J. Phyeiol. (1977), 268, pp. 271-289 With 8 text-ftgurem Printed in Great Britain

271

RELAXATION EXPERIMENTS USING BATH-APPLIED SUBERYLDICHOLINE BY P. R. ADAMS* From the Abteilung Neurobiologie, Max-Planck-Institut fur biophysikalische Chemie, D-3400 G6ttingen-Nikolausberg, Am Fasberg, W. Germany

(Received 30 June 1976) SUMMARY

1. The effect of step changes in membrane potential on the end-plate conductance change produced by bath-applied suberyldicholine was studied in voltage-clamped frog muscle fibres. 2. The suberyldicholine-induced conductance increased exponentially from its previous equilibrium level to a new equilibrium level following a step hyperpolarization. 3. For low suberyldicholine concentrations the time constant of this relaxation was independent of the concentration. 4. For low suberyldicholine concentrations the voltage dependence of equilibrium conductance and relaxation time constants was identical. 5. Bungarotoxin pretreatment did not affect the responses beyond a simple reduction in their amplitude. 6. The conductance evoked by high suberyldicholine concentrations was less voltage-sensitive than that evoked by low concentrations. 7. A new model for explaining noise and relaxation data is proposed. This postulates rate-limiting binding steps followed by a voltagedependent isomerization. INTRODUCTION

The application of a suitable agonist to the end-plate membrane produces a conductance increase which appears to be due to the opening of identical independent channels of about 25 pmho conductance (Katz & Miledi, 1972; Anderson & Stevens, 1973; Neher & Sakmann, 1976a). The fraction of the available channels that are open at equilibrium is determined primarily by the nature and concentration of the agonist and by the membrane potential (Rang, 1973; Dionne & Stevens, 1975; Adams, 1976a). There are two main techniques for studying the opening and * Present address: Laboratoire de Neurobiologie, 1&oie Normale Sup6rieure, 46 rue d'IJlm, 75230 Paris Cedex 05, France. 11-2

P. B. ADAMS 272 closing kinetics of end-plate channels. The first, noise analysis, relies on the existence of spontaneous thermal fluctuations at equilibrium which on average relax back to equilibrium along a characteristic time course (Katz & Miledi, 1972, 1973a, b; Anderson & Stevens, 1973; Ben-Haim, Dreyer & Peper, 1975; Neher & Sakmann, 1975, 1976b). The second technique, voltage jump relaxation analysis, examines the time course of transitions from one equilibrium state to another following a potential step (Adams, 1975b; Neher & Sakmann, 1975; see also Sheridan & Lester, 1975). Both these techniques lead to the same conclusion - that when only a small fraction of the channels are open the dominant kinetic process is usually a single exponential whose time constant is the mean channel lifetime. The voltage dependence of this time constant accounts for the voltage dependence of equilibrium responses (Neher & Sakmann, 1975; Dionne & Stevens, 1975; Adams, 1976a). Furthermore the similarity of the acetylcholine (ACh) relaxation time constant and the end-plate current (e.p.c.) decay constant under various conditions strongly suggests that the e.p.c. decay represents first order channel closing following an essentially instantaneous ACh transient. Unfortunately the kinetic studies available all share the disadvantage that the agonist was applied iontophoretically, so that the effective concentration was unknown, and perhaps in some cases non-uniform over the receptive surface. The study presented below is concerned to rectify this situation by using bath agonist applications. An abstract has appeared (Adams, 1975c). METHODS

The technique was basically a combination of that of Neher & Sakmann (1975) and of Adams (1975a). Sartorius muscles of Rana e8culenta or R. temporaria were pinned out on to the domed Sylgard base of a small Perspex bath. Superficial endplates free of connective tissue and favourably located with respect to the solution flow were located by trial iontophoresis of suberyldicholine (Sub). The clamping electrodes were placed one to two fibre diameters apart in the centre of the region showing high agonist sensitivity. The current electrode contained potassium acetate or sulphate and was shielded with grounded insulated silver paint to near the tip (Neher & Lux, 1969). The voltage electrode was filled with KCl. Both electrodes routinely had resistances in the range 1-3 MC. Despite twin impalement with low resistance electrodes it was possible to maintain the fibres in a good state (typical drift in holding current < 1 nA/min) for long periods. The electrodes were constructed to have low resistance but excellent penetrating properties in the following way. Pyrex tubing was pulled on a horizontal puller to give a short-shanked electrode configuration. The electrode shaft was then filled with the appropriate solution. A finely tapering hollow glass probe (pulled by hand from Pyrex tubing of inside and outside diameters 1-3 and 0.8 mm) was then pushed down to near the tip, causing the solution to flow down the probe and beyond to the tip. The probe is then removed with a twisting motion which leaves no bubbles behind. This method seems to give sharper tips than boiling and lower resistances than the usual glass fibre method. It is also much more convenient than either.

