Ionic flow enhances low-affinity binding: a revised mechanistic view into Mg2+ block of NMDA receptors

Abstract

The N-methyl-d-aspartate receptor (NMDAR) channel is one of the major excitatory amino acid receptors in the mammalian brain. Since external Mg(2+) blocks the channel in an apparently voltage-dependent fashion, this ligand-gated channel displays intriguing voltage-dependent control of Na(+) and Ca(2+) permeability and thus plays an important role in synaptic physiology. We found that the essential features of Mg(2+) block could not be solely envisaged by binding of a charged blocker in the membrane electric field. Instead, the blocking effect of Mg(2+) is critically regulated by, and quantitatively correlated with, the relative tendency of outward and inward ionic fluxes. The 'intrinsic' affinity of Mg(2+) to the binding sites, however, is low (in the millimolar range) in the absence of net ionic flow at 0 mV. Besides, extracellular and intracellular Mg(2+) blocks the channel at distinct sites of electrical distances 0.7 and 0.95 from the outside, respectively. The two sites are separated by a high energy barrier for the movement of Mg(2+) (but not Na(+) or the other ions), and functionally speaking, each could accommodate 1.1 and 0.8 coexisting permeating ions, respectively. Mg(2+) block of the ionic flow thus is greatly facilitated by the flux-coupling effect or the ionic flow (the preponderant direction of permeant ion movement) per se, as if the poorly permeable Mg(2+) is 'pushed' against a high energy barrier by the otherwise permeating ions. Extracellular and intracellular Mg(2+) block then is in essence 'use dependent', more strongly inhibiting both Na(+) and Ca(2+) fluxes with stronger tendencies of influx and efflux, respectively. In conclusion, although permeant ions themselves could compete with Mg(2+), the flow or the tendency of movement of the permeant ions may actually enhance rather than interfere with Mg(2+) block, making the unique current-voltage relationship of NMDAR and the molecular basis of many important neurobiological phenomena.

Figure 4. The binding and unbinding kinetics of block at different voltages with 150 mm extracellular and 50 mm intracellular Na⁺ in hippocampal neurons

A, representative currents after rapid application and wash-off of 6.5 μm to and from the steady-state NMDAR currents at −90 mV. The decay and recovery of the currents are fitted with monoexponential functions with time constants (τ_on and τ_off) of 4.15 and 9.73 ms, respectively. B, the inverses of τ_on and τ_off are plotted against [Mg²⁺]_o. The lines are best linear regression fits to the data, and are of the form: 16.5 μm⁻¹ s⁻¹×[Mg²⁺]_o+ 125.7 s⁻¹ and 1.97 μm⁻¹ s⁻¹×[Mg²⁺]_o+ 128 s⁻¹ for 1/τ_on and 1/τ_off, respectively (n= 4–19). The very small slope for 1/τ_off again indicates that τ_off is insignificantly related to the concentrations of . Also, the y-intercepts of the regression lines for 1/τ_on and 1/τ_off are essentially superimposed on each other. C and D, k_on,app and k_off,app are plotted against membrane voltage (n= 3–15). k_off,app and k_on,app are obtained from the y-intercept and slope of the regression fits to the mean values (with errors smaller than 15% of mean) of 1/τ_off and 1/τ_on as shown in B, respectively. For comparison, the values of k_on,app and k_off,app in Fig. 3 are redrawn as dotted lines in the plots. The k_on,app and k_off,app with 150/50 mm (extracellular/intracellular) Na⁺ are distributed in a very similar pattern to those with 150/150 mm Na⁺, but are rightward shifted by ∼20–30 mV on the voltage axis. The extent of shift is reasonably close to the shift in the reversal potential (∼28 mV) for the different ionic milieu.

