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Copyright © 2000 The Biophysical Society. All rights reserved.
Biophysical Journal, Volume 79, Issue 3, 1324-1335, 1 September 2000

doi:10.1016/S0006-3495(00)76385-5

Channels, Receptors, and Transporters

Quantitative Analysis of Tetrapentylammonium-Induced Blockade of Open N-Methyl-D-Aspartate Channels

Alexander I. Sobolevsky^,  

Institute of General Pathology and Pathophysiology, Baltiyskaya 8, 125315, Moscow, Russia

Address reprint requests to Alexander I. Sobolevsky, Department of Neurobiology and Behavior, State University of New York at Stony Brook, Stony Brook, NY 11794-5230. Tel.: 631-632-4406; Fax: 631-632-6661.

Unique properties, such as high Ca²⁺ permeability (MacDermott et al), voltage-dependent Mg²⁺ block (Nowak et al), and slow activation kinetics (Johnson and Ascher, 1987,Lester et al), as well as complex regulation of NMDA channels, underlie their implication in synaptic plasticity and development, learning, and memory, as well as a variety of pathological processes occurring in the brain (McBain and Mayer, 1994,Dingledine et al). The important physiological role of NMDA channels explains the broad interest in their properties, structure, and regulation. Identification of the NMDA channel blocking mechanisms is important not only because the blockers are used in the clinical practice for treatment of a variety of neurological disorders (Danysz and Parsons, 1998,Parsons et al,Parsons et al), but also because they proved to be one of the most effective tools in the study of the gross architecture of NMDA channels (Koshelev and Khodorov, 1992,Koshelev and Khodorov, 1995,Subramaniam et al,Benveniste and Mayer, 1995,Zarei and Dani, 1995,Antonov et al,Sobolevsky and Koshelev, 1998,Sobolevsky et al,Sobolevsky et al,Sobolevsky et al,Antonov and Johnson, 1999,Sobolevsky, 1999).

According to their action on NMDA channel gating, all blockers can be subdivided into two main groups: those that prevent the channel closure and those that do not prevent it. The latter group, or the group of trapping blockers, includes MK-801, phencyclidine, NEFA, ketamine, aminoadamantanes, N-2-(adamantyl)-hexamethylenimine (A-7), tetramethylammonium, tetrapropylammonium and Mg²⁺ (MacDonald et al,MacDonald et al,Huetter and Bean, 1988,Johnson et al,Blanpied et al,Chen and Lipton, 1997,Dilmore and Johnson, 1998,Sobolevsky et al,Sobolevsky et al,Sobolevsky and Yelshansky, 2000). In contrast, the blockers such as 9-aminoacridine, tacrine, long-chain adamantane derivatives, and tetrapentylammonium (Koshelev and Khodorov, 1992,Koshelev and Khodorov, 1995,Costa and Albuquerque, 1994,Vorobjev and Sharonova, 1994,Antonov et al,Antonov et al,Benveniste and Mayer, 1995,Johnson et al,Antonov and Johnson, 1996,Sobolevsky, 1999,Sobolevsky et al) are thought to prevent the closure of the channel activation gate according to the “foot-in-the-door” mechanism. All currently known foot-in-the-door blockers show relatively fast binding/unbinding kinetics. To describe this kinetics, single-channel rather than whole-cell recordings were extensively used (Costa and Albuquerque, 1994,Nelson and Albuquerque, 1994,Antonov et al,Antonov et al,Johnson et al,Antonov and Johnson, 1996). Using TPentA as an example, this study provides a quantitative description of fast foot-in-the-door blocker binding/unbinding kinetics based solely upon whole-cell recordings.

Another important question considered in the present study is the estimation of the maximum NMDA channel open probability, P₀. Both trapping (MK-801: Huetter and Bean, 1988,Jahr, 1992,Hessler et al,Rosenmund et al,Dzubay and Jahr, 1996,Chen et al) and foot-in-the-door blockers (9-aminoacridine: Benveniste and Mayer, 1995,Chen et al) were used to determine the value of P₀. However, both MK-801 and 9-aminoacridine methods have a number of disadvantages (Benveniste and Mayer, 1995,Dilmore and Johnson, 1998). This study presents an alternative method for P₀ estimation. The application of this method to the TPentA-induced blockade revealed rather a low value of the maximum NMDA channel open probability, P₀∼0.04.

