control of flashing in fireflies - school of...

J Comp Physiol (198l) 144:287-298 Journal of Comparative Physiology. A ~ Springer-Verlag 1981

Control of Flashing in Fireflies V. Pacemaker Synchronization in Pteroptyx cribellata

John Buck*, Elisabeth Buck*, James F. Case**, and Frank E. Hanson*** National Institutes of Health, Bethesda, Maryland 20205, USA

Accepted June 23, 1981

Summary. The restrained male of the firefly Pteroptyx cribellata of Papua New Guinea responds to exogenous light signals with a latency of about one second, which equals the period of the natural spontaneous rhythm of flashing and includes about 800 ins of central nervous delay. The response is cycle-by-cycle and all-or-none and the duration of the response time is independent of the phasing of the driver in relation to the free run rhythm (Figs. 1, 2). The firefly can be entrained to rhythms over a period range of 800 ms to 1,600 ms, during which it leads or lags the concur- rent signal by an amount equal to the difference between the driving period and the animal's period (Figs. 3, 4). The phase-response line is nearly straight and is inclined 45 ~ (Figs. 2, 5). Normally an exogenous signal dictates interflash timing but occasionally may fail to entrain the firefly (Figs. 7 B, E) or may fail to evoke a flash (Figs. 7F, G). Persistence of endogenous control of timing period duration even during driving is occasionally seen as spontaneous drift in response time (Fig. 9). It is proposed that during entrainment each exogenous signal resets the pacemaker immediately to the start of its endogenous cycle, from which point it then begins a new series of free run periods. Thus each flash is timed in relation to the signal of the preceding cycle (Fig. 3). We devised a model of the endogenous timing cycle which fits the empirical data and achieves entrainment by a single mechanism involving phase advance or delay rather than change in actual rate of endogenous timing (Fig. 12). The proposed mechanism by which single males entrain to light signals seems compatible

* Laboratory of Physical Biology, National Institutes of Health, Bethesda, Maryland 20205, USA

** Department of Biological Sciences, University of California, Santa Barbara, California 93106, USA

*** Department of Biological Sciences, University of Maryland in Baltimore County, Catonsville, Maryland 21228, USA

also with the mass synchronous flashing which is the characteristic behavior of field congregations.

Introduction

Males of most fireflies flash rhythmically under control of a pacemaker in the brain (Case and Buck 1963; Bagnoli et al. 1976). In many species in South- east Asia males congregate in trees and flash in syn- chronized rhythm (lit. in Buck 1938; Buck and Buck 1978). Since the mutual entrainment must involve ac- celeration or retardation of individual flashing as a result of seeing neighbors' flashes, the mechanism of the photically-induced phase-shifting is of much phys- iological interest.

In a study of Pteroptyx cribellata of Papua New Guinea we have given a comprehensive description of spontaneous flashing in intact male fireflies showing, among other findings, that the endogenous period is regulated cycle-by-cycle and that the pacemaker can cycle independently of the actual flash (Buck et al. 1981). We also found that the variance of the brain-to- photocyte conduction-excitation delay is negligible in comparison with that of the timing process in the central nervous system. That finding made it possible to equate the flash-to-flash interval directly with the timing cycle of the pacemaker and thus to use stimulation of the intact firefly via controlled exogenous light signals as a non-invasive probe of the endogenous control of rhythm and the phase-shifting of flashing.

In a preliminary study we had found that rhythmic light stimuli can override normal pacemaking and reset the flashing and that the firefly can duplicate exogenous rhythms with periods from 800 to 1,600 ms (Hanson et al. 1971). We now deal with (1) responses of intact, isolated individuals to single photic signals presented in various phase relations to the endoge-

288 J. Buck et al. : Flash Pacemaker Synchronization in Firefly

nous flashing period, (2) transitions and interactions between free run flashing and entrainment and (3) rhythmic driving over frequency ranges both within and beyond those inducing 1:1 entrainment. These data suggest how mass synchrony in large populations is initiated and maintained. A theoretical model of a phase-shiftable pacemaker is also put forward.

Materials and Methods

Methods for restraining individual fireflies, preventing them from seeing their own flashes, and recording their flashing in the dark- room are given in the preceding paper (Buck et al. 1981). For stimulation, square pulse 40 ms flashes from a Sylvania Rl166 glow modulator lamp (' signals '), controlled by a Grass S-4 physio- logical stimulator, were led to the eyes via fiber optics. The stimulator was also used in establishing electrical latency at various sites in the nervous system. Measuring procedure and statistical tests were as described previously. During artificial driving the overall coefficient of variation in measured signal period, due to variations in stimulator period, recorder drive speed and chart reading estima- tion, was 0.5%. Laboratory temperatures varied between 26 and 29 ~ We use 'period' for the basic pacemaker rhythm cycle of about 1,000 ms and 'interflash' for any interval from one flash in a series to the next (measured peak-to-peak or rise-to-rise).

Because of the differences in free run flashing between different males, each firefly was designated not only as to collection locality on New Britain, Papua New Guinea [Cape Hoskins (H), Navunar- am (N) or Kerevat (K)], but individually. This allows the spontaneous flashing of each animal (Buck et al. 1981) to be compared with its responses to driving (present paper).

Results

1. Timing Cycle Duration in Relation to Neuroeffector and Sensory Delays

To establish the durations of the motor portions of the excitation pathway we stimulated males electri- cally in brain, in thorax (after decapitation) and in lantern tissue, using fine wire extracellular electrodes and stimulus trains of 3 ms, 8 V pulses at 240-per- second. Typical minimal latencies at 26 ~ were about 120, 90 and 70 ms, respectively, indicating that central conductional and synaptic delays amounted to about 30 ms f rom brain to cord and 20 ms in cord to lantern, and that 70 ms were occupied in conduction and transduction in the photogenic tissue prior to chemi- luminescence (see also Case and Buck 1963). These values, however, are minima derived f rom serial stimulation involving considerable facilitation. Overall brain-lantern latency to the initial stimulus of a series or to a single shock was not infrequently of the order of 200 ms.

The sensory physiology of P. cribellata is as yet unexplored but the measurements of Bagnoli et al. (1976) on Luciola lusitanica of Italy and of Lall et al. (1980) on PhotinuspyraIis of the USA suggest a visual

latency of 10-20 ms. Motor and visual delays com- bined are thus relatively brief compared with the total flash-to-flash interval of about one second. Even when the animal does not flash, the duration of the constantly running pacemaker ' s free run timing cycle is close to one second (Buck et al. 1981). It is thus evident that the approximately 200 ms occupied by neuromotor processes must run concurrently with 200 ms of a one second timing cycle.

