The effect of extracellular and intracellular Na+ on the single-channel kinetics of Mg2+ block was studied in recombinant NR1-NR2B NMDA receptor channels. Na+ prevents Mg2+ access to its blocking site by occupying two sites in the external portion of the permeation pathway. The occupancy of these sites by intracellular, but not extracellular, Na+ is voltage-dependent. In the absence of competing ions, Mg2+ binds rapidly (>108 M−1s−1, with no membrane potential) to a site that is located 0.60 through the electric field from the extracellular surface. Occupancy of one of the external sites by Na+ may be sufficient to prevent Mg2+ dissociation from the channel back to the extracellular compartment. With no membrane potential; and in the absence of competing ions, the Mg2+ dissociation rate constant is >10 times greater than the Mg2+ permeation rate constant, and the Mg2+ equilibrium dissociation constant is ∼12 μM. Physiological concentrations of extracellular Na+ reduce the Mg2+ association rate constant ∼40-fold but, because of the “lock-in” effect, reduce the Mg2+ equilibrium dissociation constant only ∼18-fold.

Introduction

At synapses, the channel domain of the N-methyl-d-aspartate receptor (NMDAR) interacts with several different metal cations, including Na+, K+, Ca2+, and Mg2+. These interactions have important physiological consequences. Activation of NMDARs depolarizes dendrites, with Na+ and K+ carrying the bulk of the current. Ca2+ entry into dendrites via NMDARs regulates synaptic strength and plasticity (Maren and Baudry 1995; Asztely and Gustafsson 1996). Voltage-dependent Mg2+ block of NMDARs may allow these receptors to respond specifically to contemporaneous excitatory inputs and, thus, serve as a substrate for Hebbian learning. Given such critical functions, it is likely that the NMDAR has specific structures that govern the passage of Na+, K+, Ca2+, and Mg2+ through its ion permeation pathway.

These four cations interact with the NMDAR protein over time scales that span more than four orders of magnitude. Na+ and K+ are highly permeable and pass through the pore rapidly. In symmetric, 100-mM divalent cation-free solutions, the NMDAR conductance is ∼70 pS for both of these ions, which means that at −60 mV, Na+ and K+ interact with the channel for <0.04 μs. The contact between these ions and the protein is too brief to be resolved as discrete events in the single-channel record. Instead, the interaction of Na+ and K+ with the NMDAR pore has been probed mainly using current-voltage relationships (Mayer et al. 1984; Nowak et al. 1984; Cull-Candy and Usowicz 1987) and by measuring their effects on channel block (Chen and Lipton 1997; Antonov et al. 1998; Antonov and Johnson 1999).

Under physiological conditions, ∼10–15% of the NMDAR current is carried by Ca2+ (Burnashev et al. 1995). This divalent cation moves through the wild-type (NR1-NR2B) channel ∼100 times more slowly than Na+, i.e., with a rate constant of ∼106 s−1 (Premkumar and Auerbach 1996). Thus, Ca2+ resides in the permeation pathway for ∼1 μs. Information regarding Ca2+ transmission has been derived mainly from measurements of macroscopic currents (Mayer and Westbrook 1987; Iino et al. 1990; Jahr and Stevens 1993; Sharma and Stevens 1996b), single-channel currents (Iino et al. 1997), or fluxes (Burnashev et al. 1995). However, certain mutations reduce the Ca2+ permeation rate constant to such an extent that its binding and unbinding are manifest as excess open channel noise (Premkumar and Auerbach 1996).

Mg2+ is the slowpoke of the group. This divalent cation typically dwells in the pore for >100 μs (Ascher and Nowak 1988; Jahr and Stevens 1990). Occupancy of the channel by one Mg2+ eliminates conduction by other ions and generates a discrete gap in the single-channel current record. Therefore, the microscopic rate constants for Mg2+ entry and exit from the pore can be determined readily using single-channel kinetic techniques (Ascher and Nowak 1988).

The compositions, characteristics, and locations of the important sites of ion interaction in the NMDAR permeation pathway are not completely understood. Mg2+ binds to a site that is (in electric distance) about half way through the channel (Wollmuth et al. 1998; Antonov and Johnson 1999). This site is formed, in part, by an asparagine residue in the M2 (pore-forming) segment of the NR2 subunit (Wollmuth et al. 1998), although mutations of other M2 residues also influence Mg2+ blockade (Burnashev et al. 1992; Sharma and Stevens 1996a). Ca2+ binds to a site that is distinct from the Mg2+ binding site and that may lie at the extracellular margin of the electric field of the membrane (Premkumar and Auerbach 1996; Sharma and Stevens 1996b). Na+ interacts with two sites that are also located at the extracellular limit of the electric field (Antonov et al. 1998). The residues that constitute the Ca2+ and Na+ binding sites have not been clearly identified. In addition, almost nothing is known about the key sites of interaction for K+ in the NMDAR channel.

The vast difference in residence times for Na+ and K+ versus Mg2+ in the NMDAR channel is such that there are on the order of 104 monovalent cation-binding/unbinding events for each Mg2+ binding event. Accordingly, the occupancy by monovalent cations is in steady state on the time scale of Mg2+ blockade. The locations and affinities of the binding sites for these mobile ions can be probed by measuring the effect of the extra- and intracellular concentrations of Na+ and K+ on the kinetics of Mg2+ block. This approach has been used to probe permeant ion binding sites in native NMDARs (Antonov et al. 1998; Antonov and Johnson 1999).

In this and in the companion paper (see Zhu and Auerbach 2001, in this issue), we present a single-channel analysis of the effects of extra- and intracellular Na+ and K+ on the kinetics of Mg2+ block of recombinant NR1-NR2A NMDAR. The results suggest that Na+ mainly interacts with two sites that are located external to the site of Mg2+ blockade, whereas K+ interacts with these sites plus an additional site located near the intracellular margin of the electric field. We extrapolate the results to estimate the kinetics, affinity, and voltage dependence of Mg2+ block in the absence of competing ions.

