Receptor Occupancy and Channel-opening Kinetics

AMPA glutamate ion channels are tetrameric receptors in which activation to form the open channel depends on the binding of possibly multiple glutamate molecules. However, it is unclear whether AMPA receptors bound with a different number of glutamate molecules (i.e. one being the minimal and four being the maximal number of glutamate molecules) open the channels with different kinetic constants. Using a laser pulse photolysis technique that provides microsecond time resolution, we investigated the channel-opening kinetic mechanism of a nondesensitizing AMPA receptor, i.e. GluR1Qflip L497Y or a leucine-to-tyrosine substitution mutant, in the entire range of glutamate concentrations to ensure receptor saturation. We found that the minimal number of glutamate molecules required to bind to the receptor and to open the channel is two (or n = 2), and that the entire channel-opening kinetics can be adequately described by just one channel-opening rate constant, kop, which correlates to n = 2. This result suggests that higher receptor occupancy (n = 3 and 4) does not give rise to different kop values or, at least, not appreciably if the kop values are different. Furthermore, compared with the wild-type receptor (Li, G., and Niu, L. (2004) J. Biol. Chem. 279, 3990-3997), the channel-opening and channel-closing rate constants of the mutant are 1.5- and 13-fold smaller, respectively. Thus, the major effect of this mutation is to decrease the channel-closing rate constant by stabilizing the open channel conformation.

The ␣-amino-3-hydroxy-5-methyl-4-isoxazole-propionic acid (AMPA) 3 glutamate receptors are ligand-gated ion channels that are activated by binding of neurotransmitter glutamate (1,2). An AMPA receptor is a tetrameric assembly with each subunit containing a glutamate binding site. The receptor can adopt multiple conductance levels, especially at high receptor occupancy, as observed in the single-channel records of wild-type and mutant recombinant receptors (3,4) as well as native AMPA receptors (5). However, it remains unclear whether receptor occupancy plays a significant role in determining the kinetic constants for an ensemble rate process of channel opening as a function of glutamate concentration. The ensemble rate process is manifested in a whole-cell current response to the binding of glutamate in vitro and best represents the glutamatergic synaptic activity in vivo, such as excitatory postsynaptic current. Therefore, determining the number of glutamate molecules bound to a receptor or the percentage of the receptor occupancy pertinent to the rate of the channel opening is a basic question to be answered for understanding the function of AMPA receptors.
To address this question, we investigated the channel-opening kinetics for a GluR1 AMPA receptor channel carrying a substitution of leucine (L) to tyrosine (Y) or L497Y. The discovery of this point mutation by Stern-Bach et al. (3) was a significant event in understanding the structure and function relationship of AMPA receptors in that (a) phenomenologically, the single leucine-to-tyrosine substitution renders the homomeric receptor channels virtually non-desensitizing (3), and (b) the phenotypic effect of this mutation is conserved at equivalent positions in all AMPA receptor subunits, i.e. GluR1-4 (6 -8). Furthermore, this mutation is thought to have no effect on either the main conductance level or the channel opening probability (3,7,9). From a crystallographic study, Sun et al. (6) revealed that this mutation resides in the receptor dimer interface of a tetrameric assembly and suggested that the rearrangement of the dimer interface is linked to receptor desensitization (6). Accordingly, the lack of desensitization for the mutant is ascribable to this mutation that prevents the dimer interface movement. In the present study, we expressed GluR1Q flip L497Y mutant in HEK-293 cells and measured the channelopening rate using a laser pulse photolysis technique and a photolabile precursor of glutamate or caged glutamate (␥-O-(␣carboxy-2-nitrobenzyl)glutamate). Photolysis of the caged glutamate liberates free glutamate with a t1 ⁄ 2 of ϳ30 s (10). Using this technique we previously determined the rate constants of the channel opening for the wild-type GluR1Q flip receptor (11). Therefore, comparison of the rate constants of the mutant with the wild-type receptor may reveal the effect of this mutation on the channel-opening process.
What were the advantages in choosing this mutant for this study? First, because the mutant receptor was non-desensitizing, we could determine the concentration of photolytically released glutamate for kinetic analysis by directly calibrating the peak current amplitude observed in the laser pulse photol-ysis with the peak current amplitude observed in solution flow measurement with known glutamate concentrations. This direct calibration would not be possible in studying the wildtype receptor because of its rapid desensitization. Second, because the mutant channel had a higher affinity to glutamate or a lowered EC 50 value (9,12), we were able to measure the observed channel-opening rate in the entire range of glutamate concentrations and thus determine the putative effect of different receptor occupancy on the channel-opening rate constant. Again, this was not possible in the study of the wild-type receptor (11).

