The Activation Mechanism of α1 Homomeric Glycine Receptors

General features of single channels

Steady-state experiments at 10–1000 μm glycine, illustrated in Figure 1, were fitted initially without reference to mechanisms (Fig. 2) (ekdist program). As in outside-out patch recordings (Beato et al., 2002), in all experiments, only one single-channel amplitude was detected, on average 4.7 ± 0.1 pA (Gaussian fit; n = 26). This is in contrast to the several conductance levels commonly reported for homomeric glycine receptors (Bormann et al., 1993; Lewis et al., 1998; but see Lewis et al., 2003). We do not know the reason for these discrepant reports. Possible contributions may come from differences in the methods of analysis, species (human vs rat clones), receptor heterogeneity, and vagaries of expression systems.

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Figure 1.

Clustering of α1 glycine receptor openings at increasing agonist concentrations. a–c, Continuous sweeps recorded in the cell-attached patch configuration showing channel openings elicited by 10, 100, and 1000 μm glycine in the recording electrode. The sweeps shown to the right of b and c are expanded displays of two clusters in the continuous record (indicated by a bar under the recording). The arrow in the expanded time scale trace of c marks an example of a long (∼5 ms) shut state within the cluster. Note that bursts of openings are observed at the lower concentration; at the higher agonist concentrations, these bursts group into progressively longer clusters with increasing P_open. d shows a P_open dose–response curve. P_open values are obtained for each cluster from the ratio between total open time (obtained from records idealized by time course fitting) and total duration. The points shown are the averages of 34–50 clusters for each glycine concentration. Here, these points are fitted by a Hill equation (solid line).

At 10 μm glycine, individual activations of the channels occur as bursts of openings separated by longer shut times that reflect primarily long sojourn(s) in the unliganded state, although some desensitization may well be present (Fig. 1a). Increasing the concentration of glycine causes the receptors to enter into long-lived desensitized states (Takahashi and Momiyama, 1991). This is clearly seen at both 100 and 1000 μm glycine (Fig. 1, b and c, respectively). Clusters are separated by long (1–10 s) shut times, and each cluster contains many activations. Clusters at 1000 μm glycine have a high P_open (approximately 0.96) and contain only short shuttings (Fig. 1c, left, expanded display), whereas clusters at 100 μm glycine (P_open ≈ 0.45) contain longer shut times (5–100 ms) (Fig. 1b, right panel). The results of empirical fitting with exponentials (ekdist) are summarized in Tables 1 and 2, and examples of fitted distributions are shown in Figure 2.

Open-period distributions are fitted with three exponential components (10 μm), two exponential components (50, 100, 200, and 500 μm), or one exponential component (1000 μm). The overall mean open period increases from 0.7 ± 0.1 ms at 10 μm to 2.7 ± 0.2 ms at 1000 μm. This reflects a progressive increase in the area of the slowest component from 22 ± 2 to 100% for increasing concentration of agonist, whereas the time constants for each component are similar at all concentrations (as found by Beato et al., 2002, over a smaller range of concentrations).

Shut-time distributions were fitted with three or four components (Fig. 2, Table 2). For the distributions observed at 10 μm, the first (shortest) three components had time constants that were similar for the different patches and were therefore considered to be within bursts. The average t_crit was 8.2 ± 1.6 ms (chosen to have the same proportion of short and long misclassified events as in Colquhoun and Sakmann, 1985). Empirical fits of within-cluster shut-time distributions showed that four components were detectable at 50 and 100 μm glycine and three at higher concentrations. The fastest three time constants (approximately 30 μs, 0.2 ms, and 1.5 ms) were similar at all concentrations tested. Note that such empirical fits are not used for the model fitting (see Materials and Methods and below), and, therefore, it is not important whether all components can be detected.

The P_open concentration–response curve

In the experiments shown in Figure 2, the separation into clusters was almost unambiguous (at 50, 100, and 1000 μm), because the inter-cluster intervals are two orders of magnitude longer than the longest of the other shut-time components.

