Opening and Closing Transitions for BK Channels Often Occur in Two

Transcription

1 72 Biophysial Journal Volume 65 August Opening and Closing Transitions for BK Channels Often Our in Two Steps via Sojourns through a Brief ifetime Subondutane State William B. Ferguson, Owen B. MManus, and Karl. Magleby Department of Physiology and Biophysis R-43, University of Miami Shool of Mediine, Miami, Florida USA ABSTRACT Single hannel urrents were reorded with miroseond time resolution from large-ondutane aliumativated K+ hannels to examine the details of the opening and losings transitions. Analysis of averaged losing transitions indiated that the initial average ondutane step for losing was to the 9-95% losed hannel urrent level. Averaged brief losings (-5 ps) reopened from the initial 9-95% level, whereas averaged longer losings (>3 ps) losed ompletely from this level over the next 5-1 ps. The 9-95% initial losed level in the averaged urrent reords resulted typially from the average of both omplete and partial losings. From 45-8% of the initial losings were omplete and 2-55% were to brief lifetime (-5 ps) subondutane levels at 65-9% of the ompletely losed level. Averaged opening transitions were typially mirror images of averaged losing transitions. To extend the analysis to the very brief ondutane hanges that underlie the flikers of the single hannel urrent toward the losed urrent level, flikers, brief losings, and longer losings were averaged separately and their slopes ompared. The slopes were similar (within the 3% resolution of the method), suggesting similar initial ondutane steps. Similar initial losing properties for both the briefer and longer losings would be expeted if the hannel first passed through the kineti and subondutane states assoiated with the briefer losings (inluding flikers) before entering the longer losed states. Suh transitions would provide an explanation for the observation that openings and losings often our in two steps. NTRODUCTON n 1977 Colquhoun and Hawkes predited that ativation of a hannel by an agonist should produe several openings in quik suession. Suh bursts of ativity were soon observed at the single hannel level (Nelson and Sahs, 1979; Colquhoun and Sakmann, 1981; Barrett et al., 1982). While bursts of ativity are now aepted as a harateristi feature of single hannel reordings, the nature of the brief losings is unlear. Some of the brief losings are omplete, others are to subondutane levels, and still others, often the majority, are so brief that they appear only as flikers of the open hannel urrent toward the losed urrent level (Barrett et al., 1982; Auerbah and Sahs, 1983, 1984; Colquhoun and Sakmann, 1985; Terman et al., 1992). Flikers ould arise from brief losings to the zero urrent level (omplete losings) or from brief losings to subondutane levels (partial losings). As detailed by Colquhoun and Sigworth (1983), it would be diffiult to distinguish between these two possibilities for any given fliker, due to the limited frequeny response and inherent noise of single hannel urrent reords. Nevertheless, it is important to establish whether flikers, on average, arise from partial or omplete losings, as different ondutane levels suggest different losed onformations. n this paper we examine whether flikers lose to the same level as longer losings by omparing the slopes of Reeived for publiation 9 November 1992 and in finalform l9april Address reprint requests to K.. Magleby.. B. MManus' urrent address is Department of Membrane Biohemistry and Biophysis, Merk Researh aboratories, P.. Box 2, Rahway, NJ by the Biophysial Soiety /93/8/72/13 $2. averaged flikers to the slopes of averaged longer losings. Similar slopes (within the 3% resolution of the method) were found for flikers and longer losings, suggesting that, on average, flikers and longer losings lose initially to similar ondutane levels. An unexpeted finding of this study was that the average initial ondutane level for flikers, brief losings, and longer losings was not the ompletely losed level, but a subondutane level at 9-95% of the ompletely losed level. Averaged flikers and brief losings then reopened from this subondutane level, and averaged longer losings then losed ompletely from this subondutane level over the next 5-1 ps, giving rise to a reep in the urrent to the baseline after the initial rapid losing step. Averaged openings were typially mirror images of averaged losings, displaying a reep before the rapid opening step. These results raise the possibility that the kineti state that underlies the flikers and brief losings (fliker state) may be assoiated with the brief duration subondutane levels. The two-step losings and openings may then result when transitions to and from the longer losed states inlude sojoums through the fliker state with its assoiated subondutane levels. A preliminary report of some of these findings has appeared (Ferguson et al. 1992). METHODS Preparation and reording Single-hannel urrents flowing through large-ondutane Ca2+ ativated K+ hannels (Marty, 1981; Pallotta et al., 1981) in surfae membranes of primary ultures of rat skeletal musle were reorded with the path lamp tehnique (Hamill et al., 1981). Reordings were made from exised "insideout" pathes of membrane, with the normal inner membrane surfae of the path exposed to solutions in a miro-hamber, allowing solution hanges (Barrett et al., 1982). The experiments for the majority of data presented in

2 Ferguson et al. Flikers in BK Channels 73 the paper, inluding the data for all the figures, exept Fig. 5, were olleted over an 18-month period of time using a single path lamp amplifier arefully adjusted and onsistently heked to provide appropriate responses to square wave inputs. Earlier experiments extending bak 6 years examined amplitude-duration plots (suh as Fig. 5) and slope omparisons. The results from the earlier experiments were onsistent with the more reent experiments and have been inluded. Analyzed single hannel data have been reorded under a variety of experimental onditions. n some experiments EGTA (typially 1 mm) was used to buffer the free Ca2l onentration (details in MManus and Magleby (1988)). TES buffer (N-tris(hydroxymethyl)methyl-2-aminoethanesulfoni aid) 2-5 mm was used in all solutions to hold the ph at 7.. Data were olleted with either (symmetrial) KC on both sides of the membrane, or with asymmetri KC solutions to inrease the amplitudes of the single hannel urrents, as indiated in the figure legends, where "extraellular solution" refers to the solution in the path pipette and "intraellular solution" refers to the solution at the inner membrane surfae of the exised path. While most data were olleted at room temperature (21-24 C), some experiments were performed at lower temperatures (5-1 C). The membrane potential of the exised pathes was held at either +2 or +3 mv, as indiated in the figure legends. Membrane potential is expressed in the onventional manner for intat ells, with the potential indiating the voltage at the normal "intraellular" side of the membrane. Currents were stored on FM tape during the experiment with a high frequeny utoff of typially 37 khz (Raal, Store 4DS). The tape speed was then slowed, typially times and the urrent filtered further for sampling by omputer. The effetive high frequeny utoff when onsidering the filtering from all omponents for experiments with symmetrial KC was typially in the range of 4-1 khz (-3 db, four-pole Bessel filtering). For experiments with high onentration gradients of K+ and resulting large urrents of 2-4 pa, the effetive high frequeny utoff for the analysis was khz, depending on the experiment, as indiated in the figure legends. Analysis A number of methods have been developed for the analysis of subondutane levels (Auerbah and Sahs, 1983, 1984; Colquhoun and Sigworth, 1983; Colquhoun and Sakmann, 1985; Sigworth, 1986; Patlak, 1988; Tyerman et al., 1992). We have used and extended some of these approahes, and devised new ones as neessary, to meet the requirements of our study. Analysis was performed on S 11/73 omputers (Digital Equipment Corporation, Marlboro MA) using DEC 11 BASC modified with assembler language programs written in the laboratory. Slowing of the tape speed for analysis allowed effetive sampling rates of 1-8,s (typially 1.5-3,us). The sampled data were then displayed, and losed intervals were seleted automatially, based on the time the single hannel urrent was above and below various threshold levels, as indiated in the figure legends. The automatially seleted intervals were then displayed to allow operator inspetion and possible exlusion of seleted intervals from the averaged displays. n some ases no intervals or only obvious artifats (suh as tape drop-outs) were exluded from the averaging. n others, intervals with obvious subondutane levels were either exluded or seleted, as indiated in the Results. Averaged intervals were aligued based on the time of rossing of a threshold level, usually set at about the midpoint of the observed urrent transition being examined. Numerial values of the slopes were alulated from the hange in urrent and time between sampled points. Aurate determination of slopes required that there be at least 1, and preferably 2, sampling points falling between the 1-9% open and losed urrent levels. nreased noise would be expeted to inrease error in estimation of slopes. For the experiments presented here the standard deviation of the urrent noise in the absene of hannel ativity was typially less than 4-1% of the single hannel urrent amplitude. n some experiments simulated single hannel urrent reords were analyzed to determine the resolution and possible artifats assoiated with the methods of analysis. Simulated urrents were obtained by first generating idealized single hannel urrents (assuming no noise and filtering) using models onsistent with the kinetis of the BK hannel (MManus and Magleby, 1991). These idealized urrents were then filtered, and filtered noise obtained from a path lamp amplifier or an experiment was added to give urrents with filtering and noise equivalent to the filtering and noise in the experimental urrents. n some of the simulated urrents brief losures were to ondutane levels other than zero. These simulated reords were then analyzed in the same manner as used for the experimental urrent reords. The perentage differene between slope A and slope B was alulated from: 1% (slope A - slope B)/slope A. For eah figure, plots with the same letter, suh as Bi and B2, are from the same hannel (experiment) or simulation, whereas plots with different letters, suh as A and B, represent data from different hannels or experiments. RESUTS AND DSCUSSON Flikers, losings to subondutane states, and omplete losings Fig. 1 shows single hannel urrent reords obtained from a large-ondutane Ca2+-ativated K+ (BK) hannel in an exised path of membrane from primary ultures of rat skeletal musle. The wide range of durations of the various open and losed intervals reflet the omplex kinetis of the gating proess arising from transitions among three or more open and five or more losed states (MManus and Magleby, 1988, 1991). t is also apparent that all losed intervals do not reah the same urrent level. Examples of flikers (F), a losing to a subondutane level (S), and omplete losings (C) are indiated. n ontrast to both the omplete losings and the losing to the subondutane level, flikers are of suh brief duration that they do not reah a steady-state level, due to the limited frequeny response of the single hannel urrent reord (Colquhoun and Sigworth, 1983). Beause flikers do not reah a steady-state level, it is not possible to determine by simple inspetion of the urrent reord whether they arise from omplete or partial losings. The reasons for this are shown in Fig. 2,A andb (Colquhoun and Sigworth, 1983; Colquhoun and Sakmann, 1985).Al and FF 1 ms 2 pa C 4 ms _ C F F FGURE 1 Currents reorded from a single large-ondutane Ca21- ativated K+ hannel in an exised membrane path. Extraellular solution: 5 mm KCl and 5 mm TES; intraellular solution: 2 M KCl, 5 mm TES, and 1,uM added Ca2. Single hannel urrent reords were filtered with an effetive high frequeny utoff of 4.9 khz and sampled by omputer with an effetive sampling interval of 4.7 p.s. The sampled data were then plotted by onneting the sampled points. The filtering was greater than used for analysis of the data (see Fig. 6A) so that the various types of losings would be learly visible: F, flikers; S, a losing to a subondutane level; C, omplete losings. Membrane potential, +2 mv.

3 74 Biophysial Journal Volume 65 August 1993 Ai C a. 6x loor 51 O Time a C a) a. 1 a v A2 _ 1:: U O_ 5 - u C -, f 82 - u g "...1 Time a. 6o O C C CD 11 a.q EC _ a) u 1 a) 6 4i *_" _l E.8-P C 1 OOr i r a a a. 4." a _e 5 a. :3 5- O A 1- --i FGURE 2 The slope of a filtered step response is proportional to the amplitude of the underlying urrent step. (Al and Bl) Current steps of different amplitudes and durations. (A2 and B2) Observed responses after filtering the urrent steps in Al and Bl, respetively, at an effetive high frequeny utoff of 6.2 khz (four-pole approximate Bessel filter). (Cl and Dl) Current steps of onstant duration and onstant amplitude, respetively. (C2 and D2) Filtered responses for the urrent steps in Cl and Dl, respetively. Note that the slopes of the filtered responses are proportional to the amplitudes of the urrent steps. The results an be saled to any level of filtering by multiplying the time by: 6.2 khz/(desired level of filtering in khz). Thus, for filtering with a high frequeny utoff of 3.1, 12.4, or 24.8 khz, eah division on the time base beomes.2,.5, or.25 ms, respetively.