Materials And Methods

Expression of NMDAR in Xenopus Oocytes

Wild-type rat cDNA for the NR1 (splice variant 1) and NR2A subunits were provided by Dr. Thomas Kuner and Dr. Peter Seeburg (Max-Planck Institute for Medical Research, Heidelberg, Germany). These two subunits were coexpressed in Xenopus oocytes by injection of 50 nl each of cRNA (1 μg/ml). Electrophysiology experiments were performed 3–10 d after injection. A more detailed description of the molecular biology and expression protocols is given in Premkumar and Auerbach 1996.

Electrophysiology and Solutions

Single-channel currents were recorded from outside-out patches. Recording pipets were pulled from borosilicate glass (World Precision Instruments) and were coated with Sylgard (Dow Corning). The pipet resistance was 10–15 MΩ. Patch pipets were filled with the following reagents (in mM): 5–100 NaCl, 2 K2ATP, 1 BAPTA, 0.25 GTP, and 10 HEPES, pH adjusted to 7.3. The extracellular solution contained 50 μM NMDA, 10 μM glycine, 2.5 mM KCl, 5 mM HEPES, and 1.5 mM EDTA (pH adjusted to 7.3) plus added NaCl, KCl, and MgCl2 (ultrapure grade from Johnson Mattey). BAPTA, EDTA, HEPES, and all other salts were obtained from Sigma-Aldrich. Without compensation by other ions, the amount of NaCl or KCl was adjusted to achieve the desired Na+ or K+ concentration. Using the parameters estimated by the program MAXC, the desired free Mg2+ concentrations were established by adding the calculated amount of MgCl2 to solutions buffered with EDTA (1.5 mM) as the Mg2+ chelator. Here, we report [Mg2+] as a concentration rather than an activity. Glucose was added to the extracellular solution or pipet solution to balance the osmolarity. The junction potentials between the pipet solution and the extracellular solution were calculated and the membrane potential was corrected accordingly (Barry and Lynch 1991). All experiments were performed at 22–25°C. Upon excision of patches in the outside-out configuration, an ALA BPS-4 perfusion system (ALA Scientific Instruments) controlled the exchange of experimental and control solutions.

Signal Processing

The currents were recorded using a patch-clamp amplifier (model EPC-7; Medical-Systems-List). The currents were low-pass filtered at 10 kHz, sampled at 94 kHz using a data recorder (model VR-10B; Instrutech Corp.), and stored on videotape. Recorded currents were stored on a PC at sampling frequency of 94 kHz using a VR-111 interface (Instrutech Corp.).

Kinetic Analysis

To study the kinetic properties of Mg2+ block, it was necessary to distinguish the blocked state from the other nonconducting (closed) states. In the absence of Mg2+, NR1-NR2A receptors have two main conductance levels: open and closed (Fig. 1 A, top trace). There were usually two components in the open interval lifetime distribution (0.1 ms, 29%; and 5 ms, 71%; data not shown) and at least three components in the closed interval lifetime distribution (0.5 ms, 22%; 7 ms, 12%; and a duration >40 ms that varied with the agonist concentration; data not shown). The addition of Mg2+ to the extracellular solution induces frequent, brief gaps (Fig. 1 A, middle and bottom traces) that reflect the binding and unbinding of Mg2+ to the NMDAR channel.

The kinetics of Mg2+ block were quantified using the QuB software suite (www.qub.buffalo.edu). First, closed-channel events longer than 3 ms were discarded (program PRE, version 1.2.0.0). The remaining segments of current were digitally low-pass filtered (fc = 5 kHz; final signal fc = 4.5 kHz) and idealized using a recursive Viterbi algorithm (program SKM; version 1.1.0.000; Chung et al. 1990). From the idealized current level sequences, rate constants were estimated using a maximum interval likelihood approach that included a first-order correction for missed events (MIL; version 2.0.6.000; Qin et al. 1996). Typically, a dead time of 50 μs was imposed. Events shorter than this time were concatenated with the adjacent intervals. To account for a short-lived component of channel closure (as distinct from Mg2+ blockade), interval durations were fitted by a three-state (C1-O2-C3) model. Thus, any fast closures that were included along with the blocking gaps were explicitly taken into account. Density functions calculated from the fitted rate constants were superimposed upon interval duration histograms to provide a visual check of the accuracy of the fit (Fig. 1 B). The open channel lifetime was defined as the time constant of the slower, predominant component of the open interval duration distribution.

We used the following kinetic model (Scheme I) to describe the transitions between open and blocked states:

(Scheme I)

where k+Mg is the extracellular Mg2+ association rate constant, [Mg2+]ex is the extracellular [Mg2+] concentration, k−Mg is the Mg2+ dissociation rate constant (i.e., back to the extracellular solution), and kpMg is the Mg2+ permeation rate constant (i.e., into the intracellular compartment). k+Mg is related to the channel open lifetime (τo) by:

\begin{equation*}\frac{1}{{\mathrm{{\tau}}}_{{\mathrm{o}}}}={\mathrm{{\alpha}}}+{\mathrm{k}}_{+{\mathrm{Mg}}} \left \left[{\mathrm{Mg}}^{2+}\right] \right _{{\mathrm{ex}}}{\mathrm{,}}\end{equation*}

where α is the intrinsic channel closing rate constant. Thus, the inverse of the channel open lifetime is a linear function of [Mg2+]ex, with a slope equal to k+Mg (Fig. 1 C). Mg2+ unbinding, either by dissociation back to the extracellular solution or permeation through the channel, relieves the block. We define the sum of k−Mg and kpMg to be koff, which is the net rate for Mg2+ release from the pore.

According to this model, the equilibrium dissociation constant for Mg2+ (Kd, Mg) is defined as the ratio of the “off” rate and the association rate constant:

\begin{equation*}K_{{\mathrm{d,Mg}}}=\frac{{\mathrm{k}}_{-{\mathrm{Mg}}}+{\mathrm{k}}_{{\mathrm{pMg}}}}{{\mathrm{k}}_{+{\mathrm{Mg}}}}=\frac{{\mathrm{k}}_{{\mathrm{off}}}}{{\mathrm{k}}_{{\mathrm{on}}}}{\mathrm{.}}\end{equation*}

In the following studies, k+Mg, k−Mg, and kpMg were estimated as a function of the concentration of permeant ions (Na+ or K+). Throughout, we use k to represent the apparent rate constant for Mg+2 block in the presence of permeant ions, and the Greek letter κ for the corresponding rate constant in the absence of competing ions.

