The dichotomous oxyregulatory behaviour of the planktonic crustacean Daphnia magna
Institut für Zoophysiologie, Westfälische Wilhelms-Universität, Hindenburgplatz 55, 48143 Münster, Germany
* Author for correspondence (e-mail: pirow{at}uni-muenster.de)
Accepted 24 November 2003
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Summary |
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Key words: Crustacea, Branchiopoda, Cladocera, Daphnia, zooplankton, nutrition, oxygen transport, ventilatory and circulatory system, diffusion, convection, mathematical modelling
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Introduction |
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The planktonic crustacean Daphnia magna (Branchiopoda; Cladocera),
a euryoxic species with oxyregulatory capacities
(Kobayashi and Hoshi, 1984;
Paul et al., 1997
), exhibits a
remarkable tolerance for environmental hypoxia (i.e. a state of reduced oxygen
availability when the PO2amb has fallen below
the normoxic values of 20-22 kPa prevailing normally at sea level;
Grieshaber et al., 1994
). The
underlying physiological mechanisms that allow the animal to maintain oxygen
uptake under environmental hypoxia range from short-term adjustments at the
systemic level (Paul et al.,
1997
; Pirow et al.,
2001
) to long-term changes in the concentration and oxygen-binding
characteristics of haemoglobin (Hb; Fox et
al., 1951
; Kobayashi and
Hoshi, 1982
; Kobayashi et al.,
1988
; Zeis et al.,
2003a
,b
).
Interestingly, the acute systemic responses to progressive, moderate hypoxia
seem to deviate from those of other oxyregulating water breathers. Whereas
fish (Dejours, 1981
;
Randall et al., 1997
) or
decapod crustaceans (McMahon and Wilkens,
1975
; Taylor,
1976
; Dejours and Beekenkamp,
1977
; Herreid,
1980
; Wheatly and Taylor,
1981
) typically increase ventilation while keeping cardiac output
(= heart rate x stroke volume) more or less constant, the situation
seems to be reversed in D. magna. Recent studies
(Paul et al., 1997
;
Pirow et al., 2001
) have shown
that the heartbeat accelerates without notable changes in stroke volume
(compensatory tachycardia) whereas the movements of the thoracic appendages,
whose ventilatory function has been demonstrated experimentally
(Pirow et al., 1999a
), remain
almost constant. It appears that hyperventilation is an inappropriate response
for D. magna to compensate for a reduction in
PO2amb.
This idea is in line with the fact that D. magna is able to
increase the concentration of Hb in the haemolymph by more than 10 times when
exposed to chronic hypoxia (Kobayashi and
Hoshi, 1982). Both responses, the tachycardia and the elevation of
Hb concentration, compensate for the reduction in ambient oxygen availability
by increasing the oxygen transport capacity of the circulatory system
(Pirow et al., 2001
;
Bäumer et al., 2002
). This
suggests that the circulatory system rather than the ventilatory system is the
limiting and controlling step of the oxygen transport cascade from environment
to cell. The reason for the suggested absence of a ventilatory controllability
of the oxygen transport cascade could lie in the filter-feeding mode of life.
The rhythmical beating of the thoracic appendages has not only a ventilatory
function but also serves an important non-respiratory need: food acquisition.
The third and fourth limb pairs are equipped with fine-meshed filter combs
that enable Daphnia to retain food particles suspended in the ambient
medium (Fryer, 1991
). Since
food particles can be highly diluted in the natural environment, the rate of
medium flow required to assure an adequate nutrition could exceed the rate
necessary to satisfy the oxygen demand of the animal, as is supposed for other
filter feeders such as sponges, lamellibranches and ascidians
(Dejours, 1981
).
The dual function of appendage movement presumably provides the key to
explaining the peculiar oxyregulatory behaviour of D. magna. However,
if nutritive requirements rather than respiratory needs drive appendage
movement under conditions of limited food availability, what controls this
activity under excess food conditions? Several studies have shown that
Daphnia spp. exhibits close to maximum appendage beating rates when
there is little or no food available, whereas high food concentrations
(104 unicellular algae ml-1) effect a pronounced
deceleration of appendage movement
(McMahon and Rigler, 1963
;
Burns, 1968
;
Porter et al., 1982
). Since
the latter effect is inevitably associated with a reduction in ventilatory
power, and since the oxygen demand increases as a consequence of the
activation of digestive processes
(Lampert, 1986
;
Bohrer and Lampert, 1988
)
despite lower energetic expenditures for appendage movement
(Philippova and Postnov,
1988
), it is possible that the oxyregulatory responses exhibited
under these conditions deviate from those described so far
(Paul et al., 1997
;
Pirow et al., 2001
). The aim
of the present paper is to analyse the oxyregulatory repertoire of D.