4 Ferguson et al. Flikers in BK Channels 75 B present urrents through hypothetial single hannels that have instantaneous opening and losing transitions to both omplete (ontinuous lines) and partial (dashed line) losed levels. A2 and B2 present the urrents that would be observed with the level of filtering typially required to redue the urrent noise in a path lamp reording to aeptable levels. The durations of the omplete and partial losings were seleted to produe flikers that reahed 7% (A) and 35% (B) of the losed urrent level. n both A and B, flikers of idential amplitudes were produed by either partial or omplete losings. Thus, a harateristi other than amplitude must be used to determine whether flikers arise from omplete or partial losings. n both A and B, the fliker arising from the omplete losing (ontinuous lines) was found to have the steeper slope, suggesting that slope may provide a tool to distinguish omplete from partial losings. Al A2 4, a U OOr 5-5 ms 5% nitial slopes indiate the magnitude of the step losing That slopes might be used to determine whether flikers arise from omplete or partial losings is shown in Fig. 2, C and D, whih present urrent steps and filtered responses for hypothetial hannels. n C2 the slope of the observed fliker was proportional to the amplitude of the urrent step for the onstant duration losings shown in Cl. n D2 the slopes of the observed flikers were idential for the losings of different durations to the same (zero) urrent level shown in Dl. Thus, a omparison of the slopes of flikers to the slopes of omplete losings would indiate the losing level that produed the fliker. For example, if the slope of the fliker were 8% of the slope of a omplete losing, then the fliker would arise from an 8% losing (a losing to a subondutane state with a ondutane 2% of the open hannel ondutane). Simply stated, the slope is proportional to the magnitude of the urrent step, sine the rate of voltage hange aross an ative Bessel filter (or a apaitor for a simple filter) is proportional to the magnitude of the harging (or disharging) urrent. Due to noise in experimental single hannel urrent reords (Fig. 1), it is not possible to make aurate estimates of slopes from a single event. However, averaging a suffiient number of flikers and longer duration (omplete) losings should average out the noise so that omparisons in slope an be made. To test whether suh an approah is appliable, simulated single hannel urrent reords with filtering and noise similar to experimental urrents were generated and analyzed. For some simulated urrent reords the brief events that gave rise to flikers were omplete losings and in others they were partial losings to various ondutane levels. A brief segment of a urrent generated by simulation is shown in Fig. 3 Al. The entire urrent reord was then analyzed by sampling the simulated urrent reord and storing the digitized amplitude in a large file. The file was then searhed to find longer losings (whih were omplete) and flikers that just rossed the dashed line at the 65% losed level in Fig. 3 Al. (The fliker just before the.6-ms E A3 4, C a E U9. 1- a- 1 4, E. lo O. l.2 Tuime le /..1.2 FGURE 3 The slopes of the averaged flikers in simulated single hannel urrents are proportional to the amplitudes of the underlying urrent steps. (Al) A simulated single hannel urrent with noise and filtering (effetive filtering, 7 khz; effetive sampling interval, 3.5,is). For this reord the urrent steps underlying the briefest losures were 9% losures. (A2) Averaged flikers (dashed line) arising from omplete (1%) losings in a simulated urrent with filtering and noise have a losing transition slope that is similar (2.2% less steep) to that of averaged longer omplete losings (ontinuous line); 49 flikers and 166 longer openings were averaged. (A3) Averaged flikers (dashed line) arising from 9% losings have a transition slope 9.1% less than the slope for averaged longer omplete losings (ontinuous line); 47 flikers and 187 longer losings were averaged. For both A2 and A3 flikers with one to seven sampling points below the 7% threshold line were averaged for omparison to longer duration (>695 ps) shut intervals. losing would have been seleted from this reord.) The seleted flikers and omplete losings were then averaged separately and displayed (see Methods). Fig. 3 A2 presents results from an analysis in whih the flikers arose from omplete losings. n this ase the flikers (dashed line) had a slope similar to the longer omplete losings (ontinuous line). Fig. 3A3 presents results in whih the flikers arose from brief partial losings that were only 9%

5 76 Biophysial Journal Volume 65 August 1993 omplete. The redued slope of the flikers arising from partial losings when ompared to the slope of the longer omplete losings is evident. Measurements indiated that the slope for the flikers was 9% less than the slope for omplete losings, in lose agreement with the expeted redution of 1%. Analysis of a series of simulated single hannel urrent reords of the type shown in Fig. 3 indiated that estimates of the urrent steps from the slopes for averaged data were typially within 3% of the urrent steps used to simulate the data, provided that the seleted flikers reahed the 4% or greater losed level. Thus, the error in estimating urrent steps from experimental data should also be within about 3% Ai sine the noise and kinetis of the experimental data are similar to those for the simulated data. Flikers and longer losings have similar slopes Fig. 4A1 presents a urrent reord from a single BK hannel. One omplete losing and six obvious flikers are apparent. To inrease the open hannel urrent, the reordings were obtained with 5 mm K+ at the inner membrane surfae and no added K+ in the pipette (whih ontained 15 mm N-methyl-D-gluamine). The high signal to noise ratio resulting from the 18-pA urrents allowed the urrent to be 81 A2 ler ms 82 lor 4J i 9 _ Q.. ).5.1 Ti me /. 15.1) l.6 A3 8r C a U 9 / - a i, i.6 FGURE 4 Flikers and longer losings from single large-ondutane Ca2+-ativated K+ hannels have similar slopes. (Al) Single hannel urrent reord. (A2 and A3) Averaged flikers (dashed line) have a losing transition slope that is similar (2% steeper) to that of longer (>78,s) losings. A3 plots the data in A2 on a faster time base. Averaged flikers had one to five sampling points below the 5% threshold line: 689 flikers and 288 longer losings were averaged. Extraellular solution, 15 mm N-methyl-D-gluamine and 5 mm TES buffer; intraellular solution, 5 mm KCl, 5 mm TES, and 5,uM added CaCl. Filtering, 15.2 khz; sampling period, 1.56 As. Membrane potential, +3 mv. (Bi ) Current reord from another hannel. (B2)Averaged flikers (dashed line) have a losing transition slope that is similar (2.3% steeper) to that of longer (>156,us) losings. Averaged flikers had one to three sampling points below a 35% (losed) threshold line, 366 flikers and 395 longer losings were averaged. Extraellular solution, 15 mm KC,5 mm TES, and 1 mm EGTA; intraellular solution, 15 mm KC, 5 mm TES, and 5,uM added Ca2+. Effetive filtering, 13.2 khz; effetive sampling interval, 3.1,us. Membrane potential, +3 mv. (C) Averaged flikers (dashed line) from another hannel at 1 C have a losing transition slope that is similar (1.9% less steep) to that of longer (>78,us) losings. Averaged flikers had one to five sampling points below a 5% threshold line. Extraellular solution, 15 mm KCl, 2 mm CaCl2, 1 mm MgCl2, 5 mm TES; intraellular solution, 5 mm KC, 5,uM added Ca2+, 5 mm TES. Effetive filtering, 11.1 khz; effetive sampling interval, 1.56,is. Average response of 61 flikers and 128 longer losings. Membrane potential, +3 mv.

