Agonist efficiency estimated from concentration-response curves

Concentration-response curves (CRCs) are characterized by a midpoint (EC50) and a high-concentration asymptote (Pomax) that relate to agonist affinity and efficacy. A third agonist attribute, efficiency, is the fraction of binding energy that is applied to the conformational change that activates the receptor. Here we show that agonist efficiency can be calculated from EC50 and Pomax, and estimate the efficiencies of 17 agonists of adult muscle nicotinic acetylcholine receptors (AChRs). The distribution of efficiency values was bi-modal with means+s.d of 52±2% (n=11) and 41±3% (n=6). Efficiency is correlated inversely with the volume of the agonists’ head-group. For 22 binding site mutations only αY190A affects significantly ACh efficiency, switching it from the high-to the low-efficiency population. If agonist efficiency is known, EC50 can be estimated from Pomax and the receptor’s level of constitutive activity can be calculated from a CRC.


Introduction
AChRs are members of the cys-loop, ligand-gated ion-channel receptor family that comprise GABA, glycine, and 5-HT3 receptors.They are pentameric allosteric proteins that have agonist binding sites in the extracellular domain, ~60A o away from a narrow region of the pore in the transmembrane domain that regulates channel conductance (1).
AChRs switch spontaneously between C(losed-channel) and O(pen-channel) conformations ('gating') to produce transient membrane currents (Fig. 1a).Agonists bind weakly to C versus strongly to O and increase receptor activity because the extra binding energy is used to facilitate the C→O transition (2).Here we are concerned with estimating the efficiency at which the agonist's chemical binding energy is converted to the mechanical work of the gating conformational change.
AChRs are the primary receptors at the neuromuscular synapse where they serve to initiate muscle membrane depolarization and contraction.They have two 1 subunits and one each of ,  and either  (adult) or  (fetal).There are 2 neurotransmitter binding sites located at − and − subunit interfaces (3).The presence of agonists at these sites increases the probability that the receptor will convert from the C to the O conformation and, hence, the probability that cations will enter and depolarize the muscle cell.
Agonists are typically characterized by an 'affinity' and an 'efficacy' (4).Affinity is a measure of how strongly the ligand binds to its target site and is the inverse of the equilibrium dissociation constant, either KdC or KdO (for binding to the site in its C or its O conformation).The concentration of agonist that produces a half-maximal response, EC50, is proportional to KdC (Eq. 3) and is sometimes called an 'apparent' affinity.Efficacy is the high-concentration asymptote of the CRC, or the maximum response elicited by the ligand (PO max ).Efficacy depends on the liganded gating equilibrium constant (Eq.4) that is proportional to the equilibrium dissociation constant ratio, KdC/KdO (Eq.2).
Recently, a third fundamental agonist attribute, efficiency (; eta), was defined as the fraction of the agonist's chemical binding energy that is converted into the receptor's mechanical gating energy that moves the protein reversibly between the C-shape and the O-shape (5).As shown previously, and again below using a different approach, efficiency is a function of the binding energy ratio, logKdC/logKdO (Eq.5).Direct, independent measurements of these two equilibrium dissociation constants obtained by detailed modeling of single-channel currents indicated that at adult-type human AChR neurotransmitter binding sites ACh and 3 structurally-related agonists convert 52% of their binding energy to gating, whereas the frog toxin epibatidine and 3 related agonists convert only 39%.An efficiency value reflects the relationship between EC50 and efficacy.
Given two agonists with the same EC50, the higher-efficiency ligand has the greater efficacy.
Here we show how agonist efficiency can be estimated from EC50 and Po max .We provide efficiency estimates from these CRC parameters for 17 agonists of mouse adulttype muscle AChRs, and show that knowledge of agonist efficiency simplifies and extends our understanding of drug action.If agonist efficiency is known, the apparent affinity (EC50) can be calculated from the efficacy (Po max ).

