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1 Physiologisches Institut, Universität Freiburg, Germany
2 Physiologisches Institut der Ludwig-Maximilians-Universität München, Germany
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(Received 4 December 2004;
accepted after revision 21 January 2005;
first published online 27 January 2005)
Corresponding author M. Heckmann: Physiologisches Institut, Hermann-Herder-Str. 7, D-79104 Freiburg i. Br., Germany. Email: heckmann{at}uni-freiburg.de
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Introduction |
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In the first patch clamp recordings, nicotinic receptor channel openings appeared as several millisecond events, invariable in amplitude and average duration over a wide range of agonist concentrations (Neher & Sakmann, 1976). With improved time resolution it became clear that these events were bursts of openings separated by very short closings. This was established in detail by Colquhoun & Sakmann (1985) for the endplate of the frog. About 20 µs closings within bursts were resolved with great difficulty, limited by filter cut-off frequencies of 4–5 kHz. According to the standard theory, the closings within bursts are determined by the rate constant of agonist unbinding and the rate constant of channel opening (del Castillo & Katz, 1957; Colquhoun & Hawkes, 1977; Colquhoun & Sakmann, 1983). Closings within bursts therefore deserve special attention. In addition to bursts, single short openings with average durations of 160 µs were seen (Colquhoun & Sakmann, 1985). At very low agonist concentrations, short openings predominated and probably many short openings were not resolved. Bursts were assumed to arise from fully liganded and short openings from monoliganded receptors. Colquhoun & Sakmann (1985) and others (reviewed in Lingle et al. 1992) noted that a large number of short openings, that appeared in some recordings at high agonist concentrations, is not consistent with this interpretation.
Unresolved single channel events confound mechanistic interpretations and nicotinic receptor single channel kinetics may have not yet been resolved sufficiently. In quartz pipette recordings optimized for time resolution, we found indications for very short components in recordings with ACh (Parzefall et al. 1998). Others found earlier that SubCh elicits longer single channel events than ACh (Colquhoun & Sakmann, 1985; Ogden & Colquhoun, 1985; Sine & Steinbach, 1986). Therefore, we turned to the kinetics of SubCh-elicited nicotinic receptor currents. Using methods of analysis that allow maximization of the likelihood of the entire sequence of open and shut times in a recording and provide estimates of the rate constants in a reaction scheme (Colquhoun et al. 2003a), we tested a physically realistic reaction mechanism (Hatton et al. 2003), focusing in particular on brief, hitherto insufficiently resolved, openings with the aim to clarify the contributions of the two ligand binding sites known from molecular biology (Changeux & Edelstein, 1998) of channel gating. We find that the most plausible physically realistic reaction mechanism does not provide a good explanation for the origin of the brief openings. Unexpectedly, the contributions of the ligand binding sites to channel gating remain thus unclear.
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Methods |
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Myotubes were prepared from toe muscles of decapitated neonatal mice, in accordance with national guidelines, taking care that the mice did not suffer unnecessarily. The myotubes were in culture prior to all recordings for at least 7 days, to ensure that they uniformly express nicotinic acetylcholine receptors with the 
2ß
subunit composition, as described by Franke et al. (1992).
Electrophysioloy
Single channel currents were recorded in the on-cell mode of the patch-clamp technique (Hamill et al. 1981) at 20 ± 2°C with thick-walled quartz pipettes. The pipettes were pulled with an improved DMZ quartz-glass puller (Zeitz Instruments, Munich, Germany) which allows precise regulation of gas pressure (Dudel et al. 2000). An Axopatch 200B (Axon Instruments, Union City, CA, USA) with a modified head stage and a custom-built pipette holder was used to amplify the currents. The latter fixes pipettes mechanically better than the holder shown in Parzefall et al. (1998). The solution in the bath (and that in the pipette tip, with SubCh) contained (mM): 162 NaCl, 5.3 KCl, 2 CaCl2, 0.67 NaH2PO4 and 15 Hepes buffer; pH 7.4 (adjusted with NaOH). Pipettes with a tip resistance of 10–20 M
were used and neither fire-polished nor coated. To increase the signal to noise ratio, the patches were hyperpolarized to 100–200 mV.