Fitting, Simulations, and Statistics

Fits and simulations were made using Microcal Origin (version 4.0; Microcal Software) and ScientisT (version 2.0; MicroMath Scientific Software). In ScientisT, the comparison of the models having different numbers of free parameters was carried out using the Model Selection Criterion (MSC):

\begin{equation*}{\mathrm{MSC}}={\mathrm{ln}}\frac{{{\sum^{{\mathrm{n}}}_{{\mathrm{i}}=1}}} \left \left({\mathrm{Y}}_{{\mathrm{obs}}_{{\mathrm{i}}}}-{\mathrm{{\hat {Y}}}}_{{\mathrm{obs}}}\right) \right ^{2}}{{{\sum^{{\mathrm{n}}}_{{\mathrm{i}}=1}}} \left \left({\mathrm{Y}}_{{\mathrm{obs}}_{{\mathrm{i}}}}-{\mathrm{Y}}_{{\mathrm{cal}}_{{\mathrm{i}}}}\right) \right ^{2}}-\frac{2{\mathrm{p}}}{{\mathrm{n}}}{\mathrm{,}}\end{equation*}

where n is the number of points, p is the number of free parameters, and Ŷobs is the mean of the observed data. The MSC will give the same ranking as the Akaike Information Criterion, but is normalized so that it is independent of the scaling of the data points. The most appropriate model, regardless of the number of free parameters, is the one with the largest MSC.

The number of intervals in each open or closed duration histogram was ∼1,000. Each symbol in the figures is the mean ± SD of from three to seven patches. In most cases, the SD was smaller than the size of the symbol and is not visible.

Results

Extracellular Na+ Decreases the Mg2+ Association Rate Constant in a Voltage-independent Manner

Fig. 2 A illustrates the effects of extracellular Na+ on Mg2+ association. At higher extracellular Na+ concentrations ([Na+]ex) openings are longer, indicating a reduced rate of Mg2+ association. In Fig. 2 B the inverse open channel lifetime is plotted as a function of [Mg2+]ex for different [Na+]ex. The slope of this relationship, which is the apparent Mg2+ association rate constant, is nearly five times slower in 150 mM [Na+]ex compared with 50 mM [Na+]ex.

We next examined the voltage dependence of the inhibition of Mg2+ association by extracellular [Na+] using the relationship:

\begin{equation*}{\mathrm{k}}_{+{\mathrm{Mg}}}^{{\mathrm{V}}}={\mathrm{k}}_{+{\mathrm{Mg}}}^{0}{\mathrm{e}}^{{\mathrm{{\psi}V}}}{\mathrm{,}}\end{equation*}
1

where kV+Mg is the apparent Mg2+ association rate constant at membrane potential V, k0+Mg is this rate constant in the absence of a membrane potential, and ψ is the apparent voltage dependence of this rate constant (i.e., the inverse of the voltage that elicits an e-fold change). The voltage dependence of kV+Mgwas the same at two different [Na+]ex (Fig. 2 C), which indicates that the inhibition of the apparent Mg2+ association rate constant by extracellular [Na+] is not voltage-dependent.

Intracellular Na+ Decreases the Mg2+ Association Rate Constant in a Voltage-dependent Manner

Fig. 3 A shows the effects of intracellular Na+ on Mg2+ association. The open channel lifetime is longer at higher [Na+]in, indicating a reduced k+Mg. Fig. 3 B shows that the reduction in k+Mg by [Na+]in decreases with hyperpolarization, i.e., that [Na+]in inhibits Mg2+ association in a voltage-dependent manner. Using , the apparent voltage dependence of Mg2+ association decreases from 44 ± 1 mV per e-fold change in 5 mM [Na+]in, to 32 ± 2 mV per e-fold change in 100 mM [Na+]in.

The Locations and Apparent Affinities of the Na+ Binding Sites

The effects of [Na+]ex and [Na+]in on Mg2+ association suggests that these ions compete for positions in the Mg2+ association pathway. In the next stage of the analysis, we invoke physically based models that assume that the presence of one or more Na+ in the permeation pathway substantially reduces or eliminates Mg2+ association.

We start with a simple “one-site” scheme to describe the effects of Na+ on Mg2+ association. It is assumed that the Na+ site is external to, or at the same location as, the Mg2+ site, and that extracellular Mg2+ can enter and block the channel only when the Na+ site is empty. Accordingly (see  ), the apparent Mg2+ association rate constant (i.e., in the presence of Na+), kV+Mg, is a function of three experimental variables ([Na+]ex, [Na+]in, and V) and five free parameters (κ0+Mg, KNaex, KNain, δ, and α):

\begin{equation*}{\mathrm{k}}_{+{\mathrm{Mg}}}^{{\mathrm{V}}}={\mathrm{{\kappa}}}_{+{\mathrm{Mg}}}^{0}{\mathrm{e}}^{\frac{-2{\mathrm{{\delta}V}}}{{\mathrm{k}}_{{\mathrm{B}}}{\mathrm{T}}}} \left \left(1+\frac{ \left \left[{\mathrm{Na}}^{+}\right] \right _{{\mathrm{ex}}}}{{\mathrm{K}}_{{\mathrm{Na}}_{{\mathrm{ex}}}}}+\frac{ \left \left[{\mathrm{Na}}^{+}\right] \right _{{\mathrm{in}}}}{{\mathrm{K}}_{{\mathrm{Na}}_{{\mathrm{in}}}}^{0}{\mathrm{e}}^{\displaystyle\frac{-{\mathrm{{\alpha}V}}}{{\mathrm{k}}_{{\mathrm{B}}}{\mathrm{T}}}}}\right) \right ^{-1}{\mathrm{.}}\end{equation*}
2

kV+Mg is the Mg2+ association rate constant in the absence of competing ions at membrane potential V, and KNaex and K0Nain are dissociation constants (koff/kon) for [Na+]ex and [Na+]in, respectively, with no membrane potential. Note that because Na+ is a permeant species, these are not equilibrium constants. The two apparent fractional electrical distances in are δ (between the extracellular compartment to the peak of the entry barrier for Mg2+) and α (between the Na+ binding site and the intracellular compartment). kB is Boltzmann's constant, and T is the absolute temperature (kBT = 25.3 mV).

