Journal of Neurophysiology

Asynchrony of Quantal Events in Evoked Multiquantal Responses Indicates Presynaptic Quantal Interaction

Maria Bykhovskaia, John T. Hackett, Mary Kate Worden

Abstract

Asynchrony of quantal events in evoked multiquantal responses indicates presynaptic quantal interaction. We have analyzed the possibility of quantal interactions by inspecting action potential-evoked postsynaptic multiquantal responses recorded extracellularly from the lobster neuromuscular junction. These recorded responses were compared with simulated multiquantal responses constructed from statistically independent quantal events. The simulated multiquantal responses were generated by random superposition of single quantal responses aligned according to the timing of the action potential. The methods of analysis consisted of 1) the comparison of quantal contents obtained from direct counting or by measuring of the size of the responses and 2) the analysis of distributions of quantal latencies. This analysis revealed a large error in the detection of quantal events for responses simulated with no quantal interaction. In contrast, very few errors in quantal detection were made in the analysis of experimental recordings. Latency histograms of recorded responses demonstrate that the proportion of late quantal events (those with latencies of ≥5 ms) increased as a function of quantal content. This shift in latency histograms was not observed for simulated responses. Our interpretation is that quanta interact presynaptically to cause asynchrony of quantal events in evoked responses.

INTRODUCTION

Neurotransmitter is released from motor nerve endings in preformed packets, or quanta. The question of whether there might be interaction between quantal events has been studied extensively both for spontaneous and evoked responses.

In initial studies the distribution of intervals between miniature endplate potentials at frog neuromuscular junction was found to be Poissonian (Fatt and Katz 1952), suggesting that at physiological conditions no interaction occurs between quantal events. This result was confirmed by Rotshenker and Rahamimoff (1970). However, the latter study also showed that, when the concentration of extracellular Ca2+ is increased, statistical interdependence of spontaneous events is observed such that a quantum is likely to be closely followed by others. A subsequent analysis of spontaneous events at rat neuromuscular junctions showed a significant deviation from the Poissonian distribution (Hubbard and Jones 1973), which was attributed to interdependence of spontaneous quantal events. More sophisticated tests applied to spontaneous events at frog and crayfish neuromuscular junctions (Cohen et al. 1974a,b) demonstrated that intervals between spontaneous quantal events can be described by a branching Poissonian process, suggesting that spontaneous release of a single quantum is likely to be followed by several successive releases. Recently, long-range correlations in the occurrences of spontaneous quantal events were discovered (Lowen et al. 1997).

Examination of quantal latencies in evoked responses recorded intracellularly at frog neuromuscular junctions (Barrett and Stevens 1972) revealed that quantal events in a multiquantal response are likely to be independent. In contrast, analysis of quantal latencies of focal extracellular recordings in the same preparation showed that quantal events unpreceded by early releases sometimes occur with a higher probability than preceded events, suggesting that the first quantal event in an evoked response may inhibit the subsequent events (Barrett and Stevens 1972). Bennett and Robinson (1990) developed a model incorporating the possibility that early quantal releases may inhibit later releases. However, analyses of latencies of the first and the second quantal events in multiquantal responses found no evidence that an early quantal release inhibits other releases (Baldo et al. 1986; Thomson et al. 1995).

There is no direct evidence that favors the hypothesis of independent quantal release (Stevens 1993), and the question of whether interaction exists between quantal events in evoked responses is still open. One way to test the hypothesis of quantal interaction is to investigate how quantal latencies change as quantal content increases. To investigate quantal latencies in evoked multiquantal responses it is necessary to 1) optimally detect quantal events in evoked responses, as can be obtained in focal extracellular recording, and to 2) collect a sufficient number of multiquantal responses. Quantal output can be conveniently modulated by frequency facilitation under steady-state conditions (Wojtowicz et al. 1994; Worden et al. 1997; Zucker 1973).

One important issue complicating studies of quantal interaction is the question of whether quantal detection is sufficiently accurate, especially when quantal content is large. Scoring errors in quantal detection may occur if individual quanta are released simultaneously or nearly simultaneously in a multiquantal response. A good agreement between the values of the quantal content obtained by the method of direct counts and by charge measurements (Cooper at al. 1995) suggests that this problem is minor as long as quantal content is low. However, as the quantal content increases, it is necessary to estimate possible errors in the method of direct counts caused by synchronous quantal releases in multiquantal responses.

