Discontinuous gas exchange in Madagascar hissing cockroaches is not a consequence of hysteresis around a fixed P_CO2 threshold

Insect ventilation is generally understood to be driven by respiratory chemoreceptors that respond to internal oxygen and carbon dioxide partial pressure (P_O2 and P_CO2, respectively) by stimulating appropriate ventilatory responses when either gas deviates from some defended threshold level. Thus, insects exposed to hypoxia and/or hypercapnia respond by opening their spiracles (Case, 1956; Förster and Hetz, 2010; Wigglesworth, 1935) and increasing ventilation frequency (Bustami et al., 2002; Harrison et al., 2006; Henderson et al., 1998; Matthews and White, 2011). While this explains changes in ventilation frequency when gas exchange is continuous, whether these same chemoreceptor responses also drive episodic patterns of gas exchange is not well understood.

Many insects display a pattern of intermittent breathing called a discontinuous gas exchange cycle (DGC) where periods of gas exchange alternate with periods of apnoea, and internal P_O2 and P_CO2 fluctuate significantly as a consequence (Förster and Hetz, 2010; Harrison et al., 1995). Stereotypical DGCs consist of three repeating phases: the closed (C), flutter (F), and open/ventilation (O or V) phase (Lighton, 1996). During the C-phase, spiracles are closed and both O₂ uptake and CO₂ release are negligible, causing P_O2 to fall and P_CO2 to rise (Buck and Keister, 1955). The C-phase then transitions into a F-phase, where spiracles begin to open and close rapidly but sporadically. During the F-phase, the rate of O₂ uptake is just sufficient to satisfy the insect's aerobic demands so tracheal P_O2 remains low and relatively constant (Lighton, 1996), whereas internal P_CO2 continues to increase (Levy and Schneiderman, 1966). Finally, the F-phase transitions to the O-phase when the spiracles open and the accumulated CO₂ is released in a large burst and O₂ is taken up rapidly. This O-phase generally coincides with a period of vigorous abdominal ventilatory movements. During DGCs, these three phases repeat in this order indefinitely.

Fundamental questions remain about the mechanisms responsible for producing DGCs. Specifically, assuming that insects regulate their gas exchange to control internal P_O2 and P_CO2 at some desired level, what happens during DGCs to cause these gas levels to decouple from these putative threshold levels? Previous research on diapausing cecropia moth pupae (Hyalophora cecropia) found that the transitions between closed, flutter and open spiracle states occurred when the pupa's tracheal P_O2 and P_CO2 crossed hypoxic and hypercapnic thresholds (Burkett and Schneiderman, 1974; Förster and Hetz, 2010). These pupae opened their spiracles once tracheal P_CO2 rose above a threshold level of ∼1–1.5 kPa, or when tracheal P_O2 dropped below a mean threshold level of ∼2.6 kPa; the actual P_O2 threshold was positively dependent on P_CO2, with hypercapnia causing the spiracles to open at a higher P_O2. Spiracle fluttering was observed only occasionally and was assumed to occur when tracheal P_O2 fluctuated around the spiracle-opening P_O2 threshold. From these experiments, Förster and Hetz (2010) outlined a simple model whereby DGCs arise as tracheal P_O2 and P_CO2 fluctuate around these fixed hypoxic and hypercapnic thresholds (referred to as the fixed-threshold model: Fig. 1).

These moth pupae data show that internal P_O2 and P_CO2 thresholds can explain the transitions in spiracle state from the C- to the F-phase, and from the F- to the O-phase, during DGCs: high internal P_O2 and low P_CO2 result in closed spiracles, and the reverse conditions result in open spiracles. Crucially, though, it cannot explain why so much CO₂ is expelled during the O-phase that internal P_CO2 falls below the P_CO2 threshold, resulting in a subsequent C-phase. Indeed, the quantity of CO₂ exhaled during the O-phase can be as much as 90% of the CO₂ accumulated in each cycle (Harrison et al., 1995; Levy and Schneiderman, 1966). A delayed response to changing internal P_CO2 has been proposed as one way to explain this behaviour, and thus explain the emergence of DGCs.

Control theory describes how a temporal lag between an animal's changing internal P_CO2 level and its detection by a chemoreceptor controlling the ventilatory response can drive the respiratory system into sustained oscillation. This begins with an initial respiratory disturbance that pushes the internal P_CO2 above the spiracle-opening threshold level. This causes the spiracles to open (O-phase) and the accumulated CO₂ to be released from the insect's haemolymph and tracheal system into the environment. If a substantial lag existed between the rapidly changing P_CO2 within the haemocoel and the P_CO2 being detected by the chemoreceptor, then spiracle closure would occur only after haemocoel P_CO2 had dropped below the spiracle-opening threshold. This would lead to a protracted corrective apnoea (C-phase), during which internal P_CO2 would again rise above the threshold level and the cycle would repeat. For the fixed-threshold model, the expulsion of excess CO₂ during the O-phase is necessary to produce a subsequent C-phase, and currently the origin of this overshoot is assumed to be the result of hysteresis, either due to a temporal lag between the chemoreceptor and haemolymph or somehow built into the chemoreceptor itself, e.g. by incorporating two P_CO2 thresholds: a high P_CO2 ‘open’ threshold and a lower P_CO2 ‘close’ threshold (Förster and Hetz, 2010). The critical importance of hysteresis in generating DGC patterns has also been borne out in more complex fixed-threshold models of insect ventilatory control, where including a delay in the response of one of two chemoreceptor feedback loops was found to be essential for the models to produce realistic DGC-like behaviour (Grieshaber and Terblanche, 2015). However, regardless of how the lag is generated, the existence of a hysteresis between CO₂ detection and the spiracle/ventilation response is currently hypothetical. Likewise, the role of active ventilation during the O-phase (as is the normal condition for most non-pupal insects) has never been considered in these models. As such, the accuracy of this fixed-threshold model has not been validated experimentally for either insects or insect pupae, and all relevant physiological parameters have never been measured simultaneously in vivo.