Data acquisition
The currents were filtered with the internal 100 kHz filter of the Axopatch 200B and also at 78 kHz with an external custom built 10-pole Bessel filter to give a final –3 dB cut-off frequency of 62 kHz. The currents were digitized at 333 kHz and the data were stored directly on the hard disk of a PC. Only recordings with r.m.s. noise values below 2.0 pA (at 62 kHz) were used. In most experiments the r.m.s. noise value was about 1.7 pA and occasionally as low as 1.45 pA.
Initial evaluation
In the initial evaluation of our data with XPATCH, a program that was developed in our department and runs under Linux, two thresholds were used (Parzefall et al. 1998). The lower was set at 0.2 and the upper at 0.8 of the single channel current amplitude. When the channel current passed the upper threshold coming from the closed level, the program detected the beginning of a channel opening. The lower threshold served to determine the end of an opening and the beginning of a closing. The duration of an opening or closing was determined at half amplitude, interpolating linearly the 3 µs digital values. The data were then plotted and fitted essentially as described below.
Time course fitting
The recordings were analysed in addition as described by Hatton et al. (2003) and Colquhoun et al. (2003a) with software from http://www.ucl.ac.uk/Pharmacology/dc.html. For time-course fitting with SCAN (Colquhoun & Sigworth, 1995), the data were refiltered with a digital Gaussian to a final cut-off of 30 kHz and re-sampled to 111 kHz with FILTSAMP. Data sections with simultaneous openings of more than one channel were marked unusable in SCAN.
Open and shut time distributions
Distributions of open and shut times were fitted in EKDIST, imposing a resolution of 6 µs, with mono- or multiexponential functions, and using the largest number of statistically allowed components, if not stated otherwise. The criterion for the number of components was: logarithmic likelihood ratio (LLR) > 4.6. For a fit with n components, the LLR was calculated comparing fits with n and n – 1 components. With LLR > 4.6 the probability of erroneously accepting n components, although n – 1 components are correct, is smaller than 1% (Rao, 1973; Horn, 1987). However, the method used to fit exponentials was only an approximation to true ‘maximum likelihood’. The likelihood is calculated as though dwell times were independent, though in fact they are not. While this is not likely to have much effect on the parameter estimates, it could have an effect on the distribution of the LLR, and so make the LLR test not very accurate.
Stability plots
The stability of mean open time was tested with plots like the one in Fig. 4 (sliding averages of 50 successive individual segments of openings) and stability of channel amplitude with plots like the one in Fig. 5. These plots allowed the detection of segments with insufficient stability, which were then not used for the subsequent kinetic analysis. To assess the stability of amplitude and duration of all three open time components individually, all recordings were in addition analysed separately in MATHEMATICA 4.1 (Wolfram Research, Champaign, IL, USA) as described in the main text (see Fig. 5). Note that in Fig. 5A and C–E, only events of which the amplitude could be determined by time course fitting (see manual for SCAN) were included. For the short openings, this led to a reduction of the number of points in Fig. 5C relative to Fig. 5B by a factor of 10.
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Bursts of openings were defined using a critical shut time, tcrit, and all openings separated by closings shorter than tcrit were grouped (Colquhoun & Hawkes, 1995). tcrit was set between 
3 and 4 of the closed time distribution using the equation:
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| (1) |
4 and 5 increased with increasing SubCh concentration, whereas closings within bursts from one channel are expected to decrease with increasing agonist concentration with a mechanism like the one in Fig. 8.
