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¹ School of Biological Sciences, University of Manchester, Manchester M13 9PT, United Kingdom
² Department of Physiology and Biophysics, Mayo Clinic, Rochester, MN 55905

Address correspondence to Richard J. Prince, School of Biological Sciences, University of Manchester, Manchester M13 9PT, UK. Fax: (44) 161-275-5600; E-mail: richard.prince{at}man.ac.uk

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
We used single-channel kinetic analysis to study the inhibitory effects of tacrine on human adult nicotinic receptors (nAChRs) transiently expressed in HEK 293 cells. Single channel recording from cell-attached patches revealed concentration- and voltage-dependent decreases in mean channel open probability produced by tacrine (IC₅₀ 4.6 µM at -70 mV, 1.6 µM at -150 mV). Two main effects of tacrine were apparent in the open- and closed-time distributions. First, the mean channel open time decreased with increasing tacrine concentration in a voltage-dependent manner, strongly suggesting that tacrine acts as an open-channel blocker. Second, tacrine produced a new class of closings whose duration increased with increasing tacrine concentration. Concentration dependence of closed-times is not predicted by sequential models of channel block, suggesting that tacrine blocks the nAChR by an unusual mechanism. To probe tacrine's mechanism of action we fitted a series of kinetic models to our data using maximum likelihood techniques. Models incorporating two tacrine binding sites in the open receptor channel gave dramatically improved fits to our data compared with the classic sequential model, which contains one site. Improved fits relative to the sequential model were also obtained with schemes incorporating a binding site in the closed channel, but only if it is assumed that the channel cannot gate with tacrine bound. Overall, the best description of our data was obtained with a model that combined two binding sites in the open channel with a single site in the closed state of the receptor.

Key Words: kinetic analysis • open-channel block • single-channel recording • maximum likelihood • anticholinesterase

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
The nicotinic acetylcholine receptor (nAChR)^* from adult mammalian muscle is a heteropentameric protein with the subunit composition 2, ß, , . Each of the subunits is structurally homologous, and consists of a large, extracellular NH₂-terminal domain, four membrane spanning segments (M1-M4), and a large intracellular loop between M3 and M4. Contained within the nAChR complex are two binding sites for acetylcholine, which are located in the NH₂-terminal domains of the subunits, and a centrally located cation selective channel (Arias, 1996).

Although atomic structural insight recently emerged for the NH₂-terminal ligand binding domain via X-ray crystallography of an ACh binding protein (Brejc et al., 2001) and a mutagenesis-based model of the muscle receptor (Sine et al., 2002), our understanding of the transmembrane domains continues to rely on lower resolution cryoelectron microscopy studies (Miyazawa et al., 1999), site-directed mutagenesis, affinity labeling, and the substituted cysteine accessibility method (SCAM) (for review see Arias, 1996). Together, these techniques lead to a model of the receptor in which the subunits are arrayed around a central ion channel, with the lining of the channel formed largely by the M2 domains of each of the subunits, and perhaps, smaller contributions from the extracellular ends of the M1 segments. (Arias, 1996; Miyazawa et al., 1999)

The M2 domains are highly conserved amongst the subunits, meaning that the overall channel structure can be viewed as a series of rings, stacked one upon the other. Each ring consists of five homologous amino acids, one from each subunit. The secondary structure of these channel lining segments is thought to be -helical but with a distinct "kink" part way along their length. At the apex of this kink in each subunit is a conserved leucine residue. In one current model of channel gating, the ring of bulky leucine residues projects into the channel and occludes ion flux when the channel complex is in the closed state. When agonists bind and the channel opens, the leucine residues swing out of the pore, allowing ions to pass (Unwin, 1995). An alternative model, derived from SCAM studies, holds that the channel gate is 10 residues more cytoplasmic than the conserved leucine ring (Wilson and Karlin, 1998).

The ion channel of the nAChR is the target of a diverse group of noncompetitive antagonists that have generally been classified as open channel blockers (for review see Arias, 1996). Open channel blockers inhibit receptor function by entering and physically plugging the open channel, thereby preventing ion flux. Because the binding site is accessible only when the channel has been activated, and is located within the membrane field, the actions of open channel blockers are use and voltage dependent. Photoactivatible open channel blockers (e.g., chlorpromazine) were instrumental in pinpointing residues that line the channel and hence in the identification of the M2 segments as the major structural components of the channel (Changeux, 1990; Arias, 1996). However, despite the historical importance of open channel blockers in structure–function studies, our knowledge of their sites and mechanisms of action is incomplete. In particular, there have been very few systematic investigations of the kinetics of open channel block at the single channel level.

In this study, we investigated the blocking mechanism of tacrine (9-amino-1,2,3,4-tetrahydroacridine) at human adult nAChRs. Tacrine is used clinically to treat Alzheimer's disease and is thought to exert its therapeutic effects via inhibition of acetylcholinesterase. However, at higher concentrations than those used in the clinic, tacrine has also been found to inhibit a wide range of other proteins, including K⁺ channels (Dreixler et al., 2000), NMDA receptors (Hershkowitz and Rogawski, 1991; Vorobjev and Sharonova, 1994), voltage-gated Ca²⁺ channels (Dolezal et al., 1997), and muscarinic acetylcholine receptors (Perry et al., 1988; Kiefer-Day et al., 1991; Kojima and Onodera, 1998). Previous studies showed that tacrine is a noncompetitive antagonist of Torpedo electric organ nAChRs (Canti et al., 1998), and speculated that the mechanism of this inhibition may involve open channel block. In the present study, we used maximum likelihood techniques to fit a series of kinetic models to single channel data. Our results suggest that tacrine is an atypical open channel blocker and interacts with at least two sites within the open- and one in the closed-state of the receptor. Thus, there may be multiple binding sites for tacrine and structurally related compounds in the nAChR complex.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
Materials
Dulbecco's modified Eagle's medium (DMEM), penicillin, and streptomycin were purchased from GIBCO BRL. Tacrine was purchased from RBI. All other materials were obtained from Sigma-Aldrich. [¹²⁵I]-labeled -bungarotoxin was obtained from Amersham Biosciences. The sources of the human nAChR subunits were as described previously (Ohno et al., 1996).