6 Ferguson et al. Flikers in BK Channels 77 analyzed with high time resolution (effetive ut-off frequeny of 15.2 khz). Deteted flikers just rossing the dashed line at the 5% level (illustrated in Fig. 4 Al) were then averaged for omparison to longer (omplete) losings from the same urrent reord. From Fig. 4, A2 and A3, it an be seen that the averaged flikers and averaged omplete losings had similar slopes (within 2%). ndistinguishable slopes (within the 3% resolution of the method) suggest that the magnitude of the initial ondutane step for the average fliker is the same as the magnitude of the initial ondutane step for longer losings. Thus, both flikers and longer losings lose initially to the same average urrent level. t an be alulated (Colquhoun and Sigworth, 1983) that the brief losings that gave rise to the average fliker in Fig. 4A had an average duration of about 11 pts. Thus, the initial losed urrent level for losings as brief as 11,us was similar to the initial losed urrent level for longer losings. (The inrease in the open urrent before the losing transition in Fig. 4A2 arises from the averaging of urrents from hannels that are open for different durations before the losing. This effet will be more pronouned in some of the later figures.) Fig. 4, BJ and B2, present results from a different membrane path bathed in symmetrial 15 mm KCl, and Fig. 4 C presents results obtained at low temperature (1 C) from another membrane path with 15 mm KCl in the pipette and 5 mm KCl at the inner membrane surfae. n both ases the slopes of the flikers and longer (omplete) losings were similar. For over 3 plots of the type shown in Fig. 4 for flikers that reahed from 4 to 7% of the losed urrent amplitude, depending on the experiment, flikers and longer losings had similar slopes for the seven examined BK hannels, and this was the ase with symmetrial 15 mm KCl and also with various K+ gradients to give up to 4-pA urrents, so that flikers arising from losings as brief as 7,ts ould be measured. Similar slopes suggest that flikers and longer losings have similar initial ondutane steps. ndividual losings with durations greater than 1-2 ps typially reah the zero urrent level Al A2 The results in Fig. 4 indiated that the initial ondutane step for the very brief losings underlying flikers was not measurably different from the initial ondutane step for longer losings. The results did not indiate, however, whether the initial ondutane steps for the longer losings used for omparison were omplete. Consequently, we examined both individual longer losings and averaged longer losings to determine if they were omplete losings. To examine individual longer losings, the steady-state urrent amplitudes and durations of the losings were measured with operator adjusted ursor lines from visual displays of urrent reords and plotted at two time resolutions in Fig. 5,,Al and A2. The 1-pA level in the plot represents the open hannel urrent and the 7.3-kHz high-frequeny ut-off allowed losings with durations > 1 p,s to reah a steady-state level and be measured diretly. To ontrol for the effets of noise, filtering, and hannel kinetis on the measured amplitudes, single hannel urrents with noise and filtering were generated by simulation using a kineti sheme that ould desribe the single hannel kinetis of the measured urrent reord (hannel 5 in MManus and Magleby (1991)). The simulated urrents were then measured and the results plotted in Fig. 5, BJ and B2. Although there is more satter in the experimental data (Al and A2) than in the simulated data (BJ and B2), both plots have a similar numbers of observed losings to urrent levels other than zero. Sine all losings used to generate the simulated data were omplete losings, then the observed deviations from the zero urrent level for the simulated data must arise from the effets of noise and filtering on the simulated hannel urrents. Similar effets of noise and filtering would be expeted for experimental hannel urrents. Thus, the similarity in the simulated and experimental data suggest that most losed events with durations greater than the 1-,ts 1- FGURE 5 Closings longer than 1,u s are typially omplete losings. Plots of the urrent amplitudes of single losings against their durations for experimental (Al and A2) and simulated (BJ and B2) single hannel urrent reords with similar amounts of filtering and noise. Eah point plots results from a single losing measured with ursors from a display. All losings used to generate the simulated urrent reord were omplete losings. Effetive filtering, 7.3 khz. Extraellular solution, 144 mm KCl, 2 mm TES, and 1 mm EGTA; intraellular solution, same as extraellular plus added Ca21 to bring the free Ca21 to 9.6,uM, as determined by method of Bers (1982). Membrane potential, +3 mv. 1 % 4J D i 4J +3 Ca U.- C E Closed time Closed time 82 % 4-. i C) ; a E 4.1." E 5 - O o-w,-'s -v;e *^**'.. o o Closed time 1-5- F;^.,-_-...'--..- l.-_ -. O.5 1. Closed time

7 78 Biophysial Journal Volume 65 August 1993 A 4r 1 2r 4 - g_ ) C.. C. 2OF. 1OF O Time 1. Time.4 B C - 2 C. C. AȮ.O.2 *..2.4 Tme 22r 6 C. 5 D3 d- U 1o a K o.2.3 Time (Ms) a Time E 14r FGURE 6 a C. C.) 7i o a..1.2 Averaged omplete losings first lose to 9-95% of the losed urrent level and then lose ompletely over the next 5-1 Ps. (A) Averaged single hannel urrents from intermediate duration losings ( ,us, dashed line) and longer duration losings (>625 ps, ontinuous line). The insert plots the data at inreased resolution. Same experiment as Fig. 1, but with effetive filtering of 22 khz and effetive sampling interval of 1.56 ps. Slope of intermediate duration losings is similar (1.6% steeper) to the slope of longer duration losings. (B) Averaged single hannel urrents from losings of brief durations (78-156,us, dashed line) and longer durations (>312,us, ontinuous line) have similar slopes and step to similar initial urrent levels. The slope of the brief losing is similar (2.6% steeper) to the slope of the longer losing. Extraellular solution, 2 mm KC and 5 mm TES; intraellular solution, 1 M KC, 5 mm TES, and 5,uM added Ca21. Effetive filtering, 2.3 khz; effetive sampling interval, 1.56,ps. Membrane potential, + 3 mv. Reords with obvious transitions through subondutane levels were exluded. (C and D1-D2) The reep after the initial losing step is not due to an artifat in -J.2.3

