Ca²⁺-Dependent Inactivation of GluN2A and GluN2B NMDA Receptors Occurs by a Common Kinetic Mechanism

Abstract

N-Methyl-d-aspartate (NMDA) receptors are Ca²⁺-permeable channels gated by glutamate and glycine that are essential for central excitatory transmission. Ca²⁺-dependent inactivation (CDI) is a regulatory feedback mechanism that reduces GluN2A-type NMDA receptor responses in an activity-dependent manner. Although CDI is mediated by calmodulin binding to the constitutive GluN1 subunit, prior studies suggest that GluN2B-type receptors are insensitive to CDI. We examined the mechanism of CDI subtype dependence using electrophysiological recordings of recombinant NMDA receptors expressed in HEK-293 cells. In physiological external Ca²⁺, we observed robust CDI of whole-cell GluN2A currents (0.42 ± 0.05) but no CDI in GluN2B currents (0.08 ± 0.07). In contrast, when Ca²⁺ was supplied intracellularly, robust CDI occurred for both GluN2A and GluN2B currents (0.75 ± 0.03 and 0.67 ± 0.02, respectively). To examine how the source of Ca²⁺ affects CDI, we recorded one-channel Na⁺ currents to quantify the receptor gating mechanism while simultaneously monitoring ionomycin-induced intracellular Ca²⁺ elevations with fluorometry. We found that CDI of both GluN2A and GluN2B receptors reflects receptor accumulation in long-lived closed (desensitized) states, suggesting that the observed subtype-dependent differences in macroscopic CDI reflect intrinsic differences in equilibrium open probabilities (P_o). We tested this hypothesis by measuring substantial macroscopic CDI, in physiologic conditions, for high P_o GluN2B receptors (GluN1^A652Y/GluN2B). Together, these results show that Ca²⁺ flux produces activity-dependent inactivation for both GluN2A and GluN2B receptors and that the extent of CDI varies with channel P_o. These results are consistent with CDI as an autoinhibitory feedback mechanism against excessive Ca²⁺ load during high P_o activation.

Significance

N-Methyl-d-aspartate (NMDA) receptor subtypes undergo a substantial shift in expression during development. We show for the first time that the juvenile subtype is highly sensitive to inactivation by intracellular Ca²⁺ contrary to previous thought. This highlights the importance of maintaining high amplitude Ca²⁺ influx during development to drive synaptic growth while maintaining a protective mechanism against excessive overexcitation in disease or during glutamate spillover at extrasynaptic regions. In addition, we derive a kinetic model that can unify the disparate observations between juvenile and adult NMDA receptor subtypes. This model can be used to generate novel hypotheses regarding the physiological role of shifting expression of NMDA receptor subtypes.

Introduction

In the vertebrate central nervous system, N-Methyl-d-aspartate (NMDA) receptors are the primary source of Ca²⁺ flux into the postsynaptic cell during synaptic transmission (1). The resulting activity-dependent intracellular Ca²⁺ elevation can initiate synaptic plasticity or excitotoxicity. Dysregulated NMDA receptor activation can produce pathological states in neural circuits typical of neuropsychiatric disorders, such as autism (2) and depression (3), and, in more severe cases, can produce excitotoxic neurodegeneration (4).

NMDA receptors are heterotetrameric channels composed of two broadly present compulsory GluN1 subunits and two GluN2 subunits, of which four subtypes (A–D) are differentially expressed in nervous tissue. During development, the spatiotemporal expression patterns of subunits undergo substantial changes. GluN2B predominates in juvenile animals, especially in the cortex and hippocampus. In adult animals, GluN2A becomes predominant, whereas GluN2B levels decline, becoming more regionally restricted. Similarly, during synaptic spine maturation, GluN2A subunits replace GluN2B subunits (5, 6) with profound consequences on neuronal physiology. Notably, the duration of the excitatory postsynaptic current (EPSC) correlates strongly with the developmental switch in synaptic NMDA receptor subtype (7, 8, 9, 10, 11), such that EPSCs are longer in young animals relative to adult animals. The shortening of EPSC during development reflects distinct kinetics of each NMDA receptor subtype (12) and results in subtype-dependent Ca²⁺ waveforms within the postsynaptic spine (13).

NMDA receptors are prone to inhibition by intracellular Ca²⁺ elevations, a type of activity-dependent feedback control, which results in shorter EPSCs (14, 15, 16). This process, known in the literature as Ca²⁺-dependent inactivation (CDI), requires direct binding of calmodulin (CaM) to the intracellular portion of the GluN1 subunit (17). Although the GluN1 subunit is intrinsic to all NMDA receptors (18, 19), the type of GluN2 subunits appears to control the receptors’ susceptibility to CDI (20). Macroscopic GluN2A currents decline more in physiologic Ca²⁺ concentrations relative to zero external Ca²⁺, indicative of CDI, whereas GluN2B currents resist a Ca²⁺-dependent change in kinetics. We found recently that in addition to a strong dependence on intracellular Ca²⁺ concentrations, CDI depends strongly on endogenous levels of CaM, which can become limiting (21). Therefore, we aimed to reexamine the subunit dependence of NMDA receptor CDI in conditions in which we control for CDI dependence on CaM and Ca²⁺.

We found that, contrary to previous interpretations, GluN2B channels can undergo CDI and that its full expression is limited, in part, by this channel’s low open probability (P_o). Further, using kinetic analyses of single-channel currents, we developed, for the first time to our knowledge, full gating models for Ca²⁺-inactivated GluN2A and GluN2B channels. These models show that small changes in gating rates cause channels to accumulate with distinct probabilities in desensitized states, thus explaining the experimentally observed differences in macroscopic CDI expression. These results provide new insights into NMDA receptor activity-dependent modulation and support a common neuroprotective function of this receptors’ CDI across subtypes.

Methods

Cell culture, recombinant protein expression, and Western blot analyses

HEK-293 cells (CRL-1573; American Type Culture Collection, Manassas, VA) were grown in Dulbecco’s modified eagle medium (Invitrogen, Grand Island, NY) with 10% fetal bovine serum, 1% penicillin-streptomycin, and 10 mM MgCl₂ and were maintained in 5% CO₂ atmosphere at 37°C. At ∼50% confluence, cells were transfected with rat GluN1–2a (U08262.1) or GluN1^ΔCTD (22), GluN2A (M91561.1), and YFP-CaM_WT in a 1:1:1 ratio using polyethyleneimine (23) (23966-1; lot: 705149; Polysciences, Warrington, PA). CaM plasmids were gifts from Drs. Takahashi Inoue (Johns Hopkins University, Baltimore, MD) and Manu Ben Johny (Columbia University, New York, NY) (24). We verified each construct by sequencing after subcloning into pcDNA3.1(+) and plasmid amplification (QIAGEN, Valencia, CA). Cells were used 24–48 h post-transfection for electrophysiological measurement.

Cells were harvested by gentle scraping from the culture plate into cold phosphate-buffered saline with Ca²⁺ and Mg²⁺ (21300-025; Gibco Laboratories, Gaithersburg, MD). Suspensions were centrifuged at 700 × g, and pelleted cells were resuspended in hypotonic lysis buffer (in mM): 15 Tris-HCl, 20 HEPES, 1 Na₃VO₄, 1 NaF, 1:100 protease inhibitor cocktail (P8340; lot: 094M4070V; Sigma-Aldrich, St. Louis, MO), and 10 μg/μL DNase I. Cells were lysed with hand-held Dounce homogenizer. The homogenate was passed through a 25-guage syringe needle three times to shear genomic DNA; unlysed cells were separated by centrifugation 5 min at 700 × g. Next, the supernatant was centrifuged for 30 min at 13,000 × g to separate a soluble “cytosolic” fraction from the pellet, which contained the total membrane fraction. Membranes were solubilized in an equal volume of 1% sodium dodecyl sulfate, and protein concentrations were determined with the Bradford assay.