Figure 3. The binding and unbinding kinetics of at different voltages with symmetrical 150 mm Na⁺ on both sides of cell membrane in hippocampal neurons

A, representative currents after rapid application and wash-off of 20 μm to and from the steady-state NMDAR currents at −90 mV. The decay and recovery of currents were fitted with monoexponential functions to obtain the time constants τ_on and τ_off (4.1 and 16.9 ms, grey lines), respectively. The initial 10% of the current change was deliberately skipped from the fitting procedure to avoid inaccuracy from incomplete solution exchange. B, the inverses of τ_on and τ_off from A are plotted against the concentration of ([Mg²⁺]_o). The lines are the regression fits to the data, and are of the form: 1/τ_on= 6.8 μm⁻¹ s⁻¹×[Mg²⁺]_o+ 89.3 s⁻¹ and 1/τ_off=−0.68 μm⁻¹ s⁻¹×[Mg²⁺]_o+ 89.3 s⁻¹ at −90 mV (upper panel, n= 4–19), and are 1/τ_on= 2.5 μm⁻¹ s⁻¹×[Mg²⁺]_o+ 78.3 s⁻¹ and 1/τ_off= 0.14 μm⁻¹ s⁻¹×[Mg²⁺]_o+ 79.6 s⁻¹ at −70 mV (lower panel, n= 8–19). The slope of the fit for 1/τ_off is close to zero, consistent with the fact that τ_off is unrelated to the concentrations of . Note that the regression lines for 1/τ_on and 1/τ_off essentially converge on the same point of y-intercept at either −90 mV (89.3 vs. 89.3) or −70 mV (78.3 vs. 79.6). C, the apparent dissociation constants (K_d,app) of can also be derived from: k_off,app/k_on,app. k_off,app and k_on,app are obtained from the y-intercept and slope of the regression fits to the mean values (with errors smaller than 15% of mean, n= 3–19) of 1/τ_off and 1/τ_on as shown in B, respectively. The derived K_d,app from kinetic data (filled squares) are plotted against membrane voltage and are very much consistent with those from direct measurement of the reduction in steady-state currents (open triangles, data from Fig. 1C). D, the k_on,app are plotted against membrane voltage (n= 3–19) and fitted with a regression line of the form: k_on,app= 5.6 × 10⁴m⁻¹ s⁻¹× e^−V/18, where V is the membrane potential in mV. E, the k_off,app are plotted against membrane voltage (n= 3–19). The regression lines of the data between −90 to −110 mV and between −50 to −30 mV are of the forms: k_off,app= 21 s⁻¹× e^−V/65 and k_off,app= 289 s⁻¹× e^V/47, respectively (see Fig. 7 for more details).

Figure 7. Analysis of the data with the concept of flux coupling

See details in Appendix A. A, the data are from Fig. 3E and fitted by eqn (3) (Appendix A). The best fitting line (the thick continuous line) gives 1.12 and 690 s⁻¹ for n and k_{off,out,0 mV}, respectively. For comparison, the thin, thick dashed, and dotted lines are the fits of eqn (3) with the assigned n values of 0.5, 1 and 2, respectively. B, the data are from Fig. 3C. The line is a derived result based on calculations using eqn (4) and n= 1.12 (see Appendix A for details). C, the data are from Fig. 5E with symmetrical 150 mm Na⁺. The thick continuous line is the best fit of the data with eqn (5) (Appendix A), giving 0.8, 150 μm and 10 800 μm for n, k_{off,out,0 mV}/k_on, and k_{off,in,0 mV}/k_on, respectively. The thin, thick dashed, and dotted lines are the fits of eqn (5) with the assigned n values of 0.5, 1 and 2, respectively.

