Effects of altered ambient pressure on the volume and distribution of gas within the swimbladder of the adult zebrafish, Danio rerio

Teleost fishes inhabit a variety of environments in which the ability to efficiently control buoyancy is crucial to their survival. Because many body tissues of fish are denser than the water in which they swim (Alexander, 1972), these animals have evolved different mechanisms to overcome their negative buoyancy and avoid sinking. The most energy efficient of these mechanisms may be the development of an internal gas-filled swimbladder, which significantly increases whole-body volume but adds negligible mass (Alexander, 1966). In addition to its contribution to overall buoyancy, the swimbladder can also affect pitch, through its position along the cranio-caudal axis, and roll, through its dorsal-ventral position (Alexander, 1966; Robertson et al., 2008). This potential for controlling gas distribution may be especially well developed in cyprinid fish, in which separate anterior and posterior chambers are joined by a narrow passage, the communicating duct (see Fig. 1). In addition to having a hydrostatic role, the anterior chamber of cyprinids also plays an important function in audition through its connection with the ear via the Weberian apparatus (Alexander, 1966; Fay and Popper, 1974; Wever, 1969; Wever, 1971).

Total swimbladder volume and the distribution of this volume within the body can therefore be critically important to pelagic fish. However, as noted by Jones (Jones, 1951) and Alexander (Alexander, 1966), the use of a gas-filled swimbladder comes at a cost. As the fish moves vertically through the water column, external pressure varies and this inversely affects the volume of gas in the swimbladder. Consequently, volume must be readjusted to return to a state of neutral buoyancy after changing depth. However, external pressure is not the sole determinant of swimbladder volume; the final volume of the gas in the swimbladder is also determined by the compliance of the organ walls. Highly compliant walls would allow the gas volume to closely follow Boyle's law, whereas non-compliant walls would permit no change in volume as pressure varied. Alexander thus argued that some degree of noncompliance may confer advantages by minimizing the amount of active volume regulation needed during excursions to different swimming depths (Alexander, 1966). Moreover, regional differences in wall compliance could have significant effects on the distribution of gas in the swimbladder and, therefore, affect the whole-body attitude of the fish (Robertson et al., 2008). Yet, despite the potential importance of swimbladder wall compliance in determining the response of fishes to pressure variations that occur with changing depth, this factor has been investigated in only relatively few species (Alexander, 1959a; Alexander, 1959b; Alexander, 1959c; Jones, 1951).

In the present study we introduce new and simplified methods for examining how variations in pressure could affect the volume of the swimbladder of the adult zebrafish, Danio rerio (Hamilton 1822), during vertical movements in the water column. We employed previously validated stereological techniques (Robertson et al., 2008) for calculating volumes of the anterior and posterior chambers in both the isolated and in situ swimbladder during changes in imposed external pressures. We then estimated swimbladder wall compliance, defined as the change in volume resulting from an incremental change in depth-related pressure. We report here that gas volumes within the zebrafish swimbladder exhibit significant deviations from those predicted by Boyle's law; specifically, ascent in the water column caused significantly less expansion of gas volume than predicted. We also found that the posterior chamber was nearly non-compliant, so virtually all changes in the total volume of the swimbladder occurred within the anterior chamber. Although differences in wall composition (e.g. regional variations in the amounts of elastin and collagen) undoubtedly contribute to differences in compliance, we have also described a novel mechanism involving two series of regular folds in the wall of the swimbladder that appear to permit relatively large changes in chamber volume without straining or collapsing the chamber wall. Finally, we examined the consequence of simulated changes in depth on the distribution of gas within the swimbladder and on the pitch angle (trim) of the whole fish. Together, the results demonstrate that the compliance of the swimbladder wall is an important factor in determining both buoyancy and trim of the fish as it transitions through changes in swimming depth over a range similar to that expected in its natural habitat (Engeszer et al., 2007; McClure et al., 2006).

All fish were maintained on a 14 h:10 h light:dark photoperiod (with lights on at 08:00 h) and fed a mixed diet of Nutrafin freeze-dried brine shrimp and Nutrafin staple fish flake food (Rolf C. Hagen Inc., Montreal, QC, Canada) two to three times a day. All procedures for fish care and usage followed the Guide to the Care and Use of Laboratory Animals established by the Canadian Council for Animal Care and experiments were approved by the Dalhousie University Animal Care Committee.

Experiments on isolated swimbladders and effects of pressure variation on pitch angles employed adult, wild-type zebrafish (20-37 mm total body length; mixed gender) acquired locally (Aqua Creations Tropical Fish Inc., Halifax, NS, Canada). Groups of approximately 20 animals were housed in 75 l aquaria filled with dechlorinated, aerated tap water at 25-28°C. These animals were overdosed in a buffered (pH 7.4) solution of 0.04% MS-222 (ethyl 3-aminobenzoate methanesulfonate salt; Sigma Chemical Co., Mississauga, ON, Canada) for at least 3 min subsequent to the arrest of respiratory movements of the operculae.

