J. Physiol. (1978), 278, pp. .513-523
513
With 7 text-figure8 Printed in Great Britain
CLUMPING AND OSCILLATIONS IN EVOKED TRANSMITTER RELEASE AT THE FROG NEUROMUSCULAR JUNCTION By HALINA MEIRI AND R. RAHAMIMOFF From the Department of Physiology, Hebrew University-Hadassah Medical School, P.O. Box 1172, Jerusalem 91000, Israel
(Received 31 May 1977) SUMMARY
1. Time series analysis of evoked transmitter release was performed at the frog neuromuscular synapse. 2. Clumping of end-plate potentials with similar amplitude was found in the time
domain. 3. At low quantal contents periodic oscillations were observed with a period of 14 sec. 4. Clumping and oscillations are phenomena of presynaptic origin. 5. The results are explained on the hypothesis that periodic fluctuations occur in Ca concentration inside the presynaptic nerve terminal. INTRODUCTION
Release of the neurotransmitter at the neuromuscular junction is a process subject to probability (Fatt & Katz, 1952; del Castillo & Katz, 1954; Martin, 1955; Boyd & Martin, 1956; Wernig, 1972; Zucker, 1973). The occurrence of the miniature end-plate potentials (m.e.p.p.s) is at random intervals and the time of their appearance cannot be predicted. Similarly, the number of quanta (quantal content, m) that form the end-plate potential (e.p.p.) fluctuates randomly from trial to trial. The amount of transmitter liberated by the nerve impulse seems to reflect an interplay between extracellular and intracellular factors which act on presynaptic membrane. These factors include the concentration of calcium ions in the extracellular medium ([Ca],) and inside the terminal ([Ca]i), the polarization of the nerve membrane and the metabolic state of the nerve terminal (cf. Katz, 1969; Rahamimoff, Erulkar, Alnaes, Meiri, Rotshenker & Rahamimoff, 1976a). If these factors are constant in time, it is expected that transmitter release will fluctuate in a completely random fashion. However if one or more of these factors varies with time, then the random fluctuations will be superimposed on the underlying variations, resulting in an increased 'order' (in the statistical sense). To examine whether such an 'order' exists, a time series analysis (Kendal, 1976) of evoked transmitter release was performed on a long series of e.p.p.s elicited at a constant frequency. It is reported that there is a positive correlation between successive members of the series and under appropriate experimental conditions periodic oscillations can be observed. Some of the experimental results were reported in brief (Rahamimoff, Meiri & Erulkar, 1976 b). T7
P HY
278
514
H. MEIRI AND R. RAHAMIMOFF
METHODS The experiments were performed on the sartorius nerve muscle preparation of the frog Rana ridibunda. The preparation was bathed in a Ringer solution with variable concentrations of Ca and Mg ions; the solutions were kept iso-osmotic by corresponding changes in the concentration of Na ions. Conventional electrophysiological methods were used for intracellular recording. The nerve was typically stimulated at the rate of 0-5/sec and 300-1250 responses were recorded. The e.p.p.s were photographed, measured and analysed by a number of FORTRAN iv programs with MACRO ASSEMBLER subroutines on the PDP15/78 digital computer of the Hebrew University Medical School.
Statstical method The statistical methods used in this work are described in detail in Kendall (1976). Here only a brief account is given. (1) Turning point In a series of fluctuating numbers a turning point appears whenever a member of a series is bracketed by two other members which are either smaller or larger. At least three numbers are needed to form a turning point; out of six possible permutations of three numbers, only four will include a turning point. Hence, if the numbers are in a random order, the probability of having a turning point is two out of three. If there are n numbers in a series which is random and there is no interdependence between the numbers, then the number of expected turning points (Ses) is:
.p= j(n-2).
(1)
If there is a positive interdependence between the members of the series (for example, if there is a clumping of e.p.p.s of similar amplitude), then the observed number of turning points (Sob) will be less than Sep, and the opposite for a negative interdependence. An obvious source for reduction in Sobs is the non-stationarity of the release process. Therefore each series was checked for drifts, by performing a regression analysis on the series of the e.p.p.s (e.p.p. amplitude against time). When the series showed a significant non-zero slope on linear regression, it was discarded. On the basis of the turning points the length of phase was calculated. A phase is defined as the distance between two successive turning points. For a phase with a length of d, at least d + 3 numbers are required. In a completely random series composed of n numbers there are (n - d -2) elements of d + 3, so the expected number of phases with a length of d is: 2(n-d-2) (d2+3d+1) (2
(d+3)! If there is a positive interdependence between the members of the series, then the number of short ds will be less and the number of long ds will be more than predicted by Eqn. 2.
(2) Autocorrelation To check whether deviation from complete randomness shows periodicity, an autocorrelation was performed. Correlation coefficients (r) were estimated from various lags between the members of the series (see eqns. 3.35 and 3.36 presented by Kendall, 1976).
