(Received 15 June 1973)

Transcription

1 J. Phyeiol. (1974), 236, pp With 5 text-fighurem Printed in Great Britain STOCHASTIC PROPERTIES OF SPONTANEOUS TRANSMITTER RELEASE AT THE CRAYFISH NEUROMUSCULAR JUNCTION BY IRA COHEN, HIROSHI KITA AND WILLIAM VAN DER KLOOT From the Department of Physiology and Biophysics, Health Sciences Center, State University of New York, Stony Brook, New York 1179, U.S.A. (Received 15 June 1973) SUMMARY 1. Miniature excitatory junctional potentials (min.e.j.p.s) were recorded with an intracellular electrode from the adductor muscle ofthe dactyl of the first or second walking leg of the crayfish, Orconectes virilis. 2. The intervals between the min.e.j.p.s were compared to the exponential prediction by five goodness of fit tests. The results indicate that the intervals are not exponentially distributed. 3. The autocorrelogram of intervals shows that the intervals are unlikely to be independent. 4. A stochastic analysis that includes the power spectrum of intervals, the variance-time curve, and the ln-survivor curve suggest that there is a clustering of min.e.j.p.s. The results are similar to those on the frog neuromuscular junction. 5. An autocorrelogram of the min.e.j.p. amplitudes suggests that sizes are not independently distributed. 6. These results, which are similar to those previously reported from the frog neuromuscular junction, support the use of the branching Poisson process as a theoretical model for the stochastic properties of spontaneous quantal release of transmitter. INTRODUCTION Dudel & Kuffler (1961) measured the intervals between 24 miniature excitatory junctional potentials (min.e.j.p.s) recorded from a crayfish muscle. They compared the distribution of the intervals with the predictions of the equation n=n t exp (-tlt), (1)

2 364 IRA COHEN AND OTHERS where n is the number of intervals observed with a duration between t and t + At, N is the total number of intervals and T is the mean interval. Visually, there was a good fit between the predictions of eqn. (1) and their data so they concluded that the min.e.j.p.s appear in a random sequence without obvious interaction between events. This conclusion was widely accepted because it agreed with results from the frog neuromuscular junction (Fatt & Katz, 1952). Our results suggest that in the frog spontaneous releases are not independent and that the intervals between events do not fit a Poisson distribution (Cohen, Kita & Van der Kloot, 1973 a, b). Therefore we have reinvestigated the timing of min.e.j.p.s in the crayfish. METHODS The experiments were performed on the adductor muscle of the dactyl of the first or second walking leg of the crayfish, Orconectes virilis. Usually the outer surface of the muscle was exposed by removing the exoskeleton. The isolated leg was clamped in a Lucite chamber. The bathing solution, modified from van Harreveld (1936) contained 21 mm-nacl, 5-25 mm-kcl, 2-8 mm-mgcl2, 14- mm-cacl2, and 1- mm-n-tris (hydroxymethyl)methyl-2-aminoethanesulphonic acid (TES) buffer at ph = 7-5. One set (C was buffered at ph = 6- with 1 mm-1,3-bis[tris-(hydroxymethyl) methylamino] propane. The experiments were performed at room temperature ( Recording was accomplished with conventional amplifiers leading to a Brush ink-writing recorder. Micropipettes were filled with 3 M-KC1 and had resistances between 7 and 15 MQ. In most instances, the min.e.j.p.s were recorded beginning several hours after the fibre was impaled to insure maximum stability. In all cases the resting potential was more negative than -7 mv and was essentially unchanged during the recording. The statistical methods and mathematical transformations that are employed are described by Cohen et al. (1973b, c). RESULTS The amplitude distribution of crayfish min.e.j.p.s range from fairly large, perhaps -5 mv in a thin fibre, down to those that are almost submerged in the background noise. To avoid missing events obscured by noise, we established a threshold amplitude well above the noise level and then measured the intervals between the min.e.j.p.s that were clearly above this threshold. The intervals were then tested to see whether the distribution was exponential (Table 1). The measured intervals clearly deviate significantly from the exponential prediction. In one case the same series was measured twice (CDlow CDhIgh), once with a threshold just above the noise level and then again with a threshold 1 mv higher; both series are unlikely to be exponential. The u statistics of the empirical data sets are displayed as Table 2. This statistic estimates the probability that the mean of any set of intervals is