magna and to provide a causal mechanistic explanation for its peculiar
oxyregulatory behaviour. These issues were tackled by an experimental
approach, in which the systemic responses to declining
PO2amb were examined under food-free and
food-rich conditions, as well as by the use of a conceptual and mathematical
model, which made it possible to predict the efficiency of ventilatory and
circulatory adjustments in improving oxygen transport to tissue.
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Materials and methods |
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In order to measure heart (fH) and appendage beating
rate (fA), single animals were tethered by gluing their
posterior apical spine to a 1-cm-long synthetic brush-hair with adhesive
(histoacryl; B. Braun Melsungen AG, Melsungen, Germany). The animal was
positioned lateral-side-down with the opposite side of the brush-hair and one
of the large antennae glued onto a cover slip. The cover slip with the
tethered animal was transferred into a transparent perfusion chamber
(Paul et al., 1997) with the
head orientated against the direction of the medium flow. The chamber was
sealed and placed onto the stage of an inverted video microscope (Zeiss
Axiovert 100; Carl Zeiss, Oberkochen, Germany). While keeping the animal under
infrared illumination (>780 nm), the frequency of the periodic movements of
the heart and the thoracic appendages were automatically determined as
described in detail elsewhere (Pirow et
al., 2001
).
The experimental chamber was perfused with culture medium (M4;
Elendt and Bias, 1990) at a
flow rate of 5 ml min-1. During the experiments, the oxygen tension
of the medium was lowered gradually from normoxia (21 kPa) to severe hypoxia
(<1.5 kPa) with a duration of five minutes for each step. This time
interval was sufficient for the animal to attain a new stable level of
fH and fA
(Paul et al., 1997
;
Pirow et al., 2001
). Different
levels in oxygen tension were obtained by using two computer-driven
peristaltic pumps (Gilson Minipuls 3; ABIMED, Langenfeld, Germany) that mix
normoxic and anoxic media at different ratios
(Freitag et al., 1998
). Both
media were prepared by equilibration with air or with a gas composed of 99.95%
N2 and 0.05% CO2. The oxygen tension of the perfusion
medium was measured behind the experimental chamber using a polarographic
electrode (WTW Oxi 92; Weilheim, Germany). In the experiment with high food
concentration, the unicellular green alga Scenedesmus subspicatus was
added to both reservoirs at a final concentration of 105 cells
ml-1. This concentration had been reported to effect a depression
of fA in D. magna
(Porter et al., 1982
), which
was confirmed in a separate experiment
(Fig. 1;
Table 1). The algal stock
solution was prepared by centrifuging the algae at 2000 g (5
min, 4°C) and resuspending the algal pellet in filtered culture medium
(cellulose acetate filter; pore size, 0.45 µm). The concentration of algae
in the stock solution was determined using a Neubauer counting chamber. The
stock solution was then appropriately diluted and kept in complete
darkness.
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All experiments were carried out at 20°C. Animals were allowed to
acclimate to the experimental conditions for 50 min before starting the
experiment. fH and fA were analysed
for the last minute of each step in oxygen tension. Data were expressed as
means ± S.D., with N indicating the number of
animals examined. For each experiment, in which multiple measurements were
made on the same animal under various treatment levels (either food
concentration or oxygen partial pressure), differences in mean values
(fH and fA) of the different
treatments levels were assessed using a repeated-measures analysis of variance
(repeated-measures ANOVA; Zar,
1999). Statistical differences were considered significant at
P<0.05. In the case of a statistical significant difference,
multiple comparisons (Tukey test; Zar,
1999
) among pairs of means using an experimentwise error rate of
0.05 were performed to determine between which means differences exist.
