glutamate receptor channel kineticsglutamate receptor-gated channel (glur) oflocust skele tal muscle...

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GLUTAMATE RECEPTOR CHANNEL KINETICS The Effect of Glutamate Concentration C. J. KERRY, R. L. RAMSEY, M. S. P. SANSOM, AND P. N. R. USHERWOOD Department of Zoology, University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom ABSTRACT Single channel recordings from the locust muscle D-glutamate receptor channel were obtained using glutamate concentrations ranging from 10-6 to 102 M. Channel kinetics were analyzed to aid in the development of a model for the gating mechanism. Analysis of channel dwell time histograms demonstrated that the channel possessed multiple open and closed states at concentrations of glutamate between lo-5 and 10-2 M. Correlations between successive dwell times showed that the gating mechanism was nonlinear (i.e., branched or cyclic) over the same glutamate concentration range. The glutamate concentration dependence of the channel open probability, and of the event frequency, was used to explore two possible allosteric gating mechanisms in more detail. INTRODUCTION Single channel recording is now the primary tool for investigating the gating mechanisms of both receptor- and voltage-gated ion channels. The most intensively studied receptor-gated ion channel is the nicotinic acetylcholine receptor (nAChR), but it remains to be established whether this is a model for receptor-gated channels in general. If a general picture of the properties of receptor- gated channels is to emerge, then it is important to investigate other systems in comparable detail. Single channel studies undertaken in our laboratory over the past nine years have concentrated on the quisqualate-sensitive, glutamate receptor-gated channel (GluR) of locust skele- tal muscle (Usherwood, 1978a, b, 1981; Gration et al., 1979), several properties of which have made it particu- larly amenable to single channel analysis of gating kinetics (Patlak et al., 1979; Gration et al., 198 la, b; Cull-Candy et al., 1981; Gration et al., 1982; Cull-Candy and Parker, 1982). One advantage of this system is that desensitization can be inhibited by exposure of the muscle membrane to concanavalin A (Mathers and Usherwood, 1976, 1978), thus permitting channel gating to be studied in isolation from desensitization. The high conductance of the GluR (115-150 pS) enables recordings to be obtained using megaohm seals, thus avoiding pretreatment of the muscle membrane with proteolytic enzymes. Previous analysis of the GluR gating mechanism focused on the channel behavior in the presence of 10-4 M glutamate (Ashford et al., 1984a, b; Kerry et al., 1987). The gating mechanism was shown to contain at least three open states, at least four closed states, and at least three Correspondence should be addressed to Dr. Usherwood. BIOPHYS. J. © Biophysical Society * 0006-3495/88/01/39/14 Volume 53 January 1988 39-52 isomerization pathways connecting the closed and open states. The work described in this paper extends such analysis over a range of glutamate concentrations, and leads to the construction of a working hypothesis for the GluR gating mechanism. As such, it prepares the way for a fuller description of the molecular details of GluR gating. METHODS Experimental The experimental methods were the same as those described in Kerry et al. (1987), and earlier publications from this laboratory (Patlak et al., 1979; Gration et al., 1982). Female adult locusts (Schistocerca gregaria) were used at 7-10 d post-fledgling. These were fed exclusively on a diet of home-grown wheat and dried food supplement, in an attempt to eliminate possible diet-dependent changes in extrajunctional GluR density. Data Reduction Recorded data was filtered at f. = 3 kHz on playback, and reduced to vectors of dwell (open and closed) times using the dual threshold crossing algorithm described by Gration et al. (1982), and by Kerry et al. (1987). Computation General Considerations. The channel dwell time vectors were input to a PDP 11/34 computer, which was used for the majority of the calculations. Some of the later stages of the analysis used an ICL 2900 series mainframe. Dwell Time Distributions Dwell time distributions are expressed as histograms, normalized to give estimates of dwell time probability density functions (pdfs) (Colquhoun and Sigworth, 1983). To facilitate the inclusion of dwell times (t) ranging over up to four orders of magnitude in the same pdf, the histogram intervals were varied as follows. The minimum (t,,,J,,) and maximum (t.) times to be represented in the histogram were input, alongside the desired $2.00 39

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Page 1: Glutamate Receptor Channel Kineticsglutamate receptor-gated channel (GluR) oflocust skele tal muscle (Usherwood, 1978a, b, 1981; Gration et al., 1979), several properties of which

GLUTAMATE RECEPTOR CHANNEL KINETICS

The Effect of Glutamate Concentration

C. J. KERRY, R. L. RAMSEY, M. S. P. SANSOM, AND P. N. R. USHERWOODDepartment ofZoology, University ofNottingham, University Park, Nottingham, NG7 2RD,United Kingdom

ABSTRACT Single channel recordings from the locust muscle D-glutamate receptor channel were obtained usingglutamate concentrations ranging from 10-6 to 102 M. Channel kinetics were analyzed to aid in the development of a

model for the gating mechanism. Analysis of channel dwell time histograms demonstrated that the channel possessedmultiple open and closed states at concentrations of glutamate between lo-5 and 10-2 M. Correlations betweensuccessive dwell times showed that the gating mechanism was nonlinear (i.e., branched or cyclic) over the same

glutamate concentration range. The glutamate concentration dependence of the channel open probability, and of theevent frequency, was used to explore two possible allosteric gating mechanisms in more detail.

INTRODUCTION

Single channel recording is now the primary tool forinvestigating the gating mechanisms of both receptor- andvoltage-gated ion channels. The most intensively studiedreceptor-gated ion channel is the nicotinic acetylcholinereceptor (nAChR), but it remains to be establishedwhether this is a model for receptor-gated channels ingeneral. If a general picture of the properties of receptor-gated channels is to emerge, then it is important toinvestigate other systems in comparable detail. Singlechannel studies undertaken in our laboratory over the pastnine years have concentrated on the quisqualate-sensitive,glutamate receptor-gated channel (GluR) of locust skele-tal muscle (Usherwood, 1978a, b, 1981; Gration et al.,1979), several properties of which have made it particu-larly amenable to single channel analysis of gating kinetics(Patlak et al., 1979; Gration et al., 198 la, b; Cull-Candy etal., 1981; Gration et al., 1982; Cull-Candy and Parker,1982). One advantage of this system is that desensitizationcan be inhibited by exposure of the muscle membrane toconcanavalin A (Mathers and Usherwood, 1976, 1978),thus permitting channel gating to be studied in isolationfrom desensitization. The high conductance of the GluR(115-150 pS) enables recordings to be obtained usingmegaohm seals, thus avoiding pretreatment of the musclemembrane with proteolytic enzymes.

Previous analysis of the GluR gating mechanismfocused on the channel behavior in the presence of 10-4 Mglutamate (Ashford et al., 1984a, b; Kerry et al., 1987).The gating mechanism was shown to contain at least threeopen states, at least four closed states, and at least three

Correspondence should be addressed to Dr. Usherwood.

BIOPHYS. J. © Biophysical Society * 0006-3495/88/01/39/14Volume 53 January 1988 39-52

isomerization pathways connecting the closed and openstates. The work described in this paper extends suchanalysis over a range of glutamate concentrations, andleads to the construction of a working hypothesis for theGluR gating mechanism. As such, it prepares the way for afuller description of the molecular details of GluR gating.

