The significance of spiracle conductance and spatial arrangement for flight muscle function and aerodynamic performance in flying Drosophila

Energetically demanding processes in animals greatly influence most physiological systems, and above all the respiratory system. In flying insects, in particular, metabolic activity may increase 10- to 15-fold over resting metabolism, forcing the tracheal gas exchange system to increase the supply of oxygen and the release of carbon dioxide(Casey, 1989; Casey and Ellington, 1989; Ellington et al., 1990; Lehmann and Dickinson, 1997). However, despite many years of investigation, there is still uncertainty about how exactly oxygen enters the tracheal system and distributes within the tracheal network, and carbon dioxide eventually leaves the respiratory system through the open spiracles (Wigglesworth,1972). In general, respiratory currents inside the tracheal system are difficult to predict because they depend not only on several physiological factors, such as the buffer capacities for respiratory gases and ventilatory strategies, but also on the morphological architecture of the tracheal system,including size and location of the spiracle openings(Weis-Fogh, 1964a; Weis-Fogh, 1964b). For example, Drosophila may store oxygen by using haemoglobin in the tracheal walls to reinforce oxygen partial pressure gradients(de Sanctis et al., 2005; Hankeln et al., 2005), and bicarbonates in the haemolymph may buffer tracheal carbon dioxide at the expense of changes in pH (e.g. Gulinson and Harrison, 1996).

In the past, several researchers have attempted to determine the significance of respiratory currents inside the tracheal system by studying the role of individual spiracles in respiration and energetics. Bailey was one of the first physiologists to investigate the interplay between thoracic and abdominal spiracles by blocking individual thoracic spiracles in the honey bee(Bailey, 1954). He found that under CO₂ stress, the resting animal produced a net tracheal air current from the thorax to the abdomen using abdominal pumping. This tracheal convection was, however, only present when the propodeal spiracle(=metathoracic spiracle) was blocked, and ceased when air was prevented from entering through the first thoracic spiracle. Similar to Bernoulli ventilation, which was later proposed for flight respiration in large beetles(Miller, 1966), Bailey also suggested that in flying bees air is inhaled by the first spiracles and exhaled via the propodeal spiracles. In locusts and cockroaches,inspired air is routed similarly from the anterior spiracles to the segmental tracheae and leaves the system through the abdominal spiracles(Miller, 1982). This type of breathing was also demonstrated in Lepidopteran pupae(Schneiderman, 1960), which may even control the activity of individual spiracles(Slama, 1999). A unidirectional air flow was reported for tethered flying hawkmoths Manduca sexta (Wasserthal, 2001). In this insect, there is an air stream towards the posterior spiracles that results from a subatmospheric (negative) pressure at the mesothoracic spiracle and a positive pressure in the mesoscutellar air sacs. By contrast, in resting wingless dung beetles the direction of air flow is inverted (retrograde convection) and tracheal gases flow forward from the posterior to the anterior body (Duncan and Byrne, 2002). These authors also reported a lateral asymmetry of air flow inside the animal and demonstrated that the right mesothoracic spiracle is the primary route for respiratory gas exchange. A study on running energetics in the ant Camponotus hypothesised that asymmetries in gas exchange rate might also occur during the discontinuous gas exchange cycle (DGC)(Lipp et al., 2005). This hypothesis arose from the finding of various numbers of `O'-peaks within a single gas exchange cycle, suggesting that multiple spiracles may be involved in tracheal gas exchange. Moreover, in the arid-adapted ant Cataglyphis bicolor, the thoracic spiracles act as high-capacity gateways to the tracheal system and are responsible for approximately 90% of the total gas exchange rate during running activity(Lighton et al., 1993a). In this ant, the abdominal spiracles combined only have approximately half the diffusive capacity of a single thoracic spiracle(Lighton et al., 1993a).

Size constraints in small insects such as the fruit fly Drosophila, make it difficult to assess tracheal air currents,spiracle function or tracheal partial pressures. The situation is even more complex in flying animals in which the spiracles may dynamically vary their opening areas according to changes in flight power requirements. For example,the results of a study on spiracle opening behaviour in flying Drosophila are consistent with at least three basic mechanisms of spiracle control (Lehmann,2001). The fly may achieve an average tracheal conductance by either (i) matching the area of each thoracic spiracle to the respiratory needs, (ii) dynamically closing and opening the spiracles over time, or (iii)closing some spiracles while other spiracles remain open. All mechanisms could give similar mean tracheal conductance when estimated within a certain time period, although the latter mechanism, in particular, might produce temporal fluctuations in the local supply of oxygen. The importance of matching at least the bilateral control of spiracle activity arises from the fact that the left side of the tracheal system is virtually isolated from the right side. In Drosophila, there are only a few tracheal commissures (pro- and metathoracic dorsal commissure, and pro-, meso- and metathoracic ventral commissures) that allow exchange of respiratory gases between the body sides(Miller, 1950). In the locust Schistocerca gregaria the thoracic system is, moreover, isolated from the abdomen (Weis-Fogh,1964b), while in Drosophila large tracheae connect the thoracic parenteric air sac with the abdominal air sac(Miller, 1950). For geometric reasons, changes in the spatial distribution of the total spiracle opening areas might directly hinder proper flight muscle function because the insect flight muscle has no anaerobic capacity and thus relies on instantaneous oxygen supply (Ziegler, 1985). By contrast, the extensive tracheal development in Drosophila, with broad latero-linear air sacs such as the parentic-, pleural- and lateroscutal sac, favours the establishment of homogenous partial pressures on the ipsilateral side even when gas exchange rates are not balanced between the ipsilateral meso- and metathoracic spiracle.

Consequently, in this study we examine how reducing the size and deleteriously interfering with the spatial distribution of gas exchange areas impair flight muscle function and aerodynamic force production in the small fruit fly Drosophila melanogaster. This was done by selectively blocking thoracic spiracles in tethered animals flying inside a flight simulator. Flow-through respirometry and simultaneous measurements of flight force production and wing kinematics allow the determination of changes in vital flight parameters under a vast variety of breathing conditions. Incorporating energetic and aerodynamic theory, we show how (i) maximum mechanical power output of the indirect flight muscle (IFM), (ii) the efficiency with which the muscle converts chemical energy into muscle mechanical power, (iii) lift and drag coefficients for flapping wing motion and (iv) aerodynamic efficiency, all change with changing arrangements of spiracle conductance.