EXPERIMENTAL PROCEDURES
Cell Culture-The cDNA encoding the GluR1Q flip L497Y mutant receptor was kindly provided by Dr. Mark Fleck. The homomeric GluR1Q flip L497Y mutant was expressed in HEK-293 cells by transient transfection as described (11), except that Lipofectamine (Invitrogen) was used. The weight ratio of the plasmid of GluR1Q flip L497Y to that of green fluorescent protein was 10:1, and 3-5 g of GluR1Q flip L497Y cDNA was used in transfection. Green fluorescent protein was used as a transfection marker for recording. The cells were maintained in Dulbecco's modified Eagle's medium at 37°C and 5% CO 2 . The cells were used for recording from 48 h after transfection.
Whole-cell Recording and Laser Pulse Photolysis-The whole-cell recordings and the laser pulse photolysis measurements were at Ϫ60 mV and 22°C, and the procedures were described previously (11). Briefly, the electrode had a resistance of ϳ3 megohms when filled with electrode solution, which contained (in mM) 110 CsF, 30 CsCl, 4 NaCl, 0.5 CaCl 2 , 5 EGTA, and 10 HEPES (pH 7.4 adjusted by CsOH). The external solution contained (in mM) 150 NaCl, 3 KCl, 1 CaCl 2 , 1 MgCl 2 , 10 HEPES (pH 7.4). A U-tube device (11) was used to apply glutamate to a cell, and the resulting rise time of the glutamateinduced whole-cell current response (10 -90%) observed was ϳ2 ms. The current traces were sampled at 5-50 kHz frequency and filtered at 2-20 kHz by an 8-pole Bessel filter. The data were acquired using pCLAMP 8 (Axon Instruments). In the laser pulse photolysis measurements, the caged glutamate (Invitrogen) was photolyzed using a 355 nm laser pulse from a Minilite II pulsed Q-switched Nd:YAG laser (Continuum). To determine the concentration of photolytically released glutamate, at least two free glutamate solutions with known concentrations were applied to a cell to calibrate the current amplitudes from the same cell before and after a laser photolysis. The current amplitudes obtained from known glutamate concentrations were compared with the amplitude evoked by photolytically released glutamate (11,13,14).
Data Analysis-Based on the kinetic mechanism of channel opening (Fig. 1), the observed rate constant, k obs , of the wholecell current rise in response to glutamate is given by Equation 1.
All other terms are defined in the Fig. 1 legend. In deriving Equation 1, the rate of ligand binding was assumed to be fast relative to the rate of channel opening. This assumption was supported by the consistent observation of a single first-order rate, in Equation 2, for the whole-cell current rise in the entire range of glutamate concentrations (see Fig. 2 results), where I t and I A represent the whole-cell current amplitude at time t and the maximum current amplitude. Using Equation 2, the k obs at a given glutamate concentration was calculated. A set of k cl and k op as well as K 1 corresponding to a particular number of ligand(s) bound, i.e. n ϭ 1-4 (see Fig. 1 legend), was obtained using Equation 1. As an independent measure, K 1 was estimated from the dose-response relationship, shown in Equation 3, based on the general mechanism of channel opening (Fig. 1).
In Equation 3, I M is the current per mole of receptor, R M the number of moles of receptors on the cell surface, and ⌽ Ϫ1 the channel-opening equilibrium constant. Unless otherwise noted, at least triplicate sets of data from three cells were collected in all measurements. Linear regression and nonlinear fitting were performed using Origin 7 software (Origin Lab, Northampton, MA).
Using the ⌽ value analysis based on the transition state theory (15)(16)(17), we calculated the change of the free energy of the transition state for the mutant and the wild-type receptor using Equation 4.
Here ⌽ is the ratio of change of free energy of activation for opening of the channel, ⌬⌬G TS-C , to the equilibrium free energy of channel opening, ⌬⌬G O-C . The ⌬⌬G values were calculated by Equation 5 using k op and k cl values for both the mutant and the wild-type receptors.
In Equation 5, R is the gas constant, T the temperature in Kelvin scale, h the Planck's constant, the Boltzmann constant, and k the rate constant. Here, A represents the active, unliganded form of the receptor, L the ligand or glutamate, AL n the closed channel state with n ligand molecules bound, and AL n the open channel state. The number of glutamate molecules to bind to the receptor and to open its channel, n, can be from 1 to 4, assuming that a receptor is a tetrameric complex and each subunit has one glutamate binding site. It is further assumed that a ligand does not dissociate from the open channel state. The k op and k cl are the channel-opening and channel-closing rate constants, respectively. For simplicity and without contrary evidence, it is assumed that glutamate binds with equal affinity or K 1 , the intrinsic equilibrium dissociation constant, at all binding steps.