General description of the conceptual model of oxygen transport
Animals with a body size in the millimetre range are distinguished from
their larger counterparts by short transport distances from the body surface
to the central body regions. Since diffusive processes are effective for short
distances only, millimetre-sized animals can rely to a greater extent on
diffusion for providing peripheral tissues (i.e. tissues close to the body
surface) with oxygen directly from the ventilated or non-ventilated ambient
medium, whereas internal convection is, in principle, only needed to deliver
oxygen to the more centrally located tissues, which are too distant from the
periphery to be sufficiently supplied by diffusion. Such a pathway deviates
somewhat from that of the basic vertebrate model
(Taylor and Weibel, 1981;
Piiper, 1982
;
Weibel, 1984
;
Shelton, 1992
), where the
transport of oxygen from the environment to the cells is thought to occur
along a linear sequence of alternating convection and diffusion steps
(ventilatory convection, diffusion across the oxygen-permeable integument,
circulatory convection, diffusion in the tissue). The proposed model for the
diffusive-convective oxygen transport in Daphnia magna incorporates
both a ventilatory-circulatory transport of oxygen to the centrally located
tissues as well as a diffusive supply of peripheral tissues directly from the
respiratory medium (Pirow,
2003
).
To keep the mathematical formulation of the oxygen transport cascade as
simple as possible, the complex body shape of D. magna
(Fig. 2A) is reduced to a
cylindrical trunk, which is enveloped by a hollow cylinder representing the
carapace (Fig. 2B). The
carapace consists of an outer and an inner wall that both enclose a haemolymph
space, the carapace lacuna. The cylindrical trunk is further assumed to be
composed of a peripheral tissue layer, a haemolymph space (trunk lacuna) and a
central tissue cylinder (Fig.
2B). The respiratory medium flows through the space between the
carapace and the trunk in a posterior direction while oxygen is released both
into the carapace lacuna and the trunk. This design takes into account that
the feeding current of D. magna is an important pathway for oxygen
(Pirow et al., 1999a) and that
the inner wall of the carapace is a significant site of oxygen uptake
(Pirow et al., 1999b
). Similar
to the real situation, the medium flow and haemolymph flow in the carapace
lacuna are in concurrent orientation to each other. Leaving the carapace
lacuna, the oxygen-rich haemolymph enters the haemolymph space of the trunk
and flows in an anterior direction while oxygen is released into both tissue
compartments. Reaching the anterior position, oxygen-poor haemolymph then
re-enters the carapace lacuna. The circulation of haemolymph takes place in a
single circuit that, of course, is a simplification compared with the real
situation, where the haemolymph flow branches into subcircuits
(Pirow et al., 1999b
). The
oxygen partial pressure of the inspiratory and expiratory medium is denoted by
Pin and Pex (kPa), respectively,
whereas that of the haemolymph entering and leaving the trunk is denoted by
Pa and Pv, respectively
(Fig. 2B).
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Model assumptions
The following simplifying assumptions are made in the model. (1) Diffusion
of oxygen in all compartments (tissue, haemolymph and medium) and across
compartment interfaces is only in a radial direction. Axial diffusion is
ignored in order to reduce mathematical complexity. (2) Oxygen diffusion
across the tissue-medium and medium-haemolymph interfaces is impeded by
cuticular barriers of the same permeability. (3) The outer wall of the
carapace is assumed to be impermeable to oxygen. (4) Axial convection occurs
only in the haemolymph and medium compartments. (5) Convective flows have
velocity profiles that are uniform in respect to the radial axis. (6) The
mixing of haemolymph leaving the lacunae at the bases of the cylindrical model
as well as the re-entrance of the mixed haemolymph into destined lacunae is
assumed to occur without a time delay. (7) Haemoglobin as the oxygen carrier
in the haemolymph is not considered in order to reduce mathematical
complexity. (8) The volume-specific oxygen consumption rate is assumed to be
constant throughout the tissue compartments.
Mathematical formulation and derivation of the numerical solution
Based on assumptions made in the previous section, the following general
oxygen transport equation (Groebe and
Thews, 1992) accounts for radial diffusion with axial convection
and oxygen consumption:
| (1) |
The solution of the partial differential
equation 1 is approximated by
numerical methods, which requires dividing the whole cylindrical body into
discrete volume elements. The cylindrical model of height
(h0) and radius (r0) is divided in the
axial direction in Nax equal intervals of length
h and in the radial direction in Nrad+1
intervals of length
r and 0.5
r, respectively
(Fig. 3). This subdivision
yields two different kinds of coaxial volume elements: solid and hollow
cylinders. As a consequence of this discretization, the radii of the
compartment interfaces (e.g. tissue-haemolymph interface) have to be rounded
to multiples of
r. Since the whole cylindrical body is
radially symmetrical, it is sufficient to further consider only that region of
the median plane that is covered by 0...h0 and
0...r0 (Fig.