Pyramidal neurons were acutely isolated from the CA-1 region of rat hippocampus using vibrodissociation techniques (Vorobjev, 1991). The experiments were begun after 3-hour incubation of hippocampal slices in a solution containing NaCl, 124mM; KCl, 3mM; CaCl₂, 1.4mM; MgCl₂, 2mM; glucose, 10mM; NaHCO₃, 26mM. The solution was bubbled with carbogen at 32°C. During the whole period of isolation and current recording, nerve cells were washed with a Mg²⁺-free 3μM glycine-containing solution of NaCl, 140mM; KCl, 5mM; CaCl₂, 2mM; glucose, 15mM; HEPES, 10mM; pH 7.3. Fast replacement of superfusion solutions was achieved by using the concentration-jump technique (Benveniste et al,Vorobjev, 1991) with one application tube. This technique allows substitution of the tubular for the flowing solution with a time constant smaller than 30ms but backward with the time constant of 30 to 100ms (Sobolevsky, 1999). Therefore, except where noted (Figure 8A), the rate of the solution exchange was fast at the beginning of any application and slightly slower at its termination. The currents were recorded at 18°C in the whole-cell configuration using micropipettes made from pyrex tubes and filled with an intracellular’ solution of CsF, 140mM; NaCl, 4mM; HEPES, 10mM; pH 7.2. The electric resistance of the filled micropipettes was 3 to 7 MΩ. Analogue current signals were digitized at 2kHz and filtered at 1kHz frequency. The magnitude of the junction potential was about 4mV irrespective of the presence of TPentA in the external solution. No correction for the junction potential was made because of its negligibility in comparison with the value of the holding membrane potential (−100mV) at which all experiments were carried out.

Statistical analysis was performed using the scientific and technical graphics computer program Microcal Origin (version 4.1 for Windows). The data presented are means±SE; a comparison of the means was done byanalysis of variance, with p<0.05 taken as significant.

The dependencies of the degree of the stationary current inhibition, 1−I_B/I_C (where I_C and I_B are the stationary control and blocked currents, respectively; see Figure 1A), the normalized charge carried during the tail current, Q, and the amplitude of the hooked tail current, (I_P−I_B)/I_C (where I_P is the maximum value of the hooked tail current; see Figure 1A), on the blocker concentration were fitted by the following logistic equation:

(1)

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Figure 1

The dependencies of the hooked tail current parameters on TPentA concentration. (A) Superposition of control and blocked currents at different concentrations of TPentA. ASP (100μM) was applied for 2s alone or with TPentA (0.04, 0.12, 0.37, 1.11, or 3.33mM). (B) The dependence of duration of the hooked tail current, t_Hook, measured at the level of the stationary blocked current, I_B, on the degree of the stationary current inhibition, 1−I_B/I_C. The solid line shows the parabolic fit. The vertical dashed line corresponds to 1−I_B/I_C=0.5. The horizontal dashed line corresponds to t_Hook=254ms. (C) The dependence of the normalized charge carried during the hooked tail current, Q, on TPentA concentration. The solid line is the fit of the Q dependence by Eq. (1) with A₁=1, A₂=2.16±0.08, p=1.01±0.23, and [B]₀=0.40±0.12mM (n=7). (D) The dependence of the amplitude of the hooked tail current, (I_P−I_B)/I_C, on TPentA concentration. The solid line is the fit of the (I_P−I_B)/I_C dependence by Eq. (1) with A₁=0, A₂=1.11±0.10, p=1.30±0.26, and [B]₀=0.47±0.10mM (n=7).

The kinetic model used to simulate the blocking action of TPentA was based on the conventional rate theory and used independent forward and reverse rate constants to simultaneously solve first-order differential equations representing the transitions between all possible states of the channel. The processes of NMDA channels activation, opening, and desensitization were described in accordance with a kinetic model proposed by Lester and Jahr, 1992. The kinetic constants for the agonist binding, l₁=2μM⁻¹s⁻¹, and unbinding, l₂=25s⁻¹, were taken to be approximately the same as those determined for NMDA (Benveniste and Mayer, 1991). The choice of the value of the NMDA unbinding rate constant for aspartate can be justified by the striking similarity in the kinetics of the current decay after short-term NMDA and aspartate applications (Lester and Jahr, 1992). The applicability of the NMDA binding rate constant to aspartate follows from the fact that EC₅₀ measured in our experiments with aspartate (15.5±1.1μM, n=6) is practically the same as EC₅₀ predicted by Model 1 at the values of l₁ and l₂ listed above (16.1±0.4μM). The kinetic constants for the entrance into (γ) and recovery from (ϵ) desensitization, determined by the previously described method (Sobolevsky and Koshelev, 1998), were 0.93s⁻¹ and 0.82s⁻¹, respectively. The choice of the value of the kinetic constant for the channel closure, α, was based on the studies of single NMDA channels (Ascher et al,Cull-Candy and Usowich, 1989,Jahr and Stevens, 1990). As the mean open time in these studies varied from 2.5 to 7ms, the value of 200s⁻¹ was taken for α. Therefore, with the exception of the rate constant of the channel opening, β, each rate constant for the NMDA channel activation scheme (Lester and Jahr, 1992) can be estimated within a short range of magnitude. In contrast, indirect methods of estimation of β, which cannot be measured directly, gave extremely scattered values. Thus, the value of the maximum NMDA channel open probability, P₀=β/(α+β), which at a given α is mutually dependent on β, was estimated in different studies in a wide range of 0.025 to 0.520 (Jahr, 1992,Hessler et al,Benveniste and Mayer, 1995,Rosenmund et al,Dzubay and Jahr, 1996,Chen et al). Due to this large scatter in values, the initially unknown value of β was estimated in the present study.