METHODS

ExperimentalThe experimental methods were the same as those described in Kerry etal. (1987), and earlier publications from this laboratory (Patlak et al.,1979; Gration et al., 1982). Female adult locusts (Schistocerca gregaria)were used at 7-10 d post-fledgling. These were fed exclusively on a diet ofhome-grown wheat and dried food supplement, in an attempt to eliminatepossible diet-dependent changes in extrajunctional GluR density.

Data ReductionRecorded data was filtered at f. = 3 kHz on playback, and reduced tovectors of dwell (open and closed) times using the dual threshold crossingalgorithm described by Gration et al. (1982), and by Kerry et al. (1987).

Computation

General Considerations. The channel dwell time vectorswere input to a PDP 11/34 computer, which was used for the majority ofthe calculations. Some of the later stages of the analysis used an ICL 2900series mainframe.

Dwell Time DistributionsDwell time distributions are expressed as histograms, normalized to giveestimates of dwell time probability density functions (pdfs) (Colquhounand Sigworth, 1983). To facilitate the inclusion of dwell times (t) rangingover up to four orders of magnitude in the same pdf, the histogramintervals were varied as follows. The minimum (t,,,J,,) and maximum (t.)times to be represented in the histogram were input, alongside the desired

$2.00 39

Page 2: Glutamate Receptor Channel Kineticsglutamate receptor-gated channel (GluR) oflocust skele tal muscle (Usherwood, 1978a, b, 1981; Gration et al., 1979), several properties of which

number of intervals (m), and used to calculate

g = (tmax/tmin)l /m

The ith interval is then defined by

tming' <t<t<tmjn gand its width is

tmin(g, )

and it is centered about

ti = t min

As discussed by Landaw and DiStefano (1984), such exponential sam-pling is optimal for data to be interpreted in terms of multiexponentialdecays, as it allows components with differing time constants to beaccurately estimated.The dwell time pdfs were displayed on log-log plots, as used by Blatz

and Magleby (1986), to reveal multiexponential components more readi-ly. Sums of exponential functions were fitted using previously describedprocedures (Kerry et al., 1987). The minimum number of componentsrequired for a satisfactory fit was determined using the AIC method(Akaike, 1974).

Autocorrelation Function AnalysisThe use of autocorrelation functions (acfs) to analyze single channel datahas been discussed by Labarca et al. (1985), Kerry et al. (1987), and byColquhoun and Hawkes (1987). Briefly, the acf for successive open timesis given by

ro(k) = Cov [to (i), to(i + k)]/Var [to(i)],where ro(k) is the autocorrelation between pairs of openings separated byk-I intervening openings, to(i) is the ith open time, Cov denotescovariance and Var variance. A similar term applies for the closed times.

Adjacent Dwell Time AnalysisThe theoretical background to this approach is given by McManus et al.(1985) and Fredkin et al. (1985). Briefly, a closed time (tJ) is assigned tointerval i if

tmin1 < tc C tmin'

where tmin and g are defined as above. For each interval i, the mean opentimes for the preceding and following openings are evaluated, and arethen plotted against tc(i).

Fitting ProceduresIn all but one case, the fits of equations to data were optimized usingGauss-Newton algorithms. The exception was the use of a simplexalgorithm (NAG routine E04CCF) when fitting the event frequencydata. In this latter case, it was also necessary to restrict the parameterspace to non-negative values of the closed -open isomerization rates (hi)by searching for optimal values of log h,.

RESULTS

Summary of the DatabaseSingle channel recordings from glutamate receptor-gatedion channels (GluR) have been obtained at 20 differentglutamate concentrations, ranging from 106 to 10 2 M(see Table I). The database used in all subsequent analysiscorresponds to recordings with a signal to noise ratio of

TABLE ISUMMARY OF DATABASE

[Glu] No. of sites No. of events Total recording time

M s1x 10-6 4 57 1,6906x 10-6 1 21 5381 x 10-5 2 3,860 1,5602 x 10-5 3 1,570 8645 x 10-5 2 5,470 2416 x 10-5 4 11,000 8338 x 10' 3 16,000 1,0801 X 10-4 6 50,600 1,1602 x 10-4 4 32,500 4154 x 10-4 4 21,900 1565x 10-4 3 10,200 686 x 10-4 3 23,400 1108x 10-4 2 5,970 301 X l0-3 3 30,200 2632x10-3 2 9,231 853 x 10-3 1 10,800 2104 x 10-3 2 1,010 995 x 10-3 5 1,640 2788 x 10' 2 759 1171x 10-2 4 3,410 383

Summary of the database used in studying the gating kinetics of theGluR. The number of events refers to the total number of channelopenings of duration -0.2 ms. All openings and closings of lesser durationare discarded so as to impose a consistent minimum dwell time.

>3:1. All events of duration <0.2 ms have been discardedso as to impose a consistent minimum dwell time (Colqu-houn and Sigworth, 1983). Such event omission distortsthe observed channel kinetics. However, corrections forevent omission (Roux and Sauve, 1985; Blatz and Magle-by, 1986; Ball and Sansom, 1988b) are model dependent,and so have not been applied at this stage of the analysis.Earlier studies (Kerry et al., 1987) have shown thatefficiency of event detection is 100% for event durations of>0.18 ms. So, 0.2 ms is a conservative estimate of thedeadtime for the recording and detection system. Overall,the database contains 240,000 events recorded from 60different membrane sites. In all except two cases, multiplerecordings have been obtained for each glutamate concen-tration. In the presence of 10-4 M glutamate, the site-to-site variation in kinetic parameters was comparable tothat observed within a recording from a single site (Kerryet al., 1987). In the current database, the maximumsite-to-site variation is seen at glutamate concentrations-5 x 10-4M.

Overall Kinetic Properties of the GluRThe overall kinetic parameters (probability of being open,PO; event frequency, f; mean open time, mi; and meanclosed time, mj) as functions of glutamate concentrationare displayed in Fig. 1. To calculate average parametervalues the total time spent open (To,j) and the total timespent closed (T,,i) are evaluated for each membrane site(i). The average probability of the channel being open

BIOPHYSICAL JOURNAL VOLUME 53 198840

Page 3: Glutamate Receptor Channel Kineticsglutamate receptor-gated channel (GluR) oflocust skele tal muscle (Usherwood, 1978a, b, 1981; Gration et al., 1979), several properties of which

11.

4

3

2-1-2-3 -

-2

-7-2

111 I[1

I

aaif

6

5

4

3

2

0

- L-7-5 -4 -3 -2

log CClu] (M)

B

I

1p I

4

-6 -5 -4log (Glu] (M)

-3

FIGURE 1 Overall kinetic parameters for theGluR single channel database. (A) The proba-bility of the channel being open as a function of[GluJ. Each point is the average, calculated as

-2 described in the text, over all sites for a givenconcentration. The error bars indicate the stan-dard deviation from the mean. (B) The channelevent frequency (where an event is defined asan opening plus the following closing) as afunction of [Glu]. Again, the points are aver-ages for each concentration (see text). (C andD) The mean open times and mean closedtimes, respectively, as functions of [Glul. Thevalues are those calculated from A and B usingEqs. 3 and 4 of the text.

