Brief intracellular Ca2+ transients initiate signaling routines that direct cellular activities. Consequently, activation of Ca2+-permeable neurotransmitter-gated channels can both depolarize and initiate remodeling of the postsynaptic cell. In particular, the Ca2+ transient produced by NMDA receptors is essential to normal synaptic physiology, drives the development and plasticity of excitatory central synapses, and also mediates glutamate excitotoxicity. The amplitude and time course of the Ca2+ signal depends on the receptor’s conductance and gating kinetics; these properties are themselves influenced both directly and indirectly by fluctuations in the extracellular Ca2+ concentration. Here, we used electrophysiology and kinetic modeling to delineate the direct effects of extracellular Ca2+ on recombinant GluN1/GluN2A receptor conductance and gating. We report that, in addition to decreasing unitary conductance, Ca2+ also decreased channel open probability primarily by lengthening closed-channel periods. Using one-channel current recordings, we derive a kinetic model for GluN1/GluN2A receptors in physiological Ca2+ concentrations that accurately describes macroscopic channel behaviors. This model represents a practical instrument to probe the mechanisms that control the Ca2+ transients produced by NMDA receptors during both normal and aberrant synaptic signaling.
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 (Kd = ∼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.
MATERIALS AND METHODS
Cells and receptor expression
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 (Ipk) was measured directly from the mean trace, and the amplitude of the steady-state current (Iss) 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+ (ICa) to that of the steady-state current measured initially in the absence of Ca2+ (Iss), 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 − ICa/Iss) × 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 (Erev) 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/γmax). 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. Ipk 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 (τslow and τfast) and area (Aslow and Afast). The weighted time constant of decay (τw) was calculated according to the equation τw = τslow(Aslow/(Aslow + Afast)) + τfast(Afast/(Aslow + Afast)).
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 (Em, 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 (Em, 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 (OP or OS) 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 (EF, EL, EM, and EH) 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 (Po) on [Ca2+].
For low Po 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 τcrit, 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; Po, 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 Iss/Ipk = 0.15; this disagrees with the whole-cell measurement, for which Iss/Ipk = 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(lnKeq), where R represents the molar gas constant, T represents the absolute temperature, and Keq 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.
Fast reversible inhibition of macroscopic responses by external [Ca2+]
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 (ICa) relative to the initial plateau obtained in 0 mM Ca2+ (Iss), which for 1.8 mM Ca2+ was 40 ± 10% (calculated as (1 − ICa/Iss) × 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+ (Iss), 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 (Po). 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.
Direct effects of external [Ca2+] on unitary conductance and permeability
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 (iNa), 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 < iNa), 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: γNa, 62.7 ± 0.7 pS in 0 mM Ca2+; γP, 53 ± 5 pS and γS, 37 ± 4 pS in physiological [Ca2+] (1.8 mM); and γP, 18.1 ± 0.5 pS and γs, 9.8 ± 0.8 pS when Ca2+ was the only permeant ion (75 mM). The Hill equation estimated the maximum effect on γP, 76 ± 4% and the IC50, 6.3 ± 0.8 mM; and on γS, 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 γS and γP 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 (Erev) for each conductance level shifted when switching from Na+-only to Ca2+-only solutions. We calculated Erev as the zero current intercept of extrapolated linear regressions to i/V data (Fig. 2 B) and found that the shift in Erev 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 (PCa/PNa) 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 PCa/PNa. 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 − ICa/Iss) × 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.
Direct effects of external [Ca2+] on gating kinetics
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, OP and OS, respectively (Fig. 3). As a measure of overall channel activity, we estimated the channel closed probability (PC) and calculated an aggregated open probability containing events at both open conductance levels as Po = 1 − PC. We found that, indeed, the aggregated Po 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 Po 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 OP and OS and found that this was not different across [Ca2+], indicating that the observed reduction in Po 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 OP and OS, we found that relative to OP, OS events were much less frequent such that the aggregated Po was very similar to the overall probability of OP openings (Fig. 3 and Table 1). Relative to 1.8 mM Ca2+, in Ca2+ only, the mean duration of OS 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 OS remained >10-fold lower than that of OP. 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 OS 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 (OS and OP) 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 Po gating modes cause the longer open component to change duration (EL, EM, or EH), whereas the fast component (EF) remains unchanged. Therefore, long recordings in which all three modes are sampled contain up to four open components: EF, EL, EM, and EH. 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 OP and OS. We found that OP 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 EF, EL, EM, and EH in 0 mM Ca2+ (Fig. 4 and Table 3). However, increasing external [Ca2+] increased the prevalence of the medium mode (aEM) 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 Po mode, such that the shorter openings (EL) were observed in only one recording in 5 mM Ca2+ and were absent in 75 mM Ca2+. Therefore, the OP 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 OS 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 OS represents a new conformation that is stabilized specifically by Ca2+ binding to an external site.
Kinetic models describing modulation of NMDA receptor responses by external Ca2+
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 OP 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 OP state substituted the O state, and an additional open state, OS, was incorporated by forming a loop between OP 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 → OP 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 OP states. Of these, the model connecting O with OP 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 (Kd = k−/k+) optimized with binding steps at C2 and C1 were similar (Kd = 0.3 mM); however, the model with the binding step between O and OP predicted slightly lower Ca2+ affinity (Kd = 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 ICa/Iss, 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.
GluN1/GluN2A macroscopic responses in physiological [Ca2+]
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 (Ipk) 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 (τw). We found that relative to 0 mM Ca2+, 1.8 mM Ca2+ reduced peak current ∼20%, whereas RT and τw 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 Kd 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, γP, for channels contained in excised patches as well as the emergence of a prominent secondary conductance level, γS, 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 γP and γS, respectively). Both of these values are slightly higher than the estimates in a previous study (Kd = ∼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 γP and γS, respectively. This observation may indicate that two or more Ca2+-binding sites are cooperative when the channel is in OS but not in OP 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 OS 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, OS, 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, OP. 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.
- Abbreviations used in this paper:
- log likelihood
- rise time
- Submitted: 13 June 2014
- Accepted: 29 September 2014
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