To test the hypothesis that quantal releases are independent in the evoked response and to evaluate the accuracy of the method of direct quantal counts over a range of quantal outputs, we examined postsynaptic responses evoked by nerve stimulation during frequency facilitation over a range of stimulation frequencies. These data were compared with simulated multiquantal responses in which quantal events occurred independently.

A preliminary account of some of these findings has appeared (Bykhovskaia et al. 1997).

METHODS

Extracellular recordings and frequency facilitation

Lobster (Homarus americanus Milne Edwards) walking legs were dissected in chilled saline containing (in mM) 462 NaCl, 16 KCl, 26 CaCl2, 8 MgCl2, 11 glucose, and 5 HEPES buffer adjusted to pH 7.4. The dorsal surface of the dactyl opener muscle in the propopodite segment of the leg was exposed by removing the overlying exoskeleton and muscle. An inhibitory axon and an excitatory axon innervating this muscle run separate courses in the large and small nerves, which were exposed in the meropodite; the nerves could be visualized with a dissecting microscope. After dissection, the preparation was pinned to Sylgard in the bottom of a chamber maintained at 6°C with a refrigerated circulator. To minimize nerve-evoked contractions, the distal cut end of the central apodeme of the dactyl opener muscle was attached to a thread, and the muscle was stretched. By using this method, it was possible to stimulate at frequencies up to 15 Hz without movement artifacts.

Presynaptic action potentials were elicited by electrically stimulating the excitatory nerve with a suction electrode. Synaptic responses in the central region of the dactyl opener muscle were recorded extracellularly with saline-filled patch pipettes of 12- to 25-μm diam (Dudel and Kuffler 1961). Focal recordings were obtained by 1) lowering the patch pipette to the surface of the muscle in regions where fine branches of the nerve could be visualized under a dissecting microscope and 2) applying gentle suction to minimize the leak currents, thus improving the signal-to-noise ratio. Postsynaptic currents corresponding to quantal release were amplified by a current-to-voltage converter (Axopatch-1D, Axon Instruments; Foster City, CA). The postsynaptic current responses were not recorded under voltage-clamp conditions.

Recordings were digitized at 50 μs/sample and analyzed with original software for quantal detection (Bykhovskaia et al. 1996). The limit of resolution of the algorithm (0.5–1 ms) is the same as the limit of resolution with visual inspection (Zucker 1973). In addition, the charge of each response was measured by calculating the area under the curve of the current trace from the beginning of the response (see Bykhovskaia et al. 1996) to the point where the current trace returned to the baseline.

Stimulus trains consisting of ≥600 stimuli were delivered at frequencies from 1 to 10 Hz. For each data set initial responses were discarded, and the quantal content was tested for stationarity (Provan and Miyamoto 1993; Worden et al. 1997). The criterion for stationarity within a subgroup of 100 trials was that the slope of the regression of the quantal content as a function of trial did not differ from 0 at a level of significance of 0.05. The criterion for stationarity between subgroups was that quantal content of each subgroup did not differ from the quantal content of the data set on the level of significance of 0.05. The rate of spontaneous releases (∼1 quantum/min) was found to be negligible and therefore does not affect the measurements of evoked quanta.

Latency analysis

The latency of each quantal event was measured as the time from the negative peak of the action potential to the peak of the quantal event (Fig. 1). In each experiment, the latencies of all quantal events occurring within 15 ms after the action potential were determined.

Fig. 1.

Example of a multiquantal postsynaptic response. Quantal latencies are measured from the peak of the action potential (A.P.) to the peaks of quantal events (horizontal arrows). The recording is from experiment I at 10 Hz.

For each data set, quantal latencies were binned in sizes of 1 or 0.5 ms (the resolution of quantal detection) to avoid the possibility that two quantal events occurring in a single postsynaptic response might have latencies falling in the same bin. In each histogram data points show the number of postsynaptic responses exhibiting quantal events with a given latency divided by the total number of responses (nonfailures). The bars of each histogram will not necessarily add to unity but instead will add to the average number of events per response because the number of quantal events is related to the number of responses.