Fig. 4 A shows the result of fitting simultaneously (using ) two groups of measurements of kV+Mg as a function of membrane potential. The first group (Fig. 4 A, left) was obtained from five different [Na+]ex (25–150 mM) at a single, high [Na+]in (100 mM). The second group (Fig. 4 A, right) was obtained from two different [Na+]ex (50 and 150 mM) at a single, low [Na+]in (5 mM). The curves drawn according to the best fit by clearly do not describe the experimental data.

Next, we modified the model to incorporate multiple Na+ binding sites in the channel. We assume that Mg2+ can access its site only when all n sites are empty, and, for simplicity, that these sites are identical and independent:

\begin{equation*}{\mathrm{k}}_{+{\mathrm{Mg}}}^{{\mathrm{V}}}={\mathrm{{\kappa}}}_{+{\mathrm{Mg}}}^{0}{\mathrm{e}}^{\frac{-2{\mathrm{{\delta}V}}}{{\mathrm{k}}_{{\mathrm{B}}}{\mathrm{T}}}} \left \left(1+\frac{ \left \left[{\mathrm{Na}}^{+}\right] \right _{{\mathrm{ex}}}}{{\mathrm{K}}_{{\mathrm{Na}}_{{\mathrm{ex}}}}}+\frac{ \left \left[{\mathrm{Na}}^{+}\right] \right _{{\mathrm{in}}}}{{\mathrm{K}}_{{\mathrm{Na}}_{{\mathrm{in}}}}^{0}{\mathrm{e}}^{\displaystyle\frac{-{\mathrm{{\alpha}V}}}{{\mathrm{k}}_{{\mathrm{B}}}{\mathrm{T}}}}}\right) \right ^{-{\mathrm{n}}}{\mathrm{,}}\end{equation*}
3

where n is a free parameter. Fig. 4 B illustrates the fit of the same two groups of experimental data by . The results are given in Table. A two-site scheme is able to describe the experimental results across Na+ concentrations and voltages.

Finally, we relaxed the constraint that the two Na+ binding sites are identical and independent. was modified to allow different dissociation constants (K1 and K2) at each of two distinct Na+ binding sites:

\begin{equation*}{\mathrm{k}}_{+{\mathrm{Mg}}}^{{\mathrm{V}}}={\mathrm{{\kappa}}}_{+{\mathrm{Mg}}}^{0}{\mathrm{e}}^{\frac{-2{\mathrm{{\delta}V}}}{{\mathrm{k}}_{{\mathrm{B}}}{\mathrm{T}}}} \left \left(1+\frac{ \left \left[{\mathrm{Na}}^{+}\right] \right _{{\mathrm{ex}}}}{{\mathrm{K}}_{1{\mathrm{,Na}}_{{\mathrm{ex}}}}}+\frac{ \left \left[{\mathrm{Na}}^{+}\right] \right _{{\mathrm{ex}}}}{{\mathrm{K}}_{2{\mathrm{,Na}}_{{\mathrm{ex}}}}}+\frac{ \left \left[{\mathrm{Na}}^{+}\right] \right _{{\mathrm{in}}}}{{\mathrm{K}}_{1{\mathrm{,Na}}_{{\mathrm{in}}}}^{0}{\mathrm{e}}^{\displaystyle\frac{-{\mathrm{{\alpha}}}_{1}{\mathrm{V}}}{{\mathrm{k}}_{{\mathrm{B}}}{\mathrm{T}}}}}+\frac{ \left \left[{\mathrm{Na}}^{+}\right] \right _{{\mathrm{in}}}}{{\mathrm{K}}_{2{\mathrm{,Na}}_{{\mathrm{in}}}}^{0}{\mathrm{e}}^{\displaystyle\frac{-{\mathrm{{\alpha}}}_{2}{\mathrm{V}}}{{\mathrm{k}}_{{\mathrm{B}}}{\mathrm{T}}}}}\right) \right ^{-1}{\mathrm{.}}\end{equation*}
4

, with eight free parameters, could not be fit to the data (i.e., the SD of the parameters became large). To reduce the number of free parameters, we imposed the constraint of a single voltage dependence term for intracellular Na+ occupancy (i.e., α2 = α1). The results are shown in Table. The fit using the constrained (MSC = 5.9) was better than using (MSC = 5.5), indicating that the two Na+ sites probably are not identical. The apparent dissociation constants differed by 7-fold for extracellular Na+ (113 ± 35 vs. 15 ± 5 mM) and 3.6-fold for intracellular Na+ (7.2 ± 5.5 vs. 2.0 ± 0.8 mM). The intrinsic Mg2+ association rate constant and fractional electrical distance were similar with and .

The results indicate that there are at least two Na+ binding sites in the external portion of the ion permeation pathway that must be empty for Mg2+ to associate with the NMDAR pore. Extracellular Na+ occupies these sites in a nearly voltage-independent manner, whereas intracellular Na+ occupies these sites in a highly voltage-dependent manner. Na+ permeates through the channel, thus, this voltage dependence cannot be directly related to a location of the external sites in the electric field.

This analysis provides information on the intrinsic rate constant of Mg2+ association in pure water (i.e., in the absence of competing ions). The association rate constant for extracellular Mg2+ is very high (>108 M−1s−1), even in the absence of a membrane potential. The peak of the barrier of the Mg2+ association rate constant is located ∼25% through the electric field from the extracellular surface.

Extracellular Na+ Reduces the Mg2+ Dissociation Rate Constant

A bound Mg2+ has two routes by which it can exit the channel. It can either dissociate back into the extracellular compartment (rate constant kV−Mg) or it can permeate into the intracellular compartment (rate constant kVpMg). Both of these processes may be influenced by the presence of Na+ in the permeation pathway, and such effects are of interest insofar as they provide information about the location of the Na+ binding sites with respect to the Mg2+ site.

