Extracellular Ca²⁺ ions reduce NMDA receptor conductance and gating

Ca²⁺ ions regulate countless biochemical processes, and their levels are therefore tightly controlled in live cells and organisms. In healthy individuals, the concentration of Ca²⁺ in blood serum is maintained within a narrow range (2.2–2.6 mM), and systemic deviations from these levels bring about a series of undesirable symptoms (Pearce and Thakker, 1997). In brain, however, extracellular Ca²⁺ levels oscillate locally on a fast (millisecond) timescale and can reach concentrations as low as 0.1 mM during normal synaptic transmission, with more prolonged global changes observed during seizures and after ischemia (Nicholson et al., 1977; Benninger et al., 1980; Heinemann and Pumain, 1980; Heinemann et al., 1986; Silver and Erecińska, 1990). Activity-dependent depletion of extracellular Ca²⁺ within the synaptic space is mediated by the opening of Ca²⁺-permeable channels, including NMDA receptors (Rusakov and Fine, 2003). NMDA receptor-mediated Ca²⁺ influx triggers a broad range of cellular processes in the postsynaptic neuron, ranging from synaptic plasticity to excitotoxicity (Hardingham and Bading, 2010). Nevertheless, whether and how these fluctuations in extracellular Ca²⁺ levels alter the amplitude and time course of the NMDA receptor-mediated flux remains unclear.

NMDA receptors generate significant Ca²⁺ transients as a result of their characteristically long activations and large unitary currents, of which a substantial fraction (∼10–20%) is carried by Ca²⁺ (Burnashev et al., 1995). They are ligand-gated excitatory channels that require for activation the binding of both glutamate and the co-agonist glycine. Functional receptors assemble from two obligatory GluN1 subunits, which are ubiquitously expressed throughout the central nervous system, and two GluN2 or GluN3 subunits, of which GluN2A is the most prominently expressed subunit in adult brain and spinal cord (Monyer et al., 1994). Each subunit has a large extracellular portion that is organized into two globular modules: the N-terminal domain and the agonist-binding domain, of which the latter connects directly with the pore-forming transmembrane domain (Karakas and Furukawa, 2014; Lee et al., 2014). The transmembrane domain is composed of three transmembrane helices and a loop-helix segment that only partially penetrates the membrane from the cytoplasmic side (Burnashev et al., 1992; Wo and Oswald, 1995; Kuner et al., 1996). Lastly, the intracellular domain consists mainly of the C-terminal domain, which contains binding sites for Ca²⁺-dependent proteins and residues that can be covalently modified by Ca²⁺-dependent enzymes (Chen and Roche, 2007; Choi et al., 2011).

GluN1/GluN2A responses are modulated directly by numerous physiological ligands, including inorganic cations. At low nanomolar concentrations, H⁺ and Zn²⁺ interact with sites on the N-terminal domain and reduce currents with voltage-independent allosteric mechanisms (Tang et al., 1990; Traynelis and Cull-Candy, 1990; Paoletti et al., 1997; Banke et al., 2005; Erreger and Traynelis, 2008; Amico-Ruvio et al., 2011). In contrast, at micromolar concentrations, Zn²⁺ and Mg²⁺ bind within the membrane pore and obstruct the passage of permeant ions with voltage-dependent blocking mechanisms (Mayer et al., 1984; Nowak et al., 1984; Christine and Choi, 1990; Legendre and Westbrook, 1990). Extracellular Ca²⁺ reduces NMDA receptor unitary conductance in a concentration-dependent but voltage-independent manner (Ascher and Nowak, 1988) distinct from the flickering block induced by Mg²⁺ (Nowak et al., 1984). However, a hypothesis that is still in circulation proposes that the Ca²⁺-dependent decrease in channel conductance also reflects a blocking mechanism. Despite this, because this “Ca²⁺ block” is voltage independent, the responsible Ca²⁺-binding site most likely resides outside of the membrane field, and under physiological conditions, its occupancy appears to be submaximal (K_d = ∼0.9 mM; Premkumar and Auerbach, 1996; Sharma and Stevens, 1996). Recent studies suggest that the site responsible for Ca²⁺ block resides along the GluN1 subunit just external to the channel gate (Watanabe et al., 2002; Karakas and Furukawa, 2014); however, whether this or other direct interactions between Ca²⁺ and receptor residues influence channel gating remains unclear.

In addition to the effect of external Ca²⁺ ions on conductance, several internal Ca²⁺-activated proteins interact with the C-terminal domain of the NMDA receptor and modify receptor gating properties over a broad time-scale (Tong et al., 1995; Zhang et al., 1998; Krupp et al., 1999, 2002; Rycroft and Gibb, 2004a,b). This additional layer of Ca²⁺-dependent effects has constrained the majority of NMDA receptor reaction mechanisms to ionic conditions with unphysiologically low or absent external Ca²⁺ levels (Popescu et al., 2004; Erreger et al., 2005; Dravid et al., 2008; Vance et al., 2013). In the few instances when reaction mechanisms have been investigated in physiological [Ca²⁺], potential gating differences between Ca²⁺-bound and Ca²⁺-free receptors were not addressed (Lester and Jahr, 1992; Banke and Traynelis, 2003; Schorge et al., 2005).

We used kinetic analyses and modeling of single-channel data obtained over a range of external Ca²⁺ concentrations to develop a comprehensive view of the direct effects of Ca²⁺ on NMDA receptor conductance and gating. We found that external Ca²⁺ reduced both the channel unitary conductance and the receptor gating kinetics with half-maximal effects occurring within the physiological range of [Ca²⁺]_e. We report a kinetic model that incorporates both of these effects and thus can be used to predict and explain the amplitude and time course of NMDA receptor macroscopic responses during dynamic fluctuations in [Ca²⁺]_e. This new knowledge will assist future efforts to delineate the roles of NMDA receptor signals in health and disease.

