Block of Quantal End-Plate Currents of Mouse Muscle by Physostigmine and Procaine

J. Dudel,1 M. Schramm,1 C. Franke,2 E. Ratner,3 and H. Parnas3

 1Physiologisches Institut and  2Neurologische Klinik, Technische Universität München, 80802 Munich, Germany; and  3Department of Neurobiology, Hebrew University, Jerusalem 91904, Israel


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ABSTRACT
INTRODUCTION
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DISCUSSION
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Dudel, J., M. Schramm, C. Franke, E. Ratner, and H. Parnas. of quantal end-plate currents of mouse muscle by physostigmine and procaine. Quantal endplate currents (qEPCs) were recorded from hemidiaphragms of mice by means of a macro-patch-clamp electrode. Excitation was blocked with tetrodotoxin, and quantal release was elicited by depolarizing pulses through the electrode. Physostigmine (Phys) or procaine (Proc) was applied to the recording site by perfusion of the electrode tip. Low concentrations of Phys increased the amplitude and prolonged the decay time constants of qEPCs from ~3 to ~10 ms, due to block of acetylcholine-esterase. With 20 µM to 2 mM Phys or Proc, the decay of qEPCs became biphasic, an initial short time constant tau s decreasing to <1 ms with 1 mM Phys and to ~0.3 ms with 1 mM Proc. The long second time constant of the decay, tau l, reached values of <= 100 ms with these blocker concentrations. The blocking effects of Phys and Proc on the qEPC are due to binding to the open channel conformation. A method is described to extract the rate constants of binding (bp) from the sums 1/tau s + 1/tau l, and the rates of unbinding (b-p) from tau 0 · tau s-1 · tau l-1 (tau 0 is the decay time constant of the control EPC). For Phys and Proc bp of 1.3 and 5 · 106 M-1 s-1 and b-p of 176 and 350 s-1, respectively, were found. Using these rate constants and a reaction scheme for the nicotinic receptor together with the respective rate constants determined before, we could model the experimental results satisfactorily.


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In a number of recent studies, we have established reaction schemes for nicotinic receptors/channels on mouse muscle using mostly patches containing the embryonic type of channels (Franke et al. 1991a,b, 1992a,b, 1993). The experimental data have been collected mainly by application of acetylcholine (ACh) to outside-out patches, using a liquid-filament switch that generated pulses of ACh at the patch with rise and decay times of the agonist concentrations of <0.5 ms (Bufler et al. 1996a; Franke et al. 1987).

Using the same techniques, we have extended these studies to the "open channel block" in embryonic channels by the local anesthetic procaine (Proc) and by physostigmine (Phys) (Bufler et al. 1996a). Phys and Proc blocked the open channels with rate constants of 6 · 106 M-1 s-1 and 2 · 106 M-1 s-1, respectively, and unblocked with rates of 200 s-1. The blocking rate constants were in the same range as those found by previous investigators (Adams 1977; Albuquerque et al. 1986; Neher and Steinbach 1978; Ogden et al. 1981). Ogden et al. (1981) reported an unblocking rate for benzocaine similar to that found by us, whereas Neher and Steinbach (1978) saw a rate of unblock for lidocaine derivatives of 2,300 s-1, corresponding to the "flickering block" caused by these substances. Such flickering block also has been seen with high ACh concentrations in hyperpolarized patches, with blocking rates in the range of 5 · 107 M-1 s-1 and unblocking rates of 5 · 104 s-1. These unblocking rates correspond to "flickering," short closings of the channel with an average duration of 20 µs (McGroddy et al. 1993; Ogden and Colquhoun 1985; Parzefall et al. 1998; Sine and Steinbach 1984; Sine et al. 1990).

Aside from biophysical aspects, the open channel block by local anesthetics is of interest for its effect on end-plate currents (EPCs). First Furukawa (1957), then Maeno (1966), Steinbach (1968), Kordas (1970), and Katz and Miledi (1975) applied local anesthetics to frog muscle and saw biphasic endplate potentials with a short initial and a long second phase. Similar effects on EPCs from toad muscle were reported by Gage and Wachtel (1984). Shaw et al. (1985) applied Phys to mouse muscle and saw an initial more rapid decay of the EPCs.

Already at low Phys concentrations, EPCs were lengthened by its well-known block of ACh-esterase, which prolonged the presence of ACh at the receptors. Both these results agree qualitatively with the respective blocking rates derived for nicotinic channels (Bufler et al. 1996a). We decided, therefore, to study the effects of Phys and Proc on quantal EPCs of adult mouse muscle up to higher concentrations than used before. We developed procedures to derive rate constants of block and unblock from the effects of Proc and Phys on the EPCs based on a simplified reaction scheme. Finally, we used the full reaction scheme found for nicotinic channels (Bufler et al. 1996a) that includes the rapid desensitization from the open state and that from the blocked state, and the highly ACh-sensitive desensitized states, to model the effects of the blockers on the EPC. There was good agreement of model and experimental results, including the rate constants of block and unblock of the channels and of the EPCs.


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Adult mice were killed by cervical dislocation, and the diaphragm was excised rapidly. Hemidiaphragms were pinned down in a bath chamber through which Bretag's solution saturated with 95% O2-5% CO2 was superfused. The solution contained (mM) 136 Na+, 3.5 K+, 117 Cl-, 1.5 Ca2+, 0.7 Mg2+, 26 HCO3-, 1.7 H2PO4-, 10 Na-gluconate, 5.5 glucose, and 7.6 saccharose, pH 7.4. The superfusate flowed through a theromostated heat exchanger before entering the bath and was held at 10 or 20°C.

EPCs were recorded through a perfused macro-patch-clamp electrode (Dudel 1989, 1992). It had an ~10-µm-wide opening and contained a current-clamp recording input as well as a stimulating electrode through which negative current pulses could depolarize the terminal in a graded manner by shifting the extracellular field potential. The recording systems had upper frequency limits of 8-10 kHz. The data were digitized at 48 kHz and stored on video tape. On read-out a 10-kHz filter was used. The electrode was perfused with a solution containing (mM) 162 NaCl, 5.3 KCl, 2 CaCl2, 0.67 NaH2PO4, 15 HEPES, and 5.6 glucose; pH 7.4. The fluid volume in the tip of the electrode was exchanged several hundred times per second. Drugs were applied by switching the perfusates, performing for instance 12 exchanges of solutions while recording from the same site in the experiment of Fig. 2. Tetrodotoxin (TTX, 0.2 µM) was added to the perfusate of the electrode to prevent triggering of action potentials in the nerve terminals by depolarizing pulses. As a precaution against the generation of twitches of the diaphragm, TTX sometimes had to be added also to the perfusate of the bath. The cholinesterase blocker physostigmine (eserine) and the local anesthetic procaine were obtained from Sigma and could be dissolved in the perfusate.