The data for this study were collected from 3- to 5-day-old fruit fly females Canton S wild-type Drosophila melanogaster Meigen. The animals stemmed from an inbred laboratory strain and were reared at room temperature (22°C) on commercial Drosophila food (Carolina Biological, Burlington, NY, USA). To estimate in vivo flight muscle mechanical power output and respiratory rate, we anaesthetized the animals on a cold stage at 4°C and tethered them to small tungsten holders using UV-light activated glue (Clear Glass Adhesive, Henkel Loctite,Düsseldorf, Germany). Curing time was 20 s using a 75 W tungsten halogen lamp. Similar to the testing procedure mentioned below, we tested the toxicity of both the non-polymerised and polymerised glue on 25 Drosophilathat had been exposed to the glue for approximately 24 h. The data show that none of the animals died within the observation period and superficially we did not observe any changes in their behaviours.

We determined the functional significance of changes in respiratory gas exchange through the four major thoracic spiracles of Drosophila by covering individual spiracle openings with small droplets of commercial two-component epoxy glue (5-min epoxy, R&G, Waldenbuch, Germany). The resin component of the glue consisted of bisphenol A- and F-epichlorhydrine,and the active component of the hardener was 2,4,6-tri(dimethylaminomethyl)phenol. The glue was selected according to its property to cure fast and in very small volumes. We tested the glue's toxicity for Drosophila by exposing 25 flies in a standard Drosophilavial to the resin, the hardener and the polymerised glue. Although the flies did physically contact the polymerised glue and its components, none of the animals died or superficially changed behaviour within the testing period of 24 h. Moreover, it seems unlikely that the small cuticle area covered by the epoxy droplets influenced the mechanical properties of the thoracic box during wing flapping, for two reasons: first, the glue droplet was only marginally larger than the opening area of the meso- or metathoracic spiracles, and second, an experiment in which we placed a glue droplet close to but not on the animal's spiracle opening did not produce any alterations in aerodynamic force production. Throughout the manuscript we use the term `unmanipulated flies' to mean tethered flying animals with none of their thoracic spiracles sealed.

The flies were allowed to recover from the tethering and sealing procedure for at least 30 min before being placed into the flight arena. To derive muscle mass-specific power output, we measured the mass of each fly after each experiment using a balance (sensitivity 0.01 mg; Sartorius MC210P,Göttingen, Germany) and assuming a flight muscle-to-body mass ratio of approximately 0.3 (Lehmann and Dickinson,1997). For body mass estimation, we did not remove the glue from the spiracle openings because its contribution to the fly's total mass was negligible. We calculated mean lift and drag coefficients from total flight force, wing velocity and wing size by employing quasi-steady aerodynamic theory and assuming that the chordwise aerodynamic circulation is maximum close to a spanwise location of 65% wing length(Birch and Dickinson, 2001; Lehmann et al., 2005; Ramamurti and Sandberg, 2001). A detailed description of this procedure is given in a previous study on Drosophila flight (Lehmann and Dickinson, 1998). Body mass (means ± s.d.) of the tested animals was 0.92±0.08 mg (N=10 flies, all thoracic spiracles left open), 0.88±0.18 mg (N=26, 1 spiracle sealed),0.94±0.20 mg (N=43, 2 spiracles sealed), 0.96±0.17 mg(N=23 flies, 3 spiracles sealed) and 0.92±0.08 mg(N=5 flies, 4 spiracles sealed). A statistical test on body mass showed no significant differences between the tested groups (ANOVA, P>0.05). Mean temperature during the experiments was 23.5°C.

To determine maximum spiracle opening area of the four thoracic spiracles,we prepared 10 females for scanning electron microscopy (SEM) using a standard laboratory protocol (Fig. 1A). In Drosophila, the prothoracic spiracle is reduced while the mesothoracic spiracle has moved anteriorly(Fig. 1B). By contrast, the metathoracic spiracle is located directly beneath the beating haltere. When at all possible, before taking pictures we oriented the thoracic spiracle openings perpendicular to the focal plane of the SEM, in order to avoid measurement errors due to image distortions. We estimated spiracle opening area from the images using self-written software routines in Scion Image(Scion, Frederick, Maryland, USA; red areas, Fig. 1). Fig. 1C,D shows that the metathoracic spiracle opening (∼2745 μm²) is approximately 20% larger than the mesothoracic opening (∼2186 μm²),resulting in a total maximum area for thoracic respiratory gas exchange of approximately 9862 μm². In comparison, a previous study described the thoracic spiracles in Drosophila melanogaster as oval openings of approximately 60 μm×25 μm at the surface(Manning and Krasnow, 1993). From these values we calculated a total thoracic exchange area of 5675μm², which is approximately 42% smaller than the value measured in the present study. There could be several reasons for this discrepancy. First, although the aspect ratio between 60 and 25 μm fairly matches the elongated shape of the mesothoracic spiracle, the metathoracic spiracle seems to be more circular with a diameter between 50 and 60 μm, and thus appears to be larger than measured by Manning and Krasnow. Second, since we measured total opening area from the size of the thick sclerite that borders the spiracle opening at the surface, we might have overestimated the inner opening size (Nikam and Khole, 1989). Third and alternatively, the females that were used in the present study were chosen according to body size and represented the largest animals from the population. Larger females typically show a better flight endurance than their smaller relatives. Consequently, since larger fruit flies exhibit larger spiracle openings (F.O.L., unpublished data), it might be that the difference between the two opening measurements is a real difference in size rather than due to substantial differences in measurement techniques.

Compared to thoracic spiracles, the area of the 14 abdominal spiracles was not measured directly, but was estimated by assuming that it represents 5% of the fly's total gas exchange area or approximately 493 μm²(Manning and Krasnow, 1993). A simple behavioural test showed that gas exchange mediated by abdominal spiracles is high enough to satisfy the oxygen needs during resting metabolism, whereas in experiments in which gas exchange through all 18 spiracles was completely blocked, the flies died within approximately 10 min after the treatment (N=5 animals). This result is similar to a study on the regulation of carbon dioxide release from the thoracic and abdominal spiracles in the ant Cataglyphis(Lighton et al., 1993a). In this animal, the abdominal spiracles have half the diffusive capacity of a single thoracic spiracle and can fully meet the ant's oxygen uptake and carbon dioxide release at resting metabolism.

To evaluate the seal of the epoxy droplets used to restrict respiratory gas exchange through the spiracle openings, we developed the experimental setup shown in Fig. 2. The animals were anaesthetized using carbon dioxide and prepared by ablating head and abdomen (N=15 flies). Subsequently, we sliced the thorax along the sagittal plane and carefully removed all tissues out of the flies' body. One side of the thorax was then mounted above a 0.5 mm hole in a 15.6 cm³ respirometric chamber using epoxy glue. We permanently sealed the metathoracic spiracle and only modified the mesothoracic spiracle opening for testing. To estimate the diffusivity of the spiracle opening for CO₂, we aligned a bell-shaped gas outlet (3.8 cm³volume) above the fly thorax. Either ambient air or 100% CO₂ was supplied via an electrically activated two-way valve. To avoid potential changes in cuticle diffusion coefficient due to dry-out processes,both gases were routed through a plastic bottle containing purified water. Similar to the in vivo respirometric measurements described below,water and CO₂ were removed from room air and pulled at a rate of 1000 ml min^–1 through the respirometric test chamber.

Fig. 2B shows a typical trace of CO₂ measurement, with periodic switching between ambient air and the supply of CO₂. After this pre-check, the mesothoracic spiracle was sealed and the testing procedure performed again. Despite the high partial pressure of CO₂ on the outside of the thorax, the small seal typically blocked the entire inflow of CO₂ into the respirometric chamber (Fig. 2C). Afterwards, in a control experiment, we carefully removed the seal that fully restored the diffusivity of the mesothoracic spiracle for CO₂ (Fig. 2D). Note that the vibrating thorax of a flying fly might cause leakage of the spiracle seal, and this effect is not simulated in the simple testing procedure. Therefore, we covered the mesothoracic spiracle of tethered flies and flew the animals for at least 15 min. We subsequently dissected those animals in a procedure similar to that described above and checked for any gas leakages. In none of the five tested flies did we measure any CO₂ flux through the sealed spiracles, suggesting that thorax vibrations during flight do not harm the quality of the spiracle seals. In sum, the outcome of the pre-tests convinced us that the epoxy seal used in this study is able to sufficiently block respiratory gas exchange through the spiracle openings in a flying fruit fly.

The tethered fruit flies were flown in a virtual reality flight arena in which stroke amplitude, stroke frequency, total force production and carbon dioxide release were measured simultaneously(Dickinson and Lighton, 1995; Fig. 3A). A more detailed description of the experimental apparatus and the procedure is given elsewhere(Lehmann and Dickinson, 1997). Under closed-loop feedback conditions, fruit flies actively modulated the azimuth velocity of a vertical dark stripe displayed in the panorama using the relative difference in stroke amplitude between the two beating wings. The feedback conditions were set according to previous experiments on tethered flying fruit flies (Lehmann and Dickinson,2001). While flying in closed-loop, Drosophila changed both kinematic and respirometric parameters in response to the vertical motion of an open-loop striped grating. We have previously shown that under those conditions fruit flies maximize their locomotor output, while trying to follow the upward motion of the horizontal stripes(Lehmann and Dickinson, 1998). This procedure is equivalent to adding weight to the animal and elicits maximum flight forces similar to those obtained in freely flying flies using a weight-lifting technique (Lehmann,1999).

Concurrently, we employed flow-through respirometry with a flow rate of 1000 ml min^–1 and used a Li-cor 7000 gas analyser (Licor,Lincoln, Nebraska, USA) to measure the rate of carbon dioxide release during flight. The internal filter frequency of the gas analyser was set to 0.2 s. Data sampling frequency was 125 Hz and wash-out time constant τ of the 15 ml respirometric chamber was approximately 910 ms (wash-out time∝e^–x/τ; Lehmann and Heymann, 2005). Respirometric data of each animal were corrected for both temporal shift due to wash-out and the gas delay due to the connecting tubings, and were eventually normalized to standard temperature and pressure (STP). Further analysis and calibration of kinematic and respiratory data were performed as described elsewhere (Barton et al.,2005). Metabolic data and power requirements for flight are given as flight-specific values by subtraction of resting rates, and if not stated otherwise also expressed as indirect flight muscle (IFM) mass-specific units.

To vary the size of total diffusive spiracle area in the flying fruit fly,we tested different combinations of spiracle sealing in random sequences and subsequently pooled the data subsets (Figs 3, 4, 5). This means that in case of a single seal, we tested flight performance under four different experimental conditions: a blockage of the left sp.ms (mesothoracic spiracle, N=6 flies), right sp.ms (N=7 flies), left sp.mt (metathoracic spiracle, N=7 flies) and right sp.mt (N=6 flies). In flies with two sealed spiracles we investigated flight and muscle performance under six different experimental conditions (sealed left and right sp.ms, N=8; left and right sp.mt, N=7; left sp.ms and sp.mt, N=8; right sp.ms and sp.mt, N=6; left sp.ms and right sp.mt, N=6; and the right sp.ms and left sp.mt, N=8 flies). Results obtained from flies with three sealed spiracles are mean values of four experimental conditions (sealed left sp.ms, sp.mt and right sp.ms, N=7; left sp.ms, sp.mt and right sp.mt,N=8; right sp.ms, sp.mt and left sp.ms, N=4; right sp.ms, sp.mt and left sp.mt, N=4 flies). Moreover, previous results on Drosophila flight energetics have shown that there is a transient effect on flight performance after the initial take-off during which flight force production and CO₂ release rate peak for a short time. This transient peak was present in most of our experiments except in flies with all four thoracic spiracles sealed. Consequently, to circumvent any transient phenomena, we excluded the first 5 s and the last 2 s of each flight sequence from our analysis. Throughout the manuscript all values are given as means ± s.d.

All flies tested in the flight arena were able to fly continuously under tethered conditions for at least 14 s per flight sequence, including those animals in which we restricted gas exchange to the abdominal spiracles. To estimate how total spiracle opening area constrains maximum locomotor capacity in the fruit fly, we compared mean values of all data points within a flight sequence that fell within the top 1% of flight force. These means are plotted in grey (Figs 3, 4, 5). Surprisingly, wing kinematics were less affected by the restriction of diffusive area than we expected, because a 95% decrease of diffusive area from approximately 10 355μm² (unmanipulated animal) to approximately 493μm² (abdominal spiracle exchange area) caused only an approximately 10.7% concomitant decrease in stroke amplitude (from 176±7.0 to 157±8.1°, Fig. 3B) and an approximately 20% decrease in stroke frequency (from 221±12.0 to 177±8.9 Hz, Fig. 3C). These small changes in wing kinematics coincided with a linear decrease in flight force production from 1.36 to 0.29 body-mass specific force with decreasing spiracular gas exchange area (linear regression fit, y=0.16+0.11x, R²=0.97, P=0.002; Table 1, Fig. 3D). The data show that active flight in Drosophila defined as the locomotor performance at which the animals produce flight forces equal to or greater than body weight,required gas exchange through at least three thoracic spiracles including the abdominal spiracles (Fig. 3D). Note that despite their small total opening area (5% of 10 355μm²), the functional relevance of the 14 abdominal spiracles for oxygen supply broadly compares with the significance of each thoracic spiracle: together, they contributed approximately 20% to maximum aerodynamic performance of an unmanipulated flying fruit fly(Fig. 3D).

The different regression slopes of kinematic measures (amplitude:1.90×10³ deg. μm^–2, frequency:4.70× 10³ Hz μm^–2 diffusive area) and relative flight force production (0.11×10³ relative forceμm^–2 diffusive area; Table 1) imply that changes in wing velocity cannot exclusively explain the changes in aerodynamic force production, because wing velocity is directly proportional to the product between stroke amplitude and frequency(Lehmann and Dickinson, 1998). Consequently, changes in total spiracular conductance also altered the lift coefficient for flapping wing motion that decreased by approximately 69%, from 1.21 at a diffusive area of 10355 μm² to 0.38 at 493μm² (Fig. 3E). Moreover, since flight force is the vector sum of lift and wing profile drag,the wing's drag coefficient decreased likewise and similarly to the lift coefficient by approximately 59%, from 0.65 at 10 355 μm²spiracle opening area to 0.38 during breathing through abdominal spiracles only (Fig. 3F).

As a consequence of the reductions in (i) wing kinematics, (ii) aerodynamic lift production and (iii) drag coefficient, the maximum power requirements for flight, such as the flight muscle mass-specific induced- and profile requirements, decreased with the decreasing number of open thoracic spiracles(Fig. 4A,B). Superficially,mass-specific induced power seemed to be more affected by the respiratory restrictions than profile power and decreased by 91% from ∼33.8 W kg^–1 in unmanipulated animals to ∼3.2 W kg^–1, when gas exchange only occurred through the abdominal spiracles (Fig. 4A, Table 1). We found significantly smaller changes for mass-specific profile power, which decreased by ∼69% with decreasing gas exchange area from ∼64.7 in unmanipulated flying Drosophila to 20.2 W kg^–1 when all thoracic spiracles were sealed (91±22% vs 69±15%, t-test, P<0.05, N=8; Fig. 4B, Table 1). According to Ellington's energetic theory for flapping wing motion, mechanical power output of the asynchronous flight muscle is the sum of induced and profile power requirements, assuming 100% energy elastic storage within the flight motor(Ellington, 1984b). Similar to induced and profile power requirements, this measure decreased with decreasing spiracle opening area by ∼7.5±1.0 W kg^–1μm^–2 spiracle area (linear regression fit, y=13.1+7.5x; Fig. 4C, Table 1). Flight-specific metabolic power was calculated from the instantaneous measurements of CO₂ release during flight and was ∼68% lower in flies that only breathed through abdominal spiracles (334 W kg^–1, Fig. 4D)compared to the unmanipulated control group (∼1031 W kg^–1; Fig. 4D, Table 1).

Due to the changes in flight muscle mass-specific mechanical power output and metabolic power, muscle efficiency changed likewise. Fig. 5A shows that muscle efficiency, defined as the ratio between metabolic and muscle mechanical power output, decreased from ∼9.8±1.2% in unmanipulated flies to∼5.6±1.5% in flies that only breathed through a single thoracic spiracle. Interestingly, muscle efficiency apparently recovered(7.2±1.8%) when Drosophila only breathed through abdominal spiracles compared to gas exchange through a combined diffusive area of abdominal and 1 (5.6±1.5%) and 2 (6.3±1.6%) thoracic spiracles(Fig. 5A). However, this result might be partly ascribed to the delayed release of CO₂ (see paragraph below) after flight initiation that produced a temporal mismatch between steady-state power requirements for flight and respiratory activity of the animal. In this sense, the apparent recovery of muscle efficiency during breathing through the abdominal spiracles does not reflect changes in the physiological state of the flight musculature but results from the measuring method.

In contrast, aerodynamic efficiency of wing motion, defined as the ratio between minimum power requirements for flight (i.e. Rankine–Froude power) and muscle mechanical power, decreased linearly with decreasing gas exchange area from a maximum of ∼26.8±0.92% to∼11.2±5.3% during abdominal breathing(Fig. 5B, Table 1)(Ellington, 1984b). Total flight efficiency is the product of muscle and aerodynamic efficiency and a measure for the overall performance of the chemo-aerodynamic conversion process of Drosophila's flight apparatus. During flight of the tiny fruit fly, total flight efficiency decreased from ∼2.61±0.35% in unmanipulated animals to a value well below 1% (∼0.77±0.30%) during pure abdominal breathing (Fig. 5C).

Most of the changes in wing kinematics, flight power requirements,metabolic rates and flight efficiencies shown in Figs 3, 4, 5 (grey data) can be explained by the changes in flight force production. It has previously been demonstrated that wing kinematics including muscle-mechanical and aerodynamic efficiency co-vary with alterations in lift production – and most of the measured alterations may be attributed to this effect(Lehmann, 2002; Lehmann and Dickinson, 1997). Thus, we separated the changes due to variations in flight force production from those caused by variations in the arrangement of spiracle conductance. This was achieved by comparing the various measures (grey bars) in Figs 3, 4, 5 with measures from unmanipulated animals at flight forces that matched (within ±2%accuracy) the maximum force of those flies whose spiracles had been manipulated. According to Fig. 3D, these body weight-specific forces are: 1.01 (1 thoracic spiracle blocked), 0.74 (2 thoracic spiracles blocked), 0.48 (3 thoracic spiracles blocked) and 0.29 relative flight force (four thoracic spiracles blocked). In other words, while the grey bars in Figs 3, 4, 5 represent measures at 1%maximum flight force production of manipulated flies (0–3 open spiracles) and the unmanipulated control group (4 spiracles open), the red data (means ± s.d., Figs 3, 4, 5) were measured in unmanipulated animals at times when the flies produced flight forces equal to one of the five force values shown in Fig. 3D. As mentioned before in the Materials and methods, the fruit flies varied flight force production between maximum (1.36 force/weight) and minimum (0.29 force/weight) values in response to the vertically oscillating horizontal background stripe grating displayed inside the virtual-reality background flight arena. To further highlight the effect of changes in local oxygen supply to the flight muscles, we subtracted these data (red) from the results obtained during spiracle manipulation (grey data, Figs 3, 4, 5) and then plotted the most essential differences as a function of spiracle opening area in Fig. 6.

We found quite complex dependencies between the various flight variables and diffusive spiracle area given by the number of open spiracles. The major results can be summarized as follows: (1) Flight force- and body mass-specific mechanical power increased when gas exchange between the tracheal system and the ambient air was forced through a decreasing number of thoracic spiracles(linear regression fit, y=60.0–6.0×10^–3x,R²=0.82, N=5, P=0.03, Fig. 6A). Pure abdominal breathing apparently permitted up to ∼64% higher muscle mechanical power output than breathing through all 18 spiracles in unmanipulated flies (at 0.29 relative flight force). The relative changes in muscle mechanical power output at 493, 3780 and 5424 μm² spiracle opening areas were significantly different from those at 7889 and 10 355 μm²(t-test, P<0.05, Fig. 6A). (2) Compared to unmanipulated animals, relative muscle efficiency did not change significantly when oxygen supply was restricted to 3(7889 μm²) and 2 (5424 μm² opening area) thoracic spiracles (t-test, P>0.05, Fig. 6B). However, muscle efficiency appeared to be significantly higher during pure abdominal breathing(5% of total spiracle opening area) when compared with unmanipulated animals(t-test, P<0.001, Fig. 6B). The tendency towards higher relative muscle efficiencies at smaller respiratory exchange areas suggests that even the worst condition for tracheal oxygen supply (abdominal breathing) does not impair the IFM chemo-mechanical conversion efficiency (linear regression fit, y=63.2–7.6×10^–3x,R²=0.41, N=5, P=0.24). (3) Relative lift coefficient significantly increased with increasing diffusive area (linear regression fit, y=–68.6+6.84×10^–3x,R²=0.97, N=5, P=0.002, Fig. 6C). During pure abdominal breathing, the lift coefficient was ∼54% of the lift coefficient determined in unmanipulated animals producing similar aerodynamic force. (4)With increasing spiracle opening area, aerodynamic efficiency increases significantly with a slope of 5.37×10^–3μm^–2 (linear regression fit, y=–55.7+5.37×10^–3x,R²=0.97, N=5, P=0.0026, Fig. 6D), suggesting that oxygen supply through all thoracic and abdominal spiracles produces the best aerial performance score in Drosophila(Fig. 6D). Aerodynamic efficiency during pure abdominal breathing was ∼48% below the maximum value obtained in unmanipulated flies. In conclusion, the latter results suggest that manipulations of the arrangement of spiracle conductance are more likely to cause subtle alterations in wing motion that alter aerodynamic efficiency, than significantly changing the chemo-mechanical conversion efficiency of the asynchronous flight musculature.

To evaluate the functional differences between meso- and metathoracic spiracle-mediated respiration, we compared kinematic, aerodynamic and energetic variables in experiments in which we sealed either the two anterior meso- or the two caudal metathoracic spiracles. Fig. 7 shows the relative performance differences (`meso- – meta-') normalized to the absolute performance measured in unmanipulated flies. The metathoracic spiracle opening area is ∼26% larger than the mesothoracic spiracle opening area(Fig. 1), so we expected an∼26% higher contribution of the metathoracic spiracle to the overall flight performance score. Although the data in Fig. 7 confirmed this hypothesis, yielding a mean relative difference of –23.6±12.6%(N=12 measures), the strength in reduction slightly differed between the various flight measures. Except for stroke amplitude, stroke frequency and metabolic power, all values were significantly different from zero(t-test, P<0.01, Fig. 7).

The results in Figs 3, 4, 5, 6, 7 represent data measured 5 s after flight initiation and 2 s before flight stop of a flight sequence (see Materials and methods). A previous study has shown that during closed-loop conditions in a flight arena, tethered fruit flies produce a pronounced force peak immediately after flight initiation(Lehmann and Dickinson, 1997). In our experiments total flight force diminished after this initial peak to a steady state value that was typically equal to hovering flight force and thus equal to the animal's body weight (Fig. 8A, black trace). The force peak, including the corresponding peak in CO₂ release rate, ceased completely when respiratory flux was limited to ∼50% total thoracic spiracle opening area(Fig. 8, red trace). During pure abdominal breathing, we found a transient mismatch between force production and CO₂ release rate, suggesting that CO₂ is partly buffered in the tracheae and haemolymph at this early stage of the flight sequence (Fig. 8, blue trace). At flight stop, the buffered CO₂ was then apparently released during the subsequent resting period (Figs 8, 9). Moreover, at the instant after flight stop, we characteristically found a transient steep decrease in CO₂ release (Fig. 9D, arrow) followed by a more moderate decrease during which flies released the remaining tracheal CO₂ over a time period of up to 40 s (Fig. 10A).

Carbon dioxide buffering and delayed release produced by nine flight starts and stops of a single fly are shown in Fig. 9A,B. Averaged data for six flies are plotted in Fig. 9C,D. The temporal dynamics of CO₂ release rate after flight stop suggests a first order exponential decay with a mean time constant of 14.6 s(y=–2.3+e^–x/14.6, R²=0.92, χ²/d.f.=1.49; Fig. 10A, red line). This is consistent with the assumption of partial pressure gradient-driven diffusive respiratory processes in the fruit fly. For comparison, in unmanipulated flies CO₂ release rate after a flight sequence returned back to 67% of the resting rate within ∼1.89±1.08 s (time constant of first order exponential fit, y=–0.11+e^–x/1.89, R²=0.79±0.15,χ ²/d.f.=4.86±3.0, N=25 fits, 9 unmanipulated animals). Approximately half of this time, however, is due to the wash-out time constant of the respirometric chamber (0.9 s; see Materials and methods).

The temporal integral of post-flight CO₂ release rate allowed us to estimate the combined in vivo haemolymph–tracheal buffer capacity for CO₂ in Drosophila. We plotted these values in Fig. 10B as a function of mean flight force that was measured within the last 2 s prior to rest (pre-resting force). According to our analysis, mean CO₂ buffer capacity of Drosophila amounted to approximately 33.5±13.9 μl g^–1 body mass (N=35 sequences, blue line, Fig. 10B). Interestingly, this buffer capacity did not significantly change with increasing pre-resting flight force production or power requirements for flight as shown by linear regression analysis (linear regression fit on pre-resting force, P=0.46, N=35 flight sequences, Fig. 10B).

In the present study we have focused on the impact of tracheal gas exchange on flight muscle function and aerodynamic performance in tethered flying fruit flies Drosophila. The most prominent results may be summarized as follows. (1) Maximum locomotor performance can only be achieved when oxygen is delivered through all thoracic and abdominal spiracles. Hovering performance requires gas exchange through at least three thoracic and all abdominal spiracles. Linear regression analysis suggests that maximum spiracle opening area apparently matches the metabolic need of the animal at maximum locomotor performance (Figs 3, 4, 5). (2) The chemo-mechanical conversion efficiency of the flight musculature is broadly independent of the arrangement of thoracic spiracle conductance(Fig. 5A). (3) We found that the spatial distribution of tracheal gas exchange areas strongly influences lift coefficient, profile power requirements for flight, and aerodynamic efficiency (Figs 3E, 4B, 5B, 6). All those measures significantly decrease with decreasing spatial homogeneity of tracheal oxygen supply. (4) The delay of CO₂ release after flight stop in flies in which breathing was restricted to abdominal gas exchange revealed that the combined CO₂ buffer capacity of the tracheal dead space and the haemolymph's bicarbonate level amounts to ∼33.5 μl g^–1body mass.

Previous analyses of tracheal partial pressure in diffusion-based respiratory systems relied on the assumption that maximum spiracle opening area in an insect matches the instantaneous gas exchange rate at maximum locomotor performance (Lehmann,2001). Originally, this assumption was reinforced by the finding that most insects have developed strategies to avoid respiratory water loss through the open spiracles, i.e. the discontinuous gas exchange cycle, DGC(Harrison and Roberts, 2000; Lighton, 1994; Lighton, 1996; Miller, 1981; Slama, 1994; Snyder et al., 1995). Gas exchange areas larger than needed would reinforce tracheal water loss at maximum locomotor performance and thus increase the risk of desiccation in xeric environments (Lighton,1994). The data in Fig. 3D provide support for this hypothesis and our experiments thus permit derivation of maximum tracheal partial pressure for CO₂(P_T,CO2) under the various breathing conditions. Employing the equations above and setting spiracle conductance according to the various maximum spiracle opening areas, we estimated the following mean values for P_T,CO2 inside the tracheal system during flight:0.98±0.23 (unmanipulated animal), 0.83±0.17 (1 thoracic spiracle sealed), 1.20±0.25 (2 thoracic spiracles sealed), 1.47±0.24 (3 thoracic spiracles sealed) and 5.52±0.36 kPa (4 thoracic spiracles sealed). A slightly higher value for tracheal partial pressure of CO₂ (1.4±0.2 kPa) at maximum flight performance in unmanipulated Drosophila was calculated in a study on spiracle control strategies (Lehmann,2001).

The above results demonstrate that according to total spiracle opening area, mean P_T,CO2 may increase approximately 1.5-fold from∼0.98 kPa in unmanipulated flies (10 355 μm² opening area)to 1.47 kPa in flies in which total gas exchange area was limited to 3780μm². A gas exchange area of 493 μm² even produces a P_T,CO2 that is 6.6 times higher than in unmanipulated flies. Although statistical analysis reveals that all estimations of P_T,CO2 are significantly different from each other(t-test, P<0.05), a linear regression fit suggests that the slope between P_T,CO2 and gas exchange area is not significantly different from zero (linear regression fit, y=4.38–4.26×10^–4x,R²=0.66, P=0.09, N=5). Nevertheless, the small trend in the data set suggests that Drosophila is able to partially cope with the reduction in spiracle opening area by increasing the partial pressure gradient for CO₂ between tracheal system and ambient air of up to 5–6 kPa.

In comparison, since ambient partial pressure for oxygen is constant,oxygen uptake rate in Drosophila can only be reinforced by ventilation or by actively lowering the tracheal partial pressure for oxygen(Wigglesworth, 1972). For example, it has recently been shown that during hovering flight force production, tethered Drosophila sporadically employ the proboscis as a pump to actively ventilate their tracheal system(Lehmann and Heymann, 2005). A possible mechanism for active buffering of tracheal oxygen is haemoglobin storage. This phenomenon is discussed in the paragraph on `the significance of CO₂ buffer capacity'.

There are comparatively few data on tracheal partial pressure estimates of respiratory gases in flying insects, and most of the available data refer to the DGC. For example, Harrison et al.(Harrison et al., 1995)reported for grasshoppers that during the DGC interburst period, haemolypmph P_CO2 rises from 1.8 to 2.26 kPa with minimal acidification of the haemolymph. The authors concluded that spiracle opening is induced at internal threshold levels between 2 and 2.9 kPa(Gulinson and Harrison, 1996). Moreover, it has previously been shown that in many insects an endotracheal partial pressure of ∼4–6 kPa triggers the peripherally mediated inactivation of the spiracle closer muscle (for reviews, see Lighton, 1996; Krogh, 1913). The highest values reported for P_T,CO2 during the DGC was for Cecropia pupae of ∼7 kPa that did not fall below a minimum threshold of about 3.6 kPa (Burkett and Schneiderman, 1974). The overall shift of P_T,CO2 in Lepidopteran pupae towards higher tracheal partial pressures has been interpreted as a consequence of the high vulnerability of the pupae to desiccation(Harrison et al., 1995).

If we consider that in an insect a high P_T,CO2, due to prolonged DGC interburst intervals, indicates a strategy to avoid respiratory water loss, the comparatively low P_T,CO2 measures in unmanipulated flying Drosophila would in turn suggest that in this insect respiratory water loss is of minor importance for total water balance. This interpretation is driven by the finding that in several insects,respiratory water loss is relatively small compared to cuticular transpiration so that the DGC does not predominantly influence the water balance of the animal. For example, the ratio between cuticular and respiratory transpiration is 98.1:1.9 in Camponotus vicina and 92.0:8.0 in the ant Cataglyphis bicolor (Lighton,1988), 87.0:13.0 in the ant Pogonomyrmex rugosus(Lighton et al., 1993b) and the cockroach Periplaneta americana(Machin et al., 1991),97.0:3.0 in the grasshopper Romalea guttata(Hadley and Quinlan, 1993) and 95.4:4.6 in the grasshopper Taeniopoda eques(Quinlan and Hadley, 1993). However, in flying Drosophila melanogaster this ratio appears to be almost inverted and amounts to ∼17.4:82.6(Lehmann, 2001). From these values we conclude that the spiracles represent a significant route for tracheal water loss in the fruit fly, and with respect to the hypothesis above, this cannot easily account for the low P_T,CO2 in the unmanipulated flying animal.

The dead volume of the tracheal system serves as a buffer space for respiratory gases. In addition, Drosophila may store oxygen using haemoglobin that is mainly synthesized in the tracheal walls and the fat body of the animal (de Sanctis et al.,2005; Hankeln et al.,2005). During transient locomotor activity, the indirect flight musculature might benefit from haemoglobin-mediated oxygen transport and storage that produces a temporal mismatch between the uptake rate of oxygen through the spiracles and flight force production. To largely circumvent this problem in our respiratory measurements, we excluded the first 5 s in each flight sequence from our analysis, expecting to achieve rather steady-state flight metabolism of 10–15 times the resting rate(Casey, 1989; Casey and Ellington, 1989; Lehmann and Dickinson, 1997). By contrast, tracheal CO₂ concentration is correlated with the haemolymph bicarbonate level that buffers CO₂ at the expense of changes in pH (Harrison et al.,1995). Gulinson and Harrison investigated CO₂ buffering in the grasshoppers Romalea guttata and Schistocerca americana by injections of NaHCO₃, HCl and NaOH into the haemolymph (Gulinson and Harrison,1996). In our experiments, by contrast, we derived CO₂buffer capacity from the delay in gas release after flight stop(Fig. 10). Since the amount of total flight-specific CO₂ released after flight was independent of pre-resting flight force production and thus of metabolic activity, we suggest that the value of 33.5 μl CO₂ g^–1 body mass may represent a maximum estimation of Drosophila's total CO₂buffer capacity (tracheal and haemolymph buffer).

