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Effect of Potential on Single-channel Gating
2 Department of Economical Cybernetics, Taras Shevchenko National University, Kiev, 01033 Ukraine
3 Pharmacology and Clinical Pharmacology Basic Medical Sciences, St. George's Hospital Medical School, London SW17 ORE, UK
Address correspondence to Alexander V. Zholos, Laboratory of Molecular Pharmacology of Cellular Receptors and Ion Channels, A.A. Bogomoletz Institute of Physiology, Kiev, 01024 Ukraine. Fax: (044) 256 2000; email: zholosa{at}sghms.ac.uk
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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S. Since in the latter case G-proteins are permanently active, it is concluded that the cationic channel is the major determinant of its own gating, similarly to the KACh channel (Ivanova-Nikolova, T.T., and G.E. Breitwieser. 1997. J. Gen. Physiol. 109:245–253). Analysis of adjacent-state dwell times revealed connections between the states that showed features conserved among many other ligand-gated ion channels (e.g., nAChR, BKCa channel). Open probability (PO) of the cationic channel was increased by membrane depolarization consistent with the prominent U-shaped I-V relationship of the muscarinic whole-cell current at negative potentials. Membrane potential affected transitions within each closed-open state pair but had little effect on transitions between pairs; thus, the latter are likely to be caused by interactions of the channel with its ligands, e.g., Ca2+ and G
o-GTP. Channel activity was highly heterogeneous, as was evident from the prominent cycling behavior when PO was measured over 5-s intervals. This was related to the variable frequency of openings (as in the KACh channel) and, especially, to the number of long openings between consecutive long shuttings. Analysis of the underlying Markov chain in terms of probabilities allowed us to evaluate the contribution of each open state to the integral current (from shortest to longest open state: 0.1, 3, 24, and 73%) as PO increased 525-fold in three stages.
Key Words: Markov chain • channel kinetics • G-protein • carbachol • smooth muscle
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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). Appropriate models have been developed as an extension of an early scheme of del Castillo and Katz (1957) that now provide a physically realistic picture of how ligand binding could change receptor-conducting conformation (Colquhoun and Sakmann, 1998). These reaction mechanisms, also often referred to as kinetic models of ion channels, allow a physically meaningful interpretation of single-channel activity and a useful explanation of the whole-cell current behavior and physiological function (Pallotta, 1997).
The much larger and diverse superfamily of seven transmembrane spanning receptors produce signals to a variety of effectors, e.g., enzymes and ion channels, via G-proteins (for reviews see Gilman, 1987; Wickman and Clapham, 1995). However, much less is known about the interactions and mechanisms which lead to channel opening in these complex multi-component signaling systems.
One level of complexity arises due to the multisignaling nature of G-protein–coupled receptors (GPCRs), since both G-GTP and Gß subunits may have separate, sometimes opposite, functions (Hamm, 1998). An added level of complexity arises as multiple receptor subtypes for the same agonist are often coexpressed in the same tissue. These can converge to activate the same channel in a subtype-specific manner depending on which type of G-protein is involved.
The muscarinic receptor–operated cationic channel, the subject of our present study, exemplifies such complexity of GPCR signal transduction. This cationic channel is widely expressed in various smooth muscle tissues such as the gastrointestinal tract and airways, where it mediates the excitatory action of acetylcholine (ACh). Two muscarinic receptor (mAChR) subtypes, M2 and M3, are colocalized in the same tissues (Eglen et al., 1996). We found that although M2 receptor activation primarily causes activation of the channel, the M3 subtype plays an important "permissive" role (Bolton and Zholos, 1997; Zholos and Bolton, 1997). Thus, both receptor subtypes control the channel opening. Further studies have shown that, consistent with early reports of the inhibitory action of Pertussis toxin treatment on the mAChR cationic current (mICAT) (Inoue and Isenberg, 1990a; Komori and Bolton, 1990), the channel is coupled to the muscarinic receptor via Go protein (presumably an M2 effect) (Yan et al., 2003), whereas PLC inhibition also abolishes mICAT (presumably an M3 effect) (Zholos et al., 2004).
