Gating at the Mouth of the Acetylcholine Receptor Channel: Energetic Consequences of Mutations in the αM2-Cap

Gating of nicotinic acetylcholine receptors from a C(losed) to an O(pen) conformation is the initial event in the postsynaptic signaling cascade at the vertebrate nerve-muscle junction. Studies of receptor structure and function show that many residues in this large, five-subunit membrane protein contribute to the energy difference between C and O. Of special interest are amino acids located at the two transmitter binding sites and in the narrow region of the channel, where C↔O gating motions generate a low↔high change in the affinity for agonists and in the ionic conductance, respectively. We have measured the energy changes and relative timing of gating movements for residues that lie between these two locations, in the C-terminus of the pore-lining M2 helix of the α subunit (‘αM2-cap’). This region contains a binding site for non-competitive inhibitors and a charged ring that influences the conductance of the open pore. αM2-cap mutations have large effects on gating but much smaller effects on agonist binding, channel conductance, channel block and desensitization. Three αM2-cap residues (αI260, αP265 and αS268) appear to move at the outset of channel-opening, about at the same time as those at the transmitter binding site. The results suggest that the αM2-cap changes its secondary structure to link gating motions in the extracellular domain with those in the channel that regulate ionic conductance.


Introduction
In the acetylcholine receptor-channel (AChR), the M2-cap lies at the junction of the extracellular vestibule and the narrow region of the ion permeation pathway (Fig. 1). In the mouse a subunit, the aM2-cap sequence is IVELIPSTSSA (residues 260-270; Table 1). There is a 4 Å cryo-EM structure of closed and unliganded Torpedo AChRs [1], a 1.94 Å resolution x-ray structure of a toxin-bound fragment of the mouse a subunit [2], and a 3.3 Å resolution structure of a prokaryotic member of the pentameric, ligand-gated channel superfamily [3]. However, as yet there are no high resolution structures of an intact AChR in either end state of the fully-liganded gating reaction, A 2 C or A 2 O (where A is the agonist). Here we report the channel opening (k o ) and closing (k c ) rate constants for 64 different mutations of nine aM2-cap residues in the mouse neuromuscular AChR (aI260-aS268), as well as the effects of these mutations on channel conductance, channel blockade and an approximate rate constant for entry into longlived desensitized states.
Estimates of the energetic consequences of individual side chain movements can be gained from measuring mutation-induced changes in the diliganded gating equilibrium constant (K eq ), which is the which is the ratio k o /k c . K eq depends on the difference in free energy between the entire protein in the C vs. O conformation. Therefore, a change in K eq consequent to a mutation indicates that the perturbation caused the AChR to change this free energy difference, and, hence, the relative structure or dynamics (entropy) in the vicinity of the mutation, in the A 2 C«A 2 O reaction. The extent to which a change in K eq is determined by a change in k o vs. k c (given by the parameter W) may reflect mutation-induced changes in the transmission coefficient of the reaction [4], in which case W is a measure of the relative time within the reaction when the perturbed side chain flips from a C-like to an O-like conformation [5,6].
The information regarding changes in energy and the transmission coefficient (K eq and W, respectively) can be mapped onto the available structures to generate a framework for understanding AChR gating. These parameters (derived from experimental measurements of k o and k c ) have been estimated for dozens of residues (hundreds of mutations) in the adult form of the mouse neuromuscular AChR. At most positions, at least one side chain substitution causes a substantial change in K eq , with the majority of these sensitive sites residing in the a subunit and falling between the transmitter binding site (TBS) and the cytoplasmic limit of the transmembrane domain (TMD). In the extracellular domain (ECD) of the a subunit, the 'moving' residues are located mainly along the ''+'' side of the subunit interface (adjacent to either the d or e subunit) as well as throughout the interface with the TMD. In the TMD of the a subunit, at least one residue in all four membrane spanning helices is mutation-sensitive, including most of those in M2. These results suggest that the energy changes realized in gating are widespread, with no one structural transition standing out as being the single 'on-off switch' that separates A 2 C from A 2 O. With regard to W, values are clustered into domains that, as a first approximation, follow a coarse-grained and decreasing gradient along the long axis of the protein. This pattern suggests that the overall framework for the gating mechanism is that of an approximately linear sequence of stochastic domain motions (a 'Brownian conformational wave') that connects structural changes that regulate transmitter affinity with those that regulate conductance [7]. However, as described below, the timing of the aM2-cap gating motions do not neatly fit this pattern.
The M2-cap contains a high affinity binding site for noncompetitive inhibitors (NCIs) that stabilize D(esensitized) conformations of the AChR, where the affinity for agonists is high (like in O) but the conductance of the channel is essentially zero (like in C) [8,9]. Some NCIs have a high affinity specifically for D AChRs, while others may also act as traditional channel blockers that bind to the open pore [10,11,12]. A second function of the M2-cap is to regulate ionic conductance. All cys-loop receptors have a charged residue (opposite sign of the conducting ion) in the M2-cap (Table 1) [13,14,15]. More generally, disulfide-trapping experiments in GABA A receptors [16] indicate that the upper portion of the M2 helix is flexible and dynamic because there is a fast rate of disulfide formation at two positions in the M2-cap of the a subunit (which corresponds to a non-a subunit in AChRs). Recently, Hilf and Dutzler [3] have suggested that channel-opening involves an outward tilt of the M2-cap domain.
Several AChR aM2-cap amino acids have previously been studied with respect to the effects of mutation on the kinetics of gating [17]. Mutations at positions a267-a269 significantly changed K eq (indicating a gating motion) mainly by changing the channel-opening rate constant, but had little or no effect on the equilibrium dissociation constant for agonist binding to the C conformation (K d ). W and changes in K eq and K d have also been estimated for the M2-M3 linker (a270-a276) [18]. Forman et al. [19] studied mutants of aE262 by using a combination of photomodification (by 3-azioctanol) and fast patch perfusion. Most constructs decreased the EC 50 for Ach, possibly by increasing K eq .
The results presented below show that aM2-cap residues have higher W-values than do the flanking residues in aM2, the aM2-M3 linker and loop 2. This pattern is discussed with respect to the overall framework for AChR gating and the conformational changes occurring at the mouth of the channel in the gating isomerization.

Results
For alignment purposes, the amino acids of the entire M2 helix can be numbered sequentially from N-to C-terminus (intracellular-to extracellular, 19-289; M243-A270 in a subunit). Table 1 shows an alignment for the M2-cap (189-289) for all mouse AChR subunits plus representative subunits of other 'Cys-loop' receptors. Position 209 is the outer charged ring of the pore and is an E in all AChR a subunits. Position 239 is a completely-conserved P in all subunits of all Cys-loop receptors. Fig. 1 shows the structure of the aM2-cap, based on the 4 Å cryo-EM model of closed, unliganded Torpedo AChRs (2bg9.pdb) [1]. Fig. 2 shows an example analysis for one position. Figure S1 displays example single-channel currents for all of the constructs. Tables S1, S2, S3 give the results in numeric form for the rate constant-, conductance-, channel block (by agonist)-and desensitization analyses.
At least one side chain substitution at each of the aM2-cap positions changed K eq by .10-fold ( Fig. 3 and Table 2). Indeed, of the 7 positions in aM2 and the aM2-M3 linker that show a $1000-fold change in K eq , 5 are in the aM2-cap, with the most sensitive residues being aP265 (239) and aS268 (269). This result indicates that side chains of the aM2-cap change their energy (structure, dynamics or both) significantly between C and O conformations.
For all positions, the cap mutations changed K eq mainly by changing k o (resulting in high W values). The average W value for the entire region (a260-a270), calculated from the W estimate for each residue, was 0.7760.12 (mean6s.d.), which is somewhat higher than for the flanking regions, the M2-M3 linker (a272-a275; 0.6360.02) and M2 139-179 (a255-a259; 0.6360.08). Three cap residues had particularly high W values, aS268, aP265 and aI260 (0.9260.04). This result suggests that the aM2-cap moves early in A 2 CRA 2 O gating.
There are two a-subunits per AChR. To address the possibility that an M2 mutation in each subunit might contribute unequally to the fold change in K eq or moves at a different point in the gating reaction as does its partner, we expressed hybrid AChRs having one mutated and one wt a subunit ( Fig. 4 and Methods). In cells that were transfected with both wt and aP265K subunit cDNAs (along with wt b, d, and e), three kinetically distinct populations of clusters were apparent. One had a K eq similar to wt AChRs (38), one had a K eq similar to the aP265K double mutant (0.015), and the remaining group had a K eq that was intermediate (0.76). We attribute this intermediate population to hybrid AChRs that contain one wt and one mutated a subunit. This pattern, a single hybrid class with a fold-change in K eq (50.3) that is approximately equal to the square root of the fold-change of the double mutant (2542), indicates that each aP265K mutation makes an approximately equal and energetically-independent contribution to K eq . Further, the W value for the aP265K hybrid was similar to that of AChR a1 The entire sequence for the AChR a1 subunit (IVELIPSTSSA) is conserved in all vertebrates. Position 239 is a proline (bold) in all cys-loop receptors. The superscripts on the conserved Pro represent the residue number. doi:10.1371/journal.pone.0002515.t001  (259)] to the next-highest and the rest [aL263 (219), aS266 (249), aS269 (279) and aA270 (289)] to the middle Wpopulation. aM2-cap residues exhibit higher W values than their flanking segments. aI260, aP265 and aS268 have W values that are similar to those for amino acids located at the transmitter binding sites (Fig. 5A) [20,21,22].
The single-site association and dissociation rate constants (k + and k 2 ) and equilibrium dissociation constant (k + /k 2 = K d ) for ACh binding to the closed conformation were determined for one mutant construct, aE262L (Fig. 2). In this mutant, K d = 155 mM, which is similar to measurements for wild-type AChRs exposed to 140 mM NaCl (100-150 mM [20,23]). The association and dissociation rate constants in the mutant, k + = 102 mM 21 s 21 and k 2 = 15,873 s 21 , were also not greatly different from the wt values (k + = 167 mM 21 s 21 and k -= 24,745 s 21 ; [21]). The failure of this mutation to change K d agrees with similar measurements for three other aM2-cap mutants, aT267I and A, and aS268I [17].
The substitution of a Q at position aE262 (the charged ring) was previously shown to reduce the single-channel conductance by ,50% [14]. For all constructs, we estimated both the singlechannel current amplitude in the absence of channel block (measured at a low agonist concentration) as well as the equilibrium constant for channel block by the agonist (K B ) (Table  S2). Excluding lysine substitutions, the average effect of the mutations on the single-channel current amplitude was substantial for only two positions, aI264 (229) and aP265 (239). At four positions the effects were moderate [aE262 (209), aS266 (249), aT267 (259) and aS268 (269)], while at three the effects were insignificant [aI260 (189), aV261 (199), and aL263 (219)]. Positively-charged side chains were substituted at four positions and caused a large decrease (by ,75%) in the current at aE262 (K and R) and aP265 (K), had a moderate effect at aL263 (K) and had no effect at aS266 (K). Note that the average consequence of a charge-removal mutation (A, C, F, G, L or V) at aE262 (in both a subunits) was a modest 32% reduction in the current amplitude.
Agonist molecules can bind to the pore and block ionic conduction. In our experimental conditions, the equilibrium dissociation constant for this blockade (K B ) in wt AChRs is ,1.9 mM for ACh [8] and ,13 mM for choline [24]. We estimated the effects of mutations on K B at 5 different cap residues (see Methods and Table S2). Only three mutations had a significant effect: aE262T (9-fold increase for ACh), aI264L (16fold decrease for choline) and aP265T (5.8-fold decrease for choline). These results suggest that the side chains of the aM2 cap domain do not have a strong effect on equilibrium block by agonist molecules.
Occupancy of the cap domain by certain ligands stabilizes desensitized AChRs. For all constructs, we estimated an apparent rate for entry into long-lived desensitized states, k * +D (Table S3). Surprisingly, most of the mutations had little, if any, effect on this rate. The biggest effects on k * +D were in aI264L and aS266K (,10-fold increase) and aL263E (,2-fold decrease). Although the rate of recovery from desensitization and the number of channels in the patch both contribute to the overall frequency of clusters, we observed no striking change in this parameter for the mutants. Overall, the effects of aM2-cap mutations on desensitization are quite modest, especially when compared to their substantial effects on gating. This result suggests that NCIs increase equilibrium desensitization mainly by perturbing regions of the AChR other than the aM2-cap, and that point side chain substitutions in this region do not mimic these perturbations. We hypothesize that the  (Table S1). W is the slope of REFER. The W values are given in Table 2 and shown as a map in Fig. 5B previously-reported effects of cap mutations on the macroscopic desensitization rate [19,25] arise from their effects on K eq rather than on microscopic desensitization rate constants.
Overall, aM2-cap mutations have substantial effects on gating but comparatively small effects on agonist binding, channel conductance, channel block and desensitization. The insertion of a positively charge side chain at aE262 (209) and aP265 (239) significantly reduces the single-channel current amplitude, which is consistent with the notion that these residues face the open pore and that there is a charged ring in this domain that influences ionic conductance.

Discussion
The residues of the pore-lining aM2 helix, along with the M2 segments from non-a subunits, form several important functional elements. These include NCI binding sites, a charged ring, residues in the pore that control conductance and an ion selectivity filter (Fig. 5C). All 27 aM2 residues (aT244-aA270) have been examined with respect to the effects of mutations on K eq and W ( Table 2). We cannot, from our experiments and the available AChR structures, correlate the magnitude of the observed changes in K eq with the magnitudes of the gating motions. However, the large excursions in K eq caused by side chain substitutions at most positions show that most of aM2 changes its structure, dynamics or both between A 2 C and A 2 O. Residues of the aM2-cap show particularly large excursions in K eq while those in the cytoplasmic portion of aM2 show relatively smaller changes (Fig. 5B). This pattern supports the notion that the most significant C«O conformational changes in aM2 (and dM2 [26]) occur at and above the equator [5].
aM2-cap W values are higher than for the rest of aM2, which is consistent with the ''conformational wave'' framework for AChR gating insofar as this domain is near the extracellular limit of the helix and moves prior to the (low-W) equatorial zone in channelopening. The pattern of W in the aM2-cap is, however, surprising in two respects. First, aM2-cap W values are higher than those of residues in the M2-M3 linker, cys-loop and loop 2, all of which are located between the cap and the TBS. Three aM2-cap residues [aI260 (189), aP265 (239) and aS268 (269)] have W-values that cannot be distinguished from those of TBS residues. If W reflects the relative timing of gating motions, this result indicates that the gating movements in these two apparently-unconnected regions are approximately synchronous and occur at the outset of the channel-opening process. Second, the map of the entire aM2 segment is complex, with all five W-values represented (Fig. 5B). With the temporal interpretation, this suggests that the gating movements in this helix are highly asynchronous, whereas we might expect that side chain motions of such a secondary structural element would either be synchronous, or, perhaps, constitute a continuous, top-to-bottom sequential conformational cascade.
Although we cannot resolve these two conundrums, we can offer some possible explanations.

1)
Unknown linkage elements. There is no obvious structural connection between the TBS and the aM2-cap in the Torpedo AChR structure, where the tip of loop A (residue aD97 [20]; W = 0.9360.02) and cap residue aS268 (W = 0.9760.11) are separated by ,17 Å . It is difficult to imagine that agonist-triggered gating structural changes at the TBS could propagate, by direct steric interactions, to the aM2-cap. It is possible that the TBS and the aM2-cap are directly linked by high W amino acids that have yet to be probed, or that there is a physical connection between these two domains that is invisible in electron density maps (e.g., is electrostatic or arises from the water). For example, gating motions of the aM1 segment, or perturbation of the aqueous milieu consequent to TBS binding or gating motions, might serve to generate the high W-values in the aM2-cap.

2)
Incomplete structural information. Protein movement consequent to agonist binding may move the two high-W domains (loop A and the aM2-cap) closer than they are in the unligandedclosed Torpedo AChR structural model. This highlights our lack of high resolution structural information regarding the ground states of the A 2 C«A 2 O reaction.

3)
Independent gating motions. Perhaps the motions at the TBS and the cap are completely independent, and these two regions just happen to move early and approximately at the same .1000-fold (blue), 10-1000 fold (cyan) and ,10-fold (grey) ( Table 2). aM2-cap residues experience large energy differences ('move') between C and O, whereas many mutants of residues near the cytoplasmic limit of the channel are iso-energetic, which may indicate relatively smaller structural changes. The three biggest excursions in K eq were observed for aP272, aP265 and aV255. Right, residues colored according to W value (see panel A for color code). Most of the residues in the aM2-cap move 'early' in gating (purple and blue), before those in the M2-M3 linker and much of M2 (green). Three cap residues (aI260, aP265 and aS268) have the same W value as those for residues at the transmitter binding sites (see panel A). In aM2, residues near the equator have the lowest W values and, therefore, move last in CRO gating. Arrow, we speculate that when the channel opens, aP265 rotates to position its side chain in the lumen of the channel. doi:10.1371/journal.pone.0002515.g005 relative time in the gating reaction in the absence of any direct interactions to couple these motions. This would mean that the microscopic structural transitions that separate C and O are not strictly sequential. There are precedents for such apparently independent-but-synchronous gating movements. Large distances separate the two a subunits. For example, in both the loop A and M4, residues on the two a subunits are separated by ,26 Å (aD97) and ,58 Å (aC418), respectively. Nonetheless, hybrid constructs of these amino acids have approximately the same W value [20,27], as do those of aP265 in the aM2-cap (,24 Å ). Given the complexity of the AChR conformational change, it is not unreasonable to think that separate domains can move independently but approximately at the same time, and will thus have similar experimental W values. The aM2 cap and the agonist-occupied TBS may be inherently unstable structures that deform early in the CRO isomerization.

4)
The interpretation of W. W may not reflect time in the aM2-cap domain. The central assumption of the temporal interpretation of W is that mutations alter the CRO rate constant by changing the transmission coefficient, but the magnitude of k o also reflects transition state (TS) energy and, perhaps, heterogeneity. Further, the weights given to these various factors (with regard to k o ) could be different for different regions of a protein or even for different individual residues.
Another assumption of the temporal interpretation is that a side chain undergoes only a single, instantaneous, all-ornone gating movement. It is, however, possible that some side chain atoms (we do not mutate the backbone) are jostled more than once within the reaction, in which case the apparent W value will be a weighted average of the relative times and energy changes of such multiple motions. We can imagine that the transition region energy changes of the three cap high-W residues (a260, a265 and a268; W = 0.92) occur mainly early in the reaction, those in the M2-M3 linker and in much of M2 occur mainly near the middle of the reaction (W = 0.64), and that the 'intermediate' residues of the cap (a261, a262, a264 and a267; W = 0.77) move twice, along with each of these other groups. The possibility of multiple side chain motions is physically plausible but further complicates the interpretation of W values.
The resolution of the electron density map of the aM2 cap in the Torpedo AChR is not sufficiently high to assess the potential for, or chemical nature of, the specific structural changes in this domain that accompany C«O gating. Also, there are as yet no published structures of a ligand-occupied intact AChR, although there are structural differences between occupied and vacant AChBP [28,29,30] and the ECDs of a vs. non-a AChR subunits that may reflect C vs. O conformations, respectively [31]. In the absence of high resolution structures of the wt and mutant AChRs it is difficult to infer specific structural events based on the functional effects of mutations.
The basic features of the aM2 cap are as follows. It is a ,9residue (260-268, which subtends the high-W amino acids), segment that is at the C-terminus of a long a-helix. Some cap side chains face the water-accessible, ion permeation pathway while others are close to M1 and M3. There is a conserved Pro near the middle of the segment. In 2bg9.pdb, the modeled W/Y backbone bonds for aP265 and aI264 are ,89u/30u and ,84u/ 12u, which are outside the typical values for proline (55u/50u) [32] and pre-proline (60u/45u) [32,33] residues.
We speculate that the central proline (aP265) of the aM2-cap distorts and destabilizes the C-terminal portion of M2, which enables the cap to readily switch its secondary structure during the C«O conformational change. This hypothesis accounts for the observations that most cap residues experience large energy changes in gating, and that some appear to move at the outset of channel-opening. The change in the backbone cannot be a full, cis-trans isomerization, because many different side chain substitutions at aP265 support efficient gating. The fact that the effect of a K substitution on the single-channel current amplitude was similar at aE262 (209) and aP265 (239) (Table S2) suggests that these two residues are aligned along the pore axis when the AChR is in an open-channel conformation (Fig. 5C). Although the specific structural changes are not revealed in our experiments, we hypothesize that the backbone angles of the central proline and preceding isoleucine change in C«O gating, and that this switch in the secondary structure of the aM2-cap permits the translation of ECD motions into the rest of M2 and, thence, to other M2 residues that regulate ionic conductance, including the latemoving 99 and 129 residues [5]. This is similar to the suggestion that channel-opening involves an outward tilt of the M2-cap [3], although our experiments suggest this motion may involve a twist. Interestingly, a different experimental approach indicates that there are only minor movements in the M2 helix of the d subunit in C«O gating [34].
We now describe a sequence of events in the a subunit channelopening cascade, based on W values and the assumption that mutations mainly affect the transmission coefficient of k o . In the following framework, all of the gating motions are stochastic (are characterized by back-and-forth, Brownian dynamics). Also, the reverse sequence describes channel-closing.
N i) Conformational changes consequent to agonist binding destabilize at least two domains of each a subunit, the TBS (loops A, B and C) and the aM2-cap. Residue aK145 in the outer b sheet of the ECD is also destabilized [22]. The gating motions of the TBS residues increase the affinity for ACh by a factor of ,10,000 [22,35], but the conductance of the channel remains low. The motion of the TBS announces the exit from the C structural ensemble and entry into the TS ensemble. The trigger for the change in structure at the TBS is the presence of the agonist itself, but that for the cap region remains obscure.
N ii) The motions of the TBS and aM2-cap trigger those in adjacent domains, including loop 2, the cys-loop and residue aY127 in the inner b sheet of the ECD. These motions are then followed by the movement of residues in the M2-M3 linker and in M2, both within the aM2-cap and below, to the equator and beyond. These intermediate events reflect structural changes that occur within the TS ensemble of the reaction, where the TBS affinity remains high but the channel conductance is still low.
N iii) The above gating motions in aM2 destabilize residues aL251(99) and aT254(129). It is possible that the movement of these residues serves to change ionic conductance (they act as a 'gate'), but it is also possible that ions begin to cross the channel rapidly when the protein is still in the short-lived TS ensemble (they act as a 'latch'). At this point in opening the TBS still has a high affinity for agonists, and the movement of the aM2 equator reflects entry into the O structural ensemble.
To confirm and complete this gating scenario we will need high resolution structures of intact AChRs in both A 2 C and A 2 O conformations, more extensive estimates of the energy changes in aM1 and the M2 segments of the non-a subunits, and more sophisticated theories for, and analyses of, the transition state of the gating reaction.

Methods
Detailed methods are given in Jha et al, (2007) [18]. Briefly, mutant AChRs (64 different mutants of 9 different amino acid positions) were transiently expressed in HEK cells, and single channel currents were recorded in the cell-attached patch configuration at 23uC. The bath and pipette solutions were Dulbecco's phosphate buffered saline containing (in mM): 137 NaCl, 0.9 CaCl 2 , 2.7 KCl, 1.5 KH 2 PO 4 , 0.5 MgCl 2 , and 8.1 Na 2 HPO 4 (pH 7.3). The currents were filtered at 20 kHz and digitized at a sampling frequency of 50 kHz. Agonist (acetylcholine or choline) was added to the pipette solution. For rate constant measurements, the agonist concentration was approximately five times K d (500 mM ACh or 20 mM choline). Choline was used to activate constructs in which K eq was similar to or larger than in the wt (gain-of-function mutants), and ACh was used to activate constructs in which K eq was smaller than in the wt (loss-of-function mutants). Rate constant estimation (12 kHz bandwidth) was done by using QUB software (www.qub.buffalo.edu). Clusters of individual-channel, diliganded C«O activity were usually selected by eye or by using a critical time of 50 ms. Typically, ,50 clusters were selected in each record. The opening and closing rate constants were estimated from the interval durations by using a maximum likelihood algorithm [36] after imposing a dead time correction of, typically, 25 ms. W was estimated as the slope of the rate-equilibrium free energy relationship (REFER), which is a plot of log k o vs. log K eq (Fig. 3). Each point in the REFER represents the mean of at least three different patches for a single mutant construct.