3). In this view, each volume element is represented by a discrete
grid point. The axial and radial coordinates of the grid points are
(j+0.5)
h and i
r,
respectively, where the indices j and i are integers with
j=0, 1,..., Nax-1 and i=0, 1,...,
Nrad.
|
By using the Taylor's series technique
(Faires and Burden, 1993;
Crank, 1975
) for solving Fick's
second law of diffusion, the following explicit finite-difference solution of
equation 1 is obtained for all
grid points not coinciding with compartment interfaces and excluding the
central and outermost grid points at i=0 and
i=Nrad, respectively:
![]() | (2) |
From the general solution given in
equation 2, three special cases
may be easily derived to describe the oxygen transport in the tissue
compartments (D=DT, v=0,
=
T), in the haemolymph compartments
(D=DH, v=vHT or
v=vHC,
=
H, a=0)
and in the medium compartment (D=DM,
v=vM,
=
M, a=0).
In these special cases, the solubility and diffusion coefficients assume the
specific values of the respective compartments (tissue -
T,
DT; haemolymph -
H,
DH; medium -
M, DM).
Flow velocities of the haemolymph in the carapace lacuna and in the trunk
lacuna are denoted by vHC and vHT,
respectively.
After having derived the balance equations for the oxygen transport within
the different compartments, it remains to describe the oxygen transfer across
compartment interfaces as well as the changes in oxygen partial pressure at
the central and outermost grid points. For the central grid points (at
i=0) belonging to the tissue compartment, the following approximation
is derived from Crank (1975):
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A somewhat more complicated mathematical formulation is required to
calculate the changes in oxygen partial pressure at grid points located at
compartment interfaces with an additional diffusion barrier (cuticle). In such
a case, a grid point referenced by j, i is characterized by two
variables, and
(kPa), which represent
oxygen partial pressure at the inner and outer side of the infinitesimal thin
diffusion barrier. The following example gives the specific solution for the
tissue-medium interface with diffusion barrier:
![]() | (4) |
![]() | (5) |
|
For all compartment interfaces lacking an additional diffusion barrier,
only one variable is required to describe oxygen partial pressure at that
location. The following two examples show the specific solutions for the
tissue-haemolymph interface (equation
6) and the outermost grid points (at i=Nrad;
equation 7):
![]() | (6) |
![]() | (7) |
The balance equations derived for all grid points were used to calculate
(1) the oxygen partial pressure distribution within the model and (2) the
total oxygen consumption rate as a function of
PO2amb. Solutions were obtained by initially
setting the oxygen partial pressure of all grid points to zero and
Pin to PO2amb. The
numerical calculation was started and continued until quasi steady-state
conditions (Pi,j<10-6 kPa for all
grid points) were reached. For
t, a value equal to or smaller
than 0.005 s was chosen, which proved to be adequate to allow the model system
to approach steady-state conditions.
Selection of parameter values
The selection of reasonable parameter values determining the geometrical
extensions and functional properties of the model is a tricky step in the
modelling process, especially when parameter values are not precisely known or
when the geometrical model deviates in some respects from structural or
physical reality. Since model parameters can depend on each other, we defined
key parameters from which derived parameters were calculated according to
functional relationships (Table
2). Following this approach, the radial extensions of all
compartments were derived taking the following assumptions into account. (1)
Volume (V) and height (h0) of the cylindrical
model are 1.12 mm3 and 2.5 mm, respectively, and refer to a 2.5
mm-long D. magna with no brood in the brood chamber
(Kobayashi, 1983). (2)
V comprises the tissue and haemolymph compartments. (3) The tissue
fraction
of V is 0.4
(Kobayashi, 1983
). (4) The
flow cross-sectional area (AM) penetrated perpendicularly
by the medium flow is 0.4 mm2. (5) The thickness
(
x) of the carapace lacuna is 0.02 mm. (6) The fraction of
total tissue (
) allocated to the central tissue cylinder is 0.25. (7) The
radial distance (
r) between two grid points is 0.005 mm.
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Whereas the first three assumptions are easy to comprehend, points 4-7
require a brief justification. The value for AM was
derived from an experimental study (Pirow
et al., 1999a; value not explicitly stated there). The value for
x represents a rough estimate since the thickness of the
haemolymph space varies across the carapace
(Dahm, 1977
;
Schultz and Kennedy, 1977
;
Fryer, 1991
). The value of
0.25 assigned to
is exactly that fraction of a solid cylinder that is
encircled by half of the cylinder radius. This choice ensured that there is a
sufficiently great sink for oxygen in the central region of the model as would
be the case if haemolymph and tissue were more homogeneously distributed
within the trunk. The value for
r was chosen to divide the
thin hemolymph compartment of the carapace lacuna into four intervals. The
influence of these somewhat arbitrarily chosen parameter values on model
behaviour is assessed by a sensitivity analysis in the Results.