This study used Madagascar hissing cockroaches (Gromphadorhina portentosa) (Schaum 1853) to determine: (a) how haemolymph P_O2 and P_CO2 co-vary during continuous gas exchange and DGCs, (b) whether these levels oscillate around a fixed P_CO2 ventilatory threshold during DGCs, and (c) how challenging the insect with ambient hypoxia and hypercapnia alters haemolymph P_O2, P_CO2 and the gas exchange pattern adopted by the insect. Miniaturised fibre optic P_O2 and P_CO2 optodes were implanted simultaneously into the haemocoel of these large insects to measure these parameters in vivo. Abdominal ventilation frequency and rate of CO₂ production (V̇_CO2) were also measured to quantify gas exchange patterns and metabolic rate, respectively. Continuous gas exchange was recorded from intact individuals, but following these measurements, decapitation was used to elicit DGCs. While decapitation is clearly an artificial way to elicit a DGC, the gas exchange pattern produced displays the same C/F/O phases that occur when this pattern is displayed spontaneously by the intact insect. It may, therefore, be safely assumed that DGCs displayed by decapitated individuals are driven by the same underlying ventilatory control system that generates DGCs in intact individuals. This is more plausible than positing the existence of a second redundant DGC control system that replicates the output of the DGC using unrelated mechanisms. As such, these intact and decapitated DGCs must be manifestations of the same control system, regardless of how the pattern was elicited, so examining how DGCs displayed by decapitated cockroaches respond to hypoxic and hypercapnic challenges should reveal how these respiratory gases are involved in the production of this gas exchange pattern.

The ultimate aim of this research was to determine the typical haemolymph gas parameters of these insects during continuous and discontinuous gas exchange, then use this information to test the hypothesis that DGCs arise as a natural consequence of a delayed ventilatory response to haemolymph P_CO2 resulting in oscillations around a fixed P_CO2 threshold.

Madagascar hissing cockroaches G. portentosa were reared for multiple generations in an insectary at the University of British Columbia. Cockroaches were held in two, 65 l black plastic storage containers at 31°C, on a 12 h:12 h light:dark cycle, and fed fruit, dry cat food (Friskies Chef's Blend, Purina, Mississauga, ON, Canada) and hydrated hydrogel granules ad libitum. Only male cockroaches were used for experiments, as the large pronotal horns possessed by the males of this species were a convenient site for the implantation of fibre optic P_O2 and P_CO2 sensors. Individual male cockroaches (mean±s.d. mass 12.75±1.82 g, n=18) were isolated and fasted for 24 h before experiments. Cockroaches were weighed to 0.01 mg on an electronic balance (XPE205D, Mettler-Toledo Inc., Mississauga, ON, Canada) directly before experimentation.

For each experiment, a cockroach was secured within a 120×35×40 mm (L×W×H; 168 cm³) clear acrylic respirometry chamber using a custom-built harness. The harness was 3D printed from ABS plastic and fitted over the cockroach's pronotum, posterior to the pronotal horns. Individual cockroaches were anaesthetised by a 30 s exposure to pure CO₂, before being fixed into the harness using a commercially available mixture of paraffin, beeswax and colophony (Brazilian and Bikini Wax, Nads, NSW, Australia) as an adhesive. A beam (15×5×5 mm) containing two horizontal holes projected from the harness over the cockroach's head, allowing the harness to be secured into a 3D printed bracket that was attached to the inside of the respirometry chamber lid using two M3 screws (Fig. 2B). When assembled, this fixed the cockroach so its pronotum was held directly beneath two 10 mm diameter holes in the lid, one above each pronotal horn, while its abdomen was positioned above an IR reflection sensor (SFH 9202, Osram Opto Semiconductors, Regensburg, Germany) mounted in the floor of the chamber. The IR sensor was connected to a circuit which produced a variable voltage in response to the distance between the sensor and the abdomen, allowing abdominal pumping movements associated with gas exchange to be measured. This voltage was measured at 2 Hz by the Powerlab 8/35 DAQ and recorded using LabChart (v.8.1.5, ADInstruments) on a desktop computer, providing a quantitative measure of abdominal ventilation frequency.

The P_O2 optodes (flat-tip, 230 µm diameter fibre, IMP-PSt7, PreSens GmbH, Regensburg, Bavaria, Germany) were connected to a Microx 4 trace meter (PreSens GmbH) and calibrated using a two-point calibration: 0 kPa P_O2 water was produced by mixing sodium sulphite into reverse osmosis (RO) water and submerging the P_O2 optodes in this solution for 10 min before calibration; room air was bubbled through RO water using an air stone for 30 min to thoroughly saturate the water with ambient oxygen, before calibrating the probe at 21 kPa P_O2. The calibrations were performed at 22°C inside the same incubator as used for the experiment.

