Oxygen and water flux across eggshells of Manduca sexta
1 Section of Integrative Biology, The University of Texas at Austin, Austin,
TX 78712, USA
2 Department of Chemical Engineering, The University of Texas at Austin,
Austin, TX 78712, USA
* Author for correspondence (e-mail: art.woods{at}mail.utexas.edu)
Accepted 28 January 2005
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Summary |
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Key words: eggshell, oxygen, water, tradeoff, inert gas substitution, chorion, wax, crystalline chorionic layer, oxygen limitation, mathematical model, moth, Manduca sexta
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Introduction |
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Recently, Woods and Hill
(2004) showed for eggs of a
sphingid moth, Manduca sexta, that this is not so. Eggs developed
more slowly in even moderate hypoxia (PO2
915 kPa) and did not survive extended exposure to
PO2 <9 kPa. Egg metabolic rates, measured as
CO2 emission, were depressed by hypoxia and stimulated by hyperoxia
and the effect of PO2 was stronger at higher
temperatures. The work presented here asks: what is the identity and structure
of the layer(s) resisting oxygen flux between environment and embryo? A
priori, we suspect that the main resistance is associated with one or
more layers of the eggshell, as these were the location of the steepest
PO2 gradient
(Woods and Hill, 2004
). To
evaluate possible answers in a formal framework, we develop here a
mathematical model of gas flux between embryo and environment. The model
contains a series of resistances, each corresponding to one or more eggshell
layers. With additional theory and a set of data on egg morphology and
physiology, we derive quantitative estimates of the resistances
finding that most of it can be localized to one or a few layers beneath the
chorion. The same layers also resist outward flux of water vapour, suggesting
that these layers are the physical locus of an oxygenwater
tradeoff.
Structure of insect eggs
The model focuses on eggshell layers common to most insect orders
(Hinton, 1981;
Margaritis, 1985
), but with
particular reference to eggs of Diptera
(Margaritis et al., 1980
) and
Lepidoptera (Fehrenbach et al.,
1987
; Fehrenbach,
1995
) and additional information specific to M. sexta
(Dorn et al., 1987
;
Lamer and Dorn, 2001
). One
could, in such a model, include explicit terms describing each distinct
eggshell layer but there are too many
(Fig. 1A) with poorly known
properties. Our approach, therefore, is to collapse sets of layers into a few
`functional layers.' We do not model plastron respiration, but such a layer
could easily be added following the work of Thorpe and Crisp
(1947
).
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The outermost layer relevant to gas exchange is the boundary layer of air around the egg. The thickness of this layer depends on wind speed around the egg and on its oviposition substrate (e.g. leaf, stem, soil). We model mass transfer of oxygen through this layer with standard equations.
The outermost component of the eggshell itself is the chorion
(Fig. 1A), which is composed
primarily of protein. Chorion thickness varies among species from thin (<1
µm in Drosophila) to very thick (>40 µm in some saturniid
moths; Margaritis, 1985). In
M. sexta, the chorion is 78 µm thick
(Orfanidou et al., 1992
).
Chorions of most species are penetrated by aeropyles: air-filled, hydrofuge
tubes of radii
1 µm, which are conduits for gases diffusing between
embryo and environment (Hinton,
1981
). At the base of the chorion, the aeropyles open into a thin
trabecular layer (TL; Fig. 1A)
so-called because it is an interconnected series of vaulted chambers.
This layer is thin (often <0.5 µm thick) and air-filled, and it extends
over most or all of the surface area of the egg. Both chorion and trabecular
layer are deposited by maternal follicular cells.
Beneath these layers are a crystalline chorionic layer (CCL), a wax layer
and the vitelline envelope (VE; Fig.
1A). These layers constitute a set they also are secreted
by maternal follicular cells and are closely apposed
(Margaritis et al., 1980). A
CCL has been found in most of the insect species examined for it (eggs of
M. sexta have not been examined)
(Furneaux and Mackay, 1972
;
Margaritis et al., 1979
;
Margaritis and Mazzini, 1998
;
Papassideri et al., 2003
). In
D. melanogaster, the layer is
40 nm thick
(Papassideri and Margaritis,
1996
) and in Leptinotarsa decemlineata it is
1 µm
thick (Papassideri et al.,
2003
). For most other species studied, CCL thickness lies between
these extremes (Margaritis,
1985
). The crystallized repeating units, likely proteins, exhibit
a periodicity of about 10 nm in D. melanogaster
(Papassideri et al., 2003
) and
similar spacing in other species
(Margaritis, 1985
).