Changes in swimbladder volume were visualized in situ through the body wall using 'cloudy' (cld) mutants (total body length 20-33 mm; mixed gender), obtained from M. Connolly (Dalhousie University). These animals had inhibited melanophore development that made the body wall translucent. We also found that MS-222 anaesthesia caused the translucent body wall of cld animals to become opaque, thus obscuring viewing of the swimbladder. For the purpose of this part of the study, we therefore anaesthetized fish in a solution of 0.04% urethane (Alexander, 1959a), which did not affect body wall transparency. Fish were anaesthetized with this agent until opercular movements had ceased for 3 min. All fish were sampled between 13:00 and 17:00 h, when they normally swam 10-20 cm below the surface of their home tanks (Lindsey et al., 2010).

Anaesthetized fish were pinned, dorsal side down, in a small Petri dish filled with saline solution (116 mmol l^-1 NaCl, 2.9 mmol l^-1 KCl, 1.8 mmol l^-1 CaCl₂, 5 mmol l^-1 HEPES; pH 7.2) (Westerfield, 2007) and an incision was made into the ventral body wall. The viscera were removed to expose the swimbladder, which was freed from the tunica externa and the Weberian apparatus. Some swimbladders were then placed directly into a pressure chamber, described below, to test compliance; in other swimbladders, either the communicating or pneumatic duct, or both (see Fig. 1), was ligated with a human hair before placement in the pressure chamber.

Changes in depth resulting from the animal swimming up or down from a set depth in the water column were simulated by imposing a range of external pressures. Previous studies have shown that zebrafish adjust the volume of the swimbladder so that they attain neutral buoyancy near the surface of the water under conditions similar to those employed in the present study (Robertson et al., 2008; Lindsey et al., 2010). Thus, when fish are removed from the water into ambient atmospheric pressure, there is negligible change in the volume of the swimbladder. We therefore designated atmospheric pressure as '0 reference pressure' for the purpose of this study. Pressures greater than the 0 reference pressure were designated '+' and those less than this pressure were designated '-'. In most experiments, a range of imposed pressures of ±175 cmH₂O (17.16 kPa) was used to simulate depth changes that replicate the reported natural depth range of zebrafish in the wild (Engeszer et al., 2007; McClure et al., 2006). However, in some experiments a greater range of ±316 cm H₂O (30.98 kPa) was used to more fully explore the compliance capability of the swimbladder. This extended pressure range was still within the absolute limits of tolerance of the swimbladder, as determined in pilot experiments (N=7). In those experiments, irreversible damage occurred when the imposed pressure reached approximately -500 cmH₂O.

Either an isolated swimbladder or a whole, anaesthetized fish was placed within a 3.5 ml chamber (internal dimensions: 1.1×6.3×0.5 cm) machined from a clear block of polycarbonate and filled with saline solution at room temperature. The chamber was covered with a polycarbonate plate sealed to the upper surface of the block by an O-ring and clamped in place with screws. Pressure in the chamber was monitored with a digital gauge capable of measuring pressures greater and less than atmospheric pressure (Model DPG9230-VAC/15, Omega Engineering Inc., Stamford, CT, USA). Pressure imposed on the samples was altered by manipulating a 10 ml syringe attached to the experimental chamber via a short length of tubing and a stopcock so that the set pressures could be maintained.

Isolated swimbladders were placed lateral side up in saline solution within the pressure chamber. After sealing the chamber and removing bubbles from the system, pressure changes were imposed in increments of 50 cmH₂O (4.90 kPa) to the maximal pressure limits described above. In general, pressures were systematically incremented in the positive direction first, and returned in the same increments to 0, then decremented in the negative direction and returned to 0 in an attempt to determine possible hysteresis or cumulative effects within the system. In preliminary experiments in which pressure was changed in random increments and directions, the results were similar to those obtained using a systematic approach, so the latter was used throughout this study.

Anaesthetized fish were anchored left side uppermost to a thin piece of silicone rubber (Sylgard, Dow Corning Corp., Midland, MI, USA) with pins positioned to avoid the coelom. Each fish was then placed into Ringer's solution in the pressure chamber, which was then sealed. Incremental pressure changes were imposed on the fish in the same manner as described above for the isolated swimbladders. The fish was then removed from the pressure chamber and the coelom was opened via an incision along the ventral midline from the pectoral fins to the anus. The fish was then placed back into the pressure chamber and subjected to the same pressure change regime as before opening the coelom. In order to test whether repeated sets of pressure increments affected the swimbladder volume independent of opening the coelom, a separate group of anaesthetized fish was exposed to changes in pressure, removed from the chamber, then returned intact to the chamber and re-exposed to the same pressure-change regimen. No significant differences were noted in swimbladder volumes in these trials (data not shown).