The P_CO2 optodes (flat-tip, 250 µm diameter fibre, IMP-CDM1, PreSens GmbH) were calibrated in 100 ml of RO water containing 0.154 mol l⁻¹ NaCl which was equilibrated with 0, 0.5, 1, 2, 3, 4 and 5 kPa P_CO2 in N₂. The calibration saline was maintained at 22°C in a 200 ml glass bottle suspended in a temperature-controlled water bath (F33-ME, Julabo, Seelbach, Baden-Württemberg, Germany). Two 500 ml min⁻¹ flow controllers (MC-500SCCM-D/5M, Alicat Scientific), controlled by gas-mixing software (Flow Vision, Alicat Scientific) running on a desktop PC, were used to generate P_CO2 in a stepwise fashion by combining 99.998% N₂ with a certified mix of 5% CO₂ in a balance of N₂ (Praxair, Mississauga, ON, Canada). Gas mixtures were bubbled through an air stone submerged in the calibration saline at 500 ml min⁻¹. Probes were held for 1 h at 0 and 0.5 kPa P_CO2, and 30 min at 1, 2, 3, 4 and 5 kPa P_CO2 to ensure complete equilibration of the calibration solution. During calibration, P_CO2 was measured at 5 min intervals with a CO₂ meter (pCO₂ micro, PreSens) and recorded onto a desktop PC using pCO₂ micro View software (v.1.0.0, PreSens). Monitoring P_CO2 over time guaranteed that the probes had reached equilibrium with the CO₂ level that was bubbled through the calibration saline. The final CO₂ measurement recorded at each CO₂ level was used to produce a multipoint calibration curve for the optode, composed of 7 points ranging from 0 to 5 kPa CO₂.

While the cockroach was still CO₂ narcotised from being mounted in the harness, two small holes were drilled into the insect's haemocoel, one hole in each pronotal horn, using a 0.84 mm diameter carbide drill bit attached by a flexible shaft to a rotary tool (Dremel 3000 series 1.2 Amp Rotary Tool, Dremel, Racine, WI, USA). As each hole was cut it was sealed temporarily by applying a dab of 2-part polyvinyl siloxane casting material (President light body dental impression material, Coltène Whaledent, Altstätten, Switzerland). Following this operation, the cockroach was secured to the respirometry chamber lid using the previously attached ABS harness (Fig. 2B). To implant a calibrated P_O2 optode, first the polyvinyl siloxane plug sealing the hole in the right pronotal horn was removed, then the optode was lowered through a 10 mm hole in the chamber lid using a micromanipulator (M3301, World Precision Instruments, Sarasota, FL, USA) and carefully inserted ∼2 mm into the haemocoel. The optode was sealed into the horn by application of more polyvinyl siloxane casting material around the optic fibre. The fibre of the optode was then secured to the respirometry chamber lid using a custom-built clamp, 3D printed from ABS plastic, that was bolted to the top of the lid. A calibrated P_CO2 probe was implanted into the haemocoel within the cockroach's left pronotal horn using the same method as described above, but with the optode passing through a second 10 mm hole in the lid and being secured using a second clamp. A 3D-printed ABS plastic ring with inwardly sloping walls had previously been epoxied to the chamber lid, forming a well around both holes. Strips of aluminium foil were placed inside this ring around each optode to cover the two holes in the lid before being covered liberally with polyvinyl siloxane, completely filling the well and forming a gas-tight seal. Low sampling frequencies were used to ensure that any photobleaching of the optode tips was minimised during the 2 day experimental run. In vivo haemolymph P_CO2 was recorded every 2 min and in vivo haemolymph P_O2 measurements were recorded every 30 s. No signal drift or change in sensor amplitude was observed for either the P_O2 or P_CO2 optode during the experiments. All experiments were conducted inside an incubator (22°C, 12 h:12 h light:dark) (Percival Scientific Inc.).

For the first 5 h of experimentation, the cockroaches were exposed to normoxic normocapnia (21 kPa P_O2, 0 kPa P_CO2) to stabilise after surgery. The next 18 h were split into two 9 h treatments. Treatments began with either a further 9 h exposure to normoxic normocapnia, or a 9 h exposure to either hypoxic normocapnia (10 kPa P_O2, 0 kPa P_CO2) or normoxic hypercapnia (21 kPa P_O2, 2 kPa P_CO2). The order of the treatments alternated between experiments such that if one experiment started with a 9 h normoxic normocapnia treatment, the next experiment began with either the 9 h hypoxia or hypercapnia exposure. After the first 23 h, the respirometry chamber was removed from the incubator, and the cockroach was anaesthetised by a 30 s exposure to pure CO₂. The lid of the respirometry chamber was removed with cockroach and optodes attached, and the cockroach was swiftly decapitated using fine scissors. The neck wound was sealed using melted beeswax. Decapitation reliably elicited sustained DGCs that began shortly after surgery and continued for at least a week thereafter. Once decapitated, the cockroach was returned to the chamber, and the chamber lid was again fixed in place. The chamber was then returned to the incubator for another 23 h of experimentation. The final 18 h of DGC experiments were again divided into two 9 h blocks, repeating the same modified atmosphere manipulations as were carried out before decapitation.