-if40

il. 1

-6 -5 -4 -3 -2log [Glul (M)

((PO)) is given by

(PO) =ZTO, IZ (TO,1 + Ta,), (1)

i-I li-I

where summation is over the M sites for a given glutamate

concentration. Similarly, the average event frequency((f )) is given by

uMI u

(f) =ENiZE (TO, + TC,i), (2)i-I I i-I

where N1 is the number of channel events recorded at site i.The average mean open time ((mo)) and mean closed((me)) times are then derived using

(f )

and

(PO))(M)=(f) (4)0

The graph of (PO) vs. glutamate concentration is a

dose-response curve for the GluR determined at the level ofthe single ion channel. Inspection of the curve reveals thatthe maximum value of (PO) is close to unity (i.e., an

efficacy of 1), and that half-maximal response is obtainedat [Glul = 8 x 10'- M. These results are in close accordwith those obtained in earlier studies (Gration et al.,1981a; Cull-Candy et al., 1981). Hill plot analysis of the

dose-response curve (Fig. 2) yields a Hill coefficient ofnH= 1.6, comparable to the value of 1.5 for extrajunctionalD-receptors of locust muscle obtained in macroscopicstudies by Cull-Candy (1976), and 2.0 for junctionalreceptors obtained by Walther and Usherwood (1972).This implies positive cooperativity in the activation of theGluR and hence the existence of more than one glutamatebinding site per receptor-channel molecule. As will be

2

++

+OH

-1 F

IL°

n = 1.6

+

-2

+

-3 F

-4

-5

-6 _-7

++

-6 -5 -4log (GluJ (M)

-3 -2 - 1

FIGURE 2 Hill plot for the GluR (P.) vs. [Glu] data. The fitted line

corresponds to log[(P0)/(l - P.)] = nH log[GluJ - logK, with nH = 1.6andK 1.4x 10-5M.

KERRY ET AL. Glutamate Receptor Channel Kinetics

A

0

I

C&

0.8

0.6

0.4

0.2

-7 -6 -5 -4 -3log CGluJ (M)

31

C

2

0

-1I1

-7 -6

O ei 4 4

6-

I

41

Page 4: Glutamate Receptor Channel Kineticsglutamate receptor-gated channel (GluR) oflocust skele tal muscle (Usherwood, 1978a, b, 1981; Gration et al., 1979), several properties of which

discussed in more detail below, the (P.) vs. [Glu] curvecan be used to determine equilibrium constants for pro-posed gating mechanisms.Maximal event frequency occurs at [Glu] = 8 x 10-4

M, i.e., at the same agonist concentration as that giving(PO) = 0.5. A qualitatively similar concentration depen-dence of channel event frequency was obtained in previousstudies using a lower time resolution (f, = 1 kHz)(unpublished results). This lends support to the view thatthe rise and fall of event frequency is a genuine feature ofGluR gating, and not an artifact resulting from eventomission.

If, instead of expressing the concentration dependence ofchannel gating in terms of P0 and f, the mean open andclosed times are used, a more complex picture is obtained.The mean open time ((min)) increases with glutamateconcentration from 0.32 ms at 10-6 M to -100 ms atsaturating agonist concentrations. This is compatible withthe earlier results (using fc = 1 kHz) of Gration et al.(1981a, b), although the increased time resolution of thecurrent study reveals a lower mean open time for [Glu] <

10-4 M. The mean closed time ((me)) decreases from-30 s at 10-6 M glutamate, to a minimum of -2 ms at 6 xi0-4 M, and then rises to -10 ms at saturating concentra-tions. Initially we were concerned that the rise in (mic) athigh glutamate concentrations might reflect residualdesensitization of the GluR that had escaped the conca-navalin A inhibition. However, inspection of the singlechannel dose-response curve fails to reveal a decline in(PO) at high concentrations, although the maximum valueof (PO) is <1.0, and so we are reasonably confident thatthe rise in the mean closed times is an inherent property ofthe channel gating kinetics.

Data for Detailed Kinetic AnalysisFor detailed kinetic analysis of channel properties, fourglutamate concentrations were selected: 10-5, 10 -4, 10- ,and 10-2 M. These were chosen to represent GluR kineticsover a wide range of agonist concentrations. A low eventfrequency (( f ) = 0.034 ± 0.031 s-') precluded detailedanalysis of data obtained in the presence of 10-6 Mglutamate. At this frequency, 16 h total recording timewould be needed to obtain 2,000 events for, e.g., dwell timepdf analysis.

Representative single channel recordings at the fourglutamate concentrations are shown in Fig. 3. The effect ofagonist concentration on (PO) is clearly seen in theserecordings. Also evident is the modal behavior of thechannel, there being distinct periods of high and lowfrequency activity, as originally noted by Patlak et al.(1979), and discussed by Gration et al. (198 1b), Ball et al.(1985), and Ball and Sansom (1988a).

Open Time DistributionsThe minimum number of open states entered by the GluRat different agonist concentrations can be obtained by

A w__w _ B "F

-1 mr vs#n1 r ml OF

,UiM"-

I - W,,.-f71 F

- -Tvp If T l'rF

° 9 z -@* t * t100 200 300 400 500

mllliseconds

'1

S2 11 * 1-*---+-- 100 20 30D 400 50

mIllIseconds

Do_C

FIGURE 3 Representative single channel recordings for the four gluta-mate concentrations which are analyzed in detail. (A) 105 M; (B) 10-4M; (C) 10' M; (D) 102 M. For each concentration, five consecutivetraces are shown, each of 0.512-ms duration. The data were filtered atfC = 3 kHz on playback, and digitized at 8 kHz before display. Channelopenings are downwards.

determining the number of exponential components neces-sary to fit the observed open time pdfs. Such an analysiswas carried out at all four glutamate concentrations, theresults being presented in Fig. 4 and Table II. Thedistributions are presented using log-log plots (see Meth-ods). The primary result of this analysis is to confirm thatthe complexity of open time distributions, first noted ati0-4 M glutamate (Kerry et al., 1987), is conserved acrossthe concentration range. Thus, between [Glu] = i0-4 and10-2 M, the channel has access to three or four kineticallydistinct open states. At [Glu] = i0' M the pdf may befitted with two components, although there is some sugges-tion that a third may be required for a complete fit.Verification of this is made difficult by the smaller numberof openings measured at 10' M glutamate (Table I).Inspection of the pdf parameters (Table II) reveals that atall four concentrations of glutamate there is a componentto the open time distribution, with time constant rl 0.4ms, corresponding to brief channel openings. At 1i-0 Mglutamate, this represents -60% of the openings, whichfalls to -20% at higher concentrations. At 10-6 M gluta-mate (M.) is 0.3 ms. This implies that the brief-lived openstate is the only one occupied at low glutamate concentra-tions.

With respect to the other components of the open timedistributions the situation is less clear. This is in part due tothe proximity of the time constants for the differentcomponents, which results in relatively high correlations

BIOPHYSICAL JOURNAL VOLUME 53 198842

&Ihol lim. -Ill, I-M L111*f' J.'.

L, -J-.,.- diu"JMr%-W-Tjjq"jjFlrr"jjjRFM-jM

Page 5: Glutamate Receptor Channel Kineticsglutamate receptor-gated channel (GluR) oflocust skele tal muscle (Usherwood, 1978a, b, 1981; Gration et al., 1979), several properties of which

-1 0 Ilog Ct) (C.)