Furthermore, intracellular Ca2+ was shown to have both a permissive and a potentiating effect on channel opening (Inoue and Isenberg, 1990c; Wang et al., 1997); hence, a rise in [Ca2+]i is necessary but not sufficient to activate mICAT. This results in a close, almost mirror, correlation between [Ca2+]i level and whole-cell current amplitude (Pacaud and Bolton, 1991; Komori et al., 1993; Gordienko et al., 1999).
Moreover, the current shows an intrinsic voltage-dependent behavior (Benham et al., 1985; Inoue and Isenberg, 1990b), such that in the presence of the agonist membrane hyperpolarization can strongly attenuate the current, but in its absence even strong depolarization does not produce any detectable channel activation. A close and intriguing relationship exists between G-protein control and intrinsic voltage dependence of this channel. Thus, increasing the agonist concentration shifts the activation curve up to 40 mV negatively (Zholos and Bolton, 1994), whereas desensitization has an opposite effect (Zholos and Bolton, 1996). Membrane depolarization, in turn, has a strong sensitizing effect on channel opening (e.g., shifting the membrane potential from –50 to 50 mV reduces the carbachol EC50 value 20-fold), reduces latency of the response from 380 to 160 ms, and accelerates on-rate and decelerates off-rate during fast agonist application and removal (Bolton and Zholos, 2003).
These various observations at present are hard to reconcile within a general mechanism. The major obstacle is the lack of information on single-channel gating. In earlier reports, this cationic channel proved to be difficult to investigate in excised membrane patches. Therefore, channel activity was resolved in the so-called "magnified whole-cell mode" (Inoue et al., 1987; Kang et al., 2001), which provided initial valuable information on channel conductance, selectivity, and voltage dependence of its open probability (PO), but channel kinetic states still needed to be studied at higher resolution. At present only a simplified two-state model is available (Inoue et al., 1987; Inoue and Isenberg, 1990b).
Here, we sought to answer—by studying single cationic channel kinetics—the many questions that arise due to the complex nature of whole-cell mICAT. This analysis was significantly facilitated by the possibility of obtaining outside-out patches in which only one channel was present. Our analysis revealed that channel activity was much more complex than previously thought, e.g., at least four open and four closed states exist with additional flicker and inactivated states. The molecular structure of this cationic channel remains incompletely defined but it may be a homo- or a heteromultimer of transient receptor potential (TRP) proteins (Walker et al., 2001; Lee et al., 2003). For this novel family of channel proteins the gating stimuli and mechanisms remain largely unknown (Clapham, 2003). We found that cationic channel activity consists of bursts of short, intermediate, and long openings with strong correlations between adjacent states. Based on this, we also tested some predictions for the whole-cell mICAT behavior.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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, 1997).
Whole-cell and single-channel currents were recorded at room temperature using borosilicate patch pipettes of 1–3 and 3–5 M
, respectively, and an Axopatch 200B (Axon Instruments, Inc.) voltage-clamp amplifier. For single-channel recordings pipettes were coated with Dow Corning R-6101 elastomer. Current noise was <0.25 pA (rms, 5 kHz bandwidth). Voltage-clamp pulses were generated and data were captured using a Digidata 1322A interfaced to a computer running the pClamp 8 program (Axon Instruments, Inc.). Currents were filtered using the 4-pole low pass Bessel filter of the patch-clamp amplifier at 1 or 2 kHz in whole-cell and single-channel recordings, respectively, and sampled at 48 kHz for storage on a digital tape recorder (DTR-1204; Biologic Science Instruments). In whole-cell experiments series resistance was compensated by 80%. For illustrations, single-channel recordings were digitally filtered (200 Hz lowpass Gaussian filter) and sampled at 500 Hz. Extended portions of the traces that illustrate brief events are shown at the original resolution.
mICAT was activated by applying carbachol at 50 µM (submaximal concentration, compare with the EC50 value of 7.6 µM; Zholos and Bolton, 1997) or by intracellular application of GTPS at 200 µM by adding it to the pipette solution in order to activate G-proteins directly, bypassing muscarinic receptors.