2. Effects of Isolated Exogenous Signals on Free Run Flashing

To obviate possible cumulative effects of stimuli repeated at intervals as short as the free run period we imposed a single 40 ms glow lamp flash randomly every 10 s or so during otherwise normal rhythmic free run flashing. Each exogenous light signal was thus intruded into an inter flash that had begun with a spontaneous flash and was scheduled to end with another spontaneous flash one cycle (one second) later.

Male H2, whose free run flashing had been studied carefully (Buck et al. 1981, Table 2, Figs. 3, 4), was tested with 21 isolated signals during about 250 cycles of free run flashing 1. Three types of effect of the exogenous light were observed, depending on when the signal was imposed relative to the last preceding free run flash (Fig. 1):

(a) One of the 21 signals happened to fall nearly simultaneously with a spontaneous flash. The first post-signal flash occurred 930 ms later, at almost ex- actly the time expected f rom the mean free run rhythm (vertical arrow, Fig. 1 A). The coinciding signal thus caused no significant change in flashing rhythm.

(b) Each of 17 signals that fell between 110 and 840 ms after a free run flash inhibited the next expected free run flash (vertical arrows in the two examples, Figs. 1 B1 and 1 B2) and was followed by a flash after 870-955 ms (920 in Fig. 1B1, 940 in 1B2). The interflash into which the signal was intruded was thereby lengthened in comparison with the average free run period (to 1,355ms in Fig. 1B1, 1,635 in Fig. 1B2), the lengthening being proport ionately greater with the later signal. Each lengthened interflash was followed immediately by a series of flashes at intervals within the range of normal free run periods (910 and 975 ms in Fig. 1B1, 985 and 985 in Fig. 1 B2).

(c) Three signals fell late in the interflash and failed to affect significantly the timing of the next expected flash (vertical arrow, Fig. 1 C). The interflash into which the signal was intruded therefore remained of free run duration (990 ms in Fig. 1 C).

1 A 22nd test is discussed in Sect. 5 b

J. Buck et al. : Flash Pacemaker Synchronization in Firefly 289

B1 t ~ 4 3 5 ~ ' ~ - 920 ~ - ~ ' ~

~ ~ - - - - ~ f f ~ - - - 4 ~ 985 ~ 98s L

c , F - 8 4 ~

SIGNA[ r~

Fig. l. Responses to single artificial photic signals (firefly H2). A Signal nearly coincident with free run flash; no effect on interflash duration. B1 and B2 Two examples of the effect of a signal introduced less than 800 ms postflash, namely, aborting the flash expected on basis of 965 +90 ms free run period (57 cycles) that prevailed just prior to tests (verticalarrows below traces). BI Signal introduced 435 ms after free run flash, inducing a transient interflash of 1,355 ms. B2 Signal 695 ms post-flash: transient interflash 1,635 ms. C Signal introduced 840 ms post-flash: did not abort expected flash (vertical arrow) but shortened next interflash (800 ms)

However, the first complete interflash after the signal was substantially shorter than the average free run period (800 ms in Fig. 1 C). This shortened interflash was then followed immediately by a series of interflashes of normal free run duration (1,000 and 965 ms in Fig. 1 C).

It is evident from Fig. 1 that identical exogenous light signals induced two remarkably different types of change in flashing rhythm. Superficially these effects could be characterized as a lengthening (Fig. 1 B) or a shortening (Fig. 1 C) of a single interflash in the midst of a series of free run periods. We propose that these opposite types of transient effect can be reconciled by considering them both to be manifesta- tions of a single event: a resetting of the pacemaker's timing cycle. By resetting we mean an immediate restarting of the cycle, so that the pacemaker immediately begins to measure off a new, full, free run period. At a later point we will consider what pacemaker resetting may involve in physical terms.

The principal evidence for pacemaker resetting is as follows:First, with all 21 signals a flash occurred within the narrow time span of 870-955 ms after the signal (930, 920, 940, and 950ms in Figs. 1A, 1B1, 1 B2 and 1 C, respectively). The fact that each exogenous signal was followed by a flash after approximately the same delay, regardless of when the signal fell in the flash-timing cycle, indicates that each of these subsequent firefly flashes was a fixed-latency response to the signal. Second, the mean duration of this nearly constant 'response time' in all 21 tests (919_+25 ms) was close to the mean free run period of firefly H 2 (965 +90 ms), suggesting that the post-signal latency interval was a normal flash-timing cycle of the pacemaker.

Whether exogenous signals do inhibit the next scheduled free run flash (Fig. 1 B) or do not (Fig. 1 C) depends, we believe, on when the signal falls in relation to the moment of dispatch of the motor message from the pacemaker to the lantern. If the signal arrives before the pacemaker reaches its endogenous flash-triggering level, the pacemaker is reset and the flash is delayed, as in the 17 lengthened-interflash experiments (Sect. 2b, above). If the signal arrives during the final 120-200 ms of the interflash, after the neural flash-excitation message is already on its way to the lantern, the signal cannot prevent that flash from occurring about one free period after the last pre-signal flash (at 990 ms, Fig. 1 C). The exogenous signal nevertheless does reset the timing cycle, evoking an additional flash one free run period later (950 ms, Fig. 1 C) and thereby making the first complete interflash after the signal shorter than free run (800 ms, Fig. 1 C).

Interflash-shortening and interflash-lengthening are equally normal and significant consequences of pacemaker resetting: Both result from the same invari- ant event, a single repetition of the endogenous timing cycle. Lengthenings greatly outnumber shortenings in the present series simply because the flash-to- triggering part of the timing cycle (roughly 800 ms) is much longer than the triggering-to-flash segment (roughly 200 ms).

3. Flash-Signal Phase Relations in Pacemaker Resetting

In Fig. 2 the durations of the 21 reset interflashes of firefly H2 are plotted against the corresponding delay intervals between firefly flash and signal in order to portray the effect of driving throughout one full interflash. Starting with the large filled circles in the negative phase range 2 between the initial flash (filled star) and the prospective next flash (hollow star) the plot indicates that the durations of the reset interflashes increased nearly in proportion to the delay of signal insertion up to about 800 ms post-flash (roughly to 1,800 ms interflash duration). At this time there was a sudden break (vertical broken line), after which interflashes shorter than one second were induced (three large filled circles in lower right corner of plot). This apparent break in the phase-response line suggested a change in frame of reference related to the moment at which the spontaneous flash-exciting message starts on its way to the lantern. A signal

2 For firefly-driver phase differences we have used the circadian convention that phase is negative when the signal delays the response, as happens when the exogenous signal falls during the first 800 or so ms after the firefly's flash (interflash lengthened)