The remaining parameters describing the functional properties of the model
refer to 20°C and a 2.5 mm-longanimal in the fasting state. The convective
flow velocities (vM, vHC,
vHT) were derived by dividing the medium flow rate
M (mm3
s-1) or the perfusion rate
H (mm3
s-1) by the respective flow cross-sectional area
(Rouse, 1978
; e.g.
vM=
M/AM).
M was calculated from
fA (360 min-1; present study) according to
functional relationships (Pirow et al.,
1999a
), whereas
H was obtained from stroke
volume (Bäumer et al.,
2002
) and fH (257 min-1; present
study).
The solubility of oxygen in water (M) was obtained from
Gnaiger and Forstner (1983
),
taking the salinity of 0.2
of the culture medium into account. The
solubility of oxygen in haemolymph (
H) was assumed to be
that of human plasma (58-85 g protein l-1;
Christophorides et al., 1969
).
Values reported for the oxygen solubility in tissue (
T) vary
in the range of 0.0097-0.0169 nmol mm-3 kPa-1
(Grote, 1967
;
Grote and Thews, 1962
;
Mahler et al., 1985
;
Thews, 1960
). For the present
model, a value of 0.0147 nmol mm-3 kPa-1 was chosen for
the tissue compartment.
Values reported for the diffusion coefficient for oxygen in water
(DM) vary in the range of 0.0017-0.0025 mm2
s-1 (Bartels, 1971;
Gertz and Loeschke, 1954
;
Goldstick and Fatt, 1970
;
Grote, 1967
;
Grote and Thews, 1962
;
Hayduk and Laudie, 1974
;
Himmelblau, 1964
;
St-Denis and Fell, 1971
). For
the present model, a value of 0.0020 mm2 s-1 was chosen.
A variety of data also exist for the diffusion coefficient for oxygen in
tissue (DT; corrected to 20°C if necessary), such as
0.0008-0.0020 mm2 s-1 for vertebrate skeletal or heart
muscle tissue (Bentley et al.,
1993
; Ellsworth and Pittman,
1984
; Grote and Thews,
1962
; Homer et al.,
1984
; Mahler et al.,
1985
), 0.0015 mm2 s-1 for rat lung tissue
(Grote, 1967
) and 0.0012
mm2 s-1 for rat grey matter
(Thews, 1960
). For the present
model, a value of 0.0010 mm2 s-1 was chosen for the
tissue compartment. For haemolymph, we assumed a diffusion coefficient to be
75% of that in water, because similar relationships (70-85%) were reported for
both bovine serum (Gertz and Loeschke,
1954
; Yoshida and Ohshima,
1966
) and an 8.5% solution of bovine serum albumin
(Kreuzer, 1950
). The
permeability of the cuticular diffusion barrier (g) was calculated by
dividing Krogh's diffusion coefficient for oxygen in chitin
(1.27x10-6 nmol s-1 cm-1
torr-1; Krogh,
1919
) by the thickness of the cuticle, for which a value of 0.001
mm was assumed (Pirow et al.,
1999b
).
The volume-specific oxygen consumption rate of pure tissue (a) was
derived by dividing the volume-specific oxygen consumption rate of the whole
animal (a0) by the tissue fraction of body volume
(). The value for a0 was obtained by dividing the
respiration rate (Y) of 23.6 nmol O2 animal-1
h-1 by body volume (V). Y was calculated
according to the allometric equation
Y=0.3087X0.95
(Glazier, 1991
) using a dry
body mass (X) of 96 µg for a 2.5 mm-long D. magna with no
brood in the brood chamber (Kobayashi,
1983
).
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Results |
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At high food concentration (105 algal cells ml-1),
progressive hypoxia induced responses in fH and
fA that deviated from those observed under food-free
conditions. During the initial normoxic conditions, food-provided animals had
a higher fH (344±62, N=11;
Fig. 5C) than those without
food (257±16, N=5). In response to the progressive reduction
in PO2amb, animals of both groups developed a
tachycardia that was more pronounced in the food-deprived group. The larger
scope for circulatory adjustment in the food-deprived group resulted from a
lower initial fH, because the maximum
fH at 4 kPa was almost the same in both groups
(412±33 min-1 vs 416±31 min-1).