The numbers of early and late quantal events per response were calculated by adding the number of responses in bins corresponding to 2, 3, and 4 ms and 5, 6,7, 8, and 9 ms, respectively. The resulting number is the total number of early (or late) events divided by the total number of responses (nonfailures).

Simulation of multiquantal responses

For each experiment, all the single quantal responses with a single peak and no inflections were selected from the data set corresponding to the lowest stimulation frequency tested. The lowest stimulation frequency was used to minimize the possibility that a multiquantal response was mistaken for a single quantal response. Double and triple responses were generated as follows: 1) in each experiment, 200 pairs and 200 triplets were randomly chosen from the data set of single quantal responses; 2) in each pair or triplet the traces of single quantal responses were aligned according to the timing of peak of the action potential and added (Fig.2). Thus the resulting simulated multiquantal responses were the result of statistically independent quanta. The simulated responses were analyzed with the same computer algorithm used to detect recorded responses (Bykhovskaia et al. 1996).

Fig. 2.

Double quantal response formed from statistically independent quantal events. A: 2 single quantal responses (- - -) aligned so that the action potential peaks (A.P.) appear at the same point in time. B: simulated double quantal response resulting from the addition of two single quantal responses shown inA.

RESULTS

Estimation of errors in scoring quantal counts

Quantal content increased as a function of stimulation frequency at four recording sites where frequency facilitation was elicited by repetitive stimulation (Table 1). At the highest stimulation frequencies, large numbers of higher-order (>2 quanta) multiquantal responses were observed (Table 1) in agreement with previous studies (Cooper et al. 1995;Wojtowicz et al. 1994; Worden et al. 1997; Zucker 1973). If the interval between quantal events is less than the limit of resolution, two or more quantal events may be scored erroneously as a single event, and quantal content will be underestimated. This error should be largest in data sets collected at high stimulation frequencies, where a relatively large proportion of responses is multiquantal.

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Table 1.

Distribution of quantal content for postsynaptic responses recorded at different stimulation frequencies and for simulated double and triple quantal responses

To determine the number of scoring errors that may occur during the analysis of evoked release, we generated for each experiment a population of multiquantal responses (see methods) simulating a release process in which several quanta are released independently from the presynaptic terminal in response to a single stimulus. Simulated and recorded multiquantal responses were compared in each of the four experiments (I–IV).

The automated analysis (Bykhovskaia et al. 1996) of simulated responses shows that the number of detected quantal events is grossly underestimated (Table 1). In the experiments I, III, and IV the average quantal content is scored as 1.5–1.6 (instead of 2) for double responses and as 2.0–2.2 (instead of 3) for triple responses. The scoring errors in experiment II are even larger because of a lower signal-to-noise ratio in that experiment. These scoring errors are much larger than those predicted by Zucker (1973), who estimated that only 9% of double responses should be scored as single responses.

This discrepancy could be explained if the distribution of quantal latencies observed in the crayfish study (Zucker 1973) differed from that obtained at the lobster neuromuscular junction. However, this possibility can be discounted because the observed distribution of quantal latencies for single quantal events in recordings from lobster (Fig. 3) is very similar to that obtained in the crayfish and used in Zucker’s (1973)calculations (his Fig. 2F). Both distributions show a pronounced peak at ∼4.5 ms, with the earliest quantal events having latencies of ∼3 ms and a small number of late quantal events having latencies of 7–10 ms. Rather inspection of Zucker’s (1973)calculations reveals that his strategy for estimating the probability that two quanta will be released simultaneously is flawed and that the corrected theoretical estimation is 40–60% (see ).

Fig. 3.

Quantal latency distributions for single quantal responses. Symbols indicate the proportion of quantal events observed at stimulation frequencies of 1 Hz in experiments I–III and 2 Hz in experiment IV.