Photographs were taken through the pressure chamber wall of the lateral aspect of each swimbladder, using a Leica digital camera (Model DFC 320; Leica Microsystems GmbH, Wetzlar, Germany) mounted on a Nikon dissecting microscope (Model SMZ 10; Nikon Instruments Inc., Melville, NY, USA), as pressure within the chamber was changed. These images were then analyzed by fitting three-dimensional geometrical shapes to the anterior and posterior chambers to estimate volume (Fig. 2A). To calculate the volume of the posterior chamber, we employed a modification of the methods described by Robertson et al. (Robertson et al., 2008). We found that the anterior chamber changed in both volume and shape as imposed pressure changed (Fig. 2B-D). We therefore adapted the method of Robertson et al. (Robertson et al., 2008) to include more geometrical segments in order to increase the accuracy of volume estimation.

The total volumes of swimbladders estimated using these procedures ranged from 15 to 30 μl, with a mean of 21.8±4.78 μl. We validated this method by collecting gas from 10 swimbladders using the methods of Robertson et al. (Robertson et al., 2008) after carrying out the above procedures, and found estimated volumes were within 2% of the amount of gas collected. Also, the accuracy of volume estimates of in situ swimbladders were checked by two independent observers and found to be within 2.5% of each other using the same photographs of the organ (N=5) taken through the body wall (see Protocol for compliance estimation, In situ swimbladder above). Swimbladder volumes at different imposed pressures were normalized either as percentages of the initial total swimbladder volume or as percentages of the volumes of individual chambers, at the 0 reference pressure.

Swimbladders were dissected as described above. A fine polyethylene cannula was then inserted through the wall of the posterior chamber and connected to a 10 μl syringe to inflate or deflate the swimbladder. Swimbladder volume was then varied by ±20% from the initial value, corresponding to the approximate volume changes predicted to occur at ±175 cmH₂O imposed pressure changes, based on our experiments on isolated swimbladders. Once the intended swimbladder volume was reached, the communicating duct was ligated to maintain anterior chamber volume. Portions of the anterior chamber wall were then imaged under darkfield illumination using a Wild M5A dissecting microscope (Wild Leitz GmbH, Wetzlar, Germany) and photographed with a Canon digital camera (Model A95, Canon Inc., Toyko, Japan).

In order to examine the structural changes in wall configuration associated with altered swimbladder volume, anterior chamber volume was altered ±20% from the initial value using a cannula and syringe as described above. The communicating duct was then ligated, and the swimbladder was fixed first for several hours at room temperature (approximately 25°C) and then overnight in 4% paraformaldehyde (Electron Microscopy Sciences, Hatfield, PA, USA) at 4°C. Swimbladders were then rinsed thoroughly in phosphate buffered saline (PBS, 0.1 mol l^-1 Na₂HPO₄, 140 mmol l^-1 NaCl, pH 7.2) and immersed in a 1:500 concentration of phalloidin conjugated to tetramethyl rhodamine isothiocyanate (TRITC) (Sigma Chemical Co., Mississauga, ON, Canada), which selectively labels F-actin in myocytes (Babaev et al., 1990; Finney et al., 2006; Tokuyasu, 1989), for 4 h at room temperature and then a further 12 h at 4°C. Tissues were again rinsed in PBS for several hours, and then portions of the wall of the anterior chamber were isolated and mounted flat on glass slides in a solution of three parts glycerol to one part 0.1 mol l^-1 Tris buffer (pH 8.0) containing 2% n-propyl gallate (Giloh and Sedat, 1982) for viewing and photography. Micrographs of the anterior chamber wall were made with an LSM 510 confocal microscope (Carl Zeiss, Ltd, Toronto, ON, Canada). Images were then processed with Zeiss ZEN 2008LE software to obtain three-dimensional renderings and wall thickness measurements.

Fish were anaesthetized with MS-222 as described above and then placed in an apparatus (supplementary material Fig. S1) that allowed the body of the fish to tilt according to the position of the centre of buoyancy along the cranio-caudal axis. Two pivot points, consisting of pins attached to the arms of a caliper, were pushed against the lateral surfaces of the body near the normal centre of buoyancy, with sufficient pressure to penetrate only the epidermis, stopping on the external surface of a scale. The centre of buoyancy was calculated to be in the lateral midline at a point on the surface of the body coincident with the projection of the communicating duct onto the body surface (Robertson et al., 2008). To estimate this position, a distance of 33% of total body length was measured caudal from the tip of the lower jaw. The apparatus holding the fish was then submerged in a water-filled polycarbonate chamber (dimensions 36×36×24 cm) and the pitch of the fish was observed. If necessary, the positions of the pins were adjusted along the body length to bring the fish to a horizontal attitude. Preliminary experiments indicated that a force of less than 1 mN (detection level of the force transducer) was needed to begin tilting the fish. The chamber was then sealed and the effects of incremental changes in imposed pressure were tested on body pitch.