Cell Culture and Receptor Expression
Human embryonic kidney 293 (HEK 293) cells were maintained in culture at 37°C, 5% CO₂ in DMEM containing 10% FCS, 50 IU/ml penicillin, and 50 µg/ml streptomycin. In all experiments, cells were transfected at 30% confluency using calcium phosphate precipitation as previously described (Prince and Sine, 1996). For each 35-mm culture dish, 2.7 µg of subunit DNA and 1.35 µg each of ß, , and were used in the transfection mixture. A plasmid encoding fluorescent green protein (pGreen lantern) was also included (0.5 µg/35 mm plate) in the transfection mixture to allow identification of transfected cells under fluorescence optics. The culture medium was replaced with fresh medium 12–16 h after transfection, and the cells were maintained at 37°C for a further 24–48 h before recordings or binding studies were performed.

Patch-clamp Recording
Recordings were obtained from transfected HEK 293 cells in the cell-attached configuration at membrane potentials of -70, -110 or -150 mV, at a temperature of 23°C. The bath and pipette solutions contained KRH buffer: (in mM) KCl 142, NaCl 5.4, CaCl₂ 1.8, MgCl₂ 1.7, and HEPES 25, pH 7.4. The patch pipette also contained various concentrations of acetylcholine (ACh) and tacrine, as required.

Recordings were made using an Axopatch 200A amplifier at a bandwidth of 50 kHz. Data were digitized at 200 kHz using an ITC-16 analogue to digital interface and recorded directly to hard-disk using the program Acquire (Bruxton Instruments). Channel openings and closings were detected off-line by the half-amplitude criterion using the program TAC (Bruxton Instruments) at a final bandwidth of 10 kHz. Open- and closed-duration histograms of the idealized data were constructed using TACFit (Bruxton Instruments) and were fitted by the sums of exponential functions.

At the concentrations of ACh (6–300 µM) used in this study, channel openings group into clusters corresponding to activation episodes of single AChRs. The long closings that mark the boundaries of clusters correspond to periods when all channels in the patch are in a desensitized conformation. Data within clusters were identified and selected for maximum likelihood analysis as described previously (Prince and Sine, 1998a). For each recording, we calculated the mean open and closed durations within clusters (m_open, m_closed) and the mean probability that the channel was open within clusters of openings (P_open). Concentration-response curves for ACh were constructed using P_open values and were fitted using the following form of the Hill equation:

(1)

where X represents the concentration of ACh, M is the fitted maximum P_open, EC₅₀ is the concentration of ACh yielding 50% of maximal P_open, and n is the Hill coefficient.

Tacrine inhibition curves were fitted using the following equation:

(2)

where X represents the concentration of tacrine, M is the P_open in the absence of tacrine, IC₅₀ is the concentration of tacrine that yields a P_open of 50% of M, and n is the Hill coefficient.

Maximum Likelihood Analysis
To determine the rate constants governing receptor activation and block by ACh, recordings obtained over a range of ACh concentrations (6–300 µM) were analyzed according to Scheme A (see Fig. 3) using the maximum interval likelihood (MIL) program developed by Qin et al. (1996). A dead-time of 22 µs was imposed on all recordings. The MIL program calculates the likelihood that a given kinetic scheme and set of rate constants gave rise to the experimental set of openings and closings. The program then systematically varies the rate constants to maximize the likelihood. Once the parameters in Scheme A had been established, recordings obtained with 100 µM ACh and 1–60 µM tacrine (data at 60 µM tacrine were included only at -70 mV) were analyzed according to mechanisms B-I (see Fig. 3), with the values of the parameters for activation and block of the receptor by ACh constrained to the values determined by fits to Scheme A in the absence of tacrine (see Table IV) . Nested models (models derived from the same parent kinetic scheme) were compared using the likelihood ratio test (LRT) statistic (Rao, 1973):

where LL₁ and LL₂ are the log-likelihood values of the models being compared. LRT is distributed as ² with the degrees of freedom being the difference in the number of free parameters between the two models.

View larger version (24K): [in this window] [in a new window]   FIGURE 3. Kinetic schemes used in maximum likelihood fitting. (Notation used for receptor states) C, AC, A2C are closed states with agonist binding sites unoccupied, singly occupied, and doubly occupied, respectively; A2O is the open state; A2BA is the open state blocked by acetylcholine; A2BT and A2BT are distinct open-blocked states that have bound tacrine to one site within the channel; A2BTT is an open blocked state in which tacrine has bound to two sites within the channel; A2CT and A2CTT are closed states which have bound one and two molecules of tacrine respectively. (Notation used for rate constants) General mechanism. (A) ß, are channel opening and closing rate constants respectively; k+1, k+2, kB+1 are association rate constants for ACh at the two agonist binding sites and channel block site respectively; k-1, k-2, kB-1 are dissociation rate constants for ACh at the two agonist binding sites and channel block site, respectively. A is the concentration of ACh. General mechanisms B–I: kT+1, kT+2, kT+3 and kT+4 are association rate constants for tacrine and kT-1, kT-2, kT-3 and kT-4 are dissociation rate constants; ß* and * are channel opening and closing rate constants with tacrine bound; m and n are the forward and backward rate constants for the diffusion of tacrine between a shallow site within the channel to a deeper site; T is the concentration of tacrine. DB indicates that the scheme was constrained by detailed balancing. In general mechanisms B–I, only the rate constants that were derived by maximum likelihood fitting are shown. Other rate constants within the schemes were fixed to values determined from fitting to Scheme A (see Table IV).

where n is the number of free parameters and LL is the log-likelihood value for the model under consideration. The model with the minimum AIC value is considered the best.