Papassideri and Margaritis
(1996
) suggesting that in
Drosophila the layer controls water movement across the eggshell; if
so, it could conceivably also affect oxygen flux. Unfortunately, no
experimental data on CCL permeability to water or oxygen are available for any
insect. Among the layers neglected in the model, the gas exchange properties
of this one are potentially the most interesting.
Below the CCL is a thin wax layer (Fig.
1A). Waxes were first proposed as waterproofing agents in insect
eggs over 50 years ago (Beament,
1946; Slifer,
1948
) and have since been identified in a number of insect orders
(Margaritis, 1985
), including
Heteroptera, Diptera and Lepidoptera. Papassideri et al.
(1991
), in a detailed analysis
of the structure of the wax in layer in D. melanogaster, showed that
it was only
5 nm thick and consisted of individual plaques of wax, each
0.51.0 µm in diameter, compressed between the overlying CCL and
underlying VE (and possibly intercalated with them,
Papassideri et al., 1991
). Wax
layers from non-drosophilids are poorly known, although they have been
identified in a number of Lepidoptera
(Telfer and Smith, 1970
;
Cruikshank, 1972; Salkeld,
1973
; Barbier and Chauvin,
1974
). Wax plates similar to those of Drosophila are seen
in eggs of Galleria mellonella (Pyralidae)
(Barbier and Chauvin, 1974
).
Each plate is
10 nm thick and three or more plates may partially overlap.
The total thickness of the wax layer appears to be <50 nm in most species.
VE-associated waxes extracted from dechorionated eggs of six species of
Diptera were composed primarily of n-alkanes and methyl-branched
alkanes (Nelson and Leopold,
2003
), similar in composition to the epicuticular waxes of pupae
and adults. The wax layer in eggs of M. sexta has not been analyzed
in comparable detail. Nelson and Sukkestad
(1970
) extracted total lipids
from batches of Manduca eggs (59.5 µg egg1),
from which a hydrocarbon fraction (3.1 µg egg1) was
isolated. The hydrocarbons, which are thought to be VE-associated, were 50%
n-alkanes (27- and 29-carbon) with the remainder primarily
dimethylalkanes. Egg waxes likely also contain polar lipids of the kinds found
by Buckner et al. (1984
) in
surface waxes of pupal M. sexta.
The VE (vitelline envelope) itself usually is thick (several µm) before
oviposition (e.g. Salkeld,
1973), but it compresses afterwards and may be very thin (e.g.
<0.5 µm, Barbier and Chauvin,
1977
; Margaritis,
1985
; Fehrenbach et al.,
1987
) by midway through development. Its permeability has not been
measured but it is probably high, as brief extraction of Drosophila
VE with wax-removing solvents (leaving the VE itself) renders the egg much
more permeable to water (Schreuders et
al., 1996
). Biemont et al.
(1981
) suggest that eggs of
the beetle Acanthoscelides obtectus are protected by a dense
vitelline envelope, although they present no supporting experimental evidence.
For model construction, we focus on the CCL, wax and VE layers as a functional
unit (Fig. 1B), both because we
have no way, practically, of manipulating them independently and because
numerous authors have suggested that the layers may act as a single unit
e.g. that there is intercalation of wax into the VE
(Margaritis, 1985
) or that the
crystalline layer organizes wax
(Papassideri and Margaritis,
1996
).
After oviposition, additional layers (serosal cuticle, serosal membrane,
serosa, embryonic cuticle and tissue) develop or are secreted in a complicated
spatiotemporal pattern beneath the VE. Excellent descriptions of these layers
in M. sexta are given by Dorn et al.
(1987), Lamer and Dorn
(2001
) and Berger-Twelbeck et
al. (2003
). Although one or
more of these layers may be relevant to gas exchange, at present too little is
known about them to afford more than guesses about their individual
permeabilities. For simplicity, we model all of the subvitelline layers as a
single material (Fig. 1B).