Recordings were stored on video tape. They were evaluated off-line by means of a series 300 Hewlett-Packard computer, a Sun-system, or PCs. To avoid influences of varying delays of quanta in multiquantal EPCs, only single quantum EPCs were evaluated. The depolarizing stimulation pulses through the electrode were arranged to release on average <0.5 quanta/pulse. Consequently more than half of the pulses produced failures of release and <9% multiquantal releases that could be recognized. Quantitative determination of the time constants, including their amplitudes, of the biphasical decay in EPCs is difficult, especially when the amplitudes of the excitatory postsynaptic currents are reduced in high concentrations of anesthetics. Therefore for the derivation of rate constants of the action of Proc in Figs. 3 and 4, two strategies for evaluation were employed, and the results of both were presented. The first used an ISO-Program developed by M. Friedrich, Köln. The recordings were searched for clearcut one quantum releases and for clearcut nonreleases. Then an average of nonrelease traces was subtracted from the one-release traces, generating artifact-free single quantum recordings (qEPCs). From the latter, the time constants of decay were evaluated automatically by a Levenberg-Marquardt routine. The second method of evaluation (implemented by E. Ratner) also used the artifact-free qEPC recordings just described. The maxima of qEPCs were detected, and the times of the maximum were used for starting an average of the decays of hundreds of qEPCs. With the consequent reduction of noise, the time constants of decay can be evaluated unambiguously. Both methods generate similar results (Fig. 4).

Simulations of three-dimensional spatio-temporal distribution of ACh, its hydrolysis and binding to receptors, R, were done using a commercial software package, FIDAP (version 7.05) (Engelman 1995) on SGI workstation. FIDAP is a computer program that employs the finite element method. Accordingly, the synaptic cleft around the terminal was represented as a space (Fig. 6) divided into variable brick-shaped elements called MESH. Shape functions link the MESH to the equations describing the processes detailed in the next paragraph (Aharon et al. 1994).

The model of the synaptic cleft where calculations took place is depicted in Fig. 6A. In this model, at time 0, ACh is being discharged from a presynaptic vesicle during 0.1 ms (Khanin et al. 1994). The discharge was modeled as a step function of 0.1-ms duration. ACh then diffuses through the synaptic cleft (50 nm width) (Parnas et al. 1989) toward the postsynaptic membrane and also throughout the active zone. The diffusion of ACh was calculated using second Fick law (Crank 1975). Concomitantly with its diffusion, ACh is also subjected to hydrolysis by ACh-esterase, E, and binds to receptors, R. E is present all over the synaptic cleft including the active zone. Hydrolysis was modeled according to Parnas et al. (1989). In contrast to E, the receptors are concentrated in the active zone only. Binding to receptors and the resulting processes were modeled according to Scheme 2.

The size of the domain (its limit is denoted by Rb in Fig. 6A) wherein calculations of ACh distributions take place affects strongly the results. We took Rb to be 3,000 nm, that is, ~10 times larger than the active zone. This distance was found to be the minimal distance needed in order not to affect the results.


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Blocking of qEPCs by Phys and Proc

To record EPCs, the electrode was shifted slowly in contact with the surface of the diaphragm in the region of the end plates while depolarizing current pulses were applied at a rate of five per second. When touching on a superficially located end plate, EPCs were elicited. The recording position then was optimized to give a maximal amplitude and a minimal rise time of the currents. It should be understood that these recordings with a 10-µm electrode opening are only from part of an end plate; they elicit ~10 quanta per pulse for saturating depolarization amplitudes, and ~2 quanta per pulse in case of triggering action potentials in the nerve terminal in the absence of TTX. The total EPC elicited by excitation of the motor axon contains ~500 quanta (see van der Kloot and Molgó 1994).

Recordings were stable for hours in successful experiments, with amplitudes and time courses of qEPCs remaining constant in the controls after the drug applications. When a control declined, the experiment was broken off. The stable recording conditions necessitate that the resting potential of the muscle fibers was at control values of -80 to -90 mV.

To study the effects of Phys and Proc, the strength of the depolarization was arranged to result in the release of on average 0.1-0.5 quanta per pulse. At this release rate, almost all endplate currents were single quanta (qEPCs), the amplitude and decay of which could be evaluated readily. In an initial set of experiments, we worked at 10°C to prolong the presence of ACh at the receptors and possibly to increase the effectivity of the blockers. An example is shown in Fig. 1. In average EPCs (Fig. 1A), on application of 30 µM Phys, the amplitude of the qEPCs increased and the time constant of their decay was lengthened to 15 ms. This potentiation and lengthening of the qEPC is interpreted to be due to the cholinesterase blocking activity of Phys (Katz and Miledi 1975). Higher concentrations of Phys decreased the average amplitude of the qEPCs progressively. Simultaneously, the decay phase of the qEPCs developed a rapid and a slow phase. The time constants tau l of the slow phase increased from 30 to ~100 ms from 30 to 1,000 µM Phys, whereas the amplitude of this component decreased (Fig. 1A). Through the respective range of Phys concentrations, the relative amplitude of the short component, tau s, grew with rising concentrations, whereas the time constant of this component decreased from 3.8 ms with 100 µM Phys to 1.4 ms with 1 mM Phys.



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Fig. 1. A: average quantal end-plate currents (qEPCs) elicited by 1 ms depolarization pulses through the perfused macropatch electrode at one synaptic spot, the electrode being perfused by a modified Bretag solution with 0.1 µM tetrodotoxin (control), and with 30, 100, 300, and 1,000 µM physostigmine (Phys) added, respectively. B: single recordings of qEPCs, from which the averages were generated for 30 µM or 1 mM Phys added to the perfusate of the electrode. Stimulation artifacts were compensated as described in METHODS. Decays of the qEPCs were fitted by 1 (30 µM Phys) or 2 (1 mM Phys) time constants; the fitting curve is superimposed as a continuous line but is mostly not discernible due to the accuracy of the fit. Time constants are inserted next to the traces. Preparation was held at 10°C by a thermostat controlling the temperature of the superfusate of the muscle. In the experiments shown in the other figures, the temperature was held at 20°C.