Both fractions were subjected to sodium dodecyl sulfate polyacrylamide gel electrophoresis (7.5%). Proteins were transferred to polyvinylidene difluoride membranes, and membranes were blocked in Tris-buffered saline with 5% bovine serum albumin overnight at 4°C. After blocking, GluN1 subunit was visualized by incubation with first mouse monoclonal anti-NR1-pan antibody (1:100; MAB1586; lot: 3146252; MilliporeSigma, Burlington, MA) overnight at 4°C and then with goat anti-mouse IgG horseradish peroxidase (1:5000, 31430; lot: LK152970; Thermo Fisher Scientific, Waltham, MA) for 2 h at room temperature. CaM was stained by incubation with first rat monoclonal anti-CaM (1:2500, ab45689; lot: GR123440-4; Abcam, Cambridge, U.K.) and then with goat anti-rat IgG horseradish peroxidase (1:10,000, 65-6120; lot: TA264501; Invitrogen) for 2 h at room temperature. Last, blots were treated with Supersignal West Pico substrate (Thermo Fisher Scientific) and imaged using a BioRad Chemidoc MP (Bio-Rad Laboratories, Hercules, CA) with an exposure time of 5 s across all blots. Densitometry was performed with ImageJ software (National Institutes of Health, Bethesda, MD), and the intensity of the bands in each region of interest was normalized to that of the corresponding bands in the whole-cell lysate lane.

Electrophysiology

Unitary currents were recorded with the cell-attached patch-clamp technique (25, 26, 27). Briefly, recording pipettes (borosilicate glass, 15–25 MΩ) contained (in mM) 150 NaCl, 2.5 KCl, 10 HEPBS, 0.1 EDTA, 0.1 glycine, and 1 glutamate at pH 8 (NaOH). Positive voltage (+100 mV) was applied through the recording pipette. Currents were amplified, low-pass filtered (10 kHz; Axopatch 200B), and sampled at 40 kHz (SCB-68 A/D converter; National Instruments, Austin, TX). All single-molecule data were acquired with QuB software (University at Buffalo, Buffalo, NY) and stored as digital files for off-line processing.

Ensemble currents were recorded with the whole-cell patch-clamp technique (26, 28). Briefly, pipettes (borosilicate glass, 4–5 MΩ) were filled with (in mM) 135 CsCl, 35 CsOH, 4 MgATP, 0.3 Na₂GTP, 0.006 FK-506, and either 1,2-bis(o-aminophenoxy)ethane-N,N,N′,N′-tetraacetic acid (BAPTA) or EGTA as indicated at the specified concentration at pH 7.2 (CsOH). For the intracellular Ca²⁺ dialysis experiments, the pipette solution contained 10 mM N-(hydroxyethyl) EDTA (HEDTA) as the low-affinity Ca²⁺ chelator, and CaCl₂ was added to the desired free Ca²⁺ concentration where indicated. Cells were perfused with extracellular solutions containing (in mM): 150 NaCl, 2.5 KCl, 10 HEPBS, 0.1 EDTA, and 0.1 glycine, in pH 8.0 (NaOH). Currents were elicited by switching to solution supplemented with 1 mM glutamate and were recorded at −80 mV membrane potential. When indicated, CaCl₂ was added to the perfused solution to produce the indicated free Ca²⁺ concentrations according to the software MAXC (Stanford University, Stanford, CA; maxchelator.stanford.edu). Solutions were applied using a focal perfusion pencil (AutoMate Scientific, Berkeley, CA) attached to a pressurized pinch-valve solution exchange system (BPS-8; ALA Scientific, Farmingdale, NY). After amplification and filtering at 2 kHz (Axopatch 200B; four-pole Bessel; Molecular Devices, San Jose, CA), currents were sampled at 5 kHz (Digidata 1440A; Molecular Devices) into digital files with pCLAMP 10.5. Series resistance was monitored to ascertain seal quality. In all experiments, cells were bathed in phosphate-buffered saline with Ca²⁺ and Mg²⁺ (21300-025; Gibco Laboratories).

Whole-cell currents were analyzed in pCLAMP 10.5 (Molecular Devices). For each cell, three to five sweeps were averaged and measured for peak and steady-state current values (I_pk, I_SS). The magnitude of CDI at equilibrium (CDI_EQ), which was observed 10 min post-break-in recordings, was calculated as follows:

$$CD{I}_{EQ}=1-\frac{{\left[I_{SS}/I_{pk}\right]}_{Ca}}{{\left[I_{SS}/I_{pk}\right]}_{Na}},$$ (1)

where [I_SS/I_pk]_Ca is the fraction of current remaining at the end of a 5-s pulse relative to the peak current at the beginning of the pulse in the presence of Ca²⁺, and [I_SS/I_pk]_Na is the same fraction measured in the absence of added Ca²⁺ (21).

Single-channel data processing, kinetic analyses, and modeling

Data obtained from cell-attached recordings were conservatively and minimally processed in QuB before subsequent analysis and modeling to extract kinetic parameters (29). Briefly, to correct recording artifacts, including noise spikes and baseline drift, current surges were eliminated by replacing the sampled amplitudes within the spike with amplitude levels averaged from the immediately adjacent (open or closed) samples. Baseline drift was corrected by forcing the amplitude level for closed events to a zero-current baseline at nodal points, as needed.

Currents were idealized with the segmental-k-means (SKM) algorithm with no digital filter and no imposed dead time (30). This procedure assigns each sampled data point to either the open (O) or closed (C) conductance class, producing a vector of open and closed interval durations (i.e., periods containing consecutive O or C class samples) and preserving the temporal sequence in which these periods occurred. Kinetic parameters were optimized in QuB by fitting user-defined state models to the sequence of SKM-idealized intervals with a maximal interval likelihood method using an imposed dead time of 0.075 ms (31). Models were ranked according to their calculated maximal value of the log likelihood function (28).

Calculating CDI from microscopic observations

To compare CDI values estimated from whole-cell current recordings (CDI_WC) to CDI values estimated from single-channel currents (CDI_SCH), we considered the following theoretical framework. For a population of channels N, the fraction of CDI-sensitive channels (i.e., bound with apocalmodulin, N_B) is represented at any time t by F_B(t) = N_B(t)/N. CaM overexpression provides the conditions of maximal CaM binding: F_B ≈ 1, and N_B ≈ N. We find this assumption consistent with previous data suggesting that variation in CaM overexpression has little influence on recorded CDI (21). Additionally, our Western data confirm overexpression of cytosolic CaM relative to membrane-associated receptor (Fig. 1 d). During whole-cell recordings, when N is sufficiently large, F_B(t) remains approximately constant such that accurate values can be quantified by averaging results from several cells. However, during single-channel observations, even in saturating concentrations of CaM, individual channels will transition stochastically between CaM-bound and CaM-free states and will gate accordingly with inactivated (P_o,I) or active (P_o,A) kinetic regimes (see scheme in Fig. 2 a, right), respectively. This random process results in recordings with heterogeneous kinetics, such that the observed or effective P_o (P_o,EFF) calculated in each recording represents the composite of these two behaviors:

$$P_{o_{EFF}}=P_A\cdot P_{o_A}+P_I\cdot P_{o_I},$$ (2)

$$P_{o_{EFF}}=\left(1-P_I\right)\cdot P_{o_A}+P_I\cdot P_{o_I},$$ (3)

where P_I and P_A are the probabilities for occurrence of the active or inactivated gating regimes, respectively. Thus, P_I can be quantified using experimentally measured parameters as follows:

$$P_I=\frac{P_{o_A}-P_{o_{EFF}}}{P_{o_A}-P_{o_I}}.$$ (4)

Figure 1.

Macroscopic CDI of NMDA receptor currents varies with GluN2 subunit. (a and b) Left: shown is the experimental set up for manipulating intracellular Ca²⁺. Right: shown are superimposed whole-cell current traces recorded in zero external [Ca²⁺] (black) or 2 mM (red) from HEK-293 cells expressing GluN1–2a, YFP-CaM_WT, and the GluN2 subunit indicated, with internal dialysis of (a) EGTA (5 mM) or (b) 50 μM free Ca²⁺. The shaded area illustrates the extent of CDI. (c) Shown is a summary of experimental results quantifying CDI elicited from extracellular Ca²⁺ (blue) and intracellular Ca²⁺ dialysis (red). GluN2D receptors were not tested for CDI with intracellular dialysis, given their prominent inactivation in physiological Ca²⁺ (^∗p < 0.05, Mann-Whitney U-test). (d) Shown are Western blots of whole-cell lysate (W), cytosolic fraction (C), and total membrane fraction (M) from HEK-293 cells transfected with indicated constructs, stained for GluN1, CaM, and GAPDH. MW, molecular weight. To see this figure in color, go online.

Figure 2.