(3) Power spectrum The power spectrum of the series of e.p.p.s amplitudes was calculated by the Fourier transformation of its autocorrelation. The fast Fourier computer programs FFT and SHU supplied by Digital Equipment Corporation were used, and the spectrum was smoothed by convolution of the Fourier transform with the Hann's smoothing window.
OSCILLATIONS IN TRANSMITTER RELEASE
515
RESULTS
Clumping Most experiments were performed in a Ringer solution containing 0.2-0-6 mM-Ca. Below 0-2 mm-Ca there was practically no evoked release and above 0*6 mM-Ca, there were usually twitches. Fig. 1 shows an experiment performed in a medium containing 0-2 mM-[Ca]. and 1 mm-[Mg].. The nerve was stimulated once every 2 see and the first 480 responses (out of 1000) are illustrated. In this section of the experiments 117 nerve stimuli 08
0-8
E
60
120
0-8 r
180
240
0-8 -
300
360
-
JiL-JL i
0.4
' 08e
420
480
540
600
660
720
A
-X
08
0-8
-
-
0-40 . .. 1V . _ 1 ~~~~~
0 8t
780
.\_._.J \ ....._\_. 1 ... _. 840
900 960 Time (msec) Fig. 1. Clumping of successes in transmitter release. Intracellular recording of 480 consecutive responses to nerve stimulation at 0.5/sec. Some of the stimuli caused release of transmitter quanta (successes) while others did not (failures). Note that many of the successes come in groups (see text). Ringer solution with 0-2 mM-CaCl2 and 1 mM-MgCl,. Mean quantal content 0-27. 17-2
H. MEIRI AND R. RAHAMIMOFF
516
produced an e.p.p. (successes), while 363 stimuli evoked no e.p.p. (failures). Hence the probability of having a success is p = I117/480 = O-244 and the probability of having a failure is 363/480 = 0-756. As a first approximation one can estimate that the probability of having four or five consecutive successes is very low (p4 is 0-00354 and p5 is 0-0086; the probability of having four successes only in a row is even A 0-8
Expt. 1 m=0-35
/*
04 10
0-8
Expt. 2
20
30
40
50
60
70
80
90
100
110
30
40
50
60
70
80
90
100
110
50660
8
9
0
1
50
80
90
100
110
=0-98.'
0
10
12
20
Expt-3
08-
10 20310
0-8 r
08-
10
20
30
40
60
70
Time (sec)
8Expt. 5m=15-6 8 4
02
0~~~~~~~~~~~~~~~~~~~~~~~~~~ 30 40 50 60 10 20 70
80
90
100
110
Expt.76 m=2595
513
With 7 text-figure8 Printed in Great Britain
CLUMPING AND OSCILLATIONS IN EVOKED TRANSMITTER RELEASE AT THE FROG NEUROMUSCULAR JUNCTION By HALINA MEIRI AND R. RAHAMIMOFF From the Department of Physiology, Hebrew University-Hadassah Medical School, P.O. Box 1172, Jerusalem 91000, Israel
(Received 31 May 1977) SUMMARY
1. Time series analysis of evoked transmitter release was performed at the frog neuromuscular synapse. 2. Clumping of end-plate potentials with similar amplitude was found in the time
domain. 3. At low quantal contents periodic oscillations were observed with a period of 14 sec. 4. Clumping and oscillations are phenomena of presynaptic origin. 5. The results are explained on the hypothesis that periodic fluctuations occur in Ca concentration inside the presynaptic nerve terminal. INTRODUCTION
Release of the neurotransmitter at the neuromuscular junction is a process subject to probability (Fatt & Katz, 1952; del Castillo & Katz, 1954; Martin, 1955; Boyd & Martin, 1956; Wernig, 1972; Zucker, 1973). The occurrence of the miniature end-plate potentials (m.e.p.p.s) is at random intervals and the time of their appearance cannot be predicted. Similarly, the number of quanta (quantal content, m) that form the end-plate potential (e.p.p.) fluctuates randomly from trial to trial. The amount of transmitter liberated by the nerve impulse seems to reflect an interplay between extracellular and intracellular factors which act on presynaptic membrane. These factors include the concentration of calcium ions in the extracellular medium ([Ca],) and inside the terminal ([Ca]i), the polarization of the nerve membrane and the metabolic state of the nerve terminal (cf. Katz, 1969; Rahamimoff, Erulkar, Alnaes, Meiri, Rotshenker & Rahamimoff, 1976a). If these factors are constant in time, it is expected that transmitter release will fluctuate in a completely random fashion. However if one or more of these factors varies with time, then the random fluctuations will be superimposed on the underlying variations, resulting in an increased 'order' (in the statistical sense). To examine whether such an 'order' exists, a time series analysis (Kendal, 1976) of evoked transmitter release was performed on a long series of e.p.p.s elicited at a constant frequency. It is reported that there is a positive correlation between successive members of the series and under appropriate experimental conditions periodic oscillations can be observed. Some of the experimental results were reported in brief (Rahamimoff, Meiri & Erulkar, 1976 b). T7
P HY
278
514
H. MEIRI AND R. RAHAMIMOFF
METHODS The experiments were performed on the sartorius nerve muscle preparation of the frog Rana ridibunda. The preparation was bathed in a Ringer solution with variable concentrations of Ca and Mg ions; the solutions were kept iso-osmotic by corresponding changes in the concentration of Na ions. Conventional electrophysiological methods were used for intracellular recording. The nerve was typically stimulated at the rate of 0-5/sec and 300-1250 responses were recorded. The e.p.p.s were photographed, measured and analysed by a number of FORTRAN iv programs with MACRO ASSEMBLER subroutines on the PDP15/78 digital computer of the Hebrew University Medical School.