1800

1700

1600

1500

1400

z o_ 12oo F-- ,<

1100 E3

lOOO

800

700

600' +300 +200+100 -100 -200 -300 -400 -500 -600 -700 -800 -900

SIGNAL INSERTION PHASE (ms)

Fig. 2. Phase-response relation for interflash durations and response times induced by randomly timed single photic signals. Reset interflash durations for 21 resettings of firefly H2 (large circles), plus 20 additional measurements from four other fireflies (normalized to 965 ms), cluster along a 45 o line, showing nearly 1 : 1 proportionality with firefly-signal phase. Signal-flash response times for firefly H2 (hollow symbols) show nearly constant latency, averaging slightly less than the 965 ms mean free run period (broken line). Solid star: initial free run flash of target period. Hollow star: expected terminal free run flash (965 ms). To emphasize the continuity in response, the three late phase resettings plotted as post-flash in right lower corner of plot are repeated as pre-flash in lower left corner, designated by arrows. The single large filled circle at - 4 5 0 phase illustrates a rare occasion when an exogenous signal failed to reset the pacemaker. The vertical broken line indicates the nominal break in the timing cycle that corresponds to the moment of triggering of the output message by the pacemaker

reaching the pacemaker before that point would de- termine the duration of the interflash in which it was inserted, whereas a later signal would time the terminal flash of the next interflash.

The suspicion that the break in the phase-response line divides different interflash cycles was strongly supported by a fortunate phasing accident. Two of the 21 signals had been inserted at 840 ms post-flash, close to the critical time of endogenous triggering. One of these -840 ms signals inhibited the next scheduled free run flash and induced a greatly lengthened interflash transient (1,760 ms; highest of the large filled circles in Fig. 2). Hence that signal presumably arrived just before spontaneous flash-triggering was due. The other signal, identically phased, failed to inhibit the impending free run flash but shortened the subsequent interflash (Fig. 1 C), hence presumably arrived just after the spontaneous excitation message had started on its way to the lantern. Milliseconds can thus make the difference between

a maximally lengthened reset interflash and a maximally shortened one.

In Fig. 2 the three shortened transients shown in the right lower corner have also been plotted in the positive phase range in the lower left corner (the three large filled circles designated by arrows). In this posi- tion the shortened interflashes are shown as if induced by stimuli that fell before the initial flash of the cycle but after the time of endogenous triggering of that flash. This plotting format represents the whole gamut of interflash duration as a consistent, quasilinear pro- gression, rather than one interrupted by a gross dis- continuity. Hence, in order to relate the empirical measurements directly to the underlying control mechanism we will, in the coming data analyses and pacemaker modeling, define the starting point of each timing cycle arbitrarily as occurring at the moment of the endogenous triggering of the flash-excitation process, about 200 ms before the flash.

When the response times for the 21 exogenous signals are added to the phase-response plot (large hollow circles, Fig. 2) their relative constancy throughout the pacemaker cycle is evident and the ostensible interflash shortenings and lengthenings are seen to be incidental consequences of time of stimulation in relation to time of flashing, instead of signify- ing real changes in the rate of cycling of the pacemaker.

Though the responses of firefly H2 to single chal- lenges indicated that normal rhythmic free run flashing resumed immediately after both shortened and lengthened interflash transients (Fig. 1), we investigated the possibility that resetting had residual effects on subsequent periods. We compared the members of 18 pairs of interflashes, each pair consisting of the last free run period before a reset interflash and the first period after that interflash. The means for the pre-signal pair members (963_+ 50 ms) and post- signal members (944 +_ 33) were not statistically different ( t= 1.34). A similar comparison within pairs of last pre-signal and second post-reset cycles also showed no significant difference. We conclude, therefore, that pacemaker resetting does not bias subsequent free run flashing - that is, that driving affects the pacemaker cycle-by-cycle.

When substantial interflash lengthening was induced by an isolated exogenous signal the free run flashing that resumed was grossly out of phase with the extrapolated rhythm of free run flashing prior to pacemaker resetting. The new series remained out of phase with the pre-reset series indefinitely. There is, therefore, no suggestion that the flash-timing endogenous pacemaker is itself regulated with respect to some independent reference oscillator.

Since there appears to be no significant carryover of the resetting perturbation into subsequent free run


flashing, an exogenous signal should reset the pacemaker regardless of whether the interflash into which it is inserted is an endogenous free run period or an interval reset by a preceding signal. This surmise was confirmed by measurements of about 50 responses of firefly H2 to single signals inserted at ran- dom phases in successive interflashes. The phase-response line for these consecutively reset transients was nearly identical with that in Fig. 2 thus strength- ening the conclusion that one resetting event induces repetition of one free run timing cycle. F rom the much larger number of measurements it was more clearly apparent that the lines for both reset interflash durations and response times followed courses that were slightly curved. Response times in the - 2 0 0 to - 3 0 0 ms phase range occasionally fell short of full free run duration by nearly 100 ms.

The phase-dependent resetting effects of exogenous signals were fully confirmed with other males. For example, the durations of the interflash transient induced by the first signal in each of 20 rhythmic driving series with males N2, H8, K1 and K2 fell on the same phase-response line as the fully isolated signals used to stimulate firefly H2 (smaller symbols, Fig. 2).

A Driving at 986 ms i---1 s-~fl

B j Driving at 1100 ms ~--1 s -~

-160 /"-540 . ~'120 . '130 . 4 4 0 , ~140 /-~60 /-~40 /-~40

C J Driving at 876 ms ~-1 s---I

§ ~130 ;'+'1i'0 .'~119 /~-110 .--~110 .'(100 .4110 .4130 .4100 /';120

Fig. 3A-C. Reset interflash duration, response time and firefly- signal phase difference during rhythmic driving. Firefly N2 (free run period 986 + 58 ms derived from 57 free run interflashes). Top row of figures, interflash ; middle row, phase; lower row (diagonal broken lines') response time. Firefly duplicates driver period, main- tains nearly fixed phase difference, and shows nearly constant response time approximating the free run period. A 986 ms driver, firefly and driver nearly coincident; mean interflash, phase and response time for entire 42 episode series, 986 + 16, -25 • 12 and 975+_22 ms, respectively. B 1,100 ms driver, firefly leads driver; means I, 100 + 25, - 135 • 25 and 964 • 24 for 49 episodes. C 876 ms driver, firefly lags driver; means 876 _+ 18, + 116 • 11 and 991 + 13 for 40 episodes

4. Responses to Rhythmic Driving

P. cribellata males proved able to entrain cycle-by- cycle to regularly repeated light signals spanning a period range from about 800 to 1,600 ms. Each series began with a unique reset transient such as those illustrated in Figs. 1 B and 1 CI whose duration de- pended on the phase of initial signal presentation, then shifted to a steady succession of equivalent interflashes. Figure 3 shows portions of long records of l : l responses of firefly N2 to drivers close to the free run period (3A), longer (3B) and shorter (3C). The following aspects of rhythmic entrainment are noteworthy:

(a) Though duplicating the driver period, entrained fireflies maintained consistent phase leads over the nearest-in-time exogenous signals when the driver period was longer than free run (e.g., Fig. 3B) and consistently lagged the contemporaneous signals when the driver period was shorter (e.g., Fig. 3C). These firefly-driver phase differences were directly proportional to the difference between firefly and driver periods.

(b) Regardless of driver period, entrainment involved individual resetting of each successive flash, with quasi-constant response times in the free run duration range (diagonal broken lines, Fig. 3; Fig. 4). When a firefly is entrained to a driver with the same

period as the free run, each successive firefly flash, though coinciding with a signal, is timed from the signal of the preceding cycle (Figs. 3 A, 4 B).

(c) During rhythmic driving the variability in duration among reset interflashes was about a third that of interflash duration during free run flashing (legend to Fig. 3; Fig. 4; see also Buck et al. 1981, Fig. 4C).

(d) In spite of identical driving signals, the intensi- ties of successive reset flashes were quite variable (Fig. 3). We were not able to correlate this variation with any external factor.

(e) Phase-response relations for mean durations and response times of interflashes reset during rhythmic driving (Fig. 5) agreed well with those obtained with isolated signals (Fig. 2). The slight concavity of the response time line over the course of the cycle involved response times of the order of 50 ms shorter than the free run in the - 3 0 0 ms phase region and 50 ms longer than free run when signals fell near + 200, just after motor message triggering (differences often statistically significant).

(f) Though considerable individual differences were observed in mean free run periods and in variability of free run flashing (Buck et al. 1981) different males showed very similar responses to rhythmic driving (Fig. 5).

(g) Entrainment to the driver rhythm was nearly always completed in a single transient cycle, as in


1700 - - q

1600

Firefly N2 1500 Firefly H8

Firefly K1

1400 Firefly K2 �9 ,~ / t

.~_ 1200

c~ 1100

- - - ~ - ; - _ _

9 0 0

/

700

6O0 +2~X) +1~0 +300

Inter Response Flash Time

�9 o

Mean Firefly-Driver Phase Difference (ms)

Fig. 5. Phase-response relations for reset interflash duration and response time during rhythmic driving of four fireflies. Twenty-five series, averaging about 40 successive stimuli each, normalized to 980 ms free run period. Cap lines are standard deviations. Shows nearly linear proportionality of reset interflash durations, near constancy of response times and closely similar response of the four fireflies

Fig. 4A-H. Rhythmic driving of firefly N2. Panels A and E, free run flashing; B and F, rhythms nearly isochronous with free run; C and D, faster than free run; G und H, slower than free run, About 10 superimposed sweeps for each panel, two cycles per sweep. Stimuli indicated by breaks in each lower trace. Shown: constancy of response time and proportionality of response phasing to firefly-driver period difference

the resettings by isolated signals (Fig. 1) but occasionally required an additional cycle to achieve a steady phase relation (Fig. 6).

(h) When we attempted to drive fireflies via signal periods longer or shorter than the empirical limits for 1:1 entrainment the driver nevertheless affected interflash duration as expected from the pacemaker- resetting hypothesis. For example, when N2 was driven for 32 cycles at 2,117 ms, the record (Fig. 7A) consisted of alternating interflashes averaging 1,120 + 49 ms and 984 +_ 23 ms, due to alternated pacemaker resetting and immediate reversion to free run flashing. Conversely, a firefly exposed to a driver with a period of 600-800 ms responded to the first signal but usually

A B

- 80O

- 700

~, -600

- 500

m 400

-300 _1

- 200 iF.

- 100

0

+100

- 200

- 100

0

+100

+200

+300

+400

10 20 30 40 50

Driver Cycles

I I I I I

10 20 30 40 50

Fig. 6 A, B. Attainment of phase lock during rhythmic entrainment. A Firefly H8 (free run 982 ms) driven at 981 ms. Mean lock-in phase, - 6 ms. B Firefly N2 (free run 1,035 ms) driven at 1,053 ms. Mean lock-in phase, - 6 8 ms. Stars: initial transients

failed to flash after subsequent signals in the series. This result would be expected if rhythmic signals falling earlier in the interflash than the 'flash-committed zone' reset the pacemaker a second time in each successive cycle before endogenous triggering of the motor message can occur.

(i) In interesting contrast to 600-800 ms driving, signals recurring at intervals of about one-half the free run period or shorter appear not to reset the


E 940 *0L 930/, I 10~91~ J 10201 900t * 0

-520 440 -410 440+6~ 0 +300 -70 430+650 -350 -430

SECONDS

Fig. 7A-G. Responses and anomalies during in-range and out-of- range rhythmic driving. Numbers between traces are interflash durations. In panel E, top row of numbers are response times, bottom row, phase. A Alternate reset and free run interflashes. Firefly N2, driven at 2,117 ms. B Single free run pacemaker cycle (I,070 ms) intercalated during 1,254 ms driving of firefly N2 and followed by a compensating reset transient (1,430 ms). C Entrain- ment to 525 ms driving. Firefly N2, responding to every other signal. D Entrainment to 525 ms driving. Firefly K2. Shows three normal-duration interflashes (the second with an adventitious flash), then an interflash of three half-cycles involving a 500 ms phase shift when flashing resumes, then a hiatus of four half-cycles but with no phase shift, either reflecting one flash skipped or a multiple resetting. E Five consecutive reversions to free run flashing during rhythmic driving, starting with the 4th interflash, followed by compensating reset transient (i,750 ms) and resumption of entrainment. Firefly N2, 1,376 ms driver period. F Apparent skipping of a single flash. Firefly K2 (free run period about 1,100 ms), driven at 1,048 ms. Note also five adventitious flashes in the third interflash. G Three consecutive flash skips. Firefly K2, 1,048 ms driving

p a c e m a k e r a second t ime in the same t iming cycle. F o r example , Fig. 7C shows pa r t o f a series in which firefly N 2 was exposed to 84 cycles o f 525 ms dr iv ing: the firefly r e s p o n d e d to every second signal and was no t reset by the in t e rmed ia te ones. Similar ly, firefly K2 , though r e spond ing i r regular ly , was c lear ly no t inh ib i ted by signals 2, 4, 6, 9 and 15 (Fig. 7D). Fa i lu re to reset at shor t in tervals was fur ther i l lus t ra ted by exper iments in which signals were del ivered in pairs consis t ing o f an ini t ia l signal r epea ted at free run f requency and a second signal in t e rposed f rom 100 to 400 ms af ter the first, thus p r o d u c i n g a pa t t e rn o f a l t e rna t ing longer and shor te r in ters ignal intervals . Wi th this reg imen it was only the pa i rs o f signals a b o u t one free run pe r iod a p a r t (1,050 ms) tha t elicit- ed responses (Fig. 8). The p a c e m a k e r was p rac t i ca l ly never reset a second t ime in the same cycle by a signal tha t fo l lowed an effective rese t t ing signal by 100-400 ms (Fig. 8B-E) . Thus an exogenous ly reset t iming cycle appea r s to be p r o o f agains t fu r ther reset- t ing for 500 ms, whereas an endogenous ly in i t ia ted cycle can be reset immedia te ly . W e suspect tha t this

Fig. 8A-F. Driving with paired-signal sequences. Firefly N3. Each panel includes about 10 superimposed consecutive sweeps, In each panel the upper number indicates that two signals were 1,050 ms apart, the animal's free run period. The lower numbers indicate the subdividing of this period by intercalation of a second signal in each cycle. Stimulus duration 50 ms in panel A, 25 ms in all others. If the firefly was reset by a signal it was not resettable again within 400 ms

effect is due to ref rac tor iness o f the eye pers is t ing for a b o u t 500 ms af ter recep t ion o f a signal.

5. Endogenous EfJects During Rhythmic" Driving

In our s tudy o f free run f lashing in P. cribellata (Buck et al. 1981) cer ta in spon taneous i r regular i t ies o f f lash t iming were ascr ibed to in t r ins ic va r iab i l i ty in the cycl ing o f the p a c e m a k e r itself. In view of the a lmos t to ta l over r id ing effect o f exogenous pho t i c signals on the initiation o f the p a c e m a k e r ' s t iming cycle it is in teres t ing tha t the fo l lowing behav iors tha t are observed dur ing free run f lashing can also persis t during rhy thmic dr iv ing:


(a) Adventitious Luminescence. Irregular and usually low-intensity extra flashes were occasionally seen as shoulders on main-rhythm flashes or during the interflash, for example, in Fig. 7A, 3rd interflash; 7B, 2nd flash; 7D, 1st, 2nd, 5th and 6th flashes; 7E, 8th flash. For reasons given in Buck et al. (1981) we attribute most such anomalies to neural noise or to local lantern response irregularities.

(b) Failure to Reset. During some driving series there were occasional interflashes that differed sharply in duration from contiguous reset interflashes. Since most of the anomalous interflashes were of free run duration we concluded that exogenous signals some- times fail to reset the pacemaker, whereupon a normal endogenous cycle occurs. The single instance of failure to reset among the 22 tests of isolated signals (Fig. 2, filled large circle at -450 ms phase) is a clear example of such occasional ineffectiveness of the usually overpowering exogenous signal. Similarly, in a 1,254 ms driving series of firefly N2, (Fig. 7B), the third interflash (1,070 ms) could well be a single free run period, particularly since it was followed by a reset transient of the proper duration to include the ' lost ' phase difference (1,430=176+ 1,254) and then by further regular resetting. Since the three such putative reversions to free run in this 41 cycle record occurred in episodes 6, 15 and 30, fatigue can hardly have been involved. In another driving series of the same firefly at 1,376 ms (Fig. 7 E), interflashes 4-8 clearly represent 5 consecutive free run periods. These were followed by a reset transient (1,750 ms) and resumption of regular entrainment.

(c) Period Drift. Figure 9 illustrates 31 response cycles of firefly N1 to driving at 1,154 ms in which, within a few cycles, mean response time and phase changed by an average of nearly 50 ms with no change in mean interflash duration. Such relatively sudden shifts in resetting time during entrainment, not inter- fering with replication of driver period, are attributed to spontaneous drifting of endogenous timing cycle duration (see also Buck et al. 1981).

(d) Flash Skipping. Flash skipping during rhythmic driving was rare in our samples of H and N fireflies but somewhat more frequent among the K animals. In Fig. 7F, for example, the flash that should have terminated the fourth interflash was missing, and in Fig. 7G three flashes in a row were apparently skipped before entrainment resumed. Such records suggest that the pacemaker can be reset and run its course without necessarily triggering an effective motor message to the lantern at the end of the reset cycle.

SUCCESSIVE CYCLES -- DRIVING AT 1154 MS

0 5 10 15 20 25 30 I I I _ _ I I I I

_~ 1100 ~_ o ~ o o Oo ~11 | oo _ _ ~_o-I V- o o o I o

1050 I- o o oo o

o o I o o o 1000 I o cz I o

RT1075_+21 I 1029_+24 o

--76 • 20 I I - - 1 2 4 _+ 2 4 I

~ 1150 • 25 I 1152_+29 t

Fig. 9. Drift in response time duration during 31 cycles of entrainment to 1,154 ms rhythm. Firefly N]. Mean response times (RT), firefly-signal phase differences (~b) and reset interflash durations (IF) calculated separately for first 15 and last 16 cycles. Differences between mean phase and mean R T durations in the two arbitrary groups are significant at well below the 0.001 level; reset interflash durations remained constant

The effects discussed above may occur together, in various combinations (Fig. 7 E). In the full 42 cycle driving record for that firefly there were 26 full reset interflashes (like the first three in Fig. 7E), 15 scattered periods of free run duration (like interflashes 4-8), 3 more transients like the ninth interflash and one interflash of 2,870 ms involving a skipped flash.

Another type of response melange is illustrated by a 99 cycle attempt to drive firefly N2 at 777 ms. In this series the animal flashed only 37 times, consistent with much multiple inhibition caused by successive resetting signals falling before preceding reset cycles reached the moment of endogenous flash-triggering. However, scattered through the intervals of flash inhibition were 8 groups of two or three consecutive responses that permitted measurements of interflash duration, putative response time and firefly-signal phase difference (means 770_+ 86, 1,054+_21 and +268_+38 ms, respectively). The 770 ms interflashes show that resetting had indeed occurred at times and the 268 ms mean interval of flash non-inhibition sug- gests that the endogenous timing cycle occasionally had been of the order of 70 ms shorter than usual. Failure to respond 1:1 to drivers in the 800 ms or shorter driving range is not due to physical inability to flash sufficiently rapidly because the P. cribellata male, in the spontaneous 'flickering' mode, may emit discrete flashes at the rate at least 5-per-second (Buck et al. 1981).

In sum, any or all of the various options of pacemaker behavior - (a) being reset, (b) ' ignoring' the signal and producing a free run timing cycle instead, (e) failing to trigger the motor lag of excitation, and (d) changing the duration of the endogenous timing


A lO64 ~ 1 0 1 0 ~ ~

+130 1320 +260 1100 +90 7190 +120 1240 +I70 1190 +t20 1340 +110 11[;0

B lSN

-220 -440 1260 -330 1490 -l[1O 1320 -26[;

2,000

1,800

I I

C �9 -- Firefly Interflash

- O--Response Time

_.E 1 , 6 O O -

CI = 1,400

1,2OO {

{ 1 , 0 0 0

+ 2 0 0

I

I I

,t, t I , I I I

0 - 2 0 0 - 4 0 0 - 6 0 0

Firefly--Signal Phase (ms)

Fig. 10A-C. Rhythmic driving of P. cribellata female (Hoskins). Free run period 1,497 ms. A Driving at 1,064 ms, resulting in firefly Iag relative to signal. B Driving at 1,594 ms, with firefly phase lead over signal. Interflash durations (top lines of figures), phase differences (signed values in lower line of figures) and response times (unsigned figures in lower line) are approximations because frequent low intensity leading shoulder on flash was easily confused with bump in photometer trace due to cross-channel feedback from stimulus. Start of stimulation marked by tick marks below photometer trace. C Phase-response relations for reset interflash durations and response times. Cap lines are standard deviations

cycle - may occur during rhythmic exogenous driving, in any sequence, and independent of preceding responses.

Anomalies and irregularities during driving have been dwelt upon because of the valuable insight they afford into both the endogenous behavior of the pacemaker and its accessibility to exogenous influences. However, evidence of variable response should not be allowed to obscure the remarkable intrinsic stabili- ty of pacemaker period not only during most runs with most males but over extended time intervals. Firefly N2, for instance, was stimulated during several hours at a total of 19 different frequencies for an

average of 50 cycles each, alternating with series of free run flashing of roughly equal durations, yet had response averages differing by only a few percent in three widely separated bouts of driving at 1,056 ms (mean response times and phase differences 966, 981 and 995, and +90, +68 and +63, respectively).

6. Response of Female to Exogenous Signals

The mated female of Pteroptyx cribellata is able to flash in a spontaneous loose rhythm (period 1,400- 1,500 ms at 26 ~ Buck et al. 1981) but does not parti- cipate with the males in the congregational synchron- ized flashing (Buck and Buck 1978).3 The female did entrain to rhythmic driving (Fig. 10A, B) albeit more loosely than the male, the responses reflecting her longer fi'ee run period and more variable flash form. The female approximately matched driver periods in the 1,050 to 2,000 ms range and showed rough phase- proportionality and response time constancy (Fig. 10 C).

Discussion

A large body of work on normal flashing behavior, responses to photic and electrical stimulation, and extracellular action potentials in roving type fireflies (reviewed by Carlson 1969; Case and Strause 1978) shows that rhythmic flashing of the male is controlled by a neural oscillator in the brain that has a fixed period usually in the 1 to 10 s range. Experiments in which light signals induced flash responses of much shorter latency, thus apparently by-passing the pacemaker, indicate that the normal flashing rhythms of rovers include much central delay (reviewed by Buck and Hanson, in preparation). Though Bagnoli et al. (1976) were able to localize flash control to the optic lobes, 'possibly in the lobula,' no photogenic volleys have been recorded from the brain nor has pacemaker response to timed inputs been tested directly. The firefly brain is not much larger than the largest Aply- sia neuron.

The present work on the habitual synchronizer Pteroptyx cribellata, which has a free run period of 1 s, yielded no evidence that the intact male has a normal short latency response to photic input. How- ever head-lantern response delays in the 120-200 ms range were recorded for electrical stimulation and the consistent finding of response time latencies in the 1 s range after exogenous visual signals makes it clear that central nervous delay occupies a major

3 Since the taxonomy of fireflies is based on male genitalia it was necessary to use females that had been collected while in copulation in order to be sure that they belonged to Pteroptyx cribellata

296 J, Buck et al. : Flash Pacemaker Synchronization in Firefly

fraction of the flashing rhythm period in Asiatic synchronizers as well as in roving species.

The facts that the photic delay approximates the species-specific free run flashing period and that the response transients equal the free run period plus or minus the corresponding driver-firefly or firefly- driver phase difference (Fig. 1) led to the hypothesis that an exogenous signal instantly aborts the timing cycle in progress and restarts the pacemaker on a new, complete, free run cycle (' resetting'). Pacemaker resetting as purely a restarting of a fixed free run timing cycle is clearly oversimplified, since mean response time ranges from about 5% longer than to 5% shorter than mean free run period, depending on stimulation phase (Fig. 5). The concept has, however, proven exceptionally valuable both in interpret- ing our empirical findings and in modeling the pacemaker (see below).

The pacemaker resetting hypothesis appears to ac- commodate all our principal empirical results. Oper- ating as an all-or-none and cycle-by-cycle response, resetting explains satisfactorily the equivalence of response time and free run period and the occurrence, direction and magnitude of the phase shifting evoked by both single, isolated, exogenous, photic signals (Figs. 1, 2) and repetitive signals delivered in a wide range of rhythms (Figs. 3-5; 7A, C). It provides for the direct proportionality of phase and reset interflash duration and accounts for that duration as the sum or difference of response time and phase.

Exogenous signals usually dominate the pacemaker completely insofar as cycle initiation is concerned but occasional failure to cause resetting is shown by the occurrence of free run cycles intercalated in rhythmic driving series (Fig. 7E). Interestingly, persistence of endogenous control of cycle duration even during exogenous driving is suggested by instances of drift in response time (Fig. 9). Flash-skipping (Fig. 7 F), another effect also seen in free run cycling, is of uncertain genesis but at least shows that the driver does not always dictate the flash.

Down to driver cycle durations of about 800 ms, each signal resets the pacemaker. Between about 800 ms and about 500 ms, each signal inhibits flashing. Of two signals that recur at 500 ms or shorter intervals, the second is not seen, presumably because of visual refractoriness (Figs. 7 C, 8).

We have no direct evidence bearing on the nature of minor arrhythmias but many such emissions may plausibly be attributed to noisy neural input to the lantern and to asynchronies of local lantern regions (Buck et al. 1981).

Our working hypothesis has been that the effects of visual stimuli on flash timing in P. cribellata reflect corresponding changes in the underlying pacemaker.

If this surmise is correct the +200 to -800 phase- response relation (Figs. 2, 5) indicates that some as- pect of pacemaker ' state' (e.g., excitation) rises nearly linearly throughout the one second endogenous timing process, triggering the flash-exciting message at its highest level and then falling to its basal level at the end of the cycle. However, if pacemaker excitation level did rise linearly, beginning about 200 ms pre-flash (Fig. 11 A), and if exogenous signals did reset the pacemaker immediately to the basal level, all reset cycles would be longer than free run regardless of whether the signal was interposed post-flash (Fig. l l B) or pre-flash (Fig. l 1 C). Cycle shortening could not occur. 4

A postulate that permits the model to accommo- data interflash-shortening is that the spontaneous re- turn of pacemaker state to the basal level occupies about 200ms rather than being instantaneous (Fig. 12A; see also Buck and Buck 1976). This model still provides for lengthened interflashes following exogenous signals that occur up to about 800 ms post- flash (Fig. 12B). Now, however, signals that reset ear- ly in the pacemaker cycle, between flash-triggering and light emission, cause shortened interflashes (Fig. 12C). The assumed identity of the 'basal' level of state, reached at the end of endogenous restoration, and the 'reset' level, reached in both pre-flash and post-flash resetting, is implicit in the constancy of response time. The model is also compatible with the apparent sudden break in interflash duration seen in the flash-to-flash phase-response representation of driving data (Fig. 2), since that point is now defined as the boundary between two control cycles rather than a point within one cycle.

Three features of the proposed model require further exposition. The first is the postulate that exogenous resetting involves instantaneous change of state to the reset (basal) level whereas spontaneous restoration to that level occupies 200 ms. In indirect support it can be said that the proposed timing cycle (Fig. 12A) resembles the time course of the generator potential of many pacemaker neurons, and that resetting could be analogous to a conventional inhibitory synaptic effect. Exogenous and endogenous state- change events are obviously different, if only in that the driven response involves vision while the spontaneous event need not. Distinctive effects of driving were seen also in the disappearance of most of the adventitious luminescences often seen in free run laboratory flashing.

The second subtle feature of our pacemaker model is the effective coincidence of the instant when sponta-

4 Inability to induce interflash shortening simply by resetting is also a difficulty with the relaxation oscillator model suggested earlier (Hanson et al. 1971)


,"TERE~S. DURAnON ,- b-ERE~ RUN4 I" LONGER " I

CYcLEFLASH END/START } . . . . ,~., ',#ir / .~..,llr ///

BASAL ( RESEl~ LEVEL

~----LONGER--~

4 * JA"

V RESEqq'ING SIGNAL ~- _ _ , E l

Fig, 11. Diagram to illustrate that if endogenous cycle initiation by the pacemaker (A) and exogenous resetting (B, C) are both instantaneous, interflash shortening cannot occur whether the exogenous signal falls post-flash (B) or pre-flash (C). Dotted horizontal lines indicate 200 ms delay terminating in a flash (star). Broken diagonal lines show expected course of rising excitatory state in the absence of resetting

rNTERFLASH DURATION-- ~ ~--FREE RUN-~D-{ {~ LONGER ~[ ~-SHORTER,~

BASAL,R SE LEVEL . V RESE~F[NG SIGNAL ~. I']

Fig. 12A-C. Model of activity cycle and responses of firefly flash-timing pacemaker. Dotted and broken lines as in Fig. l I except that broken vertical line indicates coincidence of time of flashing with lowest level of state. A Free run cycle showing rapid fall to basal excitation followed by slow rise in excitation state to flash-triggering level. B Resetting effect of signal intruded after the flash and before the moment when the flash-exciting signal is triggered and pacemaker state begins to fall toward the basal level: reset interflash is lengthened. C Resetting effect of signal intruded after the triggering point but before state reaches the basal level: subsequent interflash is shorter than normal

neous ly decl ining state reaches its nad i r and the mo- men t of f lashing (Fig. 12A, ver t ical b r o k e n line). There seems to be no inherent mechanis t i c reason why the overal l t ime requ i red for p a c e m a k e r state to fall spon taneous ly f rom f lash- t r igger ing level to basa l level should a p p r o x i m a t e the t ime requ i red for the m o t o r message to run f rom the t r igger ing po in t in the bra in to t h e photocy te . Occurrence o f the f lash near the t ime o f m i n i m u m rese t tab i l i ty m a y be pre- sumed to be useful, however , since there should then be less occas ion for the male to become se l f -ent ra ined by visual f eedback f rom his own flash. This deduc t ion is also consis tent wi th the obse rva t ion tha t spontaneous rhy thmic f lashing seems to be ent i rely n o r m a l when the f i ref ly 's eyes are covered (Buck et al. 1981). There is thus g r o u n d for surmis ing tha t co inc idence o f f lashing t ime and t ime o f basa l exci tabi l i ty is an evolved a d a p t a t i o n .

The th i rd elusive fea ture o f the m o d e l relates to the connec t ion be tween a t t a inmen t of highest pace- m a k e r state and the t r igger ing o f the m o t o r message to the lantern. The two events are n o r m a l l y s imul taneous , and the quan t i t a t ive re la t ion be tween t iming and o u t p u t du ra t ions can be def ined sa t i s fac tor i ly on the basis tha t the t iming cycle ends /begins at the t ime o f t r igger ing (Fig. 6 in Buck et al. 1981) but the occas iona l pers is tence o f the t iming r h y t h m in the absence o f f lashing shows tha t s t a t e - re s to ra t ion is not ob l iga to r i ly l inked to the f lash- t r igger ing p ro - cess. On the basis o f the model , the 40 ms mean cycle- shor ten ing assoc ia ted with free run flash sk ipp ing

(Buck et al. 1981, Sect. 3b) could be though t o f as a sl ight phase advance caused by state s tar t ing back spon t aneous ly t o w a r d its basa l level wi thou t hav ing risen qui te to the f lash- t r igger ing level.

