Gating Reaction Mechanisms for NMDA Receptor Channels

Expression of cRNA in oocytes

RNA was transcribed in vitro from cDNA by standard methods. To express NMDARs, the RNAs of rat NR1a and NR2A were coinjected at a nominal ratio of 1:1 in Xenopus oocytes. Patch-clamp recordings were made 3–10 d after injection. A detailed description of the molecular biology and expression protocols has been described previously (Premkumar and Auerbach, 1996).

Electrophysiological recording

Single-channel and macroscopic currents were recorded from outside-out or cell-attached patches (Hamill et al., 1981). The temperature was 23–25°C. Agonists were contained in the pipette solution (cell-attached patches) or applied to outside-out patches by using a fast perfusion system. The perfusion pipette was pulled from double-barreled glass tubing (tip diameter, 200 μm) and attached to a bimorph actuator (model QP22B; ACX, Cambridge, MA) using epoxy resin. External solutions were delivered to each of the two barrels by using air pressure. The actuator was controlled by QUB software (http://www.qub.buffalo.edu) to move the solution interface across the tip of patch pipette. The command voltage pulses were low-pass filtered at 150 Hz. The actual solution-exchanging rate was routinely measured on the same patch pipette at the end of each recording by open-tip response (Jonas, 1995). The 10–90% rise time of this system was ∼200 μs (see Fig. 4a, inset).

Patch pipettes were pulled from borosilicate capillary glass (Sutter Instruments, Novato, CA), coated with Sylgard 184 (Dow Corning, Midland, MI), and fire-polished before recording. The pipette resistance ranged from 0.5 to 2 MΩ for macropatches and 10 to 20 Ω for single-channel recording. The pipette solution contained the following (in mm): 100 Na gluconate, 10 NaCl, 10 BAPTA, 10 HEPES, 2 K₂ATP, and 0.25 GTP. The pH of the pipette solution was adjusted to 7.3 by using NaOH. The extracellular solution contained the following (in mm): 100 NaCl, 2 KCl, 1 EDTA (to eliminate Mg²⁺ block), 10 N-(2-hydroxyethyl)-piperazine-N[E-(4-butanesulfonic acid)], pH adjusted to 8 (to minimize proton inhibition) by using NaOH. All chemicals were purchased from Sigma (St. Louis, MO) or Aldrich (Milwaukee, WI). Currents were amplified (PC-505B; Warner Instruments, Hamden, CT), low-pass filtered at 20 kHz (eight-pole Bessel; LPF-8; Warner Instruments), and digitized at 40 kHz directly to a hard disk using a MIO-16E digital board (National Instruments, Austin, TX).

Data analysis

Conductance level detection and amplitude histograms. The conductance levels of NMDARs were detected by variance–mean analysis (Patlak, 1988). A window of length N sampling points was centered over each sample of current, and the variance (σ²) and mean amplitude (I) of the current within the window were calculated. The window was advanced by one sample, and the pair of σ² and I values was again calculated, with this process repeated for the entire record. If the sliding window covers more than one conductance level, the variance will increase. Changes in conductance were identified by the transitions in the variance points relative to that of the baseline (σ²_b). This analysis was performed by a program written in OriginC language (OriginLab, Northampton, MA).

Simulation, idealization, and maximum likelihood fitting. QUB software was used for simulation, idealization, and modeling of single-channel currents. Data were corrected for slow and nonperiodic baseline drifts using manually specified piecewise linear functions and then idealized by a segmental k-means method (Qin, 2004). Clusters of single-channel current openings were chosen by excluding the longest closed events (desensitization) by invoking a critical shut time (t_crit) that was based on an equal number of misclassified events (Magleby and Pallotta, 1983; Clapham and Neher, 1984). Bursts from patches having only one active channel were concatenated as a continuous “active-time” record. To test for kinetic homogeneity, this record was divided into 1 s segments and idealized by using a two-state (C⇆O) model to calculate a segment mean open and closed time. The kinetic modeling was based on clusters rather than the segmented record. The currents were idealized using the segmental k-means (SKM) algorithm and the rate constants for a given model were estimated by using a full maximum likelihood approach (Qin et al., 1996; Qin, 2004) after imposing a “dead time” of two to three sampling intervals (50–75 μs). The dwell times given by the SKM method are integer multiples of the sampling interval (25 μs).