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Failure to detect short open and shut times can make open and shut times appear to be considerably longer than they actually are. Calculations were therefore done with an exact correction for missed brief events (Hawkes et al. 1990, 1992), and the distributions of apparent open times, shut times, etc. were therefore referred to as HJC distributions. The likelihood of the entire sequence of apparent open and shut times, in the order in which they occurred, was calculated using HJCFIT and maximized adjusting the values of the rate constants of the mechanism in Fig. 8 (Colquhoun & Hawkes, 1995; Colquhoun et al. 2003a). The start values for the rate constants were taken from the left column of Table 1 in Hatton et al. (2003). To judge the reliability of the rate constant estimates, standard deviations of the rate constants' estimates were calculated with the numerical estimate of the Hessian matrix and were usually below 20%.
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Voltage dependence
In recordings with 100–175 mV hyperpolarization, final filter cut-off and imposed resolution were reduced (e.g. 20 kHz and 15 µs with 100 mV hyperpolarization), but otherwise the evaluation was the same as described above. Rate constant estimates were plotted versus holding potential and fitted with an exponential curve. In Table 4, the potential that is needed to increase the rate constant e-fold is given.
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) or the standard error of the mean (S.E.M.), or with the coefficient of variation of the mean (C.V.M.) expressed as a percentage of the mean. |
Results |
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Examples of single channel currents, evoked by 1 µM SubCh in a typical recording from a cultured mouse myotube, are shown in Fig. 1. The uppermost trace in Fig. 1A shows a 3-s-long current segment, and below successive tenfold temporal expansions. The example of a brief opening from the bottom of Fig. 1A is shown again in Fig. 1B with an idealization (red line) obtained by time course fitting (Colquhoun & Sigworth, 1995). Figure 1C shows the start of a group of longer openings with a 6 µs and a 13 µs closing and time course fitted idealizations in red.
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) for the exponentials did not depend on SubCh concentration, and amounted to approximately 4 µs (1), 89 µs (2) and 860 µs (3). At the lowest concentration, 1 accounted for 36%, 2 for 9% and 3 for 55% of apparent open periods. At higher agonist concentrations, the proportion of the areas of the two shortest time constants (1 and 2) decreased, and that of 3, the area attributable to the longest time constant, increased (Table 1).
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Examples of shut time distributions, fitted with mixtures of five exponential probability density functions, are shown in Fig. 3, and the parameters of the fits are given in Table 2. The shortest component had a mean time constant, 1 of 2.9 ± 0.2 µs with 0.1–10 µM SubCh. These extremely short closings are so frequent that despite the imposed resolution of 6 µs there are enough to allow a fit. The relative (extrapolated) area of this component is more than 90% of all shut times. A second, 10 times longer component 2 with a mean value of 27 ± 8 µs accounts for 3.8 ± 0.4% of the relative area. These first two components appeared consistently up to 10 µM SubCh. (Table 2). While the third component is assumed to be contained in bursts (see below) and amounts to only a few per cent, the fourth and fifth component are also small and reflect the number of channels present in a patch and the degree of desenitization. The latter are disregarded in subsequent discussion.
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The original data were filtered to 62 kHz, but it was necessary to refilter them to 30 kHz for time course fitting (Colquhoun & Sigworth, 1995). Evaluation of the 62 kHz data with another program (Parzefall et al. 1998) gave essentially the same results as those in Figs 1–3. For the recordings with 0.1 µM SubCh, open time components 1
= 13 µs, 2
= 158 and 3
= 573 µs were obtained. The respective shut time components were 5, 44 and 562 µs, 15 and 135 ms. Time course fitting tended to improve the resolution, resulting in shorter brief components in comparison to the initial evaluation.
Stability plots
To address the question whether the data presented so far arise from a homogeneous channel population, ideally from one channel in each patch, the following tests were performed. To asses the temporal stability of the open times we formed averages of 50 consecutive openings each and plotted these averages as a time series. Figure 4 illustrates this for one experiment. There is no drift of the average open time, as similarly seen in all other experiments.