Finally, the characteristics of yolk may be important to gas exchange,
although the bulk of yolk lies to the interior of the embryo. In M.
sexta, yolk does become cellular
(Lamer and Dorn, 2001
) and
presumably consumes oxygen.
Gas flux model
The first serious attempt to model oxygen flux into insect eggs was by Tuft
(1950), who experimented with
eggs of the bug Rhodnius prolixus. Eggs of this species obtain oxygen
only through a set of pores (pseudomicropyles) located near the rim cap end of
the egg. Using simple equations for the penetration of O2 into
tissues of different geometry, Tuft
(1950
) showed that eggs could
obtain sufficient oxygen only if the trabecular layer was air-filled and
extended over the whole egg surface under the chorion. Later, Hartley
(1971
) used detailed
measurements of the chorion of eggs of a tettigoniid (Homorocoryphus
nitidulus vicinus) to parameterize a flux model through the outer
chorion. He concluded that water-filled, but not air-filled, parts of the
chorion resist oxygen movement. Recently, Daniel and Smith
(1994
) developed equations
describing the diffusive resistance of the single aeropyle in eggs of a
bruchid beetle, Callosobruchus maculatus. None of the efforts to
understand gas exchange by insect eggs approaches the sophistication and
detail of efforts for bird eggs (see especially
Wangensteen et al., 1970/1971
;
Wangensteen and Rahn,
1970/1971
; Paganelli et al.,
1975
; Paganelli,
1980
).
Our model is the first to consider individual layers explicitly. Consider a shell composed of three layers (Fig. 1B; Table 1), each with a diffusive resistance to mass-transfer of gas. The first two layers, the chorion and trabecular layer, contain air-filled pores of differing microstructure. The third, representing a composite of crystalline chorionic layer, wax and vitelline envelope, is considered to be a solid into which diffusing gas may dissolve. In addition, on the outside and inside of the layers described there may be additional resistance to mass-transfer e.g. resistance by boundary layers of still air around the egg or from liquid between the bottom-most eggshell layer and the embryo. Note that at the interface between the second porous layer and adjoining third solid layer, there is a thermodynamic partitioning of the gases. Likewise, there is thermodynamic partitioning at the interface between the third, solid layer and the liquid interior of the egg. Throughout, our model refers to gas concentrations rather than partial pressures (see Appendix 1 in supplementary material, which shows how to convert between them).
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If the thickness of each layer (di) is much less than
the radius of curvature, R, we can neglect the effects of curvature
and model the mass-transfer as occurring in one Cartesian direction
(Fig. 1B; Hartley, 1971). At steady
state, the flux J through each of the five regions (one external,
three diffusive layers and one internal) is constant and is given by the
expressions:
![]() | (1a-e) |
Assuming a linear thermodynamic relationship,
C3=H3C3*
and
C4=H4C4*,
where H3 and H4 are constants
(partition coefficients) and rearranging the terms above so the right-hand
side involves only differences in concentration, one finds that:
![]() | (2a-e) |
![]() | (3) |
![]() | (4) |
![]() | (5) |
Below, using both experiments and additional theory, we derive quantitative estimates for the resistance of each of the main eggshell layers to oxygen flux.
How large is a large resistance?
Equation 5 shows that the
overall mass transfer coefficient km is the reciprocal of
a sum of individual resistances, each corresponding to a different diffusion
step. Evaluating whether individual resistances are large requires a benchmark
for comparison. We therefore calculated the value of km
that would depress the internal concentration of oxygen CI
to the values observed by Woods and Hill
(2004). In particular,
3-day-old eggs at 24°C had minimum, central
PO2 levels of approximately 2 kPa as measured
by an O2 microelectrode, or about 10% of atmospheric
PO2 at sea level (
21 kPa). If we assume
the egg's liquid contents are mostly water, then at air saturation the
contents would contain 0.255 mol m3
(Denny, 1993
); thus, at 10% of
saturation, CI=0.0255 mol m3.