8 Ferguson et al. Flikers in BK Channels 79 resolution of the analysis are omplete losings. These findings an be ompared to those ofauerbah and Sahs (1983) for the aetylholine reeptor in embryoni hik skeletal musle where losings with durations of 25 p,s (the briefest measured) to about 1.5 ms were not usually omplete losings, but were typially to a 9% losed level. Averaged longer losings first lose to 9-95% of the ompletely losed level and then lose ompletely over the next 5-1 ps The advantage of plots like those shown in Fig. 5 A is that they display the urrent levels of individually measured losings. A disadvantage is that the usefulness of the measurements for estimating the underlying losed urrent levels is greatly redued for losings with durations less than about 3,us, due to the effets of filtering and noise. This is shown by the satter in the measured urrent levels for brief losings in the simulated data in Fig. 5 B. To overome the diffiulties assoiated with the effets of noise and filtering on estimating the urrent levels of intermediate and brief duration single losings, we averaged losings with durations long enough to reah a steady state level. Closings of different durations were averaged separately. The slopes and losed levels of the different duration losings were then ompared. n this way, losings with durations longer than the flikers examined in Fig. 4 and shorter than the longer losings examined in Fig. 5 ould be evaluated. Results from an experiment of this type are shown in Fig. 6 A, where averaged losings of intermediate duration ( ,us) an be ompared to averaged losings of longer duration (>624 pzs). The intermediate duration losings (dashed lines) reahed the same ompletely losed level as the longer losings (ontinuous lines), and the losing transitions for the intermediate and longer losings superimposed, yielding indistinguishable slopes (within 1.6%). Thus, exept for duration, intermediate duration losings had similar losing properties as the longer duration losings. A typial feature of both the intermediate and the longer losings in experiments of this type, was that the averaged urrent typially fell rapidly to a level that was about 9-95% of the ompletely losed level, and then fell more slowly over the next 5-1,ts to the fully losed level. An example from another membrane path is shown by the ontinuous lines in Fig. 6 B. The reep ould also be smaller, or absent, depending on the experiment and how the data were seleted for analysis, as will be disussed in a later setion. Analysis of square wave urrents and Ba2+ blok indiates that the reep during longer losings is not an artifat of the reording and analysis system A possible explanation for the reep in the losings shown in Fig. 6, A and B is that it arises in some manner from an artifat in the reording and analysis of the data. To investigate this possibility, square wave urrents were introdued into the path lamp amplifier, and the resulting output was analyzed in the exat same manner (inluding averaging) as used to analyze urrents from single hannels. Typial results are shown in Fig. 6 C. Following the step transition, the averaged urrent from the square wave fell below the baseline slightly, and then returned to the losed urrent level, just as would be expeted from the small amount of ringing assoiated with Bessel filtering of a square wave; no reep was evident. As a further test of whether the reep arose from an artifat, urrents were reorded from a membrane path with 5,uM Ca2' added to the solution at the inner membrane surfae or with both 5,uM Ca2' and.5 mm Ba2' added. As detailed previously (Vergara and atorre, 1983; Miller, 1987; Neyton and Miller, 1988), the BK hannel was almost ontinuously open with the high Ca2+; adding.5 mm Ba21 then led to the appearane of longer losed intervals. The averaged longer losed intervals, whih presumably arose from Ba2' blok, sine they were seldom observed in the absene of added Ba2+, appeared as omplete losings without reep (ontinuous lines, Fig. 6 D1), similar to the response obtained from the square wave urrent immediately after the experiment (Fig. 6 C). The same hannel whih had no reep with presumed Ba2' blok showed reep in the absene of Ba21 (ontinuous lines, Fig. 6 D2). Thus, the reep was not an obligatory artifat arising from the analysis, sine it was not present with Ba2' blok or from analysis of square wave urrent steps. Furthermore, the reep in the experimental urrent reords is probably underestimated, sine the slight ringing of the Bessel filter would at to derease the reep. The detetion the analysis. Averaged urrents from a square wave introdued into the path lamp amplifier (C) or from averaged longer losings arising mainly from Ba2+ blok (Dl, ontinuous line, see text) do not show reep when reorded and analyzed in the same manner as for the data in D2 in the absene of Ba2+ blok where reep is apparent. D presents averaged single hannel urrents from losings with brief durations of 5-1 its (dashed lines, average of 85 events) and longer durations > 53,us presumably due to Ba2' blok (ontinuous lines, average of 53 events). Same experimental onditions as Fig. 4 A, exept that.5 mm Ba21 was added to the intraellular solution. (D2 and D3) Averaged single hannel urrents for losings with brief durations of ,us (dashed lines) and longer durations >312 p.s (ontinuous lines) in the absene of Ba2+. Averages of 542 brief losings and 172 longer losings are presented in D2; the slope of the brief losings was 4% less than the longer losings. Notie the reep in D2 (ontinuous line) in the absene of Ba2 blok. The data averaged for D2 were then seleted to exlude transitions through possible subondutane levels giving the results shown in D3, whih presents averages of the 381 brief losings and 138 longer losings remaining after seletion; the slope of the brief losing was 3% less than the slope of the longer losing. Same experimental solutions and membrane potential as Fig. 4A. (E) Averaged single hannel urrents from brief losings with durations of ps (dashed lines) and losings with longer durations > 234 p,s (ontinuous lines). Reords were seleted to exlude apparent transitions through subondutane levels. There were 119 brief and 81 longer losings before seletion and 55 brief and 7 longer losings after seletion. 1 C. Same hannel and experimental onditions as Fig. 4 C.

