Interspike Interval Relationship Among Flight Muscle Fibres in Drosophila

The motor units to the dorsal longitudinal flight muscle (DLM) of Drosophila are apparently driven by a common input (Wyman, 1966, 1969a, b; Levine, 1973; Harcombe & Wyman, 1978) while an additional input spaces apart or synchronizes the firing times of the units (Wyman, 1969 a; Levine, 1973; Harcombe & Wyman, 1977; and preceding paper, Koenig & Ikeda, 1980). In this paper, the influences of the driving input and the spacing inputs upon the firing pattern of the motor units are distinguished from each other, allowing further characterization of the driving input.

Adult Drosophila (Oregon R, 3–5 days old) were suspended on the tip of a tungsten needle and glass microelectrodes were inserted into the DLM fibres for intracellular recording, as described in the preceding paper (Koenig & Ikeda, 1980). Intracellular recordings were made from all ten motor units comprising the bilateral pair of DLMs while the animal was in stationary flight. A time calibration was always included during recording to eliminate any possible error due to fluctuation in tape or camera speed.

The terms interspike interval, concurrent interval, phase, and motor unit are defined in the Methods section of the preceding paper (Koenig & Ikeda, 1980).

Figs. 3–5 of this paper plot the percentage that an interspike interval is of the preceding interval in the same unit. For example, if an interval of unit 1 is 150 ms and the preceding interval of unit 1 is 140 ms, then the percentage of the last interval is (150 ×100)/140 = 107%. In these plots the intervals of the five ipsilateral motor units are considered as a group of successively occurring intervals without regard for which unit any particular interval represents. Thus, a moving average (n = 3) of the percentages of the five ipsilateral motor units was plotted. For example, if the percentages of last interval for successive intervals of the ipsilateral units were 102 (unit 1), 98 (unit 3), 99 (unit 2), 105 (unit 4), 94 (unit 5), 92 (unit 1), etc., the average was taken of the 1st, 2nd and 3rd percentages (102, 98, 99 = 100) for the first point; the average of the 2nd, 3rd, and 4th percentages (98, 99, 105 = 101) for the second point; the average of the 3rd, 4th and 5th percentages (99, 105, 94 = 99) for the third point, etc. These averages were plotted at the time of occurrence (end) of the interval for the first of the three percentages, e.g. the first was plotted at the time of occurrence of the interval for unit 1 (102%).

Those intervals which have been affected by the neural input which is involved in spacing apart or synchronizing the firing times of the units. These intervals are recognized by firing configuration as defined in the Results section of the preceding paper (Koenig & Ikeda, 1980).

The frequencies of both ipsilateral and contralateral motor units are positively correlated (Levine, 1973; Harcombe & Wyman, 1978). A clearer picture of the phenomenon emerges when many units are considered at one time and when the intervals involved in a spacing interaction (interacting intervals) are excluded. This phenomenon is best observed by plotting the units of the bilateral pair of DLMs together in an interspike interval v. time-of-occurrence plot, as in Fig. 1. In this plot, the noninteracting interval points of the ipsilateral units are connected, resulting in a line which is collectively produced by all of the ipsilateral units together. Thus, the ipsilateral intervals are observed as a group of successively occurring intervals, disregarding which unit represents which interval. As can be seen, the units of the two sides each collectively delineate a similarly fluctuating line made up of a progressively increasing and decreasing series of points. Thus, in this plot, the interval durations of the individual ipsilateral units, when observed collectively, demonstrate a type of serial correlation (e.g. longer, longer, longer). This correlation is not due to one unit’s intervals always being a certain duration relative to another’s, since any unit can occur at any position relative to the collectively delineated waveform.

In another interval v. time-of-occurrence plot (Fig. 2 A) the intervals of both sides appear to be fluctuating simultaneously above and below 150 ms in loose groupings, but the sequential nature of the interval durations (i.e. longer, longer, longer, etc.) is not observed. In Fig. 2B, points for units of the right side from Fig. 2 A are plotted, while points for the left side are plotted in Fig. 2C. Lines are drawn connecting noninteracting intervals of unit 1 with those of unit 2, and intervals of unit 3 with those of unit 4, and it can be seen that the pairs of connected units (1–2R, 3–4R, 1–2L, 3–4L) all delineate similar cyclically fluctuating waveforms which are sometimes displaced slightly from each other in timing and amplitude. The sequential nature of the durations which was observable in the previous figure has been obscured in this example by these displacements.