Measurements of O₂ and CO₂ levels were recorded as percentage of total gas dissolved in haemolymph. These raw values were converted into partial pressures (P_O2 or P_CO2 in kPa) by dividing each value by 100 then multiplying by 101.3 kPa. Mean continuous P_CO2 and P_O2 values were taken from the longest sustained period of stable haemolymph P_CO2 in each treatment. When DGCs were displayed, the maximum and minimum P_CO2 and P_O2 values were determined for each C–F–O cycle in the final 6 h of each treatment using the peak analysis function in LabChart software (ADInstruments) and averaged. The durations of different phases of the DGCs were measured in both treatment gases and compared. The O-phase and interburst duration were determined using the haemolymph P_O2 trace. The interburst duration was defined as the period of continuous haemolymph P_O2 decline, while the O-phase duration was defined as the period when P_O2 began to rise before a subsequent fall. Total cycle duration was determined by adding the O-phase and interburst phase durations. The C-phase duration was determined by the absence of ventilatory movements, whereas the F-phase was determined by the presence of relatively low-frequency ventilatory movements which corresponded with no observable change in haemolymph P_O2. The experiment also measured the mean rate of CO₂ release during each DGC in hypoxic and normoxic conditions. The cockroach's rate of CO₂ release was recorded using the IRGA and then averaged over each DGC to calculate mean V̇_CO2 (μl s⁻¹). The method used to identify specific parts of the DGC for analysis is illustrated in Fig. 3 using typical data traces recorded from cockroaches displaying continuous ventilation and DGCs.

All DGC data from individual cockroaches represent the average obtained from the final 6 h of DGCs recorded in each treatment gas. All data are available from Dryad (https://doi.org/10.5061/dryad.b8gtht7ct). Paired measurements obtained from individual cockroaches represent measurements made during exposure to normoxic normocapnia (21 kPa P_O2, 0 kPa P_CO2), and a treatment of repeated normoxic normocapnia (control), hypoxic normocapnia (10 kPa P_O2, 0 P_CO2) or normoxic hypercapnia (21 kPa P_O2, 2 kPa P_CO2). Differences between values obtained in normoxic normocapnia exposure and the treatment gas were tested using a 2-tailed paired t-test in Prism 8 (GraphPad Software Inc., San Diego, CA, USA) with statistical significance being set at α=0.05. The Benjamini–Hochberg (BH) procedure with an α=0.05 was applied to control the false discovery rate associated with performing multiple tests on each treatment group: 11 tests on data from the normoxia–hypercapnia manipulation and 12 tests on the normoxia–hypoxia and normoxia–normoxia manipulations. t-Tests were used despite often low (n≤5) sample sizes, as any significant changes in values resulting from different gas exposures would still be detected so long as the data showed strong correlation coefficients within treatments and a large effect size (De Winter, 2013). However, overall the statistical analysis employed here is conservative. Given that the small sample sizes increase the likelihood of Type II errors, while the BH procedure controlled for Type I errors, this study is more likely to commit errors of omission, rather than generate false positives.

Median changes in P_O2 and P_CO2 during continuous ventilation and DGC, as well as median changes in phase duration are summarised in Table 1.

Changes in mean haemolymph P_O2 and P_CO2 are shown in Fig. 4. Intact G. portentosa displaying continuous ventilation in normoxic normocapnia maintained stable haemolymph P_O2 and P_CO2 levels with a mean (±s.d.) of 17.1±2.9 kPa (n=14) and 1.9±0.4 kPa (n=15), respectively. Neither mean haemolymph P_O2 nor P_CO2 changed significantly between the first and second 9 h period of exposure to the normoxic normocapnic gas mixture (t₄=1.7417, P=0.1565 and t₄=1.1952, P=0.2980, respectively). Three of six intact cockroaches exposed to hypoxia (10 kPa P_O2) exhibited sustained DGCs in lieu of continuous breathing. Unfortunately, equipment failure meant that reliable P_CO2 measurements could be obtained from only two of the three continuously breathing cockroaches. Mean haemolymph P_O2 was significantly lower in continuously ventilating cockroaches exposed to hypoxia (t₂=9.8835, P=0.0101), falling by between 7.9 and 11 kPa. There was no significant change in haemolymph P_CO2 when cockroaches were exposed to hypoxia (t₁=3.333, P=0.1855). During exposure to hypercapnia (2 kPa P_CO2), neither haemolymph P_O2 nor P_CO2 changed significantly relative to levels in normoxic normocapnia (t₂=1.152, P=0.3809, and t₃=2.8947, P=0.0628, respectively).

All decapitated cockroaches displayed robust DGCs. Minimum P_O2 level fell close to 0 kPa during the C-phase in most experiments. Exposure to 10 kPa P_O2 or 2 kPa P_CO2 did not cause any of the decapitated cockroaches to stop displaying DGCs. Changes in minimum and maximum haemolymph P_O2 during DGCs in decapitated cockroaches exposed to control, hypoxia and hypercapnia treatments are shown in Fig. 5A,B. Cockroaches exposed to two periods of normoxic normocapnic air showed no significant change in either maximum P_O2 (t₄=1.4698, P=0.2156) or minimum P_O2 (t₄=1.000, P=0.3739). When cockroaches were exposed to hypercapnia, there was no change in mean minimum P_O2 (t₄=2.2361, P=0.089) or mean maximum P_O2 (t₄=1.0461, P=0.3546). Unsurprisingly, maximum haemolymph P_O2 was reduced significantly during exposure to hypoxia (t₄=17.3003, P=0.0001), but minimum P_O2 did not change significantly (t₄=1.7833, P=0.1491). However, minimum P_O2 was still reduced in all cockroaches that did not reach 0 kPa during their normoxic normocapnia control treatment.

Changes in minimum and maximum haemolymph P_CO2 during DGCs in decapitated cockroaches exposed to control, hypoxia and hypercapnia treatments are shown in Fig. 5C,D. Sustained exposure to normoxic normocapnia did not significantly change either mean maximum P_CO2 (t₅=0.1152, P=0.9128) or mean minimum P_CO2 (t₅=0.0000, P=1). However, of the six cockroaches measured, one showed increasing and one showed decreasing haemolymph P_CO2 over time, despite constant ambient P_O2 and P_CO2 levels. Cockroaches exposed to hypercapnia had significantly increased mean maximum and mean minimum haemolymph P_CO2 (t₄=4.2055, P=0.0136 and t₄=5.8987, P=0.0041, respectively). Conversely, cockroaches exposed to hypoxia had significantly lower mean maximum and minimum haemolymph P_CO2 (t₄=4.1386, P=0.0144 and t₄=3.5, P=0.0249).

Plotting haemolymph P_CO2 against P_O2 on an x/y scatter plot revealed that, relative to DGCs in normoxia, hypoxia reduces overall haemolymph P_CO2 and P_O2 (Fig. 6A), while exposure to normoxic hypercapnia only elevates P_CO2 (Fig. 6B). The range of gas tensions seen in the haemolymph of cockroaches exposed only to normoxia was usually consistent (Fig. 6C), but could drift over time (Fig. 6D). Of the five control cockroaches, one experiment showed haemolymph P_CO2 increasing, and another showed haemolymph P_CO2 decreasing over time.

Changes in cycle duration, interburst duration, and C-, F- and O-phase duration during DGCs in decapitated cockroaches exposed to normoxia, hypoxia and hypercapnia treatments are shown in Fig. 7. Cockroaches exposed to repeated normoxic normocapnia exposure showed no significant change in O-phase duration (t₅=2.3284, P=0.0673), F-phase duration (t₃=2.9765, P=0.0588) or interburst duration (t₅=2.2158, P=0.0775). After applying the BH procedure, changes in mean total cycle duration and C-phase duration were also non-significant (t₅=4.6515, P=0.0056, and t₃=3.7444, P=0.0332, respectively). In cockroaches exposed to hypercapnia, there was no significant change in mean total cycle duration (t₅=2.5012, P=0.0544), F-phase duration (t₄=2.4057, P=0.0739), C-phase duration (t₄=0.5380, P=0.6191) or mean interburst duration (t₄=3.1219, P=0.0262). However, mean O-phase duration did increase significantly (t₅=4.3797, P=0.0072). Cockroaches exposed to hypoxia showed no significant change in C-phase duration (t₃=1.6903, P=0.1896), F-phase duration (t₃=0.4430, P=0.6878) or O-phase duration (t₅=1.2295, P=0.2736). However, cockroaches exposed to hypoxia showed significantly decreased mean total cycle duration (t₅=4.4931, P=0.0064) and mean interburst duration (t₅=5.9467, P=0.0019).

Mean V̇_CO2 was not significantly different in the control group when exposed to repeated normoxic normocapnia (t₅=1.1773, P=0.2920), or in the hypoxia group between control and treatment (t₅=0.928, P=0.3959). As V̇_CO2 could not be measured in a hypercapnic atmosphere, any changes in V̇_CO2 associated with this treatment could not be determined.

The mean haemolymph P_O2 and P_CO2 values measured during continuous gas exchange (17.1 and 1.9 kPa, respectively) are similar to values observed in other insect species displaying continuous ventilation (Förster and Hetz, 2010; Harrison et al., 1991; Matthews and White, 2011). Assuming that continuous ventilation displayed by G. portentosa in normoxic normocapnia is due to respiratory chemoreceptors stimulating a continuous ventilatory drive, this suggests that a haemolymph P_CO2 of ∼1.9 kPa and P_O2 of ∼17.1 kPa represent steady-state threshold levels required to maintain this continuous ventilatory drive. As such, exposure to either the 2 kPa hypercapnia or 10 kPa hypoxia treatment should elicit a corrective ventilatory response. Exposing cockroaches to hypercapnia did indeed cause them to hyperventilate, as haemolymph P_CO2 did not increase by 2 kPa, instead showing a non-significant median increase of only 0.35 kPa (Table 1), while exposure to hypoxia (10 kPa P_O2) has previously been shown to induce hyperventilation in continuously breathing G. portentosa (Harrison et al., 2016). These same O₂ and CO₂ partial pressures were also sufficient to increase ventilation in the speckled feeder roach Nauphoeta cinerea (Matthews and White, 2011). Thus, during continuous gas exchange, G. portentosa respond to hypoxic and hypercapnic challenges in the same way as other insects, and most air-breathing animals, by increasing ventilation. But once DGCs were elicited by decapitation, the ventilatory responses of these cockroaches changed substantially.

During DGCs in normoxic normocapnia, ventilation during the O-phase caused haemolymph P_O2 to rise to the same near-ambient levels as observed in continuously breathing individuals, but during the C-phase, haemolymph P_O2 fell to ∼0 kPa (Fig. 6). Haemolymph P_O2 often remained at or near 0 kPa for a substantial period of time during the C- and F-phases, before rising rapidly during the O-phase once ventilation began. Given this protracted internal hypoxia, the O-phase is clearly not triggered when haemolymph P_O2 reaches some hypoxia threshold. This is in agreement with previous studies on moth pupae, locusts and other species of cockroach, which all indicate that while internal hypoxia does not trigger the open phase, it does appear to stimulate spiracular fluttering as a corrective response (Matthews and White, 2011; Matthews et al., 2012; Schneiderman, 1960). Assuming that respiratory chemoreceptor thresholds drive the transition from the C- to the O-phase, this leaves only elevated P_CO2 as the trigger.