L inear phase response has been d e m o n s t r a t e d in a var ie ty o f inver tebra tes by direct in t race l lu la r record ing and it is t empt ing to suggest specific neurona l corre la tes for the p a c e m a k e r mechan i sm that we have inferred f rom responses o f in tac t f i ref l ies? Since, however , we have l imited ourselves to a single s t imu- la t ion pa rad igm, 6 have no t exp lored the sensory l ink in exci ta t ion and have no t yet r eco rded ei ther the exogenous ly evoked or endogenous neura l signals in Pteroptyx cribellata it seems best to l imit our charac-

5 The data could also be fitted by an alternative model, closer in contour to the phase-response plot but more complex in regard to necessary permeability changes and ionic fluxes. In this model the endogenous restoration process, like exogenous resetting, is instantaneous. However, it carries state below the reset level, as in the momentary hyperpolarization following an action potential. State then rises linearly, crossing the reset ]evel at the time of flashing (200 ms after the start) and continuing for another 800 ms. Exogenous interflash shortening is achieved by resetting ' up ~ to the reset level when the signal intrudes between restoration and flashing and 'down' thereafter, as in clamping to the equilibrium potential of some ion

6 In preliminary tests, signal durations ranging from l ms to 100 ms seemed equally effective with our standard intensity of signal light (which was chosen to elicit a high percentage of responses without exceeding the inhibition threshold). However, a strength-duration effect in stimulation is not excluded as a factor in some responses; further, visual refractoriness may limit the frequency of exogenous resetting (Fig. 8).


terization of the pacemaker of this species to empha- sizing the following three special properties:

The first unusual property of the pacemaker is its immediate and all-or-none response and close relation to phase. Under our experimental conditions the phase-response to driving approaches linearity and a slope of 1.0 across the entire cycle. The pacemaker thus stands near one pole of the range of oscillators that stretches between the discontinuous sawtooth type and the smoothly cycling non-linear type repre- sented by the sine wave or pendulum (e.g.; Wever 1965; Hanson 1978).

The second unusual feature of the firefly flash control is its capacity to phase-shift in either direction with no qualitative change in input signal. Whereas neurons often effect phase advance via excitatory postsynaptic input and phase retardation via inhibitory PSPs (e.g., Perkel et al. 1964), the firefly seems to achieve both phase advance (interflash shortening) and phase retardation (interflash lengthening) simply as a consequence of signal timing, putatively in relation to fixed quasi-linear intervals of rising or falling excitatory state during the pacemaker ' s fixed-duration cycle (Fig. 12B, C). The ability of resetting to achieve entrainment to both faster and slower rhythms via a single type of response also avoids the necessity for postulating that the male is able to 'distinguish the relative order of occurrence of his flash and that... of his influential neighbor ' (Buck and Buck 1968).

The third special feature of the P. cribellata pacemaker is its capacity for being phase-shifted in either direction without changing the duration of its intrinsic cycle. The endogenous timing process runs at a constant rate whether in a period interrupted by resetting or an undisturbed full free run period. Presumably, timing cycle duration does vary with temperature but no systematic study of this matter has been made in P. cribellata.

Incessant activity is perhaps part of the definition of pacemaker, so hardly a special property of the flash control mechanism in fireflies. However, among most roving species the less regular rhythm, the ten- dency for extended pauses in flashing and the lability to disturbance, as well as the usually very limited period of evening activity in nature, contrast strik- ingly with the rapid and nearly unremitting flashing of Oriental synchronizing species. This constant rhythmic cycling, persisting through physical restraint and experimental manipulation, is certainly a noteworthy characteristic of the P. cribellata pacemaker.

The pacemaker resetting mechanism seems to offer no obstacle to extending the behavior of single restrained males of P. cribellata to the striking mass synchrony observed in field congregations of males of this firefly. Since no lasting period adjustments occur in response to exogenous flashes the degree

of natural mass synchrony should be limited by the closeness and variances of the endogenous periods among the individual males and might not be as close as in species like P. tener in which actual change in period duration can occur (Hanson 1978). Observa- tionally, the mean period durations of individual fireflies are reasonably close (Buck et al. 1981) and the communal synchrony is impressively precise (unpubl- ished movie records). Possible additional effects of the enhanced intensity of the natural group signal were not investigated but the immediate resetting behaviour should insure that an ensemble could quickly reach and maintain synchrony. Likewise, the sensitivity of the pacemaker to both phase-advancing and phase-retarding signals should promote cycle-by- cycle fine-tuning of the communal rhythm.

We are much indebted to Drs. D. Alkon, T.H. Bullock, A. Carlson, F. Dodge, J. Enright, H. Gainer, R. Josephson, H.M. Pinsker, C.L. Prosser, A. Winfree and the late K. Roeder for various infor- mation, suggestions and editorial assistance. We thank especially Dr. Laurens Mets for valuable insights. The research was made possible by grants GB8158 and GB8400 from the National Science Foundation to the Scripps Institution of Oceanography in support of the 1969 Alpha Helix Expedition to New Guinea. Supplementary support was received by J.B. from the American Philosophical Society (Penrose Fund grant 5017) and the National Geographic Society; by J.F.C. from ONR Contract N0014-69-A-022-8006 and from the University of California Faculty Research Fund; by F.E.H. from a Faculty Grant, University of Texas. Mrs. Betty Morris cheerfully endured the typing of endless drafts.

References Bagnoli P, Brunelli M, Magni F, Musameci D (I976) Neural mech-

anisms underlying spontaneous flashing and its modulation in the firefly Luciola lusitanica. J Comp Physiol 108:133-156

Buck JB (1938) Synchronous rhythmic flashing of fireflies, Q Rev Biol 13:301-314

Buck J, Buck E (1968) Mechanism of rhythmic synchronous flashing of fireflies. Science 159:1319-1327

Buck J, Buck E (1976) Synchronous fireflies. Sci Am 234:74-85 Buck J, Buck E (1978) Toward a functional interpretation of synch-

ronous flashing by fireflies. Am Nat 112:47D492 Buck J, Buck E, Hanson FE, Case JF, Mets L, Ana GJ (1981)

Control of flashing in fireflies. IV. Free run pacemaking in a synchronic Pteroplyx. J Comp Physiol 144:277-286

Carlson AD (1969) Neural control of firefly luminescence, Adv Insect Physiol 6 : 51-96

Case JF, Buck J (1963) Control of flashing in fireflies. II. Role of central nervous system. Biol Bull 125:234 ~250

Case JF, Strause LG (1978) Neurally controlled luminescent sys- tems. In: Herring PJ (ed) Bioluminescence in action. Academic Press, London, pp 331 366

Hanson FE (1978) Comparative studies of firefly pacemakers. Fed Proc 37:2158-2164

Hanson FE, Case JF, Buck E, Buck J (1971) Synchrony and flash entrainment in a New Guinea firefly. Science 174:161-164

Lall AB, Chapman RM, Trouth CO, Hollaway JA (1980) Spectral mechanisms of the compound eye in the firefly Photinus pyralis (Coleoptera: Lampyridae). J Comp Physiol 135:21-27

Perkel DH, Schulman JH, Bullock TH, Moore GP, Segundo JP (1964) Pacemaker neurons : Effects of regularly spaced synaptic input. Science 145 : 61q53

Wever R (1965) Pendulum versus relaxation oscillation. In: Aschoff J (ed) Circadian clocks. North-Holland, Amsterdam, pp 74-83

control of flashing in fireflies - school of...

Documents