Correlation analysis. To help ascertain the connectivity of the states in the model, two-dimensional (2D) dependency plot analysis (Magleby and Song, 1992) and open–open, closed–closed, and open–closed autocorrelation analyses (Fredkin et al., 1985; Labarca et al., 1985) were performed on idealized single-channel data without correcting for missed events. The autocorrelation coefficient for two intervals T₁ and T₂ in an idealized single-channel current is as follows: (1) where the means are μ₁ = E(T₁) and μ₂ = E(T₂).

Thus, the autocorrelation coefficient between an open (or closed) interval T and the kth open (or closed) interval T′ behind is as follows: (2) where μ is the mean and σ² is the variance of open (or closed) dwell times in the recording. The autocorrelation coefficient between an open interval T_O and the kth closed interval T_C behind is as follows: (3) According to theorem 5.1 of Fredkin et al. (1985), the autocorrelation coefficient decays geometrically with increasing lag k if there is more than one entry/exit state between open and closed aggregates. The correlation coefficients were used to test the activation mechanisms of ACh receptor in adult frog muscle (Colquhoun and Sakmann, 1985).

The 2D dependency, d(t_O,t_S), is as follows: (4) where f(t_O,t_S) is the observed 2D probability density function and f ′(t_O,t_S) = f_O(t_O)f_S(t_S) is the expected 2D probability density function if there is no dependence between paired open and closed intervals. To create the 2D dwell-time distribution of adjacent open and shut intervals, the logs of the durations of each open interval and the following closed interval were used to locate a bin on the x–y plane, with the z-axis indicating the square root of the number of interval pairs in each bin (Sigworth and Sine, 1987). The 2D dwell-time distributions were then smoothed by using the weighted average value of nine bins in a 3 × 3 array with three bins per side moving through the x–y plane (Song and Magleby, 1994). The weighted average is calculated as follows: (5) where a₁₁ through a₃₃ are the elements in the moving array: (6) Programs written in OriginC language were used for the correlation analyses and 2D dependency plots. Autocorrelation coefficients of open–open, closed–closed, and open–closed interval pairs predicted by kinetic models (Colquhoun and Hawkes, 1987) were calculated by using a worksheet written in Maple 7 (Waterloo Maple, Waterloo, Ontario, Canada).

Macroscopic current analysis. Normalized macroscopic currents were computed from each kinetic model (Colquhoun and Hawkes, 1995a,b) by using a Maple 7 worksheet. The 5–95% rising and decay phases of the computed and experimentally recorded macroscopic currents were compared by eye and by calculating the deviation of simulated response from experimental current by using the following function: (7) All data are expressed as the mean ± SD.

Single-channel activity of NMDARs

Under physiological conditions, the kinetic behavior of NMDARs at the single-channel level is difficult to interpret because of the binding of multiple agonists and inhibition by several types of ions, including protons and Mg²⁺. To simplify matters, we used supermaximal concentrations of glutamate and glycine (to saturate the binding sites at steady state or to maximally accelerate binding after a concentration jump) and high pH, divalent cation-free extracellular solutions (to reduce or eliminate ion inhibition). Figure 1a shows single-channel currents from an outside-out patch exposed to 1 mm glutamate and 100 μm glycine. Figure 1b shows the corresponding variance–mean amplitude histogram fitted by the sum of two Gaussian components, one for the ion-conductive level and the other for the nonconductive level. Although brief superconductance- and subconductancelevel events occasionally appeared (Fig. 1a, bottom traces), they were rare and were not analyzed further. The mean conductance of NMDARs measured from six patches was 73.2 ± 2.3 pS, which is ∼40% greater than in physiological solutions containing 1 mm CaCl₂ (Stern et al., 1992, 1994).

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Figure 1.