VOLTAGE JUMPS

273

The chamber was perfused by gravity feed from one of two funnel reservoirs and excess aspirated. The flow rate was 1 ml./sec and the effective bath volume 1-2 ml. All solutions passed through a long tortuous channel drilled in a stainless-steel block before reaching the bath. This block was cooled by three Peltier elements

(Melchior MC 3-3-32-16, 32 couple, from Thermoelectric Devices, Reading) powered by a Farnell L30F power supply. Despite the rapid flow of Ringer a bath temperature of 4-10° C could be maintained with a room temperature of 20-24° C. Rectangular voltage steps were imposed just before and then during the plateau of bath agonist action. The total clamp currents in the absence of agonist were subtracted from those in its presence by playing tape recordings (Racal Store 4, 15 inches/sec) into a Fabritek averaging computer, as described and illustrated by Neher & Sakmann (1975). There are several possible defects of this method that should be considered. (1) The point clamp may not be perfect. However, in the present experiments using low resistance electrodes and high feed-back gain (2000-8000 x) the recorded potential was identical with the command after 100 /zsec. (2) If the tips of the current and voltage electrodes are very close, then the apparent membrane potential will be in error due to ohmic drops in the cytoplasm produced by the injected current. Although increasing the separation of the electrodes produces an apparent deterioration of the clamp, manifested as ringing or poor subtraction of capacity and leakage components, this deterioration is probably illusory, provided the electrode separation is small compared to the space constant in the relevant frequency range. (3) The space clamp of the end-plate region acted on by agonist is imperfect. If a rectangular potential is imposed at a point on the fibre and the potential some distance away monitored with a separate electrode it is seen that the recorded potential is composed qualitatively of a fast component followed by a gradual increase to the steady state. This is illustrated by Schneider & Chandler (1976) and in the present experiments was even more evident since no lag was used on the command. The paper of Schneider & Chandler should be consulted for a detailed discussion, but basically the effect arises because part of the membrane capacity is being charged through a significant series resistance. In one experiment the potential was monitored at various distances from the point clamping electrodes, and it was found that the high frequency space constant measured from the spatial decrement of the fastest component of the potential transient was about one quarter of the DC space constant. Under these conditions the space clamp of the longest end-plates would be rather poor during the major part of the capacity transient (- 2 msec). But for the shortest end-plates conditions should still be acceptable. The experiments reported below were conducted using Sub at low temperatures in order to obtain slow responses. Experimental evidence that the clamp is adequate is reported below. (4) The DC space clamp may deteriorate during agonist action. However, in the present work the current at the holding potential was usually less than 200 nA and this problem does not seem to be important (Adams, 1975d). Also it can be noted that the space clamp for high frequencies will deteriorate much less than the DC space clamp. The composition of the Ringer was as follows (mM): Na 116; K 2-5; Ca 1-8; HCO3 1; Cl 123; pH 8-0. Neostigmine, carbachol and acetylcholine (ACh) were all obtained from Sigma. Theory The following assumptions provide a convenient framework in which to describe relaxation experiments (Adams, 1975 b; Neher & Sakmann, 1975). The receptorchannel complex ('converter') can adopt two states, Q and Q*. The effective channel

274

P. R. ADAMS M

274P.RAD

conductance in state Q is zero and in state Q* is y. The states interconvert with sate constants ft and a. 46

Q=Q* a

(1)

Both states Q and Q* may comprise numerous sub-states; however, these sub-states are assumed to be in equilibrium on the time scale investigated. No assumption as to the molecular significance or relative magnitude of ft or a is made. The fraction of converters open at equilibrium, y, is

Y= ,@ +a(2) Following a step change in membrane potential ft and a change instantaneously to new values ft' and a', and y moves exponentially from its initial value -yo to its final

value y.:

yW = Y -(YOl-YO) exp-(t'+Ma')t. (3) The measured currents I(t) are assumed related to y(t) by I(t) = y(t) y(V-Erev) N, (4) where V = membrane potential, Ere, = reversal potential, and N is the number of channels per end-plate. The symbols used to refer to the various parameters of the responses to voltage jumps are explained in Fig. 4. The prime ' is used to refer to currents flowing during the hyperpolarizing step, and unprimed quantities refer to currents flowing at the holding potential. The subscript oo is used to refer to currents which flow when the conductance has equilibrated to a level appropriate to the hyperpolarized state, and the subscript 0 to currents flowing when the conductance is at the equilibrium level appropriate to the holding potential. Thus on applying the step the current jumps from 10 to Is', since although the potential at which the current flows has changed, the conductance which allows the current to flow has not yet changed from its pre-existing equilibrium value. The ratio y.,/yO can be obtained from experimental relaxations as (IF -I (I'O - I1) or as IF I'O (see Fig. 3). These experimental 'step ratios' are referred to as SR1 and SR2. RESULTS