In every fly tested (more than 50), successively plotted intervals of these units were always observed to collectively delineate an irregularly fluctuating wave, at times expressed sequentially, as in Fig. 1, and at other times loosely, as in Fig. 2. Three phenomena could occur which tended to make recognition of the collectively produced waveform more difficult:

Although all units (of both sides) always fired at about the same rate, it was often observed that the base firing rates of units 1 and 2 (ipsilateral) were very similar to each other but somewhat faster (or occasionally slower) than units 3 and 4 (which were also very similar to each other). In addition, units of the right side could all be firing slightly faster or slower by a similar amount than units of the left side.

Although the waves delineated collectively by the units of both sides fluctuated in unison, the two waves were often seen to slide in and out of precise synchrony with each other. For example, in Fig. 1 the wave delineated by the units of the right side appears to transiently lag behind the wave delineated by units of the left side. The same kind of temporal sliding was also sometimes observed between the wave delineated by units 1 and 2, relative to the wave delineated by units 3 and 4 (ipsilateral). This temporal sliding appeared to be independent of the relative firing rates of the units since the units could all be firing at the same rate and still display temporal displacements, or could be firing at different rates without displaying temporal displacements.

Differences in firing rate and timing thus cause a distortion in the sequencing displayed by the fluctuating intervals of these units. However, because of the apparent coupling in timing and frequency between ipsilateral units 1 and 2, and units 3 and 4, this distortion is minimal between the intervals of these pairs. Thus, the basic skeleton of the wave can usually be observed by considering these pairs separately, while other combinations (1–3, 2–4, 1–4, 2–3) often would obscure visualization of the wave. This is the reason for connecting the points of pairs 1–2 and 3–4 in the plots of Figs. 2 B and C.

Intervals involved in spacing interactions (defined in preceding paper, Koenig & Ikeda, 1980) can also greatly distort the collective waveform. In Fig. i, for example, three pairs of interacting (encircled) intervals are seen to be displaced from the waveform defined by the other units. In each instance one is shorter, the other longer than would be expected. It was also shown in the preceding paper (Koenig & Ikeda, 1980) that the interactions between units 1 and 2 or between units 3 and 4 have a greater effect on interval size than do interactions between other pairs (1–4, 2–3, 1–3, 2–4). This is also observable in Fig. 1, where pairs 1–4 and 1–3 appear less displaced than 1–2.

The above three factors can be dealt with as follows :

• To deal with the effect of differences in base firing rate, the change in interspike interval relative to the preceding interval in that unit (expressed as a percentage of the last interval) can be plotted instead of simply plotting interspike interval. Thus, these fluctuations are observed relative to the individual firing rate of each unit.

• Slight differences in timing between ipsilateral pairs can be dealt with by taking a moving average (see Methods) of the points of all the ipsilateral units, which essentially smooths out minor discrepancies in sequencing of the ascending and descending series of points which occur when the units are all plotted together.

• Interacting intervals are dealt with by substituting the predicted duration for that interval, i.e. the concurrent reference interval (defined in the preceding paper, Koenig & Ikeda, 1980) for the actual interval duration.

These three procedures can cause minor distortions of the actual Waveform. However, all characteristics of the processed waveform which are discussed below were clearly observable in the original (unprocessed) data. An example of how the above three procedures clarify the unprocessed waveform is given in Fig. 3, which shows the processed form of the data presented in Fig. 2 A.

The waveform delineated collectively by the fluctuating intervals of these units was complex, and in general seemed to consist of both fairly large fluctuations of longer periodicity and small fluctuations of shorter periodicity. This form was reminiscent of the type of wave which might be created by the summation of two (or more) sine waves sliding in and out of phase with each other. An example of this is seen in Fig. 4, where six consecutive seconds are presented. As can be seen in this figure, for the 1^st second the waves delineated by both sides are made up of relatively large fluctuations of fairly regular periodicity, which then become smaller and irregular in the 3rd second. By the 6th second, the fluctuations again display a similar amplitude and periodicity to the 1st second.