Only the sum of the exit rate constants, kVoff, can be measured directly from the duration of the blocking gaps in the single-channel current record. However, because the exit routes require Mg2+ to move in opposite directions in the electric field, kV−Mg and kVpMg will have opposite voltage dependencies, the former decreasing and the latter increasing with hyperpolarization. Using the standard barrier framework, the apparent exit rate constants can be estimated using the relationships:

\begin{equation*}\begin{matrix}{\mathrm{k}}_{{\mathrm{off}}}^{{\mathrm{V}}}={\mathrm{k}}_{-{\mathrm{Mg}}}^{{\mathrm{V}}}+{\mathrm{k}}_{{\mathrm{pMg}}}^{{\mathrm{V}}}\\ {\mathrm{k}}_{-{\mathrm{Mg}}}^{{\mathrm{V}}}={\mathrm{k}}_{-{\mathrm{Mg}}}^{0}{\mathrm{e}}^{\frac{2{\mathrm{{\epsilon}V}}}{{\mathrm{k}}_{{\mathrm{B}}}{\mathrm{T}}}}\\ {\mathrm{k}}_{{\mathrm{pMg}}}^{{\mathrm{V}}}={\mathrm{k}}_{-{\mathrm{Mg}}}^{0}{\mathrm{e}}^{\frac{-2{\mathrm{{\lambda}V}}}{{\mathrm{k}}_{{\mathrm{B}}}{\mathrm{T}}}}{\mathrm{,}}\end{matrix}\end{equation*}
5

where k0−Mg and k0pMg are the apparent exit rate constants in the absence of a membrane potential, ɛ is the fractional electrical distance from the Mg2+ binding site to the peak of the dissociation barrier, and λ is the fractional electrical distance from the binding site to the peak of the permeation barrier (see Fig. 6).

Fig. 5 A shows single-channel currents and interval duration histograms at different extracellular Na+ concentrations. The lifetime of the blocked state increases with an elevation of [Na+]ex. This suggests that extracellular Na+ inhibits Mg2+ dissociation from the channel (“lock-in”). Fig. 5 B shows that similar effects were observed over a wide range of membrane potentials. For each [Na+]ex, both kV−Mg and kVpMg were estimated by fitting koff versus membrane potential by . Because the occupancy of the Na+ sites by extracellular Na+ is voltage-independent, in this procedure, we assumed that the effect of [Na+]ex on the Mg2+ exit rate constants was also voltage-independent (i.e., ɛ and λ were assumed to be constants).

The results (Fig. 5 B and Table) show that Mg2+ dissociation to the extracellular solution decreases with increasing [Na+]ex. This suggests that occupancy of an external site(s) by Na+ reduces significantly the rate of Mg2+ dissociation to the extracellular compartment. This lock-in effect is consistent with the notion that Na+ exerts its effects on Mg2+ association and dissociation by binding to specific sites in the ion permeation pathway rather than by acting via a nonspecific charge screening mechanism. Moreover, the lock-in effect indicates that Na+ binds to one or more sites that are distinct from, and extracellular to, the Mg2+ binding site. There was no significant effect of extracellular Na+ on the Mg2+ permeation rate constant.

The inhibition of Mg2+ dissociation by extracellular Na+ was analyzed using a model in which Mg2+ can dissociate back to the extracellular solution only when all of the external Na+ sites are empty. Accordingly ( ), kVoff is a function of [Na+]ex and V:

\begin{equation*}{\mathrm{k}}_{{\mathrm{off,\;Mg}}}^{{\mathrm{V}}}={\mathrm{{\kappa}}}_{-{\mathrm{Mg}}}^{0}{\mathrm{e}}^{\frac{2{\mathrm{{\epsilon}V}}}{{\mathrm{k}}_{{\mathrm{B}}}{\mathrm{T}}}} \left \left(1+\frac{ \left \left[{\mathrm{Na}}^{+}\right] \right _{{\mathrm{ex}}}}{{\mathrm{J}}_{{\mathrm{d,Na}}_{{\mathrm{ex}}}}}\right) \right ^{-{\mathrm{n}}}+{\mathrm{k}}_{{\mathrm{pMg}}}^{0}{\mathrm{e}}^{\frac{-2{\mathrm{{\lambda}V}}}{{\mathrm{k}}_{{\mathrm{B}}}{\mathrm{T}}}}{\mathrm{.}}\end{equation*}
6

n is the number of (independent and identical) sites that must be occupied to lock-in the Mg2+, κV−Mg is the Mg2+ dissociation rate constant when all of the salient external Na+ sites are empty at membrane potential V, and Jd,Naex is the equilibrium dissociation constant of [Na+]ex for each Na+ site, and is assumed to be independent of the membrane potential. Note that Jd,Naex is a true equilibrium dissociation constant for Na+ when there is a Mg2+ in the pore, whereas KNaex is an apparent dissociation constant for extracellular Na+ when the pore does not contain a Mg2+.

Four sets of experimental data were fitted by , either with n as a fixed parameter (equal to 1 or 2) or as a free parameter. ɛ and λ were fixed at their previously determined values (0.36 and 0.03, respectively), leaving only κ0−Mg, Jd,Naex, and k0pMg as free parameters. The predicted curves match the experimental results (Fig. 5 C), with the best-fit parameters shown in Table. The results indicate that a model having a single Na+ site (with an equilibrium dissociation constant of 88 mM), or one with two independent Na+ sites (each with an equilibrium dissociation constant of 251 mM) can account for the results. In pure water, the Mg2+ dissociation rate constant is ∼9,000 s−1, and the Mg+2 permeation rate constant is 624 s−1.