To assess the flight time during which an unmanipulated fruit fly may rely on CO₂ buffering instead of CO₂ release through the spiracles, we converted the value of 33.5 μl CO₂g^–1 body mass into units of time that yielded 2.30±0.95 μl s^–1 g^–1 body mass. Subsequently, we compared this measure with the mean CO₂ release rate produced during hovering flight conditions, that is 2.8 μl s^–1 g^–1 body mass(Lehmann et al., 2000). The ratio between both values (2.3/2.8) suggests that CO₂ buffer capacity ensures flight for only ∼0.82 s and thus for a relatively short flight time. Moreover, this value might explain why the large thoracic spiracles open immediately after flight initiation in this insect(Fig. 8)(Lehmann, 2001). In a resting fruit fly that exclusively breathes through the abdominal spiracles, a tracheal CO₂ partial pressure threshold of 5.52 kPa (see previous paragraphs) would be reached within 3.1 s at the given CO₂ buffer capacity (resting metabolism=0.74±0.33 μl s^–1g^–1 body mass) (Lehmann et al., 2000). Ignoring all potential errors associated with these findings, the latter result might explain why Drosophila melanogasterrarely employs a clear DGC pattern during rest compared to many other insects(Harrison et al., 1995; Lighton, 1994; Lighton, 1996; Williams and Bradley, 1998). During discontinuous breathing the spiracles open only sporadically with typical time periods in the range of several minutes. Within a DGC interburst interval of several minutes, however, Drosophila's P_T,CO2 would exceed the critical threshold value of 4–6 kPa several-fold, suggesting that the fruit fly must allow continuous gas exchange through the thoracic spiracles even during rest.

Nevertheless, we should keep in mind that this conclusion, among the other results in this study, may critically depend on the simple assumption that respiratory gas exchange in Drosophila relies on diffusion alone and can be described by the simple analytical model above. This approach neglects any dynamics resulting from both buffering of respiratory gases and tracheal ventilation. In addition, there are potential errors associated with our measurement technique including the difficulty to temporally match locomotor performance and CO₂ release rate of the flying animal. The outcome of this study should thus be regarded with care and direct measurements of tracheal partial pressures at the various experimental conditions have still to verify our predictions.

One of the most unexpected results of the present study is the finding that muscle efficiency changes only slightly in response to manipulations of the spatial distribution of spiracle exchange areas. The pronounced relative difference in muscle efficiency of 143±60.3% at 0.29 relative flight force production appears to be an exception and probably is partly due to the fly's CO₂ buffering capacity (Figs 6B, 10). Nevertheless, we found a trend in the data set suggesting that relative muscle efficiency is inversely correlated with spiracle diffusive area(Fig. 6B). The same trend is also visible in the second muscle physiological parameter, i.e. mechanical power output (Fig. 6A). Note that these results run counter to the results on the relative lift coefficient(Fig. 6C), relative drag coefficient (data not shown) and relative aerodynamic efficiency(Fig. 6D), which taken together show a significant decrease in magnitude with decreasing spiracle exchange area. In sum, the findings above suggest that changes in the spatial distribution of tracheal oxygen supply due to local blocking of individual spiracles negatively affect the ability of the animal to produce flight force– but reinforce the production of mechanical power and the efficiency of the mechano-chemical conversion process of the indirect flight musculature.

The results above are rather surprising because in unmanipulated fruit flies, muscle efficiency decreases with decreasing flight force production(Lehmann, 2002). It has been suggested that low muscle efficiency either reflects a decreased crossbridge activation between actin and myosin filaments or an unfavourable strain regime of the asynchronous flight muscle(Josephson, 1999; Josephson et al., 2001; Lehmann and Dickinson, 1997). Therefore, we originally hypothesized that at flight forces below maximum performance, an inhomogeneous supply of oxygen to the IFM would even reinforce this attenuation in crossbridge activation. Instead, our data apparently show that the geometry of the tracheal system and the location of gas exchange areas (spiracles) are of minor importance for IFM overall efficiency. A possible explanation for this finding might be the fact that the large air sacs of the dorsal and lateral tracheal system [pleural-, notopleural-,lateroscutal- and medioscutal sacs(Demerec, 1965)] homogenize oxygen concentration within the fly body. However, if this explanation is true, it still remains puzzling why muscle mechanical power output so strongly depends on the changes in the arrangement of spiracle conductance.

We also unexpectedly found that relative mean lift coefficient and aerodynamic efficiency differ up to approximately 50% between flies facing alterations of oxygen supply distribution and unmanipulated animals(Fig. 6C,D). By contrast,kinematic variables such as stroke amplitude were affected relatively little,and stroke frequency was even widely indistinguishable between unmanipulated and spiracle-manipulated flies at the various flight forces (1.44±11.7 Hz, mean difference ± s.d., N=5 forces, Fig. 3, Table 1). Previous studies on the mechanisms of unsteady aerodynamics in flapping insect wings have shown that flight force production linearly decreases with decreasing wing velocity,thus following conventional aerodynamic laws(Ellington, 1984a; Lehmann and Dickinson, 1998). Apparently, wing velocity (the product between stroke amplitude and frequency)in unmanipulated animals decreases to a greater extent than in flies in which flight force reduction is forced by a reduction in diffusive exchange area. As a consequence, mean lift coefficient in unmanipulated flies varies less dramatically with changing flight forces than in the spiracle-manipulated animals (Fig. 3E). From these findings, we hypothesize that alterations in the spatial distribution of gas exchange areas ultimately alter the fine structure of wing motion such as the angle of attack, the velocity profile during wing translation or the wing's rotational speed and timing during the stroke reversals. For example, it has been shown that in a robotic model of Drosophila, changes in wing rotation may alter both flight costs and lift production(Dickinson et al., 1999; Sane and Dickinson, 2001). An 8% advanced rotational timing, during which the wing rotates prior to the stroke reversal, may reinforce aerodynamic force production by more than 70%of total force, compared to a delayed rotation that occurs at the beginning of each half stroke (Dickinson et al.,1999). Somewhat smaller increases in lift production have been reported for increases in the wing's angular velocity during rotation(Sane and Dickinson, 2002). Changes in rotational speed and timing, moreover, may alter the benefit of the wake capture mechanism and clap-and-fling lift enhancement that also contribute to Drosophila's high lift coefficient(Lehmann et al., 2005).

Besides the changes in relative lift coefficient, the findings in Figs 3F, 4B, 5B suggest that changes in the arrangement of spiracle conductance may also decrease the ratio between lift and drag coefficients and thus increase the relative profile power requirements for wing flapping. However, since lift and drag forces are vectors of total flight force, an attenuation in lift would likely cause a relative decrease in drag rather than a relative increase. The same 3-dimensional robotic model wing of Drosophila mentioned above has demonstrated a tremendous increase in wing drag towards higher angles of attack (Dickinson et al.,1999; Usherwood and Ellington,2002). While at angles of attack <45° lift and drag coefficients are positively correlated, lift and drag coefficient are inversely correlated at angles >45°. Increases in angle of attack above this threshold could thus explain, for example, why the mean drag coefficient may relatively increase while the mean lift coefficient decreases during flight (Lehmann, 2004). A detailed reconstruction of the wing kinematic pattern by means of high-speed video technique should allow us to tackle this hypothesis for the underlying aerodynamic mechanisms in the future.

The clap-and-fling mechanism for lift enhancement supposedly may not contribute to the relative change of lift-to-drag ratio in Drosophila, because its occurrence changes the lift-to-drag ratio only slightly, from 0.57 to 0.58(Ellington, 1975; Lehmann et al., 2005; Weis-Fogh, 1973). Altogether,the results suggest that respiratory gas exchange based on the usage of multiple thoracic and abdominal spiracles appears to be beneficial for maintaining an elevated efficacy of aerodynamic force production in the fruit fly. The ultimate explanation for this finding might be that changes in the arrangement of spiracle conductance alter the contraction dynamics or muscle stiffness of the IFM and thus the movements of the mechanical thoracic oscillator (Josephson, 1999; Josephson et al., 2001; Josephson and Stokes, 1999; Vigoreaux, 2001; Vigoreaux et al., 2000). These parameters were not covered by our measurement technique.

Alternatively, we should consider whether the above results are simply due to the different mechanisms used by the flies for modifying flight force production. While unmanipulated flies `voluntarily' altered flight forces in response to the vertical motion of the visual lift stimulus, the spiracle-blocked flies probably reduced flight force due to the restriction in mechanical power output of the flight musculature. Consequently, our findings can be interpreted such that changes in wing kinematics mediated by active control of flight steering muscles produce more favourable stroke kinematics than a passive change via mechanical power limits (Götz, 1983; Heide and Götz, 1996). Numerous kinematic and electrophysiogical studies have shown that 17 flight control muscles (steering muscles) tune several aspects of wing motion during manoeuvring flight, such as stroke amplitude, stroke frequency, the timing of wing rotation, angle of attack or the wing trajectory in Drosophila(Götz, 1983; Heide and Götz, 1996; Lehmann and Götz, 1996)(for a review, see Dickinson and Tu,1997). In this case, the data plotted in Fig. 6 would highlight the energetic and aerodynamic consequences of wing kinematic alterations due to different flight control strategies rather than reflect the significance of respiratory constraints. It appears to be difficult to distinguish unambiguously between both interpretations in our experiments because changes in the arrangement of spiracle conductance also involve changes in total diffusive area. However, the comparison between gas flux through the meso- and metathoracic spiracles should be noted as an exception(Fig. 7). As already mentioned,the mean difference in the performance measures of 26% approximately matches the difference in spiracle opening area between meso- and metathoracic spiracles, which suggests a negligible 2.4% difference in oxygen supply rate between the meso- and or metathoracic spiracle. However, due to the large ipsilateral tracheal trunks and air sacs, this ipsilateral effect was expected to be small a priori (Miller,1950).

The in-depth evaluation of the significance of tracheal gas exchange in Drosophila potentially provides several new insights onto how the spatial distribution and the size of spiracle exchange areas determine the function of the flight motor in a flying insect. The present results provide direct evidence for the general assumption in respiratory research that the tracheal development of a simple diffusion-based system matches the respiratory need at maximum metabolic activity of the animal. Under those conditions, respiratory water loss would be minimal, which in turn prevents water stress on animals living in xeric environments(Lighton, 1994; Lighton, 1996). Moreover, our findings apparently show that changes in the arrangement of spiracle conductance primarily effect aerodynamic phenomena in addition to flight muscle mechanical power output, but not predominantly muscle efficiency. The exact reason why relative muscle mechanical power output depends more strongly on the spatial distribution of spiracle areas than muscle efficiency remains unknown and will require further research on the indirect flight musculature in the behaving animal. Since it has been assumed that insects have no anaerobic capacity, the magnitude of oxygen and CO₂ buffer capacity might play a crucial role in breathing behaviour and spiracle control in the fruit fly (Ziegler, 1985). On the one hand, CO₂ buffer capacity may explain why spiracles have to open immediately after flight initiation and match their opening area to metabolic need (Lehmann,2001). On the other hand, the small CO₂ buffer capacity might also partly explain why inbred lines of Drosophila reared on commercial food do not exhibit a clear DGC pattern during resting metabolism(Williams and Bradley, 1998). Eventually, in conjunction with the small safety margin for tracheal respiration at maximum locomotor capacity, we conclude that Drosophila may apparently maximize the efficiency of its locomotor system for flight by well-balancing respiratory gas flow between the four large spiracles in the fly's thorax.

 
• A_T

  total spiracle exchange area

 
• \(\overline{C_{\mathrm{D}}}\)

  mean drag coefficient for wing flapping

 
• \(\overline{C_{\mathrm{L}}}\)

  mean lift coefficient for wing flapping

 
• D

  diffusion coefficient

 
• DGC

  discontinuous gas exchange cycle

 
• F_T

  total flight force

 
• G

  spiracle conductance

 
• IFM

  indirect flight muscle

 
• L_T

  typical tracheal length

 
• Ṁ

  rate of gas flux

 
• n

  wing stroke frequency

 
• P_A

  partial pressure of the gas in the ambient air

 
• \(\overline{P_{\mathrm{ind}}^{{\ast}}}\)

  mean flight-specific and flight muscle mass-specific induced power

 
• \(\overline{P_{\mathrm{mech}}^{{\ast}}}\)

  mean flight-specific and flight muscle mass-specific mechanical power

 
• \(\overline{P_{\mathrm{MR}}^{{\ast}}}\)

  mean flight-specific and flight muscle mass-specific metabolic power

 
• \(\overline{P_{\mathrm{pro}}^{{\ast}}}\)

  mean flight-specific and flight muscle mass-specific profile power

 
• \(\overline{P_{\mathrm{RF}}^{{\ast}}}\)

  mean flight-specific and flight muscle mass-specific Rankine–Froude power

 
• P_T

  tracheal partial pressure of a gas

 
• SEM

  scanning electron microscopy

 
• sp

  tracheal and abdominal spiracles

 
• STP

  standard temperature and pressure

 
• w_b

  body weight of the animal

 
• Φ

  wing stroke amplitude

 
• β

  capacitance coefficient

 
• ηA

  aerodynamic efficiency

 
• ηM

  muscle efficiency

 
• ηT

  total efficiency of flight motor

 
• τ

  time constant

We like to thank the two anonymous referees for their helpful comments and Ursula Seifert for carefully reading the manuscript. This work was generously funded by the BioFuture grant 0311885 of the German Federal Ministry for Education and Research to F.O.L.