in the ECD do, perhaps, as expected simply on the basis of distance. As was the case for the wild-type human α7-AChR, the Hill coefficient for MLA turned out to be ∼1 for the two chimeric constructs, thus suggesting that the neurotransmitter-binding sites remained identical and independent despite the mutations.

The structure of the α7-AChR bound to MLA has not yet been solved, and MLA is a larger molecule than both epibatidine and EVP-6124 (Fig. 9). Therefore, we cannot rule out the possibility that the different MLA affinities of the human and chicken α7-AChR’s ECDs (Fig. 14 A) are due to close contacts between MLA and one or more of the 13 amino acids that differ between these two orthologs. Of these, residue 172 (residue 149 in the alternative numbering system used in Noviello et al. [2021]) approaches epibatidine the closest (4.1 Å in PDB accession no. 7KOX; Noviello et al., 2021), whereas residue 56 approaches EVP-6124 the closest (3.1 Å in PDB accession no. 7EKP; Zhao et al., 2021); all other 11 residues lie farther than 5 Å from these bound agonists. Hence, we mutated only these two residues of the human–C. elegans chimera (Ser-56 and Ser-172) to their chicken counterparts (both threonine) to estimate the degree to which the different MLA affinities of the human and chicken α7-AChR’s ECDs may be attributed to these closer-to-the-orthosteric-site substitutions. MLA–toxin competition curves for this double mutant revealed that the half-competition concentration only changed from 68 ± 6 nM in the human–C. elegans chimera to 32 ± 4 nM in the S56T + S172T mutant, whereas that of the chicken–C. elegans chimera is 4.9 ± 0.5 nM (Fig. 14 A and Table 1). Thus, it follows that it is the other 11 chicken-versus-human amino-acid substitutions that account for most of the ∼14-fold difference between the MLA closed-state affinities of these two α7-AChR orthologs.

The notion that changes in the amino-acid sequence of the TMD have a comparatively minor effect on the ligand-binding properties of α7-AChR ECD, inferred above from the observations with MLA, is likely to hold true for other orthosteric ligands as well. If this idea were valid for nicotine and carbamylcholine, then the differences observed between the competition curves of the human α7-AChR and the human–C. elegans α7-AChR–β-GluCl chimera with these two agonists (Fig. 14, B and C) would largely arise from differences in these channels’ unliganded-gating equilibrium constants. We found the chimera’s curves to be right-shifted relative to those of α7-AChR, regardless of the competing agonist, consistent with the chimera having a lower-than-wild-type unliganded-gating equilibrium constant (Fig. 2, A and B; and Table 1). Also consistent with this notion are the lower Hill coefficients obtained for this chimera, for both nicotine and carbamylcholine (Fig. 2 C and Table 1).

The toxin–agonist competition curves obtained with the chicken–C. elegans chimera, on the other hand—left-shifted for nicotine and nearly overlapping for carbamylcholine relative to those obtained with its human–C. elegans counterpart (Fig. 14, B and C)—exemplify the difficulty in comparing the behavior of pairs of receptors when both the unliganded-gating equilibrium constant and ligand affinities are expected to be different. Indeed, although these chimeras share the same TMD, the 13 amino-acid differences at the ECD are also likely to have caused changes in the equilibrium constant of unliganded gating. The effect of these mutations on the unliganded-gating equilibrium constant is, of course, the same irrespective of the agonist used, but the effects on agonist affinities are likely to be ligand specific.

Although probing the function of ion channels without measuring the transport of ions through them may seem oxymoronic, a number of experimental situations call for such indirect approaches. Here, working on members of the Cys-loop-receptor superfamily of LGICs, we focused on the practical implementation of, and the interpretation of results from, ligand-binding assays. To some extent, it could be said that the latter are to LGICs what gating-current recordings are to voltage-dependent channels: a means to probe the function of a domain that, at least in wild-type channels, is coupled to the channel’s activation gate. An important difference, however, is that ligand-binding studies do not require that the two ends of the ion channel face electrically separate compartments, and thus, binding assays can also be applied to detergent-solubilized or nanodisc-reconstituted receptors.

Ligand-binding studies of pLGICs are not new (Fulpius et al., 1972; Maelicke et al., 1977; Miledi et al., 1971; Miledi and Potter, 1971; Weber and Changeux, 1974a, 1974b, 1974c). Therefore, we were surprised to note a lack of uniformity in published protocols, large disparities in the estimates obtained by different groups for the same parameter, and a general disregard for constraints placed on the experimental observations by simple theoretical considerations. We decided to pursue the equilibrium-type of ligand-binding assays rather than the (much faster and more frequently used) protection-type kinetic assays because the former seemed, overall, more straightforward. Indeed, we surmise that some of the inconsistencies associated with the application of the kinetic approach may have arisen from the (admittedly challenging) accurate estimation of only the initial rate of labeled-ligand binding.

