Structural implications of agonist efficiency estimated from concentration-response curves Running title : agonist efficiency

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 Y190A 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 receptors level of constitutive activity can be calculated from a CRC.


Introduction
Nicotinic acetylcholine receptors (AChRs) are members of the cys-loop, ligandgated receptor family that in mammals also comprise GABAA, glycine, 5-HT3 and zincactivated receptors (1). They are 5-subunit, liganded-gated ion channels with agonist binding sites in the extracellular domain, far from a narrow region of the pore in the transmembrane domain that regulates ion conductance (2,3).
AChRs switch between global C(losed-channel) and O(pen-channel) conformations ('gating') to produce transient membrane currents. Agonists promote channel opening because they bind more strongly to the O conformation. The energy (structure) of the binding site at the gating transition state resembles O (4). When a receptor begins its journey from C to O, the extra (favorable) binding energy eases the pathway, thereby increasing the probability of reaching and residing in O (PO) (5,6).
AChRs are the primary receptors at vertebrate neuromuscular synapses where they initiate muscle membrane depolarization and contraction. Neuromuscular AChRs have two 1 subunits and one each of ,  and either  (adult) or  (fetal). There are two neurotransmitter binding-sites located at − and − subunit interfaces (7) that are approximately equivalent for ACh in adult-type AChRs (5). AChRs switch conformation spontaneously (only under the influence of temperature), with the presence of neurotransmitters at both adult sites increasing the opening rate constant by a factor of ~5 million and the lifetime of the O conformation by a factor of ~5.
Agonists are typically characterized by a potency (proportional to affinity) and an efficacy. Affinity is a measure of how strongly the ligand binds to its target site and is the inverse of an equilibrium dissociation constant. The constants KdC and KdO correspond to low-affinity (weak) binding to the C conformation and high-affinity (strong) binding to the O conformation. (The logarithm of an equilibrium dissociation constant is proportional to binding energy.) The high-concentration asymptote of a CRC, or the maximum response elicited by the ligand, is called PO max in single-channel or I max in whole-cell currents. This limit gives the agonist's efficacy and depends only on the fully-liganded gating equilibrium constant.
The midpoint of a CRC, or the agonist concentration that produces a half-maximal response, is called EC50 or potency. EC50 is proportional to KdC but also depends on the gating equilibrium constant.
The low-concentration asymptote of a CRC, or the level of constitutive activity in the absence of agonists (PO min or I min ), depends on the unliganded gating equilibrium constant that is typically extremely small and difficult to measure. However, it is important to know the exact value of this constant because it multiplies the fully-liganded gating equilibrium constant to influence potency, efficacy and synaptic current profiles.
Allosteric modulators and AChR mutations (8), including some that cause slow-channel myasthenic syndromes (9), alter EC50, efficacy, and the time course of synaptic currents by increasing or decreasing the unliganded gating equilibrium constant without making a noticeable change in baseline activity.
Recently, efficiency (; eta) was defined as the fraction of an agonist's chemical binding energy that is converted into the mechanical (kinetic) energy for gating (10). As shown previously (and again below by using a different approach),  is a function of the resting/active binding energy ratio, logKdC/logKdO. Direct, independent measurements of these two equilibrium dissociation constants obtained by detailed kinetic modeling of single-channel currents indicated that at adult-type human AChR neurotransmitter binding sites, ACh and 3 related agonists on average apply ~50% of their binding energy to gating whereas at the − binding site the frog toxin epibatidine and 3 related agonists on average apply only ~40% (10).
Here, we show that agonist efficiency can be estimated from the asymptotes and EC50 of a CRC constructed from either single-channel or whole-cell currents. Given two agonists with the same EC50, the one with the larger efficacy has the greater . We provide separate efficiency estimates for 20 agonists of mouse adult AChRs and show that knowledge of agonist efficiency broadens our understanding of drug action. and 5 EGTA, pH adjusted to 7.2 using KOH. Cells clamped at -80 mV were exposed to a 2 s agonist application followed by 90 s wash between applications to allow recovery from desensitization. IonFlux software (ver.4.5) was used for cell capture, seal formation, compound application and data acquisition.

