‘quantal’ calcium release operated by membrane voltage in frog skeletal muscle

The term ‘quantal Ca¥ release’ was introduced by Muallem,

Pandol & Beeker (1989) to indicate that in pancreatic acinar

cells, Ca¥ release induced by submaximal concentrations of

inositol trisphosphate (IP3) cannot completely deplete the

internal Ca¥ stores. The observation was rapidly extended

to other cells, and is now considered to be a fundamental

feature of IP3-activated Ca¥ release (reviewed by Bootman,

1994). This characteristic appears to be physiologically

important because it endows cells with a repertoire of

graded responses (Pandol & Rutherford, 1992) and the

property of increment detection (Meyer & Stryer, 1990). The

simplest of its proposed explanations invokes the existence

of different storage compartments with channels of different

sensitivities to the agonist (Ferris, Cameron, Huganir &

Snyder, 1992). Even though this ‘heterogeneous model’ is

disputed, it is useful for descriptive purposes. Thus a

working definition of quantal Ca¥ release may be: release

that depends on agonist concentration and time, as if

resulting from the activation of distinct subsets of channels,

with different sensitivities to the agonist.

Many similarities exist between the IP3 and ryanodine-

sensitive intracellular release channels (reviewed by Berridge,

1993), including pore sequence homology, homotetrameric

Journal of Physiology (1997), 501.2, pp.289—303 289

‘Quantal’ calcium release operated by membrane voltagein frog skeletal muscle

Gonzalo Pizarro*, Natalia Shirokova, Alexander Tsugorka and Eduardo R� úos †

Department of Molecular Biophysics and Physiology, Rush University, Chicago,

IL 60612, USA and *Departamento de Biof� úsica, Facultad de Medicina,

Universidad de la Rep�ublica, Montevideo, Uruguay

1. Ca¥ transients and Ca¥ release flux were determined optically in cut skeletal muscle fibres

under voltage clamp. ‘Decay’ of release during a depolarizing pulse was defined as the

difference between the peak value of release and the much lower steady level reached after

about 100 ms of depolarization. Using a double-pulse protocol, the inactivating effect of

release was measured by ‘suppression’, the difference between the peak values of release in

the test pulse, in the absence and presence of a conditioning pulse that closely preceded the

test pulse.

2. The relationship between decay and suppression was found to follow two simple arithmetic

rules. Whenever the conditioning depolarization was less than or equal to the test

depolarization, decay in the conditioning release was approximately equal to suppression of

the test release. Whenever the conditioning depolarization was greater than that of the test,

suppression was complete, i.e. test release was reduced to a function that increased

monotonically to a steady level. The steady level was the same with or without conditioning.

3. These arithmetic rules suggest that inactivation of Ca¥ release channels is strictly and

fatally linked to their activation. More than a strict linkage, however, is required to explain

the arithmetic properties.

4. The arithmetic rules of inactivation result in three other properties that are inexplicable with

classical models of channel gating: constant suppression, incremental inactivation and

increment detection. These properties were first demonstrated for inositol trisphosphate

(IP3)-sensitive channels and used to define IP3-induced release as quantal. In this sense, it

can now be stated that skeletal muscle Ca¥ release is activated by membrane voltage in a

quantal manner.

5. For both classes of intracellular Ca¥ channels, one explanation of the observations is the

existence of subsets of channels with different sensitivities (to voltage or agonist dose). In an

alternative explanation, channels are identical, but have a complex repertoire of voltage- or

dose-dependent responses.

6276

Keywords: Sarcoplasmic reticulum, Ion channel, Excitation—contraction coupling

†To whom correspondence should be addressed.

structure and sensitivity to physiological diffusible agonists.

The functional similarities are interesting as well. Dettbarn,

Gyorke & Palade (1994) showed that activation of ryanodine-

sensitive channels by chemical agonists has quantal properties

analogous to those of IP3 receptors. Additionally, inactivation

processes are present in both types of release channels, and

appear to be essential for function.

For IP3 receptors, Hajn�oczky & Thomas (1994) and Meyer &

Stryer (1990) demonstrated that inactivation, interacting

with activation, is at the basis of the quantal properties. In

cardiac muscle (Yasui, Palade & Gyorke, 1994) and skeletal

muscle (Baylor, Chandler & Marshall, 1983; Melzer, R� úos &

Scheider, 1987), Ca¥ release through ryanodine-sensitive

channels, activated by depolarization, has a potent

inactivation mechanism that causes it to decay rapidly after

a transient peak. In cardiac muscle, where Ca¥ channels are

activated by Ca¥ (Fabiato, 1985), this decay (Yasui et al.

1994) is essential to make Ca¥ release graded, rather than

explosive (Stern, 1992). In skeletal muscle, where the control

mechanisms are not fully understood, this inactivation,

generally believed to be mediated by Ca¥ (Schneider &

Simon, 1988; Jong, Pape, Baylor & Chandler, 1995), is even

faster.

The features of inactivation were exploited to demonstrate

that activation of Ca¥ release by membrane voltage in

skeletal muscle has the quantal properties described for IP3-

induced release.

