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The Journal of Neuroscience, December 1, 2004, 24(48):10924-10940; doi:10.1523/JNEUROSCI.3424-04.2004

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Cellular/Molecular
Single-Channel Behavior of Heteromeric 1 Glycine Receptors: An Attempt to Detect a Conformational Change before the Channel Opens

Valeria Burzomato, Marco Beato, Paul J. Groot-Kormelink, David Colquhoun, and Lucia G. Sivilotti

Department of Pharmacology, University College London, London WC1E 6BT, United Kingdom

	Abstract

Top Abstract Introduction Materials and Methods Results Discussion References

 
The 1 heteromeric receptors are likely to be the predominant synaptic form of glycine receptors in the adult. Their activation mechanism was investigated by fitting putative mechanisms to single-channel recordings obtained at four glycine concentrations (10-1000 µM) from rat 1 receptors, expressed in human embryonic kidney 293 cells. The adequacy of each mechanism, with its fitted rate constants, was assessed by comparing experimental dwell time distributions, open-shut correlations, and the concentration-open probability (P_open) curve with the predictions of the model. A good description was obtained only if the mechanism had three glycine binding sites, allowed both partially and fully liganded openings, and predicted the presence of open-shut correlations. A strong feature of the data was the appearance of an increase in binding affinity as more glycine molecules bind, before the channel opens. One interpretation of this positive binding cooperativity is that binding sites interact, each site sensing the state of ligation of the others. An alternative, and novel, explanation is that agonist binding stabilizes a higher affinity form of the receptor that is produced by a conformational change ("flip") that is separate from, and precedes, channel opening. Both the "interaction" scheme and the flip scheme describe our data well, but the latter has fewer free parameters and above all it offers a mechanism for the affinity increase. Distinguishing between the two mechanisms will be important for our understanding of the structural dynamics of activation in the nicotinic superfamily and is important for our understanding of mutations in these receptors.

Key words: glycine; binding; gating; single channel; dose-response; patch clamp; kinetics

	Introduction

Top Abstract Introduction Materials and Methods Results Discussion References

 
For ligand-gated ion channels, the big question, at the molecular level, is how binding of an agonist causes the channel to open. The binding site for the agonist is a long way from the channel gate (approximately 50Å) (Miyazawa et al., 1999). What are the steps that make up this reaction? How are these steps connected? Which steps involve binding and which are conformation changes? How fast is each step? Why are partial agonists partial? Only by answering these questions can we achieve the aim of relating function to structure.

For channels in the nicotinic superfamily, extensive single-channel work, particularly on the muscle-type nicotinic acetylcholine receptor itself, has established some key facts about the activation process, in terms of both function (Colquhoun and Sakmann, 1985; Sine et al., 1990; Grosman et al., 2000) and structure (Brejc et al., 2001; Unwin et al., 2002; Miyazawa et al., 2003; Celie et al., 2004). Changes at the binding site precede channel opening, and the two may be linked by a wave of conformational changes in which successive discrete subdomains between the binding site and the pore move in a sequence of rigid body movements (Chakrapani et al., 2004). For both nicotinic (Lester et al., 2004) and glutamate (Gouaux, 2004) receptors, structural changes that occur after agonist binding have been described, although only Torpedo channels have been imaged in both the closed and (at lower resolution) open (Unwin, 1995) state. The goal of understanding gating as a dynamic change in structure remains unattained.

The structural studies suggest that binding of agonist causes closure of the molecule around the bound ligand (which, presumably, results in an increased affinity). One of the outstanding questions is how this domain closure is related to the opening of the channel.

In this study we extend our recent work on the homomeric glycine receptor, another member of the nicotinic superfamily (Beato et al., 2004), to an investigation of the main synaptic form of glycine receptors in the adult CNS, the heteromeric 1 channel. Direct fitting of activation mechanisms to single channel data shows that conventional mechanisms can describe channel behavior only if it is postulated that the affinity for binding of glycine to the shut state increases when other binding sites have already been occupied by glycine. This suggests that binding sites interact while still shut, and in view of the large separation between the sites, this in turn suggests that a substantial conformation change is caused by binding while the channel is still shut. A mechanism that postulates such a pre-opening conformation change fits the data well (although not uniquely) and provides an explanation for the apparent "cooperativity" of binding along exactly the same lines as first proposed by Wyman and Allen (1951) for the apparent cooperativity of binding of oxygen to hemoglobin (Colquhoun, 1998).

	Materials and Methods

Top Abstract Introduction Materials and Methods Results Discussion References

 
Heterologous expression of rat 1 glycine receptors in human embryonic kidney 293 cells. Human embryonic kidney 293 cells (HEK293) (American Type Culture Collection-CRL-1573; LGC Promochen, Teddington, UK) were maintained at 37°C in a 95% air/5% CO₂ incubator in DMEM supplemented with 0.11 g/l sodium pyruvate, 10% v/v heat-inactivated fetal bovine serum, 100 U/ml penicillin G, 100 µg/ml streptomycin sulfate, and 2 mM L-glutamine (all from Invitrogen, Paisley, UK) and passaged every 2-3 d, up to 20 times.

Cells were plated on dishes, incubated for 10 hr, and then transfected by a calcium phosphate-DNA coprecipitation method (Groot-Kormelink et al., 2002) with cDNAs for the rat 1 and glycine receptor subunits. For the amplification and cloning of the rat 1 (GenBank accession number AJ310834 [GenBank] ) and (GenBank accession number AJ310839 [GenBank] ) GlyR subunits into the pcDNA3.1(+) vector (Invitrogen, Breda, The Netherlands) see Beato et al. (2002) and Burzomato et al. (2003), respectively. The subunit plasmid was transfected in a 40 or 20x greater quantity than the 1 plasmid to minimize contamination by homomeric 1 receptors. In all cases the marker enhanced green fluorescent protein plasmid (EGFP-c1) (BD Biosciences, Oxford, UK) was cotransfected (18% and 37% of the total plasmid DNA for the 1:40 and 1:20 transfections, respectively) to allow detection of transfected cells. Each dish was transfected with 3 µg of DNA. Patch-clamp recordings were made 14-48 hr after transfection.