Bath application and neoatigmine effect The experiments reported below were performed using 3 /M neostigmine Ringer. It was noticed that the potency of bath applied suberyldicholine (Sub) was very variable in untreated preparations, and that the potency became considerably greater, and more consistent, after adding neostigmine. In two end-plates the effect of neostigmine was followed over a long period under voltage clamp. Responses to carbachol, Sub and ACh were measured before and at various times following the first addition of neostigmine. The doses of the agonists were adjusted to keep the responses approximately constant, and the relative potency, i.e. the reciprocal of the dose-ratio, calculated from semilog dose-response curves. The carbachol potency declined somewhat, probably due to the cumulative

275 VOLTAGE JUMPS desensitization produced by repeated challenges with agonist rather than a depressant effect of neostigmine per se. The potencies of both ACh and Sub were considerably enhanced (Fig. 1). This effect appeared with a time constant of about 20 min, possibly corresponding to the time required for formation of a stable neostigmine-enzyme complex. 6 5

4

0

V

2

0

10 20 30 40 50 60 70 80 Minutes

Fig. 1. The effect of neostigmine (3 FM at time zero) on end-plate currents produced by bath applied Sub (0), ACh (@) and carbachol (0). Control log dose-response curves to ACh, Sub and Carbachol were first obtained. These were reasonably straight and parallel for 50 nA responses. Then the three agonists were tested at various times following introduction of neostigmine, the doses being adjusted to keep the response around the 50 nA level. The dose-ratio (DR, concentration in the presence of neostigmine required to match control response relative to control concentration) was calculated for each response assuming the log dose-response curves to remain parallel T = 18° C. Holding potential 77 mV. It should be noted that since no evidence was obtained against the existence of a component of potentiation that appears very rapidly following wash-in, the form of the initial part of the curves is speculative.

Curiously, in neostigmine Ringer perfusion of Sub led to responses that consistently developed more slowly (- 1-5-2 x ) than responses to carbachol, ACh or any other agonist tested (Fig. 2). This difference was completely absent when neostigmine was not used, suggesting that this difference does not reflect a different type of action on the receptors (e.g. activation of receptors not activated by ACh or carbachol). Under the conditions of these experiments it seems that the kinetics of onset and offset of the response are governed not by exchange of the bath solution

276 P. R. ADAMS but by diffusion through an unstirred layer overlying the muscle (Adams, 1975d). However, it seems unlikely that the above effect is due to a smaller diffusion coefficient for Sub since a similar difference is not seen between tetramethyl-ammonium and decamethonium. 1-0

- - -----

0..

0-6~~~

0-4

lo

0

0-2 0 _ 0 20 30Do0 50

sponses

0 10 20 30 40 50

and 3014 and Su 0 105

10 330 30beor 50simne

3

nm after

neostigmine) were bath applied to a voltage-clamped end-plate. The ordinate shows the agonist-induced current during the rising and falling phases of the response relative to the plateau current. Abscissa: time elapsed from turning flow tap. Note 10 see dead space time. It is possible that this effect arises from the receptor buffering effect proposed by Rang (1966) to account for slow atropine kinetics and subsequently applied to the end-plate (Katz &r Miledi, 1973b; Adams, 1975e; Colquhoun, 1975). To obtain a delay of several seconds the overall affinity of Sub for the receptors would have to be at least as great as that of curare (see Crank, 1956, Fig. 4.1). In view of the great potency of Sub this cannot be excluded. Another possible explanation might be that the foot of the dose-response curve has a different shape from that for carbachol. Although this point has not been studied in detail, log-log plots of Sub or ACh current against concentration usually had limiting slopes of near two (P. R. Adams and B. Sakmann, unpublished) as is found for carbachol (Rang, 1971; Jenkinson & Terrar, 1973).