Single-channel activity of NMDARs elicited by 1 mm glutamate and 100 μm glycine in the presence of 1 mm EDTA. a, Continuous record from an outside-out patch at –80 mV. Occasional alternative conductance levels are displayed on an expanded time scale below. b, Amplitude histogram constructed from activation bursts and the corresponding mean–variance analysis (inset, 10-sample sliding window). There is primarily one conducting amplitude level with a mean of 5.99 pA. c, The mean closed and open durations for each second of active time are stable. An interval duration stability analysis from a cell-attached patch is shown (inset). d, Duration distributions of intracluster closed (top) and open (bottom) intervals. Mean lifetimes and relative areas of each exponential component are shown (right). fract., Fraction.

The activation of NMDARs at saturating agonist concentrations occurs as groups of closely spaced openings (“clusters”) separated by sojourns in long-lived nonconducting states that reflect desensitization (Sakmann et al., 1980; Banke and Traynelis, 2003; Popescu and Auerbach, 2003). The desensitized sojourns were excluded from our analyses after invoking a t_crit, and only the intracluster currents were considered to be part of the overall gating isomerization event. NR1/NR2A NMDARs expressed in human embryonic kidney (HEK) cells [and cotransfected with green fluorescent protein (GFP)] adopt at least three activity patterns (“modes”) that have characteristic mean open times (Popescu and Auerbach, 2003). However, in our experiments, these same subunits (expressed in oocytes by mRNA injection) gave rise to NMDARs that were kinetically homogeneous. As shown in Figure 1c, the mean open and closed times for each second of “active time” were, in general, constant throughout the recording period (>20 min). Similar results were obtained from data recorded from cell-attached patches (Fig. 1c, inset).

Distributions of intracluster closed and open intervals recorded from outside-out patches were best fitted by three and two exponential components, respectively (Fig. 1d, Table 1). The three closed components had mean time constants (relative areas) of 0.16 ± 0.014 ms (52 ± 2.1%), 1.42 ± 0.31 ms (17 ± 6.6%), and 3.53 ± 0.31 ms (31 ± 5.0%). The corresponding values for the two open components were 0.18 ± 0.012 ms (12 ± 2.1%) and 13.61 ± 2.01 ms (88 ± 2.1%) (n = 4). These distributions are similar to those of M-mode NR1a/NR2A NMDARs expressed in HEK cells (Popescu and Auerbach, 2003). However, the mean time constants of the two briefest closed components were longer than those recorded in the presence of low concentrations of agonist and divalent cations (Stern et al., 1994; Wyllie et al., 1998). It is possible that this difference is attributable to the absence of fast Mg²⁺ block in our divalent cation-free solution.

The interval duration distributions of intracluster, single-channel events recorded from cell-attached patches were also well fitted by three closed and two open components. The mean time constants (relative areas) of three closed components were 0.075 ± 0.021 ms (50 ± 1%), 0.48 ± 0.1 ms (28 ± 7%), and 4.29 ± 0.14 ms (22 ± 7%). For the two open components, these values were 0.42 ± 0.23 ms (14 ± 9%) and 10.63 ± 4.41 ms (86 ± 12%) (n = 3). The distributions from cell-attached and outside-out recordings were similar. The kinetic studies described below were mainly derived from analyses of currents from outside-out patches.

Kinetic modeling of single-channel data

The duration distributions of intraburst events indicate that a parsimonious activation scheme for NMDARs must have three closed and two open states (Colquhoun and Hawkes, 1981, 1982). These five states can be arranged to constitute 15 noncyclic kinetic models, six of which have coupled open states (Table 2). All 15 models were fitted to the intracluster interval durations (four patches) by using a full maximum likelihood approach, with all eight rate constants allowed to vary. Seven of these models gave an equivalent maximum log likelihood (LL) value that was higher (>10 LL units) than those from the other eight models (Table 3). The models having coupled open states always gave higher log likelihood values than those with uncoupled open states.

The seven best models can be further classified by their connectivities. In models 4, 5, and 7, there are two entry/exit states between the open and closed aggregates (O₁ and O₂), whereas in models 1, 8, 11, and 12, there is only one (O₁). A model with connectivity >1 predicts the existence of an autocorrelation between open, closed, or open–closed interval pairs in single-channel data (Fredkin et al., 1985; Colquhoun and Hawkes, 1987).