Statstical method The statistical methods used in this work are described in detail in Kendall (1976). Here only a brief account is given. (1) Turning point In a series of fluctuating numbers a turning point appears whenever a member of a series is bracketed by two other members which are either smaller or larger. At least three numbers are needed to form a turning point; out of six possible permutations of three numbers, only four will include a turning point. Hence, if the numbers are in a random order, the probability of having a turning point is two out of three. If there are n numbers in a series which is random and there is no interdependence between the numbers, then the number of expected turning points (Ses) is:
.p= j(n-2).
(1)
If there is a positive interdependence between the members of the series (for example, if there is a clumping of e.p.p.s of similar amplitude), then the observed number of turning points (Sob) will be less than Sep, and the opposite for a negative interdependence. An obvious source for reduction in Sobs is the non-stationarity of the release process. Therefore each series was checked for drifts, by performing a regression analysis on the series of the e.p.p.s (e.p.p. amplitude against time). When the series showed a significant non-zero slope on linear regression, it was discarded. On the basis of the turning points the length of phase was calculated. A phase is defined as the distance between two successive turning points. For a phase with a length of d, at least d + 3 numbers are required. In a completely random series composed of n numbers there are (n - d -2) elements of d + 3, so the expected number of phases with a length of d is: 2(n-d-2) (d2+3d+1) (2
(d+3)! If there is a positive interdependence between the members of the series, then the number of short ds will be less and the number of long ds will be more than predicted by Eqn. 2.
(2) Autocorrelation To check whether deviation from complete randomness shows periodicity, an autocorrelation was performed. Correlation coefficients (r) were estimated from various lags between the members of the series (see eqns. 3.35 and 3.36 presented by Kendall, 1976).
(3) Power spectrum The power spectrum of the series of e.p.p.s amplitudes was calculated by the Fourier transformation of its autocorrelation. The fast Fourier computer programs FFT and SHU supplied by Digital Equipment Corporation were used, and the spectrum was smoothed by convolution of the Fourier transform with the Hann's smoothing window.
OSCILLATIONS IN TRANSMITTER RELEASE
515
RESULTS
Clumping Most experiments were performed in a Ringer solution containing 0.2-0-6 mM-Ca. Below 0-2 mm-Ca there was practically no evoked release and above 0*6 mM-Ca, there were usually twitches. Fig. 1 shows an experiment performed in a medium containing 0-2 mM-[Ca]. and 1 mm-[Mg].. The nerve was stimulated once every 2 see and the first 480 responses (out of 1000) are illustrated. In this section of the experiments 117 nerve stimuli 08
0-8
E
60
120
0-8 r
180
240
0-8 -
300
360
-
JiL-JL i
0.4
' 08e
420
480
540
600
660
720
A
-X
08
0-8
-
-
0-40 . .. 1V . _ 1 ~~~~~
0 8t
780
.\_._.J \ ....._\_. 1 ... _. 840
900 960 Time (msec) Fig. 1. Clumping of successes in transmitter release. Intracellular recording of 480 consecutive responses to nerve stimulation at 0.5/sec. Some of the stimuli caused release of transmitter quanta (successes) while others did not (failures). Note that many of the successes come in groups (see text). Ringer solution with 0-2 mM-CaCl2 and 1 mM-MgCl,. Mean quantal content 0-27. 17-2
H. MEIRI AND R. RAHAMIMOFF
516
produced an e.p.p. (successes), while 363 stimuli evoked no e.p.p. (failures). Hence the probability of having a success is p = I117/480 = O-244 and the probability of having a failure is 363/480 = 0-756. As a first approximation one can estimate that the probability of having four or five consecutive successes is very low (p4 is 0-00354 and p5 is 0-0086; the probability of having four successes only in a row is even A 0-8
Expt. 1 m=0-35
/*
04 10
0-8
Expt. 2
20
30
40
50
60
70
80
90
100
110
30
40
50
60
70
80
90
100
110
50660
8
9
0
1
50
80
90
100
110
=0-98.'
0
10
12
20
Expt-3
08-
10 20310
0-8 r
08-
10
20
30
40
60
70
Time (sec)
8Expt. 5m=15-6 8 4
02
0~~~~~~~~~~~~~~~~~~~~~~~~~~ 30 40 50 60 10 20 70
80
90
100
110
Expt.76 m=2595