FIGURE 4 Open time pdfs for thefour glutamate concentrations. (A)10-5 M, 3,860 events; (B) 10-4 M,50,600 events; (C) 10-3 M, 30,200events; (D) 10-2 M, 3,410 events.For each concentration, events of

2 duration 2 0.2 ms from all mem-brane sites are combined in the samedistribution before fitting using

-1

2 -2Cap.

-3

-4

a 1 2 3log-CO) Cos)

D

-1 0 1 2log Ct) (Ca)

No

fO(t) = E (ai/ri) exp (-t/ri).i-1

The parameter estimates are listedin Table II. The distributions areshown as log-log plots. The crossesrepresent the observed distributionand the solid lines the fitted pdfs.The broken lines indicate the indi-vidual exponential componentswhich go together to make up thefitted pdf.

3 4

between parameter estimates. r2 1.2 ms at both 10- andO-4 M, but a2 iS greater at the higher concentration. At

iO-' M the third component also makes a significantcontribution to the pdf.

Attempting to relate pdf components at iO-' and 10-2M proved quite difficult. Simulation studies suggest thatsuch an approach can be problematic, even when theunderlying mechanism is known (unpublished results).Consequently, at this stage of the analysis it suffices toconclude that at higher glutamate concentrations (a) atleast four open states are accessible to the GluR, and (b)the occupancy of the longer lifetime open states increaseswith increasing glutamate concentration.

Closed Time Distributions

Analysis of closed time distributions yields information on

the minimum number of kinetically significant closedstates. Closed time distributions at four glutamate concen-

trations have been fitted with sums of exponential func-tions. The results are presented in Fig. 5 and Table III. Theanalysis of closed time distributions extends the earlierobservation of four closed states in the presence of IO-4 Mglutamate (Kerry et al., 1987). Four closed states are alsoobserved at i0-3 and 10-2 M. At 10' M the closed timepdf is biphasic, i.e., N, = 2. However, bearing in mind therelatively low number of events recorded with [Glu] = 1o0

TABLE IIOPEN TIME PROBABILITY DENSITY FUNCTIONS

[Glu] N. i a, CV CV

M msi0-5 2 1 0.616 0.086 0.310 0.141

2 0.384 0.138 1.25 0.092

10-4 3 1 0.379 0.366 0.424 0.2692 0.532 0.178 1.22 0.2293 0.089 0.908 2.94 0.279

10-3 4 1 0.192 0.172 0.512 0.1602 0.386 0.143 2.49 0.1773 0.371 0.166 7.49 0.1264 0.051 0.357 27.7 0.140

10-2 4 1 0.241 0.077 0.516 0.1092 0.176 0.117 4.39 0.1603 0.291 0.103 50.6 0.1354 0.292 0.111 232.0 0.082

The open time pdfs are defined byN.

f,(t) = EI (ja/T) exp (-tt/T).i-1

For each concentration the pdf is derived by combining open times fromall membrane sites in a single normalized histogram, and fitting theequation above as described in Methods. N. was determined by obtainingfits for successively greater numbers of components until a significantlybetter fit, as judged by use of the AIC, cannot be obtained. The coefficientof variation (CV) is given for each parameter estimate.

KERRY ET AL. Glutamate Receptor Channel Kinetics

A

I

0

-1

,bo -2wa

-4 1

0

-i

t,0 -2

- -3

-4

-50 Ilog Ct) CM)

2

0

-1

at -2

-3

-5 1_1

_5

43

Page 6: Glutamate Receptor Channel Kineticsglutamate receptor-gated channel (GluR) oflocust skele tal muscle (Usherwood, 1978a, b, 1981; Gration et al., 1979), several properties of which

0 0

_ -2-2IbP

I? -3-4

-45-

-1

I I

-1

wg '-2

-3

-4

-5

A

0 1 2log (t) (Ms)

3 4

I-1

Of -2-

-4

-5-1

C0

-1Of

.° -2

-4

1 0 1 2 3log Ct) (CM)

- I

0 1 2log (t) (es)

0 1 2log (t) Cus)

FIGURE 5 Closed time pdfs forthe four glutamate concentrations.

3 4 (A) 10-5 M,3,860 events; (B) 10-4M, 50,600 events; (C) 10-3 M,30,200 events; (D) 10-2 M, 3,410events. The pdfs are described by

Nc

fc(t) = E (a,/ir) exp (-t/ Tr)i-1

and the parameter estimates arelisted in Table III. Other detailsare as for Fig. 4.

3

TABLE IIIPROBABILITY DENSITY FUNCTIONS

[Glul N, i ai CV Tj CV

M ms0- 2 1 0.103 0.237 0.746 0.135

2 0.897 0.027 468.0 0.047

10-4 4 1 0.206 0.048 0.432 0.0702 0.350 0.153 7.52 0.1143 0.389 0.131 22.5 0.0934 0.055 0.259 122.0 0.105

lo-1 4 1 0.633 0.087 0.380 0.0912 0.303 0.168 1.22 0.1293 0.047 0.508 9.74 0.3124 0.017 1.483 32.4 0.357

10-2 4 1 0.486 0.088 0.311 0.1292 0.264 0.133 1.41 0.2163 0.181 0.176 7.76 0.1924 0.069 0.492 34.1 0.160

The closed time pdfs are defined by

fC(t) = E7 (ag/lr) exp (-t/Tj).i-I

The tabulated parameters are obtained in the same manner as for theopen time pdfs.

M (Table I), Nc = 2 must be regarded as a minimumestimate of the number of closed states. A constant featureat all four glutamate concentrations is the component (rl10.4 ms) corresponding to brief channel closings. Theproportion of this component (a,) increases with glutamateconcentration until its peak value at 10-3 M, and thendeclines somewhat.When attempting to analyze the ai as functions of

concentration, a similar difficulty is encountered to thatalready described for the open time distributions. Conse-quently, at this stage our conclusions are again limited tothe following (a) there are at least four kinetically distinctclosed states when [Glu] 2 10' M; and (b) as glutamateconcentration increases, the relative contributions of thecomponents shift in favor of briefer closings, until amaximum is reached at _10-3 M.

Autocorrelation FunctionsDwell time autocorrelation functions (acfs) provide infor-mation on the number of channel isomerization pathways(Np) linking the closed states with the open states, and viceversa (Fredkin et al., 1985; Labarca et al., 1985; Ball andSansom, 1988b; Colquhoun and Hawkes, 1987; Kerry etal., 1987). Earlier studies at 10-' M have now beenextended to the four glutamate concentrations. The resultsare presented in Figs. 6 and 7. Non-zero acfs indicate that

BIOPHYSICAL JOURNAL VOLUME 53 1988

CLOSED TIME

0

-

44

Page 7: Glutamate Receptor Channel Kineticsglutamate receptor-gated channel (GluR) oflocust skele tal muscle (Usherwood, 1978a, b, 1981; Gration et al., 1979), several properties of which

A 0.2 F

0.1

L

10 20 30 40 50

k

B

0.0 _

-0. 1 -

-0.2 -

00.3 1 2 3 40 10 20 30 40

k

FIGURE 6 Autocorrelation func-tions for successive open times deter-mined at (A) 10-' M glutamate; (B)10-4 M; (C) 1o-0 M; and (D) 10-'M. For each concentration, the acf isthe average for all membrane sites.The jagged lines represent the

50 observed acfs and the broken lines

the fits (see Table IV) of

Np-I

r(k) = E Ai wk.

i-I

0.3

0.2C

0. 1

C-L

10 20 30k

40 50

L

0 10 20 30k

D

^-: s.A......