Photographs were taken of the lateral aspect of each fish using a Hewlett-Packard digital camera (Model HP407, Hewlett-Packard Co., Houston, TX, USA). Leica Application Suite software was employed to calculate differences in body pitch angle from horizontal under altered pressures.

All statistical analyses were performed using SPSS 15.0 software (SPSS Inc., Chicago, IL, USA). One-way ANOVAs with repeated measures were performed to determine effects of pressure on volume of the swimbladder and its chambers, and two-way ANOVAs were performed to test whether increasing and decreasing increments of pressure differences produced significant hysteresis. Post hoc t-tests with Bonferroni corrections were used for pairwise comparisons. Regression analyses were also performed to test the linearity of the pressure-volume function for various groups and to calculate slopes for pressure-volume relationships of swimbladders from individual fish. Group means of those slopes were compared via two-tailed t-tests. To test for differences in the periodicity of anterior chamber wall infolding, group means were compared using Kruskal-Wallis one-way analysis, and one-way ANOVAs were used for wall thickness comparisons. All data are expressed as means ± 1 s.d.

Changes in external pressure were imposed on two sets of swimbladders that had no ligations on either duct. One set (N=8) was exposed to pressures ranging ±175 cmH₂O from 0 reference pressure to simulate changes in depths which might be normally encountered by zebrafish in the wild. A second set of swimbladders (N=8) was exposed to a wider range of pressure changes (±316 cmH₂O from 0 reference pressure). The resultant changes in volume (Fig. 3), expressed as proportional changes from the initial total swimbladder volume, were nearly identical for both sets of data.

Changes in external pressure caused significant inverse changes in total volume of the isolated swimbladder (one-way ANOVA with repeated measures; P<0.05). Incremental increases in pressure up to 316 cmH₂O above 0 reference pressure evoked graded decreases in total swimbladder volume, to 77.8±3.2% of initial volume at the maximal pressure (Fig. 3, inverted triangles). This response conformed closely to the ideal pressure-volume relationship predicted by Boyle's law over the same pressure range (Fig. 3, dashed line). However, when external pressure was decreased incrementally from 0 reference pressure to a minimum pressure of -316 cmH₂O, total swimbladder volume increased to 120.1±4.6% of the initial value (Fig. 3); this maximal volume was significantly less than the value of 144.1% predicted by Boyle's law (t-test, P<0.05; Fig. 3, dashed line).

A strong inverse linear relationship existed between total swimbladder volume and imposed pressure (r=-0.99) over the entire range of tested pressure changes. This relationship had a mean slope of 0.07±0.01% volume change per cmH₂O (averaged across slopes calculated for all individual fish), which translated to a change in volume of approximately 0.01 μl cmH₂O^-1 for the size fish used in this study.

The possibility of hysteresis in the pressure-volume relationship of the swimbladder was investigated by displacing pressure first in increments away from 0 reference pressure to the maximum or minimum value, then returning in the same increments to 0 reference pressure. Thus the means of two sets of volume estimates were plotted for each pressure increment in Fig. 3 to represent mean relative changes in volume obtained during opposite directions of pressure change. We found no significant differences between means for each increment as pressures were shifted away from or towards the 0 reference pressure (two-way ANOVA with repeated measures; P>0.05), indicating that the whole swimbladder did not exhibit hysteresis within these ranges of imposed pressures. Furthermore, after these trials, mean total swimbladder volume returned to within 0.6±2.5% of the value at the start of the trials.

The effects of changes in imposed pressure on total swimbladder volume were almost entirely due to volume changes in the anterior chamber (Fig. 3, closed circles). This chamber comprised 54.5±7.9% of total swimbladder volume at 0 reference pressure and changes in external pressure caused significant changes in the volume of the chamber (one-way ANOVA with repeated measures; P<0.05). The pressure-volume relationship for this chamber was strongly linear (r=-0.99) and the slope was identical to that for total swimbladder volume at -0.07±0.01% cmH₂O^-1.

In contrast, the posterior chamber volume did not change significantly over the tested pressure range (one-way ANOVA with repeated measures; P<0.05); the pressure-volume relationship of the posterior chamber (Fig. 3, open circles) exhibited little correlation between these variables (r=0.4) and the slope of the pressure-volume relationship was 0.002±0.001% cmH₂O^-1.

To further investigate the contribution of each chamber to the overall response and to determine whether gas passage from one chamber to another contributed to this response, we isolated the chambers by ligating the connection between the entire swimbladder and the environment (via the pneumatic duct; N=8; Fig. 4A), between the two chambers (via the communicating duct; N=8; Fig. 4B) or both (N=8; Fig. 4C). Under certain combinations of ligature position and imposed pressure, the posterior chamber collapsed (see below), thus preventing calculations of total swimbladder volume using our stereological procedures. The volume responses of each chamber were therefore normalized to represent the percent change from its own initial volume at 0 reference pressure, and tests were run over a limited range of pressure (±175 cmH₂O).