RESULTS
Channel-opening Kinetics for GluR1Q flip L497Y-A glutamate-induced, whole-cell current from the mutant channel exhibited a sustained current response, whereas the wild-type response showed rapid desensitization ( Fig. 2A). This is consistent with the original observation by Stern-Bach et al. (3). Only when the glutamate concentration approached saturation did the mutant channel desensitize. For instance, at 0.5 mM glutamate, a saturating concentration for the mutant, the desensitization rate constant was 25 s Ϫ1 . In contrast, the wild-type GluR1Q flip homomeric receptor channel desensitizes rapidly, with a maximum rate constant of ϳ300 s Ϫ1 (11,18,19).
Using the laser pulse photolysis technique, we measured the channel-opening rate for the GluR1Q flip L497Y channel as a function of glutamate concentration. Photolysis of the caged glutamate led to a whole-cell current rise (Fig.  2B). At least 95% of the whole-cell current rise followed a single exponential rate process (i.e. Equation 2 under "Experimental Procedures") and remained so in the entire range of glutamate concentrations, i.e. from 10 to 140 M. The range of the glutamate concentration corresponded to 14 -92% of the fraction of the open channel (see the dose-response curve in Fig. 3). That a monoexponential rate for channel opening was persistently observed throughout the entire range of glutamate concentrations supported the assumption that the rate of ligand binding was fast relative to the rate of channel opening. Therefore, the current rise reflected the channel opening (Fig. 2B). Based on this assumption and a general mechanism of channel opening (in Fig. 1), Equation 1 was derived in which k obs represented the rate of transition from the AL n state to its corresponding open state, AL n . Note that Equation 1 represents a general formulation of the rate law, taking into account all of the possible number of ligands that can bind to and open the channel, namely n ϭ 1-4. The permitted values of n in integer are based on the notion that an AMPA receptor is a tetramer and each subunit contains one ligand binding site (7,20).
The Minimal Number of Glutamate Molecules Bound to the Receptor to Open the Channel Is Two-The rate of channel opening as a function of glutamate concentration (Fig. 2C) was analyzed as described below. First, using Equation 1, we found that the best nonlinear fit returned the value of n, the number of glutamate molecules bound to open the channel, to be close to 2 (see the legend for Fig. 2C). Along with this analysis, we obtained a set of k cl , k op , and K 1 as the best fit values for the channel-opening kinetic mechanism.
From the same analysis, a k cl value of 160 Ϯ 91 s Ϫ1 was obtained (Fig. 2 legend). This value agreed with the rate constant we observed at the lower end of the glutamate concentration range, namely k obs Ϸ 200 s Ϫ1 (Fig. 2C). This was expected because, when L Ͻ Ͻ K 1 , Equation 1 was reduced to k obs Ϸ k cl suggesting that (a) the rate constant at a low glutamate concentration would reflect k cl , and (b) the value of k cl was independent of whatever might be the n value. Based on this reasoning, we further examined our regression analysis by fixing k cl (Table 1). In so doing, we reduced one variable, which enabled us to improve the regression analysis. Using various k cl values close to 160 s Ϫ1 , we found that the fitted values of n continued to be tightly close to 2 (Table 1). These results were consistent with n ϭ 2 being the best fit to our data in the entire range of glutamate concentrations.
The analysis described above also yielded a K 1 of 70 Ϯ 41 M (see Fig. 2 legend). To independently verify this value, we deter-   mined the dose-response curve using the amplitude of the whole-cell current (Fig. 3). The regression analysis of the doseresponse relationship using Equation 3 yielded the best fit of K 1 to be 68 Ϯ 38 M (Fig. 3 legend), consistent with the value obtained from the rate measurement (Fig. 2C).
We also noted that the value of k op was unchanged even when different k cl values were used in data analysis (Table 1); the same was true for K 1 . We then asked whether k op would change with different n values. The results show that k op remained invariant when n increased ( Table 2 and supplemental Fig. 1), presumably with a concomitant increase of glutamate concentration and receptor occupancy (5,7). Taken together, our results (from Fig. 1C and Tables 1 and 2) suggest that it is sufficient to use k op and k cl at n ϭ 2 to represent the channel-opening kinetics of the mutant channel in the entire range of glutamate concentrations. We thus favor an interpretation of k op ϭ (1.9 Ϯ 0.1) ϫ 10 4 s Ϫ1 and k cl ϭ 140 Ϯ 160 s Ϫ1 at n ϭ 2 as the representative values of the channel-opening and channel-closing rate constants (see Fig. 2 legend). We emphasize that statistical F-criteria could not completely deny other n, although our analysis did yield n ϭ 2 as the best fit for the channel-opening kinetics (Table 2). However, n ϭ 1 was rejected because a negative k cl value was returned from the data analysis (Table 2 and supplemental Fig. 1).