METHODSSegments of singly dissected semitendinosus muscle fibres from

Rana pipiens (killed by pithing after being deeply anaesthetized by

immersion in a 15% ethanol—water solution) were voltage clamped

in a double Vaseline-gap, held at −90 mV, and stimulated to release

Ca¥ by pulse depolarization. The pool of data also includes that

from three fibres from the South American frog Leptodactylus

ocellatus, prepared in the same way and studied by G. Pizarro in

Montevideo. The cut ends of the segment were permeabilized with

saponin and exposed to an internal solution that contained (mÒ):

100 glutamate, 125 Cs¤, 5·5 Mg¥, 5 ATP, 15 EGTA, 5 glucose and

5 phosphocreatine, with Ca¥ added for a [Ca¥] of 50 nÒ, and the

Ca¥-sensitive dye antipyrylazo III (ApIII, 0·8 mÒ). In one of the

experiments with R. pipiens, and all the experiments with

L. ocellatus, [EGTA] was 5 mÒ, and glutamate was increased

accordingly. The working central portion of the segment was in an

external solution that contained (mÒ): 130 CH×SO×, 122·5 TEA,

10 Ca¥ and channel-blocking quantities of TTX (0·001 mÒ),

3, 4_diaminopyridine (1 mÒ) and anthracene 9-carboxylic acid

(1 mÒ). Both solutions contained 10 mÒ Hepes, were titrated at

pH 7 and adjusted to 260 and 270 mosmol kg¢, respectively. The

experiments were carried out at 13°C. Contractile movement was

prevented by high [EGTA], and in several experiments, stretching

(to 3·4—3·8 ìm per sarcomere) was also used. The modified upright

microscope, voltage clamp and PC-based pulse generation and data

acquisition used in these experiments have been fully described

(Gonz�alez & R� úos, 1993).

Ca¥ transients were determined in all cases with the absorption

dye ApIII, whose low affinity and fast equilibration makes it

convenient for quantification of large changes in [Ca¥] (methods as

described by Brum, Stefani & R� úos, 1988). The fluorescent dyes

fluo-3 and Calcium Green_1 were also used (Shirokova, Garc� úa,

Pizarro & R� úos, 1996), with similar results. All dyes were loaded by

diffusion from the cut segment ends. When the records were taken,

ApIII concentrations, measured in the central (working) segment

of the fibre, were between 600 and 1100 ìÒ, with fluo-3 they were

600—900 ìÒ, and with Calcium Green-1 they were 300—600 ìÒ.

Ca¥ transients were derived using methods described by Shirokova

et al. (1996), using as kinetic parameters of ApIII, koff = 700 s¢

(Baylor, Quinta-Ferreira & Hui, 1985) and kon = 0·025 s¢ ìÒ¦Â

(Kovacs, R� úos & Schneider, 1983).

Ca¥ release flux was derived from Ca¥ transients by the removal

method of Melzer et al. (1987, updated by Brum et al. 1988 and

Gonz�alez & R� úos, 1993). The removal parameters had standard

values, except for the maximum pump rate (MPR) and

concentration and rate constants of EGTA, which were determined

by fitting the model predictions to the recorded decay of the Ca¥

transients. The standard values of the removal parameters were the

same used by Shirokova et al. (1996), namely kon,Ca-troponin,

125 ìÒ¢ s¢; koff,Ca-troponin, 1200 s¢; kon,Ca-parvalbumin, 100 ìÒ¢

s¢; kon,Mg-parvalbumin, 0·03 ìÒ¢ s¢; koff,Ca-parvalbumin, 1 s¢;

koff,Mg-parvalbumin, 3 s¢; KD,pump, 1 ìÒ; [pump Ca¥-binding sites],

100 ìÒ; [troponin], 240 ìÒ; [parvalbumin], 1 mÒ. The parameter

[EGTA] in the model was usually set to the concentration in the cut

ends, although in some cases lower values, down to 50% of the

concentration in the ends, gave better fits. The fitted values of

kon,Ca-EGTA varied from 0·6 to 4·0 ìÒ s¢ and koff,Ca-EGTA was

between 0·6 and 6 s¢. As discussed by Gonz�alez & R� úos (1993) and

Schneider et al. (1987a), this method does not necessarily yield good

estimates of actual physical properties of individual Ca¥ buffers

and removal molecules but, if applied properly, provides a robust

estimate of release flux.

In some cases (specified in text and figure legends), the release flux

caused significant depletion of sarcoplasmic reticulum (SR) calcium

(shown by a slow decrement in flux following the initial fast decay

phase). In these cases the waveforms of release flux were corrected

for depletion (Schneider et al. 1987b). In this correction, release flux

is normalized to the continuously varying content of the releasable

calcium remaining in the SR, which is calculated as the difference

between an initial content and the time integral of the release flux.

In turn the initial SR content ([Ca¥]SR, relative to accessible aqueous

cytoplasmic volume) is estimated as the value that makes the

corrected release steady after a fast decaying phase. Release

waveforms thus corrected are proportional to the voltage-elicited

time-dependent Ca¥ permeability (Shirokova, Gonz�alez, Ma,

Shirokov & R� úos, 1995). If the uncorrected release waveform reached

a steady value, it was assumed that the release observed did not

substantially reduce the SR content at the times of interest, and

consequently the uncorrected flux was proportional to Ca¥

permeability.

RESULTSAn arithmetic feature of release inactivation

Use of the indicator ApIII in voltage-clamped muscle fibres

allowed us to measure transient increases in [Ca¥]é (Ä[Ca¥],

‘Ca¥ transients’) induced by depolarization, as illustrated in

Fig. 1A. The Ca¥ release flux waveforms, derived from the

Ca¥ transients by the removal method, are shown in Fig. 1B.

As is generally observed, a depolarization to 10 mV, test,

G. Pizarro, N. Shirokova, A. Tsugorka and E. R� úos J. Physiol. 501.2290

caused a flux that rose to a peak value (Pref), then decayed

to a steady value (S). In any release waveform, decay is

defined as the difference between peak and steady value (in

this case, Pref − S).

In a second record (thicker trace), a conditioning pulse to

−45 mV preceded the test pulse. It elicited release (of peak

value Pc, and steady value Sc) and determined a reduction in

the peak release elicited by the test pulse from Pref to Pcond.

Suppression, a measure of the conditioning effect, is defined

as Pref − Pcond. Remarkably, and under vastly different

pulse patterns, suppression was approximately equal to

decay in the conditioning release (Pc − Sc). It will be shown

that the same process, an inactivation, underlies both decay

and suppression. This section demonstrates a simple

relationship between decay and suppression with different

combinations of conditioning and test pulses. The

quantitative aspects of the relationship depend on the method

used to derive release flux from Ca¥ transients. Because of

the use of high [EGTA], however, the Ca¥ transient

waveforms are qualitatively similar to the release waveforms,

and the qualitative aspects of the relationship are visible

already in the unprocessed Ca¥ transients.