Relaxation Several records of total clamp current during rectangular hyperpolarizations, in the absence of agonist were made on tape. The same rectangular steps were then applied when the current had reached a plateau during bath agonist action, and the total current recorded again. Later the

277 VOLTAGE JUMPS records were played back into the Fabritek and the 'capacity and leakage' currents (i.e. current during steps in the absence of agonist) subtracted to obtain agonist-induced current, exactly as described by Neher & Sakmann (1975). Fig. 3 shows a typical response during bath Sub action. This response strongly resembles the effects seen using iontophoretic applications (Adams, 1975b; Neher & Sakmann, 1975). On applying the step the agonist current jumps to a new 'ohmic' level and then climbs exponen'T

50 msec

~ ~ ~

00

I200 nA

j o10.._ Fig. 3. Typical relaxation produced by 60 mV rectangular hyperpolarization during the action of bath-applied Sub (0-5 #M). BTX pretreatment 2 x 10-6 g/ml. for 5 min. Holding potential 82 mV, jump 60 mV, T = 6-3° C. In this and all subsequent records inward current is shown as an upward deflexion and the straight line at the bottom of the record indicates the zero current level. It should be noted that in this and all subsequent Figures the current records show the net agonist-induced current, after subtraction of the holding current recorded in the absence of agonist. Thus the zero current level shown is simply the current that would have been recorded if the subtraction procedure had been carried out without applying agonist. In the presence of Sub a steady current Io flows at the holding potential. On applying the voltage step the current jumps to a new level I'o and then rises exponentially with time constant r' to an equilibrium value I'o. On removing the step it jumps down to a new level I.0 and then relaxes back to its original steady-state value Io with time constantT. For this response 'r' = 21 msec, = 14-5 msec, 'r'/r = 1-45 and SR = 1-43. ,

tially to its new equilibrium value. On removing the step the current shows a rapid ohmic fall which is larger than the initial jump, and then the current relaxes exponentially to its equilibrium value, with a time constant which is shorter than that for the rise. In some cases a slower process that appears as an inclined base line intervenes. The time constant of this slow process is similar for Sub, ACh and carbachol and is typically around 100 msec. This process has not yet been studied in detail and when it was present the records were analysed on the assumption that for short

278

P. R. ADAMS

times it could be approximated as a linearly rising or falling current superimposed on the relaxations. It was subtracted by using inclined base lines for the measurement of relaxing current. The slow component is most noticeable when the postsynaptic current is large, and is much reduced after bungarotoxin (BTX) action. It disappears when using very high agonist concentrations, even if the response is large. It seems likely that it is due to iontophoresis of agonist into the cleft.

It will be shown in the next section that the results obtained using bath agonist application are in good agreement with the results previously obtained using iontophoretically applied agonist (Adams, 1975b; Neher & Sakmann, 1975), suggesting that the clamp of the end-plate region was adequate in the present experiments. However this point has been checked in two further ways. Firstly, the relaxations during iontophoresis of Al

A2 _

8,

Cl

lki

_

_

_

_

__ _

_

_

_

_

_

o10 msecl m200 JnA

J

~~~~~~~nA

100

1 JnA

C2(~___

Fig. 4. Comparison of relaxations in the presence of bath-applied Sub (A), ACh (B) or carbachol (C). Left-hand records: T = 20° C; holding potential = 80 mV; jump = 50 mV. A,, Sub 170 nl; Bp, ACh 11 M; Cp, carbachol 22 EM; right-hand records: holding potential 80 mV; jump = 40 mV; T = 170 C. A2, Sub 330 nM; B2, ACh 3-3 FM; C2, carbachol 27 FM. Note fast time base and high temperature.

Sub near to (51 ,um), and 195 ,sm away from the clamping electrodes (at the presumed edge of the end-plate) were found to be practically identical. Secondly, relaxations produced by bath applied Sub, carbachol or ACh showed the usual difference in time constants (Katz & Miledi, 1973a; Adams, 1975b; Neher & Sakmann, 1975; Colquhoun, Dionne, Steinbach & Stevens, 1975; Dreyer, Walther & Peper, 1976). In four fibres in which the time constants of the 'on' relaxation for carbachol and Sub were compared, the mean ratio T'carb/T'Sub was 0-19+ 0-04 (± s.E.; nineteen responses analysed). In three further fibres the mean ratio 7'ACh/7'.ub was 0-55± 0-09 (± s.c.; nine responses analysed). An experiment of this type is illustrated in Fig. 4.

VOLTAGE JUMPS

279

Low 8uberytdicholine concentrations The terms 'low', 'medium' and 'high' will be used to describe Sub concentrations in the three ranges 17-170 nm, 170 nM-1-7 ,UM and 1-7 ,UM and above. Relaxations obtained using various low concentrations of Sub differed only in absolute magnitude and not in any other respect. Fig. 5 shows a typical example of the effects of low concentrations. For a sixfold variation in concentration there was a more than twelvefold variation in Io, However, r', T and the step ratio (I'. - -o)(I'-IO) did not vary beyond the usual degree of scatter. The various quantities were evaluated from semilog plots of relaxing current as previously described (Adams, 1975b; Neher & Sakmann, 1975). 3 n

2_ I _

40 soL

A E

20