Equation 4 can be rearranged to
give:
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Material and methods |
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Microscopy
Both light and electron microscopy were used to measure aeropyle density
and cross-sectional area. Density was measured on 10 isolated chorions washed
gently in saline to remove yolk and other debris. Cleaned chorions were
mounted under oil and visualized with a Zeiss Axioplan2 compound microscope
fitted with an ocular micrometer grid (400x magnification, at which the
grid was 250 µm on a side, or 62,500 µm2 total). On each
chorion the grid was positioned randomly over 57 locations and the
number of aeropyles within the grid was counted.
For scanning electron microscopy (SEM), fresh chorions were washed in saline and fixed overnight in 2% glutaraldehyde in sodium cacodylate buffer (200 mmol l1, pH 7.4, 4°C). Subsequently, they were rinsed, dehydrated in an ethanol series and stored over desiccant at room temperature. Samples were then sputter-coated with gold, mounted and viewed (Hitachi S-4500 Field Emission SEM, 5 kV). On each of five eggs, 10 randomly picked aeropyles were photographed and two orthogonal diameters on each aeropyle image were measured using image analysis software (Scion Image v. beta 4.0.2, Scion Corporation, Frederick, MD, USA), from which cross-sectional areas could be calculated using the equation for the area of an ellipse.
Inert gas substitution
The diffusion coefficient of gaseous O2 in a binary mixture
depends on the molecular mass of the other gas. Air, for example, consists
essentially of O2 and N2 and the diffusion coefficient
of O2 in air, Dair, is 2.09 x
105 m2 s1. If N2
(molecular mass 28) is replaced entirely by He (molecular mass 4) of the same
partial pressure, Dair rises 2.2-fold to 4.60 x
105 m2 s1. Importantly,
substitution of He for N2 does not affect the diffusion of
O2 in liquids (e.g. water, yolk) or solids (e.g. wax). Therefore,
if the chorion and trabecular layers really do not resist flux, then
substituting He for N2 should not rescue O2-starved
eggs.
We tested this prediction by measuring metabolic rates while simultaneously
manipulating O2 content and the inert carrier identity of gas
mixtures supplied to batches of eggs. Metabolic rate was measured as
CO2 emission using flow-through respirometry. Batches of eggs
(M. sexta) that were either 1.5 or 3 days old and weighing between
330 and 690 mg(approximately 210450 eggs per batch) were placed into a
glass chamber (large enough so that the eggs were in a monolayer) and
submerged in a temperature-controlled water bath set to a temperature
(37°C) that we knew from previous work
(Woods and Hill, 2004) gave
maximal metabolic rates. To ensure that incoming air was thermally
equilibrated, gas upstream of the chamber was first directed through 0.5 m of
coiled, submerged,
copper
tubing. Gases were mixed from cylinders of pure O2, N2
and He using calibrated mass flow controllers (2 Tylan FC-2900, Torrance, CA
and UNIT UFC-1100, Yorba Linda, CA, USA) and mixing electronics (MFC-4, Sable
Systems, Las Vegas, NV, USA). The gas stream (100 ml STPD
min1) was directed past the eggs, through a small volume of
indicating Drierite to remove water vapour and into a carbon dioxide analyzer
(CA-2A, Sable Systems), which was calibrated frequently with pure
N2 (zero) and 505 p.p.m. CO2 in N2 (span,
Airgas, Radnor, PA, USA). Data were logged using Datacan V software (V5.4,
Sable systems) receiving digital signals from an A/D converter (UI2, Sable
Systems), which itself received analog signals from the instruments. In
addition to CO2, we logged temperature in a separate chamber
otherwise identical to the experimental chamber but fitted with a T-type
thermocouple (connected to a TC-1000 thermocouple meter, Sable Systems).
Because flows of N2 and He were both controlled by the same mass
flow controller (factory-calibrated for N2 flow), we first needed
to determine the appropriate thermal conversion factor. To do so, we generated
a gas stream consisting of (all gas volumes STPD) 5 ml
min1 span gas (505 p.p.m. CO2 in N2
controlled by a calibrated mass flow controller), 21 ml min1
O2 and 74 ml min1 N2 or He (through
the same controller). By switching repeatedly between N2 and He, we
empirically identified a thermal conversion factor (1.37) that, in our system,
gave identical readings from the CO2 analyzer (25 p.p.m.