0.0 -

-0. 1 _

-0.2 -

-0.30 10 20 30 40 50

k

0.3

0.2 B

0.1

0.0-

-0. 1

-0.2

-_n .

40 50

0.3

0.21-

0.1

X 0.0L.

0.0 -

-0.1

-0.2

-0.3L0

The two horizontal lines are the 95%confidence limits for a null acf, givenN, events at each concentration.These limits are defined by

-N-, + 2N4 '/2.

Only those values of the observedacfs outside these limits were used infitting.

10 20 30 40 50 FIGURE 7 Autocorrelation func-k

tions for successive closed timesdetermined at (A) 10-5 M gluta-mate; (B) 10-' M; (C) 10' M; and(D) 105 M. Other details are as forFig. 6.

10 20 30 40 50

KERRY ET AL. Glutamate Receptor Channel Kinetics

0.3i

0.2 _

0. t

0.1C.-L

-0.

-0.

1I-

.2 -

2Z .---U.5 _0

0.3

0.2 A

0. 1

Y-= 0.0 _-7

-0. 1 _

-0.2

-0.3L_0

0.3

0.2

i 0.0L

0.3

0.21-

0. 1

L

-O. I _

-0.2

-0.30 10 20 30 40 50

I .-

,.. x A 1-to

0.31

_n

-U.3

45

Page 8: Glutamate Receptor Channel Kineticsglutamate receptor-gated channel (GluR) oflocust skele tal muscle (Usherwood, 1978a, b, 1981; Gration et al., 1979), several properties of which

TABLE IVDWELL TIME AUTOCORRELATION FUNCTIONS

[Glu] E Np-1 i Ai CV w, CV

Mi0-, 0 1 1 0.069 0.203 0.936 0.038

C 1 1 0.119 0.126 0.894 0.026

10-4 0 2 1 0.064 0.141 0.623 0.0952 0.060 0.033 0.987 0.001

C 2 1 0.194 0.046 0.810 0.0202 0.072 0.139 0.971 0.004

10-, 0 2 1 0.058 0.086 0.701 0.0012 0.165 0.067 0.979 0.085

C 2 1 0.278 0.723 0.189 0.7412 0.079 0.076 0.932 0.006

10- 0 2 1 0.203 0.187 0.723 0.1422 0.115 0.330 0.977 0.016

C 1 1 0.167 0.102 0.791 0.035

The acfs are defined (see text) by the equation:

Np- I

rE(k) = E Ai7iriI,

where E = 0 or C. That is, the acf is described by the sum ofNp- 1 geometrically decaying components, where Np is the number ofisomerization pathways linking the closed states with the open. The valuesofNp are obtained in a similar manner to that used in analysis of the pdfs.As in Tables II and III, the parameter error estimates are expressed ascoefficients of variation (CV).

there is more than one isomerization pathway, i.e., thegating mechanism is nonlinear. Therefore, there must beeither branches and/or cycles in the gating mechanism.The acfs have been analyzed as sums of geometricallydecaying components (Table IV). As discussed by Fredkinet al. (1985) and by Kerry et al. (1987), if there are Nppathways linking the open states with the closed, then thereshould be Np - 1 geometrically decaying components tothe acf. The results suggest that at IO-5 M, Np 2 2 and thatNp 2 3 at the higher glutamate concentrations. Theseconclusions place quite strong constraints on possible mod-els of the gating mechanism.

Adjacent Dwell Time AnalysisThe results described suggest that the following is areasonable description of the classes of models describingthe GluR gating mechanism:

Cl~_CV C3- C4 PCnI1 I I I01- -'02'r-"3- '-'04'-- OVn.

Increasing glutamate concentration shifts the equilibriumfrom the left- to the right-hand side of the equation. If sucha mechanism applies, the durations of adjacent open andclosed intervals should be correlated. The magnitude of thecorrelation will be dependent on, amongst other things, therelative rates of the horizontal and vertical steps in theabove scheme, being increased if the horizontal steps are

(5)

relatively slow. Therefore, analysis of adjacent open andclosed intervals (McManus et al., 1985) can provide aconfirmation of the results of autocorrelation functionanalysis. Adjacent dwell time analysis has been applied tothe GluR data. In the presence of IO-4 M glutamate thereis a particularly clear negative correlation, i.e., brieferopenings are adjacent to longer closings and vice versa(Fig. 8). This observation also places constraints on possi-ble gating mechanisms.

Possible MechanismsThe analyses described above provide firm indications ofthe class of gating mechanisms applicable to the GluR.One attractive class of models is that originally proposedby Monod et al. (1965) with respect to allosteric proteins,and discussed in the context of channel gating by Karlin(1967) and by Colquhoun and Hawkes (1977, 1981,1983). A cooperative model with four identical glutamatebinding sites has been explored, in advance of moredetailed analysis of the GluR gating mechanism:

C - CA- CA2 -CA3 CA4

O 1OA11OA2 OA3 OA4.(6)

("A" represents an agonist, i.e., glutamate, molecule in theabove scheme.) Such a model, with No = 5 and Nc = 5, hasbeen selected since it displays a large (i.e., 2 3) number ofkinetically significant open and closed states over a rela-tively wide glutamate concentration range.

1.4k-

1.2 -

tn

0

S0.8 _

0.6 _

0.4-1 0 32

log mc(t) (ms)

FIGURE 8 Adjacent dwell time analysis for the GluR in the presence of10 'M glutamate. Channel closings are sorted into 50 intervals on thebasis of closed time duration, and, for each interval, the mean open timefor the preceding and following openings determined. A marked negativecorrelation is observed, indicating that long closings are adjacent to briefopenings and vice versa. The superimposition of the curves for thepreceding (solid line) and following (broken line) openings is as predictedfor a channel gating mechanism at thermodynamic equilibrium.