The solution exchange was assumed to be a single-exponential process (Benveniste et al). The time constant of the solution exchange at the beginning of the agonist and the blocker coapplication measured by the method of sodium concentration jumps (Vyklicky et al,Chen and Lipton, 1997) varied in a wide range of 5 to 25ms and in the modeling experiments was accepted as 10ms. The initially unknown values of the time constant of the solution exchange at termination of the agonist and the blocker coapplication, τ_wash, as well as the rate constants of the blocker binding and unbinding, k_on and k_off, respectively, were estimated. Up to the moment of estimation, the value of k_on was taken arbitrarily (3.5μM⁻¹s⁻¹ as for tetrabutylammonium in the previous study by Sobolevsky, 1999) but the blocker concentration was measured in the values of the microscopic K_d=k_off/k_on.

Differential equations were solved numerically using the algorithm analogous to that described previously (Benveniste et al).

Tetrapentylammonium was purchased from Aldrich (Milwaukee, WI).

Ionic currents through NMDA channels were elicited by fast application of 100μM aspartate (ASP) in a Mg²⁺-free, 3μM glycine-containing solution. At the holding potential of −100mV, ASP induced an inward current that, after an initial fast rise (τ<30ms) up to the value, I₀, indicating the opening of NMDA channels, decreased gradually (τ_D=570±25ms, n=7) down to a certain plateau level, I_C (Figure 1A). Such a current decay under the continuing action of the agonist is considered to be the result of desensitization of the receptor-channel complex. The fraction of desensitized channels, d=1−I_C/I₀, was, on average, 0.44±0.06 (n=7). TPentA inhibited the ASP-induced currents in a concentration-dependent manner with both the initial and the stationary currents decreased with an increase in the TPentA concentration (Figure 1A). The dependence of the degree of the stationary current inhibition (1−I_B/I_C) on the blocker concentration was well fitted by Eq. (1) (not shown). The parameter A₁ was fixed at 0 (when TPentA concentration, [B]=0, the current inhibition was absent). The value of A₂ when this parameter was left free proved to be indistinguishable from 1 (1.00±0.11, n=7). As this value is predicted by kinetic modeling (see Eq. (2) below), A₂ was fixed at 1 in order to minimize the errors for the varied parameters. The values of the varied parameters were as follows: p=0.55±0.04 and IC₅₀=[B]₀=0.54±0.05mM (n=7).

The termination of each agonist and blocker coapplication was followed by a transient increase in the inward current (hooked tail current) that was absent when ASP was applied alone (Figure 1A). The duration of the hooked tail current, t_Hook, measured starting from the beginning of the solution exchange at the level of the stationary blocked current, I_B, increased almost linearly with an increase in the degree of stationary current inhibition, 1−I_B/I_C, but was better fitted by a parabola (Figure 1B). The value of t_Hook corresponding to 50% stationary current inhibition, t_Hook⁵⁰, was 254±9ms (n=7).

The electrical charge (measured by integrating the current curve starting from the beginning of the solution exchange) carried during the hooked tail current, Q_hook, was higher than that carried during the control tail current, Q_control. Their ratio, Q=Q_hook/Q_control, increased with an increase in the TPentA concentration. The dependence of Q on the TPentA concentration was well fitted by Eq. (1) at fixed A₁=1 (when the TPentA concentration, [B]=0, the control and blocked currents coincide and, correspondingly, Q=1). The values of the varied parameters were as follows: A₂=2.16±0.08, p=1.01±0.23, and [B]₀=0.40±0.12mM (n=7; Figure 1C).

The amplitude of the hooked tail current, (I_P−I_B)/I_C, also increased with TPentA concentration. The (I_P−I_B)/I_C dependence on the TPentA concentration was well fitted by Eq. (1) at fixed A₁=0 (when TPentA concentration, [B]=0, the control and blocked currents coincide and, correspondingly, the hooked tail current is absent). The values of the varied parameters were as follows: A₂=1.11±0.10, p=1.30±0.26, and [B]₀=0.47±0.10mM (n=7; Figure 1D).