It should be noted that the data analysis described above did not assume a biased number of glutamate molecule(s) bound to the receptor in order to open its channel. Furthermore, the experimental basis for these conclusions was from the study of the L497Y GluR1 mutant rather than the wild-type receptor, although the major conclusions from the study of the mutant described here and the wild-type receptor we reported earlier (11) are the same.

DISCUSSION
The Channel-opening Rate Is Dominated by the Receptor Bound with Two Glutamate Molecules-Evidence from all of our experiments and data analysis was well corroborated and supported the argument that binding of two or more glutamate molecules per receptor, i.e. n ϭ 2-4 but not n ϭ 1, was all sufficient to open the channel, and k op remained essentially invariant among n ϭ 2-4. If receptor complexes bound with more than two glutamate molecules have higher conductance levels, higher conductance levels associated with higher agonist occupancy do not give rise to different channel-opening rate constants as compared with k op at n ϭ 2. One possible explanation is that open channel conformations in different receptor occupancy, or n ϭ 2-4, are similar. In this case, once the receptor accepts the minimal number of agonist molecules (i.e. n ϭ 2) so that a sufficient amount of energy can be harnessed from agonist binding to open the channel, a higher receptor occupancy may simply stabilize the open channel conformation to different extents (21). Alternatively, the receptor complexes with higher occupancy could have k op values different from the value at n ϭ 2. However, the fractions of these complexes in the overall receptor population that undergo the channel-opening reaction could not have been significant enough to alter k obs , despite the fact that we did not know at what concentration(s) higher receptor occupancy or higher conductance levels began to contribute to the whole-cell current. Previously, it has been proposed that AMPA receptors with two to four glutamate molecules bound enter desensitization at similar rates and recover from the desensitization with similar rates as well (22).
Even though an AMPA receptor can adopt higher conductance levels observed in single-channel recording when glutamate concentration increases (4,5,7), it has been hypothesized that glutamate may not be able to populate higher conductance levels of synaptic AMPA receptors in vivo (5). Furthermore, the glutamate concentration in the synaptic cleft is estimated to be no higher than 1 mM for more than a few hundred s (23,24). Therefore, it is reasonable that AMPA channels actually function as a receptor complex activated predominantly by the binding of two glutamate molecules. Obviously, it should be noted that the conclusion drawn from our study was based on a homomeric mutant channel rather than heteromeric native AMPA receptors in vivo.
The binding of two glutamate molecules per receptor to open the channel is a plausible stoichiometry (11), if an AMPA receptor is considered a dimer of "dimers" (25). As such, binding of one glutamate molecule per dimer or two per dimer of dimers is possible. Interestingly, two subunits acting as a dimer in a tetrameric receptor composition, undergoing a concerted transition between inactive and active states, was also proposed for intracellular cyclic GMPgated channels (26), where the opening of the channels also depends on the receptor occupancy (26,27).