Equivalence between CDI_WC and CDI_SCH. (a) Whole-cell Na⁺ current recorded at break-in (black, 0 min) and after 15 min (red) with intracellularly dialyzed Ca²⁺ (50 μM) to reveal the CDI_max (full inactivation). During individual channel gating, the observed effective P_o (P_o,EFF) alternates between P_o,A (active, CDI = 0) and P_o,I (inactivated, CDI_max), according to the illustrated model (right). (b) Whole-cell currents (left) were recorded with 0 (black) or 2 mM (red) external Ca²⁺, and intracellularly dialyzed BAPTA (10 mM) preserve only the local Ca²⁺ signal as the driver for CDI (right). Shown are cell-attached unitary currents recorded in the presence (red) and absence (black) of 2 mM external Ca²⁺. (c) Shown are recordings as in (b) from cells expressing GluN1^ΔCTD and GluN2A to isolate the effect of Ca²⁺-dependent non-CDI inhibitory mechanisms in both macroscopic (left) and microscopic (right) configurations. (d) Shown is the summary of P_o,EFF observed with unitary currents from the indicated constructs in the absence (gray) and presence (red) of external Ca²⁺ (^∗p < 0.05; Mann-Whitney U-test). (e) Shown are cell-attached unitary Na⁺ currents (0 Ca²⁺ in pipette) recorded before and after ionomycin (iono) treatment with 10 μM Ca²⁺ in bath (top) and calculated intracellular free Ca²⁺ waveform (bottom) (see Methods). (f) Shown is the evaluation of CDI magnitudes measured from whole-cell (CDI_WC) and single-channel (CDI_SCH) recordings under comparable conditions by pairing whole-cell Ca²⁺ dialysis with single-channel ionomycin treatment for GluN2A (blue) and GluN2B (red) receptors as well as pairing BAPTA-dialyzed whole-cell recordings with single-channel external Ca²⁺ conditions (yellow). Dashed line indicates hypothetical model of perfect congruence between measurements. Solid line indicates best-fit linear regression of CDI_SCH = m·CDI_WC + b. Data are represented as mean ± standard error. To see this figure in color, go online.

The extent of CDI in both macroscopic and microscopic regimes is quantified as the occupancy of the inactivated state scaled by the maximal CDI (CDI_max) observed empirically (21):

$$CDI=CD{I}_{max}\cdot P_I.$$ (5)

CDI_max can be determined from Eq. 4 by considering the hypothetical case of complete inactivation (CDI = 1; P_I = 1), in which inactivated channels do not open, and P_o,I = 0. Empirically, however, CDI_max is below unity reflecting the nonzero P_o of inactivated channels (21, 32). In this configuration, the measured P_o,EFF corresponds to the P_o of the inactivated mode, P_o,I:

$$CD{I}_{max}=\frac{P_{o_A}-P_{o_I}}{P_{o_A}}.$$ (6)

Therefore, by combining Eqs. 5 and 6, CDI_SCH can be estimated experimentally from gating parameters as the fractional change in channel P_o relative to P_o,A:

$$CD{I}_{SCH}=\frac{P_{o_A}-P_{o_{EFF}}}{P_{o_A}}.$$ (7)

Note that external Ca²⁺ exerts an additional allosteric inhibitory effect via direct binding to residues in the external vestibule (33, 34). Thus, to exclude this influence and therefore quantify exclusively CDI_SCH, experimental conditions must ensure that Ca²⁺ ions do not have access to the external Ca²⁺-binding site during recording. In measuring CDI_WC, the influence of external Ca²⁺ is eliminated with the following precautions: 1) whole-cell currents are normalized to their peak amplitudes in zero Ca²⁺, thus accounting for Ca²⁺ block that reduces channel conductance, and 2) Ca²⁺ is pre-equilibrated in the wash solution to ensure the time course of CDI is not influenced by the time course of Ca²⁺ binding. In measuring CDI_SCH, the external solution contained in the cell-attached pipette is free of Ca²⁺, and intracellular Ca²⁺ concentrations are elevated by applying ionomycin to the solution bathing the recorded cell.

Single-channel patch-clamp fluorometry

For all fluorescence measurements, cells were plated on custom-fabricated glass-bottom culture dishes. The glass coverslip was coated with poly-D-lysine before seeding cells at low density. All measurements were taken from individual cells. To monitor intracellular Ca²⁺ changes in cells expressing YFP-CaM constructs, we first prepared a stock solution of 200 mM XRhod-1-AM (X14210; lot: 1760314; Molecular Probes) fluorescent indicator in dimethyl sulfoxide. Next, a volume of stock XRhod1-AM, which will give a final concentration of 5 μM when added to the culture medium, was mixed in equal volume of 20% v/v Plurionic F127 (P2443; Sigma-Aldrich) in dimethyl sulfoxide to facilitate solubilization (35). The mixture was added to the culture medium, and cells were incubated at 37°C for 20 min. Next, cells were washed twice in Hank’s balanced salt solution (HBSS; 14065; Gibco Laboratories) and allowed to rest at room temperature for 15 min before recordings. Fluorescence calibrations were performed on HEK-293 cells bathed in external solution containing (in mM) as follows: 150 NaCl, 2.5 KCl, 10 HEDTA, 10 HEPBS, and CaCl₂ buffered to increasing free Ca²⁺ concentrated as indicated. To initiate Ca²⁺ influx, ionomycin (407953; lot: 272551; MilliporeSigma) was added in the bath to a final concentration of 10 μM. Fluorescence was captured using a wide-field Olympus IX51 inverted microscope with an Olympus 40× 0.6 NA objective lens. The shutter was adjusted to capture only light from a single cell of interest to visualize the spatially averaged, bulk Ca²⁺ elevations within a single cell. Changes in fluorescence were detected with a photomultiplier tube module (Hamamatsu Photonics, Hamamatsu City, Japan) driven by a low-voltage power supply held at 0.5 V. Fluorescence signals were sampled as unitary currents (40 kHz, Digidata 1440A), low-pass filtered (10 kHz), and stored as digital files (pClamp10 software; Molecular Devices). For analysis, fluorescence signals were digitally filtered at 1 kHz.

To calibrate changes in the fluorescence signal, we first determined the average background fluorescence (F₀) by measuring the fluorescence through the red channel filter upon focusing the shutter on a single YFP-CaM-positive cell that was not treated with XRhod1-AM before imaging. No significant bleed-through of YFP could be detected in the red channel. This background measurement was made on n = 10 cells each day measurements were taken. Minimal fluorescence (F_min) was measured in single YFP-CaM-positive cells pretreated with XRhod1-AM and 20 μM BAPTA-AM (2787; lot: 5A/153906; Tocris Bioscience, Bristol, U.K.). Maximal fluorescence (F_max) was measured by ionomycin treatment of cells bathed in HBSS supplemented with a free external Ca²⁺ concentration of 5 mM. We then measured intermediate fluorescence signals from single YFP-CaM-positive cells loaded with XRhod-1-AM upon ionomycin application in a bath solution containing either 0.1, 0.3, 1.0, 5, 10, or 50 μM free extracellular Ca²⁺ buffered in 10 mM HEDTA. All fluorescence changes were measured as the ratio of the fluorescence measured to the F₀ measured that day. The following relation was fit to the resulting data to determine the in situ K_d for our system:

$$\begin{array}{l}\left[C{a}^{2+}\right]=K_d\frac{F-F_{\min }}{F_{\max }-F}\\ F=\frac{F_{\max }\left[C{a}^{2+}\right]+K_d{F}_{\min }}{K_d+\left[C{a}^{2+}\right]}.\end{array}$$ (8)

We found K_d to be 5.94 μM, consistent with other in situ reports for X-Rhod-1 (36).

During Na⁺-only single-channel recordings, cells were bathed outside the recording pipette in HBSS supplemented with 10 μM free Ca²⁺. Ca²⁺ flux was initiated by adding ionomycin to the bath to a final concentration of 10 μM. Only cells positive for XRhod1 and YFP-CaM were selected for patching.