3 CRA YFISH MINB..J.P. TIMING 365 X W4 l Cv 6 O oo 4 C l 1 o 1 m 1 w ;.4 rq 1.4 Ez 1 ID ftb Ca+; m1 Om i6 6,=w o s.m e X c 14 ro.e v.v : aq 6 :-. to o 4H mb t 1 G 1 a ci It X eq ~~~~~~~~~~~~~~~~~~ 4C e PC PH "O. f.. -4 CI.. rm -I. 4 t m o1 I? o V V v v ;V p 9 VVVV B: S I w 3 Ca ~ f.h g 1 1 > t to 6,:4 i'- 6 c w T- > ei aw _- aq t4 CD C r X u. ~ ~ i 11 m P Q

4 366 IRA COHEN AND OTHERS changing with time. The results show that if the series of intervals are generated by Poisson processes the mean of four out of five sets must be changing monotonically with time. Set CA contains 1575 intervals and appears to be stationary in time as determined by the u statistic. It was recorded from a junction impaled about 15 min before recording was begun. The resting potential was -76 mv. This set will be used as a demonstration set for the remainder of the paper. The autocorrelation of intervals for this series appears as Fig. 1. There is an excess of significant autocorrelation coefficients, most of which are positive. Since a trend is unlikely in this data set, the excess of autocorrelation coefficients above the significance limits implies that unlike a Poisson process, the intervals are not independent. The periodogram for this series shows an excess of variance at the low frequencies (Fig. 2). This result would be expected from the autocorrelogram, because the events that are correlated appear to be relatively far apart. Similar spectrums were found for the other data sets. The variance-time curve for the 1575 intervals is shown as Fig. 3; the empirical curve is significantly above the line predicted for a Poisson process, indicating that there is clustering in the series. The ln-survivor curve for the long crayfish data set shows that there are two components, instead of the single line expected for a Poisson process. The other examples from the crayfish generate similar curves (Fig. 4). As we discussed in detail previously (Cohen et al. 1973b), there are two models that generate an excess of positive autocorrelations, a variancetime curve indicating clustering, and an excess of variance at the low end of the periodogram. First, there is a Poisson process with a mean that is changing in time. Secondly, a branching Poisson process, in which a random primary event is followed by a chance of having one or more subsidiary releases from the same point on the nerve terminal. There is no known way to distinguish between these two possibilities from the interval data alone. Calculated parameters for a branching Poisson model are shown as Table 3. If, however, there are subsidiary releases from the same point on the nerve terminal, the amplitudes of the min.e.j.p.s would not be randomly distributed, since one expects that releases from sites near the recording electrode will generate relatively large min.e.j.p.s. For this reason we calculated the autocorrelations of the min.e.p.p. amplitudes (Fig. 5). There is an excess of autocorrelations outside of the 5 % confidence limits (5 found; 2-5 expected). This lends some support to the branching Poisson model. To check whether the assumptions that lead us to calculate the auto-

5 -12 r CRAYFISH MIN.E.J.P. TIMING 367 C ).i co to C co ). o I I l1l I1. I I '1,i 1. I II I I. I II I. Lag -12L Fig. 1. The autocorrelation between intervals, calculated for set CA for lags 1-5 and displayed as an autocorrelogram. The Poisson expectation is that 2X5 of the fifty autocorrelation coefficients exceed the 95 % by chance significance limits. Set CA shows five significant coefficients, double the Poisson expectation. 6 8 r l/t o Wp Fig. 2. The periodogram of intervals for set CA is shown for lags of 8 (smaller initial value) and 16 (larger initial value). Both spectra show a significant initial peak beyond the 5% by chance confidence limits of the Poisson expectation (shown as the straight line). This type of deviation indicates clustering in the data set. it

6 IRA COHEN AND OTHERS 5 Time (sec) Fig. 3. A variance-time curve of intervals from set CA. The cumulative variance is plotted on the ordinate. Time is the abscissa. The Poisson prediction is the straight continuous line. The empirical result is the curved continuous line. The empirical curve exceeds the Poisson prediction. A variance-time curve of this type indicates clustering. Interval length (sec) Fig. 4. The ln-survivor function for data set CA along with the Poisson prediction. The ln-survivor function shows two phases. An early phase below the Poisson prediction indicates an excess of short intervals, and a later phase above the Poisson prediction indicates a scarcity of longer intervals. This type of hn-survivor function is also found in the frog, and indicates clustering of the spontaneous releases.