The next step was to test for a homogeneous single channel current amplitude. The right hand part of Fig. 5A shows a clear, single peak gaussian distribution for the openings in the experiment from Fig. 4, with a slight excess of events with amplitudes between –10 and –5 pA. To check the three open time components separately, we selected characteristic ranges of the open time distribution (Fig. 5B). First, with the very short open time component the problem arises that due to the limited resolution of our recordings only a minor part of this component is resolved. Due to the overlap of the three open time components, events with a duration between 6 and 10 µs (blue area in Fig. 5B) contain 59.5% openings from the shortest exponential component (1
= 1.8 µs in this case), 5.2% openings from the intermediate exponential component (2
= 161 µs) and 35.3% openings from the third exponential component (3
= 387 µs). Thus the plot of the amplitude distribution in the right part of Fig. 5C is still from a rather mixed population in which only 60% are from the short opening component 1. The corresponding gaussian distribution is relatively wide but peaks at the same amplitude as the overall amplitude. For the second component a time range of 100–170 µs was chosen (yellow in Fig. 5B) and the amplitude distribution of the events with this duration is shown in the right hand part of Fig. 5D. Finally the amplitude distribution of the longest component 3, represented by openings longer than 300 µs (red area in Fig. 5B), is shown in the right hand part of Fig. 5E.
The final criterion was the temporal stability of the current amplitudes. While this is a precondition for forming averages, temporal heterogeneity might also reveal the existence of different channel types. The left hand part of Fig. 5A shows the temporal stability lumped for all amplitudes, and the left hand parts of Fig. 5C–E shows the same for the three different components 1,
2 and 3. Figure 5D and E shows a small percentage of clearly resolved subconductance events.
All other recordings which were evaluated and included in the tables showed similar stabilities. To illustrate this, we plotted in Fig. 6 the overall mean single channel current amplitude (indicated by a grey line) and mean amplitude ± standard deviation of short, medium and long openings (defined and colour coded as in Fig. 5) for 12 recordings. In three out of the 12 experiments, a significantly different single channel current amplitude was found for the three open time components, but no clear trend was apparent. Thus there was no evidence for more than one channel type in our recordings. However, this is only negative evidence.
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Openings of channels occur typically grouped in bursts, i.e. series of openings with relatively short closed intervals. With suitable limiting shut times tcrit (see Methods and Table 3), the idealized records were separated into bursts, and examples of burst length distributions for three SubCh concentrations are shown in Fig. 7. The distributions can be fitted with a mixture of four exponential probability density functions. The longest component of the burst length distributions (4), in the 10 ms range, carries the majority of the charge. This component corresponds to the long bursts identified by Colquhoun & Sakmann (1985), and there should be a similar component in the decay of the response to a short pulse of agonist and in synaptic currents. Two such long bursts are shown in the second line of Fig. 1A, one 0.4 ms intermediate burst in the third line of Fig. 1A, and one short burst consisting of one short opening in the last line of Fig. 1A and in Fig. 1B.
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With three types of openings, and biochemical and physiological evidence obtained by others that the two receptor binding sites differ (reviewed in Colquhoun et al. 2003b), the scheme shown in Fig. 8 (Scheme 1) appeared appropriate as a physically realistic kinetic mechanism. In addition to the kinetic mechanism, Fig. 8 illustrates the receptor configuration with one binding site (blue) between and , and the other (red) at the interface of and subunits. The rate constants of binding (k+) and unbindig (k–) of the agonist (A) are assumed to be different at the two binding sites, and the sites consequently contribute differently to the gating of the channel pore. This scheme does not include openings without ligands (Jackson, 1984; Grosman & Auerbach, 2000) and does not include desensitization and channel block by agonist.
Maximum likelihood fitting of scheme 1
To reduce the number of free parameters, we assumed that binding of an agonist molecule (A) to the a site does not affect binding of a second agonist molecule to the b site and vice versa. Following Colquhoun et al. (2003a) we consequently constrained the following rates:
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| (3) |
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| (4) |
Scheme 1 was fitted to the recording from Fig. 2A with a maximum likelihood approach. Figure 9A shows the experimentally found open period distribution (in black), and in blue the HJC open time distribution predicted by the fitted values of the rate constants. Note that the blue line is not fitted to the histogram. It is calculated from the estimates of the rate constants that have been found by the maximum likelihood fit of rate constants of scheme 1 (see Colquhoun et al. 2003a). The histograms are used here and in the following in the context of maximum likelihood fitting as a visual test of the quality of the fit. The broken red line is the distribution calculated directly from the rate constants, by the Colquhoun & Hawkes (1982) methods that make no allowance for missed events, so the broken line is the best estimate of the true distribution. Figure 9B shows the same type of plots for the shut times. The blue lines fit the experimental data reasonably well.