HEK293 cells (ATCC number CRL-1573 at passages 22–32) were maintained in Dulbecco’s modified Eagle’s medium (DMEM) supplemented with 10% fetal bovine serum and 1% penicillin/streptomycin. Cells were transiently transfected with the Ca²⁺ phosphate method (Chen and Okayama, 1987; Kussius et al., 2009) using pcDNA3.1 (+) plasmids expressing rat GluN1-1a (P35439-1), rat GluN2A (Q00959), and GFP using a total of ∼3 µg DNA in a 1:1:1 ratio. Proteins lacking intracellular domains were expressed from constructs encoding stop codons at residues K838 in GluN1-1a and K844 in GluN2A (Krupp et al., 1999, 2002). Cells were incubated with transfection mixture for 2 h, after which they were washed twice with PBS and allowed to recover in growth medium supplemented with 2 mM MgCl₂. Cells were used for electrophysiological measurements 24–48 h later.

Whole-cell currents were recorded with borosilicate glass pipettes (2–5 MΩ) filled with intracellular solution containing (mM) 135 CsCl, 33 CsOH, 2 MgCl₂, 11 EGTA, 1 CaCl₂, and 10 HEPES, adjusted to pH 7.4 (CsOH). Cells were held at −70 mV, unless indicated otherwise, and were perfused with extracellular (wash) solutions containing (mM) 150 NaCl, 2.5 KCl, 0.01 EDTA, 10 tricine, 0.1 glycine, and 10 HEPBS (N-(2-Hydroxyethyl)piperazine-N′-(4-butanesulfonic acid)), adjusted to pH 8.0 (NaOH), some of which were supplemented with 1 mM glutamate and/or CaCl₂ concentrations as indicated. For each condition, currents were recorded for 5 s, with or without 5-s wash periods between protocols, as indicated. For each cell, 5–10 runs were recorded sequentially and traces were averaged. Currents were amplified and filtered (2 kHz, Axopatch 200b) and then sampled (5 kHz, Digidata 1440A) into digital files (pCLAMP software; Molecular Devices) and stored. For each cell, the amplitude of the peak current (I_pk) was measured directly from the mean trace, and the amplitude of the steady-state current (I_ss) was determined from fitting a single exponential function to the decaying phase of the trace (as indicated in Fig. 1 A). The inhibitory effect of [Ca²⁺]_e-dependent inhibition was monitored by determining the ratio of the steady-state current measured with Ca²⁺ (I_Ca) to that of the steady-state current measured initially in the absence of Ca²⁺ (I_ss), and the maximum inhibitory effects and half-maximal inhibitory concentrations (IC₅₀) were calculated by fitting the Hill equation to the data. The percent inhibition across [Ca²⁺]_e was expressed as (1 − I_Ca/I_ss) × 100.

Unitary currents were recorded from outside-out excised patches using borosilicate glass pipettes (15–25 MΩ) filled with the intracellular solution described above for whole-cell recordings. Patches containing one to five receptors were perfused with Na⁺-containing external solutions composed of (mM) 150 NaCl, 2.5 KCl, 10 HEPBS, 10 tricine, 1 glutamate, and 0.1 glycine, adjusted to pH 8.0 (NaOH) and supplemented sequentially with 0, 0.5, 1.8, 5, or 10 mM CaCl₂, followed by a Ca²⁺-only solution composed of (mM) 75 CaCl₂, 2.5 KCl, 10 HEPBS, 10 tricine, 1 glutamate, and 0.1 glycine, adjusted to pH 8.0 (Tris-OH). Patches were first exposed to the Ca²⁺-free solution and held at membrane potentials ranging from −100 to 20 mV, varied step-wise in 10-mV increments. At each holding potential, the currents were recorded for several seconds, so that the record contained a sufficient fraction of unitary currents to allow accurate determination of the unitary current amplitude, and the protocol was repeated using extracellular solutions of increasing [Ca²⁺]. Data were amplified and filtered (2 kHz, Axopatch 200B), sampled (5 kHz, Digidata 1400A), and digitally stored using pCLAMP software. Within each experimental condition, segments containing runs of openings to a single amplitude level were selected for analyses, and the remaining periods, which often included openings to two or more amplitude levels, were discarded. Data were processed and analyzed using QuB software. After digitally filtering (12 kHz) the record, unitary current amplitudes (i) were estimated statistically with the SKM algorithm while imposing no dead time (Qin, 2004). For each [Ca²⁺] and amplitude level, the unitary conductance (γ) and the unitary reversal potential (E_rev) were computed as the slope and intercept, respectively, of a linear fit to the i/V data. The Ca²⁺-dependent inhibition at each [Ca²⁺] for both principal (P) and secondary (S) conductance levels were determined as the ratio of the mean conductance relative to that measured in 0 and 1.8 mM Ca²⁺, respectively (γ/γ_max). Maximal inhibitory effects and IC₅₀ were calculated by fitting the Hill equation to the data.

Macroscopic responses to brief (10 ms) agonist exposures were recorded from outside-out excised patches with borosilicate glass pipettes (5–15 MΩ) filled with the internal solution described above for whole-cell measurements. External solutions were exchanged by moving the patch rapidly with a piezo translation system (Burleigh LSS-3100/3200) across the interface formed by wash and agonist-containing solutions from a double-barrel theta-glass tube (Amico-Ruvio et al., 2011). Only current traces exhibiting 10–90% solution exchange time between 0.15 and 0.25 ms, as measured by open tip potentials immediately after the experiment, were used for analysis. Currents were amplified and filtered (Axopatch 200b) and then sampled and digitally stored with pCLAMP software. I_pk and the 10–90% rise time (RT) of the current were measured directly from the trace mean, and the kinetics of current decay upon removing glutamate were determined by fitting a double exponential function to the declining phase of the mean trace, with each component having a corresponding time constant (τ_slow and τ_fast) and area (A_slow and A_fast). The weighted time constant of decay (τ_w) was calculated according to the equation τ_w = τ_slow(A_slow/(A_slow + A_fast)) + τ_fast(A_fast/(A_slow + A_fast)).