Experimental design
Analysis. Scheme 1 (Fig. 1) shows the main states of AChR activation/de-activation.
When agonist-binding and channel-opening rate constants are sufficiently large, singlechannel openings occur in clusters (11) (Fig. 2A, Fig. S1-S4). Shut intervals within clusters represent mainly agonist binding to C and channel opening (bold in Fig. 1), whereas shut intervals between clusters represent mainly long-lived desensitization (not shown in Fig.   1; for connections see (6)). We selected for analysis clusters that appeared by eye to arise from a homogeneous PO population and, in order to exclude sojourns in desensitized states, limited our analyses 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 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 single-channel (outward) currents were performed by using QUB software (12). A cluster was defined as a group of openings flanked by shut intervals longer than a duration that depended on the agonist concentration (range, 7-20 ms).
Open and shut currents within clusters were idealized into noise-free intervals by using the segmental k-means algorithm after digitally low-pass filtering the data at 10 kHz (13).
Idealized interval durations were fitted by multiple exponential components using a maximum interval likelihood algorithm (14). Cluster PO at each agonist concentration was calculated from the time constants of the predominant components of the shut-(s) and open-time distributions (o): o/(s+o) (Fig. 2B). The single-channel CRC was a plot of the absolute PO (not normalized) versus the agonist concentration.
Whole-cell currents were digitized using a sampling frequency of 10 kHz and were analyzed using IonFlux Data Analyzer v5.0. Peak currents were normalized to a maximum response (I/I max ), where I max was either the response to 300 M ACh or 1. The 20-80% rise time to a step to 300 M ACh was ~400 ms, a time we attribute to solution exchange.
The rate of entering a long-lived desensitized state is proportional to cluster PO and occurs with a rate constant of ~5 s -1 (15). Hence, when PO is 1 the whole-cell current declines with a time constant of ~200 ms. As a consequence, the peaks of currents elicited by high-concentrations of high-efficacy agonists are truncated because of the solution exchange time. This has the effect of shifting EC50 to lower concentrations. Responses at lower agonist concentrations or from lower-efficacy agonists were unaffected by desensitization.
The midpoint, maximum and slope of each CRC (EC50, PO max or I max , and nH) were estimated by fitting by Eq. 1 using GraphPad Prism 6. Eq. 9 was solved numerically for E2 by using the symbolic math program Wolfram Alpha.
Voltage, E0 and background mutations. Depolarization to Vm=+70 mV reduces channel block by the agonist but has the undesired consequence of shortening o to make singlechannel current detection and idealization 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 the unliganded gating equilibrium constant E0 as does depolarization by +140 mV but has no effect on agonist binding (16). With this mutation, o and E0 at +70 mV were the same as in wild-type (wt), adult 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 (17).
Hence, we estimate that in our experiments at Vm=+70 mV and with S450W, Eo was 5.2 x 10 -7 . In the whole-cell experiments, Vm=-80 mV and we estimate E0 was 5.9x10 -7 .
With the low-efficacy agonists varenicline, tetraethylammonium and tetramethylphosphonium, current clusters generated by wt AChRs were poorly defined because the channel-opening rate constant was 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 (18,19). From the uncorrected CRC, we estimated an E2 value from the PO max (Eq. 4) and KdC from EC50. We divided this E2 by 1084 to arrive at a corrected E2 from which we calculated corrected PO max and EC50 values that pertain to wt AChRs (Table 1).
Equations. Single-channel CRCs were constructed from PO values after eliminating extraneous events arising from channel block, desensitization and modal activity (20).
Whole-cell CRCs were constructed from peak currents. EC50 and PO max (or I max ) were estimating by fitting the CRC, Eq. 1 Scheme 1 (Fig. 1) was used to estimate  from EC50 and PO max (I max ). Because microscopic reversibility is satisfied, Eq. 2 has been confirmed by experiment (5).
Constitutive and mono-liganded activity are both rare, so in wt AChRs the only significant pathway that generates current is the clockwise, linear activation route highlighted in Fig. 1 . Eq. 4 Agonist efficacy depends on the gating equilibrium constant that from Eq. 2 is a function of the affinity ratio, KdC/KdO. Taking the log of Eq. 2, we see that efficacy is determined by the difference between the binding energies, log(KdC)-log(KdO). Partial agonists experience smaller increases in O versus C binding energy compared to full agonists, antagonists experience no change in binding energy, and inverse agonists experience a decrease in favorable binding energy upon receptor activation.
In contrast,  depends on the ratio of these binding energies, log(KdC)/log(KdO), as shown previously (10) 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). The product of the equilibrium constants (or sum of the energy changes) for steps linking these states in the clockwise direction (the highlighted, physiological activation route) is the same as in the rarely-taken, counter-clockwise direction. The product of the counter-clockwise constants is E0/KdO 2 , the negative log of which is proportional to the total energy required for constitutive gating and binding to O at 2 sites, 2log(KdO)-logE0.
The product of the equilibrium dissociation constants connecting C with A2C is 1/KdC 2 , the negative log of which is proportional to the energy for just the binding part of clockwise activation, 2log(KdC). We are interested only in the agonist component of the total energy and, because Eo is agonist-independent, it can be ignored. Hence, the fraction of the total agonist energy that is used in binding is 2logKdC/2logKdO, so efficiency, or the fraction of this total that is applied to gating, is Eq. 5 Efficacy and efficiency are distinct, but related, agonist attributes. In terms of energy, efficiency is equal to efficacy (logKdO-logKdC) divided by logKdO (Eq. 5). An agonist can be high efficacy and low efficiency (epibatidine) or low efficacy and high efficiency (choline), but within limits. If an agonist had PO max =0.75 (the same as TMA) and =30% it would have unreasonably small equilibrium dissociation constants, KdC=27 nM and KdO=15 pM. In practice, high-efficacy agonists will also have high efficiencies.
Agonist efficiency was calculated from EC50 and PO max by using Eqs.   We also calculated ACh from published values of KdC and KdO obtained either from wild-type mouse AChRs (23) or from individual − and − human AChR binding sites (5), in both instances estimated by kinetic modeling of single-channel currents. The efficiencies calculated from these independent datasets are both 50% (Table 1).
At adult AChR binding sites, half of the neurotransmitter binding energy is applied to the gating conformational change. That is, at each of the 2 binding sites the energy change when ACh binds to the C conformation is approximately equal to the increase in binding energy that happens within C-to-O.  (23)). There is an inverse correlation between EC50 and PO max (