Discussion

The rate constants of Mg2+ block and unblock determined from single-channel kinetic analysis were used to report on the steady-state occupancy of the recombinant NR1-NR2A NMDAR permeation pathway by Na+. The framework for the analyses was the “Woodhull” formalism (Hille 1992) using a two (asymmetric) barrier, 1-well model that attributes all of the voltage dependence to the movement of the ion through the electric field. Such a simple scheme is probably a reasonable approximation for ions that have long, exponentially distributed lifetimes in the pore, such as Mg2+ and Ca2+. However, it is unclear whether or not this simple framework can be used to approximate the free energy profile for a highly mobile species such as Na+. Moreover, it is reasonable to suspect that the ionic environment and/or voltage can deform the channel protein to influence Mg2+ block and permeation parameters. Nonetheless, we are optimistic that the barrier formalism provides some information about regions of the ion permeation pathway where Na+ lingers during its brief sojourn in the NMDAR channel.

Changes in the Mg2+ parameters as a function of the intra- and extracellular Na+ concentrations were interpreted as arising from occupancy of specific sites in the ion permeation pathway by the monovalent ion. Because the ionic strength was not constant, it is also possible that some of the effects can be attributed to different degrees of surface charge. Several results lead us to suspect that charge screening was not a major factor. First, the magnitudes of the observed changes in k+Mg are greater than those predicted by charge-screening effects alone. In native hippocampal NMDAR, a reduction in extracellular Cs+ from 150 to 10 mM creates an excess local negative potential of ∼6.5 mV (Zarei and Dani 1994), which would be expected to increase k+Mg only e6.5/12.5 = 1.7-fold. We observe a 4.6-fold increase in this rate constant between 150 and 50 mM extracellular Na+ (Fig. 2). Second, increasing the intracellular Na+ concentration reduces the apparent association rate constant for extracellular Mg2+ in a voltage-dependent manner, which is not predicted by a simple charge-screening mechanism. Third, the difference in the apparent affinity of the external sites for extracellular Na+ versus K+ (see Zhu and Auerbach 2001, in this issue) suggests specific binding rather than a nonspecific surface charge effect. Fourth, the ability of extracellular Na+ to prevent Mg2+ dissociation (the lock-in effect; Table) is more consistent with occupancy of a binding site than with a charge screening mechanism. Overall, the results suggest that monovalent cations exert their effects on Mg2+ association and dissociation predominantly by binding to specific sites in the ion permeation pathway rather than by acting via a nonspecific electrostatic shielding mechanism.

The Na+ Binding Sites

The results suggest that occupancy of either of the two external sites by Na+ (arising from the extracellular or the intracellular compartment) slows or prevents Mg2+ entry into the channel from the extracellular solution. When the pore is free from Mg2+, extracellular Na+ binding is voltage-independent, whereas intracellular Na+ binding is strongly voltage-dependent. When the pore is blocked by Mg2+, a voltage-independent occupancy of a single external site by Na+ is sufficient to prevent Mg2+ dissociation to the extracellular compartment, but is without effect on Mg2+ permeation.

In unblocked NMDAR, the voltage sensitivities of the Na+ effect cannot be used to pinpoint the locations of the external sites in the electric field because we do not know the extent to which Na+ release is determined by its dissociation back to the extracellular solution versus permeation. If dissociation dominates, then the voltage independence of the dissociation constant for extracellular Na+ would indicate that both sites lie near or beyond the external margin of the electric field. However, if Na+ release is predominantly determined by its permeation to the intracellular compartment, the voltage sensitivities would suggest that at least one of the external sites is located deep in the pore. Under this condition, Na+ occupancy of a deep site would show a reduced voltage dependence because the on and off rates to the site will change in the same direction with a change in the membrane potential. The apparent voltage dependence of occupancy would disappear if the electrical distance from the site to the peak of the permeation barrier was similar to that from the extracellular solution to the entry barrier (i.e., δ ≈ α, for Na+). At the same time, intracellular Na+ occupancy of that site would exhibit a steep voltage dependence because the on and off rates would change in opposite directions with voltage.

Our results do not allow us to unequivocally pinpoint the locations of the Na+ sites. Some results point to a separation of the Na+ sites, with one external Na+ site located near or beyond the extracellular margin of the electrical field and the other being close to, or perhaps the same as, the Mg2+ site (which is 0.6 though the electric field). First, the higher apparent affinity of the external sites for intracellular (compared with extracellular) Na+ suggests that the barrier to Na+ dissociation to the external compartment is higher than the Na+ permeation barrier. Thus, Na+ release is likely to be dominated by permeation. Second, although occupancy of either of two external sites prevents Mg2+ association, the results are consistent with a scheme in which only a single site must be occupied to prevent Mg2+ dissociation to the extracellular solution. The occupancy of this lock-in site for Na+ is not voltage-dependent. Because this affinity constant is determined under equilibrium conditions (i.e., no permeation), this indicates that this site lies near or beyond the extracellular boundary of the electric field. These arguments are not definitive, and the existence of two nonidentical Na+ sites near or beyond the extracellular limit of the electric field remains a possibility.

Mg2+ Block in Pure Water

The intrinsic parameters for Mg2+ binding to the NMDAR pore, i.e., in the absence of competing permeant ions, are shown in Fig. 6. In pure water and no membrane potential, the association rate constant for extracellular Mg2+ is 7.8 × 108 M−1s−1. This is 100 times faster than the apparent association rate constant in 140 mM extracellular Na+. The large magnitude of this rate constant indicates that, in the absence of competing ions, Mg2+ has unhindered access to its blocking site in the channel.

In pure water and no membrane potential, Mg2+ exits the NMDAR pore mainly by dissociating to the extracellular solution (at ∼9,000 s−1), but it can also permeate into the intracellular compartment (at 62 s−1). Thus, under these conditions, Mg2+ stays in the pore ∼0.1 ms and ∼6.5% of the blocking events results in the permeation of a Mg2+. The Mg2+ permeation rate constant is slow and predicts that this ion can carry only a tiny current (∼0.2 fA) that would normally be an insignificant fraction of the total single-channel current. From the rate constants, we estimate that in the absence of competing ions and at zero membrane potential, the intrinsic equilibrium dissociation constant of the NMDAR for Mg2+ is ∼12 μM.