Only a few clusters (3–25) were analyzed for each experiment, because one cluster can contain up to 10,000 transitions. For each individual cluster, the P_open was estimated as the ratio between the total open time per cluster and the cluster length. Average P_open values are given in Table 3 and plotted as a concentration–response curve in Figure 1d. When fitted empirically with the Hill equation, this gave an EC₅₀ of 106 ± 8 μm (two-unit likelihood interval, 91–124 μm; this corresponds to a 95% confidence interval; Colquhoun and Sigworth, 1995) (weighted least squares fit, errors from observed information matrix; cvfit program, http://www.ucl.ac.uk/Pharmacology/dc.html), a Hill slope of 1.82 ± 0.24 (two-unit likelihood interval, 1.37–2.36), and a maximum P_open of 0.98 ± 0.03 (two-unit likelihood interval, 0.92–1.05). The P_open concentration–response curve (Sine and Steinbach, 1987; Colquhoun and Ogden, 1988; Sine et al., 1990) represents an “ideal” dose–response curve in that it is corrected for desensitization, contrary to what inevitably occurs for macroscopic dose–response curves, regardless of the speed of the perfusion system. Indeed, it is likely that the impact of desensitization on macroscopic responses explains why such concentration–response curves have lower EC₅₀ (within the 30–80 μm range) and higher Hill slopes than those obtained by single-channel recording (Bormann et al., 1993; Rajendra et al., 1994; Beato et al., 2002). Note also that only the P_open concentration–response curve can give us an estimate of the maximum P_open value, because it is measured on an absolute scale, rather than a relative scale. These three parameters, EC₅₀, Hill slope, and maximum P_open, should be predicted accurately by the rate constants that are fitted by hjcfit, a test that is applied below.

Although ideal in principle, P_open curves are themselves subject to errors, and, in view of the surprisingly low Hill slope, these were checked. (1) Is there only one active channel? The lack of double openings within each cluster confirms that only one channel is active within the cluster. In fact, if two channels were simultaneously active, even for the lowest observed average P_open (0.2 at 50 μm), the probability of observing even a few openings without any doubles is very low (less than 0.001% for 60 consecutive openings) (Colquhoun and Hawkes, 1990, 1995). It is true that a short cluster might superimpose on a longer one without producing a double opening, but the reproducibility of the P_open values makes this unlikely. (2) Are the appropriate shut times included in clusters? The t_crit value used to define clusters is inevitably imperfect. The clearest example is seen in the experiments at 100 μm glycine, where a t_crit of 400–500 ms includes in the clusters the extra long shut times observed in the tail of the slowest component of the shut-time distribution (Fig. 2) at 100 μm glycine. To address this problem, P_open calculations were repeated with a lower t_crit (100–150 ms) that excluded these extra long shut times. These events were very few (on average, three to four in each of the six experiments) and reclassifying them increased the number of separated clusters from 46 to 67 but did not change the P_open (0.47 ± 0.03, very close to the value measured with the higher t_crit, 0.45 ± 0.04). This is probably because clusters at this concentration of glycine are very long (approximately 2 s), and including a few shut times of approximately 200 ms has but little effect on the total P_open. When the whole P_open curve was refitted using the lower t_crit, the estimate of the Hill slope barely changed (from 1.82 to 1.78). (3) Are estimates of P_open values affected by missed shut times within a cluster? This problem is potentially most serious at the highest glycine concentration (1 mm). An approximate estimate of the time occupied by the missed shut times (Colquhoun and Sakmann, 1985) showed that missing shut times would at worst increase the P_open at 1 mm glycine by 0.4%. Note that the correction assumes that no openings are missed (a reasonable approximation, given that we miss approximately 4% of openings and 51% of shut times at this concentration).