Efficiency of other agonists
We fitted other previously-published, single-channel CRCs (23) to estimate EC50 and PO max , and from these calculated agonist  values as described above (Fig. 3 and Table   1). Despite the wide ranges in both EC50 (43 M to 6.7 mM) and PO max (0.26 to 0.96), all 8 of these agonists (including ACh) have a similar efficiency, =52+2% (mean+s.d.) (Fig.   3B). The efficiency of the lowest-efficacy agonist in this group, DMP, was greater than that of the highest-efficacy agonist, ACh. This highlights the distinction between efficiency (that depends on the binding energy ratio) and efficacy (that depends on the binding energy difference).
Next, we measured efficiencies for 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 (24) that KdC and KdO values estimated by modeling singlechannel kinetics at the human − site indicate has a similar efficiency as does ACh (10).
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 (25,26). 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  is 50% for both agonists (Table 1). Despite the substantial range in affinity and efficacy afforded by the different H-bond propensities, all three of the choline agonists have the same efficiency that is similar to the efficiencies of 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. Fig. 4A left also shows the CRC of dimethylphenylpiperazinium (DMPP), a nicotinic receptor agonist that is selective for the  (ganglionic) subtype (27). The result was DMPP=52% (Table 1).
Overall, the mean+s.d efficiency calculated from CRCs for the 11 agonists described     (mean+s.d), which is comparable to the mean efficiencies discussed above.

CRCs from whole-cell currents
Single-channel CRCs offer the most accurate method for estimating KdC and E2, but CRCs constructed from whole-cell responses are far more common. In order to ascertain the extent to which  estimated from whole-cell CRCs might be influenced by slow perfusion (that allows desensitization to reduce current amplitudes in high-PO conditions) and heterogeneous receptor properties, we measured whole-cell current amplitude as a function of concentration using 4 agonists, 3 from the high-efficiency group (ACh, CCh and TMA) and 1 from the low-efficiency group (Ebt).
In whole-cell CRCs with maximums normalized to the response to 300 M ACh response (Fig. 6A), EC50 values were left-shifted compared to those in single-channel CRCs by an amount that increased with agonist efficacy ( Because the number of receptors contributing to responses varies from cell to cell and with time, whole-cell CRCs are often normalized so that to the maximum response for each agonist is 1. We did this for the 4 whole-cell CRCs to estimate new values for EC50 ( Fig. 6B and Table 2). It was not possible to estimate efficiency from these plots because information regarding efficacy was removed, but below we show that with knowledge of efficiency and I min , I max can be estimated from the EC50 of a CRC that has been normalized to a maximum of 1.