As with the non-ligated swimbladder, pressure changes imposed on the swimbladder with a ligature around the pneumatic duct caused significant changes in the volume of the anterior chamber (one-way ANOVA with repeated measures; P<0.05), which were strongly linear (r=-0.99) and had a mean slope of -0.12±0.018% cmH₂O^-1, as shown in Fig. 4A. When calculated as a percentage change in volume relative to the initial total swimbladder volume at 0 reference pressure, the slope for the pressure-volume relationship of the anterior chamber was found to be identical (-0.07±0.01% cmH₂O^-1) to that of this chamber without ligation (see Isolated swimbladder: communicating and pneumatic ducts patent, Responses of individual swimbladder chambers above). The posterior chamber showed no significant change in volume across the range of tested pressures after ligation of the pneumatic duct (one-way ANOVA with repeated measures; P>0.05). The mean slope of the pressure-volume relationship for this chamber was -0.004±0.002% cmH₂O^-1 (r=-0.31; Fig. 4A).

After ligation of the communicating duct, pressure changes imposed on the swimbladder again caused significant changes in the volume of the anterior chamber (one-way ANOVA with repeated measures; P<0.05) but the mean slope of the pressure-volume relationship was reduced to -0.08±0.007% cmH₂O^-1 (r=-0.99) (Fig. 4B); this slope was significantly less than the mean slope of the pressure-volume relationship after ligation of the pneumatic duct (t-test comparing means of slopes calculated for individual fish in both groups, P<0.05; Fig. 4A). The pressure-volume response of the posterior chamber was also altered after ligation of the communicating duct (Fig. 4B). Imposed pressures greater than 50 cmH₂O above the 0 reference pressure caused the posterior chamber to collapse. After removal of the imposed pressure increase, the chamber returned to its initial shape and the volume returned to within 0.20±2.23% of its initial value. Also, in contrast to swimbladders with ligated pneumatic ducts, pressures imposed over the range of -175 to +50 cmH₂O caused the volume of the posterior chamber to change significantly by a total of 2.2±1.5% (one-way ANOVA with repeated measures, P<0.05). The mean slope of the pressure-volume relationship of this chamber, -0.01±0.007% cmH₂O^-1 (r=-0.70), was significantly greater than the mean slope of this relationship when the pneumatic duct was ligated (t-test comparing means of slopes calculated for individual swimbladders in both groups, P<0.05; Fig. 4A).

Volume responses of both chambers after ligating the pneumatic and communicating ducts together (Fig. 4C) were nearly identical to responses after ligation of the communicating duct alone. The volume of the anterior chamber changed significantly (one-way ANOVA with repeated measures, P<0.05) and linearly (r=-0.99) over the tested pressure range; the mean slope of the pressure-volume relationship was -0.08±0.009% cmH₂O^-1, a value significantly different from that of the anterior chamber after ligation of the pneumatic duct alone (t-test, P<0.05; Fig. 4A) but not significantly different from the value after ligation of the communicating duct alone (t-test, P>0.05; Fig. 4B). The posterior chamber again collapsed when pressures greater than 50 cmH₂O above the 0 reference pressure were imposed. Changes in pressure over the range of -175 to +50 cmH₂O resulted in significant changes in the volume of the posterior chamber (one-way ANOVA with repeated measures, P<0.05) with a mean slope of -0.02±0.009% cmH₂O^-1 (r=-0.71). This slope was significantly greater than the corresponding value for the posterior chamber after ligation of the pneumatic duct alone (t-test, P<0.05), but was not significantly different from the value for this chamber after ligation of the communicating duct alone.

In order to examine potential contributions of the body wall and intracoelomic pressure to the pressure-volume relationships of the in situ swimbladder, we calculated volume changes from images of the swimbladder taken first through the intact body wall (closed coelom) and then after opening the coelom (opened coelom) in the same specimens (N=8). A typical example of these experiments is shown in Fig. 5 and the results are summarized in Table 1. In intact animals the total swimbladder volume exhibited a strongly linear relationship with imposed pressure over the range of ±175 cmH₂O, with proportional changes in the volume of total swimbladder as well as those of the anterior and posterior chambers statistically similar to those observed in isolated swimbladders without ligatures on any ducts (see Fig. 3 and Isolated swimbladder: communicating and pneumatic ducts patent, Total swimbladder volume above). Opening the coelom had no significant effect on the pressure-volume relationship (Table 1).

To examine how the anterior chamber accommodated the large changes in volume described in the preceding sections, we examined the structure of the chamber wall, focusing first on the ventral aspect, which has been described previously to be thickened by a layer of smooth muscle and possessing a series of regular infoldings of the chamber wall (Dumbarton et al., 2010; Finney et al., 2006). Fig. 6 shows three-dimensional views of segments of the ventral wall of the anterior chamber, re-constructed from confocal z-stack images to indicate how the wall structure changed as chamber volume was varied. The results (summarized in Table 2) indicated significant differences in the periodicity of folding along the luminal and serosal surfaces (Kruskal-Wallis, P<0.05) and in the thickness of the muscular chamber wall as the volume of the anterior chamber was increased and decreased by 20% from that normally observed at 0 reference pressure (one-way ANOVA, P<0.05).