Figure 2 shows Ca¥ transients (Fig. 2A) and corresponding

release records (Fig. 2B) obtained when conditioning pulses

of different voltages preceded a large, nearly maximal test

pulse. Figure 2C plots suppression of a large test release vs.

decay in the conditioning release for this and four other

fibres, demonstrating their near equality at all conditioning

voltages lower than or equal to the test voltage. The

following section illustrates the result when test releases

were less than maximal.

Suppression and decay when the test pulse was varied

Figure 3 shows the effect of a small conditioning pulse on

release induced by test pulses of different voltage, equal to

or greater than the conditioning. Suppression in the test

records was approximately equal at all test voltages, and

similar to decay in release during the conditioning pulse

(bar). This is illustrated in the inset, where the filled

symbols represent suppression (normalized to decay in the

conditioning release that caused the suppression) plotted as

a function of peak release. The horizontal line represents the

identity between decay and suppression (and corresponds in

this case to about 9% of maximum release).

Quantal release activated by voltageJ. Physiol. 501.2 291

Figure 1. Conditioning of the release elicited by a large pulse

A, Ca¥ transients elicited by voltage-clamp pulses shown (bottom), in a cut frog skeletal muscle fibre.

Change in [Ca¥] was derived from changes in light transmission associated with binding of Ca¥ to ApIII.

B, Ca¥ release flux records, derived from Ca¥ transients. When a pulse to −45 mV was given before the

pulse to −10 mV, the large test release was reduced from a peak value Pref to Pcond. The conditioning pulse

itself elicited a flux with peak value Pc and steady value Sc. Note that suppression (Pref − Pcond) is

approximately equal to the decay in conditioning (Pc − Sc). Fibre 1111. Vertical path through fibre, 66 ìm;

diameter, 70 ìm. [ApIII] = 967 ìÒ at the time the records were made.

A nearly constant suppression at different test potentials

and near equality with decay in the conditioning release

were found consistently. The open symbols in the inset of

Fig. 3 plot the averages, and the bars represent the ranges of

values, grouped in five bins, from three experiments in

which the conditioning pulse elicited between 9 and 20% of

the maximum peak release. The results were generally

consistent with equality of decay and suppression, with the

exception of suppression at test pulse voltages eliciting some

30% of maximum release, which on average was greater

than decay by 33%. This deviation from equality amounts

to 3 or 4% of maximum release.


Figure 2. Suppression of release by pulses of different voltage

A 70 ms test pulse to −10 mV is preceded by 150 ms pulses to the voltages listed. A, Ca¥ transients;

B, release flux records. The dotted line is the reference record. Release flux was corrected for depletion.

Note the approximate equality between suppression of release in test and decay after the peak in

conditioning. Same fibre as in Fig. 1. [ApIII] increased from 783 to 967 ìÒ in the 18 min that elapsed

while the records were taken. [Ca¥]SR = 5·0 mÒ. C, suppression vs. decay in conditioning in the fibre of

A (þ), for which release was determined measuring absorption with a 30 ìm wide slit of light centred at the

fibre axis (inset). 1, same experiment, using a 7 ìm slit placed near the surface of the fibre (inset).

0, 8 and 2, three other fibres (1079, 1087 and 1143), measured at the axis. ±, an additional experiment

(fibre 1107, in which the internal solution contained 5 mÒ EGTA) at the fibre surface. In all cases

suppression and decay were normalized to the maximum decay recorded in the experiment. The regression

line was fitted to the fibre axis data. [Ca¥]SR was 6·8, 7·8, 3·6, 5·0 and 4·5 mÒ, respectively, for fibres 1079,

1087, 1107, 1111 and 1143.

Suppression and decay with conditioning and testpulses of equal voltage

In the type of experiment illustrated in Fig. 4, a pulse to

30 mV was repeated several times at 10 ms intervals. Decay

was almost complete in the first pulse, and in all successive

pulses suppression was almost complete (Pref is in this case

the first peak value, and suppression, Pref − Pcond is approx-

imately 91% of the full decay, Pref − S). In five similar

experiments, decay was on average 74 ± 11% of peak

(mean ± s.e.m.), and suppression was between 2 and 12%

less than decay (66 ± 7%). Rather than equality, there was

a slight excess of decay over suppression, which may simply

reflect recovery during the interval between pulses.

The experiment also illustrates that the release waveform in

the successive repetitions of the pulse did not appear to be

altered. The waveform was the same, with about 9% of the

inactivatable portion remaining, in spite of a substantial

change in the starting value of Ä [Ca¥], which went from

0·4 ìÒ in the first iteration to 0·75 ìÒ in the last iteration

of the pulse. This observation and others described later

imply that increases in [Ca¥] up to 1 ìÒ have little or no

inactivating effect on Ca¥ release.

Suppression and decay for conditioning pulses ofvoltage greater than that of the test

In the experiments illustrated in Fig. 5, the conditioning

effect of a high voltage pulse on the release elicited by a

small pulse was studied, with special attention to the final

level S. It was clear in this and five other experiments that S

in the response to the small test pulse was the same whether

the large conditioning was present or not. The experiment

illustrated is convenient to demonstrate this property of

inactivation because the records shown, and others of longer

duration, failed to exhibit the slowly decaying phase that

indicates SR depletion. The result, however, was obtained

regardless of depletion (it applied to the corrected records

whenever there was evidence of depletion). The conclusion is


Figure 3. Suppression of release at different test voltages

Continuous lines, reference releases elicited by pulses to the voltages listed. Dashed lines, release records

when a conditioning pulse to −40 mV preceded the test. The vertical bar before the conditioning release

(only shown for the test pulse to 10 mV) spans the decay, Pc − Sc. In the repetitions of this conditioning

pulse, decay varied by less than 15%. Inset, suppression as a function of peak release in the test pulse.