Constructing and simulating a full kinetic model of CDI

To validate the kinetic models obtained from fittings to single-channel data, we tested their ability to predict the degree of macroscopic CDI (CDI_WC) elicited under two experimental configurations: 1) direct Ca²⁺ influx through the recorded channels and 2) intracellular Ca²⁺ dialysis. To construct a full, tiered kinetic model that encompasses CaM-free and CaM-bound channels, we connected the active and inactivated gating schemes by the CDI rate constant determined in this study (Fig. 4 a) and the recovery from inactivation rate constant determined previously (21). With one channel isolated in a patch, the local Ca²⁺ fluxing through the pore is, by definition, the only driver of channel inactivation by engaging local CaM. Thus, we connected the two arms of the full model with the Ca²⁺-dependent forward rate constant from the open state of the active tier to the open state of the inactivated tier. The recovery rate was determined by a two-pulse protocol to measure recovery from desensitization in the presence and absence of external Ca²⁺. Because the recovery rate was measured by removing glutamate, we connected the recovery step to the unliganded glutamate conformations. However, CaM can likely dissociate from any state in the model; even so, because the rate of CDI recovery is much slower relative to gating rate constants, connecting the recovery step at any point in the model, did not significantly influence the simulation results. Finally, although there are two C0 CaM binding sites on a functional receptor, biochemical evidence suggests CaM/receptor stoichiometry is 1:1 (37); however, the functional stoichiometry is unknown. The nature of the GluN1/CaM interaction can theoretically have an important impact on the rate of inactivation. However, because both the forward and reverse rate constants were determined using macroscopic recordings, the underlying molecular mechanism is reflected in the measured effective rate constants, including Ca²⁺ binding and association of one or both CaM molecules.

Figure 4.

Kinetics of CDI development in GluN2A and GluN2B receptors. (a) Whole-cell currents recorded in several external [Ca²⁺] from GluN1–2a/GluN2A receptors (left) were used to calculate the time course of CDI development (τ_CDI) (right). (b) The rate of CDI equilibration relative to local intracellular Ca²⁺ concentration generated by channel activity reveals the microscopic rate constant for channel transition from active (A) into inactivated (I) modes (inset). Data are represented as mean ± standard error. (c) Tiered gating models were derived from one-channel recordings before (top) and after (bottom) ionomycin application for GluN1–2a/GluN2A (left) and GluN1–2a/GluN2B (right) receptors. (d) Whole-cell recordings (experimental) and calculated (simu) traces with models in (c), in Ca²⁺ free (black), or 2 mM Ca²⁺ (red), applied as indicated. To see this figure in color, go online.

All simulations were performed in MATLAB 2017a (The MathWorks, Natick, MA) using the built-in matrix exponential function, expm. We used the rate constants derived in QuB to construct a Q-matrix of n × n size, where n is the number of states in the full tiered model (16 states in total). A deterministic simulation of the occupancy of all 16 states with time resolution, dt, was performed by iteratively solving the following:

$$P\left(t+dt\right)=expm\left(dt\cdot Q\right)\cdot P\left(t\right).$$ (9)

The final macroscopic response was calculated by summing the occupancies of both open states in the model at each time point. To simulate the macroscopic response in the absence of Ca²⁺, at t = 0, we started all channels in the unliganded state of the active arm and set the glutamate concentration to 0. At time t = dt, the glutamate concentration was instantly jumped to 1 mM and kept constant for 5 s. The Ca²⁺ concentration was kept at 0 throughout the 5 s to reflect that no Ca²⁺ would be experienced by the local CaM molecule under Ca²⁺-free conditions. To simulate the macroscopic response in the presence of 2 mM extracellular Ca²⁺, at t = 0, we started all channels in the unliganded state of the active arm, given that channels have not opened yet to allow in Ca²⁺ and trigger inactivation, and set the glutamate concentration to 0. At time t = dt, the glutamate concentration was instantly jumped to 1 mM and kept constant for 5 s, whereas Ca²⁺ concentration was stepped to 90 μM, which corresponds to the predicted intracellular free Ca²⁺ concentration at 10 nm away from the pore (21). To simulate currents inactivated by intracellular Ca²⁺ dialysis, we first determined the proportion of channels in each arm of the model during 50 μM dialysis by calculating the equilibrium occupancies of a two-state model reflecting channels transitioning between active, A mode and inactive, I mode (Fig. 2 a) with experimentally determined k₊ = k_on,EFF[Ca²⁺] and k_- = k_rec (Fig. 4 b) (21). The Ca²⁺ concentration was set to 50 μM, with k_on,EFF = 0.11 μM⁻¹s⁻¹ and k_rec = 0.01 s⁻¹. This predicted that at equilibrium, A mode occupancy was 0.17, and I mode occupancy was 0.83. The full tiered model was then initialized such that 17% of channels began in the unliganded state on the active arm (A mode), whereas 83% of channels began in the unliganded state of the inactive arm (I mode) of the model. For both simulation strategies, the magnitude of CDI was calculated at the end of the 5-s simulation using Eq. 1.

Statistics

All statistical analyses were performed using R statistical software version 3.5.3. Distribution normality was first determined using the Anderson-Darling and Lillifore’s tests in the R nortest package. Non-normal distributions were compared using the nonparametric Mann-Whitney rank-sum test with the R wilcox.test function, whereas normal distributions were compared using the two-tailed Student’s t-test with the R t.test function. Macroscopic CDI measurements tended to follow non-normal distributions.

To estimate the statistical significance between two models fit to the same data, we first calculated the residual sum of squared error for each model. Next, the F-statistic was calculated by the residual sum of squared error ratio of the two fitted models. This F-statistic was then compared to the F distribution with the appropriate degrees of freedom determined from the data to determine the p-value. This method was used to determine the agreement between steady-state CDI measured from single-channel recordings (CDI_SCH) and macroscopic recordings (CDI_WC), whereby model 1 was an unconstrained linear regression of form CDI_SCH = m·CDI_WC + b, and model 2 was a theoretically perfect 1:1 linear relationship, fixed at intercept 0 and slope of 1 (Fig. 2 f). This method was also used to determine whether CDI was linearly or exponentially related to channel P_o (Fig. 5 c). Here, model 1 was a standard linear equation of form CDI(P_o) = m·P_o + b, whereas model 2 was an exponential equation of form CDI(P_o) = A·exp(−P_o/τ). All parameters were kept free during fittings.

Figure 5.

Magnitude of CDI correlates nonlinearly with P_o. (a and b) Left: representative on-patch one-channel Na⁺ currents were recorded from HEK-293 cells expressing the indicated subunits. Right: shown are whole-cell currents in the absence (black) and presence (red) of 2 mM Ca²⁺, with 10 mM EGTA as intracellular Ca²⁺ buffer. (c) Left: shown is a summary of whole-cell CDI values (^∗p < 0.05, Mann-Whitney U-test). Right: pooled data sets of P_o,A were measured by single-channel Na⁺ currents and CDI_WC estimated from whole cell from wild-type GluN1–2a (gray) or mutant GluN1–2a^A652Y (red) co-expressed with GluN2A (circle) or GluN2B (diamond). Data are represented as mean ± standard error. Also included in the fit are whole-cell recordings for GluN1–2a/GluN2A and GluN2B (blue) obtained with intracellular Ca²⁺ dialysis (approximating maximal Ca²⁺ flux, P_o,A = 1). Dashed line indicates fit by linear regression of form CDI(P_o) = m·P_o + b, and red curve indicates best fit with exponential function of form CDI(P_o) = A·exp(−P_o/τ). Green shaded region indicates the range of NMDA receptor activity predicted to produce Ca²⁺ fluxes too low to engage CDI; red shaded region indicates the range of NMDA receptor activity predicted to elicit CDI. To see this figure in color, go online.

Results

Revealing CDI of macroscopic GluN2B currents

CDI is structurally mediated by the intracellular tail of the obligatory GluN1 subunits of NMDA receptors, yet its magnitude is dependent on GluN2 subunit identity (20). This dependency was observed in whole-cell recordings of NMDA receptor currents by monitoring an activity-dependent decrease in activity, which became more prominent as levels of extracellular Ca²⁺ were increased. Under these conditions, only GluN2A and GluN2D currents displayed CDI, whereas GluN2B and GluN2C did not, despite having the same CaM effector site on the GluN1 subunit. We previously reported that in physiologic conditions (2 mM external Ca²⁺), the CDI of GluN2A currents is submaximal when intracellular Ca²⁺ is supplied by the monitored channels, whereas supplying Ca²⁺ through intracellular dialysis increases CDI to a maximal level (CDI_max) (21). Similarly, we found that in HEK-293 cells, low levels of endogenous CaM limit the full expression of GluN2A current CDI. With these new observations, we asked whether the reported lack of CDI in GluN2B and GluN2C receptors reflects 1) a structural intrinsic inability of these subtypes to inactivate or 2) that CDI is not sufficiently engaged because of either low Ca²⁺ influx and/or low CaM expression.