Single recordings (Fig. 1B) on which the averages in Fig. 1A were based are generally shorter than the respective averages. This difference was small in the long EPCs with 30 µM Phys; here the mean decay time constant of the single qEPCs was 13.6 ms compared with 14.5 ms in the averaged recordings. With 1 mM Phys, the average short decay time constant tau s was 0.86 ms, clearly less than tau s = 1.4 ms in the average current (Fig. 1, A and B). The lengthening of the decays in averaged recordings is due to the temporal spread of the delays of release of quanta, which amounts to several milliseconds at 10°C (Dudel 1984). This temporal dispersion of the quanta lengthens the averaged recordings, and this distortion is relatively more effective for short qEPCs. The temporal dispersion of the short spikes also depresses the amplitude of the average EPC, especially when the qEPCs are short. We stress these points because the total EPC produced by an action potential in the motor axon is the sum of several hundred qEPCs, and short components of the decay will reduce the amplitude but not necessarily the duration of such endplate currents.

In recordings at 20°C, the temporal dispersion of the quantal releases is smaller and the respective distortion of the average EPCs is less developed than at 10°C. In the experiment of Fig. 2, the effects of Proc and of Phys were compared at 20°C. On application of 10 µM Phys, the cholinesterase was blocked to a large extent and the decay time constant of the EPCs increased from 3 to ~8.5 ms. Because the open channel block effect is very small at this low concentration of Phys, these recordings with 10 µM Phys represent the "control" condition for the further effects of Proc and Phys. In averages of the recordings (not illustrated), the amplitude clearly was reduced only with 500 µM Proc or Phys and more so, to a quarter of the control amplitude, with 1,000 µM Proc or Phys.



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Fig. 2. Evaluations of the time courses of qEPCs like those in Fig. 1B from 1 synaptic spot. Top: decay time constants of qEPCs, tau s, and tau l. Bottom: proportion of the amplitude of the short component, As(As + Al)-1, all vs. the concentrations of Phys or procaine (Proc). Experiment started with a control with no Phys or Proc present (×). Then 10 µM Phys was added to the perfusate; this blocked the acetylcholine (ACh)-esterase and prolonged the qEPCs. Then Proc was added in rising concentrations. After washing out the Proc between applying 200 and 500 µM Proc and after 1 mM Proc, the qEPCs returned to the control decay times with 10 µM Phys. Then the Phys concentration was raised stepwise, with some intermediate periods with 10 µM Phys.

The evaluations in Fig. 2 are from single traces like in Fig. 1B and show tau s and tau l as well as their relative amplitude As (As + Al)-1 versus the blocker concentration. Control qEPCs have average time constants of decay of 2-3 ms at 20°C (see also Figs. 3 and 4). On application of <= 10 µM Phys, the qEPCs decayed with one time constant that was higher than in the controls due to block of cholinesterase. With 10 µM Phys in Fig. 2, this time constant became 8.0 and 8.9 ms in different controls at the beginning, in the middle, and at the end of the experiment. On further increasing the Phys concentration, the decay of qEPCs became obviously biexponential (see also Fig. 1A). An initial spike was shortened from tau s = 4 ms with 20 µM Phys to 0.7 ms with 1,000 µM Phys. Concurrently, a long decay component developed that reached 90 ms with 1,000 µM Phys. With regard to the amplitude of the qEPCs, the proportion of the initial spike [As (As + Al)-1 in Fig. 2] increased with rising Phys concentration, amounting to 94% of the qEPCs with 1,000 µM Phys, the long component forming a 6%, 90-ms time constant tail. Proc was almost as effective in changing the time course of the qEPCs as Phys, becoming somewhat more efficient at high concentrations. For both blockers, the reduction of average EPCs seems to be due completely to the reduction of the amplitude of qEPCs. There is no evidence that the quantal content of EPCs was reduced by Phys or Proc---their effect seems to be completely postsynaptic.



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Fig. 3. Left: examples of single qEPCs with fitting curves and values of tau s and tau l like in Fig. 1B. Three control qEPCs (top) and 3 qEPCs (bottom) in presence of 300 µM Proc, note the doubled amplification for the latter. Right: from the same experiment, average decays of qEPCs measured in presence of 0 (control), 0.01, 0.03, 0.1, 0.3, and 1 mM Proc. Two graphs are presented better to distinguish the different traces. Averages were generated aligning the peaks of single traces like in the left at time 0 and subsequent summation of the traces. Time constants were 1.65 ms for the control, 1.31 and 3.4 ms for 10 µM Proc, 0.14 and 4.8 ms for 30 µM Proc, 0.9 and 5.6 ms for 100 µM Proc, 0.54 and 13.2 ms for 300 µM Proc, and 0.36 and 32.5 ms for 1 mM Proc.



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Fig. 4. Evaluations of the decay time constants and of their relative amplitudes vs. the Proc concentration for the same experiment as presented in Fig. 3. , averages of evaluations of single traces like in Fig. 3, left, (statistical deviations in Table 1). , evaluations of average recordings like in Fig. 3, right. · · · , evaluated from simulated qEPCs using schemes 1 and 2 and the parameters of Table 2.

In the experiment of Fig. 2, the effect of Proc was shown on the background of a constant low Phys concentration, which largely blocked the ACh-esterase and thus prolonged the presence of ACh at the receptors (see Fig. 1). The blocking of the cholinesterase, by lengthening the presence of ACh, increases the effectivity of the local anesthetics but, on the other hand, adds a second drug effect. When applying another blocker of acetylcholinesterase, diisopropylfluorphosphate (DFP), the qEPCs were prolonged much more than with 10 µM Phys, and we are not sure whether 10 µM Phys totally blocks the esterase or DFP has additional effects on the decay of the qEPC. We plan to pursue this matter further elsewhere. To extract the rate constants of the blocking effect of Proc, we avoided block of the acetylcholinesterase and applied only rising concentrations of Proc.

For the evaluation of rate constants of block by Proc, we used optimal recordings of qEPCs as shown in Fig. 3. The controls had rise times of on average 0.33 ms and decayed with the time constant of 1.65 ms (Fig. 3 and Table 1, preparation A). The tau s were distributed with a standard deviation of 0.12 ms. On application of 300 µM Proc, the rise time shortened to 0.25 ms and the decay of the EPCs split into short and long components, tau s and tau l of on average 0.33 ± 0.075 (mean ± SD) and 12 ± 3.8 ms, respectively (Fig. 3 and also Table 1, preparation A).


                              
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Table 1. Time course of qEPC

Figure 3 also presents average decays of qEPCs from the same experiment as the single traces and for more Proc concentrations. These averages used single traces like shown to the left, starting the averaging in each trace from the peak of the qEPC and thus eliminating the averaging error caused by varying delays of qEPCs from the depolarizing pulse (see METHODS). Also these averages demonstrate the development of short and long decay phases of the qEPC with rising Proc concentrations.