0, suppression in the experiment shown, normalized to decay in the individually paired conditioning

release, plotted against Pref in the test pulse, normalized to the maximum release (10·7 mÒ s¢, recorded at

+20 mV). The horizontal line indicates equality between suppression and decay. 1, average values in four

experiments with a similar protocol. After normalization, data were pooled in five bins, with ranges of Pref

shown by the horizontal bars. The vertical bars span the standard error of the bin average. Fibre 1315;

vertical path, 44 ìm; diameter, 55 ìm. [ApIII] increased from 455 to 690 ìÒ in the 37 min that elapsed

while the records were taken. [Ca¥]SR, 3·2 mÒ. Fibres averaged in inset: 1312, 1313 and 1315. Four sets of

data were used on average, one from fibre 1312, in which conditioning pulses were at −30 mV, one from

fibre 1313, at −45 mV, and two from fibre 1315, at −35 and −40 mV. Fibre 1312: vertical path, 72 ìm;

diameter, 65 ìm. Fibre 1313: vertical path, 86 ìm; diameter, 85 ìm. [Ca¥]SR, 2·0, 3·5 and 3·2 mÒ,

respectively, in fibres 1312, 1313 and 1315.

that the high voltage pulse did not reduce the steady level of

release in a small pulse, below the level attained by decay

during the small pulse applied alone.

The piecemeal observations described above can be

summarized as two simple arithmetic rules that approximate

the results of every combination of conditioning and test

pulse amplitudes: if the test voltage was greater than or

equal to the conditioning voltage, then suppression was equal

to decay in the conditioning release; when the test voltage

was less than the conditioning voltage, then suppression was

complete (equal to Pref − S, or decay in the test).

Paradox and controls

That small conditioning pulses suppress only a small fraction

of a test release, ‘Simon’s paradox’, was first pointed out by

Dr Bruce Simon (Electrobiology Inc., Parsippany, NJ,

USA), who also noted the inherent contradiction between

this observation and his own model of the inactivation

mechanism (Schneider & Simon, 1988; Simon, Klein &

Schneider, 1991). The near equality between suppression

and decay that is now described here implies and extends

Simon’s paradox. If all channels were equivalent and the

effect of the conditioning pulse was to inactivate a fraction

of them, then a simple scaling down of release would be

expected, and (Pcond − S)Ï(Pref − S) would measure

approximately the fractional inactivation induced by

conditioning. Indeed, the simulations using the quantitative

model of Schneider & Simon (1988) as modified by Simon et

al. (1991) consistently show approximate constancy of

(Pcond − S)Ï(Pref − S), regardless of test pulse voltage.

Instead, the loss of channels available to open by a maximal

stimulus is shown here to be approximately equal to the loss


Figure 4. Suppression by a train of pulses of equal amplitude

A, protocol; B, Ca¥ transients; C, release flux, corrected for depletion. Two protocols were used. In one, a

350 ms pulse to −30 mV preceded an 80 ms test to the same voltage (interrupted lines). In the other, seven

pulses to −30 mV were applied. In all cases, the pulses were separated by 10 ms at the resting potential.

Note that suppression, which can be calculated as the difference between the peak of release elicited by the

first depolarization and the peak of release in any of the subsequent pulses, is approximately the same for

all pulses, in spite of continued increase in [Ca¥]é. Suppression was 91% of decay, measured on the

waveform of release elicited by the long duration conditioning pulse. Fibre 1087; vertical path, 100 ìm;

diameter, 95 ìm. [ApIII], 805 ìÒ. [Ca¥]SR, 7·8 mÒ.

of open channels during the conditioning pulse, even when

the conditioning pulse was small. This also implies that

(Pcond − S)Ï(Pref − S) varies sharply with test pulse voltage.

One might say that inactivation, in its usual fractional sense,

is not defined.

Several tests were carried out to rule out the more trivial

explanations of the near equality of suppression and decay.

To make sure that the result was not a consequence of errors

in calculation of release, high internal EGTA was used, in

which the Ca¥ transients already had qualitative features of

the release waveform. Thus in Fig. 1, the Ca¥ transients

directly indicate that the effect on peak release is small.

Additionally, in many experiments carried out for other

purposes using high-affinity fluorescent dyes, with which

Ca¥ release can be determined more directly (Shirokova et

al. 1996), we found only minor deviations from equality of

suppression and decay. To avoid possible inhomogeneities in

voltage, which could reduce the effect of small depolar-

izations, the measurements were repeated using a window

of light focused on a peripheral region of the fibre (indicated

in Fig. 2C, inset). The data sets plotted with open symbols

in Fig. 2C were obtained in this configuration; they lay even

closer to the identity line than the data from measurements

near the longitudinal axis of the fibre.

Additionally, the suppression caused by low voltage pulses

might be small if the inactivated state reached by low

voltage pulses was different and less persistent than that

reached with larger pulses. The time course of recovery

from inactivation was determined using conditioning pulses

of low voltage (to between −35 and −45 mV in four

experiments), all of which were found to elicit less than 8%

of maximum release. Figure 6 shows the Ca¥ transients and

release waveforms for the experiment in which the

recovering release was lowest (3% of maximum). Recovery

was an approximately exponential function of the interval,

with a time constant of 141 ms. It averaged 117 ± 17 ms

(mean ± s.e.m., n = 4, 13°C) in the experiments with small

pulses. With pulses to 10 mV in two other fibres a range of

time constants (120—127 ms) was found. In these

experiments, therefore, suppression caused by low or high

voltage conditioning pulses recovers at similar rates. In the

biophysical sense, there is no need to assume more than one

inactivated state, induced by large or small conditioning

pulses. In the present experiments, and for unknown reasons,

recovery was slower than in the studies of Schneider & Simon

(1988; time constant of 90 ms at 6—10°C) and Jong et al.