The main barrier to Mg2+ association is located 0.25 through the electric field (i.e., this process increases e-fold with a 46-mV hyperpolarization). At −60 mV, the Mg2+ association rate constant in pure water is ∼2.2 × 109 M−1s−1. The entry barrier appears to be nearly symmetric, as a bound Mg2+ must traverse 0.35 of the field to return to the extracellular compartment (35 mV for an e-fold change). The sum of these two positional parameters indicates that the Mg2+ binding site is located 0.6 through the electric field from the extracellular solution. In contrast, the barrier to Mg2+ permeation is very steep, as the ion, once bound, must traverse only 0.03 of the field to reach the intracellular compartment. Thus, hyperpolarization has very little effect on Mg2+ permeation, per se, whereas it significantly speeds the association from, and slows the dissociation of Mg2+ to, the extracellular solution.

In the absence of competing ions, equilibrium block by Mg2+ increases e-fold with a hyperpolarization of ∼21 mV, so that at −60 mV, the Mg2+ equilibrium dissociation constant is only ∼0.7 μM. Under these conditions, almost one out of every three Mg2+ that binds permeates through the channel.

Comparison with Native NMDARs

There have been several excellent studies of the effects of extracellular Na+ and intracellular Cs+ on block of native NMDAR (embryonic rat cortical neurons, probably composed of a mixture of NR2A and B subunits) by adamantine derivatives (Antonov et al. 1998) and Mg2+ (Antonov and Johnson 1999). For the most part, our results using recombinant NMDARs are in good agreement with these studies. Both sets of results show that extracellular Na+ binds to two sites (average KNaex = ∼40 mM) that are in the external portion of the channel to thereby prevent the entry of Mg2+ into the pore. In addition, both sets of results show a lock-in effect, i.e., that the occupancy of either site prevents Mg2+ dissociation back to the extracellular solution. Our results also agree with those of Antonov and Johnson 1999 with respect to the intrinsic parameters for Mg2+ association. Both sets of results indicate a similar electrical distance of the association barrier from the extracellular solution (0.25 vs. 0.23) and a large association rate constant at zero potential in pure water (∼8 vs. 11 × 108 M−1s−1).

Our measurements indicate that the intrinsic Mg2+ dissociation rate constant is ∼10 times slower, and that the Mg2+ permeation rate constant is ∼10 times faster than was reported by Antonov and Johnson 1999. As a consequence, we estimate a higher intrinsic affinity (in pure water and the absence of a membrane potential) of the pore for extracellular Mg2+ (12 vs. 101 μM). Moreover, our estimate of the location (in electrical distance) of the Mg2+ binding site (0.60) is different from that of Antonov and Johnson (0.47). We doubt that these differences arise from a different subunit composition of recombinant (NR2B) versus native systems (NR2A and NR2B). Rather, we speculate that these differences arise from the fact that they used 130 mM Cs+ in their intracellular solution, whereas we used 5 mM Na+. Occupancy of an internal monovalent cation-binding site by Cs+ will increase the apparent rate constant for Mg2+ dissociation and slow the apparent rate constant for Mg2+ permeation (see Zhu and Auerbach 2001, in this issue).

Mg2+ Block and Unblock as a Function of the Na+ Concentrations and the Membrane Potential

and can be combined to describe Mg2+ block kinetics as a function of [Na+] and the membrane potential (in the absence of other competing ions). Using the parameters shown in Table and Table, at −60 mV and under the conditions [Na+]ex = 140 mM and [Na+]in = 10 mM, the apparent Mg2+ block and unblock rates are, respectively, 2 × 108 M−1s−1 and 1,270 s−1, with about equal probabilities of release to the extra- and intracellular compartments, yielding an apparent Kd of ∼0.6 mM. These conditions are not “physiological” because they do not incorporate the effects of K+, which is present at a high concentration in the intracellular compartment. In the companion paper (see Zhu and Auerbach 2001, in this issue) we describe the effects of extra- and intracellular K+ on the kinetics of Mg2+ blockade.

Acknowledgments

We thank Thomas Kuner and Peter Seeburg for the rat NR1 and NR2A subunit cDNAs, and Jon Johnson for insightful comments on the manuscript.

This work was supported by a grant to A. Auerbach (NS-86554).

We assume that (1) there is a single Na+ binding site; (2) Mg2+ can bind to the channel only when this site is empty; and (3) the Na+ association and dissociation rate constants are much faster than the Mg2+ association rate constant. Thus,

\begin{equation*}{\mathrm{k}}_{+{\mathrm{Mg}}}^{{\mathrm{V}}}={\mathrm{{\kappa}}}_{+{\mathrm{Mg}}}^{0}P_{{\mathrm{Na}}}^{{\mathrm{e}}}{\mathrm{,}}\end{equation*}
A1.1

where kV+Mgis the apparent Mg2+ association rate constant at membrane potential V, (i.e., in the presence of Na+), kV+Mgis the Mg2+ association rate constant in pure water at membrane potential V, and PeNa is the probability of the Na+ site being empty. PeNa is a function of the equilibrium dissociation constants and ion concentrations:

\begin{equation*}P_{{\mathrm{Na}}}^{{\mathrm{e}}}= \left \left(1+\frac{ \left \left[{\mathrm{Na}}^{+}\right] \right _{{\mathrm{ex}}}}{{\mathrm{K}}_{{\mathrm{Na}}_{{\mathrm{ex}}}}}+\frac{ \left \left[{\mathrm{Na}}^{+}\right] \right _{{\mathrm{in}}}}{{\mathrm{K}}_{{\mathrm{Na}}_{{\mathrm{in}}}}^{{\mathrm{V}}}}\right) \right ^{-1}{\mathrm{,}}\end{equation*}
A1.2

where KNaex and KVNain are the unidirectional dissociation constants (koff/kon) for [Na+]ex and [Na+]in, respectively. kV+Mgis related to the membrane potential by:

\begin{equation*}{\mathrm{{\kappa}}}_{+{\mathrm{Mg}}}^{{\mathrm{V}}}={\mathrm{{\kappa}}}_{+{\mathrm{Mg}}}^{0}{\mathrm{e}}^{\frac{-2{\mathrm{{\delta}V}}}{{\mathrm{k}}_{{\mathrm{B}}}{\mathrm{T}}}}{\mathrm{,}}\end{equation*}
A1.3