Average values describing the time course of the EPC are listed in Table 1 and Fig. 5 for a wider range of Proc concentrations for two experiments. The average delays of the qEPCs from the beginning of the depolarizing pulse are not affected by Proc. The rise times of the qEPCs are reduced clearly by >100 µM Proc, and with 1 mM Proc this reduction amounts to about one-third of the control value (Table 1). Obviously at high Proc concentrations, the rapid block open channel shortens the rise of the EPC (see also the simulation in Fig. 8). The decay time constants and their amplitudes in the graphs of Fig. 4 were determined either as averages of single trace evaluations (Figs. 3, left, and 4, ) or from average decays (Figs. 3, right, and 4, ). The results of both evaluations agree well. The dotted line approximately fitting the results was generated by simulations and will be discussed later. The general shape of the graphs in Fig. 4 is quite similar to that in Fig. 2; in the latter the tau  values are naturally higher due to the block of ACh-esterase.



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Fig. 5. Evaluations of 2 experiments ( and ) with Phys. Left: decay time constants tau s and tau l. Right: relative amplitude of the short component As (As + Al)-1; both sides are vs. the concentration of Phys. Decay time constant in the absence of Phys was 3.0 ms. · · · , simulations like in Fig. 4.

The effects of Phys on the EPC can be evaluated more easily from single quantal currents than those of Proc because a very low concentration of Phys blocks the acetylcholinesterase and prolongs the EPC. Even with 1 mM Phys, the open channel block shortens the initial decay phase only to a time constant tau s of 0.6-0.7 ms (Fig. 5), which can be evaluated easily.

Figure 5 presents evaluations from two experiments, which have almost identical results. Single quantal currents were evaluated, analogous to the evaluations of Fig. 4 (). With 10 µM Phys in Fig. 6, the EPCs decayed with a single time constant of 8.5 ms. This corresponds to the EPCs in Fig. 1 with 30 µM Phys, which decayed with one time constant of ~14 ms at 10°C lower temperatures. With higher Phys concentrations, the decays of the EPCs became biexponential with a short initial decay tau s and long later decay tau l (Fig. 5). As in case of Proc (Fig. 4), tau s decreased and tau l increased with rising concentrations of Phys. Very similar to the situation with Proc, both the shortening of tau s and the lengthening of tau l amounted to about a factor of 10 in the concentration range from 10 µM to 1 mM Phys. The proportion of the amplitude of the short decay component, As in relation to the total amplitude of the EPC (As + Al) rose from 0.4 with 20 µM Phys to 0.9 with 1 mM Phys (Fig. 5).



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Fig. 6. Calculated spread of ACh released by 1 quantum within the synaptic cleft to the receptors. A: sketch of the release site with presynaptic vesicle opening, the synaptic cleft, and the postsynaptic membrane, dimensions, and concentrations in Table 2. B-D: spatial distributions of the ACh concentration 0.1, 0.2, and 0.5 ms after opening of the vesicle, respectively. , with 0.01 mM Phys, ACh-esterase blocked; triangle , with 1 mM Phys, esterase blocked; black-lozenge , ACh esterase present, with 0.01 mM Proc; , esterase present, with 1 mM Proc. Parameters in Table 2.

Calculation of the spatio-temporal concentration profiles of ACh at the receptors

The first step on modeling the EPC is to calculate the time course of the ACh concentration in the synaptic gap after release of a quantum of ACh from a terminal (Fig. 7A). Calculations were done as described in METHODS. The dimensions and concentrations used are given in Table 2 with the rates e+1 and e-1. ACh is bound to cholinesterase (E) and then is split with a rate e+2 into acetyl and choline (Scheme 1), even before reaching the receptors R. 
When reaching the receptors, ACh (A) is bound to R according to Scheme 2 (Table 2), which describes opening and desensitization of the nicotinic receptor to A2O and A2D, respectively (Franke et al. 1993), and adds open channel block by binding of P to A2BP (Bufler 1996a)
At the assumed end of emptying of the vesicle, at 0.1 ms, the ACh concentration at the receptors in Fig. 6B was 4.7 mM at the center of the active zone and down to almost zero 300 nm from the center. These concentrations were little affected by the activity of ACh-esterase. Approximately at the peak of channel opening (0.2 ms, Fig. 6C), A declined already to about one-eighth of the initial concentrations when E was blocked and to about one-tenth when E was fully active. Increasing the concentrations of Phys and Proc depressed A in addition to the effects of ACh-esterase and diffusion; at the higher concentrations of these drugs, the state of open channel block (A2PB) is occupied rapidly to a significant extent (Scheme 2, see also Fig. 8), and this slows unbinding of A from R. Half a millisecond after the beginning of release of ACh (Fig. 6D) the concentrations of A have dropped further and to almost insignificant levels in case of active ACh-esterase with the Proc curves. On the other hand, with 0.1 mM ACh, channel opening is almost maximal (po = 0.9) and with 0.05 mM ACh po is still ~0.8 (Franke et al. 1991b). With block of ACh-esterase, almost maximal channel opening triggered by binding of ACh thus can proceed for >0.5 ms over a relatively wide region of the active zone.



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Fig. 7. A: plot of tau s-1 + tau l-1 vs. the Proc concentration for decay time constants of the experiments of Fig. 4. Decay time constants plotted were evaluated from average decays (Fig. 3, right). ---, fit of the whole set of points; - - -, all points except that at 1 mM Proc. Numbers next to the lines give their slopes in 106 M-1 s-1. These slopes serve to estimate the blocking rate constant, bp (Eq. 10). B: equivalent plot for the Phys results in Fig. 5. Regression line represents also the values at 1 mM Phys.


                              
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Table 2. Parameters of models



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Fig. 8. Calculated time courses of channel states during a qEPC, using reaction schemes 1 and 2 and the constants of Table 2. Top: control with 0 Proc and Phys; bottom: in presence of 1 mM Proc. Both linear plots and plots with a logarithmic time scale are presented. R is the unliganded receptor, A2O the open channel (the time course of the qEPC), A2D the main desensitized state, and A2BP the "open channel" blocked by Proc.

When the rate constants in the model will have been determined completely, the complex spatiotemporal concentration profiles of ACh for the different conditions of block of ACh-esterase, and channels will be entered into the reaction scheme of the channels to describe the generation of the EPC.