Figure 2. block with preponderant outward or inward current flows in hippocampal neurons

A, the blocking effect of 100 μm is markedly reduced in preponderant outward currents (with 0 mm external and 150 mm internal Na⁺, upper panel). In contrast, the blocking effect is so strengthened in preponderant inward currents (with 150 mm external and 0 mm internal Na⁺) that 100 μm still significantly blocks the NMDAR currents even at +10 mV (lower panel). The arrows mark the ‘fixed’ direction of Na⁺ flow. In the outward current experiments, small ‘tail’ inward currents were present because the extracellular solution was changed to an agonist-free solution containing 150 mm Na⁺. B, relative currents in the presence and absence of 100 μm in different current-flow conditions (n= 3–10). The curves are the fits of the form: relative current = 1/{1 +[Mg²⁺]_o/(4170 μm× e^V/13)} and relative current = 1/{1 +[Mg²⁺]_o/(160 μm× e^V/21)} for the solution containing 150/150 mm Na⁺ (extracellular/intracellular) and 150/0 mm Na⁺, respectively. V denotes membrane potential in mV.

Figure 1. Extracellular Mg²⁺ block of the NMDAR channel with symmetrical 150 mm Na⁺ on both sides of cell membrane in hippocampal neurons

A, representative NMDAR currents in the absence (grey lines) and presence (black lines) of 100 μm at different voltages (indicated on the top of the currents). B, inhibition of NMDAR currents by 1–1000 μm of (n= 3–14). Relative steady-state currents in the presence and absence of are plotted against the concentration of ([Mg²⁺]_o) on a semilogarithmic scale. The curves are the fits of the form: relative current = 1/[1 + ([Mg²⁺]_o/K_d,app)], where K_d,app stands for the apparent dissociation constant of , and is 583.0, 94.5, 26.3, 8.6, 4.5 and 2.9 μm at −30, −50, −70, −90, −110 and −130 mV, respectively. Note that the ‘shift’ between two adjacent curves in the plot is not constant but gradually increased toward more positive potentials. C, the mean values (taken from B) of K_d,app of at different voltages are plotted on a semilogarithmic scale. We connected every two points with a straight line by hand. The slopes of the lines are evidently shallower toward more negative potentials.

Figure 5. Flow dependence of intracellular Mg²⁺ () block

A, an inside-out patch of an oocyte expressing NMDAR channels was first held at 0 mV and stepped to a pre-pulse of −100 mV, and then to test pulses of different voltages from −100 to +100 mV in 10 mV increments. With symmetrical 150 mm Na⁺ on both sides of the cell membrane, NMDAR currents elicited at more positive voltages are readily blocked by 716 μm of intracellular Mg²⁺ (middle traces), an effect readily reversible by washing out Mg²⁺ (right traces). B, the I–V (current–voltage) curve in the absence and presence of 716 μm from the data in A. C, the experimental protocols are the same as those in A, except that the patch was held at −40 mV with 0 mm extracellular/150 mm intracellular Na⁺. The inset shows the magnification of current traces elicited at +40 to +100 mV. Note the paradoxical increase of current amplitude at +90 to +100 mV, as if the block is relieved at these strong positive membrane potentials. D, the I–V curve in the absence and presence of 716 μm from the data in C. E, the blocking effect of 716 μm (n= 3–37) with symmetrical 150 mm Na⁺ and with 0 mm extracellular/150 mm intracellular Na⁺ are compared over membrane voltages. The relative current is defined as the ratio of the currents with and without 716 μm.

Figure 6. block at different voltages with symmetrical 150 mm Na⁺ on the extracellular and intracellular sides of the oocyte expressing NMDAR channels