The increase in the mean fH of the food-provided group
from 344 min-1 at normoxia (20.9 kPa) to 395-416 min-1
at hypoxia (15.3-2.0 kPa) was statistically significant
(Table 4).
For PO2amb values higher than 8 kPa, the fA of food-provided animals was always lower, on average by 93 min-1, than that of animals without food. The depressing effect of the high food concentration on the normoxic fA was, however, not as great as expected from the food modulation experiment (cf. Fig. 5D and Fig. 1B). As in the food-deprived group, the reduction of PO2amb had no effect on the fA of food-provided animals in the range from 20.9 kPa to 6.8 kPa (Fig. 5D; Table 4). However, below 8 kPa, both groups showed diverging changes in mean fA. Whereas the fA of food-provided animals started to rise significantly from 265±48 min-1 at 9.5 kPa to 326±47 min-1 at 3.0 kPa (Table 4), that of the food-deprived group declined non-significantly from 360±50 min-1 at 8.8 kPa to 321±76 min-1 at 2.3 kPa (Table 3).
Comparing the shape of individual response curves for fH and fA with that of the respective mean response curves shown in Fig. 5A-D, there was always a good correspondence between individual and mean curves except for the fA of the food-provided animals. This group showed large interindividual variations in the initial, normoxic fA ranging from 153 min-1 to 356 min-1 and, as a consequence, nonuniform responses to declining PO2amb (Fig. 6A). All animals that had attained an initial, normoxic fA lower than 260 min-1 exhibited a pronounced hypoxia-induced increase in limb beating activity whereas those with a rate higher than 300 min-1 were hardly able to further elevate their fA (Fig. 6B).
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Efficiency of systemic adjustments predicted by the model
To estimate the efficiency of ventilatory and circulatory adjustments in
improving oxygen transport to tissue, we examined the behaviour of the
conceptual model (Fig. 2B) and
determined the critical ambient oxygen tension
(PO2crit) at which the rate of oxygen
consumption decreased to 99% of the maximum
(Fig. 7A). The data that were
initially entered into the model referred to a fasting 2.5 mm-long D.
magna exposed to food-free, normoxic conditions at 20°C
(Table 2). For this
physiological state, the numerical evaluation yielded a
PO2crit of 10.1 kPa. At this
PO2crit, the oxygen partial pressure
distribution in the medium lacuna and the carapace lacuna revealed an almost
complete equilibration of medium and haemolymph at the posterior part of the
model (Fig. 8). The depression
in oxygen consumption rate resulted from the formation of an anoxic corner in
the anterior part of the central tissue cylinder. The convective contribution
of the circulatory system to total oxygen supply above the
PO2crit was 32% (grey-shaded area in
Fig. 7A). A hypothetical
doubling of medium flow rate
(M) had almost no effect on
the PO2crit under these conditions
(Fig. 7A). The
PO2crit decreased only by 0.3 kPa. By contrast,
a doubling of perfusion rate
(
H) caused a pronounced
reduction of PO2crit to 7.9 kPa.
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|
To assess the efficiency of systemic adjustments for a fed animal exposed
to food-rich, normoxic conditions, new parameter values characterizing this
changed physiological state were entered into the model. This state is
characterized by an increased metabolic rate
(Lampert, 1986;
Bohrer and Lampert, 1988
), a
reduced fA and an elevated fH (cf.
Figs 1,
3). The volume-specific,
whole-body oxygen consumption rate (a0) was assumed to be
50% higher than that of the fasting state (see Discussion). In addition,
M was halved and
H was set to 135% of the
rate of the fasting state, thus assuming that the observed relative changes in
fA and fH translate into the same
relative changes in the respective flow rates. For this physiological state,
the model yielded a PO2crit of 14.3 kPa
(Fig. 7B). A doubling of
M reduced the
PO2crit by 0.7 kPa, which was more than twice
as large as the decrease determined for the fasting state. Nevertheless, the
change in
H was still most
effective, because the doubling of
H caused a reduction of
PO2crit by 3.0 kPa.