Spinal cord slices. Acute spinal cord slices (350 µm thickness) were obtained from postnatal day 17 (P17)-P18 rats (Takahashi et al., 1992). The animals were anesthetized with an intraperitoneal injection of urethane [10% (w/v) solution; Sigma-Aldrich, Gillingham, UK) and decapitated. The spinal cord was exposed after ventral laminectomy. The midthoracic to lumbar region was removed and fixed vertically to an agar block using tissue glue (Vetbond, World Precision Instruments, Hertfordshire, UK). The block was glued to the base of the slicing chamber of a Leica VT1000 Vibratome, and 8-10 slices were taken from the lumbar region spanning the L2-L5 segments. After 30 min of incubation at 37°C, slices were left at room temperature for another 30 min and then transferred to the recording chamber as needed. Slices were bubbled continuously with 95% O₂/5% CO₂.

Electrophysiological recording. All single-channel recordings from transfected cells were obtained in the cell-attached configuration; a total of 21 patches were selected for analysis. Cells were bathed in an extracellular solution containing (in mM): 102.7 NaCl, 20 Na gluconate, 4.7 KCl, 2 CaCl₂, 1.2 MgCl₂, 10 HEPES, 14 glucose, 15 sucrose, 20 TEACl, pH adjusted to 7.4 with NaOH; osmolarity, 320 mOsm. HPLC-grade water was used to prepare the solution to minimize contamination of glycine.

Extracellular solutions for dissecting and recording from acute spinal cord slices had the same composition (in mM): 113 NaCl, 3 KCl, 25 NaHCO₃, 1 NaH₂PO₄, 2 CaCl₂, 2 MgCl₂, 11 D-glucose, pH 7.4. The intracellular solution for whole-cell recordings consisted of (in mM): 140 CsCl, 4 NaCl, 1 Mg₂Cl, 0.5 CaCl₂, 5 EGTA, 10 HEPES, 2 Mg-ATP, pH 7.3 with CsOH.

Patch pipettes for cell-attached single-channel recording were pulled from thick-walled borosilicate glass (GC150F; Harvard Apparatus, Edenbridge, UK), coated with Sylgard (Dow Corning, Coventry, UK), fire-polished to a resistance of 10-15 M, and filled with extracellular solution containing 10-1000 µM glycine. Cell-attached patches were voltage clamped at +100 mV, and single-channel currents were recorded with an Axopatch 200B amplifier, prefiltered at 10 kHz with the amplifier four-pole Bessel filter, and stored on digital audio tape (Bio-Logic Science Instruments, Claix, France). Recordings were replayed from the tape, filtered at 3 kHz with a eight-pole Bessel filter, and digitized at 30 kHz (Digidata 1322A; Molecular Devices, Wokingham, UK; Clampex software) for off-line analysis.

We discarded all patches in which homomeric channels were detected, even if homomeric openings were few. For openings that are long enough to reach full amplitude, homomeric openings are easily distinguishable from heteromeric ones on the basis of their conductances (for review, see Legendre, 2001). At a holding potential of +100 mV (no junction potential correction), the channel amplitude was 4.7 ± 0.1 and 3.1 ± 0.1 pA for homomeric and heteromeric channels, respectively (Burzomato et al., 2003; Beato et al., 2004).

Recordings from acute spinal cord slices were performed from ventral horn neurons visually identified as motoneurons on the basis of their location, size, and shape, with an infrared-differential interference contrast microscope. Microelectrodes were pulled from thick-walled borosilicate glass (GC150F; Harvard Apparatus) to 1-1.5 M resistance and fire polished to a final resistance of approximately 2.5 M. Cells were voltage clamped at -70 mV, and only those cells with stable holding current (less than 40 pA) for the duration of the experiment were included for analysis. Series resistance (6-10 M) was compensated (70-90%). To isolate glycinergic miniature IPSCs (mIPSCs), 0.5 µM tetrodotoxin, 5 µM SR95531 hydrobromide, 20 µM AP5, and 10 µM CNQX were added to the recording solution to block sodium action potentials, GABA_A, NMDA, and AMPA-kainate receptors, respectively.

Analysis of single-channel recordings. Recordings were idealized by time-course fitting with the program SCAN (Colquhoun and Sigworth, 1995). This produced a list of openings and shuttings together with the (fitted) amplitude values for each opening. All programs used in our analysis can be obtained from http://www.ucl.ac.uk/pharmacology/dc.html.

The first stage of analysis was to construct distributions of fitted amplitudes, shut times, and open periods from the experimental data. These distributions were fitted (EKDIST program) by a single Gaussian for the amplitude histogram and by a mixture of exponential densities for dwell times. Only openings longer than twice the rise time of the filter contributed to the fitted amplitudes histogram. A time resolution of 30 µs (for both open and shut times) was imposed retrospectively (Colquhoun and Sigworth, 1995). This stage of fitting is purely descriptive and empirical: the parameters so estimated (number of components, time constants, areas; see Table 1) were not used in the subsequent stage (the testing of mechanisms; see below). These fits were needed only to choose the critical shut time (t_crit) value that was used to divide recordings into sections (bursts or clusters) that are believed to originate from one individual channel. At low agonist concentrations, the groups will be individual channel activations.

View this table: [in this window] [in a new window]   Table 1. Dwell-time distributions

 
Single-channel open probability-concentration curve. At glycine concentrations >10 µM, channel openings occurred in clusters separated by long quiescent periods, probably reflecting sojourns in long-lived desensitized states (Sakmann et al., 1980; Colquhoun and Ogden, 1988). Only clusters that contained more than 5 openings and no double openings were selected for further analysis (17-91 clusters analyzed per concentration; clusters contained up to 3147 openings; mean 340 openings). Each of these clusters is likely to represent the activity of a single glycine channel (see Results).

For each patch (three to four per concentration; see Table 2) the open probability (P_open) was estimated as the ratio between the sum of the open times within clusters and the sum of the durations of the clusters (both obtained from the idealized recordings). This procedure effectively weights the contribution of each cluster to the P_open value according to their duration, because P_open estimates derived from longer clusters are more precise.