The following model was used to simulate the blocking effect of TPentA on NMDA channels (Sobolevsky et al):

where C, D, and O represent the channel in closed, desensitized, and open states, respectively. The subscripts A, AA, and B indicate the binding of one agonist, two agonist, and one blocker molecule to the channel, respectively, and [A] is the agonist concentration. The conducting state is marked with an asterisk.

Model 1 implies that the blocker prohibits the channel closure and, consequently, desensitization and the agonist dissociation from the blocked channel. This model predicted hooked tail currents. Their characteristics, t_Hook, Q and (I_P−I_B)/I_C, strongly depended on the unknown parameters, the time constant of the solution exchange, τ_wash, the rate constant of the channel opening, β, or the maximum open probability, P₀=β/(α+β) (β and P₀ are mutually dependent at a given α and only P₀ will be mentioned further), and the blocker unbinding rate constant, k_off (Fig. 2). The hooked tail current became smaller and wider with an increase in τ_wash (Figure 2A). Its duration, t_Hook, did not change significantly with the maximum open probability, but its amplitude, (I_P−I_B)/I_C, decreased with P₀ (Figure 2B). (I_P−I_B)/I_C increased with the blocker unbinding rate constant, whereas t_Hook remained approximately constant at different k_off (Figure 2C).

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Figure 2

The hooked tail currents predicted by Model 1 at different values of τ_wash, P₀ and k_off. Each hooked tail current (thick line) is shown in a superposition with the control tail current (thin line). The degree of the stationary current inhibition is the same, 1−I_B/I_C=0.65. The values of parameters, except where noted, were τ_wash=70ms, P₀=0.041, k_off=14s⁻¹, and [B]=105 K_d. (A) The hooked tail currents predicted by Model 1 at different τ_wash. (B) The hooked tail currents predicted by Model 1 at different values of P₀. A smaller blocker concentration was used at higher P₀ to achieve the same degree of stationary current inhibition. Thus, at P₀=0.02, 0.04, 0.09, 0.2, and 0.5 the values of the blocker concentration, [B], were 211, 88, 45, 19, and 6 K_d, respectively. (C) The hooked tail currents predicted by Model 1 at different k_off.

The dependencies of t_Hook, Q, and (I_P−I_B)/I_C on τ_wash, P₀, and k_off under the conditions of Fig. 2 are shown in Fig. 3. The duration of the hooked tail current, t_Hook, depended strongly on τ_wash (Figure 3A) but did not change significantly with P₀ and k_off (Figure 3BC). The normalized charge carried during the hooked tail current, Q, depended on both τ_wash and P₀ (Figure 3DE) but did not change significantly with k_off (Figure 3F). Finally, the hooked tail current amplitude (I_P−I_B)/I_C, depended on all three parameters (Figure 3G−I).

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Figure 3

The dependencies of t_Hook, Q and (I_P−I_B)/I_C on τ_wash, P₀ and k_off predicted by Model 1. The points connected by the lines represent the dependencies of duration of the hooked tail current, t_Hook (A, B, C), the normalized electrical charge carried during the hooked tail current, Q (D, E, F), and the amplitude of the hooked tail current, (I_P−I_B)/I_C (G, H, I), on the time constant of the solution exchange, τ_wash (A, D, G), the maximum NMDA channel open probability, P₀ (B, E, H), and the blocker unbinding rate constant, k_off (C, F, I). The values of parameters are the same as listed in the Fig. 2 legend.

The dependencies shown in Fig. 3 permit the estimation of the unknown parameters τ_wash, P₀, and k_off by measuring t_Hook, Q, and (I_P−I_B)/I_C. Indeed, by comparing the t_Hook dependencies on the degree of the stationary current inhibition predicted by Model 1 at different values of τ_wash, one can identify the one that simulates the experimental t_Hook dependence (Figure 1B). The corresponding value of τ_wash will be an estimate of the experimental time constant of the solution exchange. At this fixed value of τ_wash, the Q dependencies on TPentA concentration predicted by Model 1 at different values of P₀ make it possible to establish the one that simulates the experimental Q dependence (Figure 1C). The corresponding P₀ value will be an estimate of the experimental maximum open probability. Finally, at fixed values of τ_wash and P₀, the dependence of (I_P−I_B)/I_C on TPentA concentration predicted by Model 1 at different values of k_off will permit determination of which one simulates the experimental (I_P−I_B)/I_C dependence (Figure 1D). The corresponding value of k_off is an estimate of the experimental value of the TPentA unbinding rate constant.