Estimating efficiency from CRC parameters.
Our first goal was to calculate agonist efficiency from EC50 and PO max using equations derived from Scheme 1 (Fig. 1).In order to ensure that the experimental measurements corresponded as closely as possible to the transitions in Scheme, we reduced the contribution from extraneous events such as channel block by the agonist, desensitization and modal activity (6), and constructed pseudo-macroscopic CRCs estimated from singlechannel currents.Each CRC was a plot of the absolute open-channel probability (PO, not normalized to a maximum value) versus [agonist], with the midpoint (EC50), maximum (PO max ) and slope (nH) estimated by fitting to the empirical equation Eq. 1 From microscopic reversibility, Scheme 1 demands that the ratio of gating equilibrium constants (with/without agonists) is equal to the ratio of equilibrium dissociation constants (to C/to O) at two sites: Eq. 2 where E2 and E0 are the diliganded and unliganded gating equilibrium constants.The exponent reflects the fact that in adult-type AChRs the 2 neurotransmitter binding-sites are approximately equivalent and independent (2).The diliganded gating equilibrium constant (that determines efficacy; see below) is equal to the constitutive gating equilibrium constant multiplied by the square of the fold-increase in agonist affinity that occurs within the C-to-O conformational change.
Constitutive and mono-liganded activities are both rare, so in wild-type (wt) AChRs the only route that generates a significant amount of current is the linear path shown in bold in Fig. 1.Transitions between these 4 states determine PO and, hence, the experimental values of EC50 and PO max .For activation by this pathway, EC50 depends on both binding (to C) and gating equilibrium constants, but PO max depends only on the diliganded gating equilibrium constant (7), Eq. 3 Eq. 4 Bold, the main physiological activation pathway.
Agonist efficiency () was calculated from EC50 and PO max by using Eqs.2-4, as follows.First, E2 was calculated from PO max (Eq.4).Second, KdC was calculated from E2 and EC50 (Eq.3).Third, KdO was calculated from E2 and KdC using a known value of E0 (Eq.2).Finally, efficiency was calculated from the two equilibrium dissociation constants (see Materials and Methods and ref 5),

=1-logKdC/logKdO
Eq. 5 Four previous results enabled us to estimate efficiency from a CRC.First, adult AChR binding sites have approximately the same affinity, so only single values of the 2 equilibrium dissociation constants needed to be estimated for each ligand.Second, Scheme 1 has been proved experimentally, so KdC could be calculated using Eqs. 3 and 4.
Third, the unliganded gating equilibrium constant Eo is known so KdO could be calculated by using Eq. 2. In an 'efficiency" plot for a group of ligands (5), E0 is estimated from the y-intercept.However, prior knowledge of E0 is required to estimate efficiency from a single CRC.

ACh efficiency
Plots of PO versus [agonist] were constructed from single-channel currents (Fig. 2).
Macroscopic CRCs for ACh and adult-type, human AChRs have been measured using automated patch clamp and whole cell currents, with the result EC50=22 M (9).A macroscopic current amplitude is equal to the product of the number of receptors contributing to the response, the single-channel current amplitude and PO.Because the number of receptors is unknown in these experiments, an absolute PO max (that pertains to Scheme 1) could not be estimated.However, using our single-channel value PO max (ACh)=0.96and E0=4.5x10 -7 (Vm=-60 mV), we calculate from the whole-cell CRC that ACh=49% (Table 1).
In addition, we calculated ACh from published values of KdC and KdO either from wild-type mouse AChRs (8) or from individual − and − human AChR binding sites (2), in both instances estimated by kinetic modeling of single-channel currents.The efficiencies calculated from these independent datasets are both 50% (Table 1).
These results indicate that at adult AChR binding sites about half of the available neurotransmitter binding energy is applied to the gating conformational change.That is, the energy of ACh binding to C is approximately half that of binding to O, and (for 2 sites) is about equal to the energy of diliganded gating.Further, the results show that agonist efficiency in AChRs can be estimated from single-channel or whole-cell CRCs (as long as contamination by desensitization is avoided by using fast agonist application), is the same whether receptors have one or two functional neurotransmitter binding sites, and is similar in mouse and human adult-type AChRs.