The Major Effect of the L497Y Mutation on GluR1 is to Stabilize the Open Channel Conformation-Comparison of the channel-opening kinetic constants of the mutant with those of the wild-type GluR1Q flip receptor, which we characterized previously (11), shows that the k op and k cl for the mutant at n ϭ 2 are ϳ1.5and ϳ13-fold smaller than those for the wild-type receptor, respectively. Thus, the major effect of this point mutation is to decrease the channel-closing rate or to prolong the lifetime of the open channel (k cl ϭ 1/, where is the lifetime expressed in time constant). As a result, the open channel state is stabilized. To better understand the effect of this mutation on stabilizing the open channel state, we applied the ⌽ value analysis to infer transition state structures from changes in kinetics on mutation, a procedure used in protein folding, catalysis, and conformational transitions (15)(16)(17). The value of ⌽ indicates the extent to which a mutated residue is involved in the formation of the transition state on a scale of 0 to 1 (i.e. 0 and 1 represent that the influence of the side chain is either absent or fully present in the transition state because of that mutation). Using Equation 4, we estimated ⌽ ϭ 0.16 (Fig. 4). A fractional value of ⌽ suggests that upon mutation, the site near L497Y was not entirely wild type-like. Instead, the local environment near tyrosine 497 has changed somewhat due to the mutation, as compared with the leucine residue at the same position in the wild-type receptor. This single amino acid substitution further affected the transition state (i.e. ⌬⌬G TS-C ϭ 0.21 kcal/mol; see the legend for Fig. 4). Thus, this analysis suggests that the major effect of the L497Y mutation in GluR1 is to stabilize the channel-opening state (by an amount of ⌬⌬G ϭ 1.3 kcal/mol; see Fig. 4). This is consistent with the structural revelation by which the same mutation stabilizes the dimer interface of the S1S2 mutant receptor (6). However, the L497Y mutation further causes a non-native, structural change near the mutation site in the closed channel state, inferred from the non-zero ⌽ value. This change may be linked to a reduction of the K 1 or EC 50 value for glutamate in the mutant (9,11,28), although how the structural change due to this point mutation affects glutamate binding affinity is not clear. Implications Based on the Kinetic Constants and Free Energy Diagram-Based on the results of this study, including the free energy diagram (Fig. 4), we predict that a change of the free energy of the open channel state compared with that of the wild-type receptor, the benchmark, affects the stability of the open channel state and thus alters the channelclosing rate constant and vice versa. For instance, the k cl of the L497Y mutant is smaller than that of the wild type, suggesting that this structural modification lowers the energy level of the open channel state by stabilizing it. In contrast, our study of the alternatively spliced variants of GluR3 or GluR3 flip and GluR3 flop shows that the flop isoform has a larger k cl than the flip isoform, presumably reflecting that the flop isoform destabilizes the channel-open state (29). By the same prediction, any mutation or change of structure (whether it is located in the dimer interface, such as the mutation in GluR2, but is equivalent to the L497Y in GluR1 (6), or elsewhere but nevertheless stabilizes the open channel state) would slow the rate of channel closing. If a mutation does not affect the stability of the open channel conformation, that mutation is expected not to affect the channel-closing rate constant and vice versa. Therefore, the assessment of the effect of a mutation on k cl provides a measure of whether the mutation exerts any structural impact on stability of the open channel conformation.
Relationship between Channel Closing and Desensitization-As compared with the GluR1Q flip wild-type receptor (11), both the channel-closing rate and the desensitization rate of the L497Y mutant are decreased. These results are consistent with the hypothesis that desensitization begins from the closed channel state, as proposed previously (30,31), but not from the open channel state. Furthermore, the channel-closing rate process kinetically controls the channel desensitization, provided that both reactions occur, such as when n ϭ 2-4. By this notion, desensitization begins in parallel to the channel-opening reaction once glutamate is bound but proceeds from the closed channel state and with a slower rate. In fact, in this and all other studies of AMPA receptor channels, we have found that the rate of channel closing is markedly faster than the rate of the channel desensitization (11,13,14,29). The common "species" that links the two reactions is the closed channel state, although it is unclear which closed channel form(s) enters the desensitization pathway. As shown in this study, a higher concentration of the open channel state for the L497Y mutant, which correlates to a longer lifetime or more stable open channel conformation, actually "inhibited" a speedy return of the channel to the closed channel state and thus a speedy entry to the desensitization state (see Fig. 1A) compared with the wild type. If the desensitization could have started from the open channel state, a higher concentration of the open channel state would have resulted in a faster desensitization rate than the wild type. Indeed, this hypothesis is consistent with previous observations that desensitization is agonist-promoted (32) and that the L497Y mutant channels can desensitize, albeit very slowly and only at very high concentrations of ligand, as observed by us and others (6,9). Moreover, that the rate of the channel closing controls the rate of desensitization is supported by our results with the GluR3 receptors in that the k cl of the GluR3 flop variant is ϳ4-fold larger than that of the flip isoform, and the flop isoform desensitizes ϳ4-fold faster than the flip isoform (29). On the other hand, for the flip and flop isoforms of GluR1, the k cl of both isoforms is identical, within experimental errors, and as expected, the channel desensitization rate constant is also no different. 4 Further studies are obviously needed to test our predictions and hypothesis.
It should be noted that the underlying assumption in our hypothesis described above is that the control of the desensitization through the channel-closing rate step requires the channel to open in the first place. An exception to our hypothesis is that at a glutamate concentration much lower than required for activation, so that a channel cannot open, desensitization can still occur (22,33,34). In this case, the kinetic control mechanism using the rapid channel-opening reaction to regulate the concentration of the ligand-bound, closed channel state through which the channel desensitizes simply does not exist.  , based on ⌬⌬G TS-C ϭ 0.21 kcal/ mol (note that the subscript "TS" stands for transition state) and ⌬⌬G O-C ϭ 1.3 kcal/mol. The ⌽ value was calculated to be 0.16.