Stationary one-channel activity was recorded with the patch-clamp technique from cell-attached patches. Fire-polished borosilicate glass pipettes (15–25 MΩ) were filled with extracellular solutions containing (mM) 150 NaCl, 2.5 KCl, 10 HEPBS, 10 tricine, 1 glutamate, and 0.1 glycine, adjusted to pH 8.0 (NaOH), and were supplemented with 0, 1.8, or 5 CaCl₂, as indicated. Currents were driven inward by applying a pipette potential of 40 mV (E_m, approximately −50 mV), where voltage-dependent block by contaminating Mg²⁺ ions is negligible (Mayer et al., 1984; Nowak et al., 1984). In addition, currents were recorded with extracellular solution containing (mM) 75 CaCl₂, 2.5 KCl, 10 HEPBS, 10 tricine, 1 glutamate, and 0.1 glycine, adjusted to pH 8.0 (Tris-OH). To resolve openings in Ca²⁺-only solutions, where current amplitudes are much smaller but Mg²⁺ block is largely relieved (Mayer and Westbrook, 1987), currents were recorded with 100-mV pipette potentials (E_m, approximately −110 mV). These data were compared with controls obtained also at 100 mV but in Ca²⁺- and Mg²⁺-free solutions (1 mM EDTA). Currents were amplified and filtered (10 kHz; Axopatch 200B), sampled (40 kHz; National Instruments PCI-6229 A/D Board), and stored into digital files (QuB software; SUNY Buffalo).

Kinetic analyses were performed on files with low-noise baseline (peak-to-peak <1 pA, RMS = 0.2–0.3 pA) and containing a sufficient number of events (>10,000 events, >10 min recording time) to increase the likelihood of observing double openings if more than one channel was present in the patch. Data were processed and idealized as described above for excised patches. To these idealized data, kinetic models containing two or three conductance classes, depending on the presence or absence of the S conductance level, were fit directly with the MIL algorithm in QuB while imposing a dead time of 0.075 ms (three samples; Qin et al., 1997). Individual closed (C) and open (O_P or O_S) states were sequentially added as necessary to increase the goodness of fit, which was evaluated by monitoring the maximum value of the log likelihood (LL) function. A threshold of 10 LL units per added state was imposed to determine best fit, and the model obtained was used to extract global kinetic parameters, time constants (τ, ms), and areas (a, %) for individual closed (E₁–E₅) and open (E_F, E_L, E_M, and E_H) exponential components and to estimate rate constants (s⁻¹) for all explicit transitions in the model. Maximal inhibitory effect and IC₅₀ were calculated by fitting the Hill equation to the measured dependence of the open probability (P_o) on [Ca²⁺].

For low P_o files, even if no double openings are apparent within any one burst, the possibility still exists that consecutive bursts originate from separate receptors, thus introducing an error in rate estimations. We tested for this possibility in two ways. First, we calculated the likelihood that the recorded currents originated from two or more alternately open channels by determining the number of bursts in an individual file and the proportion of bursting activity in that file, as previously described (Colquhoun and Hawkes, 1995). We defined bursts as groups of openings that were separated by closed events shorter than a τ_crit, which was calculated to exclude events pertaining to E4 and E5 components, and misclassified the same number of E₃ and E₄ events (Magleby and Pallotta, 1983). With this method, we determined that for all files used in our analyses the likelihood that all bursts originated from the same channel was >95%. For example, for the shortest record used (10 min; P_o, 0.06; 1.7 × 10⁴ events), we observed 70 bursts that represented 8% of the recorded time, thus indicating a 95.6% chance that all bursts were produced by the same channel. As a second test, we used the model deduced for 75 mM Ca²⁺ (see Fig. 6, bottom arm) and simulated 10 min of data from one channel. We then refitted our model to this simulated data assuming the trace was produced by two channels. With this assumption, only one rate changed: the recovery from the longest lived closed state, which is the primary state that produces gaps between bursts, was approximately threefold slower (0.2 s⁻¹ vs. 0.06 s⁻¹). This result was replicated for the model and rates obtained with 1.8 mM Ca²; the only rate that changed by assuming two channels in the patch was the recovery rate from the longest lived closed state (0.2 s⁻¹ vs. 0.08 s⁻¹). However, the model with this much slower recovery rate predicted macroscopic responses with I_ss/I_pk = 0.15; this disagrees with the whole-cell measurement, for which I_ss/I_pk = 0.40 (see Fig. 1 B). Based on these tests, we conclude that in the records we selected for analyses all of the bursts most likely originated from a singular channel.

Free energy profiles were calculated and illustrated relative to the free energy of their respective C₃ closed state, which represents the first fully liganded state along the glutamate-initiated activation reaction. Calculations were performed using the measured rate constants in each model according to the relationship ΔG⁰ = −RT(lnK_eq), where R represents the molar gas constant, T represents the absolute temperature, and K_eq represents the equilibrium constant for the indicated transition calculated as the ratio of the forward and reverse reactions (k₊/k₋). Barrier heights (E‡) were calculated according to the relationship E‡ = ΔG⁰ + (10 − lnk₊). Individual peaks and wells were arbitrarily equally spaced along the reaction coordinate.