Fitting mechanisms to the data: five binding sites

Some of the mechanisms that were fitted are shown in Figure 3. Experimental records were divided into groups of openings that were thought to come from one channel (see Materials and Methods). For 10 and 50 μm, the t_crit was chosen between the third and fourth components of the shut-time distribution. For experiments at 100 μm, the t_crit was between 200 and 500 ms to include all shut times within the cluster and to exclude the longer (1–100 s) sojourns in desensitized states that separate clusters. The t_crit for the experiments at 1000 μm was set to a much shorter value, 0.6–0.8 ms, to exclude as far as possible the last small component in the shut-time distribution (Fig. 2d, Table 2) (see Materials and Methods). An example of a shut time in this component is indicated by the arrow in Figure 1c (see Materials and Methods).

In choosing putative mechanisms, we started from the simplest plausible physical assumption. Homomeric glycine receptors have five identical subunits and thus a maximum number of five symmetrical binding sites. Therefore, our first guess includes five binding sites that are initially identical. In the first instance, we also assumed that the binding sites did not interact, so the binding and unbinding rate constants for each (shut) site are not affected by occupancy of the others. This assumption is specified by applying the following constraints during the fitting of Scheme 1 (Fig. 3). (2) Thus, each agonist binding site is assumed to have the same equilibrium dissociation constant, K (Fig. 4c), once corrected with the appropriate statistical factors that allow for the number of available sites. To maintain generality, we postulated the existence of one open state for each ligation state of the receptor, and the gating constants for each open state were fitted as free parameters. The resulting fit is shown in Fig. 4.

The histograms in Figure 4 show the open and shut time distributions for the same experiments in Figure 2, and the HJC distributions calculated from the fitted rates (Table 4) are shown (continuous line) superimposed on the observations. The dashed line in each histogram represents the prediction of the distribution that would be observed at ideal resolution (i.e., if no brief events were missed). The difference between this and the continuous line gives a measure of how much the observed distributions are distorted as a result of omission of short open and shut times.

The distributions shown are not simple mixtures of exponentials fitted to the experimental distributions of apparent open or shut periods, as in Figure 2, but are the actual HJC density functions calculated (with exact allowance for missed events) from the rate constants estimated by hjcfit for this particular mechanism, resolution, and set of observations. The lines will fit the data histogram only if the mechanism used and the estimated rate constants represent an adequate description of the observations. In this case, open-period data are well fitted, although there is a little discrepancy for both long and short open periods at 10 μm. However, the fit of the shut times is entirely inadequate at 10 μm, and most of the fast shut time component is not fitted for the three remaining concentrations. The third row of plots shows the predicted and observed correlations between adjacent open and shut times. In each plot, filled diamonds (joined by a continuous line) represent the experimental value for the mean open period adjacent to a shut time in the specified range. For instance, the leftmost symbol in the plot for 10 μm glycine shows that the open times adjacent to the shorter gaps (less than 0.1 ms) were relatively long (on average, approximately 1 ms). The filled circles are the predicted values for the mean open time adjacent to gaps in each of the specified ranges (calculated on the basis of the fitted model and rate constant values). The dashed line is the theoretical continuous relationship between mean open time and adjacent shut time. Correlations were predicted satisfactorily only for the 50 and 100 μm experiments, whereas at the highest and lowest concentrations, the predicted line lies well below the experimental data. Finally, the prediction of the P_open dose–response curve was adequate (Fig. 4, bottom). Note that in this and subsequent figures, the curve shown is not a Hill equation but the dose–response relationship predicted by the mechanism; this is not fitted to the P_open data points but is calculated from the rate constant value estimated by hjcfit.

It is possible that the poor agreement of the dwell time distributions with the calculated ones for the fit of Scheme 1 is a result of having imposed unrealistic binding constraints, and that the agonist binding sites do in reality interact while the channel is still shut. In Figure 5, we show a fit of the same data to the same model (Fig. 5c) but without any constraints, thus increasing the number of free parameters from 12 to 20.