To test these possibilities, we measured NMDA receptor CDI by recording whole-cell currents elicited by prolonged (6 s) applications of glutamate (1 mM) and glycine (0.1 mM) in 0 and in 2 mM external Ca²⁺ (Fig. 1, a and c) from cells overexpressing YFP-CaM to saturate all receptor binding sites. Consistent with previous reports in cells expressing only endogenous CaM, we found that GluN2A and GluN2D currents showed substantial CDI (0.42 ± 0.05, n = 10; and 0.38 ± 0.07, n = 6, respectively), whereas Glu2NB and GluN2C currents remained unchanged relative to the 0 Ca²⁺ condition (CDI, 0.08 ± 0.07, n = 5; and 0.02 ± 0.05, n = 4, respectively). Next, we measured CDI upon direct intracellular dialysis of 50 μM free Ca²⁺, which we have previously established to be sufficient to elicit maximal CDI in GluN2A receptors (21). This approach eliminates differences in fluxed Ca²⁺ due to differential gating kinetics, conductance, or Ca²⁺ permeability between receptor subtypes. Notably, in these conditions, GluN2B currents developed strong CDI (0.67 ± 0.02, n = 5), the CDI of GluN2A currents increased as reported previously (0.75 ± 0.03, n = 6), and GluN2C currents remained unchanged relative to externally applied Ca²⁺ (0.08 ± 0.07, n = 5, p = 0.3) (Fig. 1, b and c). These results show that, in conditions of CaM overexpression, 50 μM intracellular Ca²⁺ produced robust CDI for GluN2A, GluN2B, and GluN2D currents and had no observable effect on GluN2C currents.

GluN2C receptors have markedly low open probability (0.011) and short open durations (0.5 ms) (38). Based on our result that even supplying Ca²⁺ through the recording pipette cannot overcome the lack of CDI for GluN2C currents, we eliminate a low Ca²⁺ flux due to low gating as the limiting factor for CDI. However, because very little is known about the gating mechanism of GluN2C receptors, our result does not exclude a masking of CDI in the conditions investigated here and previously. For example, GluN2C currents may desensitize substantially before opening, such that changes in macroscopic desensitization would be invisible in our experimental setup.

Given that GluN2A and GluN2B receptors are the most broadly expressed, we aimed to reveal for these two principal receptors the mechanism by which intracellular Ca²⁺ elevations decrease their currents and to understand why their CDI is differentially sensitive to channel-fluxed Ca²⁺. To test whether CaM levels were limiting relative to receptor expression, we visualized proteins in the cytosolic and membrane fractions of cells co-expressing YFP-CaMWT and GluN1–2a with either GluN2A, GluN2B, GluN2C, or GluN2D. We measured the relative abundance of cytosolic CaM relative to membrane-bound receptors and found that, in all cases, CaM was sufficiently overexpressed relative to the receptor levels. This observation led us to reject the hypothesis that CaM levels were insufficient to produce measurable CDI (Fig. 1 d). This is consistent with our prior results suggesting that cell-to-cell variability in YFP-CaM expression had little impact on the measured CDI magnitude (21). Further, to gain mechanistic insight into CDI differences between GluN2A and GluN2B receptors, we sought to develop a full kinetic model of inactivated receptors.

Revealing CDI of single NMDA receptor currents

To delineate the kinetic mechanism of CDI, it is necessary to compare the gating mechanism of “inactivated” channels to that of Ca²⁺/CaM-naive or “active” receptors. This is best achieved with kinetic analyses of single-channel currents recorded in conditions favoring inactivated (I) or active channels (A), respectively (Fig. 2 a). However, NMDA receptors in particular require specific experimental conditions to resolve gating kinetics and to separate intracellular effects of Ca²⁺ (i.e., CDI) from the direct effects of Ca²⁺ binding at an external high-affinity binding site (33, 34, 39). The kinetics of active GluN2A and GluN2B receptors have been well characterized and can be accurately inferred from cell-attached one-channel Na⁺-current recordings (28, 40, 41). To observe similar Na⁺ currents from inactivated channels, it would be best to expose channels to intracellular Ca²⁺ while recording inward Na⁺ currents.

In addition, quantifying CDI from single-channel currents (CDI_SCH) poses a more general sampling challenge that relates to the random nature of the CaM/channel interaction (42, 43). This randomness renders uncertain whether in any one recording, sufficient on/off events are captured to recapitulate the full range of kinetic changes and thus to converge on the macroscopically observed CDI_WC. To circumvent this uncertainty, it has been common to estimate CDI_SCH from low-resolution parameters such as open probability (P_o) or by averaging multiple single-channel recordings to aggregate a macroscopic current, which can then be subjected to conventional analyses (44, 45). However, such approximations of CDI_SCH provide insufficient mechanistic information for NMDA receptors, whose gating reaction is complex and encompasses a broad timescale. Therefore, before proceeding to kinetic modeling, we aimed to test whether single-channel recordings can provide information to obtain CDI_SCH values that converge onto CDI_WC values. We set up to compare CDI_SCH values estimated using Eq. 7 from microscopic parameters with CDI_WC values estimated using Eq. 1 from macroscopic parameters in 2 mM external Ca²⁺.

Relative to Ca²⁺-free conditions, when the cell-attached pipette solution included 2 mM Ca²⁺, the observed or effective P_o (P_o,EFF) (defined as in Fig. 2 a) decreased significantly for single wild-type GluN2A channels from 0.58 ± 0.02 (n = 10) to 0.29 ± 0.04 (n = 6), respectively (p = 0.0001) (Fig. 2, b and d). In this condition, the P_o,EFF reflects the combined inhibition of both intracellular actions by fluxed Ca²⁺ and external allosteric actions. However, for Eq. 7 to hold and therefore to reflect the effect of only intracellular Ca²⁺, the term P_o,A must report on the activity of receptors that are inhibited only by allosteric effects. Therefore, to measure P_o,A, we measured the activity of channels lacking the CaM binding site (GluN1^ΔCTD) (22). As expected, these channels exhibit no CDI_WC (Fig. 2 c, left), and the slight decrease in individual channel activity, from 0.63 ± 0.03 (n = 6) in zero Ca²⁺ to 0.50 ± 0.07 (n = 5, p = 0.15) in 2 mM Ca²⁺, likely reflected allosteric inhibition by direct Ca²⁺ binding to the external binding site. We used the P_o,EFF of GluN1^ΔCTD/GluN2A receptors in the presence of external Ca²⁺ as the P_o,A term in Eq. 7 and calculated CDI_SCH = 0.42 from single-channel parameters. For an isolated channel gating in the presence of external Ca²⁺, the only driver of CDI is the local Ca²⁺ fluxed through the receptor. To mimic these conditions, we measured whole-cell currents in 0 and 2 mM Ca²⁺, from cells dialyzed with 10 mM BAPTA and measured CDI_WC = 0.34 ± 0.03 (n = 5) (Fig. 2 b). These two values appear to be congruent. However, because this approach relied on unpaired measurements from two independent receptor constructs, a rigorous statistical comparison was not feasible.

To address this, we next embarked on a more challenging approach to elicit CDI_SCH specifically in wild-type receptors recorded in the absence of external Ca²⁺. This approach allows for paired measurements of activity using the observed channel. We used patch-clamp fluorometry, which permits simultaneous, real-time estimation of intracellular Ca²⁺ elevations and of cell-attached patch-clamp current in intact cells. We have previously shown that following intracellular dialysis, NMDA receptor currents develop CDI with a half-maximal dose of 4.7 μM free Ca²⁺ (21). Therefore, we aimed to monitor elevations above this critical concentration, and as such, we selected a low-affinity nonratiometric Ca²⁺ indicator, XRhod1-AM, which we tested in our system. We used ionomycin-elicited Ca²⁺ flux and measured fluorescence levels in several concentrations of external free Ca²⁺. With this approach, we were able to confirm the indicator binding constant in our system (K_d, 5.94 μM; see Methods). Thus, the sensitivity of the indicator is appropriate for ensuring that intracellular Ca²⁺ levels remained well above those necessary to elicit CDI. As a last necessary control, we sought to ensure that following ionomycin treatment, the concentration of intracellular Ca²⁺ remained above that necessary to induce CDI_max during the entire period of single-channel data collection. Separately, we tested YFP fluorescence to ensure CaM-YFP overexpression, and only cells positive for both XRhod1 and YFP were selected for electrophysiology in subsequent experiments. In these cells, we recorded Na⁺ currents across cell-attached one-channel patches for 10–15 min before ionomycin addition. These were assumed to represent active channels and represented paired controls for each data point obtained after ionomycin treatment.