Adjustment of rate constants to fit the time course of control EPCs

When control EPCs (no ACh-esterase or channel blockers) were simulated using reaction Schemes 1 and 2 and the rate constants estimated by Franke et al. (1991b) for the adult type of nicotinic channel, the EPCs decayed with a time constant of 2.2 ms (not illustrated). Experimentally, we found average decay time constants of control EPCs of 1.6-2.4 ms at 20°C (Table 1, 0 Proc). As seen in Fig. 6D, the ACh concentration has declined to insignificant levels under these conditions after <0.5 ms, allowing most of the ACh liganded receptors to reach the states A2R and A2O within 0.2 ms. In Scheme 2, once A2R is reached, the receptor oscillates rapidly between A2R and A2O, forming a "burst of openings" independent of the fact that the concentration of A might be high or zero. The short spike of high ACh concentration in the control EPCs thus will generate a burst of openings, which will be terminated by the unbinding of A from A2R with the rate 2k-1. The burst duration according to Scheme 2 is given by (Colquhoun and Sakmann 1985)
&tgr;<SUB>B</SUB> = <FR><NU>&bgr; + 2<IT>k</IT><SUB>−1</SUB></NU><DE>&agr;  ·  2<IT>k</IT><SUB>−1</SUB></DE></FR>  +  <FR><NU>1</NU><DE>2<IT>k</IT><SUB>−1</SUB></DE></FR> (1)
tau B should be equivalent to the time constant of decay of control EPCs, and to fit the measured control decay time constant in Fig. 4, tau B should be adjusted from 2.2 to 1.7. This can be achieved by either changing alpha  or k-1 or beta  in the opposite direction. The smallest changes are necessary in adjusting alpha  from 1,100 to 1,600 s-1, and we have adopted this change for the list of parameters in Table 2. In Franke et al. (1991b), alpha  was estimated without direct measurement, and the change made here is not in conflict with the experimental evidence. Direct measurement of alpha  would need to resolve the duration of single openings within a burst, which is almost impossible at present for the adult channel at resting potential. It generally is seen that the control decay time constants of EPCs, and also the tau B, vary considerably from preparation to preparation for reasons unknown. We assume here that the variation is in alpha .

When the ACh-esterase is blocked by low Phys concentrations, the EPCs are lengthened by the prolonged presence of ACh (Fig. 6), which is determined largely by diffusion of ACh from the active zone. The diffusion constant of ACh given in the literature is DACh = 4 · 106 cm2 s-1 (Anglister et al. 1994), and qEPCs simulated with this value decay with a time constant of 6.1 ms (not illustrated). With 10-5 M Phys, the decay time constant of the EPCs was 8.6 ms (Figs. 2 and 5), but when a value of DACh = 2 · 106 cm2 s-1 is adopted (Table 2), a satisfactory decay time constant of 8.7 ms results.

Extraction of the blocking rate constants of Phys and Proc from the time courses of EPCs

Scheme 2 is inconveniently complicated for extracting the blocking rates bp and b-p from the decay phase of the EPC. Because the decay phase of the control can be fitted adequately by a single exponent even in case of block of the cholinesterase, we lumped all the relevant steps in Scheme 2 into one step with a rate constant of 1/tau 0. This treatment disregards desensitization from A2BP, but this is a slow process in comparison to the time course of the EPC. With these simplifications the open channel block is formulated by Scheme 3.
Scheme 3 is described by the differential equations
<FR><NU>d<IT>O</IT></NU><DE><IT>d</IT><IT>t</IT></DE></FR><IT>=</IT>−<FENCE><FR><NU><IT>1</IT></NU><DE><IT>&tgr;</IT><SUB><IT>0</IT></SUB></DE></FR><IT>+</IT><IT>b</IT><SUB><IT>p</IT></SUB><IT>·P</IT></FENCE><IT>·</IT><IT>O</IT><IT>+</IT><IT>b</IT><SUB><IT>−p</IT></SUB><IT>·</IT><IT>B</IT> (2)

<FR><NU>d<IT>B</IT></NU><DE><IT>d</IT><IT>t</IT></DE></FR><IT>=</IT><IT>b</IT><SUB><IT>p</IT></SUB><IT>·</IT><IT>P</IT><IT>·</IT><IT>O</IT><IT>−</IT><IT>b</IT><SUB><IT>−p</IT></SUB><IT>·</IT><IT>B</IT> (3)
with the initial conditions
<IT>B</IT>(<IT>0</IT>)<IT>=0 </IT><IT>O</IT>(<IT>0</IT>)<IT>=1</IT> (4)
The solution of these equations is a superposition of 2 exponents
<IT>O</IT>(<IT>t</IT>)<IT>=</IT><IT>A</IT><SUB><IT>1</IT></SUB><IT>·exp−</IT><FR><NU><IT>t</IT></NU><DE><IT>&tgr;</IT><SUB><IT>1</IT></SUB></DE></FR><IT>+</IT><IT>A</IT><SUB><IT>2</IT></SUB><IT>·exp−</IT><FR><NU><IT>t</IT></NU><DE><IT>&tgr;</IT><SUB><IT>2</IT></SUB></DE></FR> (5)
in which
&tgr;<SUB>1</SUB>=<FR><NU>&tgr;<SUB>0</SUB></NU><DE>2·<IT>b</IT><SUB><IT>−p</IT></SUB></DE></FR><IT>·</IT><FENCE><FENCE><FR><NU><IT>1</IT></NU><DE><IT>&tgr;</IT><SUB><IT>0</IT></SUB></DE></FR><IT>+</IT><IT>b</IT><SUB><IT>p</IT></SUB><IT>·</IT><IT>P</IT><IT>+</IT><IT>b</IT><SUB><IT>−p</IT></SUB></FENCE><IT>−</IT><RAD><RCD><FENCE><FR><NU><IT>1</IT></NU><DE><IT>&tgr;</IT><SUB><IT>0</IT></SUB></DE></FR><IT>+</IT><IT>b</IT><SUB><IT>p</IT></SUB><IT>·</IT><IT>P</IT><IT>+</IT><IT>b</IT><SUB><IT>−p</IT></SUB></FENCE><SUP><IT>2</IT></SUP><IT>−4·</IT><FR><NU><IT>b</IT><SUB><IT>−</IT><IT>p</IT></SUB></NU><DE><IT>&tgr;</IT><SUB><IT>0</IT></SUB></DE></FR></RCD></RAD></FENCE> (6)

&tgr;<SUB>2</SUB>=<FR><NU>&tgr;<SUB>0</SUB></NU><DE>2·<IT>b</IT><SUB><IT>−p</IT></SUB></DE></FR><IT>·</IT><FENCE><FENCE><FR><NU><IT>1</IT></NU><DE><IT>&tgr;</IT><SUB><IT>0</IT></SUB></DE></FR><IT>+</IT><IT>b</IT><SUB><IT>p</IT></SUB><IT>·</IT><IT>P</IT><IT>+</IT><IT>b</IT><SUB><IT>−p</IT></SUB></FENCE><IT>+</IT><RAD><RCD><FENCE><FR><NU><IT>1</IT></NU><DE><IT>&tgr;</IT><SUB><IT>0</IT></SUB></DE></FR><IT>+</IT><IT>b</IT><SUB><IT>p</IT></SUB><IT>·</IT><IT>P</IT><IT>+</IT><IT>b</IT><SUB><IT>−p</IT></SUB></FENCE><SUP><IT>2</IT></SUP><IT>−4·</IT><FR><NU><IT>b</IT><SUB><IT>−</IT><IT>p</IT></SUB></NU><DE><IT>&tgr;</IT><SUB><IT>0</IT></SUB></DE></FR></RCD></RAD></FENCE> (7)

<IT>A</IT><SUB><IT>1</IT></SUB><IT>=</IT><FR><NU><IT>&tgr;<SUB>2</SUB>−&tgr;</IT><SUB><IT>0</IT></SUB></NU><DE><IT>&tgr;<SUB>2</SUB>−&tgr;</IT><SUB><IT>1</IT></SUB></DE></FR> <IT>A</IT><SUB><IT>2</IT></SUB><IT>=</IT><FR><NU><IT>&tgr;<SUB>0</SUB>−&tgr;</IT><SUB><IT>1</IT></SUB></NU><DE><IT>&tgr;<SUB>2</SUB>−&tgr;</IT><SUB><IT>1</IT></SUB></DE></FR> (8)

<FR><NU><IT>A</IT><SUB><IT>1</IT></SUB></NU><DE><IT>A</IT><SUB><IT>1</IT></SUB><IT>+</IT><IT>A</IT><SUB><IT>2</IT></SUB></DE></FR><IT>=</IT><FR><NU><IT>&tgr;<SUB>2</SUB>−&tgr;</IT><SUB><IT>0</IT></SUB></NU><DE><IT>&tgr;<SUB>2</SUB>−&tgr;</IT><SUB><IT>1</IT></SUB></DE></FR> (9)
Hence, we can calculate the unknown parameters (i.e., bp and b-p) from the experimental results using the following
<FR><NU>1</NU><DE>&tgr;<SUB>1</SUB></DE></FR>+<FR><NU>1</NU><DE>&tgr;<SUB>2</SUB></DE></FR>=<IT>b</IT><SUB><IT>p</IT></SUB><IT>·</IT><IT>P</IT><IT>+</IT><FENCE><FR><NU><IT>1</IT></NU><DE><IT>&tgr;</IT><SUB><IT>0</IT></SUB></DE></FR><IT>+</IT><IT>b</IT><SUB><IT>−p</IT></SUB></FENCE> <IT>b</IT><SUB><IT>−p</IT></SUB><IT>=</IT><FR><NU><IT>&tgr;</IT><SUB><IT>0</IT></SUB></NU><DE><IT>&tgr;<SUB>1</SUB>·&tgr;</IT><SUB><IT>2</IT></SUB></DE></FR> (10)
So, bp is a slope of the regression curve of 1/tau 1 + 1/tau 2 versus P, and b-p is an average of tau 0/(tau 1 · tau 2) at any blocker concentration, tau 1 and tau 2 being equivalent to the time constants of short and long decay of EPCs blocked by Phys or Proc, tau s and tau l, respectively. Equations 6 and 7 have been derived already by Adams (1976), Beam (1976), Ruff (1977), and McLarnon and Quastel (1984) and Equation 9 by Gage and Wachtel (1984) by another route. Different from these, our treatment also contains desensitization from A2O.

1/tau s + 1/tau l are plotted against the concentration of Proc or Phys in Fig. 7, using the values from the experiment of Figs. 4 () and 5, respectively. The sums of reciprocal tau  values rise with a greater slope at low Proc concentrations than at high concentrations (Fig. 7A). The values plotted for 1 mM Proc especially deviate. Regression lines for the plot in Fig. 7A result in slope bp = 2.8 · 106 M-1 s-1 (Eq. 10). If the value at 1 mM Proc is excluded, a higher bp of 6.1 · 106 M-1 s-1 results. The same trend is seen in all six experiments of this type.

Evaluated from single traces (Fig. 3, left), bp for the whole range of Proc concentrations (<= 2 mM Proc) was on average 3.1 · 106 M-1 s-1, and, excluding measurements with Proc concentration >0.5 mM, bp = 4.6 · 106 M-1 s-1 resulted. In contrast to the deviation of bp, the b-p calculated from Eq. 10 was little influenced by including or excluding data at Proc >0.5 mM. The respective b-p for the experiment of Fig. 4 was 357 s-1, and with 1 mM Proc tau  values excluded it was 323 s-1. For all experiments, the average b-p was 349 s-1, and, excluding measurements for Proc >0.5 mM, it was 336 s-1.

Plots analogous to Fig. 7A were made for the Phys experiments of Fig. 5 (Fig. 7B), and the average slope representing bp was 1.3 · 106 M-1 s-1. In this case, values at 1 mM Phys did not much deviate from the trend of the other values and were included into the evaluation. The value of b-p derived from the products tau s · tau l was 176 s-1.

Finally we calculated time courses of EPCs (Figs. 8 and 9) using the time courses and spatial distributions of ACh-concentration at the receptors (Fig. 6) and reaction Scheme 2 for the reaction of the receptors with ACh and Proc or Phys. In the case of Proc, from the simulated EPCs, the decay time constants and their amplitudes were evaluated and compared with the experimental results. To specifically fit the results in Figs. 4 and 5, we first had to adjust alpha  to obtain the measured decay time constant of the control. For the experiment of Fig. 4A, alpha  = 1,600 s-1 and for those of Fig. 5 alpha  = 750 s-1 had to be assumed (see preceding text). When using the bp and b-p derived from tau s and tau l by means of Eq. 10 including measurements also at high Proc, the fit was good for 1 mM Proc but not for lower Proc concentrations. Much better fits for tau s and tau l in Fig. 4(· · ·) were obtained when tau s and tau l were included only from Proc concentrations <0.5 mM, i.e., bp = 6 · 106 M-1 s-1 and b-p = 360 s-1. The resulting fits reached r = 0.98 and deviated only at 1 mM Proc. As an average estimate, including also the four other experiments discussed earlier, we suggest bp = 5 · 106 M-1 s-1 and b-p = 350 s-1. Another shortcoming of the fits in Fig. 4 are the relative amplitudes of the tau s component: they tend to be higher in the simulations than in the measurements. This divergence is not reduced when decreasing bp to half.



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Fig. 9. Same as Fig. 8 but for 10 µM Phys (top), which essentially only blocks the ACh-esterase. Bottom: effects of 1 mM Phys, which blocks the open channel like Proc in addition to blocking the ACh-esterase. Blocking and unblocking rate constants from Table 2.

The deviation of the measured tau s from the fitting simulations in Fig. 4 may indicate an error of measurement. In fact, EPCs with 1 mM Proc are short and small (Fig. 3), and their time course is difficult to evaluate. However with bp = 5 · 106 M-1 s-1 we have found consistently tau s of ~0.3 ms with 1 mM Proc when the blocking rate should be 5,000 s-1 at 1 mM Proc. When the ACh-esterase was blocked and ACh present for a longer period of time, tau s was even 0.54 ms at 1 mM Proc (Fig. 2). One possibility for obtaining too-large values of short tau s is filtering by the recording system. We have simulated such a filtering function and found a 2-kHz low-pass filter to produce approximately the measured 0.3-ms values of tau s with bp = 5 · 106 M-1 s-1. However, the macropatch systems including the electrodes used in our experiments were checked to present 8- or 10-kHz low-pass filters. Another possible error could arise by misinterpreting double releases as single ones in the short, low-amplitude recordings at 1 mM Proc. Two qEPCs with a 0.2-ms decay time constant, starting with a 0.1-ms interval, may look like one qEPC and would present an average decay lengthened to 0.3 ms. However, with a mean quantum content of the release in the experiments in Fig. 5 of 0.5, there would not be enough double releases to affect the average decays sufficiently. Further, if double releases were responsible for apparently lengthening the decay of the EPC, the tau s should be correlated positively with the amplitudes of EPCs. However, there was absolutely no such correlation. We thus do not see an obvious error of measurement responsible for the tau s at 1 mM Proc to be longer than predicted by the theory.

It should be noted that also in the patch-clamp measurements of the reaction of nicotinic channels to ACh and Phys or Proc (Bufler et al. 1996a) (Figs. 3 and 5), the decay time constants for 1 mM blocker concentration are lower than predicted by the reaction Scheme 2. Like in our experiments with Phys, the bp value fitting the experimental results at 1 mM Proc or Phys would have to be about half that producing a good fit for lower blocker concentrations.

In case of the results with Phys, the values of bp = 1.3 · 106 M-1 s-1 and b-p = 176 s-1 derived by means of Eqs. 9 and 10 produce good fits of the results in simulated EPCs (Fig. 5). Even the proportions of the short and long decay components of the EPC [As (As + Al)-1] in Fig. 5 are fitted impressively well. Also the measured tau s and tau l at 1 mM could be included, deriving the blocking and unblocking rate constants. The absence of a deviation of the tau  values with 1 mM Phys from the regression lines fitted for low concentrations may reflect the 4.5-times lower blocking rate constant of Phys in comparison with Proc.

Time courses of occupancies of receptor states in simulated EPCs

As discussed earlier, EPCs under different conditions were simulated with the parameters in Table 2, and their time courses were evaluated. Such simulations generate not only the time course of the open state A2O equivalent to that of the EPC but also of other states of the receptor. The most interesting ones are plotted in Fig. 8 for a control and for 1 mM Proc. Figure 8, left, has graphs with a linear time scale, those in Fig. 8, right, have a logarithmic one to show the beginning of the EPC in greater detail. The open state, A2O, reaches its peak after 0.33 ms in the control and much earlier, after 0.18 ms, in presence of 1 mM Proc. This shortening of the rise time is due to the rapid filling of the blocked state, A2BP, which attains a maximum occupation of 0.55 after 1 ms. Shortened rise times with high Proc concentrations were found also experimentally (Table 1). The block by Proc reduces the amplitude of the peak of A2O from 0.58 in the control to 0.35 in 1 mM Proc. The decay of the A2O shortens dramatically, from 2.4 ms in the control to 0.3 ms in 1 mM Proc. In Proc, a slow further decay follows described by tau l. During this long decay, A2O is refilled continuously from the blocked state, A2BP, when P unbinds. Occupation of A2BP declines slowly, from 0.55 at 1 ms to 0.08 at 50 ms. P unbinds from A2BP with the rate b-p = 350 s-1, i.e., with a time constant of ~3 ms. However, during the average life time of A2O before dissociation to A2R right-arrow AR + A, which is equivalent to the burst duration of 2.4 ms, the binding of 1 mM Proc with the rate of 5,000 s-1 will return most of the open channels back to the blocked A2BP state. The slow decay of the tau l of the EPC in presence of 1 mM Proc thus is generated by multiple cycles of unbinding and binding of P that are terminated only when A2R can dissociate to AR + A in one of the short time intervals at A2R. In control EPCs, the desensitized state A2D reaches an insignificant occupation of 0.03, which lasts for >50 ms. In presence of 1 mM Proc, the filling of A2D is delayed and reduced because after 1 ms, most of the channels are in the blocked state and desensitization from this state is slower than that from A2O and goes first to the A2DP state, which is not plotted here.

Figure 9, top, in comparison with the control in Fig. 8, demonstrates the effect of block of the acetylcholine-esterase on the EPC. This block by 10 µM Phys (Fig. 9, top) increases the amplitude of the EPC relative to the control in Fig. 8, from 0.58 to 0.82, and prolongs its decay time constant to 8.1 ms (see Fig. 2). This slow decay leads to relatively much desensitizitation to A2D in Fig. 9. The maximal occupation of the open channel block state A2BP is 0.025 and does not affect the time course of the EPC appreciably. With 1 mM Phys (bottom), the peak of the EPC is relatively less depressed than with 1 mM Proc in Fig. 8, and the decay time constant is reduced to 0.8 ms with 1 mM Phys. In Fig. 2, the respective value is 0.7 ms. These weaker effects of Phys in comparison to Proc reflect the 4.5-times lower blocking rate constant bp. Other characteristics of the block by 1 mM Phys in Fig. 9 are qualitatively the same as with 1 mM Proc; with 1 mM Phys the rise time of the EPC decreases, the blocked state A2BP rises to a level higher than the initial open state, A2O, and the desensitized state remains almost empty.