where κ0+Mgis the Mg2+ association rate constant in the absence of a membrane potential, δ is the fractional electrical distance between the extracellular compartment and the peak of the entry barrier for Mg2+, kB, is the Boltzmann constant, and T is the absolute temperature (under our conditions, kBT = 25.3 mV). We assume that KNaex is voltage-independent (2 C), and that KVd,Nain is voltage-dependent (3 C) and is related to the membrane potential by:

\begin{equation*}{\mathrm{K}}_{{\mathrm{Na}}_{{\mathrm{in}}}}^{{\mathrm{V}}}={\mathrm{K}}_{{\mathrm{Na}}_{{\mathrm{in}}}}^{0}{\mathrm{e}}^{\frac{-{\mathrm{{\alpha}V}}}{{\mathrm{k}}_{{\mathrm{B}}}{\mathrm{T}}}}{\mathrm{,}}\end{equation*}
A1.4

where K0Nain is the intracellular Na+ equilibrium dissociation constant at zero membrane potential, and α is the fractional electrical distance of the Na+ site from the intracellular solution. We now generate a description of kV+Mg as a function of three experimental variables ([Na+]ex,, [Na+]in, and V) and five free parameters (κ0+Mg, Kd,Naex, Kd,Nain, δ, and α):

\begin{equation*}{\mathrm{k}}_{+{\mathrm{Mg}}}^{{\mathrm{V}}}={\mathrm{{\kappa}}}_{+{\mathrm{Mg}}}^{0}{\mathrm{e}}^{\frac{-2{\mathrm{{\delta}V}}}{{\mathrm{k}}_{{\mathrm{B}}}{\mathrm{T}}}} \left \left(1+\frac{ \left \left[{\mathrm{Na}}^{+}\right] \right _{{\mathrm{ex}}}}{{\mathrm{K}}_{{\mathrm{Na}}_{{\mathrm{ex}}}}}+\frac{ \left \left[{\mathrm{Na}}^{+}\right] \right _{{\mathrm{in}}}}{{\mathrm{K}}_{{\mathrm{Na}}_{{\mathrm{in}}}}^{0}{\mathrm{e}}^{\displaystyle\frac{-{\mathrm{{\alpha}V}}}{{\mathrm{k}}_{{\mathrm{B}}}{\mathrm{T}}}}}\right) \right ^{-1}{\mathrm{.}}\end{equation*}
A1.5

We assume that there are n identical and independent Na+ binding sites that must be empty for Mg2+ to dissociate back to the extracellular compartment. The apparent Mg2+ dissociation rate (i.e., in the presence of extracellular Na+) is:

\begin{equation*}{\mathrm{k}}_{-{\mathrm{Mg}}}^{{\mathrm{V}}}={\mathrm{{\kappa}}}_{-{\mathrm{Mg}}}^{{\mathrm{V}}} \left \left(P_{{\mathrm{Na}}}^{{\mathrm{e}}}\right) \right ^{{\mathrm{n}}}{\mathrm{,}}\end{equation*}
A2.1

where κV−Mg is the Mg2+ dissociation rate constant in pure water at membrane potential V and PeNa is the probability that all of the Na+ sites are empty. Because intracellular Na+ cannot reach the external site(s) when Mg2+ is bound, was modified so that PeNa depends only on [Na]ex:

\begin{equation*}P_{{\mathrm{Na}}}^{{\mathrm{e}}}= \left \left(1+\frac{ \left \left[{\mathrm{Na}}^{+}\right] \right _{{\mathrm{ex}}}}{{\mathrm{J}}_{{\mathrm{d,Na}}_{{\mathrm{ex}}}}}\right) \right ^{-1}{\mathrm{,}}\end{equation*}
A2.2

where Jd,Naex is the equilibrium dissociation constant of [Na+]ex for each Na+ site and is assumed to be independent of the membrane potential. Note that Jd,Naex is a true equilibrium dissociation constant for Na+ when there is a Mg2+ in the pore, whereas KNaex is an apparent (nonequilibrium) dissociation constant for Na+ when the pore does not contain a Mg2+.

We now describe kV−Mg as a function of [Na+]ex and V:

\begin{equation*}{\mathrm{k}}_{-{\mathrm{Mg}}}^{{\mathrm{V}}}={\mathrm{{\kappa}}}_{-{\mathrm{Mg}}}^{0}{\mathrm{e}}^{\frac{-2{\mathrm{{\epsilon}V}}}{{\mathrm{k}}_{{\mathrm{B}}}{\mathrm{T}}}} \left \left(1+\frac{ \left \left[{\mathrm{Na}}^{+}\right] \right _{{\mathrm{ex}}}}{{\mathrm{J}}_{{\mathrm{d,Na}}_{{\mathrm{ex}}}}}\right) \right ^{-{\mathrm{n}}}{\mathrm{.}}\end{equation*}
A2.3

and kVoff as a function of the experimental variables [Na+]ex and V:

\begin{equation*}{\mathrm{k}}_{{\mathrm{off}}}^{{\mathrm{V}}}={\mathrm{{\kappa}}}_{-{\mathrm{Mg}}}^{0}{\mathrm{e}}^{\frac{2{\mathrm{{\epsilon}V}}}{{\mathrm{k}}_{{\mathrm{B}}}{\mathrm{T}}}} \left \left(1+\frac{ \left \left[{\mathrm{Na}}^{+}\right] \right _{{\mathrm{ex}}}}{{\mathrm{J}}_{{\mathrm{d,Na}}_{{\mathrm{ex}}}}}\right) \right ^{-2}+{\mathrm{k}}_{{\mathrm{pMg}}}^{0}{\mathrm{e}}^{\frac{-2{\mathrm{{\lambda}V}}}{{\mathrm{k}}_{{\mathrm{B}}}{\mathrm{T}}}}{\mathrm{.}}\end{equation*}
A2.4

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Abbreviations used in this paper: MSC, model selection criterion; NMDAR, N-methyl-d-aspartate receptor.