Ensemble currents through 100 receptors were simulated using the experimentally determined unitary conductance and the tiered kinetic model in Fig. 6 A. Two identical glutamate-binding steps were appended to the C₃ state in each model using association and dissociation rate constants measured previously (1.7 × 10⁷ M⁻¹s⁻¹ and 60 s⁻¹, respectively; Popescu et al., 2004), and all receptors were placed initially at the resting, unliganded state. Responses to phasic (10 ms) and tonic (5 s) stimuli were calculated as the time-dependent accumulation of receptors into the open state or states upon exposure to 1 mM glutamate. Simulated responses were processed and analyzed as described for the experimentally recorded currents.

All results are presented as means with the associated standard errors (SEM). Statistical significance of differences were evaluated with the paired t test for data obtained from the same cell and with the unpaired t test for data obtained from separate cells, as indicated. Differences were considered significant for P < 0.05.

To examine the concentration-dependent effects of external Ca²⁺ on macroscopic NMDA receptor currents, we recorded whole-cell responses from HEK293 cells transiently expressing recombinant rat GluN1/GluN2A receptors. Currents were elicited in the absence of Ca²⁺ (1 mM EDTA) with suprasaturating concentrations of glutamate (1 mM, EC₅₀ = 3 µM; Popescu et al., 2004) and glycine (0.1 mM, EC₅₀ <1 µM; Johnson and Ascher, 1987; Kleckner and Dingledine, 1988) and were allowed to equilibrate for 5 s before applying increasing concentrations of Ca²⁺. We observed a rapid and concentration-dependent reduction in the steady-state current level (I_Ca) relative to the initial plateau obtained in 0 mM Ca²⁺ (I_ss), which for 1.8 mM Ca²⁺ was 40 ± 10% (calculated as (1 − I_Ca/I_ss) × 100; Fig. 1 A). In the 0–50-mM range tested, the Hill equation predicted a maximum fractional inhibition of 92 ± 9% and a half-maximal dose (IC₅₀) of 2.4 ± 0.7 mM (n = 5; Fig. 1 A, inset). From the fast onset of the observed inhibition and its rapid and complete reversibility (Fig. 1 B), we inferred that it arose from direct interactions between Ca²⁺ ions and channel residues rather than through indirect, second-messenger effects of Ca²⁺, whose kinetics are slower.

To test this inference directly, we examined responses from NMDA receptors that lacked the C-terminal tails of both GluN1 and GluN2A subunits (ΔCTD). These receptors have altered gating kinetics and produce macroscopic responses that desensitize faster and deeper (Maki et al., 2012). Despite a reduced response in 0 mM Ca²⁺ (I_ss), neither the extent of inhibition (94 ± 12%) nor the IC₅₀ (1.8 ± 0.7 mM) were significantly different relative to full-length receptors (n = 7, P > 0.05, unpaired t test; Fig. 1 A). This result demonstrates that the observed [Ca²⁺]-dependent inhibition of the NMDA receptor response was independent of intracellular receptor domains and thus it was likely mediated by external or permeating Ca²⁺ ions.

To distinguish whether current inhibition occurred via interactions between Ca²⁺ ions in the bulk solution with the receptor’s extracellular domains or between permeating Ca²⁺ with residues along the transmembrane pore, we recorded responses at a depolarized holding potential (−40 mV), where binding to residues within the pore would be reduced (Woodhull, 1973). We found that the extent of inhibition and IC₅₀ values were not statistically different from those measured at −70 mV (96 ± 13% and 2.5 ± 0.9 mM, respectively; n = 5, P > 0.05, unpaired t test; Fig. 1 C), thus confirming previous reports that the inhibitory effect of Ca²⁺ on NMDA receptor currents is voltage independent (Premkumar and Auerbach, 1996; Sharma and Stevens, 1996).

Together, these results indicate that Ca²⁺ ions inhibit NMDA receptor current fluxes through direct interactions with extracellular receptor residues. The observed reduction in macroscopic current may reflect a decrease in the number of channels present, their unitary conductance (γ), and/or their gating kinetics (P_o). Given that the inhibition of whole-cell currents was rapid and fully reversible, we conclude that the number of channels assayed did not change over the course of our measurements; therefore, we examined next the effects of external [Ca²⁺] on unitary channel properties.

We first examined the [Ca²⁺]-dependent effects on unitary conductance by measuring unitary current amplitudes (i) at several membrane voltages in excised patches. This configuration allowed us to control and vary both the extracellular [Ca²⁺] (0–75 mM) and the membrane potential (−100 to 20 mV), while recording activity continuously from the same small channel population (Fig. 2 A). Consistent with literature reports, we found that, relative to Na⁺-only currents (i_Na), adding Ca²⁺ in the extracellular solution produced two observable effects on the unitary current amplitude (Ascher and Nowak, 1988; Jahr and Stevens, 1993). First, its mean level decreased with increasing [Ca²⁺] (i < i_Na), and second, in addition to a principal conductance level (P), a secondary conductance level (S) developed (Fig. 2 A). For each [Ca²⁺] we calculated the unitary conductance (γ) as the slope of linear regressions to the i/V data (Fig. 2 B) and found that this was as follows: γ_Na, 62.7 ± 0.7 pS in 0 mM Ca²⁺; γ_P, 53 ± 5 pS and γ_S, 37 ± 4 pS in physiological [Ca²⁺] (1.8 mM); and γ_P, 18.1 ± 0.5 pS and γ_s, 9.8 ± 0.8 pS when Ca²⁺ was the only permeant ion (75 mM). The Hill equation estimated the maximum effect on γ_P, 76 ± 4% and the IC₅₀, 6.3 ± 0.8 mM; and on γ_S, 74 ± 2%; and the IC₅₀, 6.4 ± 1.0 (Fig. 2 C).