    DISCUSSION
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

The paper compares experimental results on the shape of EPCs with predictions by models. These contain the reactions of the receptor with the transmitter, but also the time course of the presence of the transmitter at the receptors. The latter implies modeling of the release, diffusion, hydrolysis, and the binding to receptors of the transmitter. The model we employ differs from that of Wathey et al. (1979). They assumed instantaneous release (as also Parnas et al. 1989) and diffusion in a plane disk. The model of transmitter action did not contain the A2R and the desensitized states. Bartol et al. (1991) used instantaneous release, another geometry with membrane folding, a high value of the ACh diffusion constant and the Monte-Carlo method of calculation, and they did not include receptor desensitization. We think that the model we used (see METHODS) describes the relevant processes sufficiently well. In the outcome, the differences to the model of Anglister et al. (1994) and Bartol et al. (1994) are small.

The reaction of a local anesthetic P with a nicotinic receptor/channel in the open state A2O according to our Scheme 2 is an expansion of the sequential open-channel block scheme suggested first by Adams (1976) that is equivalent to our simplified Scheme 3. This scheme explains the steep and the following slow phases of the decay of the EPC in presence of the blockers by the rapid binding of the blocker, which closes the channel, followed by a relatively slow return from the blocked state by dissociation of the blocker, which leads to reopenings generating the slow phase of the decay. In this reaction scheme, there is only one open state, A2O. Adams (1977) supported his scheme by ingenious voltage-jump experiments and Katz and Miledi (1975) by measurements of membrane noise spectra.

Neher and Steinbach (1978) first measured single channel currents in presence of ACh and lidocaine derivatives; they saw the one open state and the openings elicited by ACh alone to break up into repeated short openings in presence of the blocker as predicted by the sequential open-channel block scheme. In a continuation of this work, Neher (1983) found quantitative discrepancies between theory and experimental results for relatively high blocker concentrations in which the number of openings due to blocker dissociation and rebinding was smaller than predicted. In our experiments, this deviation would be equivalent to shorter than predicted slow decays of the EPCs, which was not observed. Gage and Wachtel (1984) applied Proc to toad end plates, and their results also could be described by the sequential open channel block scheme. But they further reported quantitative deviations from the theoretical predictions. In their experiments, the proportion of the long phase of the EPC, Al(As + Al)-1, was larger than calculated from the theory; in our results, there was the same tendency at the Proc concentration they used (100 µM), but the fit improved at higher Proc concentrations (Fig. 4). For Phys the fit was excellent.

There were some early alternatives to the open channel block scheme, assuming two different open states produced by the binding of the blockers (Ruff 1976, 1977; Steinbach 1968). Such schemes were ruled out mainly by the single channel recordings, which consistently showed only one species of open channels.

Some of the studies estimated blocking rate constants of the local anesthetics and found 106-107 M-1 s-1 in the different preparations and with different drugs (Adams 1976; Gage and Wachtel 1984; Neher and Steinbach 1978; Shaw et al. 1985). The blocking rates in our studies also were in this range (Table 2). For the lidocaine derivates, Neher and Steinbach (1978) reported a high unbinding rate of 2,200 s-1, producing rapid "flickering" of the channel. For other local anesthetics, lower unbinding rates of 200-400 s-1 were seen, in agreement with our results (Table 2).

In the present study, the experimental conditions were varied by blocking the ACh-esterase with 10 µM Phys. This prolonged the presence of ACh at the receptors considerably; although 0.5 ms after opening of the vesicle the ACh concentration in presence of the esterase is <10-5 M and causes negligible further channel opening, while with the esterase blocked the ACh concentration is eight times higher and contributes to channel opening. Even at 5 ms, the ACh concentration with blocked esterase is still 17 µM, which could elicit about one-tenth maximal channel opening (Fig. 6) (see Franke et al. 1991b). In the simulations, the slower decay of the ACh concentration with blocked esterase prolonged the time constant of decay of the qEPC to 8.1 ms (Figs. 5 and 9). Although thus the duration of presence of ACh was greatly altered, the simulations with the open channel block model fitted the effects of high Phys concentrations on the pEPCs very well, even better than in case of the unblocked esterase (Figs. 4 and 5).

Although the model fitted the results with Phys very well, there was one significant discrepancy between the predictions of the model and the experimental results with Proc. At high Proc concentrations, the EPCs did not decay as fast as predicted. We have discussed possible errors of measurement and think that we can exclude them. Similar defects in the effectivity of the block at high drug concentrations were reported also by Gage and Wachtel (1984) and also in our channel measurements (Bufler et al. 1996a). It may be concluded that the reduced blocking effectivity at high drug concentrations in the experiments in comparison with the predictions reflects a defect of the reaction scheme. Already Neher and Steinbach (1978) pointed out that reduced blocking efficiency at high blocker concentrations is in conflict with a pure open channel-block mechanism. It would be necessary to add at least another binding step of the blocker to accommodate the experimental results more completely, and tentative simulations show that additional competitive block at R with an equilibrium near 1 mM Proc and a rate of unbinding of ~10,000 s-1 would do this.

A combination of open channel block with competitive block was found also for tubocurarine. In the competitive block component, the main difference between Proc and curare would be a 105-times lower rate constant of unbinding from R for the latter (Bufler et al. 1996b).

In the single-channel measurements, we have derived blocking rate constants for Phys and Proc of 6 · 106 and 2 · 106 M-1 s-1 and unblocking rates of 200 s-1 for both. In the present study, analysis of the changes in shape of the EPC rendered bp = 1.3 · 106 M-1 s-1 for Phys and 5 · 106 M-1 s-1 for Proc, with the b-p = 176 s-1 and 350 s-1, respectively. These values are not far apart, Phys being more potent in the channels and less potent than Proc in the EPCs. It should be noted that the investigated channels were of the embryonic type and that the "adult" channels of the EPCs had one different subunit of the receptor. This may explain the small quantitative differences in blocking efficacy.

Thus we have shown that the reaction schemes developed for nicotinic channels (Bufler et al. 1996b) serve also to predict the effects of Proc and Phys on EPCs. They do this for a much larger concentration range than used so far, relying also on evaluations of serverely blocked EPCs. For the first time in this type of studies, the evaluations and models extend also to EPCs in which cholinesterase was blocked, and the same models and rate constants cover these quantitatively quite different situations. Last, the derivation of the Eq. 10 allows a quantitative evaluation of the blocking rate constants in EPCs.


    ACKNOWLEDGMENTS

The authors thank I. Horstmann for technical assistance and M. Griessl and W. Reinhardt for secretarial help.

This work was supported by Deutsche Forschungsbemeinschaft Grant SFB 391.


    FOOTNOTES

Address for reprint requests: J. Dudel, Physiologisches Institut der Technischen Universität München, Biedersteiner Str. 29, 80802 Munich, Germany.

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

Received 15 April 1998; accepted in final form 8 January 1999.


    REFERENCES
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

0022-3077/99 $5.00 Copyright © 1999 The American Physiological Society