9 71 Biophysial Journal Volume 65 August 1993 Ai A O C: C. 4r 21 Ms i ms. 1 ms 2 pa..3.6 FGURE 7 Transitions to subondutane levels. (AJ,A2, and BJ) Single hannel urrents showing apparent transitions to subondutane levels. The dashed lines indiate the losed hannel urrent levels. For Al and A2 the experimental onditions were the same as Fig. 6 D, but without Ba2. (B2) Averaged losings to a subondutane level (dashed line) at about the 7-75% losed level have a slope that is about 74% of the slope for omplete losings (ontinuous lines). Reords with transitions to the subondutane level shown in B2 were seleted from the omplete urrent reord and averaged for omparison to longer losings. For Bl and B2 the hannel and experimental onditions were the same as Fig. 6 A. of the reep in the experimental data required high time resolution (high frequeny ut-off greater than 8 khz) beause of its brief duration. Averaged brief losings are to the 9-95% losed level and have slopes similar to longer losings The reep assoiated with the longer losings in Fig. 6, A, B, andd2, suggests that, if the hannel reopened before it losed ompletely, then averaged losings with durations less than the duration of the reep (<1,us) may not be omplete. To test this possibility, brief losings with durations (below the 5% threshold level) of lus were averaged for omparison to longer losings (> 312,us). A minimum duration of 78,us for a brief losing assures that the urrent would reah the ompletely losed urrent level if the losing were omplete. This is the ase sine only about 3,us would be required for the urrent to reah a steady-state level after a urrent step. The averaged brief losings (dashed lines) losed to about 9-95% of the ompletely losed level, before reopening, as shown by the dashed lines in Figs. 6, B and D2. Comparison of the slopes of the losing transitions indiated that the slopes of the averaged brief losings were indistinguishable (within the 3% resolution of the method) from the slopes of the averaged longer losings. Thus, both averaged brief and averaged longer losings first typially losed to an apparent subondutane level that was about 9-95% of the ompletely losed level. The averaged brief losings then reopened from the subondutane level and the averaged longer losings then losed to the ompletely losed level over the next 5-1,us. Similar results were obtained in about 8% of the 2 plots of this type for data obtained from seven hannels for brief losings with durations in the examined range of about 5-2 p,s. n the other 2% of the plots there was little or no apparent reep in the longer losings, and the brief losings approahed the zero urrent level (not shown). Thus, in some ases most brief and longer losings step diretly to the ompletely losed level. The reason for the variability among different pathes was not apparent, but some variability might be expeted sine individual hannels an possess differenes in alium sensitivity and kinetis (MManus and Magleby, 1991). The reep in the averaged reords is due mainly to step losures to subondutane levels Averaged brief losings that lose to the 9-95% losed level, as in Fig. 6, B and D2, ould arise if all of the averaged losings were to subondutane levels, or if some of the losings were to subondutane levels and others were omplete losings. To examine these possibilities, individual urrent reords were visually inspeted to identify losings to subondutane levels. onger duration losures (> 1-2 ms) to subondutane levels typially ourred so infrequently, about one per 1 openings (Barrett et al., 1982), that they would have had little effet on the results, even if they had not been typially exluded before averaging. Examination of the reords at higher time resolution indiated, however, that there were frequent losings of muh briefer duration (<5-2,us) to various subondutane levels. Examples are shown in Fig. 7, Al and B1. n some ases the subondutane levels were at about 1% of the open level (Al), and in other ases they were at about 25-35% (B1). The frequenies of apparent losings to the brief duration subondutane levels varied from as low as one per 1-1 losings to as high as one per two to three losings, depend-

10 Ferguson et al. Flikers in BK Channels 711 ing on the partiular single hannel path and temperature, with higher frequenies often ourring at lower temperatures (5-1 C versus room temperature). ower temperatures are known to inrease the frequeny of transitions to subondutane levels (Tyerman et al., 1992). Exluding obvious transitions to subondutane levels for the data averaged for Fig. 6 D2 gave the results shown in Fig. 6 D3. The averaged longer losings (ontinuous line) now losed diretly to the ompletely losed level and the averaged brief losings (dashed line) were almost omplete, to within about 2% of the ompletely losed level. As was the ase before exlusion, the slopes of the brief and longer losings were typially similar (usually within < 4% in experiments of this type and within < 1% in a high resolution experiment with 4-pA urrents). n seleting the data for Fig. 6 D3, about 3% of the brief losings and 2% of the longer losings were exluded. Thus, an observation of omplete averaged losings after exluding 2-3% of the individual losings suggests that about 7-8% of the losings were diretly to the ompletely losed level in this experiment. Another example of omplete losings for averaged data after exluding only a fration of the individual events is shown in Fig. 6 E. Both averaged brief and averaged longer losings losed diretly to the same ompletely losed level after exluding 55% of the brief losings and 15% of the longer losings (Fig. 6 F), suggesting that about 45-75% of the losings were diretly to the ompletely losed level in this experiment performed at 1 C. n some experiments (room temperature), averaged losings did not lose diretly to the ompletely losed level even after exluding apparent losings to subondutane levels. (The plot in Fig. 6 B shows an experiment of this type.) This ould our if the subondutane levels in the individual reords were less than about 1-15% and too small to be onsistently seleted for exlusion, or if the ondutane atually rept down in these experiments, rather than going through well defined subondutane levels. The subondutane losings and reep in the averaged longer losings for the BK hannel appear similar to the subondutane losings and reep observed by Auerbah and Sahs (1983, 1984) for aetylholine reeptor hannels in ultured hik musle, exept for the muh briefer time ourse for the BK hannel. The -5-gs mean lifetime of the apparent lass of brief subondutane losings for the BK hannel is about 1-2-fold briefer than the.5-1-ms mean lifetime of the lass of subondutane losings in aetylholine reeptors (both estimates at room temperature). Diret losures to subondutane levels Transitions to subondutane levels might result from losings diretly to the subondutane level, or alternatively, the hannel might first lose ompletely and then swith to a subondutane level, as shown in Fig. 7 A2. Although the swithing is apparent in Fig. 7A2, if the time spent in the full losure before swithing would have been slightly less, then it would have appeared that the losing was diretly to the subondutane level. To distinguish between losings diretly to the subondutane level or omplete losings with partial reopenings, losings to subondutane levels like those in Fig. 7 BJ were averaged for omparison to omplete losings. Of the 457 losings in the examined streth of data, the 25 losings to a subondutane level of about 25-35% of the open hannel ondutane were seleted for averaging. Results are shown in Fig. 7 B2. The slope of the averaged losing to the subondutane level was 26% less than the slope of the averaged omplete losings. This is onsistent with what would be expeted if most of the subondutane losings in this experiment were diretly to the subondutane level, and not rapid reopenings from omplete losures. Although the subondutane levels appear obvious in Fig. 7, it has not been ruled out that they arise from the time average of very rapid transitions between the open and losed urrent levels (e.g., Blatz and Magleby (1986)). t is also diffiult to rule out the possibility that the subondutane levels and reep in the averaged data result from the averaging of suh brief openings that they annot be identified for exlusion in the individual reords. For example, the lower urrent reord in Fig. 1 has an apparent brief opening after the last losing. f this opening were briefer still, it might appear as a subondutane level. Opening and losing transitions are typially symmetrial n most experiments in whih all opening and losing transitions were averaged without exlusion of obvious subondutane transitions, a reep similar to that observed in the longer losings also preeded the openings, as shown in Fig. 8 Al, suh that the openings and losings were approximate mirror images of one another (Fig. 8 A2). Suh symmetry in opening and losing transitions would be expeted if the gating kinetis were onsistent with mirosopi reversibility, so that the numbers of transitions between any two given states would be the same in the forward and bakward diretion (e.g., Colquhoun and Hawkes (1983)). With mirosopi reversibility, there is no net energy input into the gating proess. Conlusions and speulation A major objetive of this study was to determine whether the flikers in single hannel urrents in BK hannels arise from omplete or partial losings. Our results suggest that flikers (durations < 5,is) arise, on average, from ondutane steps to the 9-95% losed level. nterestingly, we also found that the initial losing transition for averaged brief losings (5-2 ps) and averaged longer losings (>3 ps) was also typially to the same apparent 9-95% losed urrent level. Flikers and brief losings then reopened, on average, from the 9-95% losed level, and longer losings then losed ompletely, on average, from the 9-95% losed level over the next 5-1,is, produing a reep in the averaged urrents to the zero uffent level.