Upon ionomycin application with 10 μM Ca²⁺ in the bath, intracellular Ca²⁺ rose to a steady-state level of ∼10 μM within 2 min, after which currents were assumed to represent inactivated channels (Fig. 2 e). This intracellular concentration is predicted to elicit ∼75% inactivation and minimal effects of Ca²⁺ block due to Ca²⁺ efflux (21). Relative to preionomycin (active), postionomycin (inactivated) currents displayed significantly reduced channel gating with no change in unitary current amplitude, which indicates the absence of current block from contaminating efflux of Ca²⁺ (Fig. 3 a; Table 1). We found that the activity of GluN1–2a/GluN2A receptors significantly decreased following ionomycin treatment (P_o,pre = 0.32 ± 0.03; P_o,post = 0.06 ± 0.02; n = 5; p = 0.0195). Using Eq. 7, we found that CDI_SCH = 0.79 ± 0.02. We observed a similar decreased activity for GluN1–2a/GluN2B receptors following ionomycin treatment (P_o,pre = 0.13 ± 0.01; P_o,post = 0.07 ± 0.02; n = 4; p = 0.0407) for a calculated CDI_SCH. To determine how these values compare with CDI_WC measured under comparable conditions (intracellular Ca²⁺ dialysis), we pooled the single-channel and whole-cell data for both GluN2A and GluN2B receptors and performed a linear regression with a constrained model through 0 intercept and a slope of 1 (perfect correlation model) and an unconstrained model in which slope and intercept were free parameters. The results indicated that the empirical data did not significantly diverge from perfect congruence between CDI_WC and CDI_SCH measurements (p = 0.84, Fig. 2 f).

Figure 3.

Kinetic mechanism of CDI in GluN2A and GluN2B receptors. (a) Shown are unitary current traces (3 s) recorded before (pre) and after (post) ionomycin application from cell-attached patches containing one GluN1–2a/GluN2A (left, n = 5) or one GluN1–2a/GluN2B (right, n = 4), with 0 Ca²⁺ in pipette and 10 μM Ca²⁺ in bath. (b) Shown are histograms of closed interval durations measured from one-channel recordings as in (a), overlaid with exponential components (thin lines) and probability density functions (thick) calculated with the models in (c) fitted to the data. Shaded regions represent significantly different changes in time constants or area parameters compared to preionomycin control (Table 2). Insets: state occupancies calculated with the models in (c). (c) Shown are kinetic schemes and optimized rate constants by fittings to the sequence of closed and open events in one-channel current recordings. Rates (s⁻¹) represent rounded average values from repeat measurements. In red, rates with statistically significant differences relative to preionomycin treatment are shown (^∗p < 0.05, Student’s two-tailed t-test). (d) Shown are energy diagrams of states along the activation pathway normalized to the open state (O) for GluN2A (top) and GluN2B (bottom) before (pre) and after (post) ionomycin treatment. (e) Shown is an evaluation of fold change in desensitized states occupancy for the preionomycin model obtained upon systematically changing the indicated rate constant in GluN2A and GluN2B receptors and simulating the state occupancy response to 20 s of saturating agonist using Eq. 9. To see this figure in color, go online.

Table 1.

Summary of Single-Channel SKM Results

Construct	Po	Mean Open Time (ms)	MCT (ms)	Po,burst	MCTburst (ms)	Unitary Amplitude (pA)	Total nevents	Total Time (min)
GluN1–2a/GluN2A (pre)	0.32 ± 0.07	3.6 ± 0.1	12.4 ± 6.5	0.57 ± 0.01	2.7 ± 0.1	9.7 ± 0.2	32,7900	59
GluN1–2a/GluN2A (post)	0.06 ± 0.01a	3.5 ± 0.4	88 ± 27a	0.44 ± 0.04a	4.5 ± 0.7	9.5 ± 0.2	89,437	91
GluN1–2a/GluN2B (pre)	0.13 ± 0.01	3.3 ± 0.3	22.1 ± 2.9	0.34 ± 0.02	6.2 ± 0.4	10.2 ± 0.5	108,821	43
GluN1–2a/GluN2B (post)	0.07 ± 0.02a	5.1 ± 0.5a	87.3 ± 28.3	0.39 ± 0.04	8.2 ± 0.5a	9.8 ± 0.4	69,871	83

All values reported as mean ± SE unless otherwise indicated.

^ap < 0.05 two-tailed t-test compared to preionomycin control.

To examine which kinetic parameter(s) contributed to the reduced open probability upon ionomycin treatment, we compared time constants obtained from one-channel currents recorded before and after ionomycin treatment for each subtype (Table 1). For both receptors, the decrease in P_o was due entirely to increased mean closed times (MCT) because the mean open time (MOT) was either unchanged or slightly increased. For GluN2A, ionomycin treatment increased the MCT sevenfold, whereas the MCT within bursts (MCT_burst) remained unchanged. Similarly, for GluN2B receptors, ionomycin increased MCT fourfold, even if not with statistical significance, and the MCT_burst increased moderately (1.5-fold). Importantly, the histograms of closed event durations revealed the same number of exponential components required to describe fully the activity for both active and inactivated channels (Fig. 3 b). Thus, in both GluN2A and GluN2B receptors, the effects of intracellular Ca²⁺ manifested by altering the receptors’ ability to transition among a predefined gating pathway rather than inducing receptors to transition into a unique “inactivated state/configuration.” These results validate previous observations from excised patches and demonstrate a purely allosteric mechanism for CDI (32). Given the congruence between CDI_WC and CDI_SCH measurements, we conclude that the use of single-channel recordings is suitable for the development of a realistic kinetic model of CDI.

CDI of GluN2A and GluN2B receptors occurs largely by a common mechanism

We examined the kinetic mechanism by which the gating equilibrium changed upon intracellular Ca₂₊ elevation using a validated NMDA receptor gating model (28). We fitted this model to the sequence of open and closed events detected in the single-channel record and estimated rate constants for each of the transitions explicitly included in the model (Fig. 3, b and c). Notably, for both GluN2A and GluN2B channels, intracellular Ca²⁺ changed rate constants directly along the activation pathway rather than tangentially related rates for entry or recovery from desensitized states C₄, C₅ (Fig. 3, b and c; Table 2). Common to both subtypes, we found that the activation rates C₃→C₂ and C₂→C₁ were significantly slower (Fig. 3 c). In addition, we found that for GluN2A, the opening rate C₁→O was also slower, whereas for GluN2B, the closing rate C₁←O was slower. Although desensitization rate constants were unchanged for inactivated receptors, the increased occupancy of preopen closed states immediately adjacent provided more opportunities for channels to desensitize and, in effect, increased substantially the occupancy of long-lived closed states for both receptor types (Fig. 3 b, inset; Fig. 3 c). Therefore, a higher energy barrier for the C₃ to C₂ transition likely represents a common mechanism for CDI for the two most abundant NMDA receptor subtypes (Fig. 3 d).

Table 2.

Summary of Single-Channel Dwell-Time Fit Results

Construct	Closed					Open
	τ1 (A1)	τ2 (A2)	τ3 (A3)	τ4 (A4)	τ5 (A5)	τo, Ao
GluN1–2a/GluN2A (pre)	0.23 ± 0.01	2.18 ± 0.07	6.9 ± 0.4	27 ± 5	3915 ± 2492	4.2 ± 0.1
	(0.31 ± 0.01)	(0.33 ± 0.01)	(0.34 ± 0.02)	(0.02 ± 0.01)	(0.001 ± 0.001)	(1.00)
GluN1–2a/GluN2A (post)	0.29 ± 0.01a	3.55 ± 0.63	15.4 ± 2.9a	1211 ± 895	5426 ± 1311	3.8 ± 0.4
	(0.27 ± 0.01)	(0.41 ± 0.06)	(0.27 ± 0.04)	(0.04 ± 0.02)	(0.01 ± 0.01a)	(1.00)
GluN1–2a/GluN2B (pre)	0.28 ± 0.01	2.61 ± 0.12	12.9 ± 1.1	54 ± 5	1385 ± 88	3.5 ± 0.3
	(0.22 ± 0.01)	(0.19 ± 0.01)	(0.52 ± 0.01)	(0.05 ± 0.01)	(0.01 ± 0.01)	(1.00)
GluN1–2a/GluN2B (post)	0.29 ± 0.01	3.04 ± 0.11a	19.9 ± 0.8a	66 ± 5	4473 ± 2341	5.5 ± 0.5a
	(0.24 ± 0.01)	(0.25 ± 0.01a)	(0.44 ± 0.02a)	(0.04 ± 0.01)	(0.02 ± 0.01a)	(1.00)

All time constants are reported as mean ± SE in units of ms.