Ligand Binding Assays
48 h after transfection, the growth medium was removed and the HEK 293 cells were harvested by gentle agitation in phosphate-buffered saline containing 5 mM EDTA. The cells were centrifuged for 5 min at 1500 g and then resuspended in KRH buffer containing 30 mg/l BSA. Tacrine affinity was determined by competition against the initial rate of [¹²⁵I]-labeled -bungarotoxin binding (Prince and Sine, 1998b). In a separate set of experiments designed to test the possibility that tacrine could desensitize the receptor, cells were preincubated for 1 h with the required concentrations of tacrine and carbamylcholine before addition of [¹²⁵I]-labeled -bungarotoxin.

Nonspecific binding was determined in the presence of 10 mM carbamylcholine. Binding data were analyzed according to the following form of the Hill equation:

(3)

where f_occ is the fractional occupancy of receptor by the competing ligand, X is the concentration of competing ligand, n is the Hill coefficient, and IC₅₀ is the concentration of the competing ligand that yields 50% occupancy of the receptor. Nonlinear regression was performed using Prism 3.0 (GraphPad Software).

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
Ligand Binding Experiments
To assess whether tacrine competes with ACh at the receptor agonist binding sites, we determined the affinity of tacrine by competition against the initial rate of [¹²⁵I]-labeled -bungarotoxin binding. Tacrine bound with an IC₅₀ of 309 ± 30 µM and a Hill coefficient of 1 ± 0.1 (n = 3) (Fig. 1 A). As described below, ACh-induced currents are antagonized by much lower concentrations of tacrine, eliminating competitive antagonism as the primary mechanism for functional inhibition of the nAChR by tacrine.

View larger version (22K): [in this window] [in a new window]   FIGURE 1. (A) Steady-state binding of tacrine to nAChRs. The smooth curve is a fit of the Hill equation (Eq. 3) to the data with the following parameters IC50 = 309 ± 30 µM, n = 1 ± 0.1. (B) Steady-state binding of ACh to nAChRs in the presence of 0, 1, 10, 100 µM tacrine. Fits of the Hill equation to the data yielded the following parameters: 0 tacrine () IC50 = 4.5 ± 0.7 µM, n = 0.8 ± 0.1; 1 µM tacrine () IC50 = 3.4 ± 0.4, n = 0.7 ± 0.1; 10 µM tacrine () IC50 = 5.5 ± 0.7 µM, n = 0.7 ± 0.1; 100 µM tacrine () IC50 = 6.1 ± 1 µM, n = 1 ± 0.1. For both types of experiment, ligand affinity was determined by competition against the initial rate of [125I]-labeled -bungarotoxin as described in MATERIALS AND METHODS. Each point is the mean of three determinations and the error bars represent the SEM.

Patch-Clamp Experiments: Initial Observations
Activation by ACh
We recorded responses to 6–300 µM ACh at three membrane potentials: -70, -110, and -150 mV. At each potential, periods of channel activity corresponding to the activation of single nAChRs were readily discernible as clusters of channel openings bounded by long closed times (Fig. 2) . For each recording, we calculated the mean P_open (probability that the channel is in the open state) within clusters and fitted the Hill equation to our data. The resulting concentration-response curves revealed Hill coefficients close to two at each potential and a voltage-dependent decrease in EC₅₀ (Fig. 2, Table I) .

View larger version (20K): [in this window] [in a new window]   FIGURE 2. Activation of human adult muscle nicotinic acetylcholine receptors by ACh. (Left) Openings of single receptors were grouped into clusters bounded by long closings. (Right) Concentration-response curves for adult human nAChRs activated by ACh (, -70 mV; , -110 mV; , -150 mV). The overall Popen for each recording was calculated at the indicated concentrations as described in MATERIALS AND METHODS. The data are the mean of 2–5 recordings and the solid lines are fits to the Hill equation (Eq. 1). Parameters for these fits are given in Table I.

The long closed times which bound clusters of openings are thought to represent periods when all receptors in the patch are desensitized. We observed three exponential components of desensitization closed times in this study. Long (7.5 s) duration closings were observed at all concentrations of ACh and were somewhat variable in duration. desensitization on this time scale has been reported in numerous studies dating back to Katz and Thesleff (1957). Medium (30 ms) duration desensitization closings could be resolved at concentrations above 10 µM ACh, but were obscured by slower components of the closed time probability density function (p.d.f.) at lower concentrations of agonist. This type of desensitization was of constant duration across the concentration range 20–300 µM and is in good agreement with results from rapid agonist application experiments which have yielded desensitization time constants of 15–50 ms (Dilger and Liu, 1992; Franke et al., 1992; Jahn et al., 2001). A similar duration closed-time component was also observed by Sine and Steinbach (1987) in single channel recordings from BC3H-1 cells. Finally, at concentrations of 60 µM ACh and above we observed a fast (2 ms) desensitization component that did not alter in duration with agonist concentration. A similar (4.5 ms) component was noted by Zhang et al. (1995) and was assumed to represent a rapid form of desensitization.