CO2, which is 5% of 505 p.p.m.).
Once the conversion factor was determined, we measured rates of CO2 emission of batches of eggs that experienced, in series over 12 h, all four combinations of the following conditions: 21% O2 in N2, 21% O2 in He, 9.5% O2 in N2 and 9.5% O2 in He.
Rates of water loss before and after solvent extraction
The three layers underneath the trabecular layer a crystalline
layer, a wax layer and the vitelline envelope are represented together
in the model by the term
d3H3/D3. Below we
focus on the wax layer, primarily because experimental manipulations are
feasible. However, the crystalline chorionic layer itself probably plays a
role in controlling the diffusion of gases, as suggested by Papassideri and
Margaritis (1996). The role of
the vitelline envelope in gas flux is unknown.
Batches of 40 2-day-old eggs were placed into a water-jacketed,
stainless-steel chamber (custom built) designed to interface with a gas
multiplexer (TR-RM8, Sable Systems) (see
Woods and Hill, 2004 for
details). The chamber temperature was maintained at 25°C by a
recirculating water bath. An air stream (50 ml min1, dry,
21% O2, mixed from cylinders of pure O2 and
N2) was directed through the egg chamber, then past a thin-film
capacitance humidity sensor (RH-100, Sable Systems) which had been calibrated
with dry air (zero) and an air stream humidified to 2.336 kPa water vapour
pressure (span; humidified by bubbling the stream through a flask of water
held at 20°C).
To remove water vapour adhering to the egg surface, eggs were left in the
chamber for 30 min prior to measurement. Subsequently, a baseline reading
was taken (through an empty chamber) and the air stream flowing past the eggs
was sampled for
5 min. This reading allowed calculation of the rate of
water loss of unmanipulated eggs. During the subsequent baselining, the batch
of eggs was removed from the water-jacketed chamber and extracted (room
temperature) for 1 min with either chloroform:methanol (2:1 v:v; a general
solvent for lipid extraction) or 100% ethanol (polar solvent), blotted briefly
and returned to the chamber. After 2 min of flushing, the air stream was
sampled again. A control batch was manipulated identically except that it was
not exposed to solvent.
Developmental changes in metabolism and water loss
Data on artificial wax membranes indicate that wax permeability to
O2 may be very low (Donhowe and
Fennema, 1993). These data suggest that the wax layer in insect
eggshells may resist both water and oxygen flux. If metabolic demand for
O2 increases over development (which preliminary experiments showed
was the case), embryos may thin or alter the wax layer to enhance
O2 delivery; if so, eggs should also lose water at higher rates
towards the end of incubation. We tested this prediction by measuring
metabolic rate (as CO2 emission) while also measuring water loss
rate over most of the period from laying to hatching.
Eggs of known synchronized age were obtained by introducing a potted tobacco plant into the adult mating cage for 2 h. Eggs were stripped from leaves, sorted randomly into three batches of 40, weighed and placed into water-jacketed (27°C) respirometry chambers within 6 h (maximum egg age 8 h). The flow-through system consisted of (calibrated) water vapour and CO2 analyzers described above connected in series, with a small Drierite column between them. The air stream (dry, normoxic; 50 ml min1 STPD) was directed sequentially, via computer control of a gas multiplexer, through each of the sample chambers and a blank (baseline) chamber. Each chamber was sampled for 30 min, during which time the other three chambers were flushed continuously (50 ml min1 per chamber).