The procedure described above for estimation of τ_wash, P₀, and k_off was carried out with the initial values of P₀=0.09 and k_off=1000s⁻¹ used in our previous study (Sobolevsky et al). To minimize the errors in estimation of τ_wash, P₀, and k_off, this procedure was repeated five times, each time taking the values of the parameters found in the previous iteration as initial values for the next one. The results of the second iteration did not differ significantly from those of further iterations. The results of the fifth iteration are illustrated in Figure 4 and Figure 5 and Figure 6.

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Figure 4

Estimation of the time constant of the solution exchange, τ_wash. The values of parameters P₀=0.043 and k_off=14.2s⁻¹. (A) Dependencies of t_Hook predicted by Model 1 on the degree of the stationary current inhibition, 1−I_B/I_C, at different values of τ_wash (30, 50, 70, 90, and 110ms). Each dependence was fitted by a parabola (solid lines). The value on a parabola at 1−I_B/I_C=0.5 (vertical dashed line) corresponded to t_Hook⁵⁰ at each τ_wash given (horizontal dashed lines). (B) The dependence of t_Hook⁵⁰ predicted by Model 1 on τ_wash. The solid line shows the linear fit. The value τ_wash=70ms corresponds to the experimental value of t_Hook⁵⁰=254ms (dashed lines).

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Figure 5

Estimation of the value of the maximum NMDA channel open probability, P₀. The values of parameters τ_wash=70ms and k_off=14.2s⁻¹. (A) The dependencies of the normalized charge carried during the hooked tail current, Q, predicted by Model 1 on the blocker concentration, [B], at different values of P₀ (0.020, 0.029, 0.041, 0.057, and 0.074). Each dependence was fitted by Eq. (1) (solid lines). (B) The dependence of the parameter A₂ value obtained from each fitting in A on P₀. The solid line shows the fitting of the A₂ dependence by a parabola. The value P₀=0.041 corresponds to the experimental value of A₂=2.16 (dashed lines).

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Figure 6

Estimation of the value of the TPentA unbinding rate constant, k_off. The values of parameters τ_wash=70ms and P₀=0.041. (A) The dependencies of the hooked tail current amplitude, (I_P−I_B)/I_C, predicted by Model 1 on the blocker concentration, [B], at different values of k_off (2, 5, 20, 100, and 1000s⁻¹). Each dependence was fitted by Eq. (1) (solid lines). (B) The dependence of the value of parameter A₂ obtained from each fitting in A on k_off. The solid line shows the fitting of the A₂ dependence by Eq. (1). The value k_off=14.0s⁻¹ corresponds to the experimental value of A₂=1.11 (dashed lines).

The dependence of t_Hook on the degree of the stationary current inhibition, 1−I_B/I_C, predicted by Model 1 was nearly linear at different values of τ_wash but was better described by a parabola (Figure 4A). The value of the duration of the hooked tail current at 50% current inhibition, t_Hook⁵⁰, increased linearly with an increase in τ_wash (Figure 4B). The value τ_wash=70ms corresponded to the experimental value of t_Hook⁵⁰ (254ms, Figure 1B) and was within the range of τ_wash values (30–80ms) estimated previously for the application system used (Sobolevsky, 1999).

The value of the normalized charge carried during the hooked tail current, Q, predicted by Model 1 increased with the blocker concentration and was well fitted by Eq. (1) (Figure 5A). The value of the parameter p changed slightly when the value of P₀ was varied. Thus, p increased from 1.03 at P₀=0.020 to 1.18 at P₀=0.074. In contrast, the value of the parameter A₂ strongly depended on P₀. Thus, the value of A₂ decreased from 4.01 at P₀=0.020 to 1.37 at P₀=0.074. The dependence of A₂ on P₀ was decreasing and in the range of P₀ tested was well fitted by a parabola (Figure 5B). The value P₀=0.041 corresponded to the experimental value of A₂ (2.16, Figure 1C).

The value of the amplitude of the hooked tail current, (I_P−I_B)/I_C, predicted by Model 1 increased with the blocker concentration and was well fitted by Eq. (1) (Figure 6A). The value of the parameter p was slightly different at different k_off: it decreased from 1.64 at k_off=2s⁻¹ to 1.05 at k_off=1000s⁻¹. The value of A₂ depended more strongly on k_off. Thus, A₂ increased from 0.38 at k_off=2s⁻¹ to 1.65 at k_off=1000s⁻¹. The dependence of A₂ on k_off was well fitted by Eq. (1) (Figure 6B). The value of k_off=14.0s⁻¹ corresponded to the experimental value of A₂ (1.11, Figure 1D).