Binding site mutations
KdC and KdO have been measured by kinetic modeling of single-channel currents from mouse, adult-type AChRs having a mutation at one of the 5 aromatic residues at each of the 2 binding sites (30). We calculated from these values ACh for 21 different mutants (Table S1). Fig. 7A shows that the distribution is Gaussian with ACh=51+4% Binding and gating equilibrium constants have also been reported for AChRs having a mutation of G153 (28). This amino acid is in loop B and close to W149 but does not appear to contact the agonist directly. However, G153 is interesting because so far it is the only binding site amino acid known where mutations decrease KdC (increase binding energy) and increase significantly E0. We calculated efficiencies from KdC, E2 and E0 values for 16 different G153 mutant/agonist combinations using agonists from the high-efficiency population (Table S2).
The distribution of these efficiencies is shown in Fig. 7B. With a G153 mutation,  42+3% or ~20% smaller than the wt. This is the same efficiency as the low-efficiency agonist population in wt AChRs. G153 mutations that increase affinity also decrease efficiency. The extent of the reduction in  was similar for all agonists and side chain substitutions, with the exception of G153K+nicotine. In summary, it appears that a glycine at position 153 allows high efficiency for small-volume agonists that otherwise take on the low efficiency characteristic of large-volume agonists.  (Table S2 and inset) (28). Gaussian fit of frequency distribution for all 16 mutation/agonist combinations gives =42 + 3 %.

Putting efficiency to use
In this section we show how knowledge of  can simplify and extend CRC analysis.
The same efficiency for a group of agonists means that for all, the logKdC/logKdO ratio is the same. Hence, the two equilibrium dissociation constants are related by an exponent, With knowledge of , only one of the equilibrium dissociation constants needs to be measured. The clustering of AChR efficiency values into 2 populations that correlate with agonist size (Fig. 5) suggests that it may someday be possible to predict approximately an agonist's efficiency a priori from its structure and that of the binding cavity. For example, it is reasonable to guess that in adult-type AChRs other small choline derivatives or ligands similar to nicotine will have ~50%, and that congeners of Ebt and TEA will have ~40%. More experiments are needed to test the hypothesis that head-group volume and binding site structure in combination can be used to estimate . We again note that E0 is agonist-independent and needs to be measured only once, so perhaps in the future this important constant will be known for many different receptors.
Given prior knowledge of  and E0, EC50 and I max (the response at a single, high agonist concentration) can be estimated from each other. First, we calculated EC50 from I max values obtained by fitting whole-cell CRCs ( Table 2, left). The procedure was to solve E2 from I max (Eq. 4), then solve for KdC (Eq. 7;  equal to the value shown in Table 2) and then EC50 (Eq. 3). Fig. 8A (top) shows that calculated and experimental EC50 values are correlated (Pearson's correlation, r 2 =0.78, P<0.0001). Fig. 8A (bottom) shows that there is a good match between experimental current amplitudes normalized to an ACh response ( Fig. 6A) and current amplitudes calculated using EC50 values obtained by fitting CRCs that were normalized to 1 (Fig. 6B).
CRCs for these agonists have not been measured, but doing so would test further the ability to use  and E0 to calculate EC50 from PO max .
Remarkably, it is also possible to use  and E0 to calculate I max from EC50 of a CRC that has been normalized to 1 (Fig. 6B, Table 2). Solving Eqs. 7 and 3 for KdC and setting them equal yields, Eq. 9 Efficiency and E0 are known a priori, and EC50 is measured. We solved Eq. 9 numerically for E2, and then calculated I max and the CRC. from single-channel CRCs. red and blue, high-and low-efficiency agonists (Fig. 5B).
Bottom, CRCs drawn using calculated EC50 and measured I max ( Table 2, left) superimposed on whole-cell current amplitudes (Fig. 6A).  for each agonist given in  Fig. 8B (bottom) shows whole-cell current CRCs normalized to an ACh response (symbols; Fig. 6A) and CRCs drawn using Imax values calculated from EC50 values from CRCs normalized to 1 (Fig 6B).
The match is good for ACh, CCh and Ebt, but bad for TMA. Increasing TMA from 0.50 to 0.55 makes the calculated and experimental curves match more closely. The I max value calculated from EC50 by using Eq. 9 is sensitive to the value of  (Fig. S6). Nonetheless, agonist efficiency allows efficacy information to be recovered approximately from a CRC that has been normalized to a maximum response of 1.
Finally, knowledge of  allows the estimation of E0 from a single CRC. E0 is of critical importance because it sets the baseline level from which agonists increase PO, but it is often small and difficult to measure directly (8,32,33). However, a fold-change in E0 caused by a mutation or a modulator will produce the same fold-change in E2 (Eq. 2) and, hence, a change in both EC50 and PO max (Eqs. 3 and 4).
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 by using Eq. 8. Fig. S7 shows E0 values so-calculated from single-channel CRC parameters. The mean result is reasonably close to the experimentally-determined value (17). If agonist efficiency is known, an approximate value of the unliganded gating constant can be estimated from single CRC. Once this value has been learned, it can be applied to all agonists.