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Results |
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The equation for forced convection around a solid sphere
(Cussler, 1997, p. 227) is
given by:
![]() | (7) |
![]() | (8) |
![]() | (9) |
It may be more realistic to model eggs attached to a leaf. The equation for
laminar flow across a plate of length L
(Cussler, 1997, p. 227) is:
![]() | (10) |
Resistance of the chorion
In eggs of M. sexta, the chorion is 7 µm thick
(d1=7 x 106 m)
(Orfanidou et al., 1992
). If
aeropyles have the same diameter (the diameter at the chorion's outer surface)
for their entire length, the effective diffusion coefficient in the chorion
is:
![]() | (11) |
Aeropyle density appeared not to vary with location on the eggshell. On
average we counted 15.08 aeropyles per grid, giving an overall aeropyle
density of 2.41 x 108 aeropyles per m2. The
average egg thus contains 1703 aeropyles (=2.41 x 108
aeropyles m2 x 7.07 x 106
m2). This value is lower than Ofanidou et al. (1992)
suggested. They observed aeropyles (p. 738) "at periodic distances of
approximately 30 µm", equivalent to 1.6 x 109
aeropyles m2 or about 10,000 aeropyles per egg. The cause of
the discrepancy is unclear; we show below, however, that variation in aeropyle
number between the two values has a negligible effect on resistance to gas
flux.
Aeropyles were obvious at a number of scales
(Fig. 2B,C). They appeared
almost perfectly round and few (14%) were obstructed by any visible material.
The average area of an aeropyle (±S.E.M.) was
0.755±0.054 µm2, in good agreement with Orfanidou et al.
(1992), who visualized
aeropyles of
1.5 µm in diameter (1.76 µm2). Together
with the estimated total number of aeropyles, we calculate that the average
egg has approximately 984 µm2 (9.84 x
1010 m2) of aeropyle cross-sectional area. The
fraction of total area occupied by aeropyles (
), therefore, is
0.000139. D1 is thus 2.91 x 109
m2 s1 and the resistance of the chorion,
d1/D1 is 2409 s m1.
Higher numbers of aeropyles would be give even lower resistances. The value is
larger than the external resistance of boundary layers but still is less than
0.3% of the benchmark resistance (8.6 x 105 s
m1).
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An objection is that we assumed aeropyles of uniform radius (cylinders),
whereas they may actually taper as they approach the inner surface of the
chorion (as in e.g. the moth Antheraea polyphemus,
Margaritis and Mazzini, 1998).
The consequences of this shape for gas diffusion have been explored for bird
eggshells by Tøien et al.
(1987
,
1988
), with the general
conclusion that the narrow, inner portion of the funnel accounts
disproportionately for the overall resistance. In eggs of M. sexta,
this effect may be important. However, if the aeropyle radius at the inner
chorion were even threefold smaller, the resistance would still be small. An
upper bound can be estimated by assuming that the entire radius was threefold
less in this case, the overall resistance to flux would be ninefold
higher, or 2.2 x 104 s m1. This value still
only represents about 2.5% of the benchmark resistance.
Resistance of the trabecular layer
A priori, the thin trabecular layer (d2=0.3
µm, or 3 x 107 m;
Orfanidou et al., 1992) would
seem not to provide much resistance but it is worth a brief
calculation nonetheless. The diffusion coefficient of O2 in the
trabecular space can be estimated as:
![]() | (12) |
Inert gas substitution
Because flows of both N2 and He were controlled by the same mass
flow controller, we first empirically determined an appropriate thermal
conversion factor (1.37). A typical control trace using this factor is shown
in Fig. 3.
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As shown in Fig. 4, only variation in O2 content affected metabolic rates. Swapping He for N2 did not rescue the depressed metabolic rates of eggs in hypoxia; nor did swapping N2 for He further depress metabolic rates of eggs already in hypoxia. This result did not depend on egg age.
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Resistance of subchoral layers
Prior to extraction with organic solvents, all three batches of eggs had
similarly low rates of water loss (Fig.
5; 46 µg mg1 h1,
comparable to values measured gravimetrically by
Woods and Singer, 2001). After
extraction, water loss from the batch exposed to chloroform:methanol rose
18-fold to 90 µg mg1 h1. Control eggs
and those extracted in 100% ethanol had rates of water loss that rose
46-fold before falling back to values only slightly above
pre-extraction values. The initial rise likely represents water vapour that
had adhered to the outer chorion during the eggs' brief removal from the
chamber. The pattern of solvent effects is consistent with Slifer's
(1948
) solubility data on
waxes extracted from eggshells of a grasshopper, Melanoplus
differentialis, which she found to be soluble in chloroform but not
alcohol.
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Developmental changes in metabolism and water loss
In the first 40 h of development, rates of metabolism and water loss rates
both were low (Fig. 6A).