A, the relative currents with different concentrations of are examined at different membrane voltages. The relative current is defined as that in Fig. 1. The lines are the best fits of the form: relative current = 1/[1 + ([Mg²⁺]_i/K_d,app)], where K_d,app stands for the apparent dissociation constant of (n= 5–37). The filled circles and continuous lines mark the data examined at positive membrane voltages, and the open circles and dashed lines mark those at negative voltages. B, the mean values of the K_d,app obtained from the fitting results in A are plotted against membrane voltages (filled and open circles for the data examined at positive and negative membrane voltages, respectively), showing evident non-linear relationship with symmetrical 150 mm Na⁺. The continuous line is an arbitrary regression line, K_d,app= 5210 μm× e^−V/42, which fits the data from +30 to +100 mV to show a trend of the voltage dependence. Note the evident deviation of the data examined at negative voltages from the continuous line. The dotted line marks the data by a simplified calculation of K_d,app from: relative current = 1/[1 + (716 μm/K_d,app)], where the values of the relative currents are from the data of 716 μm in A, and shows very similar results to the more accurately measured K_d,app described above (i.e. the circles). In this regard, the apparent dissociation constants of calculated from: relative current = 1/[1 + (716 μm/K_d,app)] with 0 mm Na⁺/150 mm Na⁺ are also plotted against membrane voltages for comparison (cross symbols). The dashed line is the regression fit of the latter set of data from −50 to +50 mV, and is of the form: K_d,app= 1141 μm× e^−V/41. V is the membrane potential in mV.

Figure 8. The energy profile of Mg²⁺ in the NMDAR channel pore and simulations of the electrophysiological consequences

A, the energy profile of Mg²⁺ in the NMDAR channel pore. See Appendix B for the detailed rationales of derivation. The external and the internal Mg²⁺ binding regions both presumably have 2–3 ion binding sites, separated by energy barriers low enough to sustain partially-coupled but high enough to interfere with completely-coupled movement of ions in this region. B, recapitulation of the composite off rates of the blocking at different voltages. Based on the energy profile in A, the hypothetical outward and inward off rates considering only intrinsic voltage dependence are calculated (dashed lines). More realistic outward and inward off rates are derived with the additional considerations of flow dependence (with n= 1.12, continuous lines). The apparent off rates of the blocking predicted by the model are thus the sum of the two continuous lines (i.e. the thick line, which is identical to the thick line in Fig. 7A, the best fit of the experimental data from Fig. 3E). C, the contribution of flux coupling to blocking effect at different membrane voltages. In the inset, the continuous line is from Fig. 7B (with flux coupling taken into consideration), and the dashed line is the calculated dissociation constants if one considers only the intrinsic voltage dependence of the blocking site but not flux coupling (the experimental data point at −30 mV, i.e. 0.58 mm, is taken from Fig. 3C as a reference point for the calculation and presentation). The blocking effect of 1 mm (roughly the physiological concentration in human cerebrospinal fluid) is then derived based on the K_d,app values from the two lines in the inset according to a simple bimolecular (one-to-one binding) reaction. The remaining current after Mg²⁺ block is normalized to the current elicited at +100 mV (in the absence of Mg²⁺) to give the relative current (the y-axis), which is then plotted against membrane voltage. The grey filled circles (connected by continuous lines) and the black filled circles (connected by dashed lines) show the data in the presence and the absence of flux coupling, respectively. The dotted line denotes the current in the absence of Mg²⁺. D, the normalized conductance is also derived form the K_d,app values in C and plotted against membrane voltage. The curves are fitted with a Boltzmann function and are 1/[1 + e^{(−22.6−V)/18.1}] and 1/[1 + e^{(−18.8−V)/12.3}] in the absence (equivalent ‘gating charges’= 25/18.1 = 1.4, black filled circles, dashed lines) and presence (equivalent ‘gating charges’= 25/12.3 = 2.0, grey filled circles, continuous lines) of flux coupling, respectively. V is membrane potential in mV. E, the normalized conductance–voltage relationship is plotted as that described in D, but the number (n) of Na⁺ accompanying Mg²⁺ in the single file region is differently assigned (assuming complete coupling between or among Na⁺ and Mg²⁺). The curves are the fits with a Boltzmann function with V_1/2 values of −27.1, −18.8, −18.0, −14.7 and −12.5, and k values of 14.8, 12.3, 10.0, 8.4 and 7.6 (and thus equivalent ‘gating charges’ of 1.7, 2.0, 2.5, 3.0 and 3.3) for n= 0.5, 1.12 (data from D), 2, 3 and 4, respectively.