Similar [Ca²⁺]-dependent reductions in NMDA receptor conductance have been measured in several native preparations (Ascher and Nowak, 1988; Jahr and Stevens, 1993), and this is believed to be a conserved property across GluN1/GluN2 isoforms. In the current literature, the phenomenon is referred to as “Ca²⁺-block,” although a blocking mechanism has not yet been demonstrated and clearly the Ca²⁺-binding site or sites responsible for this effect lie externally to the membrane field (Ascher and Nowak, 1988; Jahr and Stevens, 1993). Similarly, the mechanism by which the two conductance levels arise is unknown. Our result indicated that γ_S and γ_P had similar IC₅₀ values (P > 0.5, paired t test) but distinct Hill coefficients: 1.1 ± 0.2 and 2.5 ± 0.2 mM, respectively (P < 0.05, paired t test). This observation may indicate that two or more Ca²⁺-binding sites of similar affinities may be coupled when the channel exists in the S level conformations but not the P level conformations.

Because in Na⁺-only solutions a second conductance is not apparent, the presence of two conductance levels in Ca²⁺-containing solutions may be explained in two ways. One possibility is that regardless of external [Ca²⁺], the pore may exist in two structural conformations, corresponding to P and S, which have similar Na⁺ but distinct Ca²⁺ permeabilities, such that higher Ca²⁺ permeation will result in lower conductance. In other words, the presence of Ca²⁺ may reveal rather than produce the lower conductance conformation. Alternatively, a separate pore conformation that is rarely visited when only Na⁺ is present may be substantially stabilized by Ca²⁺ binding. To distinguish between these two possibilities, we examined the relative Ca²⁺ permeabilities of the P and S conductance levels.

As an index of relative Ca²⁺ permeability, we measured the extent to which the reversal potentials (E_rev) for each conductance level shifted when switching from Na⁺-only to Ca²⁺-only solutions. We calculated E_rev as the zero current intercept of extrapolated linear regressions to i/V data (Fig. 2 B) and found that the shift in E_rev was similar for both P and S levels: 24 ± 2 and 28 ± 5 mV, respectively (P > 0.05, paired t test; Fig. 2 C), corresponding to a relative Ca²⁺ permeability (P_Ca/P_Na) of ∼7–8 for each. This result indicates that the proportional composition of passed current is largely similar for both P and S, and thus, the secondary level does not arise from increased Ca²⁺ permeation, ruling out the first scenario.

Together, these results show that Ca²⁺ binding (IC₅₀, ∼6 mM) to one or more external sites can decrease the unitary NMDA receptor conductance as much as approximately threefold. Ca²⁺ binding may stabilize receptors into a state of even lower conductance (S), which is not significantly populated in Na⁺-only solutions, and may be indicative of a receptor conformation in which Ca²⁺-binding sites are coupled. Importantly, despite the lower conductance of S compared with P, both have similar P_Ca/P_Na. Based on these results, we estimate that physiological Ca²⁺ (1.8 mM) will decrease GluN1/GluN2A conductance by ∼10 pS, or 15%, relative to Na⁺-only solutions. Whereas this decrease is substantial, it does not fully account for the 40% inhibition observed in whole-cell currents (calculated as (1 − I_Ca/I_ss) × 100; Fig. 1 A). Therefore, we inferred that the difference may reflect slower gating of Ca²⁺-bound GluN1/GluN2A receptors. Next, we investigated this possibility by examining direct effects of external [Ca²⁺] on channel gating.

Using cell-attached patches containing one GluN1/GluN2A receptor, we recorded uninterrupted steady-state activity for long (>10 min) periods. As described for excised patches above, increasing external [Ca²⁺] produced two resolvable amplitude levels, P and S, indicative of two distinct open states, O_P and O_S, respectively (Fig. 3). As a measure of overall channel activity, we estimated the channel closed probability (P_C) and calculated an aggregated open probability containing events at both open conductance levels as P_o = 1 − P_C. We found that, indeed, the aggregated P_o decreased with increasing [Ca²⁺] from 0.38 ± 0.08 in 0 mM Ca²⁺ to in 0.27 ± 0.03 in 1.8 mM Ca²⁺, corresponding to a ∼30% reduction in channel activity under physiological conditions. A fit with the Hill equation to the dose dependency of P_o across the range of [Ca²⁺] predicted a 65 ± 4% maximum inhibition and IC₅₀ = 1.7 ± 0.2 mM (Fig. 3 and Table 1).

Single-channel observations allow the direct measurement of dwell durations in each conductance level. We measured the mean duration of openings (MOT) as the aggregated durations for O_P and O_S and found that this was not different across [Ca²⁺], indicating that the observed reduction in P_o was caused entirely by a lengthening of closed intervals. Indeed, the mean closed time (MCT) increased progressively by ∼6- and ∼17-fold in 5 and 75 mM Ca²⁺, respectively (Fig. 3 and Table 1). When we segregated events measured for the O_P and O_S, we found that relative to O_P, O_S events were much less frequent such that the aggregated P_o was very similar to the overall probability of O_P openings (Fig. 3 and Table 1). Relative to 1.8 mM Ca²⁺, in Ca²⁺ only, the mean duration of O_S events increased slightly (from 2.6 to 3.5 ms) and its fractional area increased ∼3-fold; however, even in Ca²⁺ only, the occupancy of O_S remained >10-fold lower than that of O_P. Combined with the relatively small difference in conductance between S and P, we conclude that quantitatively, the [Ca²⁺]-dependent reduction in channel conductance by the appearance of O_S is negligible. Importantly, the observation that the channel MOT was relatively constant across Ca²⁺ concentrations, whereas the MCT was substantially increased, argues against a classic open-block mechanism as the explanation for the decrease in conductance (Neher and Steinbach, 1978). Instead, an allosteric mechanism appears more plausible.