^ap < 0.05 two-tailed t-test compared to preionomycin control.

To learn how these kinetic changes contributed to the CDI sensitivities of GluN2 subtypes, we sought to determine the relative contributions by each rate constant change to the increased accumulation of receptors in desensitized states. We took a simulation approach and examined how perturbations of a varying degree in individual rate constants influenced the magnitude of C₄ and C₅ occupancies. In the active channel model (preionomycin), we systematically scaled each CDI-sensitive rate by 10-fold (∼5 kJ energy barrier) above and below its measured value while leaving all other rate constants unchanged. We next calculated the fold change in desensitization states occupancy at equilibrium (Fig. 3 e). This analysis indicated that for all rates examined, GluN2A desensitization showed the largest dynamic range, supporting the more pronounced effects of Ca²⁺ on macroscopic CDI in this subtype. Further, focusing on the rate constants commonly affected in both GluN2A and GluN2B, C₃→C₂ and C₂→C₁, we found that these were both highly effective at increasing the occupancy of desensitized states such that small decreases in these rates resulted in a large increase in desensitization (Fig. 3 e, left). Last, focusing on subtype-specific rate changes, we found the most effective rate constants were the activation rate C₁→O for GluN2A and the deactivation rate C₂←C₁ for GluN2B (Fig. 3 e, right). Therefore, CDI engages both common and subtype-specific kinetic mechanisms, and subtle changes in rate constants produce large effects on desensitization occupancies.

Low P_o of GluN2B currents limits their autoinhibition by CDI

Notably, the largely common kinetic mechanism for CDI_SCH for GluN2A and GluN2B channels leaves unexplained the large differences in CDI_WC observed when Ca²⁺ flux is mediated directly by NMDA receptor activity. To address this, we sought to develop a full kinetic model that can reproduce dynamically the equilibrium between active and inactivated channels during Ca²⁺ flux through open NMDA receptors. To do this, we assumed that at rest, all channels are in the active mode and, therefore, will gate initially with active kinetics. Upon glutamate binding, as channels open stochastically, only channels that open, and therefore pass Ca²⁺, can inactivate. Last, upon inactivation, channels will gate with inactivated kinetics until 1) CaM dissociates, when they become active again, or 2) glutamate dissociates, when they deactivate and initially populate resting inactivated states and, upon Ca²⁺/CaM dissociation, transition into resting active states (Fig. 2 a) (21). This scenario can be represented with a tiered model in which the active channels, when open, can transition into inactivated open channels upon Ca²⁺ binding. Such a model is consistent with the observation that CDI is mediated by intracellular Ca²⁺ elevations within a local nanodomain around the channel pore and, therefore, is an autoinhibitory effect of fluxed Ca²⁺ binding to receptor-bound CaM (21).

To determine rate constants for transitions between tiers, we estimated rates for channel inactivation and recovery from whole-cell current recordings. We measured the time course of inactivation (τ_CDI) in increasing concentrations of extracellular Ca²⁺ for cells dialyzed with intracellular 5 mM BAPTA, which preserves the local Ca²⁺ signal as the dominant driver of CDI. We used the Lineweaver-Burk analysis to determine the Ca²⁺ dependency of the forward rate constant. Ca²⁺ concentrations used in the analysis reflect the Ca²⁺ experienced by the local CaM molecule during a channel open event, which we estimated previously to reside at ∼10 nm from the pore (21). We found the forward rate to be 0.011 μΜ⁻¹ s⁻¹. We have previously measured the time constant of recovery from inactivation (τ_REC) to be 9.2 s, which corresponds to k_REC = 1/τ_REC = 0.108 s⁻¹ (21). In both cases, these measured rate constants reflect the net result of several processes that engage and relieve CDI combined with the intramolecular receptor changes during inactivation and recovery (Fig. 2 a).

Using these rate constants and glutamate binding/dissociation rate constants determined previously for each subtype (46, 47), we built the tiered model illustrated in Fig. 4 c (see Methods). We aimed to simulate population responses as time-dependent open probabilities during a 5-s pulse of Glu (1 mM) in conditions resembling physiological Ca²⁺ (2 mM external, as in Fig. 1 a) and with dialyzed Ca²⁺ (50 μM internal, as in Fig. 1 b, see Methods). To simulate currents in control (no Ca²⁺) conditions, we started the channels in the resting active state (upper tier) and set the Ca²⁺ concentration to zero to prevent access into inactivated states (Fig. 4 d, black traces). As reported previously, these models reproduce well whole-cell currents measured in similar conditions from GluN2A (28, 48) and GluN2B (46) channels.

To simulate population responses in physiologic Ca²⁺, we started all channels in the resting active state (upper tier) and set the Ca²⁺ concentration to 90 μM (the predicted local Ca²⁺ concentration upon influx detected by resident CaM on GluN2A channels) (21). Using the GluN2A model, the predicted CDI level was observable but submaximal, consistent with whole-cell currents recorded in similar conditions (Figs. 1 a and 4 d). In contrast, the model optimized for GluN2B channels predicted minimal CDI as observed with macroscopic measurements. Simulations for Ca²⁺ dialysis conditions were carried out by setting the Ca²⁺ concentration to 50 μM and initializing 83% of receptors in the unliganded state of the inactive arm and 17% in the unliganded state of the active arm, as approximated from an equilibrated two-state model connected by the measured k_on and k_off for CDI with [Ca²⁺] set to 50 μM (Fig. 4 b). These results suggest that intrinsic differences in gating kinetics between GluN2A and GluN2B channels produce Ca²⁺ fluxes that are sufficiently distinct as to produce subtype-specific levels of CDI.

Autoinhibition of GluN2B currents by CDI unmasked in high P_o receptors

To test the hypothesis that in physiologic Ca², the marked difference in between GluN2A and GluN2B CDI_WC reflects intrinsic differences in channel P_o, we tested receptors containing a high P_o GluN1–2a mutant. NMDA receptors with mutations in the highly conserved SYTANLAAF sequence along the M3 transmembrane helix typically show increased activity (49, 50). This region is critical for channel activation, and mutations in this region have been associated with neurodegeneration (51) and epilepsy (52). In particular, we found that when paired with GluN1^A652Y, GluN2B receptors have fourfold higher P_o relative to wild-type channels (P_{o, A652Y} = 0.81 ± 0.08 versus P_o,WT = 0.13 ± 0.07; n = 5, p = 0.005). In contrast to wild-type GluN2B, this mutant exhibited robust CDI in physiological conditions (Fig. 5, b and c). Given a common mechanism of CDI across receptor subtypes, we pooled data together across all experimental conditions examined in this study. From this larger data set, we observed that the intrinsic activity patterns of GluN2A and GluN2B receptors in Ca²⁺-free conditions (P_o,A) predict a nonlinear relationship with their autoinhibitory macroscopic CDI_EQ (Fig. 5 c, right). This observation suggests that contrary to previous claims (20), both GluN2A and GluN2B receptors are highly sensitive to inactivation by intracellular Ca²⁺ elevations. Even so, our results predict that Ca²⁺ fluxes passed by receptors gating with P_o,A lower than ∼0.1 would be insufficient to produce observable CDI (Fig. 5 c, right).

Based on these results, we propose that although the overall Ca²⁺ permeability and conductance of GluN2A and GluN2B channels are similar, their intrinsic differences in gating kinetics result in distinct levels of local Ca²⁺ elevation, and for GluN2B receptors, these are insufficient to effectively engage CDI in physiologic conditions (Fig. 6). By extension, mutations, chemical modulators, or other perturbations that increase channel P_oA will also increase their sensitivity to CDI.

Figure 6.

Proposed model of local CDI during development. (a) Shown is a schematic of CaM-bound GluN2A and GluN2B receptors at rest and after activation. At rest, apocalmodulin resides on the C0 cassette of GluN1. After activation, the magnitude of CDI generated by local Ca²⁺ influx is proportional with channel P_o. High P_o receptors allow robust Ca²⁺ influx that can engage CaM and initiate CDI. In contrast, low P_o receptors results in Ca²⁺ flux that is insufficient to trigger CDI. (b) Hypothetical macroscopic currents predicted based on results in this study as allosteric modulators or disease mutations modulate channel P_o throughout development. To see this figure in color, go online.