7 CRAYFISH MIN.E.J.P. TIMING 369 correlation of amplitudes were reasonable, we selected the high amplitude min.e.j.p.s and counted the number of times in the entire series that a large min.e.j.p. was immediately followed by another large min.e.j.p., when the second following min.e.j.p. was large and so forth. A large min.e.j.p. was defined as one whose amplitude was greater than the mean amplitude x the standard deviation of the amplitudes. The results are summarized for the first 13 intervals in Table 4. There is an apparent excess of large intervals at lags of 8 and of 13 intervals. This is suggestive evidence favouring the branching Poisson model. TABLiE 3. Branching Poisson parameters for empirical data sets Set CA CB CC CD,., E(Z) (sec) E(Y) (sec) E(S) (sec') _ W as C ru tj a) U -75 Fig. 5. An autocorrelogram of amplitudes for the 1576 min.e.j.p.s in set CA. The 5 % by chance limits for the Poisson prediction are depicted as the almost horizontal lines above and below the zero line. The five autocorrelation coefficients that exceed the 5 % by chance expectations are double what would be expected if the amplitudes were distributed independently. DISCUSSION The intervals between min.e.j.p.s recorded from crayfish muscle do not fit the criteria for a Poisson process. If a sufficient number of intervals are examined the distribution of intervals is not exponential; there is an excess of short intervals. Interval durations are not independent of one another.

8 37 IRA COHEN AND OTHERS The transformations of the data are remarkably similar to the results obtained in more extensive experiments on the frog neuromuscular junction. The reasons are detailed in the discussion of the results from the frog (Cohen et al c), we suggest that the min.e.j.p.sare generated by a Poisson process with a mean that oscillates in time, or by a branching Poisson process. The lack of independence of the amplitudes of the min.e.j.p.s gives some support to the branching Poisson model. TABLE 4. The number of large amplitude min.e.j.p.s at different lags following a large amplitude min.e.j.p. No. of large Lag m.e.j.p.s Expected in each interval by chance = x2=22.98,p<5%. A large amplitude min.e.j.p. was defined as one larger than mean+ 1-2 X S.D. of the series. A branching Poisson model also predicts that each stimulation of the motor nerve should generate a number of primary releases, which should be followed by subsidiary. Consequently, stimulation of the motor nerve should increase min.e.j.p. frequency; this is known to occur (Dudel & Kuffler, 1961). A more detailed analysis of this effect could be used to test the branching Poisson model further. This investigation was supported by PHS Research Grant NS 132 from the NINDS. I. C. was supported by training grant GMO 1668 to the New York University School of Medicine. REFERENCES COHEN, I., KITA, H. & VAN DER KLOOT, W. (1973a). Miniature end-plate potentials: evidence that the intervals are not fit by a Poisson distribution. Brain Res. 54, COHEN, I., KITA, H. & VAN DER KLOOT, W. (1973 b). The intervals between miniature end-plate potentials in the frog are unlikely to be independently or exponentially distributed J. Physiol. 236,

9 CRAYFISH MIN.E.J.P. TIMING 371 COHEN, I., KITA, H. & VAN DER KLOOT, W. (1973c). The stochastic properties of spontaneous quantal release of transmitter at the frog neuromuscular junction. J. Physiol. 236, DUDEL, J. & KUIFFLEER, S. W. (1961). The quantal nature of transmission and spontaneous miniature potentials at the crayfish neuromuscular junction. J. Physiol. 155, FATT, P. & KATZ, B. (1952). Spontaneous subthreshold activity at motor endings. J. Physiol. 117, VAN HARREVELD, A. (1936). A physiological solution for fresh-water crustaceans. Proc. Soc. exp. Biol. Med. 34,