(1995; time constant of 48 ms at 13°C), both of which used

high-voltage pulses.

The experiments shown in Fig. 6 are remarkable because

they document inactivation with only small increases in

[Ca¥]é. As shown in Fig. 6, after pulses to −45 mV, and

during the approximately 200 ms that it takes for 90% of

recovery, [Ca¥]é remained elevated by about 2 nÒ above the

resting value, and returned to the resting value very slowly,

due to the presence of 15 mÒ EGTA. In spite of the meagre

increase in [Ca¥]i, suppression was greater than 60% of

Pref. It is instructive to compare this with the cases in which

[Ca¥]é had been elevated much more at the time of the test

pulse. For example, after the conditioning pulses to −30 mV

in the five experiments of Fig. 2, [Ca¥]é was increased by

between 420 and 920 nÒ. Suppression after those pulses

was, on average, 62% of Pref. Therefore the fractional

suppression did not correlate with the elevation of [Ca¥]é

after conditioning. The rate of recovery from inactivation

did not correlate either. In the experiments illustrated in

Fig. 6, the recovery rate was similar to that after pulses to

−10 mV, in spite of large differences in measured [Ca¥]é. If,

as proposed by Schneider & Simon (1988), inactivation is

due to elevation of [Ca¥]é, then the concentrations that

caused inactivation in the present experiments must have

been highly localized (to explain the substantial inactivation

caused by a small pulse), and at least above 1 ìÒ (because


Figure 5. Suppression of release when conditioning was greater than test voltage

A conditioning pulse to −10 mV preceded a test depolarization to −40 mV. The conditioning eliminated

the peak of test release, but did not affect the level S, in the test release waveform. Release was determined

at the centre of the fibre. Fibre 1100; vertical path, 78 ìm; diameter, 62 ìm. [ApIII], 602 ìÒ. [EGTA] in

the internal solution was 5 mÒ.

recovery is insensitive to the presence of hundreds of

nanomoles of Ca¥).

Suppression by a conditioning pulse increases sharply with

pulse duration during the initial phases of the release

elicited by the conditioning pulse (Schneider & Simon,

1988). The main observation above, that suppression is equal

to decay in the conditioning release waveform, requires that

suppression does not change after decay has been completed.

In these experiments it became constant for pulse durations

greater than 100—120 ms. Figure 7 illustrates Ca¥ transients

and release flux in one experiment (in L. ocellatus), copying

the pulse pattern of Fig. 1. A pulse to −45 mV, of either

200 ms (thin continuous trace) or 400 ms conditioned release

elicited by a pulse to −10 mV. By comparison with the

reference release (interrupted trace), suppression was

approximately the same as decay in the conditioning, for

both conditioning durations.


Figure 6. Recovery from inactivation after small conditioning pulses

A pulse pattern consisting of two 80 ms duration pulses (conditioning and test) to −45 mV, separated by

an interval at −90 mV, was applied repeatedly, varying the interpulse interval. The repeated applications

of the pattern were separated by 3 min intervals. Records obtained in repeated applications of the pattern

are shown superimposed. A, Ca¥ transients; B, release flux. The dependence between release flux in the

test (normalized to the peak value in the conditioning release flux) and interval t between conditioning and

test was fitted with the function a + b exp(−tÏô), with a = 0·52, b = 0·44 and ô = 141 ms. Fibre 1088;

vertical path, 92 ìm; diameter, 91 ìm. [ApIII], 1204—1255 ìÒ.

Two other aspects of this experiment are worth noting. The

release records shown in Fig. 7C have been corrected for

depletion (with [Ca¥]SR = 1·95 mÒ). Because cumulative

release during the conditioning pulse was much less than

that amount, the correction barely affected it or the value of

peak release in the test, and the near equality of the peak

values in the two tests (conditioned at 200 and 400 ms) was

found independently of the depletion correction.

Additionally, the increase in [Ca¥]i prior to the test pulse

went from 100 nÒ (after the shorter conditioning pulse) to

250 nÒ (after the longer one). That suppression was the

same in both cases again shows that [Ca¥]é in the

submicromolar range does not affect inactivation.

DISCUSSION

In summary, it was observed that suppression and decay are

approximately equal (Figs 1—4) and that suppression is

never greater than decay in reference (Fig. 5). It will now be

shown that these properties have two important implications.

One is that the inactivation process is strictly linked to

activation. The other is that membrane depolarization causes

this activation in a ‘quantal’ manner.

A basic model of the release channels

The interpretation of the results uses a three state model of

the release channels, represented in Scheme 1. This minimum

model will help derive the main conclusions, but will also

prove to be fundamentally insufficient. Two alternative

models will be introduced later.

In the model channels can be closed, open or inactivated.

The transition from closed to open is controlled primarily by

the T_tubule membrane voltage sensor (e.g. Melzer, Schneider,

Simon & Szucs, 1986; R� úos, Karhanek, Ma & Gonz�alez, 1993;

Jong et al. 1995), through largely undefined mechanisms.

Most channels in a resting cell are closed, and depolarization

increases the occupancy of open and inactivated.

(voltage operated)

Closed

Inactivated

Open

Scheme 1

Fatal inactivation of open channels

In terms of the model, and assuming that activation is much

faster than inactivation (so that all activated channels can be

pictured as simultaneously open at the peak of release), decay


Figure 7. The inactivation effect at long conditioningdurations

Effect of a 200 ms (thin trace) or 400 ms conditioning pulse

on a large test release. A, voltage pulses; B, Ca¥ transients;

C, release flux records corrected for depletion. The

interrupted line plots the reference record. Note that the

two conditioning pulses caused the same suppression, in

spite of a perceptible increase in [Ca¥]é during the longer

conditioning pulse. The internal solution contained 5 mÒ

EGTA. Fibre 404 (L. ocellatus); vertical path, 92 ìm;

diameter, 121 ìm. [ApIII], 711—821 ìÒ. [Ca¥]SR, 1·95 mÒ.

gives a proportional measure of the number of channels that

inactivated from open. This is also true in the hypothesis

that inactivation and activation have voltage-independent

kinetics (a reasonable approximation, considering that time

to peak of release is almost constant at all but the lowest

test pulse voltages, e.g. Figs 2 and 3).