While continuously breathing cockroaches maintained a stable internal P_CO2, once decapitated and breathing discontinuously, all cockroaches displayed a mean maximum haemolymph P_CO2 (i.e. the P_CO2 reached immediately preceding O-phase ventilation) that was higher than the P_CO2 observed during continuous ventilation in the same individual (Fig. 8), indicating internal CO₂ was accumulating above the level regulated during continuous gas exchange. Furthermore, during exposure to normoxic normocapnia, spiracles were generally observed to open at the same maximum P_CO2 during each DGC. However, in two of the six control experiments, it was observed that minimum and maximum haemolymph P_CO2 drifted over time. In the first of these experiments, minimum and maximum haemolymph P_CO2 decreased and in the second experiment, they increased (Fig. 6D). These two experiments indicate that strict P_CO2 thresholds may not be responsible for maintaining DGCs, as the F→O and O→C transitions did not occur at a fixed P_CO2. Exposing cockroaches displaying DGCs to hypoxia and hypercapnia further tests whether fixed thresholds are responsible for driving the transitions between phases required to produce DGCs.

Hypercapnia-exposed G. portentosa experienced an ambient P_CO2 of 2 kPa, a level that approximates the mean haemolymph P_CO2 observed during continuous ventilation in normoxic normocapnic air (1.9±0.4 kPa, n=15). Assuming insects actively regulate internal P_CO2 around this level, a P_CO2 of 2 kPa hypercapnia should force cockroaches displaying DGCs to instead breathe continuously as they could never become hypocapnic – a condition required to generate the C- and F-phases of the DGC, assuming hysteresis around a fixed threshold. However, this did not occur. During hypercapnia exposure, both minimum and maximum haemolymph P_CO2 increased significantly relative to levels in normoxic normocapnia (Fig. 8B), while internal P_O2 continued to vary between ∼0 kPa and near ambient. If a fixed P_CO2 threshold was present then the maximum P_CO2 should not vary between normoxic and hypercapnic exposures as breath holding would be terminated once haemolymph P_CO2 reached this threshold value. However, the data presented here show that the transitions from F→O and from O→C continued to occur in hypercapnia, but at a significantly higher haemolymph P_CO2 compared with normocapnic air (Fig. 8B). Given that these cockroaches were all capable of transitioning from the O- to C-phase while their minimum internal P_CO2 was elevated significantly demonstrates that oscillations in haemolymph P_CO2 around a fixed CO₂ chemosensory threshold cannot account for the appearance of DGCs in G. portentosa.

To examine whether a higher haemolymph P_CO2 would abolish DGCs in G. portentosa, a single decapitated cockroach was exposed to an ambient P_CO2 of 3 kPa. This cockroach continued to display DGCs despite its haemolymph P_CO2 never once falling below levels previously recorded in normoxic normocapnia (Fig. 9). Although this is only one individual, it demonstrates that in this instance the DGC could not be explained by hysteresis around a fixed P_CO2 threshold, as cycles continued even though the minimum haemolymph P_CO2 never once fell below the maximum P_CO2 value recorded in normoxia. However, this extreme hypercapnia exposure also caused both maximum and minimum haemolymph P_O2 to increase (Fig. 9), again showing that although persistent hypercapnia does not abolish the DGC, it does stimulate increased ventilation during the O-phase. Likewise, cockroaches exposed to hypercapnia significantly increased the duration of their O-phase (Fig. 7). Thus, exposure to hypercapnia results in a longer O-phase and enhanced ventilation to compensate for elevated haemolymph P_CO2.

These results point to substantial differences between the DGCs displayed by different insect orders. For example, previous research has shown that exposure to hypercapnia >2.9 kPa eliminates DGCs in intact grasshoppers and moth pupae (Harrison et al., 1995; Terblanche et al., 2008), whereas our results show that decapitated Madagascar hissing cockroaches would probably require their haemolymph P_CO2 to be elevated well beyond these levels to abolish DGCs – an effect that may be physiologically irrelevant. This apparent insensitivity of the DGC to hypercapnia has been shown for at least one other species of cockroach, with Miller (1981) reporting that quiescent burrowing cockroaches (Blaberus craniifer) switch from DGC to continuous breathing only when ambient P_CO2 exceeded 5–10 kPa.

Decapitated G. portentosa maintained DGCs in hypoxia despite this treatment resulting in significantly depressed minimum and maximum haemolymph P_CO2 (Fig. 8C). This trend was previously observed in decapitated N. cinerea displaying DGCs (Matthews and White, 2011), indicating either that hypoxia increases sensitivity to CO₂, reducing the P_CO2 threshold that initiates the O-phase, or that these cycles are being generated by a ventilatory rhythm that is largely insensitive to CO₂ chemosensory feedback (Matthews, 2018). The latter explanation appears to be the case here, as haemolymph P_O2 before the start of the O-phase was around 0 kPa in both the normoxia and hypoxia treatments while the average maximum P_CO2 was 2.9 kPa in normoxia but only 2.1 kPa in hypoxia. Thus, equally hypoxic insects initiated their O-phase at different P_CO2, indicating that neither a hypoxia-induced change in P_CO2 sensitivity nor crossing a fixed P_CO2 ventilatory threshold appears to initiate the O-phase. However, while alternating episodes of gas exchange and apnoea are not eliminated by hypoxia, some aspects of the DGC are modulated by hypoxia. For example, the decreased minimum haemolymph P_CO2 during exposure to 10 kPa O₂ indicates that hypoxia stimulates increased ventilation during the O-phase, resulting in increased CO₂ clearance. Hypoxia was also associated with a significantly decreased interburst duration which contributed to a significantly decreased DGC duration (Fig. 7).