Figure 9C shows the conditional HJC distribution (blue line) of apparent open times for open times that are adjacent to shut times in the range t < 0.1 ms; this is superimposed on the experimentally observed histogram of open times that are adjacent to shut times in the same range. The broken blue line repeats the HJC distribution of all open times, as shown in panel A. Figure 9C shows that short openings very rarely occur adjacent to short shuttings.
Figure 9D shows a conditional mean open time plot. The black diamonds with error bars (joined by black lines) show the experimental data. The blue circles show the HJC predictions for the same shut time ranges that were used for the data and the blue line shows the continuous relationship between mean open time and adjacent shut time, calculated from the fitted rate constants. There was again reasonable general agreement between observation and prediction.
Figure 9E addresses also the temporal grouping of openings and closings. It plots the dependency d (vertical dimension) of shut times (abscissa) on adjacent (preceding or following) open periods (ordinate) (Magleby & Song, 1992). Dependency is defined as described in the Methods (eqn (2)) and is positive if the shut times are positively correlated to the preceding open period, and negative, if they are negatively correlated, i.e. the red elevations in Fig. 9E signal areas of positive correlation of open and shut times. The peak positive correlation is for long open periods of 0.5–12 ms and 4–40 µs shut times. This represents the long bursts of openings with short closings apparent in Fig. 7. There is a weak correlation for 4–20 µs openings followed by 50–80 µs shut times, and a stronger correlation for 4–50 µs openings and 5–900 ms shut times. This red seam at the right hand frontal aspect of Fig. 9E represents single short openings. The peak dependencies for the very short closings are d = 0.43 and for the long closings are d = 0.62.
Dependencies like in Fig. 9E for experimental results are shown in Fig. 9F for the rate constants obtained in the maximum likelihood fit. In Fig. 9F two red ridges are seen, one at about 140 µs open time and 0.06–1.5 ms shut time (d
= 2), and another one at 5 µs open time and 9–800 ms shut time (d
= 3.3). Relative to these ridges, the elevation of the plateau between 0.14 and 4 ms open periods and following 4–30 µs shut times is low (d
0.2). But the adjacent blue depression at longer shut times is strongly negative, d
=
–0.7, enhancing the contrast. In conclusion, the groupings of experimental data and of the ones generate for scheme 1 agree in their tendencies, but the agreements are much less detailed than that of the fits in Fig. 9A and B.
With the same procedure as in Fig. 9, the mean rate constants with their coefficients of variation were obtained for four experiments with 0.1 µM SubCh, and mean rate constant values are listed in the left hand column of Table 4, with the same fix of k+1a as in Fig. 8. The double liganded receptor state presents extremely high on-rates ß2 that generate about 4 µs gaps in bursts. Also the closing rate 1b from the single-liganded Ra–ARb* state is extremely high, generating openings of around 3 µs duration. In comparison, the closing rates of the single-liganded state ARa–Rb*, 1a, are 20 times lower, generating about 70 µs openings.
Among the binding rate constants, k+1a = k+2a are fixed at the diffusion limit. However, the other binding rate constants k+1b = k+2b = 3.6 x 109 M–1s–1 are clearly above the diffusion limit and should be physically impossible. With k+1a and k+1b fixed at the diffusion limit, the general fits clearly deteriorate.