Next, we examined the duration of dwells observed in closed (C) and open (O_S and O_P) states. It is well established that, in the absence of Ca²⁺, GluN1/GluN2A receptors produce closed duration distributions that can be reliably described with five exponential components (E₁–E₅; Kussius et al., 2009). The faster components (E₁–E₃) occur within activation bursts, and the two slowest components (E₄ and E₅) represent dwells in desensitized states, which terminate bursts. We found that with increasing external [Ca²⁺], the number of closed components remained unchanged; however, their time constants were gradually increased (Fig. 4 and Table 2). In addition, the fraction of very short (E₁) and very long (E₅) events increased, mostly at the expense of E₃ events.

The distribution of openings changed in a different manner. In the absence of external Ca²⁺, GluN1/GluN2A receptors open to a uniform amplitude level with two kinetic components (Popescu and Auerbach, 2003). Shifts between low, medium, and high P_o gating modes cause the longer open component to change duration (E_L, E_M, or E_H), whereas the fast component (E_F) remains unchanged. Therefore, long recordings in which all three modes are sampled contain up to four open components: E_F, E_L, E_M, and E_H. The distribution of receptors across gating modes determines the shape of synaptic current; therefore, it is important to examine whether modal gating persists when Ca²⁺ is present and whether it is apparent for both O_P and O_S. We found that O_P had a kinetic distribution that very closely resembled the behavior of open states in 0 mM Ca²⁺ (O). Thus, in 1.8 mM Ca²⁺ we resolved four kinetic components whose time constants were not statistically different from E_F, E_L, E_M, and E_H in 0 mM Ca²⁺ (Fig. 4 and Table 3). However, increasing external [Ca²⁺] increased the prevalence of the medium mode (a_EM) from 34% in 0 mM Ca²⁺ to 48, 58, and 77% in 1.8, 5, and 75 mM Ca²⁺, respectively. This increase occurred at the expense of the low P_o mode, such that the shorter openings (E_L) were observed in only one recording in 5 mM Ca²⁺ and were absent in 75 mM Ca²⁺. Therefore, the O_P state behaved kinetically in a manner similar to the singular O state observed in 0 mM Ca²⁺, and Ca²⁺ binding to an external site may favor openings in the medium mode, by an allosteric effect. In contrast, openings in O_S were kinetically homogeneous across concentrations, being consistently well described with one exponential whose lifetime was slightly increased in 75 mM Ca²⁺. This observation is consistent with the hypothesis that O_S represents a new conformation that is stabilized specifically by Ca²⁺ binding to an external site.

We attempted to capture the [Ca²⁺]-dependent changes in conductance and gating into one comprehensive scheme. However, given the kinetic multiplicity of open states observed and the necessarily limited experimental observations, we opted to represent each open level as a single state, with the understanding that the O and O_P states represent aggregates of several kinetically distinct classes. Previous work established that during activation in the absence of Ca²⁺, three fully liganded closed states are accessed sequentially C₃-C₂-C₁ before the channel opens (Popescu and Auerbach, 2003; Popescu et al., 2004; Auerbach and Zhou, 2005; Zhang et al., 2008); in addition, two desensitized states, C₄ and C₅, can be accessed from C₂ and C₃, respectively (Kussius et al., 2009). We fit several models to the single-channel records obtained in the presence of Ca²⁺ and ranked these according to their LL values. We found that data were best described by a model in which the overall arrangement of states was maintained with the following changes: the larger conductance O_P state substituted the O state, and an additional open state, O_S, was incorporated by forming a loop between O_P and C₁, the fastest closed state (Fig. 5 A). The rates optimized by fits to data obtained in 1.8 mM Ca²⁺ were slower within the activation sequence (C₂ → C₁ → O_P and C₂ ← C₁) and were faster for entry into the main desensitized state (C₃ → C₅) and slower for recovery (C₅ → C₃). These changes in reaction mechanism predict that active receptors will drain into desensitized states at the expense of all other states, especially preopen closed states (Fig. 5 A, inset). The calculated energy landscapes illustrate that Ca²⁺ binding increased the stability of the principal desensitized state C₅ and slightly elevated energy barriers along the activation pathway (Fig. 5 B).

Given that Ca²⁺ inhibits channel gating with a half-maximal concentration of ∼1.7 mM, the kinetic models describing channel gating patterns in the presence of physiological levels of Ca²⁺ likely represents a mean of gating rates for Ca²⁺-free and Ca²⁺-bound receptor states. To capture the concentration dependence of gating modulation by Ca²⁺, we developed a tiered model with Ca²⁺-free and Ca²⁺-bound arms (Fig. 6 A). To limit the number of variables in this expanded model, within the Ca²⁺-free arm we fixed all of the transitions rates to those experimentally determined in the absence of Ca²⁺, and within the Ca²⁺-bound arm we fixed those rates that were not significantly changed in 1.8 mM Ca²⁺ relative to 0 mM Ca²⁺ (Fig. 5 A). Next, to determine whether Ca²⁺ binding occurred preferentially to particular states, we connected the two arms with a single binding step whose position varied between models and evaluated the goodness of fit for each model based on an LL criterion (see Materials and methods). Only three models produced good fits, those with the binding step connecting (1) the C₂ states, (2) the C₁ states, or (3) the O and O_P states. Of these, the model connecting O with O_P produced the largest LL values. Notably, models that included a Ca²⁺-binding step between the C₃, C₄, or C₅ states in each tier failed to converge on an acceptable fit. Importantly, this model implies that Ca²⁺-bound receptors may occupy all closed states, even though association/dissociation occurs with observable probability only when receptors are actively gating (C₂, C₁, and O). The Ca²⁺ dissociation constant calculated from microscopic association and dissociation rate constants (K_d = k₋/k₊) optimized with binding steps at C₂ and C₁ were similar (K_d = 0.3 mM); however, the model with the binding step between O and O_P predicted slightly lower Ca²⁺ affinity (K_d = 1.2 mM). These values match well with those previously determined (Premkumar and Auerbach, 1996; Sharma and Stevens, 1996).