In addition to the series of parallel folds observed in fixed tissue from the ventral aspect of the anterior chamber, we observed regular folding of the wall at the caudal end of the anterior chamber in the region of the communicating duct in unfixed, isolated swimbladders viewed under darkfield microscopy. When the volume of the chamber was unaltered from that observed at 0 reference pressure (Fig. 7A) or was increased by 20%, the folds were minimally apparent. However, when chamber volume was decreased by 20% from that observed at 0 reference pressure, the pattern of pleats in the wall became more prominent (Fig. 7B). At this volume, a total number of 6.0±1.1 folds 100 μm^-1 could be distinguished in the lateral aspect of the wall and 9.2±2.2 folds 100 μm^-1 were present in the dorsal and ventral aspects of the wall (N=4).

To analyze the potential effects of changes in distribution of gas within the swimbladder system on the whole-body pitch angle, we altered imposed pressure over the range of ±175 cmH₂O while observing changes in the angle of the cranio-caudal axis (with positive values denoting an upward tilt of the head) of anaesthetized fish set up to pivot around the centre of buoyancy at 0 reference pressure (Fig. 8). As pressure was varied, body pitch changed significantly (one-way ANOVA with repeated measures, P<0.05) and linearly (r=-0.90) with a slope of -0.009 deg cmH₂O^-1. In all cases, the attitude of the fish returned to within 0.1 deg of horizontal when pressure returned to 0 reference pressure.

The stereological techniques that we employed here permitted the rapid and accurate calculation of volumes of the entire swimbladder and its individual chambers. Moreover, the techniques permitted repeated estimates of these volumes during changes in external pressure and gave reliable comparisons between different swimbladders to provide the first tests for variations between individuals and following different experimental procedures.

In this study, we employed the conventions (i.e. change in volume per change in pressure) applied to descriptions of another gas-filled organ, the lung (Gommers et al., 1993; Hughes and Vergara, 1978). On one level, changing external pressure permitted a simple and convenient means of exploring biophysical properties (e.g. viscoelasticity) of the swimbladder wall, a goal shared by Alexander (Alexander, 1959a; Alexander, 1959b; Alexander, 1959c) (see also supplementary material Fig. S2). However, our results also allow direct inferences of changes that would occur in swimbladder volume as fish swim to different depths in the water column. Such changes in depth are described relative to the pressure at the depth at which a fish is neutrally buoyant. Previous studies have shown that zebrafish collected under circumstances similar to those used in the present study are neutrally buoyant at or near the surface; the pressure at such depths is very close to ambient atmospheric pressure (Robertson et al., 2008). Increases from this 0 reference pressure thus relate directly to changes in swimbladder volume that would occur as the fish descends from the surface. Little is known, however, of the depth limits to which zebrafish swim or the ranges of depth that they transit in the wild. Under certain circumstances, individuals may become displaced from their normal habitats (e.g. after being washed into deeper pools or small lakes after seasonal rains) and may attain neutral buoyancy at greater water depths. The use of pressures negative to the 0 reference pressure thus helps to define the challenges that zebrafish would face if they were to occupy different habitats and ascend from greater depths at which they were neutrally buoyant. Equally importantly, the present study offers a framework by which the properties of the zebrafish swimbladder can be compared with those of other species that normally inhabit great depths and transverse greater ranges in depth.

Here we report that the adult zebrafish swimbladder system, as a whole, consistently exhibited a compliance of 0.07-0.10% change from its initial volume for each 1 cm change in depth. These values fall within the spectrum of what Alexander (Alexander, 1959a) referred to as the 'effective extensibility' for other cypriniformes, which ranged from 0.03 to 0.32% cmH₂O^-1, with values for most cyprinids falling between these extremes. As also demonstrated by Alexander (Alexander, 1959c), other cyprinids similarly exhibited a nearly linear function of volume changes over the range of pressures tested. We also found that changes in volume closely followed those predicted by Boyle's law when external pressures were increased, but diverged increasingly from the predicted values as external pressures were decreased. Both the magnitude of compliance and the linearity of the pressure-volume relationships that we observed in the present study thus appear to be common features of the cypriniform swimbladder and perhaps also the perciform swimbladder (Jones, 1951), although swimbladders from other groups of teleosts examined by Alexander (Alexander, 1959c) had more compliant walls, which more closely followed Boyle's law.