Inhibition by tacrine.
To determine the effects of tacrine on ACh-evoked single channel activity, we recorded responses to 100 µM ACh in the presence of 1–100 µM tacrine at membrane potentials of -70, -110 and -150 mV. We chose 100 µM ACh because it allowed clusters to be identified over a wide range of tacrine concentrations. Inclusion of tacrine in the patch pipette produced a concentration- and voltage-dependent reduction in channel open probability with fitted IC₅₀ values close to 3 µM (Fig. 4 , Table II) . In a separate series of experiments, we recorded responses to 300 µM ACh in the presence of 10 µM tacrine. As predicted for noncompetitive antagonism, the reduction in P_open (expressed as percentage change from control) produced by 10 µM tacrine at 300 µM ACh (74%) was essentially the same as that produced at 100 µM ACh (77%). To determine whether tacrine can act as an agonist at the nAChR we made recordings with 10 µM tacrine and no ACh in the patch pipette. No responses were observed in the presence of tacrine alone (n = 3).

View larger version (18K): [in this window] [in a new window]   FIGURE 4. Tacrine inhibition of responses to 100 µM ACh at -70 mV (), -110 mV (), and -150 mV () membrane potential. The data are the mean of 2–4 recordings and the solid lines are fits to the Hill equation (Eq. 2). The parameters derived from these fits are summarized in Table II. The top of each curve was fixed to the mean Popen obtained in the absence of tacrine.

In Scheme B1 (Neher and Steinbach, 1978), the open-blocked state (A₂B_T) is connected only to the open state (A₂O). This simple connectivity means that the rate constants k_T+1 and k_T-1 can be determined by examining the effects of blocker on the distributions of open, burst, and closed durations. As in most previous studies of nAChR channel block, therefore, Scheme B1 was our starting point from which to investigate the kinetics of block.

Open Time Distributions
More-detailed examination of the open-duration histograms (Fig. 5 A) revealed that the tacrine-induced decrease in mean channel open time was concentration and voltage dependent. Neglecting for the moment block of the channel by ACh itself, Scheme B1 predicts the reciprocal of the mean channel open duration (_open) to be related linearly to the concentration of open channel blocker (T):

(4)

View larger version (42K): [in this window] [in a new window]   FIGURE 5. (A) Tacrine alters the closed and open times distributions of responses to 100 µM ACh. Representative open and closed time distributions of responses to 100 µM ACh at -70 mV in the presence of the indicated concentrations of tacrine. The arrows indicate the component of the closed time histogram attributed to block by tacrine. Data are plotted using a square root scale y-axis. (B) Apparent open time plot. As described in the text and in APPENDIX A, the simple sequential mechanism for open channel block (Fig. 3, Scheme B1) predicts a linear relationship between tacrine concentration and the reciprocal apparent mean open time, 1/app (Eq. 5). The slopes of the lines approximate to kT+1 and are given in Table III. (C) Blocking frequency plot. Blocking frequency is the number of blocking events per unit time and was calculated as described in the text (Eq. 6). Scheme B1 (Fig. 3) predicts a straight-line relationship between blocking frequency and tacrine concentration. The slopes of the lines are predicted to be equal to kT+1 and are given in Table III. (D) Mean durations of channel closings arising from block by tacrine. The symbols used in B, C, and D are as follows: -70 mV (), -110 mV (), and -150 mV ().

_app

(5)

where ₀ is the apparent mean open time at zero tacrine concentration. Plots of Eq. 5 are shown in Fig. 5 B.

Burst-duration Distributions
An alternative method of investigating channel block is the integration method of Neher (1983). The integration method makes use of the fact that for sequential block, burst duration increases with blocker concentration, but the total open time per burst does not vary. On the other hand, "parallel block" models such as Scheme C2 (Fig. 3) that provide the receptor with a pathway back to the closed state, thereby bypassing the unblocked open state, predict a decrease in the total open time per burst. Therefore, in theory, the integration method can distinguish between sequential and parallel block mechanisms. However, a limitation of the integration method is that it can only be used when individual bursts can be identified unequivocally, i.e., at low concentrations of agonist where the mean duration of block closings is shorter than 1/ß'. In the present study, this condition cannot be met because even at the lowest concentrations of tacrine, the mean block duration is considerably longer than 1/ß'.

Closed-time Distribution
Predictions about the closed time distribution can also be made from Scheme B1. First, open channel block should produce a new class of closings and these closings should increase in frequency with increasing blocker concentration. Ogden and Colquhoun (1985) exploited this predicted increase in "blocking frequency" to calculate blocker association rate constants. Blocking frequency (B_f) is simply the number of blocking events per unit time and is calculated thus:

(6)

where N_block is the number of closings attributable to block by tacrine, N_open is the number of channel openings (corrected for missed openings), and m_open is the apparent mean channel open time. For blockers that follow Scheme B1, plots of B_f against blocker concentration should be straight lines with slopes of k_T+1. As predicted by Scheme B1, tacrine produced an additional exponential component in the closed time distribution, the relative area of which increased with tacrine concentration (Fig. 5 A). Blocking frequency plots for tacrine derived using this component (Fig. 5 C) were straight lines and yielded values of k_T+1 close to, but consistently smaller than, those derived from Eq. 5 (Table III) . As discussed below, these differences are predicted by our kinetic modelling studies.

A final prediction of Scheme B1 is that the time constant of block closings should depend solely on the dissociation constant of the blocker (k_T-1) and thus should be concentration independent. Contrary to Scheme B1, however, the duration of block closings increased with increasing tacrine concentration (Fig. 5, A and D).

Taking our initial analyses of open and closed distributions together, our data strongly suggest that tacrine inhibits the nAChR by interacting with the open channel but the mechanism of this inhibition is incompatible with Scheme B1. To gain further insight into how tacrine interacts with the nAChR we therefore decided to fit a series of kinetic models to our single channel data using maximum likelihood techniques.