~~~~~50 nA

0

_

150

-

~ ~ ~

*8

200 nA

< 100

0o

,

50 0

0

50 Sub (nM)

100 100 msec

Fig. 5. Lack of variation of relaxation parameters with low Sub concentration. Holding potential 86 mV, jump 50 mV, T = 6-5° C. Record A: Sub 33 nm; record B: Sub 100 nm. Note different current calibrations. The graphs show (from top to bottom) step ratios (SR1 and SR2, V and A), relaxation time constants (r', 0; r, @) and equilibrium current at holding potential (IO) all as a function of Sub concentration (abscissa). The straight line in the upper graph shows the mean r'/r ratio obtained from the straight lines in the middle graph. The curve in the bottom graph is arbitrary.

Experiments using low Sub concentrations were performed in twentysix fibres. The data clearly showed the near equality of the ratio '/r with the step ratio (Neher & Sakmann, 1975) since in twenty-nine observations

280 P. B. ADAMS the mean ratio of these ratios, r'/('r. step-ratio) was 1-08+ 0-06 (± s.E.). The ratio r'/r changed over-all e-fold for 79+6mV (mean+s.E.) potential change, consistent with previous observations (Adams, 1975b; Neher & Sakmann, 1975; see also Anderson & Stevens, 1973). Many of the experiments were also analysed to determine Erev as described by Neher & Sakmann (1975). Although there was great scatter the mean obtained, -6.6 mV, is quite similar to their value, and to values obtained by inver300 A1

A2 100 30

,|^

10 100 ] nA

10

100 msec

30

50

70

300

81

B 100 C

30 10

10

30 50 Milliseconds

70

Fig. 6. Lack of effect of BTX on relaxation parameters. A, shows control relaxation (Sub 240 nm, holding potential 82 mV, jump 60 mV, T = 6.50 C) and B. shows relaxation under same conditions but after 5 min BTX treatment (2 x 10-6 g/ml.). A2 and B2 show semilog plots of relaxing current from A, and B1 respectively (O on relaxation, * off relaxation). The time constants in A2 were aT' = 30 msec, r = 13 msec and in B2 r' = 27 msec and 7r = 11 meec. The r ratios were 2 2 and 2 6. The step ratios for the responses in A, and B1 were 2-1 and 2-0.

sion of iontophoretic responses (Dionne & Stevens, 1975; Adams, 1976a; Mallart, Dreyer & Peper, 1976). The over-all mean T value, obtained by normalizing to -80 mV and 80C assuming a Q10 of 3 and the above mean voltage dependence, was 11X4+ 0 5 (S.E.) msec. This value is larger than that of Neher & Sakmann (1975), possibly because the low conductance limit did not strictly obtain in all their experiments.

VOLTAGE JUMPS

281

Medium and high concentrations Two factors complicate experiments with Sub concentrations of 170 nm or above. Firstly the currents become very large, so that the space clamp deteriorates and also local membrane damage seems to occur at the make and break of the command. In order to maintain the current at clampable levels, and also to check the importance of current-density related effects, a-bungarotoxin (BTX; 2 x 10-6 g/ml. for 3-5 min) was often employed. 20 msec J nA

200-

0

100

k

20 b a

10

4

0

e

C

gh

50

0 50 Time from jump (msec)

0

50

Fig. 7. Kinetics of Sub 'on' relaxations in the low and medium concentration ranges. Holding potential 85 mV; jump 50 mV; T = 5.70 C. Graphs show semilog plots of on relaxations. A, before BTX, B, after 5 min BTX (2 x 10-6 g/ml.); C, after 10 min BTX. Left-hand ordinal scale applies to all plots except in i and k where the scale calibrations should be doubled. Plot k was shifted up one log unit for clarity. The following Sub concentrations were used: a, 33 nM; b, 66 nM; C, 100 nM; d, 100 nM (after BTX); e, 170 nM;f, 330 nM; g, 330 nm (after further BTX); h, 660 nM; i, 1 /SM;j, 1-3 /%M; k, 1-7 Am. Inset shows photographically super-imposed responses b and k.

This BTX treatment was sufficient to attenuate considerably the absolute response level but did not significantly affect the characteristics of the relaxations (Figs. 6 and 7). Table 1 summarizes experiments in four fibres in which the effect of BTX pre-treatment on r' was measured. Secondly desensitization becomes apparent even at low temperatures. However, in agreement with the observations of Anderson & Stevens (1973), desensitization seemed to affect only the amplitude of the responses and not the time course or relative amplitude. This point will be documented in a future publication.