The changes in DGC phases observed in G. portentosa here are similar to the findings of Chown and Holter (2000), who found that both C- and F-phase duration in the scarabid beetle Aphodius fossor decreased in response to hypoxia, resulting in more frequent ventilatory periods. However, research on the locust L. migratoria showed that although hypoxia reduced the C-phase duration, it increased the F-phase duration, resulting in no net change in interburst duration (Snelling et al., 2011). In addition, whereas our research found no significant effect of hypoxia on O-phase duration, hypoxia has variously been observed to decrease (Chown and Holter, 2000), increase or have no substantial effect (Lighton and Garrigan, 1995) on O-phase duration in other insect species. Clearly, there is substantial variation in the effects of hypoxia on DGC phase duration in different species. This considerable interspecific variation is further evidence that DGCs do not arise from predictable ventilatory responses to oscillating gas tension. Overall, our results suggest that although the gas exchange portions of the DGC are modulated by hypoxia, a specific P_O2 threshold is not required to trigger phase transitions.

Several models of the DGC have been developed that explicitly incorporate fixed P_O2 and P_CO2 ventilatory thresholds as the key mechanism for generating an episodic gas exchange pattern (Förster and Hetz, 2010; Grieshaber and Terblanche, 2015). The data presented here provide the first complete record of multiple respiratory parameters from a single insect species displaying DGCs in both hypoxia and hypercapnia, thus allowing the predictions of these fixed-threshold models to be tested against empirical observations.

From the fixed-threshold model of Förster and Hetz (2010), it may be predicted that exposure to hypoxia would decrease the duration of the C-phase by reducing the time taken for internal P_O2 to fall to the F-phase threshold, and that this in turn would result in a longer F-phase (Fig. 1B). The effect of hypoxia on the duration of the O-phase is not clear as the mechanism that determines O-phase duration has not been defined, other than it is likely to be governed by some unspecified hysteresis. Finally, the maximum haemolymph P_CO2 level during the DGC would continue to reach (or exceed) the P_CO2 ventilatory threshold to trigger the start of the O-phase. The data presented here do not agree with any of these predictions as exposure to hypoxia caused both the interburst period and total DGC duration to decrease significantly, while O-phase duration did not change. Maximum P_CO2 coincident with the initiation of the O-phase also fell significantly in hypoxia. Likewise, the predicted effects of hypercapnia on a fixed-threshold DGC are also not met. As ambient P_CO2 approaches the insect's P_CO2 threshold, DGC cycle duration should decrease (Fig. 1C), ultimately reaching zero as ambient P_CO2 converges on the threshold level and the insect transitions to continuous gas exchange. Assuming this P_CO2 threshold is approximately 2 kPa in G. portentosa, breathing air with a P_CO2 of 2 kPa should have caused their ventilation to become continuous, or at the very least severely curtailed the duration of the DGC. But the data show that not only did DGCs persist in all cockroaches exposed to hypercapnia but also it was associated with only a statistically insignificant reduction in DGC cycle duration (an average decrease of 18±14%, n=6).

A set of mathematical models describing multiple ways in which DGCs could be generated has been developed by Grieshaber and Terblanche (2015), again assuming hysteresis around fixed P_O2 and P_CO2 thresholds, but using haemolymph pH as a proxy for P_CO2. Three models were presented that could replicate the main features of the DGC, and explicit predictions were made describing how hypoxia or hypercapnia would change the C-, F- and O-phases of these model DGCs. Moderate hypoxia was predicted to reduce the duration of the F-phase and increase the O-phase. Again, the data presented here do not support these predictions: F- and O-phase duration were both unchanged by hypoxia. All three DGC models predicted the same responses to hypercapnia: an increase in both F-phase duration and total DGC duration, while in extreme hypercapnia the breathing pattern would shift to continuous ventilation. These predictions are also not supported, as both F-phase and total DGC duration did not change significantly (and trended towards shorter durations), while O-phase duration, which was not predicted to change, increased significantly in hypercapnia.

Models of the DGC that assume the pattern is governed by fixed-level thresholds fail to accurately predict the behaviour of DGCs displayed by Madagascar hissing cockroaches when perturbed by exposure to hypoxic and hypercapnic atmospheres. This mismatch between predictions and observations leads to an obvious conclusion: a fixed P_CO2 threshold is not required to generate DGCs.