Maximum Likelihood Analysis
Kinetics of activation of the receptor by ACh.
Detailed kinetic analysis of the mechanism by which tacrine inhibits the nAChR requires knowledge of the rate constants that govern activation of the receptor by ACh in the absence of tacrine. To estimate these rate constants we recorded currents at 6–300 µM ACh and analyzed the resulting open and closed dwell times using maximum likelihood fitting (MATERIALS AND METHODS). We used a standard linear scheme (Fig. 3, Scheme A) to describe activation of the receptor and block by ACh itself. Scheme A does not include monoliganded openings of the receptor, but at the concentrations of ACh used in this series of experiments only a single class of openings was observed. Scheme A should therefore be a good approximation of reality under the conditions used in this study. A global set of rate constants (Table IV) for Scheme A was obtained by simultaneous fitting to data obtained over the range of ACh concentrations, and the resulting probability density functions are shown as smooth curves superimposed on the open and closed time histograms (Fig. 6) . The rate constants derived from this series of experiments are, at -70 mV, very similar to those observed by Ohno et al. (1996). Our results reveal that the voltage dependence of the EC₅₀ of ACh is largely due to decreases in the channel closing rate () and the rates of dissociation of ACh from the agonist binding sites (k_-1, k_-2).

View larger version (28K): [in this window] [in a new window]   FIGURE 6. Kinetics of activation of nAChRs by acetylcholine. Left panels show traces of individual clusters from patches recorded at the indicated concentrations of ACh. The traces are displayed at a bandwidth of 5 kHz. The smooth curves through the open and closed time histograms are theoretical probability density functions calculated from the fitted rate constants for Scheme A (Fig. 3), with values given in Table IV. At least two recordings were obtained at each of the following concentrations of ACh: 6, 10, 20, 30, 60, 100, 200, 300 µM. For each concentration, the number of clusters selected for analysis ranged from 85–198 (-70 mV), 49–111 (-110 mV) and 43–135 (-150 mV), while the number of events ranged from 7,330–11,190 (-70 mV), 7,686–14,080 (-110 mV) and 4,658–15,638 (-150 mV).

First, we considered the classic sequential scheme for open channel block (Scheme B1). A priori, Scheme B1 cannot account for the inhibition of the nAChR by tacrine because it predicts that the durations of block closings should be independent of tacrine concentration. However, fitting Scheme B1 to our data provides a baseline for comparing the merits of other models. As expected, Scheme B1 yielded a poor fit to our data, particularly in the closed time distribution.

Next, we fitted a series of kinetic schemes to our data that described more complex interactions between tacrine and the receptor (Fig. 3). We considered three general mechanisms by which tacrine might bind to and inhibit the function of the nAChR: (a) competitive inhibition at the nAChR agonist binding sites; (b) binding to the closed channel; and (c) binding to the open channel. The individual schemes are described in detail in the DISCUSSION. However, the following general observations can be made by considering AIC ranking (Table V) : (a) schemes that allowed tacrine to bind within the closed channel of the receptor produced an improved fit relative to the sequential scheme, but only if it was assumed that the channel could not open or close with tacrine bound (Schemes C4, G2); (b) improvements relative to the sequential model were also obtained with models that allowed tacrine to bind only to the open channel but also allowed the channel to close with tacrine still bound (Schemes C3, G1); (c) schemes that postulated two binding sites for tacrine within the open channel of the receptor (Mechanisms E–I) yielded dramatic improvements in goodness of fit; (d) the best schemes had two binding sites in the open state and allowed interactions between tacrine and the closed state (Mechanisms G–I). Taking into account our results from maximum likelihood analysis and from single channel simulations (see below), the best overall description of our data is achieved with Scheme G2. Fig. 7 shows the predicted probability density functions for Scheme G2 superimposed over our experimental data.

View larger version (27K): [in this window] [in a new window]   FIGURE 7. Kinetics of activation of nAChRs by 100 µM acetylcholine in the presence of the indicated concentrations of tacrine. Left panels show traces of individual clusters from patches displayed at a bandwidth of 5 kHz. The smooth curves through the open and closed time histograms are theoretical probability density functions calculated from the fitted rate constants for Scheme G2, with parameter values given in Table VI. At each concentration of tacrine, the number of clusters analyzed ranged as follows: -70 mV 44–127, -110 mV 59–136, -150 mV 51–88, whereas the number of events ranged from 4,932–11,580 (-70 mV), 6,020–12,940 (-110 mV) and 3,140–11,904 (-150 mV).

(7)

where is the channel closing rate, T is the concentration of tacrine and k_T+1 is the association rate for tacrine. Eq. 7 has the same form as Eq. 5 and comparing the k_T+1 values in Table VI with the values of k_T+1 derived from apparent open time plots (Table III) demonstrates excellent agreement between experimental and predicted association rates.

For the closed time distribution, the situation is more complicated because of intercommunication between the open-blocked states with one and two bound tacrines, and between the closed-blocked state and the closed states of the receptor. Considering first the open-blocked states, it is clear that any given channel-block event might consist solely of a dwell in the mono-liganded A₂B_T state followed by dissociation of tacrine and return to the open state. Alternatively, it might consist of a dwell in A₂B_T followed by multiple transitions to A₂B_TT before return to the open state. These two types of block events are predicted to give rise to two exponential components in the closed-time distribution, but the rate constants describing these exponentials do not relate directly to the lifetime of any individual states in Scheme G2. As described by Colquhoun and Hawkes (1981)(1995), the rate constants (₁, ₂) of these exponentials must calculated by solving the quadratic equation ² + b + c = 0, where:

Similarly, the relative areas (a₁, a₂) of the two components are given by the formulae:

The derivations of these equations are given in full in APPENDIX B. As shown in Fig. 8 , Scheme G2 predicts that the component of the closed-time distribution described by ₁ becomes briefer and that its relative area (a₁) decreases as the concentration of tacrine is increased. However, we could not identify this closed-time component in our experimental data, probably due to temporal overlap of the ₁ component with closings arising from agonist binding and channel gating (ß'). Conversely, Scheme G2 predicts that the component of the closed-time component described by ₂, increases in duration and relative area (a₂) with increasing tacrine concentration. The time constants of these closings are in excellent agreement with our experimental data (Fig. 8).