Thus, if quanta are released independently from the presynaptic terminal, approximately one-half of the double quantal responses will be scored erroneously as singles, and a great majority of the triple quantal responses will be scored erroneously as doubles or singles. As the number of higher-order multiquantal responses increases as a function of stimulation frequency (Table 1), quantal size should appear to increase as a function of stimulation frequency. However, amplitude histograms reported in previous studies show that the size of single quantal responses is frequency independent (Bykhovskaia et al. 1996; Worden et al.,1997; Zucker 1973).

As an additional test of the accuracy of quantal scoring, charge measurements (integration of current traces, see methods) of experimental and simulated data sets were compared. Two data sets with similar apparent quantal content were chosen from experiment II, the responses recorded at 5-Hz stimulation (scored quantal content is equal 1.76) and the simulated population of triple quantal responses (scored quantal content is equal 1.68, see Table 1). Figure4 A illustrates the averages of all single, double, triple, and quadruple quantal responses recorded at 5 Hz as well as the average of all the responses including failures (dotted line). The charge measurements of the average double, triple, and quadruple quantal responses were found to be equal to 1.93, 2.94, and 4.19, respectively, of the charge measurement of the average single quantal response. The excellent agreement between the charge measurements and the number of quantal events detected in double, triple, and quadruple responses (2, 3, and 4, respectively) suggests that the quantal content is not underestimated. This conclusion is supported by the observation that the charge measurement of the combined average of all failures, single, double, and triple quantal responses (dotted line, Fig. 4 A) is equal to 1.74 of the charge measurement of the average single response, in very close agreement with the value of the quantal content obtained by direct counts (1.76; Table 1).

Fig. 4.

Comparison of averaged currents for experimentally recorded and simulated postsynaptic responses. A: average currents for single (1), double (2), triple (3), and quadruple (4) responses recorded in experiment II at 5-Hz stimulation. The number of responses averaged was 217, 266, 118, and 22 responses, respectively. The average current for all 683 postsynaptic responses (including failures) at 5-Hz stimulation is shown by a dotted line. B: averaged currents for responses scored as singles, doubles, and triples in the analysis of 200 simulated triples. The number of responses averaged was 92, 70, and 38, respectively (see Table 1).

For comparison, similar analysis was performed for the data set consisting of simulated triples (experiment II). The average traces of the triple responses scored as singles, doubles, and triples are shown in Fig. 4 B. All the three traces are similar, which is not surprising, given that three quantal events occur in all the responses. Charge measurements of the average observed single, double, and triple quantal responses differ by <5%. Thus, for the simulated data sets, the quantal content obtained by charge measurements (1.00 and 1.04 for double and triple quantal responses, respectively) strongly disagrees with the quantal content determined by direct quantal counting (1.57 and 1.73 for double and triple quantal responses, respectively, Table1).

Thus comparison of quantal counts and charge measurements for experimental and simulated data sets demonstrates that quantal events are likely to be scored correctly in experimental recordings, but substantial scoring errors would result if the quantal events in the multiquantal responses occurred independently. We therefore considered the possibility that the timing of individual quantal events in multiquantal responses is sufficiently asynchronous to permit direct quantal counts with a high degree of accuracy.

Indeed, if quantal releases in multiquantal responses were statistically independent, then the average time course of recorded responses would be similar to the average time course of simulated responses. (The average time course of simulated responses is identical to the average time course of single quantal responses because simulated responses are obtained by random superposition of single quantal responses.) However, for the data sets with a majority of multiple responses the average time course is broader than the time course of single quantal responses (Fig.5). To investigate quantal asynchrony we examined the distribution of quantal latencies in multiquantal responses.

Fig. 5.

Average time course of the responses recorded at 10 Hz (solid lines) compared with average time course of single quantal responses (dotted lines) in the 4 experiments (I–IV). The amplitudes are normalized. Numbers of responses averaged in each trace are given in Table 1.