11 712 Biophysial Journal Al 4 Volume 65 August 1993 SJTFJ7G11C g 3 A2 a u 2 4r _ FGURE 8 Averaged openings are typially mirror images of averaged losings. (Al-A2) Creep before opening (ontinuous lines) superimposes the reep after losing (dashed lines); the averaged opening is plotted with reverse time in A2. Opening transitions following and losing transitions preeding losed intervals >312 gs were averaged separately (averages of -185 eah). The opening and losing transition slopes were within 1%. Same experimental onditions as Fig. 6 A. ndistinguishable average ondutane steps (within the 3% resolution of the method) for flikers, brief losings, and longer losings are onsistent with the possibility that the initial onformational hanges that diretly derease hannel ondutane for all these events are, on average, typially the same. The high time resolution of the reordings extends this onlusion to losings as brief as 7,us. Even if the initial onformational hanges for the various losings are typially the same, the large differenes in durations between the various losings, and the time-dependent derease in the average ondutane for the longer losings suggests that additional states are entered for the longer losings, onsistent with onlusions from kineti studies (MManus and Magleby, 1991). Similar to the 5-1-,ts reep following averaged longer losings, averaged openings were preeded by a reep, so that, in general, opening and losing kinetis were symmetrial in time. Thus, for longer losings, the hannel first initially losed, on average, to the 9-95% losed subondutane level, followed by a losing to the ompletely losed level. This proess was reversed on opening, with, on average, an initial opening to the 9-95% losed level, followed by a transition to the fully open level. The 9-95% FGURE 9 An idealized single hannel urrent reord for Sheme. Opening and losing transitions an our in two steps through a subondutane level with a mean lifetime of about 5,us. Some of the very brief losings (flikers) reopen from the brief lifetime subondutane level without losing ompletely. losed level reahed in the average initial losing transition arose typially from the average of losings diretly to the fully losed level and losings to subondutane levels. About 45-8% of the losings were diretly to the ompletely losed level, and about 2-55% were to subondutane levels. The subondutane levels were at about 65-9% of the ompletely losed level and the mean duration of time spent in the subondutane levels was about 5,As. Thus, about 2-55% of the losings with durations longer than about 5,us ourred in two steps. n these ases, the hannel first losed to a 65-9% losed level for about 5,us and then losed ompletely. A similar perentage of the openings also ourred in two steps through a reversal of the proess. n a few experiments, most of the losings appeared omplete, and in some other experiments it was not possible to exlude the possibility that the reep observed in the averaged data arose from a slowly hanging urrent in the individual urrent reords. Subondutane levels of longer durations, of the types desribed previously (Barrett et al., 1982; Rae et al., 199) ourred muh less frequently than the subondutane levels of brief duration desribed above. The brief duration subondutane levels esaped detetion in our previous studies beause they were too brief to be apparent in the slower time bases typially used to examine the urrent reords. A simple model that summarizes our major observations is indiated by Sheme, where the onformational states of the hannel assoiated with the ompletely losed (C), subondutane (S), and open states () are indiated. C S Transitions an our diretly between the open and losed states or by passing through the subondutane states S. An idealized single hannel urrent reord for some typial transitions between the various ondutane states is shown in Fig. 9. A minimal kineti gating mehanism for the BK hannel is onsiderably more omplex than Sheme, as shown in Sheme, where C and represent losed and open kineti states (MManus and Magleby, 1991). C8 = C7 = C6 =C5 = C = 2 = 1 (1) (2)

12 Ferguson et al. Flikers in BK Channels 713 The relationship between the ondutane states in Sheme and the kineti states in Sheme is not lear, but it may be useful to speulate on this question for the purpose of designing further experiments. Although all the states in Sheme are usually entered during hannel ativity, the typial gating sequene for moderate levels of ativity involves transitions mainly within the ompound state desribed by: C8-C7-C6-C5-2-1 (MManus and Magleby, 1991). The losed state C5 has a mean dwell time of about 5,us, and the other losed states have onsiderably longer dwell times. Thus, in terms of Sheme, most flikers and brief losed intervals result from transitions to C5 from the ompound open state 1-2, suh as: 1-2-C5-2-1 (MManus and Magleby, 1991). f it is assumed that the ondutanes of the losed states C8-C7-C6 are zero, that the ondutanes of the open states 1 and 2 are 1%, and that the ondutane of the "losed" kineti state C5 is, on average, 5-1% of the open hannel ondutane, then openings would, on average, be preeded by a ondutane step to the 5-1% open level as the hannel passed through C5 on its way from the longer losed states to the open states, suh as: C8-C7-C6-C Conversely, the initial losings would, on average, be to the 9-95% losed level as the hannel makes transitions from 2 to C5. Reopenings from C5 would then give rise to flikers and brief losings with, on average, a 9-95% losed level assoiated with C5. Transitions suh as: 1-2-C5-C6-C7-C8, from the open states through C5 to one or more of the longer losed states would result in omplete losings preeded by a reep in the averaged data, as