Discussion
The notion of agonist efficiency arose from an experimental observation -the binding energy ratio logKdC/logKdO is the same for many different nicotinic agonists (23).
Later, this ratio was associated with the efficiency at which agonist binding energy is converted into receptor gating energy (10). Here, we have shown that this efficiency can be estimated from CRC parameters. Below, we discuss the nature and distribution of efficiency values obtained from single-channel and whole-cell CRCs, some structural implications of efficiency, and the application of efficiency to CRC analysis.

Efficiency
Agonist efficiencies are the same whether obtained from single-channel or wholecell currents, and from a CRC or by detailed kinetic modeling. They are the same in wildtype AChRs that have 2 binding sites and in crippled AChRs that have just 1 operational site. Efficiency values are the same in mouse and human AChRs and with many mutations at the binding sites (exceptions discussed below) or in distant regions that do not affect binding. In AChRs, efficiency is a robust agonist attribute. At adult neuromuscular synapses, half of the available neurotransmitter binding energy is converted into kinetic energy of the channel-opening conformational change.
Despite the small standard deviations, we suspect that the variance within each group arises from actual, ligand-specific differences rather than from measurement errors, for the following reasons. i) Efficiency is a ratio of logarithms and therefore is not sensitive to errors in the measured values of EC50 and PO max . For example, changing EC50 (Table  1) by +10% changes the calculated  value by <1%. ii) The order of -values within the high efficiency group is the same in single-channel and whole-cell experiments (TMA>CCh>ACh). iii) A small difference in efficiency leads to a large difference in efficacy calculated from EC50 (Fig. S6). Indeed, using Eq. 9, the single-channel -value for TMA predicts the experimental, whole-cell CRC more-accurately than the group value (Fig. 8B, bottom). We hypothesize that the efficiency difference between, for example, ACh and TMA is meaningful (Fig. 3B).
The observation that mutations of G153 shift  for 4 agonists from the high-to the low-efficiency population supports the existence of two discrete  populations.
Although the distribution of agonist efficiency appears to be modal rather than continuous, the high accuracy of experimental  estimates must be considered. More experiments might reveal if other  populations exist or if small differences between agonists or mutations are meaningful. For example, the observations that  is modestly lower with P121 substitutions (Table S1), higher with most non-aromatic substitutions of Y198 (Table S1) and usually lowest with a K substitution at G143 (Table S2)