View larger version (20K): [in this window] [in a new window]   FIGURE 8. Predicted block closed-time distributions for Scheme G2. (A) Data are the observed time constants of closings arising from tacrine block at -70 mV. (Inset) Low concentration range. The lines are the time constants () 1/1 (dashed) and 1/2 (solid) calculated as described in the RESULTS section and in APPENDIX B. (B) Predicted relative areas of the closed-time distribution components arising from 1 (dashed) and 2 (solid). The lines were calculated as described in the RESULTS section and APPENDIX B. (Inset) Low concentration range.

At 60 µM tacrine (-70 mV) P = 0.11, suggesting that even at the maximum concentrations of tacrine examined in this study, only marginal changes in ß' should be observed. In agreement with this prediction we found no tacrine-dependent changes in the value of ß' in our experimental data.

A somewhat unexpected finding in our initial analysis was that the tacrine association rates predicted by the blocking frequency were consistently slower than those derived from apparent open time plots. In contrast, previous studies have demonstrated that these methods yield essentially identical results (Ogden and Colquhoun, 1985). To understand these findings in the context of Scheme G2, it is important to realize that while blocking frequency and apparent open time plots are both used to derive the same parameter (k_T+1), they make use of very different information. In the apparent open time plot we measure interruption of channel openings by blocking events. Providing these block closings are long enough to be resolved, they will shorten the mean channel open time whether they follow a single- or multiple-component distribution. Apparent open time plots are therefore a robust method for deriving values of k_T+1. By contrast, the blocking frequency plot requires us to determine the number of block-closings. This can be a problem for mechanisms that yield multicomponent and/or concentration-dependent distributions of block closings. As detailed above, the distribution of block closings predicted by Scheme G2 is described by two exponential functions. One component increases in mean duration and relative area with increasing tacrine concentration, and because this is the only clearly identifiable new component in the closed-time histogram, only closings from this exponential contribute to the block frequency plot. The second exponential component becomes briefer and has a smaller area as the concentration of tacrine increases. This component cannot be identified in the closed-time histogram because it becomes submerged beneath the exponential components that arise from channel gating and agonist binding. Neglect of the brief block exponential, which at 60 µM ACh (-70 mV) still comprises 10% of all block closings, therefore leads to an underestimation of blocking frequency and hence k_T+1.

Effects of Tacrine on Cluster Duration
To allow data to be analyzed using the MIL program, clusters of channel openings corresponding to the activation of single channels must be identified. Our procedure involves selecting groups of openings bounded by long closed times that correspond to periods when all channels in the patch are desensitized. In the absence of tacrine, responses to 100 µM ACh at -70 mV (Fig. 5) revealed three distinct components of closings attributable to desensitization: fast _d1 2.2 ± 0.8 ms, 1.1 ± 0.3% total closings; medium _d2 30 ± 7 ms, 0.7 ± 0.2% total closings; and slow _d3 7,400 ± 3,100 ms, 0.4 ± 0.1% total closings; mean ± SEM of three recordings). In each recording, cluster boundaries are defined using the fastest resolvable type of desensitization closing. At 100 µM ACh, fast desensitization closings are readily identifiable and including them when computing cluster duration yields a mean duration of 37 ± 7 ms (mean ± SEM, n = 3). However, the fast and medium rate desensitization closings occur primarily between activation episodes of the same channel so single channel clusters can, in principle, also be defined using the medium or slow desensitization closings. At 100 µM ACh this results in mean cluster durations of 71 ± 17 ms (medium) and 365 ± 33 ms (slow). In the presence of 10 µM tacrine and 100 µM ACh, fast desensitization closings cannot be used to define cluster boundaries because they are obscured by closings due to channel block. The medium and slow desensitization closings, however, can be readily resolved and yield clusters with mean durations of 86 ± 37 ms (medium) and 355 ± 97 ms (slow) (mean ± SEM, n = 4). These values are not significantly different from the corresponding cluster durations in the absence of tacrine (P > 0.7 by Student's t test). The failure of tacrine to alter cluster duration is consistent with a mechanism in which the receptor can desensitize from open-blocked states at the same rate as from the open-state.

Simulation of Single Channel Data
The concentrations of tacrine used in this study give rise to closed times which overlap with closed times arising from fast and medium onset desensitization. Although desensitization closings make only minor contributions to the closed time histogram, our modelling results might be biased by their inclusion. In particular, we were concerned that (a) improvements in fit relative to the classic sequential model for channel block (Scheme B1), and that (b) the improved fits yielded by Schemes F4–I1 relative to Scheme F3 were due to contamination with desensitization closings. To address this question we simulated single channel open and closed dwell times using the method of Clay and DeFelice (1983). First we expanded Scheme A by adding two desensitized states arising from the diliganded open state (Fig. 9 , Scheme Ax) and simulated single channel responses to 100 µM ACh according to the best-fit parameters for Scheme A. We then varied the rate constants governing desensitization to replicate the time constants and weights of the fast and medium rate desensitization closings in our experimental data (final values given in Table VII) . Next, we incorporated the fast and medium desensitization closings in Schemes B1 and F3 assuming (a) that desensitization occurs from open or open-blocked states but not closed-states of the receptor and (b) that the binding of tacrine to the receptor did not alter the desensitization rate constants (the expanded schemes, given in Fig. 9 are denoted by the suffix x i.e., Scheme B1x, F3x).