282 P. B. ADAMS The effects of various medium or high Sub concentrations were tested in fourteen fibres. In most of these fibres low Sub concentrations were also tested. Two features of the responses to voltage steps were analysed in detail, the time constant of the 'on' relaxation, I'r, and the ratio of the equilibrium currents during and before the step, I'I,,,/IO. This latter parameter was chosen because it can be measured directly from the records TABLE 1. Effect of BTX treatment on 7' and 10. The fibres were tested with Sub before and after BTX (2 x 10-6 g/ml. for 3-5 min). T'BTuI/T'on is the ratio of the time constants of the 'on' relaxation after washing out and before BTX. 'O.BTXIIOcon is the ratio of the equilibrium currents at the holding potential after and before BTX. In fibre 1 two separate BTX treatments were made. In fibre 2 the Sub concentration tested after BTX treatment was higher than that used before BTX Fibre 1

Sub nm 100 330

T BTX/Tcon

0-13 0-16 0v80

1.09

0-12 0 44 0-21

2

661 170)07408

3 4

170 170

Mean+ s.E.

IOBTXIIO, con

1.11 1-06 074

0*90 0-98 +0-07

+0*08

independently of any interpretation in terms of relaxation processes. If it altered with agonist concentration this would indicate a change in the voltage sensitivity of the agonist-induced equilibrium conductance. Little change in either r' or I'YjIOo occurred in the medium concentration range. A detailed experiment is illustrated in Fig. 7. Relaxations in the presence of Sub concentrations of 1-7 #UM or above showed decreases in both I'I,/I, and r' compared to lower concentrations tested in the same fibre (Fig. 8 and Table 2). It seems unlikely that the lower voltage sensitivity of conductance evoked by high Sub concentrations is simply due to a decreased space constant, since the responses remained voltage insensitive even when desensitization had greatly reduced their amplitude. Furthermore an ohmic step without a subsequent relaxational increase in current after a voltage step is also seen with high Sub concentrations when using focal recording, where space clamp problems are less severe (Adams, 1976b). The explanation of the reduced voltage sensitivity of responses to high Sub concentrations depends on which step in receptor activation is voltage sensitive. It seems that high Sub concentrations can either (a) saturate most of the receptors, in the case that the binding step is voltage sensitive,

283

VOLTAGE JUMPS

TABLE 2. Comparison of kinetics and voltage sensitivity of conductances evoked by medium (0-33-1 /tM) and high (3 1-7 /tM) Sub concentrations. The numbers in brackets show the number of responses analysed in each case. Average temperature 7.50 C. Holding potentials -70 to -90 mV, jumps 40-60 mV. T' = time constant of 'on ' relaxation. Dashes indicate responses where the component of relaxing current was too small to measur,e T' High concentrations Medium concentrations Fibre 1 2 3 4 5 6

T' (msec)

I'tO/IO

21 (3) 16 (2) 19 (3) 13 (1) 22 (1) 18 (1)

2-8 (3) 3-9 (2) 2-9 (3) 3-1 (1) 5.4 (1) 5-6 (1)

1i01Io

T' (msec) 16 (2) 12 (2) 15 (1)

2-4 (2) 2-2 (2) 2-2 (1) 2.3 (1) 2-9 (2) 3.0 (2)

16 (2)