Solutions and Chemicals
The external solution in which cationic current was recorded consisted of (in mM): CsCl 120, glucose 12, HEPES 10, pH adjusted to 7.4 with CsOH (total Cs+ 124 mM). Pipettes were filled with the following solution (in mM): CsCl 80, adenosine 5'-triphosphate magnesium salt (ATP) 1, creatine 5, guanosine 5'-triphosphate lithium salt (GTP) 1, D-glucose 5, HEPES 10, BAPTA 10, CaCl2 4.6 ([Ca2+]i clamped at 100 nM), pH adjusted to 7.4 with CsOH (total Cs+ 124 mM). GTP was omitted when guanosine 5'-O-(3-thiotriphosphate) (GTPS) was added to the pipette solution to activate mICAT directly. The Cs+ solutions were used to block currents through potassium channels.
Collagenase (type 1A), adenosine 5' triphosphate (ATP, magnesium salt), guanosine 5' triphosphate (GTP, lithium salt), guanosine 5'-O-(3-thiotriphosphate) (GTPS, tetralithium salt), creatine, N-2-hydroxyethylpiperazine-N'-2-ethanesulphonic acid (HEPES), 1,2-bis(2-aminophenoxy)-ethane-N,N,N',N'-tetraacetic acid (BAPTA), N-methyl-d-glucamine (NMDG), and carbamylcholine chloride (carbachol) were obtained from Sigma-Aldrich. All other chemicals were from BDH Laboratory Supplies (AnalaR grade).
Data Analyses
Data were analyzed and plotted using pClamp (Axon Instruments, Inc.) and MicroCal Origin software (MicroCal Software, Inc.). For kinetics analyses, the presence of one channel in the membrane patch could be confidently judged since PO was high (0.43 ± 0.06 in 11 patches selected for kinetics analysis) and no double openings were seen. Quantitatively, the probability of our runs of single openings if there were actually two channels present was estimated according to the equation given by Colquhoun and Hawkes (1995):
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= (1 – PO)/(1 – PO/2), and no is the number of single openings. In the above 11 patches the maximum probability of more than one channel present was of the order 10–20. Single-channel events were identified on the basis of the half-amplitude threshold-crossing criteria. Transitions <0.16 ms (e.g., rise time for 2 kHz filter, see Fig. 3 A, c) were ignored. This was aimed mainly to ensure consistent time resolution for both openings and shuttings. Imposed resolution in principal makes allowance for missed events but this was not used. Thus, "open" and "closed" intervals were "apparent" intervals.
Histograms of open and closed durations were constructed conventionally as distributions of the logarithm of duration (in ms) (20 bins per decade) with exponential components fitted by the method of maximum likelihood (Colquhoun and Hawkes, 1995). The frequency density and fitted functions were plotted after a square root transformation. The number of probability density function components was determined using the automatic "compare models" routine of the pClamp software at the confidence level of 0.99. Current amplitude histograms were fitted with Gaussian functions. Although four closed states of the channel exist, no burst analysis was done since burst definition would be dubious (e.g., 
10 or more-fold difference in the mean closed times is required).
PO was determined from idealized traces as the ratio of the sum of all open durations to the total trace duration. All other analysis (correlations, durations of adjacent dwell times, opening frequency analysis, and analysis of channel activity over intervals of certain duration) was done using custom programs.
Cationic conductance activation curves, or PO values measured at different test potentials, were fitted by the Boltzmann equation in the following form:
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For each particular state the probability of being in that state, Pj, was calculated using the following equation:
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j is its time constant (mean dwell time). Values are given as the means ± SEM; n represents the number of measurements. To determine the statistical significance of differences between the means an ANOVA or a t test were used. Differences were judged to be statistically significant when P < 0.05.
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RESULTS |
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S present) three types of ion channels have been identified in cell-attached (n = 89) and outside-out patches (n = 123) based on the differences in their unitary conductances, kinetics, and voltage dependence. Their ion selectivity properties were not studied in detail (see Inoue et al., 1987; Kang et al., 2001), but it was verified that their unitary currents depended on the Cs+ (NMDG+ substitution experiments) but not the Cl– (methanesulfonate substitution) gradient. Also, unitary currents through the three types of channels reversed close to the caesium equilibrium potential, 0 mV. Using Cs+ as the main charge carrier suppressed currents trough K+ channels while various TRP channels are similarly permeable to Na+, K+, and Cs+ (for review see Nilius, 2003).