Distribution of quantal latencies

Quantal latency distributions were examined as a function of average quantal content for all four experiments. Figure6 A and Table2 show latencies of all the quantal events detected in nonfailure responses. (The bars of the histograms do not add to unity but do add to average quantal content for nonfailure responses because all the events in the responses are considered.) The peak of the quantal latency distribution for experiment I (Fig.6 A) shifts to longer latencies as stimulation frequency increases, from 4–5 ms at 1 Hz to 6–7 ms at 10 Hz. In addition, the number of responses with late quantal events (those with latencies of ≥4.5 ms) increases as a function of stimulation frequency (Fig. 6, Table 2). In contrast, the number of responses with early quantal events (those with latencies of <4.5 ms) is frequency independent (Fig. 6, Table 2). Similar results were observed in three other experiments (Table 2). In contrast, different results were obtained from the analysis of multiquantal responses simulated under the assumption that quantal events occur independently. Quantal latency distributions for simulated double and triple quantal responses have a peak at 5 ms and are similar in shape to the distribution of the single quantal responses from which the simulated multiquantal responses were generated (Fig. 6 B). In addition, the numbers of responses with early or late quantal events both increased (Table 2) as the actual quantal content increased from 1 to 3 and the observed quantal content increased from 1 to 1.5 (see Table 1).

Fig. 6.

A: quantal latencies from experiment I. Symbols indicate the proportion of responses containing a quantal peak with a given latency. Different stimulation frequencies are indicated with 1 Hz, columns; 2 Hz, squares; 3 Hz, circles; 4 Hz, up triangles; 5 Hz, down triangles; 7 Hz, diamonds; 10 Hz, stars. B: quantal latencies from single quantal responses (columns) and from simulated populations of double (squares) and triple (stars) quantal responses (experiment I). Data are normalized by dividing by the total number of responses (nonfailures); therefore bars of the histograms add to average quantal content for nonfailure responses.

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Table 2.

Number (%) of recorded and simulated (doubles and triples) responses containing quantal events with given latencies

To test the statistical significance of the increase in the number of late quantal events observed in the experimental recordings, regression analysis was applied to the relationship between the number of the early and late events and the quantal content (Fig.7, Table3). For all the four experiments (Table 3) a statistically significant increase in the number of late events (P > 99%) and no significant trend in the number of early events were observed. In contrast, the simulated data sets demonstrated some increase in the number of both early and late events (Fig. 7), which is significant in most of the cases (Table 3). For three of the four simulations, the increase (slope of the regression b, Table 3) in the number of early events is stronger than the increase in the number of late events. In summary, simulated data sets demonstrate comparable trends for the number of early and late events, whereas experimental data sets show strong increase in the number of late events and no trend in the number of early events. These results clearly indicate that the increase in the quantal content caused by repetitive stimulation appears as an addition of later quanta, which is not the case for the simulated data sets.

Fig. 7.

Relationship between the number of early (●, ○) and late (▴, ▵) quantal events and average quantal content for recorded (experiment I, ●, ▴) and simulated (○, ▵) responses. ———: fit by linear regression (see Table 3).

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Table 3.

Regression of the number of responses with early and late quantal events on the quantal content

A possible explanation for the frequency dependent increase in the number of late quantal events observed in experimental recordings is that as the quantal content (or stimulation frequency) increases the time necessary for vesicle release becomes longer. To test this possibility, we compared specifically the latencies of the first, the second, and the third successive quantum in each postsynaptic response over a range of stimulation frequencies. It was found that the shapes and the peaks of the resulting latency distributions do not depend on stimulation frequency (Fig. 8). Thus the increase in the proportion of late events with the frequency facilitation is not due to the prolongation of the release process. Rather it must be due to the two factors, 1) the number of multiquantal responses increases as the stimulation frequency increases (Table 1) and 2) quantal events do not occur synchronously in a multiquantal response.

Fig. 8.

Quantal latency distributions corresponding to the first (A), second (B), and third (C) quantal event in multiquantal postsynaptic responses recorded in experiment IV. Symbols represent different stimulation frequencies: 2 Hz, bars; 4 Hz, squares; 5 Hz, triangles; 10 Hz, stars. Data are normalized by dividing by the total number of multiple responses.

It follows that, if several quanta are released in response to a stimulus, some of them will appear very late. This situation is illustrated in Fig. 1 (experiment I) where the latencies of the two latest events are 10.5 and 14.3 ms. At the same time, the longest latency observed in experiment I in responses where a single quantum is released is <10.5 ms (Fig. 3). Therefore the appearance of these two late events in the same trace would be improbable if the events were independent.