Structural implications
That a group of agonists have the same efficiency means that all members have the same binding energy ratio, logKdC/logKdO (Eq. 5). Below, we discuss implications of this result with regards to i) rearrangements at the binding site, ii) agonist volume, iii) the bimodal efficiency distribution and iv) binding-site mutations.
The energy of low-affinity binding is proportional to logKdC and is determined mainly by a local rearrangement at the binding site called 'catch'. The energy of the switch from low-to high-affinity is proportional to (logKdO-logKdC), occurs at the beginning of the global, channel-opening isomerization and is called 'hold' (30,34). As discussed elsewhere (34), 'hold' is related to, and possibly the same as, an intermediate (preopening) gating state called 'flip' that has been detected directly (35,36). 'Flip' refers to a brief shut state that is high affinity, and 'hold' refers to the rearrangement of the binding site that generates such a state (37). Regardless, the energy change in hold is 1/(1-) times that of catch, or a factor of ~2 for high-and ~1.7 for low-efficiency agonists.
This linear relationship between catch and hold energies suggests that the associated conformational changes, too, are related. Accordingly, the observation that many agonists have the same efficiency suggests that these two binding-site rearrangements are stages of a single conformational sweep. Although 'binding' and 'gating' have long been considered to be distinct processes (38), a group efficiency implies that they should be considered as components of a single structural cascade. In AChRs, this cascade begins with a 'touch' by the agonist that takes place after the ligand has diffused to its target but before rearrangements that form the low-affinity complex, and ends when ions begin to cross the membrane. The 'catch-and-hold' sweep at the binding sites is the first part of the 'binding-gating' cascade ('wave') of the receptor.
It remains to be determined whether or not a shared binding energy ratio for a group of related agonists is a general feature of receptor activation. It appears that in some receptors other than neuromuscular AChRs there is a linear relationship between log gating and log binding equilibrium constants for related ligands, and that association to C is slower than diffusion. These results raise the possibility that a shared logKdC/logKdO ratio and a correlation between structural changes in low-and high-affinity complex formation are not exclusive to AChRs (10).
Members of both efficiency populations can have a quaternary amine (TMA, TEA) or a secondary amine (DMPP, Ebt). Hence, it does not appear that the bimodal distribution in efficiency reflects this aspect of the agonist's head group. The inverse correlation between agonist head-group volume and efficiency is more relevant (Fig. 5B).
Simulations of AChR structures suggest that the agonist binding cavity is smaller in O compared to in C and, hence, that binding site contraction is a structural correlate of 'hold' (25). In addition, kinetic analyses of AChR gating indicate that in the channel-opening isomerization, 'hold' is followed by a rearrangement of the extracellular domain (4,34,39,40).
These results lead to hypothesize that large-volume, low-efficiency agonists encounter steric hindrance when the binding cavity contracts in 'hold', to limit the shrinkage and, hence, the mechanical force applied to the next element in the gating sequence, the extracellular domain. We imagine that small, high-efficiency ligands fit comfortably into both C and O pockets but that large, low-efficiency agonists do not fit easily into the smaller O cavity and so support a smaller contraction. According to this hypothesis, large ligands transfer less energy to the next step in the conformational cascade and thus have low efficiencies.
In support of this idea, the smallest agonists we tested, DMP, DMT and TMA, have the largest efficiencies (Fig. 3B). Further, simulations show that compared to ACh, the binding cavity is smaller with TMA and the extent of cavity contraction is smaller with the low-efficiency agonist Ebx (25). However, the relationship between agonist volume and efficiency is not simple because Ebt and TEA have similar efficiencies despite a substantial difference in volume (Table 1).
There are 2 efficiency populations (Fig. 5A). One possible explanation is that each efficiency group reflects a different 'hold' binding site conformation. In this view, the high-affinity cavity can adopt only a limited number (so far, 2) of 'preset' structures and is not malleable or able to adapt its shape to each agonist. Perhaps small versus large agonists allow the pocket to adopt alternative contracted shapes, with all agonists larger than some threshold forcing the less efficient shape. Another hypothesis for the bimodal distribution of  is that there are two discrete energy transfer pathways that supply energy for activating the extracellular domain. Both paths are activated with smaller agonists but one (or both) is compromised when the pocket is 'stretched' by a large ligand. Both of these hypotheses are speculations that can be tested experimentally.
Aromatic side chains at the binding site govern agonist affinity. While most mutations of these have little or no effect on , another clue regarding the structural basis of efficiency is that the efficiency of ACh is reduced by 30% by the mutation Y190A (in loop C) and increased by 20% by the mutation W149A (in loop B). Y190 appears to be the most-important aromatic side chain with regards to the propagation of structural changes from the binding site in channel opening (22,41). That the mutations Y190F and Y190W have little effect on ACh efficiency suggests that the key interaction here is with the aromatic ring rather than with the OH group.
All 4 mutations of G153 (in loop B) reduced the efficiency of all 4 tested agonists.
Again, the drop appeared to be modal, reducing the average efficiency from 51% to 42%.
At this juncture we do not have a hypothesis for the structural basis for this decrease in efficiency. Perhaps flexibility of the loop B backbone promotes high efficiency. It will be worthwhile to ascertain the extent to which the W149A and G153 mutations are correlated.
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 (10). 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. Agonist affinity is greatest at the fetal (−) neurotransmitter binding sites (56% for ACh) and it is possible that the some of the small, agonist-dependent differences in  between adult sites are meaningful.

Utility of efficiency in CRC analysis
Knowing agonist efficiency is useful because it allows EC50 and I max to be estimated from each other. With knowledge of , an entire CRC can be calculated knowing only the responses at the low-and high-concentration asymptotes (Fig. 8A, bottom).
Given  and E0, the response at just one agonist concentration, that which produces I max , needs to be measured in order to estimate EC50. Having this ability could facilitate drug screening.
It is common practice in CRCs to normalize I max to 1 and lose information regarding agonist efficacy. We have shown that given prior knowledge of  and E0, and an experimental estimate of EC50, Eq. 9 can be solved numerically for E2 and, hence, I max .  Fig. 1). , efficiency (Eq. 5); head-group volume (A 3 ).