All dwell-time distributions are now fitted quite well, including the fast shut time components at all concentrations. Furthermore, the predicted correlations were in excellent agreement with the observed data (third row of plots). However, the predicted dose–response curve was too steep (Fig. 5b). The predicted EC₅₀ and maximum P_open (98 μm and 0.98, respectively) were quite good, but the predicted Hill slope (evaluated at the EC₅₀) was much steeper (3.1) than the observed value (1.8). This may be because of the initial positive cooperativity in the binding of the first three molecules (Table 4, rate constants). Similar conclusions were reached for a similar model with four binding sites only; this gave satisfactory fits of dwell-time distributions but a slope at EC₅₀ of 2.8 (data not shown). Because five (or four) agonist binding sites predicted a steeper concentration–response curve than we observed (unless the sites were identical and independent, a possibility we have already excluded) (Fig. 4), we next chose to test schemes with a smaller number of binding sites.

Fitting mechanisms to the data: three binding sites

The same combinations of data sets were therefore fitted with mechanisms with two or three binding sites. Two binding sites failed to produce good fits (data not shown), but the mechanism with three binding sites (Fig. 3, Scheme 2) was more promising. Initially, we constrained binding sites to be equal and independent (with the same constraints used for Scheme 1 in the fits of Fig. 4); this gave very poor results (data not shown). We therefore proceeded to perform unconstrained fits for the three-site scheme, allowing interaction between binding sites in the shut conformation (“cooperativity in binding”); these are shown in Figure 6 for the same set of experiments as before.

In this case, all of the dwell-time distributions were fitted adequately, and the dose–response curve calculated from the fitted rate constants was in good agreement with the experimental data. The quality of the correlation plot is also satisfactory, although there is a slight tendency to overestimate the duration of mean open periods for the 50 μm experiment. It is worth noting that some degree of open–shut correlation was still detectable even at 1000 μm. This happens because the occupancy of partially bound open states is not negligible even at this concentration. In particular, the open state with two molecules bound (the lifetime of which is approximately 0.7 ms) has occupancy of 13% at this concentration. The fit shows that efficacy increased with the number of bound molecules, from 0.4 with one bound to 8 with two bound and 43 with three bound (Table 5). Note also that the values of the rate constants were well determined, as seen both from the errors calculated through the Hessian matrix (Colquhoun et al., 2003a; Hatton et al., 2003) and from the coefficient of variation of the mean of each rate constant between different sets of experiments (Table 5).

In contrast, the equilibrium constants for binding do not exhibit such a regular pattern. In fact, the first equilibrium constant (corrected with a statistical factor of 3) was approximately 3200 μm, whereas the second binding equilibrium constant was only 110 μm and the last increased again to 420 μm. In other words, there must be some form of interaction between binding sites in the shut conformation to account for our experimental results, but such cooperative behavior is not regular. Indeed, the first binding is rather low affinity, but the second is much higher, whereas having two bound molecules reduces the affinity of the shut state for the third binding, which is the most important for the operation of the channel in physiological conditions, given that the receptor with three molecules bound has the highest probability of opening. There is no obvious physical interpretation for this mixed cooperativity; however, one possibility is that the model we are using to fit the data is not adequate.

Fitting mechanisms to the data: five binding sites and saturation of gating

Thus, so far, only the mechanism with three unconstrained binding sites has given an adequate prediction of the Hill slope of the P_open curve. An obvious question is whether the remaining two binding sites in the receptor pentamer can bind agonist. The fits of a mechanism with five binding sites shown in Figures 4 and 5 did not test the possibility that the binding of a fourth and fifth agonist molecule does occur but does not increase the efficacy of gating beyond that seen with three molecules bound. This can be tested by fitting Scheme 1 while constraining all gating rate constants for receptors with four and five glycine molecules bound to be the same as for those with three bound (E in Fig. 7c). The constraints were as follows: (3) Results were very similar to those obtained with three binding sites (Scheme 2), namely adequate fits of the open and shut time distributions (Fig. 7), similar rate constant values, and a predicted Hill slope of 2.1. The fit is slightly better (because there are more free parameters), but the improvement is not obvious by eye, and the values of the rate constants for the fourth and fifth bindings were not very well defined (Table 4, third column of rate constants). In summary, at least three glycine molecules must bind for efficacious opening of the glycine channel; if a fourth and fifth molecule bind, their ability to open the channel is not greatly different from having only three bound.