Mean single-channel conductances at potentials around –50 mV were 10.3 ± 0.2 pS (n = 55), 57.1 ± 7.0 pS (n = 52), and 131.8 ± 2.6 pS (n = 51). These three types of cationic channels were identified as channels gated by muscarinic receptor stimulation as Fig. 1
shows. They were also activated by G-proteins since intracellular GTPS (without agonist application) induced similar channel activation (e.g., Fig. 2).
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7 pA in maximal size produced by 130-pS channel openings (similar to that shown in Fig. 1 B); longer and hence better defined events of 3.1 pA in size (i.e., 62-pS conductance given the membrane potential of –50 mV) and small openings visible during a few periods of low activity as shown magnified in the inset. The latter were 0.7 pA in size (i.e., 14-pS channel conductance). Fig. 1, C and D, further illustrates that the activity of the 57-pS channel recorded in an outside-out patch (formed after bath 50 µM carbachol application to the whole cell) was terminated upon agonist withdrawal (Fig. 1 C) or could be reversibly inhibited by the M2-AChR–selective antagonist tripitramine (Fig. 1 D). These observations support the idea that the channel was primarily gated by the M2 receptor activation (Bolton and Zholos, 1997; Zholos and Bolton, 1997). In the experiment of Fig. 1 A the 130-pS channel activity lasted 17 min, but it was fairly quickly lost in outside-out patches (on average within 81 ± 19 s, n = 18; see top trace in Fig. 1 B showing two channels present initially which cease to open 164 s after carbachol application). This suggests the importance of some freely diffusible second messenger(s). 130-pS channel activity consisted of clear bursts of very brief openings as an expanded trace segment in Fig. 1 B shows, i.e., in this patch at –50 mV mean open times and relative proportions of two fitted exponential components were 0.75 ms (0.69) and 3.53 ms (0.31) resulting in a low PO, typically <0.1. At positive potentials PO somewhat increased while single-channel conductance decreased (Fig. 1 B, bottom right), which resulted in average patch current being an almost linear function of voltage.
In contrast, the activity of the 10- and 57-pS channels lasted tens of minutes after patch excision (Figs. 2, 3 A, 9, and 11 A) suggesting that freely diffusible second messengers are not so important for their gating. However, the 57-pS channel could rarely be activated in cell-attached patches (4 in 77) with carbachol in the pipette and/or in the bath (Fig. 1 A), or by carbachol when applied after an outside-out patch was formed (1 in 11).
When a cell-attached patch was formed after cell dialysis with GTPS (e.g., by using double-patch configuration, or by withdrawing a first patch pipette containing GTPS and creating an on-cell patch on the same cell using another pipette) then the 57-pS channel activity was more likely (4 out of 12). A similar proportion was also observed when an outside-out patch was pulled after the whole-cell current had fully developed in response to 50 µM carbachol application (15 out of 50). Thus, it appears that important signaling links need to be established in the whole cell that then remain after patch excision. It is less clear why so few patches with channel activity were obtained in the conventional cell-attached configuration. Kang et al. (2001) noted the same difficulty (2 successful recordings out of 121 trials in their experiments).
In the present work the behavior of the 57-pS channel was analyzed in detail. We have found that this channel has properties that account for the major part of the whole-cell current in the negative range (see below); thus, from the standpoint of the physiological function of the muscarinic cationic conductance this channel type is the most important.
61% of outside-out patches formed after whole-cell mICAT activation were blank (33 out of 62 in case of GTPS and 35 out of 50 in case of carbachol stimulation), 19.5% had one (12 out of 62 in case of GTPS and 10 out of 50 in case of carbachol stimulation), and the remaining 19.5% had multiple active 57-pS channels (from 2 to 7; 17 patches out of 62 in the case of GTPS and 5 patches out of 50 in the case of carbachol stimulation). In the latter case the probability of seeing 1,2,3...N channels simultaneously open followed a binomial distribution closely; thus, the channels gated independently of each other but at the same time they appeared to be clustered in the membrane.
Fig. 2
shows typical examples of single-channel currents activated by carbachol or GTPS in outside-out and cell-attached patches, as indicated. The membrane potential of outside-out patches was held at –40 mV; the same value was assumed for the cell-attached patch since the holding potential was set at 40 mV and the cell was dialyzed and then kept in a high-Cs+ solution that would zero its resting potential.