Suppression in a maximal test pulse, on the other hand,

measures the number of channels that stayed inactivated

after the conditioning. With these hypotheses the equality

between decay and suppression implies that the loss of

channels available to open by a maximal stimulus is

approximately equal to the loss of open channels during the

conditioning pulse, even when the conditioning pulse is

small. Although other possibilities exist, the simplest

interpretation is that all channels that were unavailable

when challenged by a large test (inactivated) reached that

state after opening in the conditioning pulse. Only channels

that moved to open then went to inactivated. Put differently,

activation is a necessary condition for inactivation.

An important additional property of inactivation is revealed

when the conditioning voltage is greater than that of the

test (Fig. 5). That the final level of release during the test


Figure 8. Properties of suppression in a classical system

Analytical solutions to a simple implementation of the model of Scheme 1. The rate constants of the

transitions between open and closed were kCO = aexp((V − VT)Ï2K, kOC = aexp((−V + VT)Ï2K, with

a = 150 s¢, VT = −40 mV and K = 10 mV. The transitions between open and inactivated were of first

order with rate constants kOI = 100 s¢ and kIO = 20 s¢. A, occupancy of open for a 100 ms pulse to 0 mV

(from −90 mV), with and without a 150 ms conditioning pulse to −45 mV. Note that suppression is much

greater than decay. B, 0, suppression by the same −45 mV pulse, normalized to decay in the conditioning,

as function of the peak occupancy of open in test pulses to the voltages indicated at each symbol (the

abscissa is the model version of the experimentally determined Pref). Suppression is greater than decay and

increases with test pulse amplitude. 1, fractional suppression, i.e. suppression normalized to peak

occupancy in the test (Pref). This measure of inactivation is almost constant. These properties are opposite

to those illustrated in Fig. 3.

cannot be made smaller by conditioning indicates that all

the channels opened by the small pulse and able to

inactivate do so, to the greatest possible extent, regardless

of the presence of the large conditioning. In other words,

opening appears to be not only necessary for inactivation,

but also sufficient. If only channels that open inactivate and

every channel that opens inactivates, the two processes of

activation (opening) and inactivation are strictly and fatally

linked. The two sets of channels, those that activate and

those that inactivate, appear to be one and the same.

In the considerations above, the origin of the steady release

flux (S) was not specified. It could be flux through channels

that make infrequent forays from inactivated into open (a


Figure 9. Two protocols of quantal release

A, the phenomenon of incremental inactivation. Decay and suppression data from one of the experiments

in Fig. 2C (fibre 1087), obtained with a conditioning pulse of variable voltage preceding a near maximal

test pulse. The data were represented vs. conditioning voltage in two different ways: 1, fractional

suppression, (Pref − Pcond)ÏPref, and 0, fractional decay in the conditioning, (Pc − Sc)ÏPc. Note that these

two measures of inactivation are very different, and converge when the conditioning voltage equals the test

voltage. Inset, analogous measures of inactivation in the release induced by a double application of IP3 to

permeabilized hepatocytes. The first IP3 application was of increasing concentration, represented in the

abscissa, and the second one was maximal (redrawn schematically from Hajn�oczky & Thomas, 1994; Fig. 2).

B, increment detection. Release flux in response to the three-step increase in voltage is shown at the

bottom. Inset, three patterns of transient response to two steps of stimulus intensity (redrawn from Meyer

& Stryer, 1990): a, ‘classical’ inactivation, if complete, results in no response to a second step;

b, desensitization (termed adaptation in the original figure), resulting in smaller response to the second

step; c, the ideal increment detection, with responses proportional to stimulus increment. Note that in the

voltage range shown, the transient portion of release in skeletal muscle has ideal increment detection

properties. Fibre 1352; vertical path, 60 ìm; diameter, 81 ìm. [ApIII], 745 ìÒ.

partial inactivation, as proposed by Schneider & Simon,

1988) or it could originate entirely from a class of non-

inactivating channels. These alternatives do not affect the

conclusion that activation and inactivation are coupled.

Inactivation is believed to be induced by Ca¥ (Schneider &

Simon, 1988; Jong et al. 1995). A current model (Simon et al.

1991) assigns it to a Ca¥ binding site with a KD of 400 nÒ.

There is increasing evidence, however, that if the process is

Ca¥ mediated, it must require concentrations substantially

greater than 400 nÒ. The evidence includes the requirement

of hundreds of micromoles to inactivate channels in bilayers

(Ma, Fill, Knudson, Campbell & Coronado, 1988; Tripathi &

Meissner, 1996) and the lack of effects in frog muscle fibres

of photorelease-induced increases in [Ca¥]é to micromolar

levels (Hill & Simon, 1991). Finally, the present results

indicate that inactivation affects only those channels that

have activated. This is also incompatible with an

inactivation site that binds at hundreds of nanomoles, since

much greater concentrations are probably reached near

many channels, not just the ones that actually open.

One way of explaining the present observations as a

consequence of Ca¥-dependent inactivation is to assume

that the KD of the inhibitory site is sufficiently high that

only the open channels will face such concentrations. This

hypothesis is analogous to the proposal by Jong, Pape,

Chandler & Baylor (1993) for a channel that ‘counts ions’,

effectively passing a constant number before inactivating. It

is consistent with the [Ca¥] dependence of channel open

probability in bilayers and with the failure of caged Ca¥ to

cause inactivation. It explains the absence of correlation in

the present results between extent of inactivation or rate of

recovery from it and the long term changes in [Ca¥]i

induced by the conditioning pulses. There is nothing in the

present results, however, indicating that inactivation is

mediated by Ca¥.