As elaborated in Results, equilibrium binding-competition assays present difficulties, too. A major one is that the interaction between the labeled ligand and the receptor (seldom of interest) gets in the way of the characterization of the interaction between the unlabeled ligand and the receptor. To address this point, we performed [¹²⁵I]-α-BgTx saturation curves with every new α7-AChR construct so as to learn what (fixed) concentration of labeled toxin had to be used in the competition assays. This is a crucial step that ensures that comparisons between different constructs are unaffected by the eventually different properties of each toxin–channel complex. Another difficulty—particularly when using slowly dissociating ligands such as α-BgTx—is the need to make a judgement as to when the system is close enough to equilibrium. In our case, we incubated the reactions at different temperatures for different times and deemed them to have approached equilibrium to a satisfactory degree when the fitted empirical parameters changed little with longer incubations. We note that the strong effect of temperature on the kinetics of approach to equilibrium seems to have gone unnoticed in previous applications of this method. Indeed, raising the incubation temperature to 37°C sped up the reactions’ time courses considerably.

Undoubtedly, equilibrium assays of the sort we described here are too time-consuming and labor-intensive to be useful as tools for the high-throughput screening of drugs. Rather, they are meant to be used in the context of the detailed mechanistic characterization of receptor-channel operation, an integral aspect of the design of new drugs that should not be overlooked (Rang, 2006). In the latter regard, it is important to bear in mind that an abundance of functional—and more recently, structural—data point to the notion that pLGICs form a mechanistically homogeneous group of proteins. Hence, conclusions drawn from studies of α-BgTx-binding AChRs may well hold true for the rest of the superfamily.

We would like to emphasize that the guidelines we provided here for the implementation and interpretation of concentration–response curves are valid for any antagonist or inverse agonist acting as the labeled ligand irrespective of their dissociation kinetics. Although assays that require the physical separation of bound from unbound label are most accurately performed with slowly dissociating labeled ligands, more recently developed technologies (for example, scintillation-proximity assays; Udenfriend et al., 1985) eliminate the need for this step, and thus open up the field to all other pLGICs for which slowly dissociating competitive ligands are not readily available. Whether this faster type of assay (intended, essentially, to allow for the high-throughput screening of ligands) yields data of high enough quality to illuminate ion-channel mechanisms remains to be ascertained.

For the sake of conciseness—and because, here, we used α-BgTx as the label—we did not elaborate on the mechanistic interpretation of concentration–response curves obtained from assays in which the labeled ligand is an agonist. However, several fast-dissociating pLGIC agonists are commercially available in radiolabeled form, and their use in equilibrium-type competition experiments has been increasing as the use of scintillation-proximity assay technology is becoming more widespread. A cursory theoretical analysis of the relationship between the empirical parameters of the corresponding ligand-binding curves and the underlying equilibrium constants of state interconversions reveals that, although some aspects remain the same regardless of whether the labeled ligand is an agonist, an antagonist or an inverse agonist, others differ in important ways. For example, among the latter, half-saturation concentrations of labeled agonists are not dissociation equilibrium constants (K_D values) from the closed state, and Hill-coefficient values from competition curves are highly sensitive to the ratio between the fixed and half-saturation concentrations of the labeled ligand. Clearly, as the use of agonist labeled ligands in equilibrium-type competition experiments increases, so does the need for enhancing the rigor and attention to theoretical detail with which these quantitative methods are applied. This is especially true if the obtained numbers are more than just mere numbers, and instead, are expected to help us understand how LGICs work.

Christopher J. Lingle served as editor.

We thank S. Gough for experiments performed during the initial stages of this project and Y. Paas (Bar-Ilan University), W.N. Green (University of Chicago), and S.M. Sine (Mayo Clinic College of Medicine) for cDNAs.

This work was supported by a grant from the US National Institutes of Health (R01-NS042169, to C. Grosman).

The authors declare no competing financial interests.

Author contributions: N.E. Godellas: Conceptualization, formal analysis, investigation, methodology, visualization, writing—original draft, writing—review & editing. C. Grosman: Conceptualization, funding acquisition, project administration, supervision, writing—original draft, writing—review & editing.