the hannel passed through C5 to the ompletely losed states. The rather limited support for this mehanism for brief subondutane levels omes from the observation that the mean dwell time in C5 of about 5 [s estimated from kineti studies (MManus and Magleby, 1991) is similar to the mean duration of the reep preeding hannel opening and following hannel losing. The kineti state C5 would represent a family of onformational states that have similar mean lifetimes of about 5,us, but different ondutanes that range from zero to about 35% of the open hannel ondutane. A family of onformational states for C5 ould aount for the observation of multiple subondutane levels of similar brief duration and also for the observation that the hannel ould also open and lose without passing through obvious subondutane levels. Possible differenes in BK hannels (MManus and Magleby, 1991) and differenes in experimental onditions ould favor some onformations over others, giving rise to the observed variability in results. t is also possible that the onformational hanges that produe the brief duration subondutane levels are independent from those that produe the kineti state C5; the two proesses may just happen to have similar lifetimes and at in parallel, giving a false appearane of oupling. Further examination of the relationship, if any, between the kineti state C5 and the brief subondutane levels ould be made by detailed omparisons of the kineti states in Sheme with the durations and ondutane levels of losings seleted on the basis of the durations of previous openings. For example, losings suh as 3-C6 should not be assoiated with transitions through subondutane levels, if the subondutane levels are all assoiated with C5. t is also possible that there might be slightly different ondutane levels assoiated with some of the other kineti states. n any ase, the omplexity of the subondutane levels in various hannels (Auerbah and Sahs, 1983, 1984; Fox, 1987; Patlak, 1988; Bosma, 1989; Rae et al., 199; Tyerman et al., 1992) suggests that the relationship between the various ondutane levels and the kineti states will be more omplex than onsidered above. This work was supported by grants from the National nstitutes of Health (AR-3285) and the Musular Dystrophy Assoiation (to K.. Magleby) and fellowships from a National nstitutes of Health Training Grant (NS 744) (to W. B. Ferguson and. B. MManus). REFERENCES Auerbah, A., and F. Sahs Flikering of a niotini ion hannel to a subondutane state. Biophys. J. 42:1-1. Auerbah, A., and F. Sahs Single-hannel urrents from aetylholine reeptors in embryoni hik musle. Kineti and ondutane properties of gaps within bursts. Biophys. J. 45: Barrett, J. N., K.. Magleby, and B. S. Pallotta Properties of single alium-ativated potassium hannels in ultured rat musle. J. Physiol. (ond.). 331: Bers, D. M A simple method for the aurate determination of free [Ca] in Ca-EGTA solutions. Amer. J. Physiol. 242:C44-C48. Blatz, A.., and K.. Magleby Quantitative desription of three modes of ativity of fast hloride hannels from rat skeletal musle. J. Physiol. (ond.). 378: Bosma, M. M Anion hannels with multiple ondutane levels in a mouse B lymphoyte ell line. J. Physiol. (ond.). 41:67-9. Colquhoun, D., and A. G. Hawkes Relaxation and flutuation of membrane urrents that flow through drug operated hannels. Pro. R. So. ond. Ser. B Bio. Si. 199: Colquhoun, D., and A. G. Hawkes The priniples of the stohasti interpretation of ion hannel mehanisms. n Single Channel Reording. B. Sakmann and E. Neher, editors. Plenum Publishing Corp., New York. Colquhoun, D., and B. Sakmann Flutuations in the miroseond time range of the urrent through single aetylholine reeptor ion hannels. Nature (ond.). 294: Colquhoun, D., and B. Sakmann Fast events in single-hannel urrents ativated by aetylholine and its analogues at the frog musle end-plate. J. Physiol. (ond.). 369: Colquhoun, D., and F. J. Sigworth Fitting and statistial analysis of single-hannel reords. n Single-Channel Reording. B. Sakmann and E. Neher, editors. Plenum Publishing Corp., New York Ferguson, W. B.,. B. MManus, and K.. Magleby Most flikers are omplete losures for maxi K' hannels in ultured rat skeletal musle. Biophys. J. 61:A289. Fox, J. A on hannel subondutane states. J. Membr. Biol. 97:1-8. Hamill,. P., A. Marty, E. Neher, B. Sakmann, and F. J. Sigworth, mproved path lamp tehniques for high-resolution urrent reording from ells and ell-free membrane pathes. PfluegersArh. Eur. J. Physiol. 391:85-1. 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13 714 Biophysial Journal Volume 65 August 1993 Miller, C Trapping single ions inside single ion hannels. Biophys. J. 52: Nelson, D. J., and F. Sahs Single ioni hannels observed in tissueultured musle. Nature (ond.). 282: Neyton J., and C. Miller Potassium bloks barium permeation through a alium-ativated potassium hannel. J. Gen. Physiol. 92: Pallotta, B. S., K.. Magleby, and J. N. Barrett Single hannel reordings of Ca2+-ativated K' urrents in rat musle ell ulture. Nature (ond.) 293: Patlak, J. B Sodium hannel subondutane levels measured with a new variane-mean analysis. J. Gen. Physio 92: Rae, J.., J. Dewey, J. S. Rae, and K. Cooper A maxi aliumativated potassium hannel from hik lens epithelium. Curr. Eye Res. 9: Sigworth, F. J Open hannel noise.. A test for oupling between urrent flutuations and onformational transitions in the aetylholine reeptor. Biophys. J. 49: Tyerman, S. D., B. R. Terry, and G. P. Findlay Multiple ondutanes in the large K+ hannel from Chara orallina shown by a transient analysis method. Biophys. J. 61: Vergara, C., and R. atorre Kinetis of Ca2+-ativated K+ hannels from rabbit musle inorporated into planar lipid bilayers: evidene for a Ca2' and Ba2' blokade. J. Gen. Physiol. 82: