aspartate and glutamate evoked mainly 50pS openings and also substantial ..... determined for 50 pS openings in the record), in order to minimize the effect of missed events on ..... These examples were chosen for illustration because they.
143
Journal of Phy8iology (1991), 432, pp. 143-202 With 23 figure8 Printed in Great Britain
CURRENTS THROUGH SINGLE GLUTAMATE RECEPTOR CHANNELS IN OUTSIDE-OUT PATCHES FROM RAT CEREBELLAR GRANULE CELLS BY JAMES R. HOWE, STUART G. CULL-CANDY AND DAVID COLQUHOUN From the MRC Receptor Mechanisms Research Group, Department of Pharmacology, University College London, Gower Street, London WC1E 6BT
(Received 15 March 1990) SUMMARY
1. Single-channel currents evoked in outside-out membrane patches from rat cerebellar granule cells by glutamate, aspartate, N-methyl-D-aspartate (NMDA), kainate and quisqualate were studied. Each agonist produced openings to five discrete amplitude levels. At a membrane potential of -70 mV, these levels correspond to single-channel conductances of about 8, 17, 30, 40 and 50 pS. NMDA, aspartate and glutamate evoked mainly 50pS openings and also substantial numbers of 40 pS events. Kainate evoked primarily 8 and 17 pS openings. 2. The relative proportion of openings to each conductance level showed no dependence on membrane potential. At membrane potentials negative to -100 mV, current-voltage plots for 30, 40 and 50 pS openings showed substantial inward rectification. 3. With NMDA, aspartate and glutamate, the most common type of direct transition was between the 50 pS open level and the shut level. Transitions between the 30, 40 and 50 pS levels were also relatively common. With few exceptions, 8 and 17 pS openings appeared to arise directly from, and return directly to, the shut level. The differences between granule cells and certain other central neurones, in the types of transitions associated with NMDA receptor channels, provide evidence for the existence of more than one type of NMDA receptor. 4. Four exponential components were identified consistently in the shut-time distributions that were obtained with NMDA, aspartate and glutamate. Mean time constants for the briefest two components were 30 to 65 ,ts and 0-65 to 1-00 ms. The mean duration of these 'gaps within bursts' differed for different agonists, but did not vary with membrane potential. 5. Two exponential components were distinguished in most open-time distributions for the 50 pS level (time constants, 0-9-1-2 and 3'2-3-9 ms at -100 mV), whereas open-time distributions for 30 and 40 pS events were described adequately by single exponentials with time constants below 1-0 ms. The duration of 50 pS openings decreased with hyperpolarization. 6. Mean open times for 8 and 17 pS events produced by NMDA, aspartate and glutamate were 0-3 to 0-7 ms. The longest such openings were observed with quisqualate. MS 8352
J. R. HOWE, S. G. CULL-CANDY AND D. COLQUHOUN 7. Three exponential components were present in distributions of burst length, and of total open time per burst, that were obtained with NMDA, aspartate and glutamate. The slowest two burst-length components had mean time constants of 1P7-2-4 and 106-13-0 ms and originated from the kinetic behaviour of the 50 pS state. Distributions of the number of open periods per burst contained two geometric components, one of which had a mean close to unity. 8. Bursts of openings were observed to occur in clusters of long duration and high probability of being open (high p0). Clusters were seen with each of the five agonists, but were most common with NMDA. The durations of open times and 'gaps within bursts' that occurred within clusters were similar to the durations of the corresponding events that occurred between clusters. 144
INTRODUCTION
Rat cerebellar granule cells in short-term explant culture respond to glutamate and aspartate, and also to N-methyl-D-aspartate (NMDA), quisqualate and kainate (Cull-Candy & Ogden, 1985; Cull-Candy, Howe & Ogden, 1987, 1988 a). Glutamate and aspartate are thought to be important excitatory neurotransmitters within the mammalian cerebellum (for references and brief review, see Cull-Candy, Howe & Usowicz, 1988 b); and the other three agonists, namely NMDA, quisqualate and kainate, are prototypical agonists for the three putative subtypes of glutamate receptors (Watkins & Evans, 1981; Fagg, Foster & Ganong, 1986; Mayer & Westbrook, 1987 a). In outside-out patches from granule cells, each of the agonists tested produced single-channel currents of distinctly different amplitudes, as many as five discrete peaks being identifiable in amplitude distributions for single-channel currents; and the relative frequency with which openings to these five conductance levels were evoked was dependent on the agonist used (Cull-Candy et al. 1988a). NMDA, aspartate and glutamate produced mainly 50 pS openings; whereas quisqualate, and especially kainate, evoked large proportions of openings to conductance levels below 20 pS (Cull-Candy et al. 1988 a). Although glutamate receptor channels have now been studied in several different types of mammalian central neurones, there is little direct and detailed information about their single-channel kinetics. In particular there is little information about the kinetics of openings to the different conductance levels, which cannot be analysed adequately with commonly employed threshold-crossing methods and which introduce rather serious complications and ambiguities into the interpretation of kinetic data obtained with any method of analysis. However, a description of these kinetics is important to the further understanding of how glutamate receptor channels work, and it is prerequisite to the quantitative description of the receptor mechanisms that underlie the action of glutamate receptor agonists and antagonists. In a previous paper (Howe, Colquhoun & Cull-Candy, 1988), we gave an initial analysis of shut-time and burst-length distributions obtained with glutamate, aspartate and NMDA; and we noted that there appeared to be some substantial differences between the kinetic behaviour of glutamate receptor channels in cerebellar granule cells and the kinetic behaviour of such channels in other types of mammalian central neurones. For example, direct transitions between conductance levels below 20 pS and those above 20 pS were reported to be relatively common in patches from
GLUTAMATE RECEPTOR SINGLE-CHANNEL CURRENTS
145
large cerebellar neurones (Cull-Candy & Usowicz, 1987), whereas such transitions were almost never observed in granule-cell patches. And Jahr & Stevens (1987) reported that the gating kinetics of 50 pS openings within the high-p0 clusters they observed in patches from hippocampal neurones differed from the gating kinetics of such openings that occurred between clusters, whereas no such difference was apparent in the single-channel records we obtained from granule-cell patches. In the present paper, we give the results of a much more complete and quantitative analysis of the single-channel currents produced in outside-out patches from granule cells by glutamate, aspartate, NMDA, quisqualate and kainate. Some of the results have been presented in abstract form (Howe, Colquhoun & Cull-Candy, 1987). METHODS
Preparation Patch-clamp experiments were performed on explant cultures of cerebellar cells obtained from rats that were 7-10 days old. These cultures were prepared as described in Cull-Candy & Ogden (1985) and Cull-Candy et al. (1988a). The cultures were used for electrophysiological experiments 1-5 days after they were prepared. Granule cells were identified by their characteristic morphology and electrophysiological properties as described in Cull-Candy et al. (1988a).
Solutions Patch pipettes were filled with a solution (pH 7 20) that contained (in mM): CsCl, 140-150; NaCl, 4; CaCl2, 0-5; K-EGTA, 5; K-HEPES, 10. Agonists were added to the external solution (pH 7-2) which contained (in mM): NaCl, 150; KCl, 2-8; CaCl, 1; Na-HEPES, 10; and were applied by local superfusion. Solutions were changed by manually switching a two-way tap. Responses were obtained within 1-3 s after switching the solutions. The agonists used were: L-glutamate (Cambrian Chemicals Ltd, Sigma), L-aspartate (Sigma), N-methyl-D-aspartate (NMDA; J. C. Watkins, Cambridge Research Biochemicals, Sigma), quisqualate (T. Takemoto, Sigma) and kainate (Calbiochem, Sigma). All solutions were nominally free of Mg2+ and glycine, both of which have been shown to produce substantial effects on currents activated by NMDA (Nowak, Bregestovski, Ascher, Herbet & Prochiantz, 1984; Johnson & Ascher, 1987).
Recordings and patch pipettes Tight-seal patch-clamp recordings were made of agonist-activated single-channel currents in outside-out membrane patches as described by Hamill, Marty, Neher, Sakmann & Sigworth (1981). Patch pipettes were pulled from filament-containing borosilicate glass (outer diameter, 1-50 mm; inner diameter, 0-86 mm; Clark Electromedical Instruments). The pipettes had resistances of 10-30 MQ when filled with the intemal solution used for recording. Patch pipettes were coated with Sylgard (Dow-Corning) and were fire-polished.
Filtering and measurement of single-channel currents Signals were stored on FM tape (bandwidth, DC to 5 or 10 kHz, -3 dB; 4-pole Bessel characteristic). To prevent saturation of the tape-recorder by high-frequency noise, signals were low-pass filtered at 10 kHz (-3 dB) before they were stored. Single-channel currents replayed from tape were filtered at 1-6 kHz (-3 dB, 8-pole Bessel type) and the signals were digitized continuously at 10-60 kHz (10 times the -3 dB frequency of this filter). The amplitude and duration of single-channel currents were measured by manually fitting the digitized signal with the measured step-response function of the recording system (Colquhoun & Sigworth, 1983). Because of the presence of multiple conductance levels, the amplitude and therefore the duration of incompletely resolved events were uncertain. Incompletely resolved events were fitted initially as 50 pS openings or complete shuttings. If the step-response function fitted poorly, the amplitude was adjusted to obtain the best fit.
146
J. R. HOWE,
0G. CULL-CANDY AND D. COLQUHOUN
Fitting and display of distributions All of the distributions were displayed as frequency histograms. When the durations of the events to be fitted varied widely, as they did for example with shut times, histograms of the distribution of log(t) were constructed to display the entire distribution at once (McManus, Blatz & Magleby, 1987; Sigworth & Sine, 1987). All of the distributions were fitted by the method of maximum likelihood (Colquhoun & Sigworth, 1983). Distributions of dwell times were fitted with probability density functions that were the sum of one or more exponential terms (Colquhoun & Sakmann, 1985). The time constants and relative areas of exponential terms fitted with this method were very similar to those obtained with log-binned fitting procedures (McManus et al. 1987; Sigworth & Sine, 1987), provided that the number of values was large. In most cases the number of exponential components required to fit a given distribution was evident from inspection of the histograms, and the 'goodness of fit' was evaluated visually by superimposing the fitted curve on the histogram. For distributions displayed on an arithmetic time scale, bin widths were chosen to be approximately one-third the time constant determined for the exponential component under inspection. For distributions with more than one exponential term, histograms of the distribution of log (t) were also examined. If the number of components in the distribution was not clear, distributions were fitted with different numbers of components. The extent to which the inclusion of an additional exponential term improved the fit was evaluated with a likelihood ratio test as described by Horn (1987). The dependence of a parameter on membrane potential was assessed by linear regression analysis of semilogarithmic plots of the parameter as a function of patch potential. The statistical significance of the slopes so obtained was assessed with a Student's t test. The significance of differences between mean values obtained for different groups was determined with one-way analysis of variance. Probability (P) values less than 0-05 were considered statistically significant. Unless indicated otherwise, the S.E.M. is reported when mean values are given.
Assignment of minimum resolvable durations The presence of multiple conductance levels complicated the imposition of minimum resolvable durations (resolutions) for openings and shuttings. As with all single-channel data, it was desirable to set these resolutions so that incompletely resolved events were safely distinguished from random noise yet the number of real events that were missed was minimized. However, because the records contained completely resolved openings of different amplitudes, there was no one resolution that was optimal for the discrimination of all single-channel events. This is readily apparent from consideration of the frequency-response characteristics of the recording system. For a Gaussian filter, to which our Bessel-type filters approximated closely in response characteristics, one filter rise time, T, is equal to 0-3321/If, where f is the -3 dB frequency of the filter. If signals are filtered sequentially by a cascade of Bessel-type filters (patch-clamp, taperecorder and filter), then the effective cut-off frequency, f0, is given to a good approximation by
1AL/()
X 1/(ft)2,
(1)
where f, are the -3 dB frequencies of the filters. The maximum amplitude, A.ma, of a low-passfiltered pulse of duration d is given by (2) Amax = AO erf (0 886 d/T), where AO is the amplitude of the original unfiltered pulse (see for example, Colquhoun & Sigworth, 1983). In the best records (taped at a bandwidth of 10 kHz and filtered at 6 kHz), f0 from eqn (1) was 4-6 kHz (after allowing for the prefiltering at 10 kHz, see above) and Tr was 74 Pss. With ratios d/l; of 0 3, 0 5, 1 0, 1P5, 2-0 and 2-5, we obtain from eqn (2) Am./Ao = 0-293, 0-469, 0 790, 0940, 00988 and 0-998, respectively. For example, a low-pass-filtered square pulse of duration d = 2-5 T attains 99'8 % of its original amplitude. Provided that the original amplitude, A., of an event is known, then Am. can be calculated from eqn (2) for any such event of duration d (i.e. for any given resolution), and the probability that an event of amplitude mar would arise from random noise is given by the false-event rate, Af, where (3) Af fc exp [-5(Amn/an)2], and where otn was the measured r.m.s. (root mean square) noise of the recording (Colquhoun & Sigworth, 1983). However, the false-event rate is a very steep function of the ratio Amx/crn and for -
147 GLUTAMATE RECEPTOR SINGLE-CHANNEL CURRENTS any given record depends markedly on Ao. For example, in records in which the majority of the completely resolved openings were 50 pS openings, the ratio of the amplitude of these 50 pS openings to the r.m.s. noise, Ao/r0, had a mean value (± s.E.M.) of 28-3 + 1-2 (n = 33). For A0! cr = 28, a false-event rate of less than 10-16 s-1 would be obtained for the f values in our experiments if the resolution were set to 0-34Tr so that AmpjAo = 0-33 (i.e. a 50 pS opening of a duration equal to the resolution would reach 33 % of its original amplitude). However, the same resolution would give a false-event rate of 10-5-10-4,s- for 30 pS openings and, even if the resolution were set to 2-01T, the false-event rate for 8 pS openings would be 0-08-035 s-1. Thus in these records the certainty with which 8 pS openings could be detected was relatively low, and therefore records that appeared to contain predominantly 8 and 17 pS openings were filtered more heavily than those that contained large numbers of 50 pS openings. In addition to deciding with what resolution single-channel events could be distinguished from random noise, it was necessary to evaluate in a way that was consistent (both within and between records) the resolution with which single-channel events with different original amplitudes could be distinguished from each other. And just as there was no one resolution that was equally good for all types of events, there was no single resolution for any one type of event that was optimal for all types of distributions. In general, errors were minimal when the resolution for the events to be analysed was set to ensure reliable assignment of their original amplitude and the resolution for all other types of events was set only to ensure the exclusion of events that arose from random noise. The characteristics of the following types of events were analysed routinely: single-channel current amplitudes, transitions between different conductance levels, shut times, open times, bursts of openings. Correlations between the length of one event and the length of subsequent similar events were also assessed for most records. Resolutions were set as described below for the different types of distributions fitted. Readers not interested in the details of this analysis should go directly to the Results.
Distributions of amplitudes For each record, the distribution of the amplitudes of all openings with a duration greater than or equal to 2-5 Tr was fitted with the sum of three to four Gaussian components. The shut-time resolution was set to give a false-event rate below 10-8 5-1 for complete shuttings that originated from the 50 pS level (with Tr in eqn (2) determined from the value off, calculated from eqn (1)). Over the range of membrane potentials at which most of the data were obtained (-80 to -140 mV), shut-time resolutions of 25-75 #s gave A, < 10-8 s-1. Although at these resolutions some of the events assigned as shuttings may in fact have been brief transitions to other open levels, we wished to ensure that all clear interruptions of well-defined openings were detected, because if such interruptions were ignored the number of well-defined openings (duration above 25 Tr) would be underestimated. For the same reason, the open-time resolution was set to give A, < 10-8 s-1 for 50 pS openings.
Distributions of 8ample-point amplitudes In the amplitude distributions just described, each completely resolved opening whatever its duration contributed one value to the distribution. In what we will refer to as open-point amplitude distributions, the amplitude of each sample point during a channel opening contributed one value to the distribution. Sample points during a duration 1-25 Tr after the onset of a transition between open and closed states were excluded from the open-point distribution. Portions of the record that contained artifacts, or the occasional double opening, were also excluded; and minor adjustments of the baseline shut level were made as necessary. Whereas the 1-25 Tr restriction ensured that sample points corresponding to transitions between the open and shut levels were excluded and that single openings less than 2-5 1r were ignored, sample points that occurred during transitions between two open levels and sample points that corresponded to shuttings of duration less than the resolution were not necessarily excluded. These latter sample points skewed the distributions so that they no longer conformed to functions consisting of the simple sum of Gaussian components. The exact form of the distribution will be a function of several variables and will depend, for example, on the number of open levels and their relative amplitudes and mean dwell times (Yellen, 1984; Sigworth, 1985). However, the distribution of sample points above (and near) the peak in the distribution that corresponds to the open level with the largest mean conductance is expected to be Gaussian, and the distribution of sample
148
J. R. HOWE,
S.
G. CULL-CANDY AND D. COLQUHOUN
points obtained from portions of the record during which no openings occurred (shut-point amplitudes) was found to be Gaussian. The standard deviations of these two types of distributions were compared in order to obtain an estimate of the 'open-channel noise' (Sigworth, 1985).
Transitions between conductance levels From the multiple-Gaussian fit to the amplitude distribution, three to five open-level ranges were defined, such that openings assigned to a given level all had amplitudes within the specified range. In most cases, adjacent individual Gaussians overlapped and, without excluding most of the events that were measured, some misclassifications of amplitudes was unavoidable. The ranges were set by finding the critical amplitude, A0, between two adjacent peaks in the distribution that minimized the total number of amplitudes misclassified. This number is proportional to
rO rA~ ~ ~ f2(A) c dA
p = al |f(A) dA +a2
= 0 5{al[1 -erf (u1/ V2)]+ a2J1 +erf(u2I,V2)]}, where fi and f2 are the Gaussian densities for the components with the smaller and larger means, respectively, a, and a2 are proportional to the relative areas of these components, erf represents the error function, u1 I(A -fl1)/aLJ and u2 = (A-12)/a_21, where s, and p2 are the means of the two distributions anda1 and a2 are their standard deviations. This is at a minimum when dp/dA = 0, i.e. when (al/a-1)exp (-u2/2) = (a /a2)exp(-ut/2). =
Thus AC may be found by solving the quadratic equation, aA2+bA +c = 0, where the coefficients are defined by: a (1/o2j)-(1/oj2) b= c=
(4)
2[#1/a2)- /(4,2)] (2/2) - 1U/al2) -2 In [(a2/a2)/(al/l)].
The frequency of occurrence of each possible type of transition between any two of the several amplitude levels (including the shut level) was counted and the proportion of each type of transition was calculated.
Distributionsof shut times Shut-time distributions usually were fitted with four exponential components. The shut-time resolution was set to the duration at which complete closures from the50 pS level attained an amplitude that ensured that if the events were not really complete closures, but actually brief sojourns in a condwctance sublevel, then they must represent types of transitions that were observed with a frequency less than 0 5 % of the total number of completely resolved transitions from the50 pS level. In every record but one, transitions that appeared to be direct between the 50 pS level and a level below 30 pS occurred in proportions less than 05 % of this total, and the number of such transitions was less (often much less) than1-0% of the number of completely resolved transitions between the50 pS level and the shut level. Therefore the shut-time resolution was usually set to ensure that events fitted as shuttings from the50 pS level were not transitions from the 50 pS level to the 30 pS level. This was done by setting the resolution for closures to the duration, d, that gave an A.m.Ao value (eqn (2)) that was equal to [A50 (A30 -2s)]/A50, where A60 was the absolute value of the mean amplitude of50 pS openings and (A30 2s) was the absolute value of the mean amplitude of 30 pS openings minus twice its standard deviation. (The means and 'standard deviation were obtained from the Gaussians fitted to the respective peaks in the amplitude distributions.) This duration was usually 04-O0-5 T. This also ensured, of course, that events fitted as shuttings from the50 pS level were not in fact brief transitions to the 40 pS level and that events fitted as shuttings from the 40 pS level were not brief transitions to the 30 pS level. Fitting of the shut-time distributions was performed with the open-time resolution set to give less than 10-8 false eventss-1 for pS openings. -
50
Distributions of apparent open times The distributions of apparent open times for openings to each of the identified conductance levels were fitted with one or more exponential components. Shut-time and open-time resolutions were
149 GLUTAMATE RECEPTOR SINGLE-CHANNEL CURRENTS set to give false-event rates below 10-8 s-1 (with Ao in eqn (2) equal to the mean amplitude
determined for 50 pS openings in the record), in order to minimize the effect of missed events on the apparent duration of well-defined openings. However, distributions of open times were only fitted for openings of well-defined final amplitudes. For openings to the 8, 17, 30 and 40 pS levels, usually only openings of duration greater than 25 Tr were included in the fitted range. In some cases, the great majority of openings measured as 30 and 40 pS events had durations less than 2M5T7. In these cases, this restriction was relaxed somewhat and openings with durations above 2-0Tr, or rarely 1.5T7, were included. The situation was rather better for 50 pS openings, because these were the largest openings observed. Any incompletely resolved opening that reached an amplitude too great for it to be an opening to the 40pS level was with high probability a 50 pS opening. From the amplitude distribution fitted for each record, the ratio (A40+2s)/Ar0 was calculated, where A50 was the absolute value of the mean amplitude of 50 pS openings and (A40 + 28) was the absolute value of the mean amplitude of 40 pS openings plus twice its standard deviation, 8. The duration, d, was found for which Amax/Ao in eqn (2) was equal to this ratio. The ratio, (A40 + 28)/A80, had a mean value (± s.E.M.) of 0 93 +0 03 (n = 38). For d = 1-54T, we find Ama/Ao = 0 94. On average, d/l; was 1P44+0-14 (± S.D.), and typically events of durations above 1-5Tr were included in the distributions of apparent open times for 50 pS openings. Distributions of the durations of contiguous openings were also analysed. Contiguous openings were defined as any series of openings, to whatever level, that were not separated by a shutting of duration greater than the resolution. The shut-time resolution was set as it was for the fitting of shut-time distributions (typically at 0.4-0.5Tr.
Analy8i8 of bursts of openings Bursts were defined as groups of openings separated by shuttings of duration less than a critical length tc, which was calculated from the distribution of shut times as described in Colquhoun & Sakmann (1985, eqn (3)). Values of t, were selected such that both of the briefest two components of shut times were classified as 'gaps within bursts'. In most cases, t4 was between 1 and 2 ms (mean+ S.D., 1-61 +0-41 ms). The distributions of burst lengths, total open time per burst, and the number of open periods per burst (1+the number of brief gaps) were analysed routinely. Distributions of total open time per burst were also fitted after excluding all time spent at conductance levels other than the 50 pS level. These distributions were fitted, as appropriate, by the sum of multiple exponential or geometric terms (Colquhoun & Hawkes, 1982). In some cases, only those bursts were analysed that consisted entirely of alternations between a given conductance level and the shut level. The distribution of bursts which had mean amplitudes within a specified range was also analysed for some records. The mean amplitude of a burst was calculated as LA tt/Z t, where A, and t4 were the amplitude and duration, respectively, of the ith opening within a burst. Analysis of clusters Some records contained well-defined clusters of bursts (Colquhoun & Hawkes, 1982), during which the open probability (p0) was markedly higher than during other portions of the record. These clusters had durations above 200 ms and contained large numbers of resolved single-channel transitions. Clusters were analysed separately and the resultant values of shut times, open times, etc. were compared to the corresponding values obtained from portions of the record during which there was no obvious clustering. Correlations between events Autocorrelation coefficients were calculated, and runs tests evaluated, as described by Colquhoun & Sakmann (1985). RESULTS
Amplitude distributions for glutamate, aspartate and NMDA Figure 1 shows histograms of amplitude distributions obtained for single-channel currents activated by glutamate, aspartate and NMDA in outside-out patches held
150
J. R. HOWE, S. G. CULL-CANDY AND D. COLQUHOUN A Glutamate 200
150 100
50 0
5
6
7
6
7
B Aspartate 125 I
100
0
,
75
>0.
,
50
0
cr 0
2
U-
25
0
1
2
3
4
5
C NMDA
200 150 -
100 50 0
1
5 Negative amplitude (pA) 2
3
4
Fig. 1. Histograms of amplitude distributions obtained for completely resolved openings evoked by 30/SM-glutamate (A), 30 ,uM-aspartate (B) and 30 ,uM-NMDA (C) in outside-out patches held at -100 mV. (Currents were inward, therefore negative amplitudes are plotted; glutamate and aspartate data obtained from the same patch.) Distributions were fitted with the sum of four or five Gaussian components. With each agonist, 75-80 % of the openings were to the largest conductance level. The current amplitudes obtained from the means of the Gausians fitted to these openings correspond to single-channel chord
151 GLUTAMATE RECEPTOR SINGLE-CHANNEL CURRENTS at -100 mV. The distributions were fitted with the sum of four or five Gaussian
components. Three to five Gaussian components were distinguished in all the amplitude distributions obtained with glutamate, aspartate and NMDA. (Only completely resolved openings, defined as those of duration greater than 2-5 filter rise times, 25 Tr, were included in these distributions.) Current-voltage plots for the respective peaks in these distributions were approximately linear between -100 mV and + 70 mV and all gave reversal potentials that were near 0 mV. Over this range of membrane potentials, mean single-channel chord conductances of 9-2 + 0-5, 188±+ 11, 33-3+1 0, 4241 +0X7 and 51X0+0X7 pS were estimated for the different open levels detected in amplitude distributions (data from eleven to thirty distributions; reversal potentials taken as 0 mV). These values are similar to values we reported before from analysis of a smaller number of granule-cell patches (Cull-Candy et al. 1988 a), and our present results support our earlier conclusion that glutamate, aspartate and NMDA primarily produce openings to a- conductance level of about 50 pS in patches from granule cells. The amplitude distributions shown in Fig. 1 were typical of those observed for these three agonists in terms of the relative proportions of openings to each conductance level; and there were no systematic or substantial differences in this regard between the results obtained with glutamate, aspartate and NMDA. In some patches, discrimination of the 33 and 42 pS levels in the distribution of current amplitudes was quite clear. For example, two separate peaks that correspond to such openings are easy to see in the histogram of the distribution depicted in Fig. 1B. That this distinction was not an artifact of the way in which the currents were measured was verified by examining the distribution of the mean low-variance current amplitude, as described by Patlak (1988). In other patches, however, this distinction was not so obvious. For example, in Fig. 1 C the Gaussian fitted to what corresponded to the 33 pS events appears only as a shoulder on the secondlargest peak (which corresponds to the 42 pS openings). However, in all of these latter cases, if openings to these conductance levels were fitted with a single Gaussian component, the standard deviation of this Gaussian was much larger than the corresponding standard deviation for the Gaussian fitted to the 51 pS openings (which because of the large proportion of openings to this level was well defined). In addition, the former standard deviation and the difference in amplitude of some of the events that fell within this current range were very much larger than expected from the measured r.m.s. noise of the recording, even when the excess noise present during channel openings was taken into account (see below). We therefore chose to fit two Gaussian components to these current amplitudes even when discrete peaks were not very clear from examination of the histogram. In a few cases, when the amplitudes of the components overlapped considerably and their relative areas were therefore not well defined, the standard deviations of the three components fitted to the largest amplitude openings were constrained to be equal. Although this procedure was somewhat arbitrary, consideration of all the results convinced us that it was justified. It was also deemed better to include an additional component, even if that component gave a relative area that was so small as to be unconvincing, if inclusion of that component resulted in a clearly better fit to the major components in the distribution.
Single-channel currents show inward rectification As we noted in an earlier brief communication (Howe et al. 1987), at very hyperpolarized patch potentials single-channel currents for openings to the largest three conductance levels were considerably larger than predicted from linear conductances of 47, 52 and 53 pS (A-C) for a reversal potential of 0 mV. The inset in panel C shows an example of an opening to the largest conductance level followed by a series of openings to a conductance level of about 40 pS in the patch superfused with NMDA. Calibration bars are 6 pA and 10 ms. The record was low-pass filtered at 3 kHz (-3 dB).
152
J. R. HOWE, S. G. CULL-CANDY AND D. COLQUHOUN -5
A 50 pS
-200
Membrane potential (mV) -50 -150 -100 I
A
a
a
I
.0
501
a
__-5
100
C
XL cJ
AdA A1-
&
A--
5 --10
0) C
_qa c
._
--15
B 40pS
-200
6
Membrane potential (mV) -150 -100 -50
100
-3
CL -w
3
C
A-
c
A'l
C
A
._
n
L-12 Fig. 2. Current-voltage relationships for the Gaussian components with the largest (A) and the second-largest (B) mean currents in amplitude distributions obtained with glutamate (0), aspartate (A) and NMDA (0). The data were least-squares fitted (continuous curve) with a linear polynomial for potentials above 0 mV and a cubic polynomial for negative potentials (see text). The dashed line shows the extrapolation of the linear portion of the fit. Some of the values obtained at the same membrane potentials were offset slightly for increased clarity. y
extrapolation of the current-voltage plots obtained at membrane potentials positive to -100 mV. This inward rectification was substantial, as is shown clearly in Fig. 2 which presents current-voltage plots for the largest (Fig. 2A), and the second-largest (Fig. 2B), conductance levels observed with glutamate, aspartate and NMDA. Each
153 GLUTAMATE RECEPTOR SINGLE-CHANNEL CURRENTS point in Fig. 2 represents the mean current calculated for a peak in the distribution of single-channel current amplitudes that was estimated from the multiple-Gaussian fit obtained from a single patch (either the peak corresponding to the largest openings (Fig. 2A) or the peak corresponding to the second-largest openings (Fig. 2B) measured at that potential). Current-voltage plots for the third-largest conductance level showed similar inward rectification. This inward rectification is also evident in Fig. 3A, which depicts point amplitude histograms from one patch held at potentials of -80, - 120, - 160 and -200 mV (panels a-d, respectively). These histograms were constructed from the amplitudes of each sample point during channel openings and therefore reflect both the number and the duration of openings to a given conductance level. Because of the presence of multiple open levels, and of shuttings of duration below the shut-time resolution, the form of these distributions is not the simple sum of Gaussian components (see Methods). However, the distribution of sample points above (and near) the mean amplitude of the largest-conductance openings is expected to be Gaussian, and the mean predicted from this distribution therefore gives an estimate of the mean amplitude of these openings at a given membrane potential. In Fig. 3A, single Gaussians (smooth curves) have been fitted to the points with the largest absolute amplitude in each distribution (filled bins); and at - 120, - 160 and -200 mV the mean currents estimated from these fits are substantially larger than those expected from the single-channel conductance of 51 pS estimated at membrane potentials of -100 mV and above. (The values calculated for a conductance of 51 pS, a reversal potential of 0 mV, and a linear current-voltage relation are indicated by the arrowheads at the top of each panel in Fig. 3A.) In order to compare results obtained at different patch potentials, it was useful to express single-channel current amplitudes as conductances. This was complicated, however, by the inward rectification just described, and by the fact that five discrete peaks were not distinguished in the amplitude distributions obtained from some patches. It was therefore desirable to fit the results in Fig. 2, even though this fit was necessarily empirical because the reasons for the non-linearity of the current-voltage curves are not known. For negative membrane potentials, the data in Fig. 2A and in Fig. 2B were fitted (equally weighted, least squares) with a cubic polynomial: (5) y= bo+blx+b2x2+b3x3, where y was the mean single-channel current and x was the membrane potential. For positive membrane potential values, b2 and b. were constrained to be zero, that is the data were fitted with a linear polynomial. The continuous curves in Fig. 2 are the combination of the cubic and linear polynomial fits to each set of data and the dashed lines are the extrapolation of the linear fits to the results at positive membrane potentials. The linear portions of the fits gave slope conductances (b1 in eqn (5)) of 47-6 and 36-8 pS for the data in Fig. 2A and Fig. 2B, respectively. At potentials positive to -100 mV, the measured currents do not deviate substantially from the linear portion of the fit. For example, at -80 mV the respective chord conductances were 51'4 and 42-3 pS. However, at -200 mV, which was the most negative patch potential examined, the fits yielded corresponding chord conductances of 68-0 and 60-3 pS.
154
J. R. HOWE, S. G. CULL-CANDY AND D. COLQUHOUN
These fits provided quantitative estimates of the dependence of the apparent single-channel conductance on membrane potential. They also gave estimates, at a given patch potential, of the mean single-channel currents expected for openings to different conductance levels, which in turn provided a basis for assigning conductance levels to peaks in those amplitude distributions in which all of the five conductance TABLE 1. Relative proportions (%) of different conductance openings 9 PS 19 PS 30 pS 40 pS 50 PS Glutamate 1P5+0 5 2 0+1-0 4-8+1-1 14-3+1-7 77-4+1-8 Aspartate 3-0+P10 1V8+0-5 5-1+1-1 15-4+1-4 75 7+2 0 NMDA 2-4+P10 1-9+1 1 2-9+006 15-2+2 6 77-6+2 9 The mean (+ S.E.M.) values are from multiple-Gaussian fits to seven, twelve and ten distributions for glutamate, aspartate and NMDA, respectively. Only openings of a duration greater than 2-5 T, were included in the distributions, which on average consisted of about 650 such openings.
levels were not well defined. For a given patch, and a given membrane potential, openings to different conductance levels were defined on the basis of the multipleGaussian fit to the distribution of single-channel current amplitudes, and the subsequent assignment of openings to open-level ranges based on calculation of a series of critical amplitudes (see Methods, eqn (4)). However, in what follows the three largest conductance levels observed will be referred to (for the sake of simplicity) as the 30, 40 and 50 pS open levels. These values are close to the values obtained from the polynomial fits at patch potentials near the resting membrane potential of cerebellar granule cells in culture (typically about -70 mV). Current-voltage plots for 9 and 19 pS openings did not show inward rectification or deviate substantially from linearity at membrane potentials negative to -100 mV, and the amplitude data obtained with glutamate, aspartate and NMDA may be summarized as follows. The vast majority of openings produced by these three agonists were to conductance levels of 30 pS and above. Table 1 gives the mean values for the relative proportion of completely resolved openings to each of the five conductance levels that were obtained with glutamate, aspartate and NMDA. It can be seen that, on average, 75-80 % of the openings produced by these three agonists were to the 50 pS level. Current-voltage plots for 30, 40 and 50 pS openings all showed similar and substantial inward rectification at membrane potentials negative to about -100 mV, whereas smaller conductance openings produced by these agonists did not.
Large-conductance openings are 'noisy' In addition to histograms of open-point amplitudes, Fig. 3A (panels a-d) also shows sample-point histograms for representative portions of the records at each potential during which there were no openings (the peak of these 'shut-point' histograms is at a current value of approximately zero in each panel). The standard deviations of the single Gaussians fitted to these distributions give estimates of the r.m.s. noise of the recording. It can be seen from comparison of the fits to the openpoint and shut-point amplitude histograms, and from inspection of the corresponding
155
GLUTAMATE RECEPTOR SINGLE-CHANNEL CURRENTS B
A
a
a -8OmV
3000-
o2000
0.17 pA
v
0.33 pA
-
if
6
01 iooo .7
0.
(0
-1 0 1 2 3 4 5 6 b -120 mV 2000 l 0.17 pA 0.36 pA < 1500
_S
0
o 1000
a' 5000
vI
c
M
om
0 2 4 6 8 10 -160 mV 15000.23 pA o 051 pA
0)
-2
a)0*
c
LL.
X 500
0.
.. .,
-3 0 3 d -200 mV 12501029 pA
6
41V
y
I
10 ms
9 12 15
d O
0 75 pA
< 1000 0
10 ms c
I
Xn 1000-
0W
10 ms
b
I
r
fop
750 J1
0)
CL 250
-3 0 3 6 9 12 15 18 Point amplitude (pA)
10 ms
Fig. 3. A, histograms of point amplitude distributions obtained from one patch at -80 (a), -120 (b), -160 (c) and -200 mV (d) for shut (left) and open (right) portions of the records. Inward currents were produced by 100 ,uM-aspartate. Distributions were fitted with single Gaussians. The means for the open-point fits were 4-25, 7-29, 10-60 and 13-24 pA (panels a-d, respectively; the standard deviations (pA) for the Gaussians fitted to the open- and shut-point histograms are given above the histograms). Only those values that fell within the black bins of the histograms were included in the open-point amplitude fits. Arrow-heads show values expected for a conductance of 51 pS and a linear I-V relationship. B, examples of single-channel currents recorded in the same patch and the same membrane potentials at which the corresponding histograms in A were obtained. Note increased noise during channel openings, which comparison of the standard deviations of the Gaussians fitted to the open and the shut distributions in A indicates is, on average, approximately 2-fold. Records were low-pass filtered at effective cut-off frequencies (from eqn (1)) of 2-5, 2-5, 3-3 and 4-6 kHz (-3 dB; panels a-d, respectively). In subsequent figures, the -3 dB frequencies refer to the filtering imposed on the replayed signals; and the records were taped at a bandwidth of 5 kHz unless stated otherwise. In this and all other figures, when single-channel currents are shown, all the data points sampled have been plotted. Note that the plots in A are scaled differently, as are the single-channel currents in B.
J. R. HOWE, S. G. CULL-CANDY AND D. COLQUHOUN examples of single-channel currents shown in Fig. 3B (panels a-d), that this noise is increased during channel openings. This excess 'open-channel noise' (Sigworth, 1985) was a consistent finding, and estimates of its magnitude were obtained from the ratio of the standard deviations of open-point and shut-point amplitude distributions such as those in Fig. 3A. On average, this ratio was about 2-0 for records in which most of the openings observed were to the 50 pS conductance level; and this ratio did not appear to depend on patch potential. It is probable that brief and incompletely resolved transitions between the 30, 40 and 50 pS open levels, as well as shuttings of duration below the imposed shut-time resolution, both contributed to this excess 'open-channel noise' present in our recordings from granule-cell patches (see below). 156
Amplitude distributions for quisqualate and kainate In two patches, quisqualate produced predominantly small-amplitude openings. We have published an amplitude histogram from one of these patches in a previous paper (Fig. 6C, Cull-Candy et al. 1988a) and have pointed out that in these two patches the relative proportions of small (below 20 pS) and large (above 30 pS) conductance openings are consistent with the single-channel conductances of 15-30 pS that were determined with quisqualate from analysis of whole-cell current noise. In two other patches, quisqualate caused mainly 50 pS openings and the amplitude distributions obtained were similar to those obtained for NMDA, aspartate and glutamate. Possible explanations for this variability were discussed in Cull-Candy et al. (1988a). The results obtained with kainate (10 or 30 #M) were most consistent. Although kainate produced openings to each of the five conductance levels seen with the other agonists, in six of the seven patches examined most of the openings produced by kainate were to open levels below 20 pS. Figure 4A shows single-channel currents evoked by 10 ,uM-kainate in a granule-cell patch held at -70 mV. In addition to four clear single-channel openings of about 1P0 pA in amplitude, there are two openings to a current level of about 3-5 pA. Figure 4B shows a histogram of the distribution of the amplitudes of completely resolved single-channel currents that was obtained from the same patch at this membrane potential. Most of the openings produced by kainate in this patch had amplitudes below 1-5 pA. Two smaller peaks in the distribution occur at inward current amplitudes of about 3-0 and 3-5 pA, respectively. This was typical of the results obtained with kainate. From consideration of all the results, there was no doubt that kainate evoked two populations of openings with conductances below 20 pS, although the two corresponding peaks in the amplitude distributions were not always obvious from simply inspecting histograms of the distribution. For example, although multiple discrete peaks cannot be distinguished in the histogram in Fig. 4B for inward currents of 2-0 pA or less, attempts to fit the entire distribution as the sum of three, or even four, Gaussian components led to fits that were obviously poor, and gave standard deviations for the Gaussians with the smallest means (for inward currents) that were much larger than those for the peaks at about 3 0 and 3-5 pA (and that were considerably larger than expected from the measured r.m.s. noise of the recording). However, a good fit was obtained (smooth curve) if the distribution was
GLUTAMATE RECEPTOR SINGLE-CHANNEL CURRENTS
157 fitted with the sum of five Gaussian terms and if the standard deviations for the three terms with the smallest means were constrained to be equal to each other and to be approximately the size of those obtained for the peaks at about 3-0 and 3-5 pA (see legend). The mean conductances determined for the smallest two open levels seen
A
4:
100 ms
8 250 200-
CL In
150 o)
5 100
LL 500 0 0
1
3 2 Negative amplitude (pA)
4
5
Fig. 4. A, about 750 ms of contiguous record showing four small-amplitude openings and two large openings (amplitudes about 3-5 pA) that were elicited by 10 AM-kainate in a patch held at -70 mV. B, histogram of inward current amplitudes for all completely resolved openings recorded from this same patch at -70 mV. The amplitude distribution was fitted with the sum of five Gaussian components with means (and relative areas) of: 0-73 pA (20-0 %), 1P07 pA (54-6 %), 1P73 pA (1P7 %), 2-85 pA (16-4 %), and 3-49 pA (7-3 %). The standard deviations of the Gaussians with the three smallest means were constrained to be equal to each other (0-20 pA). The standard deviations for the other two Gaussian components were 0-22 and 0-23 pA.
with kainate (results from seven patches) were 8-1 and 15-3 pS. The relative frequencies with which kainate evoked openings to the five observed conductance levels were: 8 pS, 40-5 ± 10-4 %; 15 pS, 38-3 ± 9-3 %; 30 pS, 5-2 + 2-7 %; 40 pS, 6-8 ± 3-0 %; 50 pS, 9-2 + 5-5 %. (The results are from six patches; the results from the one patch in which most of the openings evoked by kainate were to the 50 pS level were not included.) With kainate, and also with quisqualate, current-voltage plots for the two peaks with the smallest mean inward currents in the amplitude distributions showed no apparent deviations from linearity over the range of potentials investigated (-140
J. R. HOWE, S. G. CULL-CANDY AND D. COLQUHOUN 158 to +40 mV), and reversal potentials estimated from these plots were not significantly different from zero. However, 30, 40 and 50 pS openings evoked by kainate and quisqualate showed inward rectification similar to that seen for similar openings evoked by NMDA, aspartate and glutamate. A 10lM-NMDA, -80 mV
..
20 ms
B 10 jM-glutamate, -100 mV
0. .... ...
(0
20 ms
C 10 jpM-aspartate,-140 mV
....
10 ms Fig. 5. Long-lived sublevel transitions in bursts of openings produced by 10 /SM-NMDA (A), 10 /SM-glutamate (B) and 10 /SM-aspartate (C). The three patches were held at potentials of -80, -100 and -140 mV, respectively (note different calibrations). The dotted lines represent the mean inward current amplitudes for openings to the largest and the second-largest conductance levels observed in each patch (estimated from the multipleGaussian fits to the amplitude distributions). The signals in panels A-C were low-pass filtered at 2-0, 3*5 and 4-5 kHz (-3 dB), respectively. Signals in panel C were taped at a bandwidth of 10 kHz.
The values of 8 and 15 pS determined for small-conductance openings evoked by kainate are similar to the values of 9 and 19 pS determined for small-conductance openings evoked by glutamate, aspartate and NMDA at membrane potentials of
GLUTAMATE RECEPTOR SINGLE-CHANNEL CURRENTS
159
-100 mV and above, and they were also similar to the conductances estimated for small-amplitude openings caused by quisqualate. It seems likely that the two smallest conductance levels seen with each of the five agonists are the same. When all of the data for the two smallest conductance levels were pooled and linear leastsquares fit performed on the resultant current-voltage plots, the fits gave singlechannel conductances of 8 and 17 pS (n = 28 and 21, respectively). The reversal potentials estimated from these fits were 12-1 and 1.0 mV for the 8 and 17 pS openings, respectively, and were not significantly different from zero. For the reporting of the analysis of the kinetics of openings to different conductance levels, the smallest two open levels observed with each of the five agonists will therefore be referred to below as the 8 and 17 pS levels. Transitions between conductance levels In each patch and with each agonist, the majority of transitions were between the shut level and the various open levels. However, considerable numbers of what appeared to be direct transitions between the 30, 40 and 50 pS open levels were also observed consistently. By far the most frequent of these transitions were those between the 40 and 50 pS levels. Examples of transitions between these two open levels are shown in Fig. 5. These examples were chosen for illustration because they contained several relatively long-lived sojourns at the 40 pS level that occurred within a contiguous 50-100 ms portion of the record. They are, however, in that sense rather atypical. In fact, most sojourns at the 30 or 40 pS levels were substantially less than 10 ms in duration (see below). Although only openings of durations above 2-5 Tr were used for the amplitude distributions (and the open-level ranges defined from them), each record contained many incompletely resolved events that were clearly not fitted well by the step-response function as single brief shuttings or brief 50 pS openings. For example, Fig. 6A shows a single-channel current produced by 30 gtM-NMDA at a patch potential of - 130 mV in which there are three brief interruptions (openings are downwards). Figure 6B shows the same current with the fit (smooth curve) obtained from the known step-response function of the recording system if it was assumed that the signal arose entirely from oscillations between the 50 pS open level and the shut level, and if it was further assumed that the three interruptions of the open level represented brief, and therefore incompletely resolved, single full closures or 'gaps'. Whereas the second and third events are fitted well as brief gaps with estimated durations of 35 and 79 Its, respectively, the duration of the first interruption is too long for it to be a partially resolved closure. The fit to this duration gave a shutting of 160 Its and it can be seen that a shutting of this duration would be expected to reach the baseline. Figure 6C shows the obviously better fit obtained if the first event was fitted, not as a closure, but as a sojourn in a conductance sublevel. The final amplitude was set to -4-35 pA, which corresponded approximately to the 30 pS open level at this potential, and the fit gave an estimated duration for this event of 228 /is (about 2-02T). However, this event could be fitted equally well as multiple brief openings and closings, as could similar events in other records. Figure 6D illustrates the fit obtained if it was assumed that the first interruption of the 50 pS open level was not a transition to a sublevel, but rather two
160
J. R. HOWE, S. G. CULL-CANDY AND D. COLQUHOUN
brief full closures separated by a brief full opening. This fit gave durations for these three consecutive events of 47, 71 and 51 ,us. There is clearly little to choose from between the fits in panels C and D. Similar ambiguities have been discussed by Colquhoun & Sakmann (1985) and are unavoidable given the limited time resolution inherent in the measurements. We A 30 pM-NMDA, -130 mV
B
C Sublevel
D Four gaps
1
Three
gaps
mC
1 ms Fig. 6. A, a burst of 50 pS openings (downwards) that was produced by 30 /M-NMDA in a patch held at a potential of -130 mV. Sequential 50 pS openings are separated by three brief interruptions. The signals were low-pass filtered at 4 kHz (-3 dB). B, the signal in A with the calculated step-response function superimposed (smooth curve). Each of the three brief interruptions were fitted as though they were incompletely resolved single full closures, i.e. as three brief gaps. C, the signal and the superimposed step-response function when it was assumed that the first interruption represented a sojourn in a conductance sublevel rather than a partially resolved shutting. The final amplitude of the current at this sublevel was set to -4-35 pA. D, the signal and the superimposed step-response function when it was assumed that the first brief interruption represented two brief full closures that were separated by a brief opening to the 50 pS open level, i.e. that the entire signal represented a series of 50 pS openings that were separated by four brief gaps. The estimated durations of the various events are given in the text. Calibration bars, 5 pA and 1 ms, apply to each of the four panels.
usually chose to fit signals that did not fit well as isolated brief gaps as transitions between two open levels, because it was evident that the records did contain many well-defined sojourns in conductance sublevels. Only when the signal was asymmetrical, or when the amplitude required to fit the transition was substantially different from the amplitude expected for any of the well-defined amplitude levels, were such events fitted as multiple brief transitions between open and closed levels. Such occurrences were rare. Table 2 gives the numbers and relative proportions of each possible type of transition between the six conductance levels (including the shut level) that were obtained with NMDA, aspartate and glutamate (the way in which the analysis was
161 GLUTAMATE RECEPTOR SINGLE-CHANNEL CURRENTS done is described in detail in the Methods; the results from one of the records in which the discrimination between 30, 40 and 50 pS openings was unclear were excluded). The results were similar with each of these three agonists and the relative proportions of each type of transition did not exhibit any dependence on membrane voltage or on agonist concentration. All the results obtained with these three agonists were therefore pooled. In Table 2, the results in the columns headed 0-3-05 Tr were obtained when transitions were counted if two adjacent events were each of a duration that solely ensured that they were not random noise (0-3-05 Tr). The results in the columns headed 25 Tr were obtained when only those transitions were counted that occurred between adjacent events that were each of duration greater than or equal to 25 Tr. The assignment of the transitions is therefore more certain in the latter case, although limiting the analysis to only those transitions that occurred between two completely resolved events resulted in a large reduction in the total number of transitions. For any number of levels, n, there are n(n-1) possible types of transitions between two of these levels, and for any transition A-B (starting in level A and ending in level B) there is a corresponding transition B-A (starting in level B and ending in level A). In Table 2 these pairs of transitions have been listed together. Two conclusions are apparent from the results given in Table 2. First, what appeared to be direct transitions between the 8 or the 17 pS level and the 30, 40 or 50 pS level were very rare. For most of these possible types of transitions, it was usually the case that no such transitions were detected in the record. Ten of the twenty-nine records examined contained none of the possible types of completely resolved transitions between the 8 or the 17 pS level and the 30, 40 or 50 pS level. In contrast, transitions between the 30, 40 and 50 p8 levels were relatively common. The second conclusion that is clear from the results in Table 2 is that none of the fifteen pairs of transitions show any convincing evidence of temporal asymmetry. The numbers of A-B and B-A transitions are similar, indicating that all types of transitions that do occur between different conductance levels obey the principle of microscopic reversibility. It is also apparent that the relative proportions of each type of transition determined with the 0-3-0-5 Tr criterion and those determined with the 2-5 Tr criterion are similar. Thus, even when brief events are included, there is no compelling evidence that transitions occur between the 8 or the 17 pS level and the 30-50 pS levels and there is no evidence of temporal asymmetry. With kainate and quisqualate, 10402 transitions were detected with the 0 3-0 5 Tr criterion, 5517 of which involved the 8 or the 17 pS open level. Of these 5517 transitions, fifty-seven of them (or about 1-0%) appeared to be direct transitions between the 8 or 17 pS level and the 30, 40 or 50 ps level. With the 2-5Tr criterion, 3750 of the 5880 apparently direct transitions that were measured involved the 8 or the 17 pS level. Eighteen of these 3750 transitions (or about 0 5 % of them) appeared to be direct between the 8 or the 17 pS open level and the 30, 40 or 50 pS level. Thus, as with glutamate, aspartate and NMDA, apparently direct transitions between these levels were rare. The results obtained with kainate and quisqualate also gave no indication of temporal asymmetry for any of the types of transitions identified.
6
PHY 432
162
J. R. HOWE, S. G. CULL-CANDY AND D. COLQUHOUN TABLE 2. Direct transitions with glutamate, aspartate and NMDA 03-057T 251T
No. No. Percentage Percentage 0-8 530 340 541 2 40 8-0 4 20 326 0-17 710 260 17-0 730 4-13 249 3-65 0-30 1172 205 30-0 1088 537 205 251 0-40 2161 740 40-0 1172 2165 759 10 15 0-50 11922 4902 12033 58 46 5075 63 19 50-0 8-17 8 13 17-8 15 006 10 010 8-30 3 1 30-8 6 0-03 0 0-01 8-40 9 2 1 40-8 15 0 05 0-02 8-50 48 15 52 0 29 50-8 13 0.19 17-30 6 26 22 012 4 011 30-17 41 17-40 8 34 8 40-17 0.15 0-13 11 17-50 65 0 45 12 50-17 113 0-25 52 30-40 170 0 84 40-30 163 49 0 70 244 30-50 1108 4 99 2 94 50-30 1026 236 40-50 1995 859 50-40 1972 10 45 847 11 04 39948 15447 The number of each possible type of transition between the shut level (level 0) and the 8, 17, 30,40, and 50 pS open levels. The mean proportion of each of the fifteen possible pairs of transitions (calculated from the individual values for each record; n = 28) is also given. Transitions were counted for the case in which the duration of each of two adjacent events was longer than 0-3-05 Tr and the case in which both adjacent events were completely resolved (2X5 T).
Distributions based on shut times In granule-cell patches, single-channel activations caused by NMDA, aspartate and glutamate consist of bursts of openings, within which sequential openings are separated by brief gaps (Howe et al. 1988). The procedure we followed for setting the resolution (see Methods) ensured in all cases that shuttings included in distributions of closed times were not transitions between open levels of a type that occurred in the record in significant proportions. With the shut time resolutions used (range,
GLUTAMATE RECEPTOR SINGLE-CHANNEL CURRENTS 163 0-29-0{69 1T; mean +S.D., 0-44 + 0-09 T,) it was virtually certain that shuttings of a duration above the resolution could be distinguished from transitions between the 30, 40 and 50 pS open levels. At these resolutions, however, it was possible that some events fitted as shuttings were in fact transitions to the 8 or 17 pS levels. Although it is clear from the results given in Table 2 that such completely resolved transitions were extremely rare, the number of these transitions would be expected to be low if such transitions were brief. For example, the number of transitions between the 8 and 50 pS levels that were obtained with the 25 1T criterion is about the number that would be expected if the events that corresponded to the briefest gap component were in fact brief transitions between these two open states. In several cases, we therefore fitted the distribution of only those shuttings that had a duration greater than 1-5 Tr. A shutting of duration 15 Tr would attain 94 % of its eventual amplitude, and an event of such amplitude would approach the shut level too closely for it to be a transition to the 8 pS level. The time constants estimated for brief gaps from these fits were similar to the time constants obtained when the resolution was set at 04-05 T, The procedure used to set the shut-time resolution therefore appears to have been sufficient to exclude significant contamination of the distribution by misclassified events; that is events that were fitted as shuttings, but that were in fact brief sojourns in a conductance sublevel. The distribution of shut times for NMDA, aspartate and glutamate always clearly contained at least four exponential components. The distributions reflected primarily the characteristics of shuttings from the 50 pS level during low po portions of the records. Figure 7 shows histograms of shut time distributions obtained from two different patches. Panels A and D show the respective four-exponential fits to each distribution (smooth curves) superimposed on histograms of the distribution displayed on a logarithmic scale. The peaks of the fitted curves correspond to the respective means of each of the four exponential components. The two briefest components in each distribution have means below 1 ms. These two components are shown on arithmetic time scales in the other panels in Fig. 7 (B, C and E, F; only events in the unshaded bins were fitted; the significance of the shaded bins is discussed below). The mean time constants and relative areas of the two briefest gap components detected with glutamate, aspartate and NMDA are given in Table 3. There was no indication that these parameters varied with agonist concentration over the range. of concentrations tested. There was no substantial variation in the time constants determined for either type of brief gap over the range of membrane potentials investigated (-200 to + 60 mV). Although with each agonist there was a tendency for the time constant of the briefest gap component to become briefer with hyperpolarization, the slopes determined from regression analysis of semilogarithmic plots of this time constant as a function of membrane potential were clearly not statistically significant and corresponded to e-fold changes per 200-60 mV. Similarly, the area of the briefest gap component did not appear to depend on membrane potential. There was also clearly no substantial or significant dependence of the time constant of the secondbriefest gap component on membrane potential. In Table 3, the measurements made of these three parameters at different membrane potentials have therefore been pooled. 6-2
*l
J. R. HOWE, S.
164 A
:r
60
-
45
-
30
U-15 2,
10
1 o-2
..I
I
B 50 U)Z o
40-
|I
30
c 20
10-
C
No
I
U-
0
4-
0.00
0.05
-
uZ o
LO o
6045.
a) L-
al
15
Ut-
0
0
''"'11I
10 1
CULL-CANDY AND D. COLQUHOUN
I'l''"'
D 80
60 =
40-
U-
I
r
'
20O
-
1
''"
1o-2 1(o-1 103 104 Shut time (ms) (log scale)
102
0 10
4
aD
0-15
iol
io0
102
103
104
E
80
-
ZLA 60
-
ch
LC)
CL
40
-
20
-
a)
a) a,
;.o.: 4,
;.F.: ie.; I
L-
rsi;
dY
0-
10O0
C
75
.,..I
10°0
lo-'
C.
000
0.20
005
0-10
0.15
0.20
1
2
3
4
0 25
F
125 Un o
LO
a
CL
100 75
u 50 r 25
a) U-
-'1
2
3
4
5
0
5
Shut time (ms)
Fig. 7. Histograms of shut time distributions obtained with 30 ,sM-aspartate (A-C) or 30 ,sM-glutamate (D-F) in two patches at membrane potentials of - 120 and - 130 mV,
respectively. Each of the distributions were fitted with four exponential components. Panels A and D show these fits (smooth curves) superimposed on histograms of all the events fitted (shuttings of durations above 40 ,us in panel A and above 50 1as in panel D). Log (t) vs. frequency is plotted and the peaks of the fitted curves correspond to the means of the exponential components. Panels B and E show histograms on arithmetic scales chosen to illustrate the briefest shut time component for each patch (bin width is 5 4as for shuttings briefer than 40 4us in panel B). The time constants for these components were 25-2 ,us (B, 40 3 % relative area) and 46 1 ,us (E, 45-6 % relative area). In these histograms, events with durations that exceeded the resolution based on calculation of the false-event rate, but that were excluded from the fit on the basis of the criteria given in the Methods, fall within the shaded portions of the histograms. For the distribution depicted in panel B, the number of such events is in good agreement with the number predicted from the fit to all other shut times. However, in panel D, far more events with durations below
GLUTAMATE RECEPTOR SINGLE-CHANNEL CURRENTS 165 However, the relative frequency with which the second-briefest type of shutting occurred did increase with membrane hyperpolarization. With each of the three agonists, the area of this component, A2, increased as the patch potential was made more negative (e-fold per 72-92 mV). With both aspartate and NMDA, the correlation between the size of A2 and patch potential was clearly significant. In TABLE 3. Characteristics of gaps within bursts A1(%) A2(%) A1/A2 r2(@Ss) r1(#s) Glutamate 62-9 + 6-3 45-9 + 3-9 664 + 88 14-7 + 2-7 3-26 + 0-18 Aspartate 31-1 + 2-6 42-3 + 4-4 673 + 58 16-1 + 1-4 2-47 + 042 NMDA 46-8 + 9-3 46-6 + 40 997 + 120 25-8 + 1P7 1P74 + 023 The mean (+ S.E.M.) values for glutamate, aspartate and NMDA are from four-exponential fits to seven, twelve and nine shut time distributions, respectively. The values given are for the time constant (r) and relative area (A) of the briefest and the second-briefest component in the distributions of shut times. A1/A2 is the ratio of the relative areas of these two components. The values for A2 and AJ/A2 were determined from the linear least-squares fits to semilogarithmic plots of the parameter as a function of membrane potential and are the antilogs of the value calculated from these fits for a membrane potential of -100 mV. The S.E.M. values given for these two parameters are one-half the difference between the antilogs of the value at -100 mV, plus and minus the logarithmic S.E.M. The logarithmic S.E.M. was determined from the regression analysis.
addition, for each of the three agonists the ratio of the area of the briefest gap component to the area of the second-briefest gap component, A1/A2, decreased with membrane hyperpolarization (e-fold per 45-100 mV), and for the data obtained with glutamate and aspartate the results of the regression analysis indicated that this was statistically significant. In Table 3, the values given for A2 and for A1/A2 are those that were calculated for a membrane potential value of -100 mV from the linear least-squares fits to semilogarithmic plots of the data obtained with each of the agonists. Although the mean durations and relative areas of the two components of brief gaps that were seen with each agonist were similar, there were some differences. The mean duration of the briefest gaps was shortest with aspartate and longest with glutamate, and the values for these two agonists were significantly different from each other (P < 0-01). The mean duration of the second-briefest gaps seen with NMDA was significantly longer than the corresponding durations determined with glutamate and with aspartate (P < 0 05) and these gaps were also more frequent with NMDA than with the other two agonists. Comparison of the values given for A2 in Table 3 indicated that the value obtained with NMDA differed significantly from the corresponding values obtained with glutamate and aspartate (P < 0 01). (Standard deviations for these values were estimated from the regression analysis in the standard way and the values were then compared with a one-way analysis of variance.) In those patches in which quisqualate evoked mostly 50pS openings, the distribution of shut times also contained four exponential components. The mean 50 ,us were observed than would be expected from extrapolation of the fit to all shuttings above 50,uss in duration. Panels C and F show histograms of shuttings of durations approximately equal to the time constants obtained for the exponential component with the second-briefest mean duration. These time constants were 477 ,us (C, 19-1 % relative area) and 661 ,us (F, 27-2 % relative area).
J. R. HOWE, S. G. CULL-CANDY AND D. COLQUHOUN 166 durations and relative areas of these components were similar to those of the corresponding components detected with glutamate, aspartate and NMDA. Shuttime histograms obtained from one such patch at a patch potential of -140 mV are shown in Fig. 8. The results obtained with kainate in the one patch in which kainate evoked large numbers of 50 pS openings were similar. B 100
A
60 co45 c4 r0
0
P'30
>.,
0.00
0.05
(75
E
*=35.6 us
0.10
~~~~~~~~~E E
c'J
0-15 0-20 0.25
0_60 ms
50
0.0
1.0
2.0
3.0
4.0
5.0
a)c~~~~~~~~~ (D
U_
vCo 30
D100
E 20 -E E 2011x, L6
r=175ms
0
a10
0
r=398ms
50 c,'-'~~~~~~
25
0
0
20
40
60
80
cq0
0 100 Shut time (ms)
500
1000
1500
2000
Fig. 8. Shut time histograms obtained from patch held at a membrane potential of -140 mV and superfused with 30 ,M-quisqualate. Quisqualate evoked predominantly 50 pS openings in this patch. The distribution of shut times above 50 ,s was fitted with four exponential components with time constants and relative areas of: 35-6 ,us, 34-5 %; 596 ,us, 32-7 %; 17-5 ms, 5-8 %; 398 ms, 27-0 %. Panels A-D show histograms with this fit superimposed. The time scales in the different panels were selected to display each of the four exponential components individually. In panel A the bin width is 30 #us above 170 I4ts. The time constants determined for the longest two gap components usually fell within the ranges 15-25 and 250-400 ms. In every patch but one, however, there were at least two channels active. Typically, three to six double openings were observed per 1000 resolved openings and the overall pr for the entire record was between 001 and 0-03. Because of this uncertainty regarding the number of channels active in each patch, the time constants of the two components of long shut times (or 'gaps between bursts') are unlikely to provide much, if any, useful information about mechanism.
The shut-time resolution that was set in order to ensure that events that were fitted as incompletely resolved full closures were not in fact transitions to the 30 or 40 pS open levels was in virtually all cases substantially above the shut-time resolution necessary to ensure that incompletely resolved events were not random noise. In panels A and D of Fig. 7, the histogram includes only those shut-times that were fitted (those of duration above 40 ,us in A and above 50 ,ts in D). In panels B and
GLUTAMATE RECEPTOR SINGLE-CHANNEL CURRENTS 167 E of Fig. 7, histograms of the briefest shut-time durations seen in each patch are displayed on an arithmetic scale; and each histogram also includes events that were too brief to be included in the fits on the basis of the criteria given in the Methods, but that were of a duration above the resolution calculated on the basis of the falseevent rate. These events fall within the shaded bins in each histogram; and in panel B include shuttings of a duration above 25 ,us and in panel E shuttings of a duration greater than 30 /ss. For the results in panels A-C, setting the value of d in eqn (2) to 25 /ts (see Methods) gave a false-event rate, Af, from eqn (3) of 1-2 x 10-12 S-1, where fc was calculated from eqn (1). Similar calculations for the other patch (panels D-F) gave a false-event rate of 8-6 x 10-1 s-5 for a shutting of duration 30 Its. In both cases it is clearly very unlikely that the events within the shaded bins resulted from random noise. However, the results in the two patches differ in one rather obvious way. In panel B the number of events that fall within the shaded bins of the histogram agrees well with the frequency of such occurrences predicted from extrapolation of the fit to shuttings with a duration above 40 ,#s, whereas in panel E the number of events that fall within the shaded bins is considerably in excess of the number predicted from extrapolation of the fit. In about 60% of the shut-time distributions there was an 'excess of brief gaps' similar to that depicted in panel E. One explanation for these different findings is that there is an additional brief gap component that was present in some patches but not in others; or alternatively, that the component may have been present in all the patches, but that it was only detected in some. However, it was generally the case that this 'excess of brief gaps' was absent or small in those recordings with the best resolution. This finding would seem to support yet another explanation, namely that the 'excess brief gaps' were in fact incompletely resolved sublevel transitions that were misclassified as complete shuttings. Indeed, given the brief duration of most of the transitions between the 50 pS level and the 30 and 40 pS open levels (see below), this seems quite plausible; and it is our conclusion that the 'excess of brief gaps' measured in some patches reflects the fact that in these patches substantial numbers of incompletely resolved sublevel transitions were misclassified as incompletely resolved full closures. It was of interest to ascertain whether either of the two components of brief gaps were associated exclusively with one of the observed levels. Figure 9 shows bursts of openings evoked by 30 /SM-NMDA in a patch held at a potential of -80 mV. The first bursts in this portion of the record consist of sequential openings to the 50 pS open level, whereas those on the right half of the figure consist of sequential openings to the 40 pS open level. It is clear from this example, and was clear from inspection of all the records, that openings to the 50 pS level and also to the 40 pS level did occur in bursts in which sequential openings to one of these levels were interrupted by brief closures. (In the example illustrated in Fig. 9 most of these closures are too brief to be completely resolved.) These observations were quantified by examining the shuttime distributions for shuttings that arose from, and returned directly to, a given open level. The shut-time distributions for shuttings bounded on either side by 50 pS openings were similar to those obtained for all shuttings. They clearly contained four exponential components and the mean durations and relative areas for these components were similar to those given in Table 3. Given the smaller proportion of 40 pS openings in each of the records, the distributions of shut times for closures
J. R. HOWE, S. G. CULL-CANDY AND D. COLQUHOUN bounded on either side by 40 pS events were not as well defined as those for the corresponding shuttings from the 50 pS level. However, consideration of the results from all the patches clearly indicated that 40 pS openings were interrupted by both types of brief gap and that the relative proportion of each type of brief gap was similar to that obtained from analysis of the distribution of all shut times. 168
30 pM-NMDA, -80 mV
.......
................
..................
....
.........rs
30 ms
Fig. 9. Bursts of openings evoked by 30 4uM-NMDA in a patch held at a membrane potential of -80 mV. Dotted lines correspond to the mean amplitude of 40 and 50 pS openings obtained from this patch at -80 mV. The duration of brief shuttings that separate sequential openings to the 50 pS open level is similar to the duration of brief shuttings that separate sequential 40 pS openings. The record was filtered at 2 kHz
(-3 dB).
Openings to the 30 pS level were also observed to occur in bursts in which sequential 30 pS events were interrupted by brief gaps; however, the relative rarity of 30 pS openings, and the consequent paucity of such gaps, precluded a quantitative analysis of the kinetics of these shuttings. Our results did not permit reliable assessment of the nature of shuttings bounded on either side by 8 or 17 pS openings. These openings were rare in the majority of the records and, because of the small amplitude of these openings, any events within these openings that were of a duration similar to that of the brief gaps detected in the distribution of all shut times would have been indistinguishable from the background noise. Apparent open times obtained with glutamate, aspartate and NMDA :50 ps openings In most of the patches examined, the distribution of apparent open times for 50 pS openings was not fitted very well by a single exponential component. Figure 10 shows histograms for 50 pS openings evoked by glutamate, aspartate and NMDA that were obtained in three different patches at membrane potentials of -100 to - 130 mV. Panels Aa-Ca of Fig. 10 show the best one-exponential fits to each set of data and panels Ab-Cb show the same results with the respective two-exponential fits (see legend for parameter estimates). Whether the two-exponential fits were significantly better than the one-exponential fits was evaluated with a likelihood-ratio test as described by Horn (1987). This analysis indicated that in each of the three cases illustrated the two-exponential fits were significantly better (P < 0 05), although in the case of glutamate and NMDA this was only marginally so. In general it was the case that the two-exponential nature of the distribution of the apparent open times for 50 pS openings was most clear with glutamate and
GLUTAMATE RECEPTOR SINGLE-CHANNEL CURRENTS
169
A 3guM-glutamate b
a
125 100 75
50
25
0
0
B 30 gM-aspartate a 125
b
E
o 100
LO
S
75-
t-
o
a
o 50 0 0)
25
U-.
C 30OgM-NMDA
b
a
180
150 120 90
-
60
30
0
-4
8
12
16
0
4
8
12
Open time (ms) Fig. 10. Histograms of dwell times for 50 pS openings evoked by: 3,uM-glutamate (A), 30,uM-aspartate (B) and 30 /sM-NMDA (C). Panel a for A-C shows the best singleexponential fits to each distribution. Panel b for A-C shows the same histograms and the superimposed fits with two exponential components (light lines show individual components). Data are from three different patches held at patch potentials of -110 mV (A), -130 mV (B) and -100 mV (C). Time constants for the single-exponential fits were: 2-52, 2-13 and 2t23 ms (panel a of A-C, respectively). Time constants (and relative areas) for the two exponential components fitted to the distributions were: Ab, 1 11 (35f8 %) and 3-24 ms; Bb, 0-64 (44t5%) and 3-16 ms; Cb, 1P30 (45 7 %) and 2-98 ms.
16
J. R. HOWE, S. G. CULL-CANDY AND D. COLQUHOUN
170
Aspartate
A 10.0
3-0 .
1.0
-
0.3
E ._
EQ
0.-1 -250
c _
-200
-150
-100
-50
0
a)0. 0 Q C
B
0. 0.
10.0
NMDA -
C a)
0
I
3.0 0
1.0
0
-
0-3
0-1 I -250
. -50 0 -150 -100 Membrane potential (mV) Fig. 11. Semilogarithmic plots of the mean apparent duration of 50 pS openings evoked by aspartate (A) and NMDA (B) as a function of membrane potential. Each point represents a single determination. The lines show the linear least-squares fits to the results. In B, two of the values obtained at -100 mV were offset slightly for increased -200
clarity.
aspartate. Thus, in four of the eight patches from which open-time distributions for 50 pS events evoked by NMDA were obtained, the distributions were fitted adequately by single exponentials, as assessed either by inspection or with a likelihood-ratio test. In contrast, similar analysis indicated that each of the seven distributions obtained with glutamate and ten of the eleven distributions obtained
171 GLUTAMATE RECEPTOR SINGLE-CHANNEL CURRENTS with aspartate contained two exponential components. In those cases in which the two-exponential fit was deemed better, the mean ratio of the time constant of the briefest component to the time constant of the component with the longer mean duration was 0-26 for glutamate and 0-29 for aspartate. For NMDA the mean value of this ratio was 0 40; and therefore in those cases in which it was felt that two components were distinguished in open-time distributions obtained with NMDA the time constants of the two components did not differ as much as they typically did with glutamate and aspartate. The mean apparent open time for 50 pS events was clearly dependent on patch potential and decreased with hyperpolarization. In those cases in which two components of open times were present, the mean duration of both components decreased as the patch potential was made more negative. There was no consistent or significant effect of membrane hyperpolarization on the relative areas of the two components. Figure 11 shows semilogarithmic plots of the mean apparent duration of 50 pS openings evoked by aspartate (panel A) and by NMDA (panel B) as a function of membrane potential. The mean durations were obtained from the one- or two-exponential fits to the open time distributions. The straight lines are the linear least-squares fits to each set of data. The slopes obtained from these fits were clearly statistically significant (P < 0.0001 and 0 0002 for the aspartate and NMDA results, respectively) and corresponded to an e-fold change per 68 mV with aspartate and an e-fold change per 56 mV with NMDA. Similar analysis of the results obtained with glutamate gave an e-fold change in mean duration per 94 mV. At -100 mV, this analysis gave mean durations of 3 04, 2-21 and 2-37 ms for 50 pS evoked respectively by glutamate, aspartate and NMDA. These values were not significantly different from each other. Similar analysis of those distributions in which two components were detected gave the following time constants for these components at a membrane potential of -100 mV: 090 and 3-88 ms with glutamate; 100 and 3-17 ms with aspartate; 1-24 and 3-21 ms with NMDA. The relative area of the briefer component was largest with aspartate (514±+56 %) and smallest with glutamate (32-1 + 7-2 %). NMDA gave a corresponding value of 42 1+ 10O4 % in those cases in which two components were distinguished with this agonist. These values were not significantly different from each other. Some decrease upon membrane hyperpolarization in the mean duration of apparent open times might be expected because of improved resolution at more negative patch potentials and because (given the complexity of the records) we have not attempted to correct the open times for missed events. In order to ascertain to what extent the observed decrease in apparent mean open times with membrane hyperpolarization was the result of improved resolution, we examined the distributions of these open times that were obtained at different patch potentials with the same shut-time resolution. Because neither the mean duration nor the relative area of the briefest component of gaps showed any substantial dependence on membrane potential, under these conditions the effect that missing brief shuttings had on the measured open times should have been similar at different potentials. Panels Aa-Da of Fig. 12 show histograms of the distributions of open times for 50 pS events measured in one patch at -80, -120, -160 and -200 mV. Openings longer than 15 Tr were fitted and are included in the histogram. The shut-time
J. R. HOWE, S. G. CULL-CANDY AND D. COLQUHOUN
172
A -80 mV
100, a 80.
E LC) 6° 0
b
100
80 CA
60 40
E un
60
°o4
-
h-40
20-
20
lp;r-m4r*"- -. -
B -120
125,
a
100
80
100 0
E 75. 6 50 0.
E 60 L0 6 L-
25
40
20
U
0: U-
0 C -160 mV a
200
80
150
co
E
In
60
L-
40
E
100
o CL
b
100
50
0
D -200 mV a
80 co
60
6
40
E
5
b
0
4
E
0
10
LO
31
0)
21
a
0.
20
0 0
5
10 15 Openings
20
u
Iu lb zu Open periods
zs
In
3u
Duration (ms)
Fig. 12. Histograms of the durations of 50 pS openings (a) and of open periods (b) that were evoked by 100 /uM-aspartate in a single patch that was held at potentials of -80 mV (A), -120 mV (B), -160 mV (C) and -200 mV (D). An open period was defined as one or more contiguous openings to any conductance level. The distributions were each fitted (smooth curves) with two exponential components. For 50 pS openings, the resolution was set at 20-50 ,us (depending on the potential); however, only events with durations above 1-5 T were fitted. For open periods, the resolution was set at 50 ,us, but only events with durations above 275 were fitted. The shut-time resolution was set to 50 #s for each distribution. The scaling of the time axis is 0-20 ms for panel a of A-D and 0-30 ms for ss
173 GLUTAMATE RECEPTOR SINGLE-CHANNEL CURRENTS resolution was set to 50 Its at each potential. Clearly, the duration of the 50 pS events decreased with membrane hyperpolarization. Each distribution was fitted by two exponential components with time constants (and relative areas) at the different patch potentials of: 2-04 ms (61-5%) and 4-78 ms, - 80 mV; 1-45 ms (69-4%) and 2-78 ms, - 120 mV; 0-41 ms (68-2%) and 1-14 ms, - 160 mV; 0'51 ms (91-3 %) and 1-94 mis, -200 mV. These fits therefore gave mean durations of 3-09 ms at -80 mV, 1'86 ms at - 120 mV, 0-64 ms at - 160 mV, and 0-63 ms at - 200 mV. A linear leastsquares fit to these four data points indicated that the mean apparent duration of 50 pS events decreased e-fold per 69 mV over this range of membrane potentials. This is similar to the corresponding change estimated from all the results with aspartate (Fig. lIA). These results therefore suggest, as did consideration of the results from all the patches examined, that the observed reduction in the apparent duration of 50 pS openings as the membrane potential was hyperpolarized did not result primarily because brief shuttings were detected at hyperpolarized membrane potentials that were missed at more positive membrane potentials. However, not only did the resolution with which brief shuttings could be detected improve with membrane hyperpolarization, but so also did the resolution for the detection of brief sojourns in other conductance levels. In order to determine whether this made a substantial contribution to the results, we therefore also looked at the effect of membrane potential on the distribution of contiguous open times. A contiguous open time was defined as the duration of any open period which consisted of a series of openings, to whatever conductance level, that was not interrupted by a shutting of duration above the resolution. Panels Ab-Db of Fig. 12 show histograms of the distributions of the duration of these open periods that were obtained from the same patch as that from which the results in panels Aa-Da were obtained. The shuttime resolution was set to 50 gs at each potential (-80 to -200 mV). It is clear that the duration of these open periods decreased with patch potential. Two exponential components were fitted to each distribution and these fits gave mean durations of: 5-34 ms at -80 mV (Ab); 2-32 ms at - 120 mV (Bb); 1-74 ms at -160 mV (Cb); and 1-61 ms at -200 mV (Db). Linear regression of these results (as in Fig. 11) gave an e-fold change per 103 mV. Therefore, although the resolution for detection of brief events certainly improved at more negative patch potentials, it appears that this is insufficient to account for the clear dependence of the duration of 50 pS openings on membrane potential.
Apparent open times with glutamate, aspartate and NMDA: 8, 17, 30 and 40 pS
openings In all of the patches examined with glutamate, aspartate and NMDA, the mean duration of 50 pS openings was longer than the mean duration of openings to the other conductance levels. (As with the 50 pS openings, no attempt was made to panel b of A-D. The time constants and relative areas for the two components estimated for each set of results are given in the text. The histograms include only those values that were included in the fits. For panel a of A-D, there were 19, 13, 48 and 9 events respectively with durations above the resolution but below 1-5T7; and for panel Aa, 3 events had durations greater than 20 ms. For panel b of A-D, there were 149, 140, 151 and 46 events respectively with durations between 50 and 275 #ts and 3, 1, 1 and 1 event with durations above 30 ms.
J. R. HOWE, S. G. CULL-CANDY AND D. COLQUHOUN correct the apparent duration of openings to other conductance levels for missed events.) Figure 13 shows open-time histograms for openings to the 50, 40, 30 and 8 pS conductance levels that were obtained from a single patch at - 130 mV with 30 UMglutamate (panels A-D, respectively). Note that the time scale is 0-15 ms for the 174
B 40 pS 40
A 50 pS 200 o 150 E u? 100
cn 30 E ° 20
0. 50
0.10
>~0
0
Cr 0~
10
5
0
0.0
15
20-
E
2.0
3.0
4.0
5.0
D 8 pS 15-
C 30 pS
@
1.0
E 10
15
-
0
o 0.
5
0~0.~ ~ ~ ~ ~ ~ ~ ~
1.5 1.0 0.5 2.0 2.0 0.0 time (ms) Open Fig. 13. Histograms of open-time distributions for openings to different conductance 0.0
0.5
1.0
1.5
levels observed in the same patch. Single-channel currents were evoked by 30,Mglutamate. The patch potential was -130 mV. Note that the time scale varies from panel to panel. A, .he distribution of open times for 50 pS openings with durations above 180 As was fitted with two exponential components with time constants (relative area) of 381 Fs (22-7 %) and 2-58 ms. B, the open-time distribution for 40 pS openings with durations above 300 tss was fitted with two exponential components with time constants (relative area) of 345 /ss (86-4 %) and 1-87 ms. C, the open-time distribution for 30 pS openings with durations above 300,us was fitted with a single exponential with a time constant of 195,u. (Note that below 600 ,ss the bin width is 50,us.) D, the distribution of open times for 8 pS openings with durations above 300 /ss was fitted with a single exponential with a time constant of 289 ,s. (The bin width is 300 ,ss for durations above 700,us.)
50 pS openings, 0-5 ms for the 40 pS openings, and 0-2 ms for the 30 pS and the 8 pS openings. The data for 50 and 40 pS events were both fitted with two exponential components, whereas single-exponential functions were fitted to the distributions for the 30 and for the 8 pS events. The parameter estimates from these fits (see the legend to Fig. 13) gave mean durations for the 50, 40, 30 and 8 pS openings, respectively, of: 2-08, 0 55, 0-20 and 0-29 ms. Figure 14 shows histograms of the distributions of the duration of 40 pS (panel A) and 30 pS (panel B) openings that were evoked by 30 ,SM-NMDA in another patch held at -130 mV. As was the case for the corresponding distributions in Fig. 13, the
GLUTAMATE RECEPTOR SINGLE-CHANNEL CURRENTS 175 majority of the openings to each of these conductance levels had durations below 10 ms. In most patches, however, there were also events of each type that were of longer duration. Especially for the 40 pS openings, it was often the case that in order to obtain a good fit to the distribution of durations below 1-0 ms it was necessary to B 30 pS 80
A 40 pS 10075
60-
Fig 50
on 40
LL 25
-20-
a)
~
C
Oe 0ie(s
pe ie(s
0
0
0.0
1.0
2.0
3.0
4.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Open time (ins) Open time (ins) 14. of times for 40 pS openings evoked by 30 /Sm-NMDA in a patch Fig. A, histogram open held at a membrane potential of -130 mV. The distribution of dwell times for all such openings with durations above 275 /4#s was fitted with two exponential components. The time constants (and relative area) of these components were 249 #8s (85-5 %) and 1-08 ms. (Events in the first bin (shaded) were not included in the fit; three openings had durations above 4 ms.) B, open-time histogram for 30 pS openings detected in the same patch at the same potential. The distribution of all open times longer than 165 iss was fitted with two exponential components with time constants (and relative area) of 93 uss (86-9 %) and 2-00 ms. Events in the first bin (shaded) were not included in the fit. (Eighteen openings had durations above 3 ms and are off-scale to the right.) In both A and B the individual exponential components are shown by the light smooth curves superposed on the histograms.
fit the entire distribution with two exponential components (eighteen of the twentysix distributions obtained for 40 pS events and eight of the twenty-four distributions obtained for 30 pS events). In Fig. 14, both of the distributions have been fitted with the sum of two exponential components (heavy smooth curves; the individual components are shown in each panel by lighter smooth curves). Typically, for openings to conductance levels below 50 pS, only durations above 2-5 T were fitted. For the patch in Fig. 14, this corresponded to events of a duration above 275 ,Is; and in panel A such events fall within the unshaded bins of the histogram. The fit to these durations agrees well with the results for durations above 175 gZs. In some cases (such as that illustrated in panel B of Fig. 14), the vast majority of events fitted as 30 pS openings had durations below 2-5 Tr. For the results shown in panel B, durations above 1-5 Tr have therefore been fitted (unshaded bins). The fit obtained describes the observations well for durations above 115 Its. The time constants of the two components fitted to the results shown in Fig. 14 were 249 ,us and 1-08 ms for the 40 pS events and 93 ,us and 2-00 ms for the 30 pS events. The relative area of the briefer component in the distributions depicted in Fig. 14 was 85-5 % for the 40 pS events and 86-9 % for the 30 pS open times. In all cases in which two exponentials were fitted to the distributions of open times for 40 and for 30 pS events, the relative area of the component with the longer mean
J. R. HOWE, S. G. CULL-CANDY AND D. COLQUHOUN duration was small. The relative areas of the brief components fitted to these distributions were similar with glutamate, aspartate and NMDA, and on average this area was 85-9 + 2-6 % for 40 pS open times and was 94-2 + 2-0 % for 30 pS open times (n = 26 and 24, respectively). 176
A 20 ,uM-glutamate 30-
¢ E 20 c
e_
B 30 pM-NMDA 20-
E
-
15 15
LOl
a)
10
00.0
01.0
2.0
3.0
4.0
5.0 0.0 Open time (ms)
1.0
2.0
3.0
4.0
5-0
Fig. 15. Histograms of open times for 17 pS openings. A, the distribution of open times for 17 pS events produced by 20 ,/M-glutamate in a patch held at a membrane potential of -100 mV was fitted with a single exponential component with a time constant of 660 ,us. B, histogram of open times for 17 pS openings evoked by 30 ,SM-NMDA in another patch at a membrane potential of -70 mV. The distribution was fitted with a single exponential component with a time constant of 700 /ts. For each distribution, only openings with durations above 2-5 Tr were fitted.
In contrast to the results obtained for 50 pS openings, neither the mean duration of 40 pS openings nor the mean duration of 30 pS openings showed any substantial or significant dependence on membrane potential. The mean time constants determined for the brief component of openings present in each type of distribution were not significantly different with the three agonists, although as for the 50 pS openings the briefest mean durations were measured with aspartate. For 40 pS events, the mean time constants of the brief component were 0-62 + 0-15 ms with glutamate (n = 6), 0-31 + 0-07 ms with aspartate (n = 11), and 0-56 + 0-13 ms with NMDA (n = 9). Mean time constants for the brief component present in opentime distributions for 30 pS events were 0-30 + 0-06 ms with glutamate (n = 6), 0 14 + 0 03 ms with aspartate (n = 9), and 0-21 + 0 05 with NMDA (n = 9). Thus, for openings to each of these conductance levels, most of the kinetic results could be described by single-exponential functions with time constants well below 10 ms. It is probable that some of the longer duration openings present in the distributions for 40 pS events were in fact openings to the 50 pS conductance level that were misclassified. As in panel D of Fig. 13, the open-time distributions for 8 pS events evoked by glutamate, aspartate and NMDA were fitted adequately by single-exponential functions. There was no indication that the mean apparent duration of these openings varied with patch potential. The low frequency with which these three agonists produced openings to the 8 pS level prevented us from obtaining as many estimates of the mean duration of these events as were obtained for the 30, 40 and
177 GLUTAMATE RECEPTOR SINGLE-CHANNEL CURRENTS 50 pS events present in the same records. Typically only thirty or so 8 pS events were of a duration above 2-5 T. The mean time constants determined from the singleexponential fits to the open-time distributions obtained with the three agonists were 0 70 + 0'19 ms with glutamate (n = 3), 0 34 + 0 04 ms with aspartate (n = 9), and 0-68 + 0 04 ms with NMDA (n = 4). Thus, as for the openings to the 30, 40 and 50 pS levels, the mean duration of the 8 pS openings was briefest with aspartate. In this case, the value for aspartate was significantly different from the values obtained with glutamate and NMDA (P < 0 05). Even fewer records contained enough 17 pS events to obtain an estimate of their mean duration. The distributions that were obtained for the duration of these openings were fitted adequately by single exponentials. Two such distributions are shown in Fig. 15. There were no obvious differences between the time constants estimated with glutamate, aspartate and NMDA; however, given the small number of estimates and the small number of events included in each distribution, unless such differences were very substantial we would not have detected them. The mean time constant calculated from the results obtained with all three agonists was 0-53+0-17 ms (n = 6).
Apparent open times determined with kainate and quisqualate In three of the six patches in which kainate produced mainly small-amplitude openings the mean duration of these openings was in the range of 2-3 ms. However, the resolution in these patches was not very good. The estimates from the other three patches gave values of about 10 ms and we believe that these estimates are more reliable. Histograms for 8 and 17 pS openings evoked at -90 mV by 10 /LM-kainate in one of these latter patches are shown in panels A and B respectively of Fig. 16. Both open-time distributions were fitted with single-exponential functions. The time constants of these exponentials gave mean durations of 1-24 and 1-38 ms for the 8 and 17 pS openings, respectively. The longest small-conductance openings were produced by quisqualate in the two patches in which the majority of openings were to the 8 and 17 pS conductance levels. Panels C and D of Fig. 16 show histograms of the apparent open times for 8 and 17 pS events, respectively, that were evoked by 10 /SM-quisqualate in a patch held at -90 mV. Note that the time scales for panels C and D are 0-40 and 0-25 ms, whereas the. time scale for the histograms in panels A and B is 0-10 ms. In this patch, some very long 8 and 17 pS events were observed. Several such openings had apparent durations above 25 ms. The mean apparent open time estimated from the fits to the illustrated distributions was 4-68 ms for the 8 pS events (C) and was 5-68 ms for the 17 pS events (D, two-exponential fit, see legend). Figure 17A depicts a histogram of the distribution of apparent open times for 50 pS events evoked by 30 /uM-quisqualate at -100 mV in one of the patches in which quisqualate evoked primarily 50 pS openings. The single-exponential function fitted to this distribution gave a mean duration of 1-77 ms for these openings. The mean duration of 50 pS events that were elicited by quisqualate ranged from 1-13 ms at -140 mV to 5-62 ms at -60 mV (data from five distributions). A histogram of the distribution of apparent open times for 50 pS events produced by 30 jtM-kainate at -70 mV is shown in panel B of Fig. 17. The results are from the one patch in which
J. R. HOWE, S. G. CULL-CANDY AND D. COLQUHOUN most of the openings produced by kainate were to the 50 pS conductance level. The single-exponential fit to the distribution gave a mean duration of 4-76 ms. At a patch potential of -70 mV, the mean duration of 50 pS openings evoked by quisqualate was 2-64+ 1-06 ms (n = 3). As with glutamate, aspartate and NMDA, some of the 178
A 10 piM-kainate, 8 pS 40
E
B 10,uM-kainate, 17 pS 150
U) 120 E o LO 90
30 -
LO
G) CL
20
60 Q0
0. 10 -
30
2
0
4
6
8
10
0
2
4
6
8
10
20
25
G)
C 10 ,M-quisqualate, 8 pS
a)
D 10 M-quisqualate, 17 pS 50
9
U-
30 tn
E
n
E 20 0
A
30
I I
-
0
a
0.
CL
10.
0.
1.
1 0.0
10
0 10
20
30
40 0 Open time (ms)
5
10
15
Fig. 16. Open times for 8 and 17 pS openings elicited by kainate (A and B) and quisqualate (C and D). Data for kainate and those for quisqualate are from different patches. In both cases, the agonist concentration was 10 /zM and the patch potential was -90 mV. Note that the time axes are scaled differently for different panels. A, open times for 8 pS openings produced by kainate and with durations above 1P2 ms were fitted with a single exponential component (smooth curve) with a time constant of 1-24 ms. B, open times for 17 pS produced by kainate and with durations above 1-0 ms were fitted with a single exponential component with a time constant of 1-38 ms. C, open times for 8 pS openings produced by quisqualate and with durations above 0-85 ms and less than 40 ms were fitted with a single exponential component with a time constant of 4-68 ms. Six openings with durations above 40 ms were excluded from the fit. D, open times for 17 pS produced by quisqualate and with durations above 0-85 ms were fitted with two exponential components with time constants (relative area) of 2-52 ms (85 1 %) and 23-7 ms. There were thirteen openings with durations above 25 ms.
distributions of 50 pS open times obtained with quisqualate and kainate contained two distinguishable components. The mean apparent open times for 30 and 40 pS events evoked by quisqualate and by kainate were below 1-0 ms.
Burst lengths obtained with glutamate, aspartate and NMDA Bursts were defined as groups of openings that were separated by shuttings less than a 'critical gap length', tc, which was calculated from the shut-time distribution (see Methods). Values of tc were typically between 1.0 and 2-0 ms.
GLUTAMATE RECEPTOR SINGLE-CHANNEL CURRENTS
179
Distributions of burst lengths contained three exponential components. The briefest component in these distributions consisted almost exclusively of isolated incompletely resolved openings, and measurements of their duration were inherently ambiguous because the final amplitude of these 'brief bursts' was uncertain. The A 30 uM-quisqualate, 50 pS , 75 E 6 °0-
B 30 ,M-kainate, 50 pS
125 100 ~~~~~~~~~~E c
50 075 0.~~~~~~~~~~~7 U ~~~~~~~~~~~~~~5025 C
25,
cr U-
0
0
5
0 10
15
0
10
20
30
Open time (ms)
Fig. 17. Histograms of open-time distributions for 50 pS openings produced by quisqualate (A) and kainate (B). The distribution illustrated in panel A was obtained from a patch superfused with 30 /SM-quisqualate and held at a potential of -100 mV. The distribution was fitted with a single exponential component (smooth curve) with a time constant of 1-77 ms. The data in panel B were obtained from a different patch at -70 mV with 30 4sM-kainate. The distribution was fitted with a single exponential with a time constant of 4-76 ms. Note that the time scales are different for A and B.
time constants of the slowest two components could, however, be estimated with reasonable certainty. Figure 18 shows histograms of the burst-length distributions obtained from three different patches with glutamate, aspartate and NMDA. The time scale was selected to show the slowest two components present in each distribution. The time constants for these two components were similar for each distribution and are given in the legend to Fig. 18. The mean time constants determined for these two components with glutamate, aspartate and NMDA are given in Table 4, as are the mean values for the ratio of their relative areas, A2/A3. (The absolute values for A2 and A3 differed from patch to patch because the area of the briefest component, A1, was often poorly defined and the values estimated for A1 therefore varied considerably between patches.) None of the parameters in Table 4 showed any significant dependence on membrane potential and the results obtained at all patch potentials have been pooled. That the burst length did not depend on membrane potential, although the length of 50 pS openings decreased significantly with membrane hyperpolarization, would appear to be due to the increase in the number of openings per burst as the patch potential was made more negative (see below). The time constants obtained with the three agonists for each component did not differ significantly. Although the mean values for A2/A3 indicate that long bursts were least common with aspartate and most common with NMDA, the differences were not statistically significant. In several cases we also examined the burst-length distributions for only those bursts that had a mean amplitude (see Methods) that correspond to the 50 pS open
180
J. R. HOWE, S. G. CULL-CANDY AND D. COLQUHOUN A 50
30 uM-glutamate
.401 0 J2I E 30
o
0.a
20I\ B
10 juM-aspartate
E
0. crL C
0' U-
C
30 uM-NMDA
50 40
A
is,
4-
-
7-
0
E 30 -
0Q
20 10'
10
15
20
25
30
Burst length (ms)
Fig. 18. Histograms of distributions of burst lengths for single-channel currents evoked by: 30 pm-glutamate (A), 10 /SM-aspartate (B) and 30 pm-NMDA (C) in three different patches, each of which was held at a membrane potential of -100 mV. Each distribution was fitted with three exponential components (heavy line). The time scales were selected to show the slowest two components (light lines). The time constants and the ratios of the
181 GLUTAMATE RECEPTOR SINGLE-CHANNEL CURRENTS level and also in many cases for only those bursts that consisted entirely of 50 pS openings. Each one of these distributions contained two components that were similar to the slowest two components in the distributions for all bursts and the mean time constants and relative areas of these two components were similar to the corresponding values given in Table 4. This suggests that both of the slowest two TABLE 4. Characteristics of burst lengths r2(ms)
T3(ms) .
A2/A3 P-15+ 041 2417 + 0 79
Glutamate 1-74 + 0 49 10-6+ ±15 2-35 + 0 43 10-9 + 1P3 Aspartate 2-44+0 43 13-0+2-2 0-65+0-14 NMDA Mean time constants (±S.E.M.) and the ratio of the relative areas (A2/A3) of the slowest two components detected in distributions of burst lengths. Values for glutamate, aspartate and NMDA are from seven, twelve and nine distributions, respectively.
components seen in the distribution of burst lengths arose primarily from the kinetics of the 50 pS open level. It is these components that correspond to the two components detected in spectra of large-conductance whole-cell current noise evoked in granule cells by glutamate, aspartate and NMDA (Cull-Candy et al. 1988 a; Howe et al. 1988). Distributions of total open time per burst Distributions of the total open time per burst were similar to the distributions of burst lengths, which is to be expected given the brevity of the 'gaps within bursts'. The former distributions, like the latter, consistently contained three components and the slowest two components had time constants that were somewhat, but not substantially, shorter than those given for burst lengths in Table 4. As for the burst lengths, there was no indication that these time constants were dependent on membrane potential. In addition to fitting the distribution of the total open time per burst, in each case we also examined the corresponding distribution after excluding all times spent at a conductance level other than the 40 pS level. Figure 19A shows a histogram of the distribution of total open time per burst from a patch exposed to 3 ,sm-glutamate at a patch potential of -110 mV. The time scale has been selected to display the slowest two components in the distribution, components which had time constants of 1P12 and 9-02 ms, respectively. The ratio of the relative areas of these components (i.e. A2/A3) was 101. In panel B, the histogram is of the corresponding distribution obtained when all times spent at a conductance level other than the 50 pS open level were excluded. The fit to these results gave time constants for the slowest two components of 1-43 and 8415 ms, and the ratio of their relative areas was 0-82. The examples illustrated in Fig. 19 were typical of the results obtained, and the sum of areas of the second and third components were: A, 2-66 ms, 13-4 ms, 0-82; B, 2-24 ms, 12-4 ms, 1-18; C, 3-19 ms, 12-9 ms, 0 57. The inset of panel C shows a long burst produced by NMDA in the patch from which the distribution was obtained (low-pass filtered at 4 kHz, -3 dB). Calibration bars are 6 pA and 10 ms.
182
J. R. HOWE, S. G. CULL-CANDY AND D. COLQUHOUN these comparisons indicated that excluding time spent at conductance levels below 50 pS had little effect on the nature of the slowest two components present in the distributions of total open time per burst, and therefore suggested that these components reflect primarily the kinetics of the 50 pS openings. A All 60 -
open
times
45.
30 15 E 0 L
20
5
6
10
15
20
25
vi 5 0.
50 pS open level only
r-
201
40-
25 15 20 10 Open time per burst (ms) Fig. 19. Histograms of the distributions of total open time per burst from a patch held at -1 1Q mV and superfused with 3/uM-glutamate. In panel A all open times were included, whereas panel B is a histogram of the distribution obtained when all times spent at an open level other than the 50 pS level were excluded. Each of the distributions were fitted with three exponential components (heavy line). The time scale was selected to display the two components with the longest mean durations. The time constants and the ratios of the areas of the second and third components were: A, 1-12 ms, 9-02 ms, 1-01; B, 1-43 ms, 8-15 ms, 0-82. The individual components are shown by the smooth curves drawn with light lines in each panel. 0
5
The number of open periods per burst Distributions of the apparent number of open periods per burst (1 + the number of brief gaps) are expected to conform to functions that are the sum of geometric terms (Colquhoun & Hawkes, 1982). Two geometric components were distinguished in all such distributions examined. Figure 20 shows two examples of these distributions.
GLUTAMATE RECEPTOR SINGLE-CHANNEL CURRENTS 183 The results are from two different patches and were obtained with 10 fSM-NMDA at a patch potential of -80 mV (panel A) and with 30 /tM-aspartate at a patch potential of -100 mV (panel B). The two-geometric fits to these distributions are shown by dashed lines. The means (and relative area) of the two components are given in the figure legend. All of the distributions contained a component with near unit mean. The average number of open periods per burst for the geometric term with the smaller mean ranged from 100 to 1-39 and on average this value was 1 15 + 003 (n = 27). (In some of the cases in which the mean of this component was higher than usual, it appeared that more than two geometric components were probably present in the distributions, but that the individual components were not sufficiently well defined for us to distinguish them.) The relative area of this component was not significantly different with the different agonists and was 604 + 9.7 % with glutamate, 56-6 + 7-2 % with aspartate, and 49-1 + 8-5 % with NMDA (n = 7, 10 and 6, respectively; membrane potentials of -30 to -160 mV). The average number of open periods per burst (calculated from the means and relative areas of the two-component fits) increased significantly with membrane hyperpolarization. This was primarily due to an increase in the mean number of open periods per burst for the geometric term with the larger mean, the relative areas of the two components being largely independent of membrane potential. The increase in the average number of open periods per burst, although significant, was not marked. With glutamate, aspartate and NMDA this increase was e-fold per 130-350 mV. Linear least-squares fits to the data (as in Fig. 11) gave values for the mean number of open periods per burst of 1-74, 1-54 and 2-11 with glutamate, aspartate and NMDA, respectively, at a membrane potential of -100 mV. The value for NMDA was significantly different from the other two (P < 0-01). The increase in the mean number of open periods per burst at more negative patch potentials was not solely the result of improved resolution for the detection of brief events. A significant relation between the mean number of open periods per burst and membrane potential was still manifest when the resolution for openings and shuttings in records obtained at membrane potential of -60 to - 160 mV was set in each case to the same value, namely 75 /is. (This resolution gave false-event rates below 10-8 s-1 in all cases.) Thus, although the mean duration of 50 pS openings decreased with membrane hyperpolarization and such openings comprised the majority of the open time during bursts evoked by glutamate, aspartate and NMDA, the number of such openings per burst increased as the patch potential was made more negative. As a result, the mean length of bursts evoked by these agonists did not vary substantially with membrane potential over the range of patch potentials that were examined. Measurement of autocorrelations of open and shut times Correlations between the length of one event and that of a later event can give information about mechanisms (see, for example, Fredkin, Montal & Rice, 1985; Colquhoun & Hawkes, 1987). With each of the five agonists we have found clear correlations between one shut time and the next, as revealed by a positive autocorrelation coefficient (for lag of 1,
J. R. HOWE, S. G. CULL-CANDY AND D. COLQUHOUN and sometimes for lag of 2 and 3 also), or by the use of the runs test which showed fewer runs than expected for a random process (a Gaussian deviate of - 25 to - 12-4 in twenty experiments shows that the correlations are clearly not due to chance variability). The durations of open times showed a similar, but rather less pro184
A 10 ,M-NMDA, -80 mV 800 -
600 U c
@ 400cr
0
0
LL.
200 -
2
4
2
4
0 0
6
8
10
12
10
12
B 30 pM-glutamate, -100 mV 250 200 C) a) a)
150 -
LL
100 50 o
-
0
2
4 8 6 Open periods per burst
Fig. 20. Histograms of the distributions of the number of open periods per burst from a patch held at -80 mV and superfused with 10 UM-NMDA (A) and a patch held at -100 mV and superfused with 30 /SM-aspartate (B). The distributions were fitted with two geometric components (fit shown by dashed lines). The means (and relative area) of the two components were: A, 1-24 (79 2 %) and 2-48; B, 1 00 (43 4 %) and 2-28.
nounced, positive correlation too. However, no correlations between the length of one burst and the length of the next were detectable (except for two experiments that showed a slight negative correlation).
185 GLUTAMATE RECEPTOR SINGLE-CHANNEL CURRENTS These observations were further confirmed by the existence of a negative correlation between the length of an opening and that of the shut period that followed it (that is, short openings tended to be followed by long shut periods and vice versa); correspondingly, distributions of apparent open times conditional on the duration of the adjacent shut period (the approach adopted by Blatz & Magleby, 1989) showed that the mean length of openings decreased as the length of the adjacent shut periods increased. These observations are similar in all respects to those made on acetyleholineactivated nicotinic receptors in frog muscle endplates, and their possible interpretation has been discussed by Colquhoun & Sakmann (1985). However, in the present case, the behaviour of the channels is more complex than that of the adult nicotinic receptors, and we cannot even be sure how many different sorts of channel molecule are being recorded from in any particular patch. It would therefore be premature to try to use these measurements of correlation for identification of particular channel mechanisms in the way that has been done for the nicotinic receptor. In their work on NMDA-activated channels, Jahr & Stevens (1990) found no correlation between the length of one shut time and that of subsequent shuttings. However, it would appear that the briefest component of shut times that we have measured was not detected in their experiments.
Burst of openings occur in clusters With the concentrations of agonists that we used the probability, P. was typically about 0-02 and in most cases it was relatively constant throughout the time that the results were collected. However, in several of the records there were periods lasting hundreds of milliseconds during which the po was very much higher and a channel was open most of the time, primarily to the 50 pS conductance level. These events were therefore similar to clusters of bursts (Colquhoun & Hawkes, 1982) seen at high agonist concentrations for nicotinic acetylcholine receptor channels, which were first described by Sakmann, Patlak & Neher (1980); and by analogy we shall also refer to these events as clusters. These clusters were most common with NMDA, but they were seen with each of the five agonists. Four such clusters are illustrated in Fig. 21. As noted above, at least two channels were active in all but one of the patches examined and a few of the clusters contained double openings. For example, two such double openings are evident in the cluster illustrated in panel B of Fig. 21. However, in most of the clusters no such events occurred. In those few in which double openings were present, the frequency of these events was similar to the frequency with which openings occurred between clusters and it was much lower than predicted if the cluster was assumed to arise from the equal activity of two channels. There is therefore no doubt that the long high-po clusters we have seen arose primarily from the activity of a single receptor channel molecule. Clusters were observed at patch potentials of -80 to - 200 mV; and there was no obvious relationship between clustering and membrane potential. Unfortunately, the dependence of clustering on agonist concentration was not clear in our experiments. Firstly, the range of concentrations that we investigated was relatively narrow. Secondly, most of the experiments were done before the report by Johnson
186
J. R. HOWE, £ G. CULL-CANDY AND D. COLQUHOUN A
NMDA,-160 mV
cr)
200
ms
B Glutamate, -130 mV
100 ms
C Aspartate, -160 mV
CTrRuvvwf1FuvJIM44rr< 50
C
ms
D Quisqualate, -140 mV
100 ms Fig. 21. Clusters of bursts of single-channel openings recorded from four different patches. Agonists and patch potentials were 30,uM-NMDA, -160 mV (A); 30 AcM-glutamate, -130 mV (B); 100,uM-aspartate, -160 mV (C) and 30 pM-quisqualate, -140 mV (D). Note that the calibrations are different for different panels. Signals were low-pass filtered at 3-5 kHz (-3 dB) and were sampled at 10 kHz.
& Ascher (1987) that glycine, at concentrations often present in primary cultures of central neurones, could markedly potentiate the action of agonists at NMDA receptors. In a few experiments we observed that the frequency of channel openings increased substantially when we stopped the superfusion after the bath volume had been completely exchanged with new agonist-containing solution. At the time we could find no reasonable explanation for these observations; however, in light of the findings of Johnson & Ascher (1987) it seems probable that this was the result of an increase in the concentration of glycine in the immediate environment of the membrane patch. As a result, any comparison of the results that we obtained at different agonist concentrations is suspect, because of possible differences in the background concentration of glycine.
GLUTAMATE RECEPTOR SINGLE-CHANNEL CURRENTS
187
The distribution of shut times and open times within and between clusters Gating behaviour similar to that illustrated in Fig. 21 has also been described for glutamate receptor channels in rat hippocampal neurones (Jahr & Stevens, 1987), and in this study it was concluded that the long component present in dwell time distributions for 40-50 pS openings arose primarily from the gating mode that gave rise to clustering. However, from a preliminary analysis of the distributions of open times during clusters we concluded that there was no obvious difference between these times and the corresponding times obtained from records in which there was no clustering (Howe et al. 1988). Because of these apparently different findings, and because the clusters arose primarily from the activity of a single channel, it was of interest to examine the nature of the openings and shuttings within clusters in more detail and to compare the results obtained in the same patch (at the same membrane potential) during portions of the records in which there was no obvious clustering. Nine of the records contained clusters (sometimes more than one) that were sufficiently long that they contained enough transitions to allow such a comparison to be made. The average p0 during these clusters ranged from 0-452 to 0 950 (mean, 0-679 + 0 047, n = 11 clusters). The average p0 for portions of the nine records during which there were no clusters ranged between 0-006 and 0-034 (mean, 0-016 + 0-003). The shut-time distributions that were obtained from a patch superfused with 30 ,Sm-NMDA at a patch potential of -100 mV are shown (logarithmic time scale) in Fig. 22. Panel A shows the distribution of shut times that occurred within two clusters seen in this patch, and panel B shows the distribution of shut times that was obtained from portions of the record in which there were no clusters. The results are typical of those obtained and clearly the time constants of the two components of shut times within clusters are similar to the time constants of the two briefest components in the distribution of shut times between clusters. The two exponential components fitted to the distribution of shut times within clusters had time constants of 35.7 ,us and 1-41 ms. The two briefest components in the distribution of shut times between clusters gave corresponding time constants of 27-7 ,us and 0 95 ms. On average, the difference between the mean duration of the briefest component of shuttings within and between clusters was -6+5,us. The average difference between the mean duration of the second-briefest shutting within clusters and the mean duration of the second briefest shuttings between clusters was 66 + 136 /ts. The ratio of the area of the briefest component of shut times to the area of the secondbriefest component of shut times was 2-66+0-58 for the results obtained within clusters and was 2-54 + 0-36 for the results obtained between clusters. Thus, within and between clusters, the characteristics of both types of 'gaps within bursts' were similar. It should be noted that a formal definition of clusters would require the identification of a component of shuttings within these clusters that corresponded to 'gaps between bursts' and that the results just given do not allow such a definition. Indeed, it might be argued that it is the secondbriefest gap component that corresponds to such shuttings and that we have misclassified these shuttings as 'gaps within bursts'. However, such shuttings occurred at similar frequency in records that contained no evidence of the sort of kinetic behaviour illustrated in Fig. 21. Therefore, to refer to these shuttings as 'gaps between bursts' would fail to distinguish what was very clearly a type of kinetic behaviour that was different from that commonly seen. It is also clear that what we have
188
J. R. HOWE, S. G. CULL-CANDY AND D. COLQUHOUN Cluster
A
20
0
15
a) Cr a)
10 U-
104 B No cluster 125
100 j A IL)
c
u) 0*
75
0) LL
50 25
102 100 101 Shut time (ms) (log scale)
Fig. 22. Histograms of the distributions of shut times obtained from a patch held at a membrane potential of -100 mV and superfused with 30 /,M-NMDA. The data shown in panel A were obtained from a portion of the record that contained two clusters, whereas the data presented in panel B were obtained from portions of the record that contained no clusters. Durations are displayed on a log scale. Peaks on the smooth curve correspond to the time constants of the different exponential components fitted to the distributions. The resolution for openings and shuttings were set at 50 iss. A, shut times within clusters were fitted with two exponential components with time constants of 357 ,us and 1-41 ms. The relative area of the briefest component was 60 2 %. B shut times between clusters were fitted with four exponential components with means (relative areas) of 27-7 iss (608 %), 0-95 ms (21P3%), 16'3 ms (4-0%), and 458 ms (13-9%). called clusters were different from what we have routinely identified as bursts. Clusters typically had durations of 300-400 ms, whereas the mean duration of the longest component of bursts that was detected in all of the records was on average about 12 ms. For an exponential component with a mean duration of 12 ms, an event longer than 200 ms would be expected to occur with a
GLUTAMATE RECEPTOR SINGLE-CHANNEL CURRENTS A No cluster 60 45
co
E
e o 0. a
30
'
15
0
co
E
20-
a10-
0
n
C 100 80
D 150 co 120
c C 0*
2)
E 30In
LO
U-
B Cluster 40 -
E
o 60 oL- 40
o
Cf
0.
I
fift
90
0 a 60 t-
20 0 Ip
°
1
,
2
2
3
3
4
5
6
30 0 -r0
1
2
3
4
5
6
Open time (ms)
E
F
co
10
ms
Fig. 23. Histograms of open-time distributions obtained for 50 pS openings that occurred between (A and C), and those that occurred within (B and D), clusters. Data in A and B are for 50 pS openings evoked by 100 #M-aspartate in a patch held at -160 mV. A, twoexponential fit for openings that occurred during portions of the record that contained no clustering. Time constants (relative area) were 240,uss (30-1 %) and 870,us. B, twoexponential fit for openings that occurred within clusters. Time constants (relative area) were 217 (55 9 %) and 970 #s. Data shown in panels C and D are for 50 pS openings evoked by 30 ,uM-NMDA in another patch held at a potential of 130 mV. C, the singleexponential fit for openings that occurred between clusters gave a mean duration for these openings of 098 ms. D, the single-exponential fit for openings that occurred within us
-
189
190
J. R. HOWE, S. G. CULL-CANDY AND D. COLQUHOUN
frequency of about one in ten million. It therefore seems likely that there was in fact a component of shut times within the clusters that did correspond to 'gaps between bursts' and that the number of such shuttings was small and that their mean duration was not sufficiently different from the second-briefest component of 'gaps within bursts' for us to detect it.
We have found no significant differences between the characteristics of openings within clusters and those between clusters. Distributions of apparent open times for 50 pS were similar whether they were obtained from analysis of individual clusters or from analysis of portions of the records that contained no obvious clustering. In patches in which two exponential components were distinguished in these distributions, two similar components were seen within and between clusters. Panel A of Fig. 23 shows a histogram of the distribution of apparent open times for 50 pS events evoked by 100 /sM-aspartate at - 160 mV. The distribution was obtained from part of the record that did not contain clustering. The two-exponential fit to this distribution (individual components shown by light smooth curves) gave time constants (relative area) of 0-24 ms (30 1 %) and 0-87 ms. The two-exponential fit to the corresponding open-time distribution obtained from the long cluster present in the same record (panel B) gave time constants (relative area) of 0-22 ms (55-9 %) and 0 97 ms. The mean durations estimated from those fits are 0-68 and 0 55 ms, respectively. In patches in which the distribution of apparent open times for 50 pS events were fitted adequately by single-exponential functions, the mean durations estimated for openings between clusters and openings within clusters were also similar. Panels C and D of Fig. 23 show histograms of the open-time distributions obtained from another patch with 30 /LM-NMDA at - 130 mV. The open times in panel C are for openings that occurred between clusters and those in panel D are for openings that occurred within two clusters seen in this patch at - 130 mV. Both distributions were fitted adequately by single exponentials. The time constants estimated from the fits were 0'98 ms for 50 pS openings between clusters and 1 13 s for 50 pS openings within the clusters. Examples of bursts of openings that occurred between and within clusters are shown in panels E and F, respectively, of Fig. 23. On average the ratio of the mean apparent duration of 50 pS openings within clusters to the mean apparent duration of 50 pS between clusters was 1-23 + 0-13 (n = 9), a value which is not significantly different from one. There were also no significant differences in the mean durations of 30 and 40 pS openings that occurred within clusters and the corresponding mean durations for 30 and 40 pS openings that occurred between clusters. Whereas the time course fitting method that we have used allowed us to measure the duration of openings to different conductance levels, Jahr & Stevens (1987) employed half-amplitude threshold-crossing routines to analyse their results. They therefore would not have routinely detected events that consisted of transitions between the 50 pS open level and the 30 or 40 pS levels. If transitions between these open levels were much more common during clusters than they were between clusters gave a mean duration for these openings of 1 13 ms. E, bursts of openings evoked by 30 ,SM-NMDA (at -130 mV) in the patch from which the data in panels C, and D were obtained that occurred in a portion of the record during which there was no obvious clustering. F, bursts of openings in the same patch and at the same potential that occurred during a cluster. Signals in E and F were low-pass filtered at 4 kHz (-3 dB).
GLUTAMATE RECEPTOR SINGLE-CHANNEL CURRENTS 191 clusters, then this might account for the longer durations than Jahr & Stevens (1987) measured for openings within clusters. Therefore we also examined the apparent open-time distributions for contiguous openings (defined as above). If transitions between the 30, 40 and 50 pS open levels are more common within clusters than they are between clusters, then the mean duration of contiguous openings should have been longer within clusters. In contrast, we found no significant differences between the distributions of contiguous open times that were obtained for events between clusters and those that were obtained for events within clusters. Analysis of the types of transitions that occurred within clusters did not reveal any marked differences in the relative frequency with which the various transitions listed in Table 2 were seen. The majority of the transitions occurred between the 50 pS level and the shut level (on average about 70 % of all transitions detected). The relative proportions of transitions that involved the 30 or the 40 pS level were similar within and between clusters. Although transitions between the 30 or the 40 pS level and the shut level were less common within clusters than they were between them, and transitions that involved one of these two open levels and the 50 pS level were somewhat more common within clusters, the differences were not statistically significant. DISCUSSION
Conductance levels Our findings that each of the agonists tested produced openings to multiple conductance levels and that glutamate, aspartate and NMDA produced primarily large-conductance openings, whereas kainate produced primarily small-conductance openings, agree with our previous work (Cull-Candy et al. 1988 a) and with studies of single glutamate receptor channels in other types of mammalian central neurones. The mean conductances of the five levels we have distinguished in granule-cell patches are similar to the values found for the five levels identified in patches from large cerebellar neurones (Cull-Candy & Usowicz, 1987, 1989); and they are in reasonable agreement with values obtained for glutamate receptor channels in hippocampal neurones (Jahr & Stevens, 1987) and in mouse central neurones (Ascher, Bregestovski & Nowak, 1988; Ascher & Nowak, 1988a). Although quisqualate produced larger proportions of 8 and 17 pS events than did glutamate, aspartate and NMDA, with quisqualate the relative proportions of openings to each conductance level varied considerably from patch to patch. Quisqualate also gave variable results in other studies (Ascher & Nowak, 1988a; Cull-Candy & Usowicz, 1989). We have found that the current-voltage curves for openings to the 30, 40 and 50 pS conductance levels show pronounced inward rectification at membrane potentials negative to -100 mV. In previous studies with other types of mammalian central neurones, the single-channel current-voltage curves that were obtained with extracellular concentrations of Ca2+ (1-2 mM) similar to that used in the present experiments were reported to be linear (Nowak et al. 1984; Cull-Candy & Usowicz, 1987, 1989; Jahr & Stevens, 1987; Ascher et al. 1988; Ascher & Nowak, 1988b); however, in all of these studies the data were obtained at membrane potentials of -100 mV and above. It is clear from our present results that at membrane potentials
J. R. HOWE, S. G. CULL-CANDY AND D. COLQUHOUN positive to -100 mV the current-voltage curves obtained for 30-50 pS openings in granule-cell patches do not deviate substantially from linearity, which is in agreement with previous reports (Cull-Candy & Ogden, 1985; Cull-Candy et al. 1988a). There is considerable evidence that the large-conductance (30-50 pS) and the small-conductance (below 20 pS) openings display different permeabilities to divalent cations. The 50 pS openings are blocked by Mg2" (Nowak et al. 1984), whereas the small-conductance openings are not (Jahr & Stevens, 1987); and the largeconductance openings shown substantial permeability to calcium ions, whereas the small-conductance openings are much less permeable to Ca2+ (Ascher & Nowak, 1986, 1988 b; Jahr & Stevens, 1987; Mayer & Westbrook, 1987 b; see also MacDermott, Mayer, Westbrook, Smith & Barker, 1986). Our findings that, unlike openings to the 30, 40 and 50 pS levels, the 8 and 17 pS openings did not display inward rectification at potentials negative to -100 mV are yet another indication that the permeabilities of the small-conductance and the large-conductance openings differ qualitatively as well as quantitatively. 192
Direct transitions We have stated previously that direct transitions between the 8 or 17 pS level and the 30, 40 or 50 pS level were rare or absent in single-channel records obtained from granule-cell patches (Cull-Candy et al. 1988a). The results given in Table 2 provide quantitative support for this statement; and we believe that they support our previous conclusion, namely that there is little evidence to suggest that the 8 and 17 pS levels seen in granule-cell patches are conductance sublevels of the same glutamate receptor channel that gives rise to the 30, 40 and 50 pS openings. These results are therefore different from those reported for glutamate receptor channels in hippocampal neurones, where Jahr & Stevens (1987) state that transitions occurred from each conductance level to every other one and that these transitions occurred at frequencies that were inconsistent with the conclusion that they arose from the superposition of independent events. They also differ from results in patches from large cerebellar neurones by Cull-Candy & Usowicz (1987, 1989), in which transitions between open levels with mean conductances of 18 and 38 pS were relatively common; and they differ from results for NMDA-activated channels in patches from mouse central neurones (Ascher et al. 1988) where direct transitions between.open levels with approximate conductances of 16 and 35 pS were observed. It is difficult to compare the different results because, with the exception of the transitions between the 18 and 38 pS levels reported by Cull-Candy & Usowicz (1987, 1989), the relative frequencies with which the various types of transitions occurred are not given in previous publications. However, it does appear as though the total frequency of direct transitions between different open levels was not substantially different in these previous studies from what we have found in granule-cell patches. For example, Jahr & Stevens (1987) reported that 73 of 1897 openings (about 3 8 %) exhibited clear transitions between open levels. Cull-Candy & Usowicz (1989) reported that, on average, about 10-20 % of the openings detected were followed by what appeared to be a direct transition to another open level rather than by a closing, the percentage of such events being somewhat different for different agonists. Comparison of these numbers with the results in Table 2 indicate that, irrespective of the levels involved, direct transitions between different open levels were at least
GLUTAMATE RECEPTOR SINGLE-CHANNEL CURRENTS 193 as common in our experiments as they were in those of Jahr & Stevens (1987) and in those of Cull-Candy & Usowicz (1987, 1989). (Ascher et al. (1988) do not give a value for the relative frequency with which the direct transitions they observed occurred, but it would appear to have been quite low.) Furthermore, in patches from hippocampal neurones the most common type of transition between two open levels was between the 50 pS level and an open level with a mean conductance of about 45 pS (C. F. Stevens, personal communication). It seems likely that these latter transitions are the same as what we have called transitions between the 40 and 50 pS levels, and which were the most common type of transitions between two open levels that we observed; and transitions between levels with similar mean conductances (38 and 48 pS) were among the most common type of open-open transition observed by Cull-Candy & Usowicz (1989). There is, however, one rather striking difference between our results and those obtained for glutamate receptor channels in large cerebellar neurones (Cull-Candy & Usowicz, 1987, 1989). The most common type of transitions between open levels that was detected by Cull-Candy & Usowicz (1987, 1989) was between open levels with mean conductances of 18 and 38 pS. These levels would appear to correspond to our 17 and 40 pS levels. In large cerebellar neurones such transitions comprised up to 20 % of the total number of transitions detected in a given patch and they displayed temporal asymmetry (transitions from the 18 pS level to the 38 pS level occurring much less frequently than transitions from the 38 pS level to the 18 pS level). In contrast, in the majority of granule-cell patches examined with glutamate, aspartate or NMDA (nine, seventeen patches) no such transitions were detected (even at 0-3-0-5 Tr resolution) and none of the fifteen pairs of transitions listed in Table 2 exhibited any convincing evidence of temporal asymmetry. Obviously, if genuinely direct transitions occur between two open levels, even if such transitions are extremely rare, then these open levels must represent conductance substates of the same channel. Indeed, if the results in column 3 of Table 2 are accepted at face value then it is clear that transitions did occur between each open level and every other one. It is equally obvious, however, that some such apparent transitions would be expected as the result of the misclassification of incompletely resolved events or from the temporal superposition of independent channel openings. For example, apparent transitions between the 50 pS level and the 8 pS level might arise from sequential brief shuttings and 50 pS openings (that is, from the type of ambiguity illustrated in Fig. 6) or, for example, from the nearly simultaneous opening of two channels, one to the 8 pS level and the other to the 40 pS level. Given the complexity of the records, formal calculation of the expected frequency of the former type of event is virtually impossible, and the results of any such calculation would necessarily be model dependent. However, it seems virtually certain that some such misclassifications did occur. The expected frequency of the latter type of event also cannot be calculated, because the number of channels active in each patch was not known. Although there is no doubt that the probability must have been very small, both in our recordings and in those of previous studies, that the opening or closing of two channels would coincide very closely in time (at least if the open probability of one channel is truly independent from the state of the other channels in the patch), there is also no doubt that because of the limited time resolutions inherent in single-channel measurements 7
PHY 432
J. R. HOWE, S. G. CULL-CANDY AND D. COLQUHOUN it is not necessary that two independent events occur at exactly the same time in order for them to appear as if they did. In fact, we believe that two independent openings or two independent closings would probably have to be separated in time by hundreds of microseconds in order for them to be clearly recognizable as independent events, and that the resolution with which such events would be recognized as being independent would certainly be worse than the resolution for the detection of isolated openings or shuttings. For example, the glutamate-evoked cluster that is illustrated in Fig. 21 B contains what are clearly two 'double openings' (two 50 pS openings are superposed on each other) and this must indicate that two channels are open simultaneously. If the signals were low-pass filtered at 2 kHz (-3 dB) and the first of these events was examined carefully, there was no detectable inflexion on the shutting and it appeared as though both channels had closed simultaneously. At 3-5 kHz filtering (-3 dB, 35 kHz sampling), a slight inflexion was apparent that coincided with the 50 pS open level for a single channel, suggesting that the two channels did not close at exactly the same time. If the signal was assumed to arise from one channel shutting and then the other channel shutting at some time, At, later, the fit of the step-response function gave an estimated duration for this At of 200 ,s. This indicates that at 3-5 kHz filtering the limit for the detection of such events was about 200 /is. In contrast, in the same record (low-pass filtered at 3-5 kHz) a 40 ,us gap within a burst of 50 pS openings would have reached one-third of the way to the baseline, would have achieved an amplitude that was 10 times the r.m.s. noise of the recording, and would have been virtually impossible to miss (false-event rate, 7 x 10-19 s-1). In summary, although calculation of the expected frequency of the sort of misclassifications discussed above is beyond the goal of this paper, it does not seem unlikely that similar misclassifications would account entirely for the observed frequency of apparently direct transitions between the 8 or the 17 pS level and the 30, 40, or 50 pS level. The simplest and most defensible interpretation of the results given in Table 2 would therefore appear to be that the direct transitions we measured between conductance levels below 20 pS and those above 20 pS were in fact other types of events that were incompletely resolved and therefore misclassified; and it seems probable that genuinely direct transitions between these conductance levels do not occur in granule-cell patches. Interestingly, the absence of 50 pS openings in organotypically cultured Purkinje cells lacking NMDA receptors (Llano, Marty, Johnson, Ascher & Gaihwiler, 1988) is in keeping with our present and previous observations that the lower conductance levels (8 and 17 pS) are unable to open to higher conductances in certain types of neurones. The fact that in granule-cell patches the NMDA receptor channels gave direct transitions between the 30, 40 and 50 pS levels, whereas in large cerebellar neurones NMDA receptor channels also gave clear and frequent transitions between the 38 and 18 pS levels, represents a clearly defined difference between the NMDA receptor channels in these two types of cerebellar neurones (Cull-Candy et al. 1988b). This finding is consistent with reports from binding studies of the presence in central neurones of more than one class of NMDArecognition site (Monaghan, Olverman, Nguyen, Watkins & Cotman, 1988). 194
GLUTAMATE RECEPTOR SINGLE-CHANNEL CURRENTS
195
Shut times and open times: comparison to previous studies Shut-time distributions obtained with glutamate, aspartate and NMDA contained four exponential components, which is consistent with our earlier results (Howe et al. 1988); and four similar components were also apparent with quisqualate and kainate in those patches in which these agonists produced substantial proportions of 50 pS openings. The way in which we have analysed the results virtually excludes the possibility that the shuttings that were included in the distributions to be fitted were not full closures, and there seems no doubt that there was a component of shuttings in all of our records with a mean duration of about 40 ,us. Although in some patches there was an 'excess of brief gaps', we believe that this was caused (at least in large part) by misclassifying brief sublevel transitions as complete shuttings. Therefore, if there is an additional component of shuttings that is even briefer than the briefest component we have detected, then it must be much briefer and would therefore be below the resolution of patch-clamp measurements. Ascher et al. (1988) detected a single component of brief gaps with a mean time constant (430 Its) that is intermediate between the mean time constants we found for the briefest two gap components present in our records. (These results and those to follow were all obtained at room temperature in solutions nominally free of Mg2+.) The briefest component of shuttings detected by Jahr & Stevens (1990) was similar to that found by Ascher et al. (1988). Cull-Candy & Usowicz (1989) consistently found three exponential components in the shut time distributions they obtained; and the briefest such component gave mean durations of about 1 ms, which is similar to the mean durations of the second-briefest component we were able to detect. It seems probable that the briefest gap component we have detected was also present in these previous investigations of glutamate receptor channels in other types of central neurones, but that the resolution in these previous studies was insufficient to measure them reliably. Indeed, Cull-Candy & Usowicz (1989) obtained time constanfs similar to those we have found in one case in which they fitted the distribution of all the gaps they detected with four exponential components. It is to be expected that the time resolution in our experiments would be better than that in these previous studies. Most of the results were obtained at more hyperpolarized membrane potentials, and therefore both the amplitude of the single-channel currents and the signal-to-noise ratio were larger. Gibb (1989), in experiments on glutamate-activated channels in acutely dissociated cells from the adult rat hippocampus, found mean durations for the briefest two components in shut-time distributions that are similar to the corresponding time constants we have found. Two exponential components were resolved in most of the distributions we obtained for the apparent open times of 50 pS events. This suggests that there are two kinetically distinguishable types of 50 pS open state, as do the distributions based on bursts of openings (see below). Cull-Candy & Usowicz (1987) reported that the mean durations for 50 pS openings evoked by glutamate, aspartate and NMDA were 5-2 to 7-1 ms at -70 mV. In patches from mouse central neurones, values of 5-9 and 5-3 ms were obtained for the mean apparent open time of 50 pS openings evoked at -60 mV by NMDA and glutamate, respectively (Ascher et al. 1988). If the effect of membrane potential is accounted for, these values are somewhat, but not 7-2
J. R. HOWE, £ G. CULL-CANDY AND D. COLQUHOUN substantially, longer than those we found for 50 pS openings evoked by glutamate, aspartate and NMDA (mean values of 4-0 to 4-8 ms at -60 mV). Jahr & Stevens (1987) reported that open-time distributions for 40-50 pS events contained two components with respective time constants of 1-3 and 10-15 ms. These time constants are considerably longer than those we have measured, even when the effect of membrane potential is considered; and they are in fact more similar to the time constants we obtained from the distributions of burst lengths. The present study represents by far the most detailed kinetic analysis of openings to conductance levels other than the 50 pS level. There are in fact no values in the literature for the mean duration of events that might correspond to the 30 and 40 pS events we have observed in granule-cell patches. Jahr & Stevens (1987) reported that the mean open time for events that would appear to correspond to our 8 and 17 pS openings was about 0 5 ms. Cull-Candy & Usowicz (1987) found values in the range of 017 to 2-0 ms for similar openings in patches from large cerebellar neurones. These time constants are not dissimilar to the values we have found for 8 and 17 pS openings produced by glutamate, aspartate and NMDA, and the different results are in general agreement that the mean duration of openings to the 50 pS level was longer than the mean duration of openings to these smaller conductance levels. In our experiments, the mean lengths of 8 and 17 pS openings produced by kainate were longer than the mean length of similar openings produced by glutamate, aspartate or NMDA; and the longest such openings were observed with quisqualate. 196
Shut times and open times: dependence on membrane potential Our findings that the mean duration of both two types of brief gaps did not become longer with membrane hyperpolarization argues strongly that these brief gaps are not primarily the result of channel blockages by residual Mg2+ present in our solutions, or by any other ion or charged molecule, including the agonists themselves. Indeed, Jahr & Stevens (1990) found no effect on the brief gaps that they observed in nominally Mg2+-free solutions when they changed either sodium, pH or calcium in the extracellular solution, or when they altered the concentration of either chloride, HEPES or EGTA in the internal solution. The results of Ascher & Nowak (1988 b) and of Jahr & Stevens (1990) indicate that over the range of membrane potentials we have examined the mean duration of Mg2+ blockages would be expected to lengthen severalfold. These same results indicate that at -80 mV the mean duration of Mg2+ blockages would be about 1 ms. Thus, the briefest gap component we have detected is much too brief to represent blockages by magnesium ions. However, this does not exclude the possibility that some such blockages were present in our recordings. Jahr & Stevens (1990) state they used very pure salts to prepare their solutions and found that the concentration of Mg2+ in solutions that were nominally Mg2+-free was about 200 nm. As we took no special precautions in this regard, it is likely the concentration of Mg2+ in our nominally Mg2+-free solutions was higher than this. It is therefore possible that blockages by residual Mg2+ may have contributed, at least in part, to the increase in the relative proportion of the second-briefest gap component, and perhaps also to the decrease in the mean duration of 50 pS openings, that occurred with membrane hyperpolarization.