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Histograms of distributions of apparent closed and open times (20 bins per decade) measured in the experiment of Fig. 3 A are shown in Fig. 4 A. These were fitted with the sum of four exponential components (continuous line, the components are plotted separately). In this and other similar figures mean dwell times and relative areas, which are equivalent to frequency probabilities of being in a particular state, are indicated near each component. Thus, as long as different mean dwell times may be regarded as reporters of different conformations of the channel protein there are at least four open and four closed states of the channel. A model with four open and four closed states will be assumed and used as a basis for further analysis (Scheme I)
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, whereby ligands interacting with the channel increase its open probability in three stages. The overall structure of cationic channel Markov chain is similar to some other ion channels, such as nAChR (Scheme V given by Colquhoun [1998]), which includes spontaneous channel openings in the absence of agonist), BKCa channel (Scheme II given by Cox et al. [1997]), or hyperpolarization-activated HCN channel (Altomare et al., 2001).
To reveal adjacent states in the model (Scheme I) durations of adjacent closed and open states were measured. Qualitatively, the plot of open intervals versus adjacent shut time in Fig. 4 B shows that with very few exceptions (6 out of 4,506) there is a strong inverse relationship between the duration of openings related to closed events. This is true for both next and previous open durations as illustrated in the insets. Quantitatively, these correlations were evaluated by measuring mean time of open events adjacent to closed durations in four ranges that corresponded to the time constants of four components of the closed time distribution (indicated by triangles in Fig. 5
, the chosen range was ±5 bins around the corresponding mean closed time) as suggested by McManus et al. (1985). The differences between mean open times were statistically significant (note that different symbols show data calculated separately for previous, next and both adjacent open intervals). The histogram shown by the dotted line illustrates the correlations over the entire range, without any assumption as to the number of channel states.
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) of open and shut states was greater than unity, which imposes a restriction on the Markov chain such that no single state should exist that, if deleted, will separate the open states from the shut states (see more about the origin of correlations in Colquhoun and Hawkes, 1995).
The possibility was considered that patch excision might have altered channel gating, for example due to cytoskeleton deformation or disruption as already mentioned in connection with difficulties of activating the channel in certain patch-clamp configurations. Alternatively, such alterations could arise due to the loss of some important diffusible cellular second messengers. Thus, control experiments were performed where mICAT was activated by intracellular application of GTPS (see Fig. 13 A as an example) and as soon as mICAT reached a peak amplitude the patch pipette was removed and an on-cell patch was formed using a second pipette filled with the standard Cs+ external solution. Since GTPS activates G-proteins almost irreversibly, channel activity could be recorded in the cell-attached configuration even though the agonist was absent.
Fig. 6
shows the results of the analyses of channel activity recorded under these conditions (original trace segments obtained from this patch were shown in Fig. 2, bottom pair). Channel conductance was 59 pS as estimated from the unitary current amplitude of 2.36 pA at a holding potential of 40 mV (membrane potential –40 mV). 13,861 events observed during 775 s were subject to the same analysis as described above. Exponential components in open and closed time distributions as well as their relative areas were very similar to those observed for the carbachol-gated channel in an outside-out patch (compare Figs. 6 A and 4 A; statistical tests presented in the Table I legend). An important conclusion that follows from this observation is: although channel PO is increased through its interaction with the Go-GTP molecule (Yan et al., 2003), likely by increasing the probability of transition toward the O4 state (see below) the channel possesses an intrinsic gating mechanism that kinetically remains the same whether Go is bound to the hydrolyzable GTP or to the much more stable GTPS (compare with similar observations in case of KACh channel by Ivanova-Nikolova and Breitwieser, 1997). In other words, bursts of long openings that account for the major part of mICAT (see below), and hence likely arise due to the interaction with activated Go-GTP, are not terminated simply because GTP is hydrolyzed and inactive Go-GDP is formed.
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From these results we conclude that the states are connected as shown in Scheme I (mean values from 11 patches are shown in Table I).
Cycling Behavior within Markov Chain of Cationic Channel
Many novel features of KACh channel in heart, such as four distinct modes of gating of the G-protein–gated KACh channel, were revealed by analysis of its PO and the frequency of openings after dividing a continuous record into consecutive segments of fixed duration (Ivanova-Nikolova et al., 1998). Thus, we have performed a similar analysis. Some of our results are consistent with the above study, but novel features were also found. Notably, while it was found that the KACh channel PO increases from mode 1 to mode 4 mainly because the channel opens progressively more frequently and for longer durations, cationic channel PO is mostly determined by cycles within the Markov chain (e.g., the number of long open states, OL, encountered before it enters a long shut state, CL).
Fig. 7
shows PO measured over 5-s intervals from the record in Fig. 3 A. Mean frequency of channel openings was 13.8 s–1, thus on average 69 openings were included in each interval yet there was a significant scatter of PO values in the range of 0.005–0.89. Since the O4 state generates 73% of the integral current (Table I) its frequent occurrence could explain periods when PO was high while frequent occurrence of the C1 state might explain periods when PO was very low. All occurrences of C1 and O4 states given the overlapping distributions are not possible to quantify but a phenomenon known as length-biased sampling is known (Colquhoun and Hawkes, 1995). This arises due to a positive skew of the exponential distribution; as a result above-average dwell times are fewer in number but make a greater functional contribution. Thus, we restricted our analysis to include only OL and CL states defined, respectively, as openings >79 ms and closings longer than 371 ms (based on distributions of Fig. 4 A). These are plotted at the top of Fig. 7. Their total contribution to the trace duration amounted to 24.3% for the CL state and 33.6% for the OL state. Considering the areas under exponential components, it can be calculated that 95.2% of CL belong to the C1 state and 97.1% of OL belong to the O4 state. Although such definitions include only 37% of C1 and O4 states because of the above-mentioned phenomenon CL and OL account for 74% of the total time occupied by C1 and O4 states, respectively.
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). In contrast, as shown in Fig. 8
A (squares) there was a close relationship between PO measured in 5 s sequential intervals and the number of visits to the OL state between consecutive visits to the CL state in the same intervals. The number varied from 0 (e.g., two CL states with no OL in between) to a maximum of 45 (i.e., 45 openings >79 ms occurred before a closing longer than 371 ms; 39 was the average value). The mean value of the number of OL openings after one CL was 5.5 ± 0.9 (n = 99).
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The mean open and closed times were also measured over the same 5-s intervals and these values are plotted against PO in Fig. 8 C, which further revealed that a decrease in the mean closed time (closed circles) makes a more significant contribution. Finally, the histogram of PO measured in 5-s consecutive intervals (Fig. 8 B) revealed that (using the same terminology as for the KACh channel) modal preferences of gating of the cationic channel exist that are not so much in the frequency domain but rather in the open probability domain (which in turn is related to the number of OL states between consecutive CL states). Thus, three modes of PO can be visualized with mean values and areas under Gaussian curves of 0.14 (16%), 0.45 (70%), and 0.72 (14%) (Fig. 8 B). This graph shows that channel gating is highly heterogeneous even if the trace is arbitrarily divided into consecutive 5-s segments (as mentioned, these include on average 69 openings in each interval). According to the mean parameters in Table I four modes should exist with characteristic PO values of 0.001, 0.085, 0.909, and 0.996 and fractional times of 0.43, 0.13, 0.12, and 0.32, respectively. However, these are not seen in Fig. 8 B because the channel changes its gating mode frequently (as evident from the occurrences of OL and CL in Fig. 7) and dividing the trace in a mode-specific segments has the same problem as burst analysis namely that channel state cannot be unequivocally identified from burst events (see MATERIALS AND METHODS).
It is interesting to note that if PO was measured over shorter intervals (e.g., 400 ms as for KACh channel) then two major peaks at PO = 0.03 and PO = 0.98 appeared while the peak at PO = 0.45 disappeared, suggesting a better discrimination between the modes. Constructing a moving average of these data points by symmetrical averaging of 15 adjacent points revealed a striking cycling behavior with a rather constant period between the peaks of 20 s (Fig. 8 D, top trace). It can be noted that the moving average filter is optimal for random noise reduction (e.g., by a factor of 151/2 in Fig. 8 D; top trace) while keeping the sharpest step response and thus is ideal for analyzing signals in the time but not in the frequency domain (Smith, 1997). Two observations suggested that the oscillations of PO were not a data filtering artifact. First, averaging PO over a window of twice the size did not noticeably reduce their frequency (bottom trace in Fig. 8 D). Second, in some patches, particularly when the channel had a lower mean PO, the cycling behavior could be visualized in the raw data (e.g., Fig. 9
B). Peaks of PO arise from runs of long openings (see Fig. 8 A and Fig. 9 A, inset) that could be related to periodic channel interaction with Go-GTP (or, less likely, other ligands), but this hypothesis needs further tests.