To assess the effect of changes in key parameters other than
M and
H, a sensitivity analysis
was performed using the data from Table
2 (referring to the fasting state and food-free normoxic
conditions). The value of each individual key parameter was then either
decreased to 50% or increased to 200% of its initial value (all others being
equal) and the percentage change in PO2crit was
evaluated (Fig. 9). Of all the
geometrical parameters tested (h0, AM,
x,
), the sensitivity was highest for
h0 (height of the cylindrical model) and for
, which
defines the allocation of tissue to the two tissue compartments. Variations in
the radial and axial grid intervals (
r,
h)
caused only minor changes (<1%) in PO2crit.
The permeability of the cuticular diffusion barrier (g) did not prove
to be a limiting factor of the oxygen transport cascade, whereas changes in
the diffusing properties of oxygen in tissue
(
T,DT) had a great influence on
PO2crit. Of all the parameters affecting the
convective and diffusive transport of oxygen in the medium and haemolymph
compartments, the solubility coefficient for oxygen in haemolymph
(
H) had the greatest impact on
PO2crit
(Fig. 9).
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![]() |
Discussion |
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Under food-free conditions, the moderate reduction in
PO2amb did not influence appendage beating rate
(fA), which was used as a measure of ventilatory
performance. Heart rate (fH), on the contrary, increased
by 61%, indicating a large regulatory scope in the circulatory system under
these conditions. This cardio-ventilatory response pattern was in line with
the previous results (Paul et al.,
1997; Pirow et al.,
2001
).
A reversed response pattern occurred when the animals had access to food in
high concentration. Exposure to food-rich conditions (105 algal
cells ml-1) instead of food-free conditions resulted in a lower
mean initial fA (265 min-1 vs 360
min-1) and a higher mean initial fH (344
min-1 vs 257 min-1). In this physiological
state, with an individual fA lower than 260
min-1, D. magna was able to respond to a reduction in
PO2amb with a compensatory increase in
ventilation. The fact that four out of 11 individuals with an
fA above 300 min-1 failed to show this
hyperventilatory response suggests that other unknown factors counteracted the
depressing effect of high food concentrations on fA. The
hypoxia-induced tachycardia was less pronounced under food-rich conditions
than under food-free conditions because of the higher initial
fH. These findings clearly demonstrate that the scope for
a short-term improvement of oxygen transport shifted from the circulatory to
the ventilatory system. The oxyregulatory repertoire of the millimetre-sized
D. magna consequently includes a systemic response pattern that is
comparable to that of large-sized, physiologically advanced water breathers
such as fish (Dejours, 1981;
Randall et al., 1997
) or
decapod crustaceans (Wheatly and Taylor,
1981
).
The decelerating effect of high food concentrations on
fA has been known for quite some time
(McMahon and Rigler, 1963;
Burns, 1968
;
Porter et al., 1982
). Above a
critical food concentration of 104 algal cells ml-1
(Porter et al., 1982
), the
amount of food retained by the filter combs of the thoracic appendages exceeds
the amount that the animal is able to ingest and/or digest
(Rigler, 1961
). The decrease
in fA reduces the imbalance between food supply (the
amount of food initially retained) and demand. However, the reduction in
fA is obviously not sufficient to remove this imbalance
completely, since a higher rate of rejection movements of the postabdominal
claw is required to remove superfluous food particles from the filter
apparatus (Porter et al.,
1982
). From the energetic point of view, one would expect a
further reduced or intermittent appendage activity, which would make
additional rejection movements unnecessary. However, taking the dual function
of appendage movement into account, it is likely that the actual
fA exhibited under these conditions represents a
compromise between the need to reduce energetic expenditures for food
collection and the need to satisfy the increased oxygen requirements of the
fed animal.
Lampert (1986) as well as
Bohrer and Lampert (1988
) have
shown that the respiratory rate (carbon loss per time interval) of well-fed
D. magna is more than twice the rate of starving animals. Taking the
change in the respiratory quotient from 0.7 (starved) to 1.15 (well-fed;
Lampert and Bohrer, 1984
) into
account, this elevation in respiratory rate corresponds to a 1.4-fold increase
in oxygen consumption rate. The higher oxygen demand arises from the digestion
and biochemical processing of food (Bohrer
and Lampert, 1988
; Philippova
and Postnov, 1988
) and the tissues involved in this physiological
task; i.e. the digestive tract and the fat cells as a storage site of reserve
mass are, to a great extent, located in the central part of the trunk rather
than in the peripheral body region. This is important to note because
centrally located tissues are more dependent on a convective supply of oxygen
via the circulatory system than are those in the periphery of the
body, which can rely to a greater extent on a direct diffusive provision of
oxygen from the ambient medium. Since the open circulatory system of
Daphnia spp. lacks any arteries and capillaries, there is no
possibility of redirecting a greater share of blood flow to these
metabolically activated tissues, and an improvement of local oxygen supply can
only be achieved by an increase in total perfusion rate. This could explain
why the initial, normoxic fH of food-provided animals was
34% higher than that of starving animals. Besides this explanation, a
circulatory compensation for the reduction in external convection cannot be
excluded. In the food-modulation experiment
(Fig. 1), we observed in two of
four animals a complete stop of appendage movement for 1.5 min after the food
concentration had been changed from 106 to 0 algal cells
ml-1. This behavioural change, which occurred under normoxic
conditions, was immediately followed by a sharp increase in
fH by 20-24%, and fH remained at this
high level until the animals resumed limb beating activity.