GLUTAMATE RECEPTOR SINGLE-CHANNEL CURRENTS
197
Shut times and open times: dependence on agonist Although in large part the results with glutamate, aspartate and NMDA were similar, there were some significant differences both in mean duration and relative areas of the brief gap components detected with the three agonists. On the one hand, this provides some evidence that these gaps are not simply the result of ion permeation through the channel. On the other hand, some such agonist dependence might be expected if the brief gaps arose from brief oscillations between fully liganded open and shut states, as has been proposed for other ligand-gated channels (Colquhoun & Sakmann, 1981, 1985; Cull-Candy & Parker, 1982; Dionne & Liebowitz, 1982; Sine & Steinbach, 1986, 1987). Some differences were also found in the distributions of apparent open times obtained with the various agonists, differences which might potentially provide information about mechanisms. However, because the range of concentrations examined was relatively narrow, and because of possible differences in the background concentration of glycine, it is difficult at present to know what to make of the observed differences in open times. Conclusions from distributions based on bursts The distributions of burst length and of total open time per burst contained three exponential components. Our analysis of these distributions indicates clearly that the slowest two components arise from the kinetics of the 50 pS open level. This in turn indicates that there are two kinetically different types of 50 pS open state. It also argues that the two components present in many of the distributions of apparent open times for 50 pS events did not result from the distortion of the distribution that can result when brief events are missed (Hawkes, Jalali & Colquhoun, 1990). Distributions of the number of open periods per burst contained (at least) two geometric components. Two similar components were obtained if only those bursts that consisted entirely of oscillations between the 50 pS open level and the shut level were considered, findings that further support the conclusion that there are two types of 50 pS open state. One of the components typically had a mean close to unity, which is similar to results reported for nicotinic acetylcholine receptor channels (Colquhoun & Sakmann, 1985). This is of interest for two reasons. Firstly, the existence of a component with a mean close to unity in the presence of limited time resolution often implies that there is indeed a component in the true distribution that corresponds to single openings. Secondly, the existence of a component in the true distribution with unit mean is likely to be informative with regard to choosing between alternative kinetic models (Colquhoun & Sakmann, 1985; Colquhoun & Hawkes, 1987). Clusters The long, high-po clusters we have observed were seen with each of the five agonists tested, but were most common with NMDA. There is virtually no doubt that these clusters arose primarily from the activity of a single channel. Similar kinetic behaviour has been observed for glutamate receptor channels in locust muscle (Patlak, Gration & Usherwood, 1970; see also, Cull-Candy, Miledi &
198
J. R. HOWE, S. G. CULL-CANDY AND D. COLQUHOUN
Parker, 1981), and was reported more recently (Jahr & Stevens, 1987) for largeconductance glutamate receptor channels in rat hippocampal neurones. Jahr & Stevens (1987) have stated that the long component of open times that they measured seemed to be associated with the gating mode that gave rise to clustering. But we have found no substantial differences in the distributions of open times, nor in the distributions of brief shut times, for portions of the records in which there was clustering and portions of the records in which there was not. This apparent difference between our results and those of Jahr & Stevens (1987) may primarily be the result of differences in nomenclature rather than the result of a genuine difference in the kinetic behaviour of glutamate receptor channels in the two types of central neurone. As noted above, the time constants of the two components Jahr & Stevens (1987) found in open-time distributions are similar to the slowest two components identified in the distributions of burst length in the present paper. Also, Jahr & Stevens (1987) state that they observed bursts of openings that lasted several hundreds of milliseconds. It therefore seems probable that what Jahr & Stevens (1987) have called openings correspond in large part to what we have defined as bursts and that the bursts in their study correspond to what we have called clusters. The definition of bursts and clusters is always somewhat arbitrary and, although the clusters we have analysed in detail could be identified unambiguously, a formal definition of clusters would require identification of a gap component within these clusters that corresponded to 'gaps between bursts'. We were unable to identify such a component. The long clusters that we have seen are similar to clusters observed for nicotinic acetylcholine receptor channels at high agonist concentrations (Sakmann et al. 1980; Ogden & Colquhoun, 1985; Sine & Steinbach, 1987; Colquhoun & Ogden, 1988). It is thought that this latter clustering is secondary to receptor desensitization and that the clusters represent brief 'escapes' from a long-lived, non-conducting, desensitized state of the channel. In our experiments, the dependence of clustering on agonist concentration was not investigated in a systematic way, and it is therefore unclear whether a similar explanation can account for the clustering we have seen. There is however, one notable difference between our results and those obtained for nicotinic acetylcholine receptor channels. High-p0 clusters of nicotinic acetylcholine receptor channel openings are typically separated by shut times that are of the order of tens of seconds. In contrast, in our experiments the p0 between clusters was similar to that observed for patches in which there was no obvious clustering (on average about 002) and the longest shut times were a few hundred milliseconds. It is difficult to explain these findings if the clusters we have observed were secondary to receptor desensitization, unless the possibility is admitted that some of the receptor channels present in the patch were desensitized while other receptor channels were not. It is doubtful that the clustering that either we or Jahr & Stevens (1987) have observed is the result of patch excision. Spectra of large-conductance whole-cell current noise evoked in granule cells by glutamate, aspartate and NMDA often show evidence of excess variance at frequencies below 5 Hz that may correspond to the clusters seen in outside-out patches (Howe et al. 1988). Furthermore, the NMDA receptor component of whole-cell excitatory postsynaptic currents evoked in cultured spinal neurones (Forsythe & Westbrook, 1988), and the corresponding
GLUTAMATE RECEPTOR SINGLE-CHANNEL CURRENTS 199 component of miniature synaptic currents evoked in cultured hippocampal neurones (Bekkers & Stevens, 1989), has a time constant that is several tens of milliseconds and that is considerably longer than the slowest component found in the burst-length distributions in the present study. The number of stateo We began these investigations in the hope that they would enable us to construct a kinetic model for glutamate receptor activation. Although we believe that it would be premature to propose a kinetic model for the glutamate receptor channels we have studied, the results do allow us to make some statements about the characteristics such a model must have if it is to describe our results. As we have discussed above, the frequency with which apparently direct transitions occurred between the 8 or the 17 pS level and the 30, 40 or 50 pS level was so low in our recordings that we believe there is no convincing evidence that the 8 and 17 pS levels are conductance substates of the other conductance levels observed. Put another way, a model which assumes that they are not conductance substates is clearly sufficient to account for the vast majority, and perhaps all, of the data. What then of the 30, 40 and 50 pS levels? The consistency and frequency with which direct transitions occurred between the 40 and 50pS open levels argues strongly that these two conductance levels are conductance substates of the same multi-conductance channel. However, the results with regard to the 30 pS level are less compelling. Firstly, the discrimination of the 30 pS events was less than clear in some of the amplitude distributions. Secondly, even in those patches in which it was clear, the sojourns at this level typically comprised only about 5% of all the completely resolved events that were observed. Although we believe that the sum of the results supports the existence of a 30 pS state, the results could also be described reasonably well by assuming that the 30 and 40 pS states were in fact one, rather 'floppy', conductance substate. This is especially so because the mean durations of the 30 and 40 pS events were similar. For these reasons, even if the 30 and 40 pS states are indeed distinct channel substates, little is lost from the descriptive power of any potential kinetic model if what we have referred to as 30 and 40 pS events are 'lumped' together and assumed to represent sojourns in the same conductance substate. As discussed above, we believe our results indicate that there are two kinetically distinguishable 50 pS open states. The relative proportions of openings to each conductance level that were observed with kainate, quisqualate and NMDA indicate that NMDA is selective for the channels that exhibit a main conductance level of about 50 pS, whereas kainate, and to a lesser extent quisqualate, are selective for the 8 and 17 pS channels. On the basis of this agonist selectivity, it seems reasonable to refer to the former channels as NMDA receptor channels, although the relative selectivity of kainate and quisqualate for the 8 and 17 pS channels is less clear. In fact, in granule cells kainate may primarily activate channels with a mean conductance of about 140 fS (CullCandy & Ogden, 1985; Cull-Candy et al. 1988a). Because of their very small conductance, openings of these latter channels would not have been resolved in the present experiments. Most of the kinetic data that we have obtained probably relates to the NMDA
200
J. R. HOWE, S. G. CULL-CANDY AND D. COLQUHOUN
receptor channel. We believe that the vast majority of the results can be described if it is assumed that this channel can exist in three open states. Over the physiological range of membrane potentials, two of these open states have a mean conductance of about 50 pS and the remaining one has a mean conductance of about 40 pS. The number of exponential components in the distributions of shut times indicates that there must be at least three distinct closed states of this channel. The mean dwell times in two of these shut states are brief, and it is these states that give rise to what we have defined as 'gaps within bursts'. In addition, there must be at least one longlived shut state, one or more entries into which gives rise to 'gaps between bursts'. Therefore, a six-state model is probably sufficient to describe almost all of the kinetic behaviour of the NMDA receptor channels in cerebellar granule cells, although additional states may be required to account for clustering (and would be required for the description of Mg2+ block). Our results also put some restrictions on the way these three open and three closed states must be connected. The model must allow for direct transitions between the 40 and 50 pS states and also for the observations that neither of the brief gap components appeared to be associated exclusively with either the 40 or 50 pS open level. The results of our autocorrelation analysis, and the presence of a component with near unit mean in the distributions of the number of open periods per burst, put additional restrictions on the way the states can be connected. What is primarily lacking at present is information about the dependence of the various kinetic parameters on agonist concentration. Note added in proof. Lester, Clements, Westbrook & Jahr (1990) using rapid solution changes have recently shown that it is indeed the kinetics of clusters, rather than the slow removal of glutamate from the synaptic cleft and the consequent rebinding of the transmitter, that results in the slow decay of NMDA receptor-mediated postsynaptic currents. We wish to thank D. C. Ogden for many helpful discussions during the course of these investigations and Steve Sine for helpful comments on the manuscript. The work was supported by the NIH, The Wellcome Trust, and the MRC. REFERENCES
ASCHER, P., BREGESTOVSKI, P. & NOWAK, L. (1988). N-Methyl-D-aspartate-activated channels of mouse central neurones in magnesium-free solutions. Journal of Physiology 399, 207-226. ASCHER, P. & NOWAK, L. (1986). Calcium permeability of the channel activated by N-methyl-Daspartate (NMDA) in isolated mouse central neurones. Journal of Physiology 377, 35P. P. & NOWAK, L.(1988a). Quisqualate- and kainate-activated channels in mouse central neurones in culture. Journal of Physiology 399, 227-245. ASCHER, P. & NOWAK, L. (1988b). The role of divalent cations in the N-methyl-D-aspartate responses of mouse central neurones in culture. Journal of Physiology 399, 247-266. BEKKERS, J. M. & STEVENS, C. F. (1989). NMDA and non-NMDA receptors are co-localized at individual excitatory synapses in cultured rat hippocampus. Nature 341, 230-233. BLATZ, A. L. & MAGLEBY, K. L. (1989). Adjacent interval analysis distinguishes among gating mechanisms for the fast chloride channel from rat skeletal muscle. Journal of Physiology 410, 561-585. COLQUHOUN, D. & HAWKES, A. G. (1982). On the stochastic properties of bursts of single ion channel openings, and of clusters of bursts. Philosophical Transactions of the Royal Society B 300, 1-59. COLQUHOUN, D. & HAWKES, A. G. (1987). A note on correlations in single ion channel records. Proceedings of the Royal Society B 230, 15-52.
ASCHER,
GLUTAMATE RECEPTOR SINGLE-CHANNEL CURRENTS
201
COLQUHOUN, D. & OGDEN, D. C. (1988). Activation of ion channels in the frog end-plate by high concentrations of acetylcholine. Journal of Physiology 395, 131-159. COLQUHOUN, D. & SAKMANN, B. (1981). Fluctuations in the microsecond time range of the current through single acetylcholine-receptor ion channels. Nature 294, 464-466. COLQUHOUN, D. & SAKMANN, B. (1985). Fast events in single-channel currents activated by acetylcholine and its analogues at the frog muscle end-plate. Journal of Physiology 369, 501-557. COLQUHOUN, D. & SIGWORTH, F. J. (1983). Fitting and statistical analysis of single-channel records. In Single-Channel Recording, ed. SAKMANN, B. & NEHER, E., pp. 191-263. Plenum Press, New York, London. CULL-CANDY, S. G., HOWE, J. R. & OGDEN, D. C. (1987). Ion channels activated by excitatory amino acids in rat cultured cerebellar granule neurones. Journal of Physiology 390, 75P. CULL-CANDY, S. G., HOWE, J. R. & OGDEN, D. C. (1988a). Noise and single channels activated by excitatory amino acids in rat cultured cerebellar granule neurones. Journal of Physiology 400, 189-222. CULL-CANDY, S. G., HOWE, J. R. & UsowIcz, M. M. (1988b). Single glutamate-receptor channels in two types of cerebellar neurones. In Excitatory Amino Acids in Health and Disease, ed. LODGE, D., pp. 165-185. John Wiley and Sons, Chichester, New York. CULL-CANDY, S. G., MILEDI, R. & PARKER, I. (1981). Single glutamate-activated channels recorded from locust muscle fibres with perfused patch-clamp electrodes. Journal of Physiology 321, 195-210. CULL-CANDY, S. G. & OGDEN, D. C. (1985). Ion channels activated by L-glutamate and GABA in cultured cerebellar neurons of the rat. Proceedings of the Royal Society B 244, 367-373. CULL-CANDY, S. G. & PARKER, I. (1982). Rapid kinetics of single glutamate-receptor channels. Nature 295, 410-412. CULL-CANDY, S. G. & Usowicz, M. M. (1987). Multiple-conductance channels activated by excitatory amino acids in cerebellar neurons. Nature 325, 525-528. CULL-CANDY, S. G. & USOWICZ, M. M. (1989). On the multiple-conductance single channels activated by excitatory amino acids in large cerebellar neurones of the rat. Journal ofPhysiology 415, 555-582. DIONNE, V. E. & LEIBOWITZ, M. (1982). Acetylcholine receptor kinetics: a description from singlechannel currents at snake neuromuscular junctions. Biophysical Journal 39, 253-261. FAGG, G. E., FOSTER, A. C. & GANONG, A. H. (1986). Excitatory amino acid synaptic mechanisms and neurological function. Trends in Pharmacological Sciences 7, 357-363. FORSYTHE, I. D. & WESTBROOK, G. L. (1988). Slow excitatory postsynaptic currents mediated by N-methyl-D-aspartate receptors on cultured mouse central neurones. Journal of Physiology 396, 515-533. FREDKIN, D. R., MONTAL, M. & RICE, J. A. (1985). Identification of aggregated Markovian models: application to the nicotinic acetylcholine receptor. From Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer, vol. 1, ed. LECAM, L. M. & OLSHEN, R. A., Wadsworth, Monterey, CA, USA. GIBB, A. J. (1989). Characteristics of channel openings activated by low concentrations of glutamate in cells dissociated from adult rat hippocampus. Journal of Physiology 415, 39P. HAMILL, 0. P., MARTY, A., NEHER, E., SAKMANN, B. & SIGWORTH, F. J. (1981). Improved patchclamp techniques for high-resolution current recording from cells and cell-free membrane patches. Pfligers Archiv 391, 85-100. HAWKES, A. G., JALALI, A. & COLQUHOUN, D. (1990). The distributions of the apparent open times and shut times in a single-channel record when brief events cannot be detected. Philosophical Transactions of the Royal Society A (in the Press). HORN, R. (1987). Statistical methods for model discrimination: applications to gating kinetics and permeation of the acetylcholine receptor channel. Biophysical Journal 51, 255-263. HOWE, J. R., COLQUHOUN, D. & CULL-CANDY, S. G. (1987). Single channels activated by glutamate and aspartate. Society for Neuroscience Abstracts 13, 98. HOWE, J. R., COLQUHOUN, D. & CULL-CANDY, S. G. (1988). On the kinetics of large-conductance glutamate-receptor ion channels in rat cerebellar granule neurons. Proceedings of the Royal Society B 233, 407-422. JAHR, C. E. & STEVENS, C. F. (1987). Glutamate activates multiple single channel conductances in hippocampal neurons. Nature 325, 522-525.
202
J. R. HOWE,
0G. CULL-CANDY AND D. COLQUHOUN
JAHR, C. E. & STEVENS, C. F. (1990). A quantitative description of NMDA receptor-channel kinetic behaviour. Journal of Neuroscience 10, 1830-1837. JOHNSON, J. W. & ASCHER, P. (1987). Glycine potentiates the NMDA response of mouse central neurones. Nature 325, 529-531. LESTER, R. A. J., CLEMENTS, J. D., WESTBROOK, G. L. & JAHR, C. E. (1990). Channel kinetics determine the time course of NMDA-receptor mediated synaptic currents. Nature 346, 565-567. LLANO, I., MARTY, A., JOHNSON, J. W., ASCHER, P. & GXHWILER, B. H. (1988). Patch-clamp recordings of amino acid activated responses in 'organotypic' slice cultures. Proceedings of the National Academy of Sciences of the USA 85, 3221-3225. MAcDERMOTT, A. B., MAYER, M. L., WESTBROOK, G. L., SMITH, S. J. & Barker, J. L. (1986). NMDA-receptor activation increases cytoplasmic calcium concentration in cultured spinal cord neurones. Nature 321, 519-522. MCMANUS, 0. B., BLATZ, A. L. & MAGLEBY, K. L. (1987). Sampling, log binning, fitting and plotting durations of open and shut intervals from single channels and the effects of noise. Pfluiger Archiv 410, 503-553. MAYER, M. L. & WESTBROOK, G. L. (1987 a). The physiology of excitatory amino acids in the vertebrate central nervous system. Progress in Neurobiology 28, 197-276. MAYER, M. L. & WESTBROOK, G. L. (1987b). Permeation and block of N-methyl-D-aspartic acid receptor channels by divalent cations in mouse central neurones. Journal of Physiology 394, 501-527.
MONAGHAN, D. T., OLVERMAN, H. J., NGUYEN, L., WATKINS, J. C. & COTMAN, C. W. (1988). Two classes of N-methyl-D-aspartate recognition sites: differential distribution and differential regulation by glycine. Proceedings of the National Academy of Sciences of the USA 85, 9836-9840. NOWAK, L., BREGESTOVSKI, P., ASCHER, P., HERBET, A. & PROCHIANTZ, A. (1984). Magnesium gates glutamate-activated channels in mouse central neurones. Nature 307, 462-465. OGDEN, D. C. & COLQUHOUN, D. (1985). Ion channel block by acetylcholine, carbachol and suberyldicholine at the frog neuromuscular junction. Proceedings of the Royal Society B 225, 329-355. PATLAK, J. B. (1988). Sodium channel subconductance levels measured with a new variance-mean analysis. Journal of General Physiology 92, 413-430. PATLAK, J. B., GRATION, K. A. F. & USHERWOOD, P. N. R. (1979). Single glutamate-activated channels in locust muscle fibres. Nature 278, 643-645. SAKMANN, B., PATLAK, J. B. & NEHER, E. (1980). Single acetylcholine-activated channels show burst kinetics in the presence of desensitizing concentrations of agonist. Nature 286, 71-73. SIGWORTH, F. J. (1985). Open channel noise. I. Noise in acetylcholine receptor currents suggests conformational fluctuations. Biophysical Journal 47, 709-720. SIGWORTH, F. J. & SPIE, S. M. (1987). Data transformations for improved display and fitting of single channel dwell time histograms. Biophysical Journal 52, 1047-1054. SINE, S. M. & STEINBACH, J. H. (1986). Activation of acetylcholine receptors on clonal mammalian BC3H-1 cells by low concentrations of agonist. Journal of Physiology 373, 129-162. SINE, S. M. & STEINBACH, J. H. (1987). Activation of acetylcholine receptors on clonal mammalian BC3H-1 cells by high concentrations of agonist. Journal of Physiology 385, 325-359. WATKINS, J. C. & EVANS, R. H. (1981). Excitatory amino acid transmitters. Annual Review of Pharmacology and Toxicology 21, 165-204. YELLEN, G. (1984). Ionic permeation and blockade in Ca2+-activated K+ channels of bovine chromaffin cells. Journal of General Physiology 84, 157-186.