View this table: [in this window] [in a new window]   Table 2. Properties of clusters of 1 channel openings at different glycine concentrations

 
The P_open values obtained for patches at the same concentration were then averaged (see Table 2). The P_open- concentration curve described by these points was fitted empirically with the Hill equation (weighted least squares fit) using the CVFIT program to estimate I_max, EC₅₀, and the Hill slope. This Hill slope was compared with that predicted by fitted mechanisms. The latter will not have constant Hill slopes, so the Hill slope at EC₅₀, defined as follows, was found numerically:

(1)

where G is the glycine concentration. For this calculation we used the apparent P_open value (that expected in the presence of missed events), which was calculated using Equations 2-4.

Fitting alternative mechanisms to single-channel data with HJCFIT. Maximum likelihood fittings for the evaluation of kinetic schemes and rate constants were performed with the HJCFIT program (Colquhoun et al., 1996, 2003). The experimental input into this program consists of one or more idealized recordings, i.e., the entire sequence of durations of open and shut times in the order in which they occur, together with the imposed resolution. Recordings were obtained at four glycine concentrations (10, 30, 100, and 1000 µM); these produced an apparent P_open of 8-98%. Three recordings at each concentration, each 12,000-19,000 transitions long, were then selected on the basis of signal-to-noise ratio. These recordings were then arranged in three independent sets; each set consisted of four experiments, one at each of the four concentrations. All experiments in a set were fitted simultaneously with HJCFIT.

From the data, the resolution, and a postulated mechanism, HJCFIT calculates a likelihood value for the experimental record(s) for a set of guesses for the values of the rate constants. The rate constants are then adjusted iteratively to maximize this likelihood. The imposed resolution (30 µs in our experiments) is taken into account by implementing the exact solution for missed events correction by Hawkes et al. (1990, 1992): hence the acronym HJC (Hawkes, Jalali, and Calquhoun).

Openings were divided into groups using a critical shut time (t_crit) so that openings within each group are likely to come from the same channel (see Results). At low agonist concentrations (10 µM glycine), the groups correspond to individual activations of the channel consisting of a few openings: the likelihood of each such group was calculated using the initial and final vectors defined by Colquhoun et al. (1996, their equations 5.8-5.11), which we refer to as CHS vectors (Colquhoun, Hawkes, and Srodzinski). We cannot interpret shut times between these groups of openings (because they depend on the number of channels in the patch, which is unknown), but CHS vectors exploit the knowledge that the true shut time between one group and the next must be longer than t_crit. At higher concentrations, at which desensitization is relevant, CHS vectors cannot be used because desensitized states are not included in the mechanism being fitted. We therefore used steady-state initial vectors. This is an approximation but one that has little effect, because at these concentrations the number of events in each group (cluster) is large, and this reduces the effect of the initial vector, as shown by the results of simulations (Colquhoun et al., 2003).

Each fit was repeated using several different initial guesses. If the likelihood surface has a single well defined maximum, the same rate constant estimates should be obtained no matter what initial guesses were used.

To test whether a postulated mechanism describes adequately the behavior of the receptor, the predictions of the mechanism together with the rate constants estimated by HJCFIT were compared with the experimental observations. This was done routinely by inspection of four types of data display, namely, the distributions of observed open time and shut time, conditional mean open time plots, and the P_open- concentration curve.

The rate constants estimated for the specified mechanism, data, and resolution were used to calculate the distributions of the observed or apparent open times and shut times (HJC distributions). Observed open times, for example, are extended by missed shut times (those below the specified resolution). The appropriate HJC distribution (solid lines in the dwell-times plots; see for example the first and second rows of plots in Figure 4) is superimposed on (not fitted to) the histogram of observed values, and insofar as it fits, the proposed mechanism and the values of the rate constants are a good description of the data. The predicted distribution at perfect resolution is also plotted, as a dashed line (see Fig. 4, first and second rows of plots). This was calculated from the fitted rate constants as described by Colquhoun and Hawkes (1982), and the separation between this and the solid line shows the extent to which failure to detect short events affected the observations.

View larger version (29K): [in this window] [in a new window]   Figure 4. Fitting of a scheme with three identical binding sites (scheme 1) to 1 glycine channel activations (8 free parameters). A, Scheme 1 was fitted with constraints (Eq. 5) that ensured that the association and dissociation rate constants were the same for each binding step (identical binding sites). For clarity, this is indicated in the figure by the same dissociation constants (K) displayed over the binding steps. B, Comparison of the predictions of the fit with the experimental data. The mechanism was fitted simultaneously to three sets of data at four different glycine concentrations; one of the three sets is shown in this and the other figures. The first two rows of plots show the apparent open and shut times distributions. The histograms are the experimental distributions (note that only shut times below tcrit are fitted; see Materials and Methods). The solid lines are predicted (HJC) distributions calculated from the mechanism, the resolution, and the values of the rate constants that were found to maximize the likelihood of the experimental sequences of single-channel openings and shuttings. These distributions allow for missed events on the basis of the imposed resolution, whereas the dashed lines are the distributions expected if no events were missed. In the third row the mean duration of openings that are adjacent to shut times in a specified range of duration is plotted against the mean duration of the shut times in each chosen range. These plots illustrate the correlation between the duration of adjacent open and shut times. Experimental points are shown as filled circles (±SDM) joined by a solid line, predicted points as open circles, and the theoretical continuous relationship between open time and adjacent shut time as a dashed line. C, Experimental Popen values (not corrected for missed brief shuttings) are plotted as filled circles against the glycine concentration. The solid line is the apparent Popen- concentration curve predicted by the fitted scheme and rate constants taking into account the effect of missed events (from Eqs. 2-4). The dashed line is the ideal curve expected if no events were missed. In this case, the predictions of the fitted mechanism and rates are quite poor, so this scheme is unlikely to be the real activation mechanism of the channel.

 
As for other channels, short open times tend to occur adjacent to long shut times. To determine whether these correlations (Fredkin et al., 1985; Colquhoun and Hawkes, 1987; Blatz and Magleby, 1989) are predicted accurately, the HJC joint (bivariate), or conditional, distributions of open time and adjacent shut time can be checked. For a synoptic view of these, we show here only conditional mean plots. In this plot, the mean of all apparent open times that are adjacent to apparent shut times in a specified range is plotted against the mean of the shut times in that range. The downward slope in this graph (see Fig. 4, third row of plots) shows that the durations of open times and adjacent shut times are negatively correlated. The HJC prediction for the conditional mean open time, calculated for the same ranges of shut times as observed values, are plotted as open circles; these are calculated as described in Colquhoun et al. (1996, section 4). Because the mechanism obeys microscopic reversibility, the predictions are the same whether we look at the preceding shut time, the following shut time, or both. The dashed line on these plots shows the theoretical continuous relationship between mean open time and adjacent shut time that would be approached if sufficiently narrow shut time ranges could be used, calculated as in Colquhoun et al. (1996, section 3).

One of the criteria used to judge how well a postulated mechanism described the data was to see how well the equilibrium concentration-response curve was predicted, the response being the probability of a channel being open, P_open, obtained from single-channel measurements. Although P_open is much less sensitive to missed brief events than the mean open and shut times, the correction for missed events was nevertheless found to be essential, so the observed P_open values were compared with the predicted apparent P_open. This is not given explicitly in Colquhoun et al. (1996), so the method will be given here. The apparent P_open is calculated as follows:

(2)

where ^eµ_open is the apparent, or extended, mean open time (extended by missed shuttings). The probability density function of apparent open time is from Colquhoun et al. (1996, Eq. 2.14) as follows:

(3)

where the matrices are defined in Colquhoun et al. (1996, Eq. 2.1, 2.10, and 2.12). The mean can be found in general by differentiating the Laplace transform of a probability density function, changing the sign, and setting the Laplace variable, s, to zero. The apparent open time is therefore as follows:

(4)

The expression for the derivative is given in Colquhoun et al. (1996, Eq. 3.6). An analogous expression gives the mean apparent shut time. These quantities are evaluated in the HJCFIT program.

The predicted apparent P_open- concentration curve (see Fig. 4C, solid line), calculated as just described, was superimposed on (not fitted to) the observed points. For comparison, the ideal (no missed events) P_open- concentration curve is also shown (dashed line). The quality of the fit was judged by eye and by comparing predicted and observed values for the EC₅₀ value and for the Hill slope at the EC₅₀.

Analysis of mIPSCs. The analysis of mIPSCs was performed on nine cells. A variable number of events (range, 120-700) were detected using Clampfit 9.2 software (Axon Instruments). The events were inspected, and all mIPSCs that were separated by less than 100 ms were excluded from analysis. Most IPSCs (72%) had 20-80% rise time lower than 0.6 ms, indicating a majority of somatic or near-somatic locations for the glycinergic synaptic inputs to motoneurons. To avoid distortions in the estimates of amplitude and decay time, events with rise times greater than 0.6 ms were not included in the analysis. No correlations were detected between rise time and amplitudes or rise time and decay time, with values for the Pearson correlation coefficient, r, in the range -0.05-0.08 (P = 0.7-0.9) and -0.01-0.03 (P = 0.7-0.9), respectively. After filtering at 3 kHz, the selected mIPSCs for each experiment were averaged and fitted with a single or double exponential from 90% of the peak to baseline.

All data are expressed as mean ± SD of the mean. For estimated rate constants, we report the average of the estimates obtained from different sets and the coefficient of variation (CV) of the mean. Equilibrium constants were calculated separately for each set and then averaged. This is the sensible thing to do when there is a strong positive correlation between the estimates of the rate constants in the numerator and denominator (as for E₃ = ₃/₃), but it means that the mean values for equilibrium constants given in the tables are not identical with the ratio of the mean rate constants in the same table.

	Results

Top Abstract Introduction Materials and Methods Results Discussion References

 
Experimental dwell-time distributions
The cell-attached recordings on the left of Figure 1 show single-channel currents evoked by four glycine concentrations. At the lowest concentration, 10 µM glycine, sparse openings occurred in groups (bursts), each of which represents a single activation of the channel. At higher concentrations there are long clusters of closely spaced openings, separated by long shut periods. These four agonist concentrations are the ones selected for the fits of mechanisms (see below). Figure 1, middle and right columns, shows the corresponding distributions of apparent open and shut times, fitted by mixtures of exponential probability density functions. The results of these empirical fits (Table 1) were used only to choose the t_crit for the second stage of analysis (see Materials and Methods), as follows.

View larger version (43K): [in this window] [in a new window]   Figure 1. Activation of heteromeric 1 channels by increasing concentrations of glycine. The left column shows continuous sweeps of cell-attached recordings at 10, 30, 100, and 1000 µM glycine (3 kHz filter). Bursts of openings are observed at 10 µM, whereas at higher agonist concentrations bursts group into clusters. The middle and right columns show the dwell-time distributions (apparent open and shut times) corresponding to the same patches for which traces are shown to the left. Distributions were fitted with a mixture of exponential probability density functions (Table 1).

 
At the lowest concentration, 10 µM glycine, the shut time distribution was fitted with six exponential components (Fig. 1, Table 1). The four fastest time constants were classified as being within-bursts if they were similar across different patches at the same concentration and across different concentrations (Table 1). Thus, a t_crit value of 4 ms was chosen between the fourth and fifth shut time component, using the criterion of minimizing the total number of misclassified events (Jackson et al., 1983). The progressive shortening at higher glycine concentrations of the longer (inter-burst) shut times is clearly visible in the distributions in Figure 1, right-hand column, and in the expanded traces shown in Figure 2 (A-E). The components become progressively harder to distinguish until, at 1000 µM, only three components can be resolved, although the real number of components cannot change.

View larger version (41K): [in this window] [in a new window]   Figure 2. Concentration dependence of the open probability of clusters of 1 channel openings. A-E, Representative clusters elicited by 30, 50, 100, 300, and 1000 µM glycine. The bars under the traces on the left indicate the regions shown on the right on an expanded time scale. F, The Popen concentration-response curve to glycine. The curve shows an empirical fit of the Hill equation (weighted least squares). The observed points in this plot (unlike later plots) have been corrected approximately for missed short shuttings (see Results). Popen values are obtained for each patch from the ratio between the total open time (obtained from records idealized by time-course fitting) and the total duration of the clusters. The points are averages of three to four patches (17-91 clusters) (Table 2) for each glycine concentration.

 
At concentrations higher than 10 µM, activations are closely spaced and separated by long sojourns in desensitized states (Sakmann et al., 1980; Colquhoun and Ogden, 1988) (for glycine receptors, see Takahashi and Momiyama, 1991; Beato et al., 2004). Because each patch contained relatively few clusters, the distributions in Figure 1 contain few of these (desensitized) intercluster shut times. These intervals were not fitted but are clearly distinct from the much shorter intracluster shuttings. Hence, gaps were classed as between clusters if longer than 1000 ms at 30 µM, 60 ms at 100 µM, and 20 ms at 1000 µM.

At all concentrations, most of the shuttings belong to the shortest component, which has a time constant (at 10 µM) of approximately 14 µs (Table 1). This is much shorter than our experimental resolution of 30 µs, and many (approximately 88%) such gaps would be missed. Nevertheless, given that 67% of shut times are "in the fast component," in a typical run with 15,000 transitions the number of "14 µs component shuttings" that are above 30 µs is almost 700, which would predict a coefficient of variation of only 4% for estimation of the 14 µs time constant. Therefore, the reproducibility of the estimates of the fastest time constant, shown in Table 1, is not surprising.

The distribution of apparent open times (Fig. 1) shows a shift toward longer apparent open times at the higher concentrations. This results from a decline in the relative area of the faster component (Table 1), which can no longer be resolved at 1000 µM. Time constants of both components were essentially unchanged with concentration, suggesting that dissociation from the open states is relatively slow. As in homomeric channels, the faster component may therefore correspond to partially liganded open states of the receptor (Beato et al., 2002).

The P_open curve
Figure 2 illustrates how the glycine concentration-P_open curve was obtained from the analysis of clusters of openings evoked by 30-1000 µM glycine. The expanded traces on the right-hand side also show the consistency of the single-channel conductance and the lack of conductance sublevels in 1 heteromeric receptors, in accord with Bormann et al. (1993). In all patches, the distribution of fitted amplitudes for single-channel currents could be fitted well with a single Gaussian density (3.1 ± 0.1 pA; data not shown).

Experimental P_open values are plotted against glycine concentration in Figure 2F, where they are fitted by a Hill equation. This plot makes no postulates about mechanism, so the exact correction for missed events that is used for subsequent P_open plots cannot be used. Therefore, for this plot only, values of P_open were corrected for missed shut times by estimating the approximate time occupied by the missed shut times, by extrapolation to t = 0 of the shut time distribution (Colquhoun and Sakmann, 1985). This gave a maximum P_open of 0.97 (two-unit likelihood interval, 0.968-0.971), an EC₅₀ of 60 µM (two-unit likelihood interval, 57-62 µM), and a Hill slope of 3.4 (two-unit likelihood interval from residuals, 3.1-3.7); for normally distributed variables, two-unit likelihood intervals are the same as 95% confidence intervals (Colquhoun and Sigworth, 1995). The Hill equation is not, of course, the correct equation to fit (it describes no possible physical mechanism), so the slope that it gives is in no sense the "right" value; it was fitted merely to obtain an empirical estimate of the steepness of the P_open curve for comparison with the predictions of postulated mechanisms (this consideration affects also the calculation of confidence intervals). In fact a Hill slope greater than 3 is not possible for any of the mechanisms that we discuss here. Thus there is some uncertainty in our Hill slope estimate, but what actually matters is not so much the value for a Hill slope but rather how well the whole predicted P_open curve fits the observed points in Figures 4, 5, 6, 7, 8 and 10. The predictions of Hill slope from fits (Figs. 4, 5, 6, 7, 8 and 12) are based on apparent (HJC) values, and therefore, strictly speaking, they are not exactly comparable with the value found from Figure 2, but the difference is very small (Table 2).

View larger version (31K): [in this window] [in a new window]   Figure 5. Test of the possibility that agonist binding sites are initially different: a scheme with two types of binding sites (scheme 2, 14 free parameters; constraints as in Eq. 6). A, Scheme 2 incorporates two types of binding sites, termed a and b, corresponding to the site and the two sites, respectively. Binding rate constants at each site are postulated not to be affected by occupancy of other sites, and therefore the site has a constant affinity of 1/Ka and each site a constant affinity of 1/Kb. B, Comparison of observed and predicted dwell-time distributions and open-shut time correlations, as in Figure 4. C, Popen- concentration data and the concentration-response curve predicted from the mechanism fit, as in Figure 4. The obvious discrepancies between experimental observations and model predictions in B (especially at the higher concentrations) and C indicate that scheme 2 fails to describe the data.

 

View larger version (28K): [in this window] [in a new window]   Figure 6. Test of a mechanism in which the affinity of the binding sites appears to be affected by the level of occupancy: a scheme with three binding sites and no constrained parameters (12 free parameters). A, All rate constants in scheme 1 were estimated as free parameters. B, Comparison of observed and predicted dwell-time distributions and open-shut time correlations, as in Figure 4. C, Popen- concentration data and the concentration-response curve predicted from the mechanism fit. Comparing this fit with that of Figure 4 shows an improvement that is consistent across all forms of data display. Nevertheless, the fit is still inadequate for data at 1000 µM and for the fast component of the shut-time distribution at 10 µM.

 

View larger version (29K): [in this window] [in a new window]   Figure 7. Test of a mechanism with three additional shut states and no constrained parameters (18 free parameters). A, Scheme 3, showing the additional shut states as D. Access to D states is not concentration dependent. B and C are as in Figure 4. Note that the predictions of this model are much closer to the observed dwell-time distributions and open-shut correlations than those of scheme 1 with no constraints (Fig. 6).

 

View larger version (29K): [in this window] [in a new window]   Figure 8. The flip mechanism: three additional shut states resulting from a pre-opening conformational change (scheme 5, 14 free parameters, constraints as in Eq. 7). A, Scheme 5 has three equivalent binding sites. Each of the bound resting states R can switch to a flip conformation F, in which the pore is still shut, but binding affinity (for all sites) is higher than for R states. From the F states the protein can open (F*). The scheme was fitted with the constraint that all binding steps in the set of R or F states have equal rate constants (and therefore the same equilibrium dissociation constant, KR and KF, for R and F states, respectively). This constraint (on the rate constants) is indicated in the figure by displaying the same dissociation constants on the binding steps. B and C are as in Figure 4. This mechanism describes the data very well with 14 free parameters. The quality of the predictions is indistinguishable from the fits with the model shown in Figure 7 (three binding sites, three additional shut states, no constraints, 18 free parameters).

 

View larger version (29K): [in this window] [in a new window]   Figure 10. Test of the flip mechanism on data from homomeric 1 glycine receptors. A, Scheme 5, with binding rates constrained to be equal within resting states (R) and flip states (F), as in Figure 8. B and C are as in Figure 4; data from Beato et al. (2004). Scheme 5 provides an excellent prediction of single-channel behavior for 1 homomeric glycine receptors. The agreement of scheme 5 with the data is of a quality comparable with that observed for the best-fitting models in Beato et al. (2004), which were scheme 1 with no constraints or an extended scheme 1, with five binding sites and saturation of gating.

 

View larger version (28K): [in this window] [in a new window]   Figure 12. A comparison of the flip mechanism (scheme 5) (A) with scheme 3 (B). The averaged rate constants (units as in Tables 4 and 5) and equilibrium constants are shown. Both mechanisms gave good fits with these values (Figs. 7, 8).

 
Although the observed EC₅₀ value, 60 µM, is well within the range reported for 1 heteromers in HEK293 cells (between 18 and 74 µM) (Bormann et al., 1993; Handford et al., 1996; Rees et al., 2002), the Hill slope is at the top end of the range of values in the literature (1.8-3.0) (Handford et al., 1996; Legendre, 1998; Shan et al., 2001). Most previous values were obtained by macroscopic methods and are inevitably more affected by desensitization than a P_open concentration-response curve. Thus, discrepancies between the two methods are not surprising. Nevertheless, because of the importance of the P_open curve as a criterion for adequacy of a postulated mechanism, we investigated the potential sources of bias in our measurements.

First, P_open values may be overestimated if the group of openings classified as a cluster originates from more than one channel, i.e., it really is two interlaced clusters. Unless the open probability of these two clusters is very low, their superposition would give rise to double openings, which would make us discard the resulting cluster. The lowest P_open that we measured was 0.084 (at 30 µM glycine). If clusters of this overall P_open were produced by two active channels, the mean number of openings in a run of single openings would be only 23, with a probability of approximately 0.01 of observing a run containing more than 104 single openings (Colquhoun and Hawkes, 1990). Most clusters (e.g., 22 of 27 at 30 µM) contained far more openings than this without a double opening being seen.

Another way in which P_open could be overestimated would be to choose inappropriately low t_crit values, because this would lead us to divide one cluster into several. To test for errors in the t_crit calculation, we tried increasing or decreasing its value by a factor of 5, but found that the P_open values barely changed (by 3%, on average). Finally, the bias caused by missing short shut times was corrected by an approximate extrapolation method in Figure 2, but for all of the fits, the apparent (HJC) P_open value, with exact allowance for missed events, was calculated from Equations 2-4.

Fits of putative mechanisms
The number of binding sites
Heteromeric glycine receptors contain three copies of the subunit and two copies of the subunit (Kuhse et al., 1993; Burzomato et al., 2003). Given that the subunit appears to be essential to the formation of the binding site (Laube et al., 2002), this stoichiometry implies a maximum number of three binding sites.

First we examined the possibility that the receptor contains two agonist binding sites, as suggested by Legendre (1998) on the basis of the shape of the rise time of macroscopic currents evoked by glycine concentration jumps on zebrafish native receptors. We tested several schemes with two binding steps and a minimum of two open states and investigated all possible combinations of connectivity and interaction between binding sites. Mechanisms tested thus included the possibility that the two binding sites are identical to start with [a "sequential" scheme, similar to scheme 1, which has three binding sites (Fig. 3)] or are different. In both schemes we also incorporated the possibility of interaction between binding sites (i.e., cooperativity in binding). Another variant tested was the inclusion of an additional fully bound reluctant shut state leading into an additional open state (Legendre, 1998). None of these variations produced a good description of our data. The predicted Hill slopes, inevitably all less than 2, were much shallower than the value that we observed. In terms of the maximum likelihood achieved, all three different mechanisms with only two binding sites were ranked in the lower 50% of all mechanisms that we tested.

View larger version (37K): [in this window] [in a new window]   Figure 3. Some of the kinetic schemes tested for 1 glycine channels. Agonist molecules are indicated by A, resting states of the receptor by R, and open states by an asterisk. Note that in scheme 2, the receptor is represented by Ra - Rb to indicate that it contains two different types of binding sites (a and b). In schemes 3-5, shut states of the receptor are denoted R, D (desensitized), and F (flipped, i.e., in the pre-opening conformation; see Results). Open channels are indicated by an asterisk (R* or F*). The names of the rate constants for the different steps of the reactions are shown, and the statistical factors in the binding rate constants have been included. These are needed to get the actual transition rates in the Q matrix, taking into account the number of sites available for each binding step.

 
Therefore, we proceeded to test mechanisms with three binding sites: these are shown in Figure 3, together with the names of the rate constants. The appropriate "statistical factors" are shown with the rate constants in Figure 3. These factors take into account the number of sites available for each (un)binding step, so that k_+n and k_-n are the association and dissociation rate constants per site for the nth binding. For example, if three identical sites are occupied, any one of the three bound molecules may dissociate, so the actual transition rate is 3 k_-3 s^-1. To maintain generality, all mechanisms tested include an open state for each ligation state of the receptor.

The simplest mechanism is scheme 1 (Fig. 3). This has sequential binding to three glycine sites that are identical to start with. In the simplest case, the binding sites do not interact with each other; i.e., the binding and unbinding rate constants for a site are not affected by whether the other sites are occupied. The assumption of independent sites is implemented by applying the following constraints to the values of the binding rate constants during the fitting:

(5)

The results of fitting this model are shown in Figure 4 (the constraint of independent sites is denoted by the three identical equilibrium constants K in the scheme in A).