BIOPHYSICAL JOURNAL VOLUME 53 1988

I1

46

Page 9: Glutamate Receptor Channel Kineticsglutamate receptor-gated channel (GluR) oflocust skele tal muscle (Usherwood, 1978a, b, 1981; Gration et al., 1979), several properties of which

The equilibrium properties of mechanism 6 are deter-mined by three parameters: a, KB, and L, where L is theequilibrium constant for the reaction C O, 0 KB is themicroscopic binding constant for association of the gluta-mate with a closed channel site, and aKB is the microscopicbinding constant for an open channel site. So, the equilib-rium constants for all 13 steps of mechanism 6 may beexpressed in these terms. The concentration dependence ofPO is given by

Po = (1 + aaKB)4/[(l + aaKB)4 + L-'(1 + aKB)4], (7)

where a is the glutamate concentration. Thus the threeequilibrium parameters may be estimated by fitting Eq. 7to the (PO) vs. [Glul data (see Fig. 9 a and Table V).A modification of mechanism 6 in which the unliganded

open state has been omitted has also been considered

C -CACA2 CA3 CA4

OA1 1OA2 _A3OA 4,

(8)

for which the [Glu] dependence of (PO) is given by

PO = [(1 + aaKB)4 -_1]/{[(l + aaKB)4 - 1]

+ L-'(1 + aKB)4}, (9)

TABLE VPARAMETER ESTIMATES FOR THE

COOPERATIVE MECHANISMS

Parameter Mechanism 6 Mechanism 8

a 14.2 9.6(±5.7) (±3.3)

KB/M 1 2.7 x I03 2.3 x 103(±0.7 x 103) (±0.7 x 103)

L 1.4 x 10-4 7.6 x 10-4(±2.3 x 10-4) (+11.4 x 10-4)

h/ls-' 1.6 x 10-9(±53)

h2/s-' 7.3 x 10-7 1.3 x 10-6(+210) (+150)

h3/s-' 150 260(±370) (+320)

h4/s- 530 460(±290) (+290)

h5/s-1 1.5 x 10-12 6.8 x 10-12(±92) (+99)

The parameter estimates are for the basic cooperative mechanism 6, andfor the modification 8 from which the unliganded open state (0) isexcluded. Parameter error estimates are given as standard deviations.

A + +3

2

-

I

if0

B

+

+

-1 F

-2

-3-3 -2

6

5

4

U

0

ao 3

2

1

C

++++

+

+ +4+1-1-1-

++

-3 -2

-7 -6 -5 -4 -3log tGlu] (M)

I D

FIGURE 9 Overall kinetic parame-ters for mechanisms 6 (solid lines)and (broken lines) compared withthe experimental (A) single channeldose-response; (B) event frequency;(C) mean open time; and (D) meanclosed time data. The (P.) vs. [Glu]curve arises from fitting Eqs. 7 or 9to the data and the ( f) vs. [Glu]curve corresponds to Eq. 10. The mnand mc data and curves are derivedusing Eqs. 3 and 4, respectively.

+

-7 -6 -5 -4log tCIu] (M)

-3 -2

KERRY ET AL. Glutamate Receptor Channel Kinetics

1.0

j 0.8

i 0.6

t0.4

0.2

0-7 -6 -5 -4

log [GluJ (M)

3

2

Ia

E

0

-1-7 -6 -5 -4

log (CluJ (M)

I

47

Page 10: Glutamate Receptor Channel Kineticsglutamate receptor-gated channel (GluR) oflocust skele tal muscle (Usherwood, 1978a, b, 1981; Gration et al., 1979), several properties of which

where a and KB are defined as before, and where L isdefined in terms of the equilibrium constant for thereaction CA - OA (aL). The equilibrium parameterestimates for this modified mechanism are also given inTable V, and the corresponding fit illustrated in Fig. 9 a.One may extend the description of mechanism 6 to

include consideration of the channel isomerization rates.Defining h1 as the rate constant for C - 0, h2 as that forCA -- OA, etc., it is relatively easy to show (Colquhounand Hawkes, 1981) that the concentration dependence ofthe event frequency is given by

f = E hipi, (10)i-1

where PI is the equilibrium probability of state C, P2 that ofCA, ... and p5 is the probability of CA4. The equilibriumprobabilities are derived from the three equilibriumparameters using

p, = (1 - Po)/(l + aKs) (1 1)

and

pj = (.I (aKB)' 'Pi' (12)

If the three equilibrium parameters are known, then byusing Eqs. 7 and 12-14, the glutamate concentrationdependence of ( f) may be used to obtain estimates of theisomerization rates hi. Application of such analysis to the( f ) vs. [Glu] data, for both mechanism 6 and for themodified mechanism 8, yields the results shown in Fig. 9 band Table V. Fitting either model suggests that there are atleast two kinetically significant isomerization pathways, inbroad agreement with the results of the autocorrelationfunction analysis. One should interpret the results cau-

tiously. In particular, the estimates of hi, h2, and h5 indicatethat the corresponding reaction rates are indistinguishablefrom zero. More accurate parameter estimates must awaitmore detailed modeling.

DISCUSSION

The results of single channel recording from the GluR over

four orders of magnitude of glutamate concentration havebeen presented in terms of overall kinetic parameters. Inparticular, a single-channel dose-response curve has beendetermined. Single channel kinetics have been investigatedin detail at four glutamate concentrations where largenumbers of events are available, and have been used toderive a minimal model of the gating mechanism. Thedose-response and event-frequency curves have been usedto exemplify the initial stages of construction of a detailedgating mechanism for the GluR.

Dose-Response Curve AnalysisIn the absence of detailed biochemical characterization,Hill plot analysis of the single channel dose-response curve

(nH = 1.6) is the main evidence for multiple binding siteson the GluR. Such analysis involves only limited assump-tions concerning the nature of the underlying gating mech-anism. However, it is important to stress that the (PO)data can, in principle, be used to determine the equilibriumparameters for any gating mechanism, and hence providean important starting point in trying to understand thegating mechanism of the GluR.

It is important to note that there is no indication of adecrease in (PO) at high glutamate concentrations. Thisexcludes the possibility of channel block by the agonist, acomplication that occurs with the nAChR (Ogden andColquhoun, 1985).

Event Frequency Curve AnalysisThe display of (f ) vs. [Glu] shows the rise and fall of theevent frequency with increasing glutamate concentration.Colquhoun and Hawkes (1981) have shown that, for anygating mechanism, the event frequency is given by

Nc

f = E pihi,i-l

(13)

where pi is the equilibrium probability of closed state i andhi is the sum of the rate constants for all steps linking closedstate i to an open state, the summation being over the Ncclosed states. As the equilibrium probabilities at a givenglutamate concentration may be calculated from the equi-librium parameters of the model, the values of hi may bereadily determined. Furthermore, if the proposed gatingmechanism is such that each closed state is linked to asingle open state, then the hi values are equal to thecorresponding closed - open isomerization rates. Conse-quently, the event frequency curve is also of importance inproviding initial parameter estimates for models of thegating kinetics.

Analysis of Dwell Time PDFs

Before detailed modeling, it is advisable to maximize theconstraints on possible gating mechanisms. One way ofachieving this is to analyze the dwell time pdfs in terms ofthe numbers of exponential components. Previous analysisof GluR kinetics in the presence of 10'4 M glutamate(Kerry et al., 1987) revealed at least three open states andfour closed states of the receptor channel. Such estimatesare necessarily minimal estimates. Additional states mayremain undetected for three reasons: (a) the time constant(X) of a component may be briefer than the cutoff time ofthe data recording and analysis system; (b) the r value fora component may be sufficiently close to that of anothercomponent that the two are not resolved; and (c) the entryof the receptor-channel into a particular kinetic state maybe so infrequent that a very large number of channel eventsmust be recorded before the corresponding component isdetected in the dwell time pdf.The first two problems are not easy to circumvent for a

fixed experimental protocol. However, c can be resolved by

BIOPHYSICAL JOURNAL VOLUME 53 198848

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exploring channel kinetics over a wide range of glutamateconcentrations, and by recording for extended periods oftime. Kinetic states rarely entered at one glutamate con-centration may be quite highly populated at another.