Quantal activation of Ca¥ release

A strict coupling between activation and inactivation

implies that all channels that activate become tagged by the

inactivation process. Surprisingly, this inference leads to a

contradiction of one of the dogmas of voltage-operated

channels, and forces the rejection of Scheme 1. Until now,

the sets of voltage-sensitive plasmalemmal channels and by

extension Ca¥ release channels under membrane voltage

control, have been pictured as statistical ensembles of

voltage-operated molecules, the activation of which can be

defined by one function of voltage (usually a Boltzmann

function) with a single set of parameters (e.g. Sigworth,

1993). This implies that parameters of a model like Scheme 1

should be the same for every channel in the ensemble. In

such a ‘classical’ framework a submaximal pulse — one that

only activates (to open) a fraction of the population at any

time — should activate every molecule the same fraction of

the time.

A problem immediately arises with this picture: since

inactivation affects every channel that opens, a long

submaximal pulse should result in inactivation of all

channels. This was not observed; a small pulse caused a

small suppression, and prolonging the pulse did not increase

suppression.

Recovery from inactivation does not provide a way out of

this contradiction. If it is assumed that inactivated is not an

absorbing state, but allows for reopenings, then a

submaximal pulse (for instance to −45 mV) will result after

some time in the placement of a steady fraction of the

channels in the inactivated state. This does not solve the

contradiction; the peak open state occupancy elicited by a

test pulse placed after this small conditioning will be

affected very differently at different test pulse voltages. The

conditioning pulse will cause much greater suppression if

the test pulse is large. These intuitive considerations proved

true for every implementation that was tried for the basic

model, one of which is illustrated in Fig. 8.

The activation of release by voltage differs from the classical

scheme in formally the same way that activation of Ca¥

release by IP3 (Muallem et al. 1989) and activation of SR

Ca¥ release by multiple chemical agonists (Dettbarn et al.

1994) differ from classical drug agonism. Three properties of

activation by voltage can be identified that are ‘non-

classical’, analogous to the so-called quantal properties of

activation by chemical agonists.

Constant suppression. Suppression of the test response by

a submaximal conditioning pulse, Pref − Pcond, is constant,

independent of the voltage of the test pulse (Fig. 3). If the

strict link between activation and inactivation is taken into

account, this is analogous to the defining property of

quantal activation of IP3 receptors: a submaximal dose of an

agonist activates as if it affected only a subset of receptors.

Incremental inactivation. When activation by IP3 is

followed by inactivation of the receptors (as described in

permeabilized hepatocytes by Hajn�oczky & Thomas, 1994),

the ensuing suppression has exactly the properties described

in this paper. Hajn�oczky & Thomas (1994) quantified the

inactivation caused by a submaximal conditioning exposure

to IP3 as the fractional reduction in the response to a

subsequent maximal exposure. They found that this

fractional measure of inactivation increased with

conditioning IP3 concentration (incremental inactivation),

even though the fractional decay of permeability during the

conditioning exposure was essentially independent of IP3

concentration. A formally similar property is demonstrated

for skeletal muscle in Fig. 9A, obtained by replotting decay

and suppression data from Fig. 2 as fractions of the

reference flux, rather than absolute quantities. The filled

symbols represent fractional decay of release in a

conditioning pulse, (Pc − Sc)ÏPc (defined in Fig. 1). As

shown by Shirokova et al. (1996), fractional decay is a slowly

varying function of voltage, with a maximum at about

−40 mV. The open symbols represent fractional suppression,

(Pref − Pcond)ÏPref, a monotonically increasing function that

only at high voltages reaches the level of fractional decay


during conditioning. The inset (redrawn from Hajn�oczky &

Thomas, 1994) shows similar properties for the fluxes

elicited in permeabilized hepatocytes by double exposure to

IP3. This property follows from the equality between

suppression and decay. As conditioning voltage (and hence

decay) is made greater, suppression increases accordingly,

affecting an increasing fraction of the peak of the response

to a constant test. For investigators of IP3-induced release,

this feature was as surprising as it was for us, because they

also expected that the availability of release would be the

same irrespective of the magnitude of the stimulus (IP3

concentration) used to explore it. The isomorphism between

the gating phenomena in IP3 receptors and those studied in

the present article extends to the language used. Hajn�oczky

& Thomas (1994) state: ‘. . . the percentage inactivation was

similar at each dose, whereas the response to maximal IP3

was inhibited in proportion to the fraction of channels

activated during the prepulse. Thus, inactivation was

limited to only the occupied fraction of receptors . . . IP3-

induced inactivation . . . parallels the quantal, or

incremental, nature of IP×-induced channel opening’.

Increment detection. The response to a step in [IP3] is a

transient increase in permeability, which tracks the

increment, rather than the tonic value of the stimulus. As

shown in the inset of Fig. 9B (redrawn from Meyer & Stryer,

1990), step increments of agonist concentration within a

certain range cause transient responses of amplitude approx-

imately proportional to each step. This proportionality

(Meyer & Stryer, 1990; Ferris et al. 1992), is in contrast to

the attenuation of the response that occurs in channels with

desensitization, or its elimination in fully inactivating

channels. As shown in Fig. 9B, in skeletal muscle the release

response to a series of three voltage steps of small size has

the property of increment detection (in addition to a tonic,

non-inactivating component).

The three characteristics given above illustrate in different

ways the analogy between the response to voltage and the

response to chemical agonists in quantal systems. It is in

this formal sense that activation of release by voltage must

be termed quantal.

Mechanisms

For the time being the term quantal release must not be

interpreted as a well-understood mechanism. It only implies

a set of properties inconsistent with the classical picture of

activation and inactivation. In the Introduction a quantal

system was defined as one in which release depends on

stimulus and time as if resulting from the activation of

subsets of channels with different sensitivity to the stimulus.