The mean outcome of the last four iterations allowed to estimate the values of the time constant of the solution exchange, τ_wash=67±3ms, the maximum NMDA channel open probability, P₀=0.042±0.002, and the TPentA unbinding rate constant, k_off=14.1±0.2s⁻¹. The only remaining parameter was the TPentA binding rate constant, k_on. It was easy to find the value of k_on at given k_off taking into account that Model 1 should simulate the effectiveness of blocking action of TPentA measured in the experiment as IC₅₀=0.54±0.05mM.

At the values of parameters τ_wash, P₀, and k_off determined, the dependence of the stationary current inhibition, 1−I_B/I_C, on the blocker concentration, [B], predicted by Model 1 was well fitted by Eq. (1) with A₁=0, A₂=1, p=1.03±0.01, and [B]₀=56.7±0.1 K_d. To simulate the experiment, [B]₀ should be equal to IC₅₀, or 56.7 K_d=56.7 k_off/k_on=IC₅₀. From the latter equality, it was easy to define the TPentA binding rate constant, k_on=56.7 k_off/IC₅₀=1.48μM⁻¹s⁻¹.

At the new value of k_on, Model 1 predicts the concentration dependence of the stationary current inhibition with IC₅₀=0.54mM which is equal to the experimental one. However, the value of the Hill coefficient, p=1, predicted by Model 1 (see also Eq. (2) below) is much higher than that determined experimentally, p=0.55±0.04. This discrepancy can be explained by the heterogeneity of the TPentA affinity due to the heterogeneity in the NMDA receptor subunit combinations expressed in the neurons under study. On the other hand, this discrepancy presumably does not reflect the heterogeneity of the mechanism of TPentA action on NMDA channels. The reason is in the striking similarity of the foot-in-the-door blockade simulated by Model 1 and that observed in the experiment. This can be clearly seen from the following tests of Model 1 at the values of parameters τ_wash, P₀, k_on, and k_off determined.

First, Model 1 was tested in an experiment with the agonist and the blocker coapplication (Fig. 7). The currents predicted by Model 1 at different blocker concentrations (Figure 7A, first line) were very similar to those observed in the experiment with TPentA (Figure 7A, second line). The coincidence of the experimental and modeling data differs only during the recovery of the current after termination of ASP application (the experimental recovery kinetics contains a slow component which is not practically resolved in the modeling recovery). This discrepancy is not surprising because the activation model used in the present study (Lester and Jahr, 1992) is simple and cannot reproduce many of the NMDA receptor properties described in single-channel studies (Ascher et al,Cull-Candy et al,McLarnon and Curry, 1990,Howe et al,Gibb and Colquhoun, 1992). Thus, the existence of a slow component in control current relaxation can be explained, for example, by more complex NMDA receptor desensitization (Sather et al) or by infringement of the principle of independence of the binding of two agonist molecules to the receptor (Benveniste and Mayer, 1991).

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Figure 7

The predictions of Model 1 for the experiment with the blocker and the agonist coapplication. The values of parameters τ_wash=70ms, P₀=0.041, k_off=14s⁻¹, and k_on=1.48μM⁻¹s⁻¹. (A) First line: Simulated currents at different blocker concentrations (0.04, 0.12, 0.37, 1.11, or 3.33mM) in superposition with the simulated control current. Second line: Experimental currents from Figure 1A. (B) The dependence of t_Hook on the degree of stationary current inhibition, 1−I_B/I_C. The solid line shows the parabolic fit. The value t_Hook=267ms corresponds to the 50% stationary current inhibition (dashed lines). (C) The dependence of the normalized charge carried during the hooked tail current, Q, on the blocker concentration. The solid line is the fit of the Q dependence by Eq. (1) with A₁=1, A₂=2.13±0.01, p=1.07±0.02, and [B]₀=0.33±0.01mM. (D) The dependence of the amplitude of the hooked tail current, (I_P−I_B)/I_C, on the blocker concentration. The solid line is the fit of the (I_P−I_B)/I_C dependence by Eq. (1) with A₁=0, A₂=1.03±0.03, p=1.37±0.10, and [B]₀=0.49±0.04mM.

Figure 7BD, tests the ability of the fitting procedure to provide reasonable fits. The dependence of duration of the hooked tail current, t_Hook, on the degree of the stationary current inhibition, 1−I_B/I_C, was fitted by a parabola (Figure 7B) and the value of t_Hook corresponding the 50% stationary current inhibition, t_Hook⁵⁰=267±15ms, was close to that observed experimentally (t_Hook⁵⁰=254±9ms, Figure 1B).

The dependence of Q on the blocker concentration predicted by Model 1 was well fitted by Eq. (1) (Figure 7C) with the following values of parameters: A₁=1, A₂=2.13±0.01, p=1.07±0.02, and [B]₀=0.33±0.01mM, which were quite similar to those observed in the experiment (A₁=1, A₂=2.16±0.08, p=1.01±0.23, and [B]₀=0.40±0.12mM; Figure 1C).