Analysis of GluR pdfs over three orders of magnitude ofglutamate concentration confirms the kinetic complexityfirst observed for 10-4 M glutamate. At high [Glu] thereare at least four open and at least four closed states; at low[Glu] fewer states are occupied. Attempts to relate pdfcomponents at different concentrations were difficult.Simulation studies suggested this to be an inherent diffi-culty of analysis of pdfs for multiple state cyclic gatingmechanisms. In part this difficulty is due to the redistribu-tion of the channel between the different states withchange in glutamate concentration. Furthermore, the timeconstant associated with a kinetic state that may be left viaa glutamate-binding reaction will change with the concen-tration of glutamate, thus confusing assignment of timeconstants to states. That such a difficulty occurs may bedue to the underlying gating mechanism containing >4open and >4 closed states. So, when considering theconstraints put upon gating mechanisms by the pdf analy-sis, one must remember that No and N, are minimumestimates.

Analysis of Correlation BetweenSuccessive Dwell Times

The dependence of successive dwell times has been exam-ined using two complementary procedures: autocorrelationfunction analysis and analysis of mean adjacent dwelltimes. As discussed by Fredkin et al. (1985), both methodsof analysis provide information on the same aspect ofreceptor-channel gating, i.e., the number of pathwayslinking the closed states with the open states of the channel(Np). Both analyses confirm that multiple channel isomer-ization pathways exist for the GluR. Fitting the acfs withsums of geometrical components suggests that Np- 3. Atthis stage of the analysis it is pertinent to enquire into theeffect of the 0.2 ms cutoff imposed on single channel eventson the conclusions drawn from the kinetic analyses. Withrespect to estimating the number of components in pdfs,both Colquhoun and Sigworth (1983) and Roux and Sauve(1985) have demonstrated that, while event omission doesdistort the pdfs, it is not expected to introduce spuriousadditional components. With respect to autocorrelationfunction analysis, a similar situation applies (Ball andSansom, 1988b). In particular, event omission does notappear to generate positive acfs from gating mechanismswith Np = 1. Therefore, even allowing for event omission,the constraints on possible gating mechanisms still apply.On this basis it is reasonable to conclude that a mechanismsuch as 5 applies to the GluR. As discussed above, theoreti-cal studies suggest that the horizontal steps (i.e., thoseinvolving interconversions between closed states only, orbetween open states only) should be slow compared with(some of) the vertical steps (i.e., channel isomerizations).

Adding the requirement for brief openings to be pairedwith long closings, and vice versa, one has quite firmconstraints on possible gating mechanisms. It is importantto note that any model satisfying these constraints willexplain the modal behavior of GluR gating (dubbed the"gearshift" phenomenon by Moczydlowski [1986]), withthe duration of the different kinetic modes being deter-mined by the (low) rates of switching between differentclosed - open isomerization pathways.

A Cooperative Model for GluR GatingThe results discussed so far lead us to investigate cyclicgating mechanisms such as 5. As noted by Fredkin et al.(1985), a problem of identifiability can arise with somecyclic schemes. In brief, if a gating mechanism comprisesNo open states and Nc closed states, then if the totalnumber of independent parameters is greater than 2NONcit is not identifiable. This places restrictions on the classesof mechanisms that can realistically be considered in termsof the single channel data. In the early stages of analysisthere is an advantage in restricting consideration to thosemodels where there are internal constraints on the rateconstants, leading to a reduced number of free parameters.One way of achieving such constraints is via symmetry inthe model, such as in mechanism 6. In the absence ofadditional constraints it has 26 rate constants. However, ifthe constraints implied by the assumption of four identicalbinding sites are included, then the number of independentparameters is reduced to 10 (i.e., a, L, KB, hi where i = 1-5,and the microscopic association rates for closed channelsites and for open channel sites). Consequently, this class ofmodels is an attractive starting point for further investiga-tions. A model with four binding sites was selected, on thebasis of simulation studies, as being likely to result in No -

3 and Nc - 4 over a wide range of glutamate concentra-tions.

It should be stressed that this mechanism is a currentworking hypothesis, and is not intended as a definitivestatement concerning the GluR gating mechanism. Inparticular, we have not as yet excluded models wheremultiplicity of open states does not correspond to multiplic-ity of binding sites, i.e., models where No- 1 is greaterthan the number of ligand binding sites on the receptor.Such models have recently been implied, for the nAChR,by the results of several authors (e.g., Colquhoun andSakmann, 1985; Auerbach and Lingle, 1986; and Chabalaand Lester, 1986). Models with multiple open states for aconstant number of bound ligands lack the internal con-straints alluded to above, and consequently have a rela-tively large number of free parameters. We have thereforereserved their analysis until a later stage of this series ofinvestigations.

Analysis of the single channel dose-response curve interms of mechanism 6 resulted in a reasonable fit to the(P.) vs. [Glul data (see Fig. 9 a). The microscopicassociation constant (KB) for closed channel sites was 2.7 x

KERRY ET AL. Glutamate Receptor Channel Kinetics 49

Page 12: Glutamate Receptor Channel Kineticsglutamate receptor-gated channel (GluR) oflocust skele tal muscle (Usherwood, 1978a, b, 1981; Gration et al., 1979), several properties of which

I03 M-l, and was a (= 14.2)-fold higher for open channelsites. In the absence of glutamate:

Po,min = L/(1 + L) = 1.4 X 10-4(+2.3 X 10-4). (14)

Channel openings for the GluR have not been detected inthe absence of glutamate (unpublished results), althoughsuch events are well documented for the nicotinic acetyl-choline receptor (Jackson, 1984). The above estimate ofPjni is compatible with the experimental result, but wealso thought it worthwhile to investigate mechanism 8,which does not include the unliganded open state 0. Forthis latter model, Po,min is zero by definition. For bothmechanisms, the maximum value of PO is

Po,max -= a4L/(I + a4L). (15)

For the basic mechanism 6, this gives Po,max = 0.85(±0.03), whilst for the modified mechanism 8, Pomax =0.87 (±0.03). Both values are reasonably close to thatobserved (=0.9). If the PO curves predicted from the fittedparameters is subjected to Hill plot analysis, nH 1.3 isobtained, again comparable to that derived from theexperimental data (nH = 1.6). So, both mechanisms (6 and8) provide a reasonable description of the dose-responsecurve of the GluR.A second feature of this class of mechanisms is that each

closed state is linked to a single open state, and hence theconcentration dependence of event frequency may be usedto estimate closed - open isomerization rates. Somedifficulties were experienced when attempts were made tofit the event frequency data, requiring the use of thesimplex algorithm for their solution. It is reasonable,therefore, to proceed cautiously, and interpret the results(Table V) as indicating that h,, h2, and h5 (and hence h,,hf, and h5) are all indistinguishable from zero, and that twochannel isomerizations are predominant:

CA2- OA2 h3 = 150 s-'(260 s-');

predicted [Glu] dependence of the mean open and closedtimes (Fig. 9, c and d) (noting in passing that thisinformation is already implicit in the predicted dose-response and event frequency curves). Between [Glu] =10-5 and 0-2M the agreement between the model and thedata are quite good. However, at lower concentrations,there is an overestimation of the mean open time, espe-cially for mechanism 6. This may reflect inadequacies ofthe modeling procedures, although studies using simulateddata suggested that this should not be the case.