We could not determine the gating rate constants for aP265F and aP265L because no currents were detected (8 patches each, 10 min/patch). Also, rate constructs could not be measured for the constructs aI260F, aS266L, aS266Y and aT267F because the openings were not organized into well-defined clusters at 500 mM ACh, most likely because these constructs had exceeding small values of K eq . Clusters from aS266C showed two distinct kinetic patterns, and k c and k o were estimated separately for each. aS268Y showed multiple kinetics patterns so no rate constants were estimated for this mutant. In total, rate constants were estimated for 57 of the 64 constructs that were examined (Table S1).
The K d for acetylcholine was estimated only for the aE262L mutant (Fig. 2). Open and closed interval durations were obtained at three different ACh concentrations (30, 50 and 100 mM). The two agonist binding sites were assumed to be equivalent and independent [37] and the interval durations at all three concentrations were fitted together by using a C«AC«A 2 -C«A 2 O kinetic model (A = agonist) that had four rate constants as free parameters: single-site association (k + , scaled by [A]), singlesite dissociation (k 2 ), k o , and k c .
In the REFERs (Fig. 3), the wt values used to normalize k o and K eq were 120 s 21 and 0.046 for AChRs activated by choline and 48,000 s 21 and 28.2 for AChRs activated by ACh. The slope of the REFER was estimated by an unweighted, linear fit in Origin Pro 7.0. All structures were displayed by using PYMOL (DeLano Scientific).
The number of W populations (Fig. 5A) was estimated statistically by using a cluster-detection algorithm (SKM), which assumes each population had a Gaussian distribution with an independent mean and s.d [5]. The overall sum-square deviation (SSQ) was estimated assuming n = 2 to 20 populations. 300 random starting assignments were used for each value of n.
In the experiments concerning hybrid AChRs (Fig. 4), cells were transfected with both wild-type and mutant (P265K) a subunit cDNAs in a 1:3 ratio, together with wild-type b, d, and e subunit cDNAs. All recordings showed populations of clusters that could be distinguished statistically according to the cluster open probability (P o ), corresponding to wild-type, hybrid (containing one wild-type and one mutant a subunit) or double-mutant AChRs. Clusters were either selected by eye or defined using a critical time of 50 ms and were segregated statistically (segmentation k-means algorithm; SKM) into separate populations for subsequent kinetic analyses with only the cluster P open as the discrimination criterion. Clusters that had P o values that were .1 SD from the corresponding population mean were rejected from these analyses.
In neuromuscular AChRs desensitization appears to proceed mainly from the A 2 O state [8] or from a transition micro-state that is near A 2 O [4,7]. An approximate rate of entry into long-lived desensitized states was determined by computing the inverse of the product of the cluster duration times the cluster open probability: k * +D = (t c P o ) 21 (Table S3). This parameter is a rough estimate of the net rate of exiting A 2 O into a long-lived D state.
An estimate of the equilibrium constant for channel block by the agonist (K B ) was determined for each construct from the relationship K  (Table S2). For normalization, the wt parameters were K B = 1.9 mM for ACh [8] and 13 mM for choline [24]. The fractional reduction in amplitude at 500 mM ACh was small (,20% in the wt), and, because of errors in the estimate of the membrane voltage, the K B estimates for such ACh-activated currents were imprecise. Therefore, only mutants that showed a .50% decrease in current amplitude at 500 mM ACh were used for K B estimation. For choline-activated constructs, the fractional reduction in the wt current amplitude at 20 mM is more substantial (,60%) so K B could be estimated for all.