A key assumption in this study is that the P_O2 and P_CO2 levels recorded by optodes implanted into the cockroach's pronotal horns are the same as, or at least a proxy for, the levels sensed by respiratory chemoreceptors located elsewhere within the insect. For this to be true, either haemolymph P_O2 and P_CO2 must be homogeneous within the insect's haemocoel or, if gas tensions vary regionally within the haemocoel, any change in P_O2 or P_CO2 at the chemoreceptor must be associated with equivalent, coincident changes in these gas tensions throughout the rest of the insect. While regional variation in P_O2 and P_CO2 within G. portentosa's haemocoel cannot be ruled out, there are three lines of evidence that suggest that haemolymph within the insect's haemocoel is well mixed. First, the rapid changes in haemolymph P_O2 and P_CO2 measured by the implanted optodes during gas exchange (e.g. Figs 3 and 9) indicate that both these gases equilibrate quickly with the tracheal system at the location of measurement. Second, because the recorded haemolymph P_O2 and P_CO2 values remained close to ambient levels during periods of gas exchange, this indicates that the pronotal horns are not regionally hypoxic or hypercapnic and that gas exchange at the measurement location occurs without restriction. Finally, as the average duration of the DGC is very long in this cockroach species (∼1 h), there is ample time for any localized difference in haemolymph gas tension generated during the C-phase to equilibrate with the air spaces in the tracheal system and the rest of the circulating haemolymph pool. Taken together, these points strongly suggest that haemolymph gas tension within the pronotal horns does not depart significantly from values in the rest of the cockroach's haemocoel.

Although the low sample sizes presented in this study increase the likelihood of type II errors, the results presented here nonetheless provide compelling evidence that insect ventilatory control may be more nuanced than previously described. Continuously breathing G. portentosa appear to regulate their ventilation in response to internal P_CO2, keeping haemolymph P_CO2 between 1 and 2 kPa in normoxic normocapnic air and hyperventilating to defend this value during exposure to hypercapnia, in agreement with observations made on other insect taxa. DGCs have been hypothesised to emerge as a result of a hysteresis between haemolymph P_CO2 and a ventilatory response that is triggered at some fixed P_CO2 threshold, with the P_CO2 observed during continuous gas exchange being a plausible threshold level. However, our results indicate that this is not the case. Preventing haemolymph P_CO2 from falling below the putative 2 kPa ventilatory threshold did not prevent decapitated cockroaches from displaying DGCs despite their significantly elevated haemolymph P_CO2. DGCs also persisted during exposure to hypoxia, despite both maximum and minimum haemolymph P_CO2 being significantly reduced compared with levels in normoxic normocapnia. It is possible that the shift from continuous to discontinuous gas exchange is associated with an increase in the ventilatory P_CO2 threshold above that seen during continuous gas exchange, as this could explain why DGCs continue when haemolymph P_CO2 is significantly elevated above levels that occur while breathing continuously. However, even if this were so, a higher threshold cannot explain why DGCs then persist in hypoxia when haemolymph P_CO2 is maintained at a significantly lower level. The data plotted in Fig. 6 clearly illustrate that there are no fixed P_CO2, P_O2 or combination of these partial pressures that coincide with the F- to O-phase transition point, in contrast with the assumptions of the fixed-threshold model of the DGC (Fig. 1). Therefore, we conclude that hysteresis around a fixed P_CO2 ventilatory threshold, including the P_CO2 regulated during continuous gas exchange or some DGC-specific elevated threshold, cannot be responsible for the production of DGCs in these cockroaches. That this long-standing assumption does not apply to at least one species of insect highlights the need to critically test this assumption in other insects. Furthermore, if this exception turns out to be widespread then this could be one explanation why models of insect gas exchange patterns generally fail (Terblanche and Woods, 2018).

If hysteresis around fixed thresholds cannot explain the origin of the DGC, then what other mechanisms could be responsible? Plasticity in respiratory chemoreceptor thresholds could be one possibility. For example, continuous exposure to hypercapnia or hypoxia could cause blunting or acclimation, whereby the respiratory chemoreceptor's threshold sensitivity shifts to a new level relative to ambient conditions. However, this explanation would still require the existence of hysteresis in the insect's ventilatory control loop so that oscillations in P_CO2 could emerge around this shifted threshold, thereby generating the alternating phases of the DGC. Alternatively, a protracted refractory period following an O-phase could temporarily suppress any subsequent ventilation from occurring, giving rise to a periodic apnoea. This explanation benefits from the fact that a refractory period could occur independently of chemosensory feedback, allowing DGCs to continue irrespective of ambient hypoxia or hypercapnia.

If DGCs arise as a result of hysteresis, then this pattern must be caused by the insect oscillating between internal hypercapnia and hypocapnia. From this point of view, internal P_CO2 should periodically fall well below the ventilation threshold, with the C- and F-phases occurring to correct this deficit. However, given that the maximum P_CO2 during a DGC was found to substantially exceed the P_CO2 during continuous gas exchange for every individual and every condition examined here (Fig. 8), it is not unreasonable to suggest that the physiological function of the DGC is to suppress ventilation in order to elevate haemolymph P_CO2, rather than to prevent it from falling too low. This function has been attributed to episodic breathing patterns displayed by dormant land snails, whereby periodic apnoea causes the snail to accumulate CO₂, thereby depressing its blood pH and, potentially, metabolic rate (Barnhart, 1986). Unfortunately, the effect of hypercapnia on the cockroaches’ metabolic rate could not be determined in this study, as the proxy for metabolic rate used here (V̇_CO2) could only be measured in acapnic treatment gases. However, this explanation for the function of the DGC is worth further investigation, as the P_CO2 data presented here reveal that DGCs are associated with P_CO2 levels that are substantially elevated relative to those in intact, continuously ventilating cockroaches. But ultimately, what causes the transitions from continuous to discontinuous gas exchange, or transitions between the F-, O- and C-phases within the DGC? These questions still remain unanswered.

We thank the two reviewers for their constructive criticism of this paper.