So, in terms of such a model, only the two microscopicglutamate association rates (kon and k' ) remain undeter-mined. Initial calculations and simulation studies suggestthat both rates are of the order of 1 O4 M-'s '- which, shouldthis prove to be correct, suggests that the associationbetween the glutamate and its binding site is rather slow,compared with the diffusion limited rate ( '108 M 's-1).However, further consideration of this must await theapplication of more powerful methods of fitting gatingmodels to the data, such as the maximum likelihoodtechnique (Horn and Lange, 1983; also see Fredkin et al.,1985, and Blatz and Magleby, 1986). It must be stressedthat the model proposed is not necessarily unique, and thatconsiderable effort will have to be invested into futuremodeling studies to objectively assess the simplest mecha-nism capable of adequately accounting for all features ofthe experimental data. Such investigations are currentlyunderway, and will form the basis of a future publication.However, one should remember that, even given suchmethods, the problem of identifiability inherent to singlechannel kinetic analysis still remains. For example, onemight wish to relax the constraint of equivalent bindingsites used in the cooperative model. This would lead to anincrease in the number of parameters, and consequentdifficulties in identification. We are attempting to formu-late the exact nature of such identifiability problems whensingle channel data are available over a range of glutamateconcentrations.

and

CA3- OA3 h4= 530 s-'(460 s-').

The corresponding open -- closed rates are

OA2 -CA2 h'3 h3/a2L 5,300 s-'(3,700 s-1);

and

OA3 -CA3 h4 = h4/a3L - 1,300 s- '(680 s- ),

where the figure in brackets represent the parameterestimates for the modified mechanism 8. Thus, negativecorrelations between adjacent dwell times would beexpected when the channel is primarily in the bi- andtri-liganded forms. Such negative correlations are seenexperimentally, particularly in the presence of 10-4 Mglutamate.One may also evaluate the model in terms of the

Comparison with Other Ion Channels

The emerging picture of a relatively complex gating mech-anism for the GluR may be compared with the results ofsimilar studies of other ion channels. Invertebrate gluta-mate receptors have also been looked at in the crayfish(Dudel and Franke, 1987; Franke and Dudel, 1987). In thelatter work the open time distributions do not appear toconsist of more than a single exponential component, andthe closed time distributions are composed of two or threecomponents. A possible reason for the difference betweenthese results and those described in Kerry et al. (1987), andin the current paper lies in the greater number of singlechannel events that have been recorded from the locustGluR. Resolution of the differences awaits a more detailedcomparison. Excitatory amino acid receptors in vertebratesystems appear to have a complex relationship between the

BIOPHYSICAL JOURNAL VOLUME 53 198850

Page 13: Glutamate Receptor Channel Kineticsglutamate receptor-gated channel (GluR) oflocust skele tal muscle (Usherwood, 1978a, b, 1981; Gration et al., 1979), several properties of which

receptor(s) and the channel (Cull-Candy and Usowicz,1987; Jahr and Stevens, 1987), precluding direct compari-son with the invertebrate GluR.The concentration of L-glutamate required to give an

open probability of 0.5 is high, but this was anticipatedfrom the results of macroscopic studies of junctionalglutamate receptors on locust muscle (Clements and May,1974). The sensitivity of glutamate receptors on embryoniclocust muscle in vitro, which have recently been studiedusing the giga-ohm seal technique, is much higher,although the reason for this difference is unclear (Cook etal., 1985; Duce and Usherwood, 1986). Dudel and Franke(1987) have shown that the glutamate receptor channels ofcrayfish muscle also exhibit a low sensitivity to L-glutamate, and have concluded that concentrations of thetransmitter in the range of 1 x 10-3 M would be requiredto generate postsynaptic currents at the glutamatergicexcitatory synapses of this muscle. The low sensitivity ofthe transmitter glutamate receptors on adult arthropodmuscle may be related to the high levels of L-glutamate,and other agonists, which are often present in the blood ofthe open circulatory systems of these animals.The most intensively studied receptor-gated ion channel

is the nAChR. Many authors (e.g., Labarca et al., 1985;Colquhoun and Sakmann, 1985) have provided evidencefor the existence of two open states in the nAChR gatingmechanism. Sine and Steinbach (1984) have emphasizedthe presence of multiple closed states. At present, there issome debate concerning the nature of the two open states(Sine and Steinbach, 1986). It is of particular interest tonote that Labarca et al. (1985) have proposed a branched(Np = 2) model for Torpedo nAChR gating.The work of Blatz and Magleby (1986) on rat skeletal

muscle Cl- channel gating has also resulted in the proposalof a branched gating mechanism. Their working hypothe-sis for the major mode of Cl- channel gating is character-ized by Nc = 5, N. = 2, and Np = 2, of comparablecomplexity to the model for the GluR. In a somewhatdifferent context, cooperative allosteric models have alsobeen proposed to account for the effects of dihydropyri-dines on the kinetics of L-type Ca2, channels (Kokubun etal., 1986).

In the light of these studies our working hypothesis forGluR gating does not seem to be unreasonably complex.Two major tasks remain to be undertaken. First, formechanisms 6 and 8, the values of k' and k', remain to bedetermined. Second, alternative gating mechanisms needto be compared in an objective manner. Although initialresults suggest that the ligand association rates may beestimated using the glutamate concentration dependenceof the acfs, adoption of maximum likelihood procedures(Horn and Vandenberg, 1984) should enable us to fufillboth tasks simultaneously. Work is underway on theimplementation of such an approach, and should result in amore detailed understanding of the molecular mechanismof GluR gating.

We wish to thank Professor J. Dudel, Physiologisches Institut derTechnischen, Universitat Muinchen, for commenting on the final draft ofthis manuscript.

This work was supported by a grant from the British Science andEngineering Research Council.

Received for publication 11 May 1987 and in final form 24 August1987.

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Ashford, M. L. J., C. J. Kerry, K. S. Kits, R. L. Ramsey, M. S. P.Sansom, and P. N. R. Usherwood. 1984b. Kinetic Analysis of channelsgated by glutamate receptors in locust muscle membrane. In Electro-pharmacology of the In Vitro Synapse. G. A. Cottrell, editor. Univer-sity of St. Andrews Press, St. Andrews. 14-15.

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Ball, F. G., M. S. P. Sansom, and P. N. R. Usherwood. 1985. Clusteringof single glutamate receptor-channel openings recorded from locust(Schistocerca gregaria) muscle. J. Physiol. (Lond.). 360:66P.

Ball, F. G., and M. S. P. Sansom. 1988a. Temporal clustering of ionchannel openings incorporating time interval omission. IMA (Inst.Math. Appl.) J. Math. Appl. Med. Biol. In press.

Ball, F. G., and M. S. P. Sansom. 1988b. Aggregated Markov processesincorporating time interval omission. Adv. Appl. Prob. In press.

Blatz, A. L., and K. L. Magleby. 1986. Quantitative description of threemodes of activity of fast chloride channels from rat skeletal muscle. J.Physiol. (Lond.). 378:141-174.

Chabala, L. D., and H. A. Lester. 1986. Activation of acetylcholinereceptor channels by covalently bound agonists in cultured rat myo-balls. J. Physiol. (Lond.). 379:83-108.

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