The ratio ß2/(k–2a + k–2b) = 48 determines how often the double-liganded receptor ARa–ARb returns to the open state before one of the ligands unbinds. The average burst of openings from ARa–ARb consequently lasts 6.3 ms which agrees with the length of the longest burst component in Fig. 7. The respective ratio for the ARa–Rb single liganded receptor is ß1a/(k–1a + A x k+2b) and amounts to 1/3 (with 0.1 µM SubCh): in only a third of the sojourns in ARa–Rb the channel opens for about 0.4 ms. Analogously, from the single liganded Ra–ARb state the receptor opens once with a probability 0.07 for on average 3 µs. At the low concentration of 0.1 µM SubCh, the great majority of the openings from the single liganded receptors thus are single openings. This is even more valid for higher concentrations: with 10 µM SubCh the probability of opening once from a sojourn in the ARa–Rb state drops to 0.003, and from the Ra–ARb state to 0.05. It is thus an inherent characteristic of reaction scheme 1, that the proportion of openings from the single liganded receptors decreases with increasing agonist concentration.
Table 4 further lists equilibrium constants Ka = k–1a/k+1a = 12 µM, and Kb = k–1b/k+1b = 1.0 µM. The EC50 for the total reaction is 0.8 µM. When the experimentally determined EC50 of 1.0 µM is introduced into the fit as a further constraint, the right hand column of Table 4 results. Comparison of the rate constants in the two columns shows that fixing the EC50 at 1 µM has little effect.
Voltage dependence of rate constants
The recordings in this study were taken at 200 mV hyperpolarized patch potential in order to increase the resolution. The physiological membrane potential is much more positive, and many other studies have been performed at more positive potentials. In order to allow the comparison of rate constants, we reduced the hyperpolarization in 15 patches and obtained the voltage dependence of the rate constants. Examples for the most interesting rates, the comformational opening and closing rates ß2 and 2 of the double liganded receptor, are given in Fig. 10. The logarithmic plot of the rates against the hyperpolarization voltage could be fitted with an exponential function. For an e-fold change of 2 less hyperpolarization (50 mV) is needed than for an e-fold change of ß2 (110 mV). Both rate constants decrease with reduced hyperpolarization, but the voltage dependence for the closing rate is twice as strong as that of the opening rate.
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Open channel block
When the agonist concentration is raised, the gaps between bursts of one channel are reduced in proportion. The receptors are driven more and more into desensitization, but when one receptor recovers, its almost continuous activation forms a cluster of closely spaced bursts (Sine & Steinbach, 1984; Colquhoun & Sakmann, 1985; Sine & Steinbach, 1987; Colquhoun & Ogden, 1988). With SubCh concentrations above 10 µM, bursts occur closely spaced.
Block of open ACh receptor channels by SubCh has already been proposed by Colquhoun & Ogden (1988). Block of open channels by SubCh is concentration dependent and more pronounced at negative potentials. An example of a trace from a recording with 1 mM SubCh is shown in Fig. 11A, with a section on an expanded time scale. Note that the channel remains closed more than half of the time during the 5 ms current stretch of the cluster of openings. At lower SubCh concentrations, the channel is open about 90% of the time during bursts (Fig. 1A). Evaluations of open and closed times from an experiment with 1 mM SubCh are shown in Fig. 11B. The average duration of the resolved openings is reduced to 35 µs compared to a main open time component of 760 µs with 1 µM SubCh in Fig. 2B. In three experiments with 1 mM SubCh the mean duration of the resolved openings was 46 ± 8 µs. The shut time distribution in Fig. 11B has only three components, a short one of 103 µs and two longer ones of 7.1 ms and 107 ms. The mean of the shortest component was 83 ± 10 µs in three experiments of this type. Assuming that the 10–30 ms stretches of continuously repeated short openings in Fig. 11A represent continuous bursting activity of one channel each until it desensitizes, the blocks between the openings are largely due to the 103 µs component of the shut time distribution. Note that in the distribution of the closed times in Fig. 11B the predominant <6 µs gap component within bursts (Fig. 3) is missing, possibly partly due to increased filtering at 20 kHz. This component drops out above 100 µM SubCh (see Discussion).