The dependence of the amplitude of the hooked tail current on the blocker concentration predicted by Model 1 was well fitted by Eq. (1) (Figure 7D) with A₁=0, A₂=1.03±0.03, p=1.37±0.10, and [B]₀=0.49±0.04mM and was in reasonable agreement with the experimental (I_P−I_B)/I_C dependence (A₁=0, A₂=1.11±0.10, p=1.30±0.26, and [B]₀=0.47±0.10mM; Figure 1D).

For further verification, Model 1 was tested in experiments which can be considered as qualitative criteria for distinguishing the fast blockers that prevent or do not prevent the channel closure, desensitization, and agonist dissociation (Sobolevsky et al).

First, Model 1 was examined to simulate the recovery of the blocker-inhibited current in the continuous presence of the agonist (Figure 8A). Both the experimental (left trace) and simulated (right trace) recovery currents exceeded the stationary level, I_C, thus forming an “overshoot”. In both cases, the falling phase of the overshoot contained the fast component reflected the closure of the unblocked channels (the transition from O^*_AA to C_AA in Model 1), and the slow component reflected channel desensitization (the transition from C_AA to D_AA). Such a two-component current recovery in the continuous presence of the agonist observed in the experiment with TPentA and well simulated by Model 1 is a characteristic feature of the blocker that prevents the channel closure (Sobolevsky et al).

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Figure 8

Verification of Model 1 in different experimental protocols. The values of parameters P₀=0.041, k_off=14s⁻¹, and k_on=1.48μM⁻¹s⁻¹. (A) Recovery of the blocker-inhibited current in the continuous presence of the agonist. Left: The experiment with 100μM ASP and 3mM TPentA. In this experiment, the faster direction of the solution exchange (see Materials and Methods) was used to remove the blocker. Right: Prediction of Model 1 at [B]=3mM and time constant of solution exchange=10ms. (B) A tail current after termination of the agonist application in the continuous presence of the blocker in superposition with the tail current after the control agonist application. Left: The experiment with 100μM ASP and 0.5mM TPentA. Right: Prediction of Model 1 at [B]=0.5mM and τ_wash=70ms. (C) The dependence of the stationary current inhibition, 1−I_B/I_C, measured in the experiment with the agonist and the blocker coapplication on the agonist concentration. Points: Experimental data at 1mM TPentA. Solid line: Prediction of Model 1 (Eq. (2)) at [B]=1mM.

Model 1 was also verified in another kinetic experiment in which the tail current after the agonist application, in the continuous presence of the blocker, was compared with the control tail current (Figure 8B). In the modeling experiment (right trace) as well as in the experiment with TPentA (left trace) the control and blocked tail currents intersected. Such a delay in the current relaxation induced by the presence of the blocker in the washout solution is a characteristic feature of the blocker that prevents the agonist dissociation from the blocked channel (Sobolevsky et al).

Finally, the ability of Model 1 to reproduce the dependence of degree of the stationary current inhibition, 1−I_B/I_C, on the agonist concentration was checked (Figure 8C). In the experiment with TPentA, the agonist dependence was increasing (solid circles in Figure 8C, the mean 1−I_B/I_C values were significantly different, p<10⁻⁶, n=6). Model 1 predicts the following equation for the degree of the stationary current inhibition (deduced by the previously described method; Sobolevsky, 1999):

(2)

Thus, at the values of parameters found, all quantitative and qualitative predictions of Model 1 showed a good correspondence to the experimental data.

Model 1 proved to be a reasonable description of the TPentA-induced blockade of open NMDA channels. An analysis of characteristics of hooked tail currents generated after termination of ASP and TPentA coapplication allowed specifying all the unknown parameters of this description.

The first parameter, the time constant of the solution exchange, τ_wash, was found by analyzing the dependence of the hooked tail current duration, t_Hook, on the degree of the stationary current inhibition (Fig. 4). This method of τ_wash estimation is new and does not require preparation of additional experimental solutions, as is the case with sodium concentration jumps (Vyklicky et al,Chen and Lipton, 1997). The t_Hook method is especially convenient for application systems wherein the solution exchange varies with time (or from experiment to experiment, or from cell to cell) because it allows one to estimate τ_wash directly during the current recordings. Under the conditions of TPentA experiments (P₀=0.04, k_off=14s⁻¹), this method is applicable if the value of τ_wash is higher than 10ms (Figure 3A). The sensitivity of this method does not depend on P₀ but increases with an increase in k_off. Thus, at k_off=1000s⁻¹, this method allows one to estimate the value of τ_wash if it is higher than 1ms (not shown).