Are the sites different before agonist binds?

The rates obtained from fitting Scheme 1 with the hypothesis of saturated gating are very similar to those obtained from the free fits of Scheme 2 (Tables 4 and 5, compare corresponding rates) and thus imply an interaction between binding sites when the channel is still shut. Such interaction is positive for the second binding but negative for the third. It is difficult to explain such a mixed cooperativity in a receptor in which all of the subunits are identical; thus, we considered the possibility that the binding sites are initially different. The idea that the binding sites in a homomeric pentamer are initially different does not seem very plausible, because such structures usually show a high degree of symmetry [however, for biochemical evidence of different subunit conformations within homomeric nicotinic α7 receptors, see Rakhilin et al. (1999)]. The lack of crystal structures for homooligomeric proteins with no ligand bound means that the evidence on this point is limited. Attempts to fit our data with mechanisms in which the sites were inherently different and non-interacting never led to an adequate fit of the data.

A mechanism with minimal interaction between subunits

In a homomeric receptor, it seems reasonable to assume that all sites are initially equivalent, but that they might no longer be symmetrical once the first agonist molecule has bound. In that case, there would be two distinct doubly liganded states that differ depending on the relative position of the two occupied binding sites. This line of thought led to Scheme 3 (Fig. 8). Two forms of this scheme were fitted, the first one (excluding the grayed states) had three binding sites and the second had five (Scheme 3 with saturated gating).

Attempts to fit Scheme 3 with three binding sites with all parameters free led to good fits of the data, but the values of some of the rate constants were badly defined (Table 6, first column, first set of rate constants). We therefore tried the more interesting idea that there is no interaction at all between the second and third binding. This is achieved by fitting with the following constraints: (4) The fourth constraint, k_{+2c =} k_+3c, was implied by the requirement of microscopic reversibility for the cycle. The number of free parameters is thus reduced by three, but nonetheless good fits were obtained, as shown in Figure 9. The calculated distributions are qualitatively similar to the ones obtained for fits to Scheme 2, and both the correlations and the P_open curve are in excellent agreement with the data. Efficacy increased with the number of bound molecules, and the two doubly liganded open states have different gating constants. More importantly, however, of the two nonequivalent binding steps, one is 10 times faster than the other (Table 6). It is appealing that a good fit can be obtained with the assumption that the second and third bindings to the shut state do not interact; however, it is still necessary to suppose that the first binding can affect other sites while the channel is still shut (see above).

One possible structural interpretation of Scheme 3 is illustrated in Figure 9c. According to this interpretation, the first agonist molecule can bind to any of five identical binding sites. However, once the first molecule is bound, the remaining binding sites are no longer equivalent. The binding of the second molecule can occur either on one of the two adjacent binding sites or on one of the other two (nonadjacent) sites. Thus, there are two possible distinct shut configurations with two agonist molecules bound. Additional binding can again occur either between two empty subunits (one available site left) or between one empty and one occupied subunit (with two available sites). Note that of all possible configurations with three bound molecules, we excluded the one with three adjacent agonist molecules bound. This would have given rise to one more fully bound shut state. According to this topological interpretation, the constraints that were used for the fits in Figure 9 should be corrected with the appropriate statistical factors, namely: (5) As above, the fourth constraint, k_{+2c =} k_+3c, is a consequence of microscopic reversibility for the cycle. Imposing these constraints has no noticeable effect on the quality of the fits shown in Figure 9 (i.e., Scheme 3) and affects only the estimates of rate constants shown in the third set of rates in Table 6.