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Plotting PO measured in consecutive 5-s intervals versus time revealed even better defined oscillations (Fig. 9 B, note that raw data are plotted, i.e., no moving average was used). Analysis of all 11 patches studied showed that the period between peaks of PO well correlated with the mean PO value which ranged from 0.18 to 0.78 (R = –0.9; P = 0.0002).
Fig. 9 C illustrates a complete sequence of changes in channel gating kinetics during a single PO oscillation indicated by the horizontal bar in Fig. 9 B (i.e., continuous 60-s record divided into 5-s segments). Clearly, the channel starts gating in the C1-O1 pair of states (two top traces), then periods of long openings with associated brief shuttings appear resulting in a gradual PO rise in Fig. 9 B (e.g., mixed gating in several modes during one segment). Finally, the channel enters an 15-s long period of C4-O4 gating resulting in a PO value close to 1.
In conclusion, activity of this channel at constant stimulation is heterogeneous because of alternating periods of low and high PO such that its mean PO is encoded by the frequency of PO oscillations. Equating OL with the O4 state, and the CL with the C1 state, will produce under- and overestimates, respectively, of the true number of O4 and C1 states; the net effect on the results may be not too different from the values shown.
The Origin of Voltage Dependence of mICAT
The whole-cell current displays a distinctive I-V relationship that is prominently U-shaped at negative potentials, whereas around the reversal potential there is another characteristic region of double rectification (Fig. 13 B). At the time this was discovered this seemed a unique property of mICAT (Benham et al., 1985), but now it is recognized as a common property of cationic channels formed by TRP proteins, particularly in the case of TRPC3 to TRPC7 (for review see Clapham, 2003). As was already mentioned, it is likely that the muscarinic cationic channel also belongs to this group. The origin of this complex I-V relationship is not so clear. Previous studies have established that the voltage dependence of PO explains the U-shaped I-V relationship in the negative potential range, whereas around 0 mV and at more positive potentials channel openings and closings could not be resolved even in the absence of intracellular Mg2+ or polyamines (Inoue et al., 1987; Kang et al., 2001). Thus, the aim of the next series of experiments was to discover which changes in channel kinetics are responsible for the voltage dependence of PO, and through this to find out which transitions in the underlying Markov chain are sensitive to membrane potential.
Fig. 10 A shows an example of open and closed times histograms obtained by observing cationic channel activity in an outside-out patch which was exposed to carbachol and recorded either at –40 mV (408 s, mean PO = 0.59) or at –80 mV (334 s, mean PO = 0.34). Fitting exponential components revealed that the decrease of PO evoked by membrane hyperpolarization was associated with changes of the mean dwell times (particularly in the case of C1 and C2 states), but at the same time there was only a small net redistribution between the states, i.e., relative areas of the components changed little.
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S (see examples in Fig. 11
A). Analysis of exponential components of closed and open time distributions revealed that the time constants showed voltage dependence while the relative areas (e.g., probability of being in one of eight closed or open states) were little affected; the latter showed some scatter but there was no particular voltage-dependent trend (Fig. 10 B, bottom).
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Unitary and mean patch currents are plotted versus test potential in Fig. 11 B (squares and circles, respectively). These I-V relationships are similar to, respectively, instantaneous and steady-state I-V relationships of the whole-cell mICAT (Benham et al., 1985; Inoue and Isenberg, 1990b; Fig. 13 B). Corresponding conductance curves denoted by the same symbols are shown in Fig. 11 C. These show that the major factor that accounts for the decrease of mICAT conductance in the range 0–30 mV is an apparent reduction of both unitary current amplitude and PO as a result of very short but frequent shuttings (Figs. 11 A and 12 A). The combined effect produces an overall N-shaped cationic conductance curve (Fig. 11 C, circles) that is similar to the whole-cell activation curve (Fig. 13 C).