The experimental findings of the present study suggest that a circulatory adjustment is the most effective measure of hypoxia adaptation in the planktonic filter feeder D. magna, at least under low food concentrations when fA is at a maximum. The apparent inability to further increase fA under these conditions might result from biomechanical or energetic constraints such as the hydrodynamic resistance of the filter combs and the energetic costs of pumping medium. But even if such constraints would not exist, it is questionable whether an enhancement of ventilatory activity would have any beneficial effect, for example, in enabling the animal to sustain its rate of oxygen uptake at a far lower PO2amb. An experimental test to answer this question is hardly possible. However, since a large amount of physiological information is available for D. magna, this question can be approached theoretically by the use of a conceptual model.
Conceptual models have proven to be a valuable complement to experimental
approaches and have made it possible to analyse, for example, the transfer
characteristics and transport limitations of the different gas exchange organs
of vertebrates (Piiper and Scheid,
1975). Contrary to the situation in vertebrates, the
millimetre-sized D. magna lacks an arrangement in which the
circulatory system links distinct sites for respiratory gas exchange and
tissue gas transfer (Taylor and Weibel,
1981
; Piiper,
1982
; Weibel,
1984
; Shelton,
1992
). The whole integument of D. magna is, in principle,
permeable to respiratory gases, and the oxygen is moved from the body surface
to the tissues by diffusion and convection as well. We have therefore devised
a conceptual model that takes a direct diffusive supply of oxygen to the
peripheral tissues via the ambient medium and a convective supply to
the centrally located tissues via the circulatory system into
account.
The predictions made by this model gave support to the hypothesis raised in the Introduction that the circulatory system is the limiting step of the oxygen transport cascade in D. magna. The model analysis showed that an increase in perfusion rate was most effective both under food-free (fasting state) and food-rich (fed state) conditions in reducing the critical ambient oxygen tension (PO2crit) at which oxygen supply to the tissue started to become impeded. By contrast, an increase in ventilation rate had almost no effect on PO2crit under food-free conditions but a moderate effect under food-rich conditions. Since the regulatory scope for an adjustment in heart rate was found to be limited in D. magna under food-rich conditions, the increase in ventilation rate is the means of choice for a fed animal to cope with short-term, moderate hypoxia. The improvement of oxygen supply in the animal by enhancing ventilatory flow may also include the reduction of fluid and diffusive boundary layers, an aspect that was not considered in the present model. Under chronic and more severe hypoxic conditions, however, the increase in the concentration and oxygen affinity of Hb represents the one and only measure for improving the transport of oxygen from environment to cells.
In the present model, Hb was not considered as the haemolymph oxygen
carrier in order to reduce mathematical complexity. This might explain why the
critical ambient oxygen concentration of 3.9 mg O2 l-1
(PO2crit=7.9 kPa), which was predicted for the
fasting state with doubled perfusion rate
(Fig. 7A), was higher than the
critical oxygen concentrations of 1.3-3.0 mg O2 l-1
reported for filtering and respiration rates of Hb-poor D. magna and
D. pulex (Kring and O'Brien,
1976; Heisey and Porter,
1977
; Kobayashi and Hoshi,
1984
). The high sensitivity of the model to changes in the
solubility coefficient for oxygen in the haemolymph (
H)
indicates that Hb can have a pronounced effect on
PO2crit, since it enhances both the convective
and diffusive transport of oxygen in the haemolymph. The implementation of
Hb-mediated oxygen transport is the next step when extending the model, which
will then allow us to provide a causal mechanistic explanation for the
expression of specific Hb-related characteristics (concentration, oxygen
affinity, cooperativity) in animals of a given anatomical disposition and
physiological constitution under different environmental conditions.
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