View larger version (25K): [in this window] [in a new window]   FIGURE 9. Schemes used in simulation experiments. In Schemes Ax, B1x and F3x, kD+1, kD-1, kD+2, kD-2 (rate constants governing desensitization and recovery from desensitization), kT+1, kT-1, kT+2, and kT-2 were set to the values in Table VII. For clarity, the rate constants governing activation and block of the channel by ACh have been omitted. In the simulations, these were set to the values given in Table IV (-70 mV data).

Similarly, fits of Scheme F3 to data generated using Scheme F3x yielded excellent agreement between the fitted parameters and the rate constants used to parameterize the scheme (maximum deviation of 4%). Relative to Scheme F3, improved fits were obtained with Schemes F4, G1, and I1 but not with Scheme G2 or any other model tested. These improvements presumably arise because the fitting process accounts for some of the desensitization closings using the additional blocked state in Schemes F4, G1, and I1. Unlike our results with Scheme B1x, however, the increases in log likelihood value with Schemes F4, G1, and I1 are of similar magnitude to improvements in fit, relative to Scheme F3, that are obtained when these schemes are fitted to our experimental data. Thus, our simulation results suggest that the likelihood values of models in which tacrine is postulated to bind randomly to two sites in the open channel or which allow for channel closing with tacrine bound, may be significantly inflated by the inclusion of desensitization closings in our data.

Scheme G2, on the other hand, does not improve fits (relative to Scheme F3) to data simulated using Scheme F3x. This indicates that for our simulated data, desensitization closings cannot be accommodated by the addition of closed-blocked states. By contrast, Scheme G2 does produce an improved fit relative to Scheme F3 with our real patch clamp data. Based on our results with simulated data, this improvement is unlikely to arise from the presence of desensitization closings and must therefore be due to dwells of the receptor in the closed-blocked state.

Voltage Dependence of Tacrine Binding
Fits of Scheme G2 to our data revealed that the dissociation constants (calculated from the fitted rate constants) for the two tacrine binding sites in the open channel decreased as the membrane potential became more hyperpolarized (Table VI). Applying the Woodhull equation (Woodhull, 1973) to these data yields electrical distances of 0.38 for the first binding site and 0.32 for the second site. Binding to the closed channel also shows apparent voltage sensitivity but inspection of the association and dissociation rate constants at this site reveals that they do not vary in a consistent manner.

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
Open channel block of the nAChR has classically been described by a simple sequential mechanism in which blockers bind to a single site within the open channel of the receptor (Scheme B1). For many compounds, e.g., QX-222 (Charnet et al., 1990), epibatidine (Prince and Sine, 1998a), and pyrantel (Rayes et al., 2001), such models provide a good, quantitative description of the interactions between the blocker and the nAChR channel, at least at lower concentrations of blocker. In other studies, simple sequential models have failed to explain fully the kinetics of nAChR block (Neher, 1983; Papke and Oswald, 1989; Dilger et al., 1997; Evans and Martin, 1996), but in most cases the merits of alternative models have not been explored systematically.

In our current study we found that the simple sequential model for open channel block can describe accurately the concentration-dependent decrease in channel open time produced by tacrine, but fails to account for the concentration dependence of the closed-time distribution. The simple sequential mechanism for open channel block predicts that the duration of closings due to channel block should depend solely on the dissociation rate constant of the blocker and thus should not vary with blocker concentration.

Concentration dependence of channel closings requires that tacrine stabilizes a state of the receptor in which ion flux does not occur. Thus, there are two general classes of mechanism that could explain the effect of tacrine on the open and closed time distributions. The first class requires that tacrine binds to and blocks the open channel of the nAChR, but also binds to a closed state of the receptor. The second class involves multiple binding sites for tacrine on the open state of the receptor. Below, we evaluate a variety of kinetic models within these two general frameworks.

Models Involving Interactions with Closed States
Parallel block mechanisms
The first general mechanism we examined (Mechanism C) allows tacrine to bind to the channel in both the open (A₂O) and closed state (A₂C) and allows channel gating to occur with tacrine bound (Adams, 1977). This type of mechanism has been termed "parallel block" because it provides two parallel pathways for the receptor to switch between open and closed states. In studies of fetal mouse receptors in a clonal cell line, Papke and Oswald (1989) found that parallel block provided a quantitatively better description than classic sequential block to explain the kinetics of tetracaine, phencyclidine, and N-allylnormetazocine on single channel currents activated by low concentrations of ACh. A similar mechanism was also proposed by Neely and Lingle (1986) to explain the kinetics of chlorisondamine block.

Our first derivative of the parallel block mechanism was Scheme C1 in which we assumed (a) that the channel could open and close at the same rate irrespective of whether tacrine was bound and (b) that the rate constants governing tacrine binding were the same in the open and closed states of the receptor. This mechanism yielded an even worse description of our data than the sequential model (Scheme B1). Next, we tested a mechanism (Scheme C2) in which the constraints on channel gating and tacrine binding were removed. However, we found that fits of Scheme C2 to our data did not yield a full, parallel block mechanism. Instead, Scheme C2 converged with values of k_T+2 and k_T-2 (association and dissociation rates governing tacrine binding to the closed channel) close to zero and yielded the same log-likelihood value as Scheme C3 (in which it was assumed that tacrine could not bind to the closed channel). The mechanism described by Schemes C2 and C3 has two main characteristics. First, tacrine associates only with the open state of the channel. Second, when the channel has bound tacrine it can access an additional nonconducting state from which tacrine cannot dissociate. Although Schemes C2 and C3 both yield better fits than the classic sequential model (Scheme B1, see Table V and Fig. 3) neither predicts concentration dependent block closings. It is therefore not intuitively obvious from where the improvement in fit obtained with these schemes arises (they probably work better by merely including a second closed state). Possible identities of the additional nonconducting state are discussed below in the context of two site models.