Voltage-operated Ca¥ release in skeletal muscle satisfies this

definition.

Indeed, a hypothetical heterogeneous system of channels,

with a distribution of sensitivities to voltage, but otherwise

described by the three-state Scheme 1 with adequate

transition rates, would have all the properties described

here. A small voltage pulse would activate the subset of

most sensitive channels, which would then inactivate,

causing the observed decay (the transition open� inactivated

would have to be heavily favoured over its opposite).

A subsequent larger pulse would find all channels in an

available state (closed), except the ones in the most sensitive

subset, thus justifying the equality between decay and

suppression. With this model, decay would equal

suppression provided that most (or the same fraction) of the

activated channels were open at the same time at the peak

of release. This would be the case if channels activated with

the same kinetics at both the conditioning and the test

voltage, or inactivated more slowly or with a fixed lag after

activation.

Before the present observations, quantal activation was

thought to be an exclusive feature of chemical processes,

first seen for IP3 agonism, then extended to multiple

agonists of the ryanodine receptor. The finding that voltage

also activates Ca¥ release in a quantal manner does not

clarify per se the mechanism of quantal activation, but

suggests that the final stages of the activation process are

fundamentally similar, whether induced by voltage or a

chemical agonist.

In a recent model of control of release channels by membrane

potential, voltage-driven movement of the voltage sensors

was formally treated as binding of a ligand to an allosteric

protein (R� úos et al. 1993). In this line of thought, the electric

field could use the voltage sensor to nudge the release

channel into a certain conformation, much as ligand binding

would.

Alternatively, and perhaps more naturally, the quantal

property may be a consequence of a chemical step in release

activation. In a current scheme (R� úos & Pizarro, 1988) it is

proposed that a fraction of the release channels are

activated by Ca¥, which exits the SR through release

channels controlled by voltage sensors, and that inactivation

of this Ca¥-activated release determines the decay in the

release flux. These two hypotheses explain the present

observations, because the quantal property described here

only applies to the inactivating portion of the flux, and

activation of skeletal muscle release channels by Ca¥ is

known to be quantal (Dettbarn et al. 1994). Increasing pulse

voltages would simply be delivering increasing concentrations

of activator Ca¥ to a chemically operated quantal system.

For either IP3 or ryanodine receptors, quantal chemical

activation may be explained by hetero- or homogeneous

models. It is possible that channels are heterogeneous in

their sensitivity to the agonist. In turn, this heterogeneity

may be the result of molecular diversity (the existence of

splice, post-translational, or other variants; Ferris et al.

1992). Additionally, local determinants of permeability

could be at work, like [Ca¥] inside the store (Irvine, 1990)

or channel density (Hirose & Iino, 1994).

It is also possible that the channels are homogeneous, but

the interaction with Ca¥ pumping (Steenbergen & Fay,

1996), with hypothetical ‘memory molecules’ (Swillens,


1992), or their intrinsic properties, render their individual

responses complex, with all the features described above for

the overall response of the cell. The existence of such

complexity in individual molecules is supported by the

demonstration of adaptive responses of single cardiac

release channels to increases in [Ca¥] (Gyorke & Fill, 1993;

Valdivia, Kaplan, Ellis-Davies & Lederer, 1995), which

appear to participate in the physiological response as well

(Yasui et al. 1994).

The present observations are relevant to the ‘steady-state’

model of quantal release (Irvine, 1990; Bootman, 1994). In

this model, intra-store [Ca¥] modulates allosterically the

sensitivity to the agonist; consequently, the decaying [Ca¥]

inside a store with open channels determines reduced

sensitivity to the agonist and eventually stops release. In

skeletal muscle SR, however, release flux can be

quantitatively described as the product of a permeability

(function of voltage and time) and a driving force,

essentially the intra-SR [Ca¥]. This implies (as has been

shown directly) that waveforms of release with the same

kinetics can be elicited by voltage pulses in the presence of

very different intra-SR [Ca¥], which is obviously

inconsistent with the modulation assumed by the steady-

state model (Shirokova & R� úos, 1996).

Because the present observations refer to release flux

averaged over large areas of the cell, they cannot help decide

between homogeneous and heterogeneous models. With

spatially resolved confocal microscopy of muscle cells

containing fluo-3 (Tsugorka, R� úos & Blatter, 1995), ‘eager

triads’ have been observed, i.e. triadic regions of the cell

where release was elicited at lower voltages (Blatter,

Shirokova, Tsugorka & R� úos, 1996). It remains to be

established whether such heterogeneity can account for

quantal activation. It should be clear, however, that the use

of voltage as a quantal agonist, with its gradability and

reproducibility, in cells where Ca¥ release can be resolved

spatially, opens a promising avenue for exploration of the

mechanisms of quantal release.

Note added in proof

A local control model recently presented by M. D. Stern, G. Pizarro

& E. R� úos, in preliminary form (Biophysical Journal 72, A273(1997)), does reproduce quantal aspects of Ca¥ release. This is of

interest because the model neither assumes a heterogeneous

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Acknowledgements

We are grateful to Dr Michael Stern for detailed discussions of

models of quantal release, and Dr Fred Cohen and

Dr Tom DeCoursey for many suggestions on the manuscript.

Supported by a grant-in-aid from the Consejo Nacional de

Investigaciones Cientificas y T�ecnicas, Uruguay (to G.P.), and

grants-in-aid from the National Institutes of Health, USA, the

American Heart Association and the Muscular Dystrophy

Association (to E.R.).

Authors’ permanent address

N. Shirokova and A. Tsugorka: A.A. Bogomoletz Institute, Kiev,

Ukraine.

Author’s email address

E. R� úos: [email protected]

Received 25 October 1996; accepted 3 March 1997.


‘quantal’ calcium release operated by membrane voltage in frog skeletal muscle

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