Autocorrelation coefficients predicted by models 4, 5, and 7 were calculated by a method provided by Colquhoun and Hawkes (1987). As shown in Figure 2a, model 4 predicts a negative correlation between open–closed pairs, a positive (but smaller) correlation between open–open pairs and a weak, positive correlation between closed–closed pairs. Similar predictions hold for the other two models having a connectivity of 2 (models 5 and 7). The open–closed correlation coefficients for lag k = 1 predicted by models 4, 5, and 7 were approximately –0.03, which could be readily detected in data simulated from these models when the number of intervals was >9000 (Fig. 2b). However, there were no significant autocorrelations between open–open, closed–closed, or open–closed interval pairs in the experimental NMDAR currents. As illustrated in Figure 2d, all three types of correlation coefficients in an activation cluster recorded from an outside-out patch were normally distributed around zero. Similar results were obtained from several long activation clusters having >9000 intervals, from cell-attached patches (Fig. 2d, inset). Moreover, the 2D dependency plots of the experimental current intervals did not show any significant excess or deficit in open–closed pairs within clusters (Fig. 2c). The above correlation analyses and dependency plots were not corrected for missed events. However, the consequence of this omission may not be crucial, because no correlations were detected in the experimental data. Thus, the results indicate that the activation model for NMDAR should have only one entry/exit state through which the open and closed aggregates communicate. Based on these analyses, four models (1, 8, 11, and 12) were selected for additional consideration.

In theory, the full maximum likelihood analysis should take into account all of the information in a single-channel record, including dependency between successive events in the record (Colquhoun and Hawkes, 1995a). However, spurious events generated by noise, errors in detection, and rare channel behaviors limit the usefulness of the LL discriminator. Dependency and autocorrelation analyses are valuable complements to maximum likelihood fitting in model selection (Magleby and Song, 1992; Colquhoun and Hawkes, 1995a; Gil et al., 2001).

Predictions of macroscopic current properties

The four best schemes can be further classified by the number of closed states that must be visited (after full binding) before the first open state is reached. This property of the reaction scheme predicts distinguishable time courses of the macroscopic current after the fast application of a high concentration of agonists. As shown in Figure 3, if NMDARs must pass through two closed states (e.g., model 8, starting from C₁), the rising phase of macroscopic current should be sigmoidal, whereas if receptors have to pass through only one closed state (e.g., model 12), then the rising phase of macroscopic current should be exponential. We sought to discriminate between models by comparing their predictions on the time course of macroscopic currents induced by a step change in the agonist concentration. Note that the models tested here pertain to only the gating reaction; thus, the NMDAR macroscopic currents should exclude ligand binding and desensitization steps.

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Figure 2.

Correlation analyses of NMDAR-idealized single-channel currents, from experimental and simulated currents. a, Autocorrelation coefficients of open, closed, and open–closed interval pairs predicted by model 4. b, Autocorrelation coefficients of open–closed interval pairs simulated by using models4, 5, and 7 (total number of events, n = 11,000). The dashed horizontal lines are , which is plus or minus twice the SE of the estimate in the case of white noise. c, 2D dependency plot of 7629 intraburst intervals from one outside-out patch. There is no significant dependency between adjacent open and closed intervals. d, Autocorrelation coefficients for the open, closed, and open–closed interval pairs from experimental NMDAR current cluster recorded from an outside-out patch (n = 3274). Autocorrelation coefficients for the open–open, closed–closed, and open–closed interval pairs from one activation cluster recorded from a cell-attached patch are shown (n = 9760) (inset). K, Step size; ρ(K), autocorrelation coefficient.

Saturating concentrations of agonists were applied by a fast perfusion system (solution change <200 μs) on outside-out macropatches (Fig. 4a). The rising phase of evoked macroscopic current was <15 ms (Fig. 4), which is much faster than the time constant of NMDAR desensitization (>100 ms) (Vicini et al., 1998; Villarroel et al., 1998). To confirm that the rising phase was independent of binding steps, a series of jumps from solutions containing various concentrations of glycine to a solution with 1 mm glutamate plus 100 μm glycine was performed (Fig. 4b). The rising phases were identical, although the glycine binding steps were different in these jumps. This indicates that that glycine binding did not contribute significantly to the rising phase of NMDAR current at saturating concentration. We could not perform the complementary experiment with glutamate binding, because it is difficult to eliminate background contamination of glycine (Kleckner and Dingledine, 1988). However, the glutamate equilibrium dissociation constant is ∼3 μm, and the association rate constant is ∼10⁸m^–1 · s^–1 (Benveniste and Mayer, 1991a,b; Lester and Jahr, 1992; Popescu et al., 2004), which suggests that we could expect full saturation of the binding sites within ∼200 μs. We therefore conclude that the rising phase of the macroscopic current evoked by the fast application of saturating concentrations of agonists can be used to examine the predictions by various models of the gating reaction.

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Figure 3.

Time course of the macroscopic current predicted by models having different numbers of preopening closed states. The solid line was simulated from model 8 with the assumption that activation starts from C₁. The dashed line was simulated from model 12 with C₃ as the starting point. The rate constants used for simulation were obtained by globally fitting activation bursts from four patches.

The best predictions by models 1, 8, 11, and 12 are superimposed on normalized NMDAR macroscopic currents in Figure 4c. The rising phase of NMDAR current was clearly sigmoidal, in agreement with models 8 and 11 using the rate constants estimated from modeling single-channel interval data. Models 1 and 12 both predicted an exponential rising phase, although in model 12, there were two closed states before the first open state. Overall, the deviations of the predictions by models 8 and 11 were much lower than those of predictions by models 1 and 12 (Fig. 4d).

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Figure 4.

The rising phase of NMDAR macroscopic current evoked by fast application of saturating concentrations of agonists is satisfied by models 8 and 11. a, Macroscopic current induced by 1 mm glutamate plus 100 μm glycine applied to an outside-out macropatch (–60 mV). The top trace is the command pulse indicating agonist application. The inset is the open-tip response recorded on the same patch pipette, on expanded scale. b, Macroscopic currents after a concentration jump from solutions containing different concentrations of glycine with no glutamate to a solution containing 100 μm glycine and 1 mm glutamate. Alignment of the 5–95 % rising phases of the currents is shown (inset). c, Comparison of experimental and simulated macroscopic currents. Only the best result from each model was used for comparison. The simulated currents from models 8 and 11 overlap. d, Deviations calculated by Equation 7 of predicted currents from experimental current. Models 8 and 11 provide equivalent and superior descriptions of the experimental current. Error bars indicate SE.

Combining the noncyclic models

After the above three rounds of model selection, we were left with two noncyclic, 3C2O models that provided adequate and equally good descriptions for the activation of NMDAR, at both the microscopic and macroscopic levels. These two models differ in the disposition of closed state C₃, which is either connected only to O₁ (model 8) or interposed between C₂ and O₁ (model 11). We could not use statistical tests to further distinguish these two models; hence, we combined them into a single cyclic scheme that preserves the key features of both two noncyclic models, namely coupled open states, a single gateway between closed and open aggregates, and multiple preopening closed states. Detailed balance was enforced for the cycle in model 16, which had one extra free parameter compared with models 8 and 11.

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Figure 5.

Both microscopic and macroscopic currents are described by model 16. a, Histograms of intraburst interval distributions. The solid lines are calculated from the model. b, Simulated (solid line) and experimental current decays after a 100 ms pulse of 1 mm glutamate plus 100 μm glycine. Binding and desensitization states (both connected to C₁) were added to model 16. The dashed line is the fit of experimental current by the sum of two exponentials. c, Simulations of the current response to short pulses (1, 2, 4, and 8 ms) of saturating agonists (model 16). The time to peak (T_peak) is the same for all pulse durations. Currents are staggered vertically for display purposes. The inset is the superimposed view of these traces.

Figure 5a shows that the experimental intracluster closed (top panel) and open (bottom panel) distributions are in good agreement with those predicted by model 16 (continuous lines). In addition, the autocorrelation function of data simulated from this model has the same flat shape as those obtained from NMDAR activation clusters. Model 16 also accurately predicts the time course of macroscopic currents evoked by fast application of agonists when C₁ is the starting state (data not shown). Although neither the LL values obtained from single-channel kinetic modeling nor the deviations of the macroscopic currents from those predicted by the model were significantly improved by the extra free parameter, model 16 is appealing in that it provides an unambiguous gating reaction mechanism for NMDARs. According to this scheme, there are two alternative conformational pathways in the gating reaction (C₁C₂O₁ or C₁C₃O₁).

To further evaluate the predictions of model 16, we simulated the decay phase of the macroscopic current after a 100 ms pulse of saturating agonists and compared it with experimentally measured decays. This decay depends on desensitization and ligand dissociation as well as the gating conformational changes (Lester and Jahr, 1992); hence, model 16 alone is insufficient. Using values from previous studies (Benveniste et al., 1990; Lester and Jahr, 1992; Popescu and Auerbach, 2003), we modified model 16 by adding binding and desensitizing steps. The rate constants are in 1/seconds. B represents all less than fully liganded NMDARs, and D represents fully liganded, desensitized NMDARs. The agonist association and dissociation rate constants are k_ON and k_OFF, and the entry and recovery rate constants for desensitization are k_D and k_R. The dissociation rate constant k_OFF was chosen as 11.4 s^–1 (2 × k_{OFF_Glu} + 2 × k_{OFF_Gly}) (Benveniste et al., 1990; Lester and Jahr, 1992), and the desensitization/recovery rate constants were set at 4/1 s^–1 (Popescu and Auerbach, 2003). The remaining rate constants were globally fitted using intervals within clusters from four outside-out patches. The desensitized state was connected, in turn, to each state of the scheme, and the best prediction of the decay phase of the NMDAR macroscopic current was obtained when D was connected to C₁ (Fig. 5c). The decay of NMDAR macroscopic current evoked by 100 ms pulse of 1 mm glutamate and 100 μm glycine was fitted by the sum of two exponentials, with time constants (relative amplitudes) of 92.4 ± 0.27 ms (85 ± 0.3%) and 702.2 ± 46.8 ms (15 ± 0.2%), respectively (n = 3). The corresponding values for the best match with D connected to C₁ were 88 ms (83%) and 899 ms (17%). The next best match was D connected to C₃, with values of 87 ms (65%) and 960 ms (35%). The predictions with D connected to states C₂,O₁, and O₂ were significantly worse (only a single exponential). This result suggests that NMDAR desensitization occurs mainly from C₁. Thus, according to model 16, there are three possible fully liganded pathways out of the first nonconducting state: two that lead to opening (after passing through a preopening closed state) and one that leads to desensitization.

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Model 16

We also simulated the response of NMDARs to short pulses of saturating glutamate (1–10 ms) using model 16. The model predicts that the time it takes for the NMDAR current to reach its peak is independent of the length of pulse (>1 ms). As shown in Figure 5c, after the binding of agonists, the time to peak was 12.6 ms for currents evoked by 1, 2, 4, and 8 ms pulses of saturating agonists. This conclusion is in accord with the observation that a pulse of saturating glutamate as short as 0.8 ms produces the maximal response of NMDARs (Lester and Jahr, 1992).

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Model 16a

Model 16 shares a structure with the kinetic scheme proposed by Banke and Traynelis for the gating of NMDAR (Banke and Traynelis, 2003). We modified their scheme by adding a second, coupled open state. Although model 17 contains four rather than three closed states, the pairs of rate constants on parallel sides of the cycle are constrained to be equal, yielding only eight free parameters. The optimal rate constants are shown in model 17.

In four patches, the average rate constants for the C₁⇆C₂ and C₂⇆C₄ steps in model 17 were essentially the same as the C₁⇆C₂ and C₂⇆C₃ rate constants obtained by using the linear, CCCOO scheme (model 11). Our estimate of the C₂⇆C₄ equilibrium constant (0.35) is >50 times smaller than that reported for NR1/NR2A NMDARs expressed in HEK cells at pH 7.3 (3140/174 s^–1 = 18) (Erreger et al., 2005). Such discrepancy cannot be completely accounted for by the different pHs (8.0 vs 7.3) (Banke et al., 2005) and is perhaps the result of different expression systems.

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Model 17