For each mechanism, the HJCFIT program (see Materials and Methods) obtained optimized rate constant values by maximizing the likelihood of the whole sequence of openings and shuttings in a recording. The data input consisted of sets of recordings (idealized by time course fitting), one at each of four different agonist concentrations (10, 30, 100, and 1000 µM), together with the value of the experimental resolution, to allow full missed-event correction. The output consists of a set of maximum likelihood estimates of rate constants. These values are then used to judge the adequacy of the mechanism (see Materials and Methods). Figure 4 B, top two rows, shows apparent open-time and apparent shut-time distributions (same patches as Fig. 1) together with the predicted (HJC) distributions (continuous lines) superimposed on the data (the predicted distribution at perfect resolution is also plotted, as a dashed line; see Materials and Methods). The failure of this mechanism to describe the experimental observations is very clear, particularly for shut times. Note that the data in these histograms are the same as in Figure 1, where the fits shown are empirical (mixtures of exponentials fitted to each distribution separately), rather than global mechanism fits using the whole sequence of events (and hence the full information contained in the data) for four concentrations simultaneously.

The plot of mean open time, conditional on adjacent shut time (see Materials and Methods), is shown in Figure 4B, bottom row (see Materials and Methods for details). The conditional mean open times predicted for this mechanism (open circles) are compared with the experimental points (filled circles joined by continuous straight lines). Again, scheme 1 with identical and noninteracting binding sites does not describe adequately this aspect of the data, because the predicted values lie well below the experimental points at 1000 µM glycine. The final criterion is provided by the apparent P_open- concentration curve (Fig. 4C), which is a poor fit, being clearly too shallow (a Hill slope of 1.84 is predicted at the EC₅₀).

The nature of the binding sites
The mechanism tested above (scheme 1, with no interaction between the binding sites) is clearly unsatisfactory. Two possible reasons for this inadequacy are that the binding sites might not be identical before glycine binds and/or that they may interact. We next tested these two hypotheses.

In ligand-gated ion channels in the nicotinic superfamily, such as glycine channels, agonist binding sites are believed to be at the interface between an subunit and the adjacent subunit in the counterclockwise direction (Brejc et al., 2001). In a glycine heteromeric receptor, it is generally assumed that the three and two subunits are arranged around the pore in a topology. This implies that of the three binding sites, two are formed by an interface and one by an interface. In addition, the two subunits that participate in the sites are nonequivalent in principle, because one contributes also to the site and the other does not. Thus one of the sites is proximal (to the site) and one is distal.

The first test of the hypothesis that the three binding sites are initially different was performed by fitting scheme 2 (Fig. 3). This mechanism incorporates two types of binding sites (one and two identical sites) and has an open state connected to each ligation state of the receptor, but we retained the hypothesis of no interaction between the sites. Thus binding and unbinding rate constants for the site were constrained to keep the same value, regardless of whether the sites are occupied; similar constraints were imposed for the sites, thus:

(6)

Note that these constraints imply that the principle of microscopic reversibility is respected for all cycles in the scheme (Colquhoun et al., 2004) and leave 14 rate constants to be fitted as free parameters. The results of this fit are illustrated in Figure 5 (same set of experiments as shown in Figs. 1 and 4). The mechanism in Figure 5A fails to describe the observed single-channel behavior. This is particularly obvious at high agonist concentrations, where predictions for apparent shut-time distributions and conditional mean open times are poor. In addition, the predicted P_open curve is a poor fit, with a Hill slope that is still too low (1.69). We found also that rate constant estimates for this scheme were very variable from one experimental set to the other (data not shown).

We next examined a scheme in which all three binding sites were different initially (, proximal, distal) but were not allowed to interact with each other. Despite the large number of states and free parameters (16 and 20, respectively), this scheme again proved inadequate, with problems similar to those found for scheme 2 (i.e., poor P_open curve with a low predicted Hill slope and a poor description of the shut-time distributions; data not shown). Thus we concluded that if there is any difference between sites in the resting state, it is too small to be detected.

Interaction between the binding sites
Most of the mechanisms tested so far have not included the possibility that the agonist binding sites may interact, namely that the binding rate constants for one site may be affected by whether the other sites are occupied, before the channel is open. To test this hypothesis in the simplest form, we fitted again scheme 1, this time relieving all constraints and therefore fitting all of the 12 rate constants as free parameters. A comparison of the resulting fit (Fig. 6) with the fit of the same scheme with the constraint of noninteraction (Fig. 4) shows a considerable improvement in the description of single-channel behavior. The rate constant values obtained in the fit (Table 3) show that binding affinity increases monotonically with each binding step by approximately fivefold. Gating efficacy also increases as more binding sites are occupied. Most importantly, this is the first mechanism fit that predicts a Hill slope (2.63 at the EC₅₀) that approaches the observed one (Fig. 6C). Note also that all rate constant estimates were well defined (Table 3), unlike the rates found previously for the fit of scheme 2, which has exactly the same number of free parameters.

View this table: [in this window] [in a new window]   Table 3. Estimated parameters from the fit of scheme 1 (with no constraints) to single-channel data

 
This suggests, as in our recent report for glycine 1 homomeric channels (Beato et al., 2004), that interaction between the agonist binding sites is an essential feature in the activation of heteromeric 1 glycine receptors. Furthermore, good fits can be obtained without having to postulate that the binding sites are nonequivalent in the resting state.

Additional bound shut states
Although releasing the constraint of independence of the binding sites improved the quality of the fit by scheme 1, as shown clearly in Figure 6B, this mechanism is still inadequate in describing shut-time distributions and high concentration open-shut correlations.

In an effort to get better fits, we next added additional bound shut states, the lifetimes of which are not concentration dependent. In one form or another, such shut states (often referred to as "short-lived desensitized" states) have been found to be an essential feature of activation mechanisms for several receptors in this superfamily. The simplest form, used for the description of single-channel behavior for the muscle nicotinic receptor (Salamone et al., 1999; Hatton et al., 2003), involves one distal shut state (connected to the fully liganded open or shut state). The more general form in this family of mechanisms is that developed by Jones and Westbrook (1995) to explain the macroscopic behavior of GABA_A receptors in response to paired short pulses of agonists and incorporates one extra shut state at each level of ligation. Although formally similar to the Jones-West-brook mechanism, in that extra shut states appear within an individual channel activation, the shut states denoted "D" in scheme 3 are more short-lived than those for GABA_A and do not account for slow components of macroscopic desensitization.

We therefore proceeded to test whether adding extra shut states to the unconstrained form of scheme 1 helped account for observed channel behavior. Only a slight improvement was detected when a single shut state was added in a position distal to either A₃R or A₃R^* (Salamone et al., 1999; Hatton et al., 2003) (data not shown). Adding a distal shut state to scheme 1 or scheme 2 (while keeping the constraint of binding site independence) also failed to produce any detectable improvements in the quality of the fit.

The results of the global fit of our data with the more general model (Jones and Westbrook, 1995) adapted to three binding sites (Fig. 3, scheme 3) are shown in Figure 7 and Table 4. Comparison of the plots in Figure 7, B and C, with those in Figure 6 clearly indicates that scheme 3 is much better at describing the behavior of 1 channels than scheme 1 without constraints. A substantial improvement is visible in the accuracy with which HJC distributions predict shut-time distributions and the conditional mean plot at 1000 µM glycine. The quality of the description of the dependence of the apparent cluster P_open on glycine concentration is similar for schemes 1 and 3. It must be noted that this improvement is achieved at the price of an increase in the number of free parameters in the mechanism (from 12 to 18).

View this table: [in this window] [in a new window]   Table 4. Estimated parameters from the fit of scheme 3 to single-channel data

 
Other mechanisms with three extra shut states
The success of the mechanism in scheme 3 in accounting for the single-channel properties of heteromeric glycine channels led us to consider related schemes, all with three binding steps, three open states, and three extra shut states. These schemes differ only in how the states are connected to each other, and the two possible alternative positions for the open states are shown in Figure 3 as schemes 4 and 5. In the first instance, we fitted both scheme 4 and a reduced scheme 5 (this means that no binding or unbinding was allowed between the F states in scheme 5) with no constraints. The results of these fits were good, nearly as good as those of fitting scheme 3 with no constraints, because both models described the data well and predicted a Hill slope value of 2.53-2.69 (data not shown). Note that all three of these mechanisms have the same number of free parameters (18). Binding site interaction was implied by all three schemes, because constraining the binding sites to be independent greatly reduced the quality of the fits (for example, predicting shallow Hill slopes of 1.8-1.9, 14 free parameters; data not shown).

Schemes 3, 4, and 5 with one open state omitted were also tested, on the grounds that the empirical fit of apparent open times with two exponentials (Fig. 1, Table 1) suggested that it might not be necessary to postulate three open states. The fits of apparent open times with two open states were visibly worse than with three open states; these models are nested, and likelihood ratio tests showed that two open states were unacceptable. The empirical fit of exponentials does not resolve all of the open time components, possibly because open times below approximately 3 t_res (90 µs in this case) are not described, in principle, by a mixture of exponential distributions when many short events are missed (Hawkes et al., 1990, 1992). This might also explain why the fastest component of shut times that was fitted empirically was approximately 14 µs, whereas the fits in Figures 7 and 8 suggest that it should be nearer 8 µs.

A conformation change produced by binding while the channel is still shut: the flip mechanism
So far, we found that the data consistently require binding sites to interact, such that the affinity for binding to the shut state appears to increase as more molecules are bound. The monotonic increase in affinity with increasing ligation (K₁ > K₂ > K₃) found for the unconstrained fit of scheme 1 (Table 3) suggests that the appearance of interaction may occur secondary to a concerted (all subunit) conformation change, in the way first postulated by Wyman and Allen (1951) and subsequently applied to enzymes (Monod et al., 1965). Wyman and Allen (1951) suggested that if a protein existed in two conformations, one of which has a higher affinity for a ligand than the other, then the ligand would cause a shift to the higher affinity form. This would give the appearance of increasing overall affinity as more ligand was bound, even if all of the sites on each conformation were independent (and so had the same affinity for the ligand, regardless of the number of the other sites that were already occupied).

This argument leads naturally to scheme 5, which we refer to, for brevity, as the flip mechanism (Figs. 3, scheme 5, 12A). This mechanism postulates that agonist binding can favor a conformation change that occurs before, and separately from, the channel opening. In the spirit of Monod et al. (1965), this conformation change is concerted, and binding to each conformation is independent. Thus there are only two equilibrium constants for binding, denoted K_R for the resting conformation (R) and K_F for the flipped conformation (F). As a result, this mechanism has 14 free parameters, 4 fewer than the other mechanisms with 3 open and 7 shut states that have been tried so far.

In this mechanism the additional closed states are between the resting state of the receptor and the open states (so they could, for example, correspond to the physical process of domain closure around a bound agonist molecule; see Discussion). Each ligation state of the resting state of the protein (R) can switch to a different closed state (F) while the channel is still shut. It is from these F states that the protein can reach the open state (F^*). The flip mechanism is appealing in that it provides a physical explanation for how binding sites that are so far apart appear to interact strongly, i.e., how binding to one can affect binding to another, and does so with fewer free parameters than other mechanisms that fit well.

The experimental results were fitted with scheme 5 with the constraint that affinity for the three binding sites remains the same as long as the protein stays in the same conformation (R or F). The different conformations of the shut protein have the same dissociation constants (K_R and K_F, respectively), regardless of how many other binding sites are already occupied. This is ensured by applying the following constraints while fitting:

(7)

Two rate constants (₁ and ₃) (Fig. 3, scheme 5) were constrained to satisfy the requirement of microscopic reversibility for the two cycles in the scheme. As usual, statistical factors are included in the rate constants to take into account the number of available sites at each binding step.

The fit of the flip mechanism, which has 14 free parameters, is shown in Figure 8. The predicted dwell-time (HJC) distributions are in excellent agreement with the data. In particular, the shut-time fast component is predicted extremely well, with no appreciable decrease in quality when compared with the fit of scheme 3 with 18 free parameters. The open-shut correlations are also well accounted for at all concentrations.

This fit provides the best agreement with the data obtained among the schemes that had 14 (or fewer) free parameters and is better than some that had more free parameters. The predicted apparent P_open curve fits quite well, and the predicted Hill slope (at the EC₅₀) is 2.44 (Table 5), a reasonable value although somewhat smaller than that found from the fit of the Hill equation in Figure 2. It is, of course, the quality of the fit of the whole apparent P_open curve that matters, not just the Hill slope values, and it must be borne in mind that the Hill equation is not a correct description of the data (see section on the P_open curve).

View this table: [in this window] [in a new window]   Table 5. Estimated parameters from the fit of the flip mechanism to single-channel data from heteromeric receptors

 
Unfortunately, t