It can also be observed in Fig. 4 that for each peak in the right side there is a tendency for an equivalent peak in the left side, although discrepancies in timing or amplitude of the peaks do occur. However, it was occasionally observed that while one side would delineate one relatively large fluctuation, the contralateral side might delineate two smaller fluctuations instead. An example of this is seen in Fig. 4 at the end of the 4th second (designated by arrow), where the units of the left side have delineated one large peak while the units of the right side have delineated two smaller peaks. This suggests that the large peak of the left side might represent a summation of two smaller peaks, so that the difference in waveform between the two sides would be due simply to a difference in the degree of synchronization of the same two inputs. Thus, the possibility again arises that this waveform might represent the summation of two or more waves.

The characteristics demonstrated by Fig. 4 are quite typical of all of the animals observed. However, certain differences from one animal to the next did occur. These were related to the periodicity and amplitude of the collectively produced waveform. Such differences are demonstrated in Fig. 5, where short sequences from three different animals are shown. As can be seen, large differences in the periodicity of the collective can occur. Furthermore, it appears that these differences in periodicity are related of differences in base firing rate of the units. Thus, the units in Fig. 5 A (4–5/s) and Fig. 5C (6—7 /s) are firing much slower than the units of Fig. 5B (10–11/s) or Fig. (9–10/s) and also demonstrate a longer period. A quantitative measure of this relationship between the base firing rate and period is difficult to make since the waveform is irregular, making an accurate estimate of period impossible. However, it appeared that in general, animals with faster firing units delineated an oscillation of shorter periodicity than animals with slower firing units.

The other variable in these oscillations was amplitude (observed as percentage of the last interval in the same unit). In general, the maximum fluctuation was about 30% shorter or longer than the last interval (not including intervals involved in a spacing interaction). However, these fluctuations would sometimes be as large as 60–100%. Furthermore, there appeared to be no relationship between the base firing rate (or periodicity) and amplitude. For example, the units of the two animals in Figs. 5 A and C were firing at about the same rate ; yet the amplitude of the waves of these two animals is quite different.

The data presented above show that the interspike intervals of the various DLM units, when considered collectively, fluctuate in a specific way, which results in a progressively increasing and decreasing series of interval sizes over time. Can this phenomenon be attributed to the effect of a common input, or might some interaction between the units produce it? The analysis presented in the preceding paper (Koenig & Ikeda, 1980) suggests that these units are firing independently of each other (i.e. do not significantly affect each other’s interval size) except at very specific times which are identifiable by firing configuration. Also, the units of both sides fluctuate in unison, even though the units of the two sides appear to fire randomly with respect to each other (Harcombe & Wyman, 1978). Thus, these interval fluctuations are most probably the result of fluctuations of a common input to these cells.

How might the relationship between these units be created ? One possibility is that the intervals of these units represent estimates of the relative strength of the common input at various points in time. Thus, the intervals would represent windows in time, each allowing a momentary glimpse of the strength of the common oscillating input. By observing these intervals collectively, the oscillations of the common input can be discerned.

If the waveform collectively delineated by these interval fluctuations represents a view of the oscillations of a common input, then the characteristics of this waveform can give some insight into the nature of that input. The collectively produced waveform was complex but often appeared typically sinusoidal with a fairly regular periodicity, suggesting that the waveform might be the result of two or more similarly fluctuating inputs sliding in and out of phase with each other. The possibility that the common input has more than one source is also suggested by the fact that overlapping intervals which are displaced from each other by only 10–20 ms are able to reflect differences in input strength (by demonstrating difference in duration). Since these intervals overlap for most of their durations, they should be receiving the same input over most of their firing cycles (spike to next spike), so that a difference in internal the between them must reflect a difference in input strength for the short period of time when they do not overlap (probably the few ms before the neurone becomes ready to fire). If these collectively expressed fluctuations are due to changes in frequencies (spikes/s) of the common input, then this driving interneurone would have to be firing at a high frequency in order to allow the follower cells to distinguish between the number of spikes occurring within a period of a few milliseconds. If there were two or more driving interneurones, each fluctuating in frequency in a similar sinusoidal manner, the follower cells would be observing a summation of the frequencies, and neither interneurone would have to be firing so rapidly.