In summary, analyses of the quantal latencies and average currents of simulated data sets show very different results from analysis of experimental data sets, indicating that the simulation fails to generate multiquantal responses with properties identical to those recorded. Because the simulated data set was generated under the assumption that individual quanta are independently released from the presynaptic terminal, these results suggest that the assumption underlying the simulation is false and quanta may interact.

DISCUSSION

The results of our study show that, in evoked multiquantal responses, quantal events occur asynchronously in such a way that each event appears to be detectable, which makes the method of direct quantal counts accurate. This asynchrony is fortuitous for studies that rely on directly counting quantal events at crustacean neuromuscular synapses (Cooper et al. 1995; Wernig 1972; Wojtowicz et al. 1994; Worden et al. 1997; Zucker 1973), for if occurrences of quantal events were statistically independent the limited resolution of quantal detection would introduce sufficiently large errors in quantal scoring that the determination of quantal content would be unreliable.

During frequency facilitation the proportion of responses with early quantal events remains constant as stimulation frequency increases, whereas the proportion of responses with late quantal events increases (Figs. 6 A and 7; Tables 2 and 3). Therefore increases in quantal content at higher stimulation frequencies are manifested entirely as an increase in the number of late quantal events. This finding supports the initial observation by Katz and Miledi (1965) that “the contribution of late units became more marked when the quantal content of the response was raised.”

Possible interpretations of this finding could be that during facilitation the process of releasing of a vesicle is prolonged or that facilitation has some generalized effect leading to late releases. However, frequency facilitation does not alter latency distribution of the first quantum in the response (Fig. 8 A). This finding is in agreement with previous studies demonstrating that synaptic delay (the delay between the stimulus and the beginning of the response) is not altered by paired-pulse facilitation (Parnas et al. 1989), by long-term facilitation (Wojtowicz et al. 1988), nor by Ca2+ modulations (Arechiga et al. 1990). Similarly, latencies of the second or the third quantum in the response do not depend on stimulation frequency (Fig. 8,B and C). These findings indicate that the process of releasing of a quantum from a nerve terminal is neither prolonged nor delayed by frequency facilitation. Instead the late events evoked by frequency facilitation (Fig. 6 A) correspond to successive quantal releases.

Thus some presynaptic mechanism of quantal interaction prevents synchronous releases.

This quantal interaction does not mean a cause-effect relationship between quantal releases. Also, we do not hypothesize that earlier quantal releases may affect the probabilities of later quantal releases, as was considered earlier (Baldo et al. 1986; Barrett and Stevens 1972;Thompson et al. 1995). Our results do not show any evidence for facilitatory or inhibitory interactions.

The mechanism of the quantal interaction is unclear, for an unresolved issue is whether a single release site may release several quanta in response to a single stimulus. The monoquantal hypothesis (Katz 1962; Korn et al. 1982;Vere-Jones 1966; Zucker 1973) states that a single presynaptic impulse evokes the release of only one quantum from each active release site. Then, to explain how quantal events rarely occur synchronously in the postsynaptic response, it must be suggested that release sites interact in such a way that a delay occurs between the releases. Alternatively, it may be suggested that a stimulus evokes the successive release of a number of quanta from a single release site. In other words, synchronous releases are prevented because quanta compete for the release site.

If the latter hypothesis is valid and quanta can be released in succession from a single site, what limits the amount of release? Obviously, it cannot be the number of vesicles near the active zones, which is on the order of hundreds or thousands. One suggested possibility is that the limiting factor is the number of release sites (Wojtowicz et al. 1994; Zucker 1973). The other possibility is that a small releasable pool of properly activated quanta exists, which is limited by the rates of exchange with the total store of vesicles around the active zones. This model was shown to provide a good quantitative description of the increase in quantal output during frequency facilitation (Bykhovskaia et al., 1999; Worden et al. 1997). Two reasons may exist that release sites do not limit neurosecretion: 1) the number of release sites is larger than the number of vesicles activated, as it was assumed by Worden et al. (1997), or 2) multiple quanta can be released from a release site in response to a stimulus. The results of this study favor the hypothesis of multiple releases.