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The maximum likelihood fit of our data with 0.1 µM SubCh in Fig. 9 and Table 4 was satisfactory, aside from opening rate constants above the diffusion limit. scheme 1 predicts agonist-concentration dependencies for the different types of openings and bursts, and a more stringent test for the applicability of reaction scheme 1 would include the concentration dependence. For this purpose, data from experiments at 0.1, 1 and 10 µM SubCh were entered into the HJCFit program, and from the lumped data a single set of maximum likelihood rate-constants was calculated. Figure 12A–C shows data (in black) for the different concentrations, and the fits (red) derived from the combined data.
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The fits illustrate the inherent property of scheme 1, that with increasing agonist concentration the openings from single liganded receptors almost disappear and bursts from the double liganded receptor with relatively long open times become prevalent. The experimental data show this clearly to a much smaller degree. It appears thus that scheme 1 cannot cover the experimental data from a 100-fold agonist-concentration range.
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Discussion |
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Heterogeneity of receptors
It is usually assumed that channel gating is sufficiently uniform for one type of channel to be interpreted within the framework of relatively simple mechanistic models (Steinbach, 2000). Is there evidence for the assumption that all three types of openings arise from one type of receptor? Mouse myotubes might express an inhomogeneous population of ACh receptors, and different types of openings might originate from different populations of receptors. However, ‘adult’ receptors with their much higher single channel conductance (64 versus 36 pS, Franke et al. 1992) have never been observed in our type of preparations (Franke et al. 1992; Bufler et al. 1996a,1996b). To further substantiate the homogeneity we analysed the stability of our recordings in detail (Figs 4 and 5). The single channel current amplitudes of short, medium and long events were seen to be stably very similar and consistent with the 36 pS conductance found for denervated muscle. This makes it unlikely that the three types of openings originate from different populations of receptors. The temporal stability of the occurrence of the three types of openings during individual recordings and from one recording to another is in line with homogeneity of the receptors.
It could be argued that the extremely short openings of about 4 µs duration, described here, are artifacts due to the recording with quartz pipettes. However, it seems unlikely that the chemically inert quartz glass produces such artifacts, and even more unlikely that the artifacts have exactly the amplitude of longer, undoubtedly single channel currents of the embryonic type of ACh receptors. Further, high SubCh or ACh concentrations do not produce short openings (Fig. 11B).
‘Open channel block’
If the results with 1 mM SubCh (Fig. 11) are interpreted as being due to open channel block, the predominant 100 µs component of the shut times represents an unbinding rate of 104 s–1 of SubCh that blocks the ARa–ARb* open state. The open time component within the bursts of 35 µs would correspond to a blocking rate of SubCh of about 3 x 104 s–1, and taking into account the SubCh concentration of 1 mM, to a rate constant of 3 x 107
M–1s–1. This rate constant of block by SubCh is in the same range as that seen for procaine (Bufler et al. 1996a) and (+)-tubocurarine (Bufler et al. 1996b). The unblocking rates for both are several orders of magnitude lower than that reported here for SubCh.
The interpretation of our data (Fig. 11) as being due to open channel block does not cover the observed disappearance of the main 3 µs shut time component (Fig. 3) that generates the closings within bursts. Similarly, in case of 1–5 mM ACh, the shortest shut time component is replaced by an increasingly longer one (Parzefall et al. 1998; Fig. 4). However, open channel block should not affect these short shut times within bursts at all; it should only add a component that is determined by the unbinding rate of the open channel blocker (and not concentration dependent!). An alternative interpretation is to assume binding of SubCh to a site that modulates the conformational change ARa–ARb to ARa–ARb*, decreasing the opening rate ß2 and increasing the closing rate 2. This may account for the shorter openings and longer closings in the ‘bursts’ of Fig. 11, in comparison to those in Fig. 1. Such a modulation of the conformational change may also account for the ‘open channel block’ effects with ACh in Parzefall et al. (1998).