Table 1
Table1.EC50 and PO max were obtained by fitting each CRC to Eq. 1 (for multiple PO measurements as mean+ s.e.m.).Calculated equilibrium constants diliganded gating (E2) and dissociation to C or O (KdC or KdO); coupling constant λ=sqrt(E2/E0) (Eq.2); =efficiency (Eq.5).Previouslypublished values from Ɨ (8), ± (10), Φ (2), Ψ (9), * (11), ǂ (5).Values after correction for background mutations that increase E0, 1 S450W and 2 (L269F+E181W).Next, we measured efficiencies for other agonists that were not studied previously by CRCs (Fig. 4).Choline (Cho) has 2 methylenes between its quaternary nitrogen and hydroxyl (OH) group versus 3 and 4 for 3OH-BTMA and 4OH-PTMA.Cho is a lowaffinity, low-efficacy agonist (11) that KdC and KdO values estimated by modeling singlechannel kinetics of the human − site indicate has the same efficiency as ACh, Cho=52% (5).Simulations of binding site structures suggest that an H-bond between the terminal OH and the backbone carbonyl of W149 serves to position the charged nitrogen of choline away from the aromatic rings that line the cavity, to reduce favorable binding energy (12,13).Inserting additional methylenes reduces the probability of this H-bond and allows a more-optimal position that increases binding energy relative to Cho.
The CRCs and associated PO max and EC50 values for 3OH-BTMA and 4OH-PTMA are shown in Fig. 4A left.From the calculated equilibrium dissociation constants we estimate =50% for both of these agonists (Table 1).Despite the substantial range in affinity and efficacy afforded by the different H-bond propensities, all three of the cholinebased agonists have the same efficiency that is the same as for the agonists shown in Fig. 3.The similarity in the C versus O binding energy ratio (but not the difference) for these 3 ligands suggests that the effect of the H-bond on the position of the nitrogen atom applies equally to C and O binding cavities.
Overall, the mean+s.defficiency calculated from CRCs for the 11 agonists described so far (ACh, Nor, CCh, Ana, TMA, DMP, DMT, Cho, 4OH-BTMA, 4OH-PTMA, DMPP) is 52+2 %.For this group of ligands, the binding energy ratio logKdC/logKdO is 0.48, indicating that on average the agonist binding energy increases by a factor of ~2.1 when the sites switch spontaneously from C to O.  To study these we added background mutations that did nothing more than increase E0 and, hence, increase PO max and left-shift EC50 (Eqs.2-4).After correcting for the effects of the background mutations, from the CRC parameters we estimate that TEA=40%, TMP=41% and var=35%.
For the group of 6 ligands shown in Fig. 4A middle and right (Ebt, Ebx, Cyt, Var, TEA, TMP) the average efficiency 41+4% (Fig. 4B).For these ligands, the binding energy ratio (logKdC/logKdO) is 0.60, indicating that binding energy increases by a factor of ~1.7 when the sites switch spontaneously from C to O.  We also estimated the volumes of the 'head' group of the agonists (v) and plotted these versus efficiency (Fig. 5B).A 2D cluster analysis again shows 2 populations with efficiencies of 1=52% (n=11) and 2=41% (n=8) with corresponding volumes of v1=70.4+8.8 and v2=102.2+17.8Å 3 (centroid+s.d.) respectively.There is an inverse relationship between agonist efficiency and head-group volume.
Binding site mutations.KdC and KdO have been estimated by kinetic modeling of singlechannel currents from mouse, adult-type AChRs having a mutation of an aromatic residue at both binding sites (15).We calculated from these values ACh for 22 different mutants.
Figure 6 shows Gaussian distribution with ACh=51+4% (centroid+s.d.), which is the same as in wt AChRs (Fig. 1).The one clear exception was Y190A that falls outside the distribution, for which  ACh =35%.The three largest efficiency-values were for mutations of W149 (Figure 6-Source Data 1 in SI).
Utility of efficiency.Knowledge of  simplifies and extends CRC analysis.The same efficiency for a group of agonists means the same logKdC/log KdO ratio and, hence, that the two dissociation constants are related by the same exponent, KdC=KdO 0.48 for the higher efficiency population and KdC=KdO 0.60 for the lower efficiency population.Hence, given this exponent (equal to 1-), one equilibrium dissociation constant can be calculated from the other.This has two useful consequences.
First, knowledge of  (along with the agonist-independent constant E0) allows the estimation of EC50 from PO max that is the response at a single, high [agonist].Combining Eqs. 2 and 5 and rearranging yields logE2 = (−)logKdC+logE0.
Eq. 6 E2 can be calculated directly from PO max (Eq.4), so with knowledge of  one can solve Eq. 6 for KdC, then Eq. 3 for EC50.If an agonist's efficiency is known, the unliganded gating equilibrium constant (E0) can be calculated from constants derived from EC50 and PO max (Eq.6).The assumed  values were either 52% (red) or 41% (blue).The calculated mean E0 of 1.1 x 10 -6 (dashed line) is approximately the same regardless of  and reasonably close to the E0 value estimated using other methods (arrow).So-calculated E0 for 17 agonists are given in Figure 7-Source Data 2 (SI).
If agonist efficiency and the unliganded gating constant are known, an entire CRC can be estimated from the response at just one [agonist].
Second, knowledge of  allows the estimation of the unliganded gating equilibrium constant (E0) from a single CRC.E0 is an important, ligand-independent constant that sets the basal level of activity (the low-concentration asymptote of the CRC, usually mistaken to be zero) from which agonists increase PO, but it is often quite small and difficult to measure directly (16)(17)(18).The procedure to estimate E0 from a CRC of a wt receptor is first to solve for E2 and KdC from PO max and EC50 as described above, then solve for E0 using Eq. 6. Fig. 7C shows E0 values so-calculated from CRC parameters using assumed -values of 52% or 41%.The mean result for Vm=-100 mV, 1.1±2 x 10 -6 (mean±s.d), is reasonably close to the experimentally-determined value of 7.4 x 10 -7 (19).
If agonist efficiency is known, an approximate value of the unliganded gating constant can be estimated from a single CRC.Once this value has been learned, it can be applied to all agonists.