We also examined a variation of the parallel block mechanism that assumes that the channel cannot gate with tacrine bound (Scheme C4), but which allows tacrine to bind to the closed state of the receptor. In parallel block mechanisms the effective channel opening rate, ß', will vary with tacrine concentration because the A₂C_T state is connected directly to A₂C and thus indirectly to AC and C. Effects on ß' will be most pronounced when k_T-2 is much faster than ß* (channel opening rate with tacrine bound) e.g., when ß* and * are set to zero: as the concentration of tacrine is raised the receptor will spend progressively more time shuttling between the A₂C_T and A₂C states. Although Scheme C4 also yielded an improved fit relative to Scheme B1, two factors suggest that this type of mechanism is unlikely. First, examination of closed time histograms (Fig. 5 A) shows that the component of the closed-time distribution attributable to ß' (mean duration 100–200 µs) is unaffected by tacrine. Second, for ß' to be lengthened significantly by tacrine, [tacrine].k_T+2 must approach or exceed (ß + k_-2), which for ACh at -70 mV is 73,000 s^-1. Tacrine-induced closings are readily distinguishable in the closed time histogram and increase approximately linearly in duration with increasing concentration. To explain these findings at, for example, 2 µM tacrine, requires k_T+2 to be >36,000 µM^-1 s^-1. This is 36-fold faster than the upper limit for a diffusion-limited association reaction and thus is physically unreasonable.

Competitive Interactions
The second type of model we considered combines sequential open channel block with a competitive interaction at the ACh binding sites (Scheme D1). This model was of interest because ligand binding studies on human cortical nAChRs (Perry et al., 1988) and whole brain tissue (Hunter et al., 1989) provided evidence for competitive binding at neuronal nAChR ACh recognition sites, with K_d values in the low micromolar range. However, more recent studies suggest a complex mode of interaction with neuronal receptors. Svensson and Nordberg (1996) and Svensson (2000) found that chronic treatment with tacrine modulates receptor number in clonal SHSY5Y and M10 cells and speculated that this may involve interaction at an allosteric site in addition to the agonist binding site. A study on 4ß2 and 4ß4 subunit combinations (Zwart et al., 2000), however, suggested that tacrine binds to the agonist recognition site and acts as a coagonist with ACh, in addition to blocking the receptor in the open state. Although it is not always possible to extrapolate results obtained with neuronal AChRs to the muscle receptor, competitive interactions combined with open channel block could, in theory, explain our present results. Thus, we tested the hypothesis that tacrine competes with ACh. We found three lines of evidence which together strongly suggest that tacrine does not exert its effects via a competitive mechanism. First, we fitted a model combining competitive interactions with open channel block (Scheme D1). Although this mechanism yielded a significantly better fit at all membrane potentials than the classic sequential model for open channel block, it ranked poorly compared with other mechanisms. The poor fit likely results because competitive interactions, like parallel block mechanisms, are predicted to alter the value of ß'. Second, we observed that the decrease in P_open produced by 10 µM tacrine at 100 and 300 µM ACh was essentially the same. A competitive mechanism predicts less inhibition at higher concentrations of agonist. Finally, we performed ligand binding assays to determine directly the Ki for tacrine competition against the initial rate of [¹²⁵I]-labeled -bungarotoxin. The affinity of tacrine in this assay is 300 µM, much higher than the IC₅₀ value determined in patch-clamp experiments.

Multiple Block Sites
We next examined general classes of mechanism involving multiple binding sites for tacrine within the open receptor channel. The first model we examined (Scheme E1) postulates that there are two block sites at different depths within the channel. Tacrine binds first to the upper site, thereby blocking the channel, and then can either dissociate or diffuse down the channel to the deeper site. A second molecule of tacrine can then bind to the upper site, trapping the first molecule in the channel. Similar models have been used to fit data for block of nAChRs by ACh itself (Maconochie and Steinbach, 1995) as well as the anthelmintic agent, morantel (Evans and Martin, 1996). As in both of these previous studies, Scheme E1 gave superior fits to our data compared with the classic sequential scheme for open channel block (P < 0.0001 by LRT).

We also considered a general mechanism in which tacrine can associate randomly with two binding sites in the open state of the receptor (Mechanism F). To our knowledge, models involving random association at two binding sites have not been used to describe open channel block previously, but a derivative of this mechanism, in which the two sites were assumed to have very different affinities, was examined by Maconochie and Steinbach (1995) as a possible mechanism for block by ACh. The first model we tested was Scheme F1, which allows random association at the two sites and permits allosteric interactions. We found that Scheme F1 yielded excellent fits to our data with log-likelihoods 1,600–2,600 U higher than the sequential model for open channel block (P < 0.0001 by LRT). However, the fitted values for k_T+3, k_T+4, k_T-3, and k_T-4 were ill-defined and very slow. This prompted us to examined three simplified versions of Scheme F1. In Scheme F2 we assumed full independence of the tacrine binding sites. This model produced significantly worse fits to our data (P < 0.0001 by LRT) than Scheme F1. Next, we assessed a model in which the state A₂B_T was eliminated (Scheme F3). Again, we found that this model did not perform as well as Scheme F1. Finally, in Scheme F4, only the transitions governed by k_T+4 and k_-4 were eliminated. We found that this model gave equal log-likelihood values to those obtained with Scheme F1 and t