Means of means (± s.:E.) 18-2+ 1-4 3-95± 0-52

Al

14-9+ 0-8 2-51 + 0-14

C,

100 msec ._

] 100

,(

~~~UA

C

I

=~~~~-

A2 100

C2

-

30 10 3

T

-I

10 msec

10 msec

10 msec

Fig. 8. Effect of high Sub concentrations on relaxation parameters. Holding potential 72 mV; jump 60 mV; T = 90 C. No BTX treatment. Al, B1, Cl: calibrations apply to all records. A2, B2, C2: semilog plots of relaxing current (V on; A off). The left-hand ordinate applies to all graphs. Each abscissal division represents 10 msec; A: Sub 1-2 /sM; SR 2-1; T' 22 = 9 msec. msec; B: 4-8 uM; SR = 1-2; T' = 15 msec; T = 6 msec. C:14-4 4m; SR = 0-7; 7' = 11 msec; = 5 msec. =

=

r

(b) open most of the available channels, in the case that the receptor isomerization is voltage sensitive. Experiments with partial agonists might allow one to decide between these alternatives. or

284

P. R. ADAMS DISCUSSION

The results presented above offer little in the way of new information, since they merely confirm under more controlled conditions what was already known, or suspected, from iontophoretic experiments. For low Sub concentrations conductance relaxes exponentially from one equilibrium level to another with a rate constant that depends on membrane potential but not upon the agonist concentration. The voltage dependence of the equilibrium response is very similar to the voltage dependence of the rate constant, suggesting that the channel closing rate rather than the opening rate is voltage dependent. Although Dionne & Stevens (1975) obtained a good fit to their measured equilibrium voltage dependence assuming a significant voltage dependence of fi, it is not clear from their presentation whether omission of voltage dependence of ,6 would have produced a marked deterioration in the fit. The published instantaneous current voltage relations (Magleby & Stevens, 1972; Neher & Sakmann, 1976b) are not adequate to exclude instantaneous rectification as an origin of the downward curvature of the peak e.p.c.-voltage relation, nor is there any evidence to exclude that this non-linearity arises from a local saturation effect. The relaxations are not altered in either relative amplitude or time course by BTX treatment sufficient to reduce the total response considerably. This confirms previous evidence (Katz & Miledi, 1973c; Adams, 1975e) that BTX totally inactivates a fraction of the receptors and does not affect the remainder. It also excludes the possibility that the observed relaxations are contaminated by current-density effects such as iontophoresis or series resistance. However, the possible significance of such effects in the case of high concentrations cannot yet be evaluated. The high channel density and conductance suggests that series resistance problems could be at least as severe as in squid giant axon (Hodgkin, Huxley & Katz, 1952) under certain circumstances. Nevertheless, the effects described above for high Sub concentrations suggest that Sub can open a sufficiently large proportion of the end-plate channels for saturation effects to occur. Kinetic models For the purposes of discussion, the process of receptor activation can, somewhat arbitrarily, be divided into three stages: (a) diffusion of agonist from the bulk solution into the synaptic cleft, (b) binding of the drug, (c) opening of ion channels (isomerization). There are nine ways in which the rate limiting step and voltage dependence can be assigned in this simplified scheme. It is not clear that any one of these nine models will account for all the presently available data. However, certain assignments seem

285 VOLTAGE JUMPS very improbable. Thus it seems unlikely that diffusion into the cleft would show appropriate voltage sensitivity. Also, if the isomerization were rate limiting and the binding step voltage dependent, it would not be possible to explain the voltage dependence of the e.p.c. decay (Kordas, 1969). The five remaining possibilities are (a) diffusion rate limiting, binding voltage dependent; (b) diffusion rate limiting, isomerization voltage dependent; (c) binding rate limiting, isomerization voltage dependent, (d) binding both rate limiting and voltage dependent; (e) isomerization both rate limiting and voltage dependent. The first two possibilities arise because diffusion into and out of the cleft will be influenced by binding to receptors (Katz & Miledi, 1973b). Although almost all of the noise and relaxation observations can be predicted from either of these models (Adams, unpublished calculations), the lack of effect of BTX on noise or relaxation parameters is impossible

to explain. Model (d) is the hypothesis of Kordas (1969) and Adams (1976a). It is interesting to note that an entirely analogous voltage dependence of interfacial absorption of rubidium ions in doped bilayers has been recently postulated (Knoll & Stark, 1976). Model (e) is the hypothesis of Magleby & Stevens (1972). In both these cases one has to postulate very unequal voltage dependence of the appropriate forward and backward rate constants, which, though physically realizable, is unsatisfactory. A version of hypothesis (c) is discussed below. In order to account for equilibrium dose-response data (Katz & Thesleff, 1957; Rang, 1971, 1973; Jenkinson & Terrar, 1973; Dreyer & Peper, 1975; Hartzell, Kuffler & Yoshikami, 1975- Dionne et al. 1975; Adams, 1975a; see also Lester, Changeux & Sheridan, 1975) it seems reasonable to postulate that the receptor is composed of n agonist binding subunits, and that a channel opens when some fraction of its subunits are in some particular conformation. A particularly simple model would be to suppose that each subunit can adopt only two states, T and R, characterized by different affinities for agonists. A further simplification would be to suppose that the subunits were equivalent, and that the channel opens only when all subunits are in the R state. The kinetic predictions of this model are still very complex, so the discussion will be confined to two extreme versions of this model (Colquhoun, 1973). In the first version, the independent model, each subunit ignores its neighbours, as in the Hodgkin-Huxley model of axon channel gating. So if y(t) is defined as the probability of any arbitrary subunit being in the R