Discussion
The main results are that in adult-type AChRs, agonist efficiency i) can be estimated from a CRC, ii) is ~50% for the neurotransmitter ACh and its breakdown product choline, iii) has a bi-modal distribution, iv) is correlated inversely with headgroup volume, and v) simplifies and extends CRC analysis.Further experiments are needed to explore the structural basis of agonist efficiency in AChRs, and whether or not groups of structurally-related agonists have a common efficiency in other receptors.
Estimating efficiency.The estimates of agonist efficiency are the same whether obtained from single-channel or whole-cell currents, from a CRC or by detailed kinetic modeling.
They are the same in wt AChRs with 2 active binding sites or in AChRs that have just 1 active site.Efficiency is approximately the same in mouse and human AChRs, and in receptors that have a mutation of a binding site aromatic residue (except for Y190A) or in distant regions that do not affect affinity.In AChRs, efficiency is a robust agonist attribute.At neuromuscular synapses, about half of the available neurotransmitter binding energy is converted into mechanical energy for the gating conformational change.
Many agonists have the same efficiency as ACh.An efficiency of ~50% implies that for these ligands the binding energy to O is approximately double that to C, regardless of affinity and efficacy (8).Further, a constant efficiency implies that the energy change in low-affinity binding to C (logKdC) is a constant fraction of (for ACh, about equal to) the energy change of the switch from low-to-high affinity (logKdO-logKdC) that happens inside C-to-O gating (5,8).That is, binding and gating energies are correlated.
Low-affinity binding to C is slower than diffusion (8) and is associated with a structural rearrangement of the binding site called 'catch'.The structural change at the binding site associated with the low-to-high affinity switch in conformation (that takes place within gating) is called 'hold'.[Note: 'hold', 'flip' (21) and 'prime' (22) all refer to intermediate events within the gating transition.See ( 23) for a discussion.]A constant efficiency for a group of agonists implies that there is a linear correlation between binding (catch) and gating (hold) energies that in turn suggests these two rearrangements of the binding site are related.The correlation between catch-and-hold energies and, possibly, structural changes blurs the distinction between binding and gating.In AChRs, the forward allosteric transition begins with ligand association, with binding-gating (catchand-hold) appearing as two stages of a single, amalgamated structural (energy) change process.
It remains to be determined whether or not a constant efficiency for a group of related agonists is particular to neuromuscular nicotinic AChRs or is a general feature of receptor activation.It appears that in some other receptors there is a linear relationship between log gating and log binding equilibrium constants for structurally-related ligands, suggesting that for these there is a constant logKdC/logKdO ratio and, hence, a constant efficiency (5), but more experiments are needed.
Bimodal distribution.There are 2 populations of AChR agonist efficiency values, at 52±2% and 41±4%.The small s.d. for each population suggests that most of the variation likely arises from measurement error rather than from actual, ligand-specific differences.
Further evidence of bi-modality in efficiency comes from the observation that the binding site mutation Y190A shifts the efficiency of ACh from 51% to 35%, or from the highefficiency group into the low-efficiency group (same as varenicline).The results so far suggest that the distribution of agonist efficiency is modal rather than continuous, but more ligands need to be examined to determine if other efficiencies are possible.It is also possible that more extensive and precise measurements might reveal consistent efficiency differences consequent to binding site mutations.For example, the the observation that Y, F and A substitutions at W149 have slightly higher ACh efficiencies compared to the wt needs to be investigated by examining more mutations and agonists.
Structural correlates.Changes in protein structure, dynamics or both undergird the conversion of chemical binding energy into mechanical gating energy.Although our experiments did not address directly the important question of understanding the molecular events that determine that 5o% versus 40% of the agonist's binding energy is applied to the gating conformational change, there are some clues.
Members of both efficiency groups (high, low) may have a quaternary amine (TMA, TEA) or a secondary amine (DMPP, Ebt).Hence, it does not appear that the bimodal distribution in efficiency reflects differences in the charge on the agonist's head group nitrogen (or phosphorous, in the case of TMP).
The inverse correlation between agonist head-group volume and efficiency may be more relevant (Fig. 5B).Simulations of AChR structures suggest the possibility that the agonist binding cavity is smaller in O compared to in C (12).Further, kinetic analyses of AChR gating suggest that channel-opening occurs as a sequence of domain motions with the energy change of the extracellular domain (a contraction or 'unblooming'; (24)) following the 'hold' energy change at the binding cavity (25).Hence, it is possible that larger-volume, lower-efficiency agonists encounter steric hindrance when the cavity shrinks, to limit the extent of the contraction and, hence, the force applied to the next region of the protein to move in the gating sequence, the extracellular domain.We hypothesize that the higher-efficiency ligands fit comfortably into both the C and O pockets but lower-efficiency agonists do not fit easily into O.Accordingly, pocket contraction is more-limited with lower-efficiency agonists, so less energy for gating is generated by the binding site's 'hold' rearrangement.However, the relationship between volume and efficiency is not simple because Ebt and TEA have similar efficiencies despite there being a substantial difference in head-group volume.
That there are 2 discrete efficiency populations suggests there could be two discrete pathways that couple binding energy to gating, for instance one that supplies ~40% of the energy and another than supplies ~10%.Perhaps with smaller agonists both pathways are utilized, but when the binding pocket is 'stretched' by a large agonist either the 10% pathway is broken, or both are compromised.
Another clue regarding the structural basis of efficiency is that the only binding site mutations that changed significantly the efficiency of ACh was Y190A, reducing it from the high to the low population.This suggests that perturbation of Y190 is part of a pathway for some (10%?) of the energy that is transferred out of the binding pocket (20,26).However, the fact that the mutations Y190F and Y190W have no effect on ACh efficiency suggests that the key interaction is with the aromatic ring rather than with the OH group.Measuring the effects of mutations on agonist efficiency may be an effective way to explore molecular pathways by which energy is transferred from the binding site into the extracellular domain, and beyond.
The efficiency estimates for the two populations are the same whether measured in whole receptors (that have − and − binding sites) or in receptors having only one functional site (5).This indicates that the energy changes that contribute to efficiency are determined mainly by local ligand-protein interactions at each binding site, with little or no energy transfer between sites.The efficiency of Ebx is somewhat higher in whole receptors compared to at − alone so it is possible that the efficiency of this agonist is modestly greater at one site (−) compared to the other.

Utility of efficiency.
Knowing agonist efficiency is useful because it allows EC50 from PO max (affinity to be estimated from efficacy).That is, an entire CRC can be estimated from an experimental measurement at just one agonist concentration.This ability could greatly facilitate drug screening.The above results raise the possibility that it may someday be possible to predict agonist efficiency a priori from ligand and binding site structures (head-group and binding-cavity volumes), in which case the need for wet-bench experiments in CRC estimation would be reduced substantially.
There are stipulations with regard to calculating agonist efficiency from a CRC.
First, the CRC must be comprised of absolute responses rather than normalized to the maximum.Normalized CRCs are more common because it is difficult to know the number of receptors contributing to the response.Our approach (single-channels) circumvents this problem by ensuring that exactly 1 receptor contributes to each PO measurement.One way to make a CRC from absolute, whole-cell responses is to count the number of receptors (27) or to calibrate each response to that of an agonist having a known, absolute response.Second, the CRC should be largely uncontaminated by events outside the core activation scheme (Fig. 1).Whole-cell responses arising from multiple receptor populations (heterogeneity) or generated by slow agonist application (desensitization) may not produce CRCs that match Eqs. 3 and 4. For some receptors the equations that relate CRC parameters with binding and gating constants may be more complicated.The extent to which such contaminations influence the efficiency estimate from a whole cell CRC remains to be determined and could be different for different receptors.Third, E0 must be known a priori.However, this constant applies to all agonists and only needs to be measured once for each receptor.Analysis.Fig. 1 shows the main states involved in AChR activation and de-activation.

Experimental design
When the agonist association and opening rates are sufficiently large, single-channel openings occur in clusters (28) (Fig. 2).Shut intervals within clusters represent mainly agonist binding and receptor gating (Fig. 1, bold) whereas shut intervals between clusters represent mainly long-lived desensitization (not shown in Fig. 1).We selected for analysis clusters that appeared by eye to arise from a homogeneous open probability (PO) population and limited the analysis to intra-cluster interval durations.
Because of the high extracellular [K + ], the cell membrane potential (Vm) was 0 mV.
The AChR agonists we examined also are channel-blockers.To both generate measurable outward currents and reduce the effect of channel block on PO, the membrane was depolarized to +70 mV by holding the pipette at -70 mV.This effectively eliminated agonist binding to the channel-block site in the transmembrane domain but did not affect agonist binding to the neurotransmitter sites in the extracellular domain.
Analyses of the currents were performed by using QUB software (29).A cluster was defined as a group of openings flanked by shut intervals longer than some duration that depended on the [agonist] (tcrit, range 7-20 ms).Open and shut currents within clusters were idealized into noise-free intervals by using the segmental k-means algorithm (SKM) after digitally low-pass filtering the data at 10 kHz (30).
The idealized interval durations were fitted by multiple exponential components using a maximum interval likelihood algorithm (MIL) (31).Cluster PO at each [agonist] was calculated from the time constants of the predominant components of the shut-time (s) and open-time distributions (o): o/(s+o) (Fig. 2, Figure 4 -figure supplement 1-3).The half-maximum (EC50) and maximum (Po max ) response were estimated by fitting to an empirical equation (Eq.1) using GraphPad Prism 6.

Definitions.
The agonist binding free energy is equal to +RTln(KdC) or +RTln(KdO), where R is the gas constant and T is the absolute temperature.In contrast, agonist efficiency depends on the ratio of binding energies, as shown previously ( 5) and as follows.Agonist activation of a resting, unliganded AChR entails connecting the resting-unliganded state C to the diliganded-active state A2O (Fig. 1).
Because microscopic reversibility is satisfied (2), the product of the equilibrium constants (sums of the energy changes) for the steps linking these states in the clockwise direction (the main physiological activation route) is the same as in the counter-clockwise direction.The product of the counter-clockwise equilibrium constants is E0/KdO 2 , the negative log of which gives the total energy required for activation by this route, 2log(KdO)-logE0.The product of the equilibrium dissociation constants connecting C with A2C is 1/KdC 2 , the negative log of which is the energy for just the binding part of activation by the clockwise route, 2log(KdC).We are interested only in the agonist component of the total energy and, because logE0 is the same for all agonists it can be ignored (set to 0).
We now calculate agonist efficiency from these energies.The fraction of the total energy that is used in binding is 2logKdC/2logKdO, and the efficiency, which the fraction that pf the total applied to gating, is 1-logKdC/logKdO (Eq.5).
Voltage, E0 and background mutations.Depolarization to Vm=+70 mV (to reduce channel block by the agonist) has the undesired consequence of shortening o making current detection and idealization more difficult.To compensate, we added the background mutation S450W (in the M4 transmembrane segment of the  subunit) that has the equal-but-opposite effect on gating as does depolarization by +140 mV, but has no effect on agonist binding (32).With this mutation, o and the unliganded gating equilibrium constant E0 at +70 mV were the same as in wild-, adult-type AChRs at Vm=-70 mV.E0 at -100 mV is 7.4 x 10 -7 and is reduced e-fold by a 60 mV depolarization (19).
Hence, we estimate that in our experiments at Vm=+70 mV and with S450W, Eo is 5.2 x 10 -7 .
With the low-efficacy agonists varenicline, tetraethylammonium and tetramethylphosphonium currents clusters generated by wild-type (wt) AChRs were poorly defined because the channel-opening rate constant was too small.For these ligands PO could not be estimated accurately using wt AChRs.To increase the diliganded opening rate constant and generate better-defined, higher-PO clusters we added two background mutations in the  subunit, L269F (in the M2 helix) and E181W (in strand 9), without S450W.Together, these two substitutions increase E0 by 1084-fold (making it 4.9x10 -4 ) without affecting agonist binding (33,34).

Statistical analysis
The goodness of fit for the efficiency frequency distribution (Fig. 5A) was done using Prism software (GraphPad Inc., San Diego, CA).The F-test rejects the null hypothesis (Gaussian fit) over sum of two Gaussian with an F-value (F=3.9) and significance (P-value, <0.05).A k-means cluster analysis algorithm (MATLAB ® , MathWorks, Natick, MA) was used to define agonist groups for 2D cluster analysis, efficiency and head-group volume (Fig. 5B).Correlation significance between log EC50, either measured from the CRC or calculated from knowledge of efficiency (Fig. 6A) was performed with Pearson's correlation test using Prism software.The P-value (two-tail) <0.0001 and r 2 =0.78 imply that there is a significant correlation.

Figure 1 .
Figure 1.Cyclic activation of receptors (Scheme 1).AChRs switch spontaneously between resting (C) and active (O) conformations.A, agonist.Horizontal arrows, binding and vertical arrows, gating.Equilibrium constants: En, gating with n bound agonists; KdC and KdO, dissociation constants to C (low affinity) and to O (high affinity).Rate and equilibrium constants for all steps have been measured experimentally in adult-type endplate AChRs that have two approximately equivalent and independent neurotransmitter binding sites.From microscopic reversibility, E2/E0=(KdC/KdO) 2 (Eq.2).Agonists increase activity above the baseline level because they bind more-strongly to O, with the extra binding energy facilitating the spontaneous channel-opening transition.

Figure 2 .
Figure 2. Activation of adult-type AChRs by cytisine.A. Low-resolution view of singlechannel currents showing clusters of openings arising from a single AChR, separated by silent periods when all AChRs in the patch are desensitized (Vm, membrane potential).B. High-resolution views of example clusters at different [agonist] and corresponding interval-duration histograms.The predominant intra-cluster shut and open interval durations (s and o) were used to calculate an open-channel probability (PO) at each agonist concentration.C. CRCs fitted by Eq. 1 to estimate EC50 and PO max (symbols, mean±s.e.m.).Efficiency () was calculated from the CRC parameters by using Eqs.2-5.

Figure 3 .
Figure 3. Estimates of agonist efficiency from previously-published CRCs. A. CRCs of 7

Figure 4 .
Figure 4. Estimates of agonist efficiency from newly-measured CRCs. A. CRCs (symbols, mean±s.e.m.).Background mutations were used to eliminate channel block (S450W; left and middle) or to increase PO max and left-shift EC50 by increasing the constitutive gating equilibrium constant (L269F+E181W; right).EC50 and PO max values in Table 1 have been corrected for these backgrounds and pertain to adult, wild-type mouse AChRs.Interval-duration histograms with corresponding predominant intra-cluster shut and open interval durations and example clusters can be found in SI (figure 4 -figure supplement 1-3).B. Efficiencies calculated from the CRCs (open bars) or from previouslyreported measurements of KdC and KdO obtained by kinetic modeling (2) (gray bars).

Fig. 4A middle
Fig. 4A middle shows CRCs for 3 agonists that have a bridge nitrogen atom.The

Fig
Fig. 4A right shows CRCs for agonists that have an extraordinarily low efficacy and

Fig
Fig. 5A shows a histogram of efficiency values for 17 agonists estimated from CRCs

Figure
Figure 6-Source Data 1. efficiency of binding site mutations.

6-Source Data 1. efficiency of binding site mutations.
Equilibrium dissociation constant Kd of ACh to closed (C) and open (O) states previously estimated by kinetic modeling (1) for wild-type (wt) and binding site residue mutations in adult-type mouse AChR.Kappa () is the ratio of their binding energies, logKdC/logKdO and efficiency () is 1-logKdC/logKdO (1-).