The fits of Scheme 3 shown in Figure 9 were for the three-binding site version. Similarly, good fits were also obtained with the five-binding site version of Scheme 3 (i.e., including the states shown in gray in Fig. 8) with the constraints that the gating saturated after the third binding as in Figure 7 (Eq. 3). Adding these extra states did not improve the quality of the fits and the estimate of EC₅₀ and Hill slope, and we cannot determine whether or not the fourth and fifth bindings occur.

The number of binding sites and the choice of a suitable model

It has often been assumed that more than three glycine molecules must bind to produce efficient channel opening, simply because macroscopic dose–response curves are fairly steep, with reports of Hill slopes up to 4.2 (Bormann et al., 1993). However, Hill slopes are impossible to interpret mechanistically in the absence of a specified model (other than as a minimum for the number of binding sites). Even more importantly, macroscopic dose–response curves are susceptible to distortion by desensitization. Our estimate of the Hill slope which is obtained from the P_open curve and is therefore unaffected by desensitization, is lower, approximately 1.8.

Another approach to the determination of the number of binding sites is the analysis of the rising phase of macroscopic current responses to glycine concentration jumps recently reported by Gentet and Clements (2002) for homomeric receptors. This was interpreted to suggest that two agonist molecules must bind (with negative cooperativity) to produce efficient receptor activation. It has also been suggested that full occupancy of the five potential binding sites is not necessary for efficacious gating of GABA_C and 5-HT3 receptors (Amin and Weiss, 1996; Mott et al., 2001).

Our previous work indicated that low-concentration single-channel data were compatible with a model with five binding sites (Beato et al., 2002). Over the wider concentration range, we now found that a free fit with five binding sites (Figs. 3, 5, Scheme 1) could indeed describe the single-channel data well but predicted a Hill slope substantially higher than observed. To get a good fit of the Hill slope with a model with five binding sites, it is necessary to suppose that there is little or no increase in efficacy after three glycine molecules have bound (Fig. 7). Some physical plausibility is lent to this saturation of gating after the third binding by thinking in terms of the breaking of bonds that form the hydrophobic girdle that keeps the channel shut (Colquhoun et al., 2003b; Miyazawa et al., 2003). The third, fourth, and fifth such bonds to be broken must all be adjacent to a bond that has already been broken and might therefore have similar properties. However, we cannot distinguish this case from mechanisms that allow only three molecules to be bound; these also gave a good description of single-channel results, Hill slope, and EC₅₀ and have the advantage of being the simplest model that accounts for the data.

A possible way to resolve the uncertainty would be to use fast concentration jumps. After rapid removal of glycine, the decline of response would in principle be more sigmoid if five agonist molecules are bound than with three, although the values of the rate constants found in our fits predict only a small difference. Both schemes predict that the major slowest decay time constant would be between 5 and 8 ms, which is consistent with the results of concentration jumps and with recordings of glycinergic synaptic currents. The 20–80% rise times predicted (by the best fits to Schemes 2 and 3) are approximately 0.2 ms for responses to 1 ms concentration jumps to 3 mm glycine, a value which, again, is in broad agreement with the experimental results of jumps on recombinant α1 receptors (0.15–0.2 ms) (Legendre et al., 2002) and recordings of glycinergic synaptic current in rat spinal cord (0.5 ms; note that the composition of these synaptic glycine receptors is not known with certainty) (Jonas et al., 1998).

Cooperativity and interaction between subunits

A very basic but still mostly unanswered question about ion channels concerns whether binding to one site can affect binding to another while the channel is still shut. Such interactions may be more apparent than real. Binding of oxygen to hemoglobin, for example, shows a strong reduction in equilibrium constant for each successive binding if fitted as a simple binding equation (the Adair equation). It was a major insight by Wyman and Allen (1951) to suggest that most, if not all, of this apparent change in affinity was actually the result of a conformation change. This was put in quantitative form in the Monod–Wyman–Changeux mechanism (Monod et al., 1965), in which binding to subunits in one conformation (the shut channel in our case) is the same, regardless of binding to other subunits. However, the ligand bound with higher affinity to another conformation (the open channel) and pushed the conformation equilibrium toward the form with higher affinity, thus giving the appearance of increasing affinity.