Zebrafish are strong swimmers (Plaut, 2000) and such contributions of the viscoelastic properties of the swimbladder to its volume may have minimal effects on behaviour of this species as it swims in shallow waters. Such factors may, however, be more significant in other species of fish. Unfortunately, although Alexander (Alexander, 1959a) examined swimbladder properties in 12 cypriniformes, no systematic attempt was made to relate compliance with the range of depths normally occupied by the species or individuals tested in that study. Moreover, although we have shown that our techniques allow direct and consistent calculations of swimbladder compliance, the techniques of Alexander (Alexander, 1959a; Alexander, 1959b; Alexander, 1959c) were indirect and only tested single specimens of each species. Although Jones (Jones, 1951) did attempt to relate fish habitat to swimbladder compliance, his study was also limited in scope and focused on physoclistic species, not on physotomes as examined by Alexander (Alexander, 1959a; Alexander, 1959b; Alexander, 1959c) and in the present study. Thus, although these earlier investigators provided an important conceptual framework for understanding swimbladder compliance, future experiments must more rigorously examine this property of swimbladders in a more diverse range of species.

Our results also suggest the need to reinvestigate previous reports of differential extensibility of the two chambers of the cyprinid swimbladder. Guyénot (Guyénot, 1909) and Alexander (Alexander, 1959c) reported that both chambers were compliant but that the anterior chamber was more compliant than the posterior chamber. We show here that this difference in compliance appears to be more extreme in zebrafish than in other species examined to date, as the posterior chamber of the zebrafish appeared to be only minimally compliant. Such differences in compliance between chambers could be explained in part by variations in the tissue composition of their walls. The anterior chamber wall contains a thick continuous layer of elastin within the muscularis whereas the posterior chamber contains densely packed collagen fibrils in two perpendicular layers (Perrin et al., 1999). In this study, we also describe an additional, novel mechanism through which the zebrafish appears to be able to accommodate large changes in the volume of the anterior chamber. Dumbarton et al. recently described a series of folds at the cranial end of the ventral wall of this chamber (Dumbarton et al., 2010). These regularly spaced corrugations appear to act like the accordion folds of a bellows, deepening when the overlying muscles contract to deflate the swimbladder. Here we show that these folds also deepen and straighten as the swimbladder is passively deflated and inflated. We also describe an additional set of regular, deeper pleats at the caudal end of the anterior chamber that also deepen and straighten with the degree of swimbladder inflation. Thus compliance of the anterior chamber may not solely be due to the viscoelasticity of the wall, but may also involve the passive stretching of muscles that are found overlying and/or adjacent to both regions of infolding (Finney et al., 2006; Dumbarton et al., 2010). The posterior chamber, in contrast, possesses only a few shallow corrugations associated with each of its lateral bands of circumferential smooth muscle fibres (Dumbarton et al., 2010).

The exact contributions of the musculature to compliance are, however, difficult to ascertain in the present study because muscle tone was not determined. Tone could have been altered significantly from its normal physiological state in the isolated swimbladder or the in situ swimbladder of anaesthetized fish. In fact, it is tempting to speculate that freely behaving fish likely possess mechanisms to actively regulate swimbladder compliance, with the muscle layers and the connective tissue folds acting together to help set the compliance of this chamber. Likewise, although our study also indicates that the body wall and intracoelomic pressure did not contribute significantly to compliance of the swimbladder as a whole or of its individual chambers, these experiments were performed in anaesthetized fish. Contributions of the body wall musculature in awake, intact and swimming fish would thus not be evident in our study but may affect compliance or even contribute to swimbladder deflation and/or inflation reflexes.

In any case, our results suggest novel mechanisms by which fish can regulate swimbladder performance. Our results also clearly demonstrate that differences in the compliance of the walls of the two chambers can have significant effects on the distribution of gases within the swimbladder system. We noted that the anterior chamber constitutes between 35 and 75% of the total volume of the entire swimbladder over the range of simulated changes in depth studied here, although a value of approximately 55% of the total swimbladder volume at the designated 0 reference pressure is likely to closely represent the normal proportion of gas volume in the anterior chamber of freely swimming zebrafish. It should be noted, however, that consistent and long-lasting changes in anterior chamber volume following exposures to stress and/or transfers to new home tanks have been observed (M.R.S., unpublished data). We therefore suggest caution in the interpretation of the wide range of relative sizes of the anterior chamber as reported by Alexander (Alexander, 1959a) for different species. Such values must be re-examined under more controlled conditions.

Although the distribution of gas volume within the swimbladder system is influenced by the compliance of the two chambers, it also depends on the passage of gases through the pneumatic and communicating ducts. Our experiments suggest that gas does not readily exit the swimbladder system via the pneumatic duct under the conditions examined in this study. The total swimbladder volume returned nearly to initial values even after the organ was greatly distended, regardless of whether the swimbladder was isolated or in situ, or whether the pneumatic duct was ligated. Presumably, musculature at the junction of the pneumatic duct and the esophagus (Finney et al., 2006) acts as a functional sphincter preventing loss of gas from the swimbladder unless specific deflation reflexes to alter muscle tone are activated.

Even though the pneumatic duct appears to be normally closed, our results suggest that the communicating duct is normally open under the conditions studied here. Ligation of this duct caused significant changes in the pressure-volume relationships of both chambers. Specifically, the slope of the pressure-volume relationship decreased for the anterior chamber and increased for the posterior chamber when gas could not move through this passage. Perhaps most dramatically, the isolated posterior chamber collapsed when external pressures were increased by more than 50 cmH₂O above the 0 reference pressure. These findings are all consistent with a normally patent communicating duct, which allowed the anterior chamber to accommodate nearly all the changing gas volume of the entire swimbladder. Thus, as external pressure decreased, the highly compliant anterior chamber accommodated the expansion of gas within its own walls and also the expanding gas that escaped from the largely non-compliant posterior chamber via the communicating duct. Conversely, as external pressure increased, gas was forced from the anterior chamber through the communicating duct and into the posterior chamber. When the communicating duct was ligated, the rate of the volumetric changes decreased for the anterior chamber, as it then only accommodated the expansion and contraction of gases within its own walls. In contrast, the only significant changes in posterior chamber volume occurred when the communicating duct was ligated, as only in this condition was the chamber required to accommodate the entirety of its own changing gas volume, forcing slight changes in the largely non-compliant chamber wall. Also, the posterior chamber collapsed when the communicating duct was ligated and external pressure was increased, because gas from the anterior chamber could not enter the posterior chamber to maintain a sufficient trans-wall pressure differential necessary to maintain its shape. In contrast, the more compliant walls of the anterior chamber allow it to accommodate larger positive pressure changes without collapsing.

Two caveats must be noted regarding the discussion above. First, we cannot preclude the possibility that the communicating duct may normally be closed, but that it can only act as a functional sphincter against a very low pressure differential between the chambers. In support of this possibility, small pressure differences have been recorded between the two chambers (Robertson et al., 2008). Second, the orientation of muscle fibres in the zebrafish swimbladder (Finney et al., 2006; Dumbarton et al., 2010) is consistent with active control over the patency of the communicating duct. The isolation of the swimbladder and the use of anaesthetics may have disrupted the control of such muscles in our study. Freely behaving fish, however, may be able to actively control the contractility of the muscles in the region and thereby also control the passage of gas through the communicating duct.

Regardless of the exact contribution of the communicating duct, our observations clearly indicate that changes in external pressure can result in large changes in the distribution of gas volumes within the swimbladder. Furthermore, as the volume of the anterior chamber changes due to depth-related pressure variations, the centre of buoyancy might be expected to shift along the rostro-caudal axis, thus causing a shift in the body pitch. Specifically, a large increase in the volume of the anterior chamber might be expected to shift the centre of buoyancy forward and pitch the head of the fish upward. Our results indicate that such shifts in pitch angles do indeed occur, although the resultant changes in attitude appeared to be small in amplitude. Presumably, mechanisms exist to dampen the effects of changing gas distribution on centre of buoyancy, although the nature of those mechanisms is presently unclear.

The present study provides the most comprehensive examination to date of the compliance of the isolated and in situ swimbladder in any fish. We examined both the overall compliance of the entire swimbladder and quantified the differences in compliance of the two chambers of the zebrafish swimbladder. In addition, we presented previously undescribed anatomical features through which the swimbladder can accommodate large variations in volume and potentially change its compliance. This work suggests novel mechanisms by which fish may regulate total buoyancy and trim, through changes in the distribution of gas within the swimbladder system. One particularly surprising observation was of the large changes in volume of the anterior chamber as it accommodated expanding and contracting gas from both swimbladder chambers. Effects of this shift in gas volume on pitch angle of the fish were examined here, but effects on other functions, such as hearing (Alexander, 1966), remain unclear, especially in light of our finding that the magnitude of the changes that occur may be larger than previously suspected. Finally, the present study helps to more sharply formulate questions for future research aimed at understanding roles of both the intrinsic muscles of the swimbladder and the muscles of the surrounding body wall in the control of buoyancy. Specifically, our measurements of compliance likely represent only the limits dictated by the passive, viscoelastic properties of connective tissue and relaxed smooth muscles in the swimbladder wall. The degree to which compliance is actively controlled by freely behaving fish has yet to be determined. The swimbladder is obviously a complex, multifunctional organ with several types of effectors activated under a variety of conditions. Neither the homeostatic roles of this organ nor the control of its effectors are yet clearly understood.

Much of this work was completed in partial fulfilment of an Honours degree in Biology by M.R.S. at Dalhousie University. We would like to thank members of that department, who gave critical advice and helpful suggestions over the course of this research. Thanks are also extended to Oliver Braubach, George Robertson, Benjamin Lindsey and Tristan Dumbarton for critical help and suggestions. Finally, thanks are also due to anonymous reviewers of an earlier version of this report for their useful comments.