As an immediate test for the tiered model, we simulated macroscopic responses (100 channels) in several external [Ca²⁺], using the measured unitary conductances and the corresponding gating models. By fitting the Hill equation to the dose dependency of I_Ca/I_ss, we calculated maximal inhibition (∼85%) and IC₅₀ (2.3 ± 0.2 mM; Fig. 6 B). These values matched closely those determined experimentally with whole-cell recordings (Fig. 1 A), indicating that the model encapsulates the relevant features of Ca²⁺-dependent effects on NMDA receptor responses. Considering that 1.8 mM Ca²⁺ produced a 15% reduction in conductance (Fig. 2) and a 30% reduction in gating (Fig. 3), these results, which correspond to a combined reduction current by ∼40–45%, fully explain the inhibition observed in whole-cell currents (Fig. 1). Importantly our calculations imply that only approximately one third of the inhibition is caused by reduced conductance, with the largest proportion of the effect contributed by reduced gating, a phenomenon which has not been appreciated as of yet.

Aside from quantitative and mechanistic explanations for the observed changes in behavior, kinetic models are also valuable if they can predict the trajectory of the receptor response in a variety of conditions, some of which, although relevant to physiological and pathological conditions, may be difficult to achieve experimentally. We therefore examined whether the Ca²⁺ effects on conductance and gating captured in our model were sufficient to recapitulate receptor responses to stimuli likely to be experienced in situ. To address this, we examined macroscopic current responses to phasic stimulation. We simulated responses from 100 resting receptors after a brief (10 ms) exposure to 1 mM glutamate in the absence and presence of physiological levels (1.8 mM) of Ca²⁺. Although slightly longer than a synaptic pulse, which was estimated to be ∼1 ms (Clements et al., 1992), a 10-ms stimulus elicits NMDA receptor responses that are larger and less variable (Popescu et al., 2004), and thus easier to record reliably, but are sufficiently short to preclude any substantial entry into desensitized states (Zhang et al., 2008). To perform the simulation, we used the measured unitary conductances for each condition (Fig. 2) and the kinetic model illustrated in Fig. 6 A. The simulation predicted that relative to 0 mM Ca²⁺, in 1.8 mM Ca²⁺ the peak response (I_pk) would decrease by ∼10%; however, the RT and time constant of deactivation would increase by ∼25 and ∼100%, respectively (Fig. 6 C). To test these predictions, we recorded macroscopic responses from outside-out patches after exposing them to glutamate (10 ms, 1 mM) using a fast piezo-driven perfusion system. Under both conditions, the decaying portion of the current trace was fit well by a double exponential function, consistent with the presence of modal gating (Zhang et al., 2008), which was not explicitly included in the tiered model used for simulations; therefore, for comparison, we determined the time course of decay as the weighted mean time constant (τ_w). We found that relative to 0 mM Ca²⁺, 1.8 mM Ca²⁺ reduced peak current ∼20%, whereas RT and τ_w increased by ∼25 and ∼100%, respectively (Fig. 6 C and Table 4). Given that the rate constants in the model were optimized to cell-attached data, the close congruence between simulated traces and the responses measured from excised patches indicates that the tiered model, although only an approximation of the true reaction mechanism, captures the most relevant features of the direct effects of [Ca²⁺] on NMDA receptor responses.

Importantly, the model highlights a consequential effect of fluctuations in external Ca²⁺ on the phasic response; it shows that although the peak current is indeed decreased by [Ca²⁺], the deactivation time constant, which is a fundamental feature of the NMDA receptor response, increased. As a consequence, the overall charge transfer (calculated as the integrated current per time) increased from 58 to 90 fC per 100 channels. Therefore, our model predicts that transient fluctuations in external [Ca²⁺] will influence both the amplitude and the time course of NMDA receptor responses.

We present here a quantitative description of the direct inhibitory effects of extracellular [Ca²⁺] on GluN1/GluN2A channel conductance and gating kinetics and include predictions as to how this modulation may shape receptor responses to phasic and tonic stimulation patterns. We found that low millimolar levels of Ca²⁺ decreased whole-cell currents independently of the receptors’ intracellular domains, and the mechanism included reductions in both channel conductance and channel activity. Furthermore, we developed a kinetic model that incorporates both of these effects and describes channel activity across the range of external Ca²⁺ concentrations typical of glutamatergic synapses. Relative to low Ca²⁺ conditions, our model predicts that 1.8 mM Ca²⁺ will almost double the charge transfer elicited by brief glutamate pulses (Fig. 6 C), but will substantially decrease the ionic flux during periods of chronic stimulation (Fig. 6 B). Importantly, because the K_d we estimated for Ca²⁺ (1.2 mM) was in the physiological range, we anticipate that local fluctuations in extracellular Ca²⁺ will influence the amplitude and time course of NMDA receptor responses in situ. Notably, synchronous activities in large populations of neurons or bouts of intense synaptic firing are likely to change the ionic composition of the extracellular space, in particular by decreasing Ca²⁺. Consequently, under normal conditions, the signal generated by NMDA receptors may vary on a rapid timescale as the availability for Ca²⁺ to modulate channel properties fluctuates.

Our observation that the [Ca²⁺]-dependent reduction in current was independent of the receptors’ intracellular domains indicates that the inhibition was mediated by direct interactions between Ca²⁺ ions and receptor residues. These results were unexpected as the current literature on inhibition of NMDA receptor gating by Ca²⁺ speaks exclusively to indirect mechanisms, even though these may represent modulatory layers that operate on longer time scales or may be preparation specific (Rosenmund and Westbrook, 1993; Zhang et al., 1998; Krupp et al., 1999). Importantly, the [Ca²⁺]-dependent reduction in current was intact at depolarized potentials, indicating that the Ca²⁺-binding site responsible for this direct inhibition is located outside the membrane (Woodhull, 1973), and therefore, the inhibition is more likely to occur through an allosteric rather than a channel block mechanism.