Discussion

In this study, we provide the first evidence, to our knowledge, that the juvenile GluN2B-containing NMDA receptor subtype can undergo robust CDI. Further, we demonstrate that NMDA receptor CDI is an ergodic process and can be measured from the activity of individual channels. We used single-molecule patch-clamp fluorometry to develop the first, to our knowledge, gating models of Ca²⁺-inactivated NMDA receptors. Our models account well for the experimental macroscopic CDI values and allow new predictions of how mutations and modulators that affect receptors’ open probability can also alter their sensitivity to CDI. These new quantitative insights into a differential modulation of NMDA receptor Ca²⁺- and CaM-dependent autoinhibition have important implications for understanding the structural bases of CDI, for delineating physiologic regulatory mechanisms at work during synaptic development, and for uncovering correlations between NMDA receptor dysregulation and neuropsychiatric disorders.

Structural insights into CDI

Our kinetic analyses reveled both common and subtype-specific energetic changes to NMDA receptor gating by Ca²⁺ association with GluN1-resident CaM. Importantly, we found that CDI changed mainly the activation pathway to stall receptors in preopen states, which produced, as a secondary outcome, an accumulation of receptors in off-pathway desensitized states. Overall, these energetic changes manifested as a more pronounced reduction of the sustained macroscopic response (i.e., increased desensitization of the macroscopic current) (Fig. 3). For NMDA receptors, kinetic gating models provide robust, quantitative descriptors of channel activity. However, the structural correlates of individual kinetic states and the movements underlying transition steps remain presently undefined. Recent cryogenic electron microscopy data have revealed several agonist-bound, nonconducting conformations consistent with the multiple preopen states identified in single-channel recordings. Even so, a direct correspondence between kinetic and structural states is yet to be determined. Similarly, the structural changes driven by Ca²⁺/CaM binding have also remained elusive.

The kinetic mechanism of NMDA receptor CDI has been difficult to ascertain because of the experimental challenge of isolating CDI from other Ca²⁺-dependent regulatory mechanisms. Typically, CDI has been studied using macroscopic current recordings with prolonged agonist applications. In these experiments, CDI has been consistently observed as an increase in current desensitization and has been assumed to be mediated by the stabilization of intrinsic desensitized states or/and entry into a new CDI-specific inactivated state(s) (17, 53). These hypothesized mechanisms were difficult to reconcile with reports that Ca²⁺/CaM specifically reduced channel open durations and accelerated deactivation, both of which indicated changes in the activation/deactivation pathway. The measurements and analyses we report here show that CDI reflects changes in the NMDA receptor activation pathway, specifically a slowing of the C₃ to C₂ transition, which in time causes receptors to accumulate in desensitized states. Importantly, the desensitized states do not appear changed (stabilized or destabilized). Consistent with this mechanism, receptors with faster activations (GluN2A or GluN2B mutants) display stronger CDI, whereas receptors with slow activation (GluN2B and perhaps GluN2C) appear to be insensitive to CDI. Therefore, Ca²⁺ binding to CaM-primed receptors is likely to control the stability of preopen rather than desensitized or unique inactivated states. These results favor the term “calcium-dependent desensitization” over “calcium-dependent inactivation” in describing the effect of intracellular Ca²⁺ on CaM-bound NMDA receptors (17). Structurally, however, given that C0, the CaM effector site on GluN1, is directly contiguous with M4, it is likely that M4 serves as a critical element to transduce conformational changes by Ca²⁺ binding to CaM from the C-terminal domain to the channel gate. Several previous reports implicated motions in the M4 helix in channel activation (32, 54, 55, 56). Thus, subtle structural variations in M4 and its relationship to other structural gating elements may regulate NMDA receptor CDI and thus neuronal excitability in physiological and disease states.

Implications for synaptic development and maturation

During development, synaptic NMDA receptor subunit expression profile undergoes dramatic shifts (57). Similarly, as a synapse matures in response to stimulation, its NMDA receptor profile shifts from GluN2B to GluN2A dominant (58). Our current and previous results (21) suggest that kinetic differences in NMDA receptor subtypes result not only in differential response kinetics but also in their sensitivity to CDI, which in turn manifests as differential sensitivity to activity-dependent inhibition. Further, our results reveal that modulators of channel activity will also influence how activity shapes the subsequent NMDA receptor response. Many physiological modulators are present at a synapse that tunes the NMDA receptor signal, some of which occur in response to different physiological states. Their presence likely produces unique CDI profiles for each NMDA receptor subtype. Our results are congruent with a model whereby immature GluN2B synapses are relatively resistant to activity-dependent inhibition and maintain steady levels of activity regardless of stimulation frequency. The stable influx of Ca²⁺ may be necessary to initiate plasticity (synapse growth and maturation) or spine retraction (pruning) necessary for circuit sculpting (59, 60). As synapses mature and become dominated by GluN2A, they become more sensitive to activity-dependent inhibition, combining high flux, perhaps necessary in larger spines, but also a robust autoinhibitory mechanism, which may limit Ca²⁺ flux, which when excessive can become neurotoxic. This arrangement provides a more dynamic range of NMDA receptor-mediated Ca²⁺ flux and is consistent with distinct roles of each subtype during development (61).

Our observation that CDI is nonlinearly related to channel activity (Fig. 5 c, right) suggests that CDI is a highly potent mechanism of inhibition of NMDA receptors. Nonlinear relationships have been shown in empirical and theoretical studies to have profound implications in boosting the computational capacity of neurons in shaping various forms of plasticity (62, 63). It has been suggested that NMDA receptor CDI is critical in setting the threshold for long-term potentiation (64). Thus, the nature of the relationship between intrinsic channel activity and subsequent CDI is important to understanding how various stimuli elicit plasticity. In previous work, we observed a linear relationship between receptor P_o and CDI (21) when we measured CDI with intracellular BAPTA to isolate CDI driven exclusively by local Ca²⁺ nanodomains. In the current work, we measured CDI with intracellular EGTA, which allows a wider spread of the Ca²⁺ transient (Figs. 1 a and 5, a and b). The apparent shift from linear to nonlinear dependence upon switching from BAPTA to EGTA suggests additional modes of recruiting CaM-dependent inhibition in addition to the local autoinhibition by resident CaM. Specifically, this observation may highlight the ability of channels to gate cooperatively as through a Ca²⁺-spillover mechanism as has been observed as well as in other channels (65) or through interactions with other channels (64, 66). In addition to these inhibitory mechanisms, Na⁺/Ca²⁺ exchangers have been shown to be important in moderating the extent of CDI (67). Thus, CDI can be recruited by local as well as global Ca²⁺ signals and may be under multiple regulatory mechanisms in postsynaptic compartments, consistent with the physiological importance of this process.

Implications for disease pathogenesis

NMDA receptors are the principal activity-dependent Ca²⁺ sources in spines and given the myriad informational content of Ca²⁺ fluxes; NMDA receptor responses are regulated with mechanisms that are complex, even if incompletely understood. Recently, mutations in NMDA receptor subunits have been shown to be causal to human neuropathologies, and the number of known disease-associated mutations is currently expanding because of genome-wide sequencing efforts in patients and their families (68, 69, 70, 71). However, it is largely unknown how these patient-derived mutations influence channel function. Also unknown is the mechanism by which these functional changes translate into disease phenotype. Here, we show that our previous results establishing the importance of receptor P_o in engaging CDI for GluN2A receptors also apply to GluN2B receptors (21). Thus, disease mutations or pharmacological modulators that increase channel P_o during development may engage stronger CDI as a protective means to curb pathological Ca²⁺ influx. Further, mutations that affect the CDI machinery within the receptor or CaM mutations that affect Ca²⁺ binding and produce calmodulinopathies may result in a boosting of channel P_o by the loss of disinhibition due to attenuated CDI. Disease-associated mutations in the M4 helix, a likely critical transduction element for CDI progression, have been shown to have severe functional perturbations (55). One study observed neurological symptoms in a pediatric sample of individuals with CaM mutations (72), although it is yet unclear whether the observed seizures were due to CaM actions in the brain or altered blood flow to the brain as a result of comorbid cardiac defects associated with the CaM mutations. Whether such mutations in either the NMDA receptor or CaM also affect NMDA receptor CDI is the subject of future research. Recent evidence has suggested the therapeutic actions of memantine may be in part due to a stabilization of the Ca²⁺-dependent desensitized state (73). Thus, CDI likely plays a critical role in NMDA receptor physiology and circuit development (60). This evidence strengthens the impetus for exploring the clinical utility of state-dependent modulators of NMDA receptors in treating disease and mental illness (74).

Author Contributions

This project was conceived, and manuscript was prepared by G.J.I. and G.K.P.; G.J.I. performed all experiments and analyzed results.

Editor: Vasanthi Jayaraman.