In the latter paper, we discussed open channel block by ACh with a further binding of ACh to the blocked state that would prolong the block. Such a two-step block would generate the observed lengthening of the respective shut time component with increasing agonist concentration. The same reaction scheme was studied and modelled by Prince et al. (2002) for the open channel blocker tacrine, also in order to account for a lengthening of the shut time component related to the block with increasing blocker concentration.
In case of the ‘open channel block’ by high SubCh or ACh concentrations, a separate study using a range of agonist concentrations and high temporal resolution of the recordings would be needed to establish either a multistep open channel block or a modulation of the conformational changes ARa–ARb to ARa–ARb* and back.
Mechanistic interpretation
The reaction scheme in Fig. 8 covers relevant molecular biological findings for the ACh receptor channel molecule (AChR), i.e. two different binding sites and much of the electrophysiological data. There do not seem to be enough data to support more complex quantitative schemes. It should be noted that the maximum likelihood fit of scheme 1 in Fig. 8 resulted in binding rate constants of SubCh that are clearly above the diffusion limit, i.e. they seem physically impossible. In schemes like this one and also in more simple linear schemes, the probability of short openings should be reduced in proportion to an increase in agonist concentration. One of our findings seems to demonstrate, that the concentration dependence of single openings is clearly less than predicted by such a scheme (Fig. 12).
Deviations from the expected about linear concentration dependence of the relative proportions of short and long openings, have been seen already by Colquhoun & Sakmann (1985). Sine & Steinbach (1986) did not even find any concentration dependence of these proportions. Hatton et al. (2003) also have a surplus of short openings at higher ACh concentrations relative to the scheme in Fig. 8 especially with the mutant 
L221F. It should be noted, that none of the cited studies resolved the 4 µs open time component which is most relevant in this context.
Arguing from the opposite direction, there is a body of evidence for opening and closing kinetics of a receptor that are independent of the state of ligand binding. Chabala & Lester (1986) covalently and irreversibly bound agonists to ACh receptors (AChRs) and saw a range of open and shut times similar to those with agonist free to move. Using receptors from a different family, nucleotide gated receptor channels, Ruiz & Karpen (1999) tethered fixed numbers of ligands to single receptors and found that such a channel ‘can assume at least nine distinct states’ differing in current amplitudes and kinetics. Another fixed ligand state is the absence of agonist. Jackson (1984) reported 0.1 and 0.5 ms openings in embryonic mouse muscle in the absence of agonist. Ferrer-Montiel et al. (1991) found that phosphorylation of AChR - and -subunits activates AChR channel opening in the absence of agonist, presenting short and long openings. Grosman & Auerbach (2000) reported multicomponent open and shut times from adult AChR and a number of their mutations. However, it is worth mentioning that in their results, only one patch out of six showed longer openings and bursts with wild-type receptor. In summary this and the inadequate concentration dependence of open time components leads to the conclusion that reaction schemes like scheme 1 that strictly correlate binding and kinetic state may be oversimplifications.
Desensitization
It has been argued that short openings could arise from desensitized AChR, since some short openings are seen in periods with largely desensitized receptors between clusters of openings (Hatton et al. 2003). However, such short openings occur at high frequency with 1 µM SubCh (Fig. 1) in which much desensitization is improbable. With 0.1 µM Ach, desensitization is absent (Franke et al. 1993; Fig. 9), but short openings are prominent (Parzefall et al. 1998). Further, at high ACh concentration, e.g. 1–5 mM, short openings are very rare although almost all receptors are desensitized (Parzefall et al. 1998).
Outlook
The optimized techniques used here allowed quantification of very short components in recordings from nicotinic ACh receptors. Unfortunately the interpretation of the additional kinetic information remains unsatisfactory and the aim, stated in the introduction, could not be reached. With more complex mechanisms estimates for all free parameters will be even more difficult to obtain. Thus further experimental work, perhaps combining techniques for fast solution exchanges (Franke et al. 1993) and time resolution optimized recordings from true single channel patches may be necessary. Ultimately, one physically realistic functional mechanism should cover both, measured channel kinetics down to the briefest detectable events and constraints of protein structure.
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