Fig. 12 A shows the voltage dependence of PO described by the Boltzmann function (Eq. 2) with the parameters indicated. Open symbols indicate the values that were estimated from all-points amplitude histograms since a channel event search algorithm could not be used in the presence of channel flicker block. Thus, at positive potentials unitary amplitudes (Fig. 11 B) and PO values (Fig. 12 A) were evaluated from, respectively, peaks and areas of two overlapping Gaussian curves fitted to all-points amplitude histograms. Mean parameters describing the voltage dependence of PO were as follows: PO maximal value 0.81 ± 0.09, potential of half-maximal activation –83.9 ± 10.7 mV and slope factor –19.9 ± 4.0 mV (n = 4). Whole-cell cationic conductance was also examined just before patch formation by applying a slow 6 s voltage ramp from 80 to –120 mV. Corresponding parameters were –89.0 ± 7.2 mV for the V1/2 value and –19.0 ± 1.5 mV for the slope. Paired t test (two-tail) showed no difference between single-channel and whole-cell current voltage dependence (P = 0.24 in case of the V1/2 value and P = 0.81 in case of the slope factor; n = 4). Moreover, when the V1/2 values were analyzed there was significant correlation (P < 0.001) between single channel and whole-cell data. This was absent for the slope factor (P = 0.34).
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S-induced current (ranged from –63 to –105 mV; n = 48).
Two factors that determined the change in PO when membrane potential was changed were an increase of the mean open time as well as a parallel decrease of the mean closed time (Fig. 12, B and C). For both mean dwell times there was an e-fold change per 24 mV, similar to the slope factor of the PO voltage dependence.
An important conclusion emerges from this analysis. In the Markov chain of the cationic channel shown in Scheme I all the vertical transitions between adjacent closed and open states are voltage dependent, but there is little horizontal redistribution between the states when membrane potential is changed. Thus, horizontal transitions are likely to be governed by ligands that interact to open this channel (see DISCUSSION) and these ligands need not interact with the channel in a voltage-dependent manner.
Markov Chain Predictions for the Whole-cell Current Behavior
A system with states and connections as shown in Scheme I has a substantial potential for shifting behavior. This was previously analyzed in detail for the BKCa channel that has 10 main "condensed" states (Scheme II of Cox et al., 1997). An important analogy is that vertical transitions are voltage dependent, whereas horizontal transitions are ligand but not voltage dependent. Although ligands are different with regard to the mechanisms of their interactions with the channel, in both cases PO is increasing when the gating shifts from left to right simply because more heavily contributing O2, O3, and O4 states generate progressively longer openings. Thus, a roughly parallel negative shift of the activation curve is to be expected according to the formalism of Eq. 4a given by Cox et al. (1997) for BKCa channel:
 | (4) |
Fig. 13
A illustrates one of our standard whole-cell experiments designed to activate cationic channels directly by intracellular application of GTPS, which was usually followed by patch excision after mICAT reached a maximum. In this experiment, however, slow voltage ramps were applied at 20-s intervals starting immediately after break-through (Fig. 13 A, triangle). As can be seen in Fig. 13 B, pronounced changes of the shape of the I-V curve accompanied current development. These were translated into conductance curves plotted in Fig. 13 C and fitted by the Boltzmann function (Eq. 2) in the range –120 mV to about –40 mV. Superimposed fitted functions were extended to 80 mV, which allowed evaluation of the effect of the flicker block of the channel described above but only the unblocked part of each trace was included in the fit range. There was, as expected, a roughly parallel negative shift of the activation curve during the time course of mICAT development that, in turn, was presumably due to the accumulation of GTPS-bound subunits of G-proteins (note that GTP was not added to the pipette solution when GTPS was used). A similar phenomenon exists when carbachol concentration is increased but the opposite shift is seen during desensitization in the absence of GTP (Zholos and Bolton, 1994, 1996). For 13 fitted traces the slope factor was –19.7 ± 1.7 mV, very close to the value of –19.9 ± 4.0 mV (n = 4) describing the slope of PO voltage dependence (Fig. 12 A). The V1/2 value shifted 40 mV in the negative direction simultaneously with the increase of the maximal conductance (Fig. 13 D). It can be noted that in this example the V1/2 shifted negatively by 20 mV more compared with the typical value of –83 mV but the starting value was also somewhat negative.
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