Schemes 1 and 2 (with five or three binding sites, respectively) were fitted initially with the constraint that all binding rate constants be the same, thus implying no cooperativity in binding to the shut state, in the spirit of Monod et al. (1965). In all cases, fits failed to describe accurately our experimental single-channel distributions. In muscle nicotinic receptors, affinity decreases (in mouse or Torpedo channels) (Jackson, 1988; Sine et al., 1990) or increases slightly (Colquhoun and Sakmann, 1985) from the first to the second agonist binding step; however, these changes cannot be attributed unequivocally to differences in the sites before the agonist binds (heterogeneity), rather than to an interaction between sites (true cooperativity), as pointed out by Colquhoun and Sakmann (1985) and Sine et al. (1990). Almost all fitting to nicotinic receptor data has assumed that binding to one subunit is unaffected by binding to another (Salamone et al., 1999; Hatton et al., 2003). Indeed, it is almost impossible to estimate all of the rate constants (in a model in which the two sites are initially different), unless the assumption that sites do not interact is made (Colquhoun et al., 2003a). Similar assumptions have been made for GABA_A and glycine receptors (Jones and Westbrook, 1995; Legendre, 1998).

Nevertheless, Hatton et al. (2003) found that to fit simultaneously single-channel data for nicotinic receptors at a wide concentration range, it was necessary either to assume some degree of interaction between binding to different sites or to include an extra short-lived (1 ms) shut state, and it was not possible to distinguish between these two possibilities. Far less can it be expected that macroscopic data (e.g., concentration jumps) could resolve the question (Gentet and Clements, 2002; Mozrzymas et al., 2003). However, the evidence for interaction between subunits is rather strong in the present work.

In the rates obtained from the fitting of Scheme 2, the values of the dissociation rate constants for unbinding from the shut channel (after correction with the proper statistical factor) (Table 5) increases as the number of bound molecules increases for one to three. This implies negatively cooperative interactions between binding sites in the shut conformation, in the sense that dissociation is faster when other sites are occupied. In contrast, the association rate constants (all quite slow compared with nicotinic receptors) seem to show positively cooperative interactions, being slow (0.1 μm^–1 s^–1) for the first binding but increasing to 7–10 μm^–1 s^–1 for subsequent bindings. It is quite hard to imagine a physically realistic mechanism for such an interaction. One possibility is that the interaction is mediated by a substantial change in conformation produced by binding while the channel is still shut. If that was so, this conformation change should really be incorporated into the mechanism, but attempts to use a step-wise gating model have been few for receptors in this superfamily (Colquhoun and Ogden, 1988; Auerbach, 1993), and it seems unlikely that such a kinetic step could be resolved.

Another possibility is an electrostatic effect between bound agonist molecules. These interactions operate at short range in aqueous medium (3 Å for the negative cooperativity in the protonation of the amino acid glycine) (Wyman and Gill, 1990). However, this range could be greater in the interior of a protein, which has a lower dielectric constant than an aqueous ionic solution (Dwyer et al., 2000), and it might be comparable with the distance between adjacent binding sites (approximately 20 Å, judging by the snail ACh-binding protein structure) (Brejc et al., 2001).

An electrostatic interaction would explain the asymmetry of the second binding in Scheme 3, in terms of binding to a subunit that is adjacent or distal to the site where the first binding occurred. It is also possible that such topological interaction results from a conformational change while the channel is still shut. However, the present knowledge of the structure of open and shut states and of the path between them is insufficient to make any predictions of the nature of interactions between subunits, and a fortiori, of how binding rate constants would be expected to vary with degree of ligation.