Another possible explanation for the fluctuations is that the common driver interneurone(s) might be a non-spiking cell with a continuously fluctuating membrane potential similar to those described in the thoracic ganglion of the cockroach (Pearson & Fourtner, 1975), in the suboesophageal ganglion in Crustacea (Mendelson, 1971), or in the metathoracic ganglion of the locust (Burrows & Siegler, 1976, 1978; Burrows 1978; Siegler & Burrows, 1979). These non-spiking interneurones, which demonstrate a sinusoidal oscillation in membrane potential, appear to be related to driving a motor output - walking in the cockroach and locust, and ventilation in Crustacea. Such neurones may be present in Drosophila, since intracellular recordings have been made from non-spiking cells, exhibiting membrane fluctuations of about 20–30 mV in the thoracic ganglion of Drosophila (K. Ikeda, unpublished observations).

If the above interpretation of the cause of the collective fluctuation is correct, the intermediary interneurones must all faithfully relay the fluctuations of the common input(s). Considering the high correlation these units display in delineating the collective waveform, the possibility that these interneurones, as well as the common driver neurones, are non-spiking cells whose membrane levels faithfully represent the amount of input received is appealing. If at each interneuronal level the oscillations of the common input had to be translated into many summating EPSPs, we might expect the responses of the individual units to be more displaced relative to each other than actually occurs at the muscle level. Such cells might communicate with each other through transmitter release or by electrical coupling.

An interesting characteristic of the collectively expressed oscillation was that slight differences in the expression of this waveform, that is, differences in amplitude or timing, were coupled in certain pairs of ipsilateral units (1 and 2, 3 and 4). How might this coupling occur? One possibility is that the pathway from the common oscillating source to the motor neurones diverges into two separate pathways, one leading to units 1 and 2, and the other to units 3 and 4; and that these two pathways distort the original oscillation in slightly different ways before reaching the muscle level (distortions could arise from differences in synaptic transmission, integrative processing, or conduction velocity between the cells of the two pathways). These distortions in the waveform would then be coupled in the two units which shared a pathway. It was often observed that unit 5/6 seemed to manifest a different distortion from that demonstrated by units 1–2 or 3–4, suggesting that this unit might represent third distinct pathway from the common oscillating source. As was mentioned above, a similar kind of distortion coupling was also observed between the units of one sida relative to units of the other side, which also might be the result of bilateral pathway which have distorted the oscillation in slightly different ways.

Another possible explanation of the observed coupling would be that these pairs of units each receive a slightly different additional input which causes the fluctuation of the common input to be distorted in slightly different ways. A third possibility is that an interaction between the units of these pairs might produce the coupling. It is interesting to note that these pairs are the same pairs which demonstrate the strongest spacing interactions (see the preceding paper: Koenig & Ikeda, 1980). However, the the nature of the spacing interactions between these units would tend to uncouple rather than couple the timing or frequency of the units of these pairs. Thus, it is most probable that the coupled units share a common pathway at some level between the oscillating source and the motor neurones.

The above discussion is based on the assumption that the waveform of the collectively produced fluctuations is a meaningful representation of the waveform of the common input(s). Certainly, one can imagine that the relationship between the common input and the output at the muscle level might be drastically distorted by the integrative mechanisms of the cells involved in the pathway. However, the amazing regularity in waveform and periodicity of these fluctuations is a compelling reason for believing that the waveform has biological significance. Furthermore, the close synchronization of the muscles of both sides suggests that the distortions of the waveform are relatively minor. Thus, the pathway from the common oscillating source to the motor neurone might be a fairly simple one, involving a relatively small number of cells. The next step is to try to record from these cells directly in the ganglion. Hopefully, the suggestions made by these data will be helpful in identifying these cells and understanding how they might be involved in producing this firing pattern.

We would like to express our thanks to Ms Lois Worth for her excellent work in preparing this manuscript. This research was supported by the USPHS NIH grant NS-07442, USA.