286 P. B. ADAMS state then following a step perturbation which brings y(t) from yo to y,,, (Y(t) = fraction of receptors in R, state) Y(t) = y(t)n = [yao - (ycx-yo) exp (-At)]n, (5) where T = R transitions are assumed first order with rate constant A (either binding or transconformation being rate limiting). Although derived by inspection this can also be viewed as the solution of an nth order differential equation with initial condition yo. In order to obtain the autocovariance of Y(t), ACVy(t), one needs to solve exactly the same equation with the initial condition Yo = 1, so the solution to within a scaling factor S will be ACVy(t) = S[{yo - (yoo - 1) exp ( At)}n - ya]. (6) It can be seen that for conductances small enough for y.O to be much less than 1, the noise time constant is 1f(nA), whereas for relaxations sufficiently small such that the absolute value of (y, - yo)/yw is much less than 1 the relaxation time constant is 1/A. Since Neher & Sakmann (1975) have shown that over a wide range of conditions the noise and relaxation time constants are virtually identical, n must equal 1. But then the independent model does not predict the observed dose-response relations. So it can be concluded that the independent model is probably inapplicable. The other possible extreme assumption is that the transitions of the subunits are completely concerted (only T. = R. transitions allowed; Monod, Wyman & Changeux, 1965, MWC). Two limiting kinetic versions of the MWC model should be considered. In the first place one can assume that the binding reactions equilibrate much faster than the isomerizations. Then essentially only two kinetically distinct species exist, and the relaxation is a single exponential whose rate constant is given by eqn. (48) of Hammes & Wu (1974). The main problem with this assumption is that the affinity of full agonists for the R form has to be quite high (since at rest only a minute fraction of the channels are open) and then it is difficult to see how the agonist could dissociate very rapidly from the R form. One possible way round would be to suppose that while dissociation from the T form is very rapid, dissociation from the R form is very slow. The model then comes to resemble eqn. (10) of Dionne & Stevens (1975). One would have to make the rather arbitrary assumption that the rate constants for the R -+T transitions were independent of the state of ligation of the receptor.

In the second place one can assume that the isomerization steps equilibrate much faster than the binding steps. This model tends to fall prey to the objections raised above for independent models since in general the relaxations and noise covariance contain n exponential whose time constants are the same but whose relative amplitudes differ. However, there is considerably more room for manoeuvre. For example, consider a kinetic version of the degenerate MWC scheme proposed to apply to

287 VOLTAGE JUMPS agonist dose-response curves (Adams, 1975 a), with the isomerization step (equilibrium constant L = (A2R)/(A2R*)) being very fast 2f

f

b

2b

L

A+R AR =A2R A2R.

(7)

For L>1 this scheme predicts kinetic behaviour which is very similar to that obtained with an independent model. But if Lo 1 and b is fast compared to experimental time resolution the scheme predicts only one time constant for relaxations or noise in the low concentration limit, 1/2bL. If L is voltage dependent the scheme predicts identical voltage dependence of time constants and equilibrium responses in the low concentration limit, whatever the voltage dependence of the isomerization rate constants. On balance this scheme seems to be the most attractive of those presently available. Although this scheme can be used successfully for ACh, Sub and carbachol, problems arise in relation to partial agonists. If these agonists are 'partial' because L is not much greater than 1, then the effective single channel conductance, which is a factor 1/(L +1) lower than the true single channel conductance, should be much smaller than for full agonists, whereas Dreyer et al. (1976) report a normal channel conductance for decamethonium. In terms of the above model their finding could have two quite different explanations: (1) decamethonium noise is generated directly by open-close flickering of channels, additional noise components related to the binding-unbinding process being slow and of low amplitude, (2) even for decamethonium L< 1 and the 'partiality' has some other explanation (such as a concomitant local anaesthetic action of decamethonium).

The arguments of the last two sections can be summarized as follows. Whether it is the binding or the isomerization that is voltage dependent, in the simplest case one would expect the forward and backward rate constants to show equal and opposite voltage dependencies. If the reaction that is voltage dependent is also rate limiting, one expects equilibrium responses to be twice as voltage dependent as the low concentration relaxation time constant. Since this is not the case, the simplest model must invoke rate limiting binding with a voltage dependent isomerization. To account for the sigmoidicity of the dose-response curve, one needs to invoke several subunits per receptor. Again in the simplest cases the subunits may interact very strongly, or not at all. But the second alternative is incompatible with the coincidence of noise and relaxation measurements. So one is lead to the above specific model (eqn. (7)). I thank B. Sakmann for his invaluable help and interest, E. Neher for his help and later his perceptive comments, Sir B. Katz for his criticism of a draft of the paper, J. Heeseman for pure suberyldicholine and F. Barrantes for comment and bungarotoxin. I was supported by a Stipendium of the Max-Planok-Gesellsehaft.

288

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