Direct interactions between Ca²⁺ ions and charged residues outside of the voltage field produce a reduction in channel conductance that is well documented in the literature (Ascher and Nowak, 1988; Jahr and Stevens, 1993; Watanabe et al., 2002). Here, we observed a 76 ± 4% maximal reduction in conductance of the principal open level, γ_P, for channels contained in excised patches as well as the emergence of a prominent secondary conductance level, γ_S, with increasing concentrations of external Ca²⁺. Increasing [Ca²⁺] lowered both the P and S levels with similar potencies (IC₅₀ = 6.3 ± 0.8 and 6.4 ± 1.0 mM for γ_P and γ_S, respectively). Both of these values are slightly higher than the estimates in a previous study (K_d = ∼1 mM); this may be primarily the result of the very low [Ca²⁺] range (10 nm to 10 mM) used in the previous study, whose goal was to characterize a higher-affinity Ca²⁺-binding site (Premkumar and Auerbach, 1996).

Although the [Ca²⁺]-dependent reduction was similar for both conductance levels, the Hill coefficients were clearly different: ∼1 and ∼2.5 for γ_P and γ_S, respectively. This observation may indicate that two or more Ca²⁺-binding sites are cooperative when the channel is in O_S but not in O_P states; how this happens, however, is unclear. The current literature indicates that mutation of the channel’s Mg²⁺-blocking site, which resides deep within the membrane pore on GluN2A subunits, increases the binding affinity of Ca²⁺ to its external binding site (Premkumar and Auerbach, 1996; Sharma and Stevens, 1996). Furthermore, mutations of the homologous residues in the GluN1 subunit produce a prominent subconductance level in the absence of Ca²⁺ (Premkumar and Auerbach, 1996; Premkumar et al., 1997). Based on these observations and our finding that increasing the concentration of external Ca²⁺ increases the probability of O_S states, it is possible that small structural perturbations in the channel’s pore region, resulting from Ca²⁺ permeation, could alter the structure of the external vestibule, leading to stronger Ca²⁺ binding at that site and subsequently lower channel conductance.

In addition to changes in conductance, we discovered that [Ca²⁺] also altered the NMDA receptor gating reaction. To approximate channel kinetics in physiological [Ca²⁺], an additional open state, O_S, corresponding to the secondary conductance level, S, was added into the model, and this was best incorporated by forming a loop with the C₁ closed state and the principal open state, O_P. Within this reaction mechanism, several transitions were sensitive to [Ca²⁺]: transitions between preopen closed states were slowed, entry into desensitization was accelerated, and resensitization was slowed. Additionally, high concentrations of Ca²⁺ abolished the very brief openings. These findings are valuable given that neither the structural correlates for individual kinetic states nor the mechanisms for desensitization are known (Borschel et al., 2011), and possibly structural information regarding Ca²⁺-receptor interactions can help elucidate the molecular mechanisms behind these phenomena. We note that although we measured IC₅₀ values for Ca²⁺ in the low millimolar range for both conductance and gating effects, we cannot determine whether these are mediated by the same or different sites.

The kinetic scheme we generated represents a valuable tool to predict the signal generated by NMDA receptors in response to various physiological stimuli across the range of external Ca²⁺ levels that occurs during normal and pathological conditions. Models that have been previously generated in the presence of Ca²⁺ have assumed a fixed external [Ca²⁺] and do not distinguish gating differences between Ca²⁺-free and Ca²⁺-bound receptors (Banke and Traynelis, 2003; Schorge et al., 2005). Therefore, the rates estimated with these models represent a mean of transition rates of Ca²⁺-bound and Ca²⁺-free receptors. Because the extent to which a receptor dwells in a Ca²⁺-bound or Ca²⁺-free state will vary substantially based on changes in external [Ca²⁺], predicted macroscopic responses based on such models can only be applied to a static condition. The model developed here bypasses this limitation and allows for sensitive changes in NMDA receptor response according to the rapid dynamics of extracellular Ca²⁺ levels to be accurately inferred.

With this model, simulations of ensemble responses to brief and prolonged pulses of glutamate predicted that the external Ca²⁺ concentration effectively shapes the NMDA receptor response. Specifically, in response to a single, brief exposure to glutamate, Ca²⁺ ions slowed both the activation and deactivation kinetics and increased substantially the charge transferred during a single activation. In contrast, Ca²⁺ ions deepened the receptor desensitization and reduced the overall flux during extended exposures to glutamate. This stimulus-dependent effect of Ca²⁺ on charge transfer may play important roles in neuronal physiology.

The distinct intracellular milieu of synaptic and extrasynaptic NMDA receptors controls the cellular effect of the Ca²⁺ influx such that activation of synaptic receptors generally promotes cell survival and synaptic plasticity, whereas activation of extrasynaptic receptors can initiate apoptotic cascades (Hardingham and Bading, 2010). Given that synaptic and extrasynaptic receptors experience fundamentally distinct glutamate transients, our result that fluctuations in external Ca²⁺ have opposing effects on the charge transferred in response to phasic and tonic stimulation adds another layer to the distinct roles played by NMDA receptors at synaptic versus extrasynaptic locations. Therefore, the quantitative description provided here will help to further elucidate the role of fluctuating external [Ca²⁺] in health and disease.

We thank Dr. Gary Westbrook (Vollum Institute, Oregon Health and Science University, Portland, OR) for providing NMDA receptor constructs lacking intracellular domains and Ms. Eileen Kasperek for assistance with cell culture, media preparation, and molecular biology.

This work was supported in part by the National Institutes of Health (RO1 NS052669), the American Heart Association Established Investigator Award (AHA 12EIA9100012), and the SUNY REACH initiative.

The authors declare no competing financial interests.

Kenton J. Swartz served as editor.