It is of interest to compare our concept with the one developed by Stevens’ group for quantal neurosecretion at hippocampal synapses (Stevens and Wang 1995). Their results show that a readily releasable pool of quanta (Rosemund and Stevens 1996) exists at a single active zone (Schikorski and Stevens 1997). Only one quantum at a time can be released, and the refractory period for quantal releases is ∼5–10 ms (Stevens and Wang 1995). Consequently, the release probability is proportional to the size of the releasable pool (Dobrunz and Stevens 1997).

Similarly, the study of frequency facilitation at the lobster neuromuscular junction demonstrated that a releasable pool of quanta limits neurosecretion and facilitation (Worden et al. 1997), whereas this study suggests that these releasable quanta are released from a single release site and compete for it. The refractory period for the quantal release can be estimated as the difference between the most probable timings of the second (5 ms, Fig.8) and the first (4 ms, Fig. 8) events or the third (5.5 ms, Fig. 8) and the second events. Thus the refractory period for the quantal releases at the lobster neuromuscular junction is ∼0.5–1 ms. This small (compared with hippocampal synapses) refractory period enables multiple releases in response to a stimulus.

Acknowledgments

This work was supported by National Science Foundation Grant IBN-9634400, National Institute of Health Grants RR1-0481 and R03 TW-00893-01, and by the Thomas F. Jeffress and Kate Miller Jeffress Memorial Trust.

Footnotes

  • Address for reprint requests: M. Bykhovskaia, Dept. of Molecular Physiology and Biological Physics, University of Virginia Health Sciences Center, P. O. Box 10011, Charlottesville, VA 22906-0011.

  • The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked “advertisement” in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

Appendix

The strategy for estimating the probability that two quanta will be released simultaneously applied by Zucker (1973) was1) to determine the minimal interval of time (Δt) in which two nearly overlapping quantal events can be just barely distinguished in the postsynaptic response;2) to subdivide the time course of the postsynaptic response into bins equal to Δt; 3) for each bin to calculate the probability (c i) that the synaptic delay is between iΔt and (i + 1)Δt [c i equals the number of responses with quantal latencies betweeniΔt and (i + 1)Δt divided by the total number of responses]; and4) to calculate the probability that two quanta will appear in the same time bin as P = Σci 2. This strategy results in a gross underestimation of P because a quantum with a latencyt will not be resolved from all other quanta that have latencies from t − Δt tot + Δt, i.e., in the interval equal to 2Δt. At the same time, Zucker’s strategy falsely assumes that a quantum with a latency t will be resolved from all the others with latencies outside a time interval equal to Δt, i.e., outside of the range fromiΔt to (i + 1)Δt, where i is such thatiΔt < t < (i + 1)Δt.

Rather than subdividing the entire time course of the postsynaptic response into bins of Δt, the correct strategy is to use all the available temporal resolution. The probability density of quantal latencies can be calculated asF(t) =N(t)/N, whereN(t) is the number of events with latencies equal to t and N is the total number of quantal events. The probabilityp(t, Δt) that a quantum with a latency t will not be resolved from any other quantum can be calculated asp(t,Δt)=F(t)tΔtt+ΔtF(u)du Then the total probability that any two quanta will occur within an interval Δt can be calculated asP(Δt)=(½)p(t,Δt)dt=(½)F(t)dttΔtt+ΔtF(u)du =F(t)dttt+ΔtF(u)du Equation 1Thus, instead of subdividing the time course in intervals equal to Δt and calculating the number of events in each bin, one calculates the number of events with latencies fromt − Δt to t + Δt for each time point t.

If quantal releases are independent, then probability densityF(t) can be estimated from the latencies of single quantal responses (Fig. 3). For the resolution of quantal detection of 1 ms (see methods), the correct estimations of P (Eq. 1 ) for experiments I–IV will be 0.37, 0.48, 0.57, and 0.37, respectively. Thus ∼50% of all the double responses will be errorneosly scored as single quantal responses, which is in agreement with the results obtained for simulations (Table 1).

REFERENCES

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