The second parameter is the maximum NMDA channel open probability, P₀, which under physiological conditions (saturating concentrations of the agonist) reflects the fraction of the total number of NMDA channels that open in response to a short pulse of the agonist. The value of P₀ was found analyzing the dependence of the normalized electric charge carried during the hooked tail current, Q, on the blocker concentration (Fig. 5) and proved to be quite low (0.04). The previous studies reported the maximum NMDA channel open probability in a wide range of 0.025 to 0.52 (Jahr, 1992,Hessler et al,Benveniste and Mayer, 1995,Rosenmund et al,Dzubay and Jahr, 1996,Chen et al). A considerable difference was observed between the values of P₀ estimated from the whole-cell current recordings (0.025–0.28) and from outside-out single-channel data (0.24–0.52; Benveniste and Mayer, 1995,Rosenmund et al). This difference can be explained by the much more rapid loss of cytoplasmic constituents that control channel gating during patch dialysis (Rosenmund et al). The P₀ value estimated in the present study (0.04) is identical to that measured by Rosenmund et al in the whole-cell experiments.

Earlier to find P₀, in some studies the trapping blocker MK-801 was used (Huetter and Bean, 1988,Jahr, 1992,Hessler et al,Rosenmund et al,Dzubay and Jahr, 1996,Chen et al). However, the value of P₀ obtained by this method can be underestimated because of the possible overestimation of the MK-801 binding rate constant, k_on (Dilmore and Johnson, 1998). In other studies, 9-aminoacridine, which is believed to act as foot-in-the-door blocker, was used (Benveniste and Mayer, 1995,Chen et al). However, this method afforded only inaccurate value of P₀ for the following reasons (Benveniste and Mayer, 1995): (i) non-instantaneous recovery from block by 9-aminoacridine, (ii) space-clamp limitations, (iii) run-down for tail currents, and (iv) desensitization during the application of 9-aminoacridine. The new method for estimation of the maximum NMDA channel open probability used in the present study is applicable in the P₀ range of 0.02 to 0.5 (Figure 3E) and is devoid of the shortcomings mentioned above.

The kinetic constants of TPentA binding and unbinding, k_on and k_off, respectively, were found by analyzing the dependencies of the hooked tail current amplitude (Fig. 6) and the degree of the stationary current inhibition on the blocker concentration. The value of the unbinding rate constant, k_off=14s⁻¹, attributes TPentA to rather fast blockers. The method for k_off estimation used in the present study is applicable for k_off>1s⁻¹ (otherwise, the hook current does not appear, Figure 2C; see also Sobolevsky et al) up to k_off=1000s⁻¹ (Figure 3I).

The major limitation of the methods to estimate τ_wash, P₀, k_on, and k_off proposed in the present study is the so-called model dependence. Thus, these methods are applicable only to blockers that interact with NMDA channels according to the foot-in-the-door mechanism (Model 1). Even if the latter is true, the values of estimated parameters depend on fixed values of the rate constants in Model 1. Correspondingly, any inaccuracy in the definition of the rate constants l₁, l₂, γ, ϵ, or α will result in an inaccuracy of the τ_wash, P₀, k_on, and k_off values.

The ratio of unbinding and binding rate constants gives the apparent value of K_d=k_off/k_on=0.009mM, which is 60 times lower than IC₅₀=0.54±0.05mM. This difference between the microscopic dissociation constant (K_d) and the characteristics of the apparent affinity (IC₅₀) is due to the prevention of TPentA to the channel closure (for a trapping blocker, a blocker which does not affect the channel closure, desensitization, and agonist dissociation, K_d=IC₅₀). The value of the IC₅₀/K_d ratio predicted by Model 1 is equal to the denominator 1+(α/β) [1+(γ/ϵ)+(2l₂/l₁/[A])+(l₂/l₁/[A])²] in Eq. (2). From this mathematical expression, the IC₅₀/K_d ratio decreases with the agonist concentration and the maximum open probability (P₀), but increases with channel desensitization. Thus, for a blocker whose action interferes with that of the NMDA channel gating machinery, the apparent blocking strength (IC₅₀) differs considerably from its binding efficacy (K_d) and, correspondingly, the former cannot be used as an estimation of the latter.

According to Model 1, TPentA is a typical foot-in-the-door blocker, that is, when bound to the open NMDA channel it prohibits the closure of the activation gate. Therefore, the constriction of the NMDA channel pore formed by the activation gate in the closed state is most probably located in the region of the TPentA binding site. If so, the diameter of the extracellular vestibule of the NMDA channel pore in the region of the activation gate localization should not be smaller than the size of the TPentA molecule (∼11Å).