Thereafter, metabolic rates rose more-or-less continuously to the end of
development; rates of water loss followed a similar trajectory.
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These correlative data indicate that the layer or layers responsible for
waterproofing the egg probably wax likely also resist the flux
of metabolic gases. A more quantitative analysis is possible. Wax permeability
to water vapour can be calculated under the following assumptions: (1) that
the wax layer accounts for all of the resistance to water vapour in the
eggshell; (2) that the vapour pressure gradient across the eggshell is 3.56
kPa (from saturation at 27°C to zero); (3) and that wax layer thickness is
50 nm (d3). If, like beeswax, eggshell waxes have an
O2:water vapour permeability ratio of 1.49%
(Donhowe and Fennema, 1993),
the permeability to O2 (K) can then be calculated from
water vapour permeabilities (averaged across the three batches). We then
calculated the magnitude of the PO2 gradient
across the wax layer using the equation
PO2=Jd3/K,
assuming that O2 influx (J) is CO2/0.84
emission. These calculations indicate (Fig.
6B, solid line) that increasing permeability of the wax over
development (shown by rising rates of water loss) largely offsets increasing
metabolic demand consequently, the PO2
gradient stays near 10 kPa. Given the number assumptions underlying these
values, they match up remarkably well with the
PO2 observed by Woods and Hill
(2004
) of 1015 kPa in
the first 100 µm across the eggshell. Likewise, values for permeability,
corresponding to resistances of 105106 s
m1, match up well with the benchmark resistance. Additional
calculations, using only a constant permeability (equivalent to that
calculated at 32 h, a point of low permeability), show
(Fig. 6B, dotted line) that
eggshell permeability must increase if rising metabolic demand is not to
create an impossibly large
PO2.
Internal resistance to flux, H3H4/kI
The resistance of layers beneath the vitelline envelope depends on the
permeability of the serosal cuticle and the geometry, location and
permeability of the embryo. One estimate of the mass transfer coefficient,
kI, is DH2O/L,
where L is the distance from the eggshell to the embryo. M.
sexta develop just under the chorion, wrapped around yolk to the interior
(Dorn et al., 1987). Assuming
a distance between eggshell layers and embryo of 75 µm and that the
diffusion coefficient of O2 in the intervening material is the same
as its value in water (2.38 x 109 m2
s1 at 25°C; Denny,
1993
), kI=3.17 x 105
m1 s1 and the fifth resistance term,
H3H4/kI, is 9.5
x 105 s1 m1, about 20% of
the benchmark value. This value surely changes as serosal and larval cuticles
form. Oxygen transport to the egg's center is even more difficult. If we set
L to the egg's radius (
0.75 mm, or 0.00075 m), then
H3H4/kI 9.5
x 106 s1 m1. This value
is more than 100% of the calculated benchmark, indicating that diffusive
O2 supply to central regions may be inadequate although the
metabolic density of yolk likely is much lower than of embryonic tissues. A
detailed analysis of flux into the embryo and yolk will be forthcoming.
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Discussion |
---|
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---|
A recent claim to the contrary (Daniel
and Smith, 1994) in fact supports this conclusion. The authors
found that the size and shape of the single aeropyle in eggs of the beetle
Callosobruchus maculatus was correlated with metabolic rate between
strains eggs from a Yemeni strain had both higher metabolic rates
(2x) and shorter, wider aeropyles than a Brazilian strain. The authors
argued that shorter, wider aeropyles are an adaptation to enhance
O2 flux. However, the drop in O2 concentration from the
top to the bottom of the aeropyle is insignificant regardless of strain. Using
the Fick equation and values for rate of oxygen consumption and aeropyle
morphology from Daniel and Smith
(1994
), it is straightforward
to show that if the Yemeni strain had aeropyles of Brazilian dimensions, the
[O2] at the bottom of the aeropyle would have been
8.37 mol
m3. For comparison, air at 30°C (their test temperature)
has a [O2] of 8.43 mol m3
(Denny, 1993
).
Previous work on M. sexta in our laboratory
(Woods and Hill, 2004) showed
that the PO2 gradient across the eggshell is
very steep, though the measurement resolution was not fine enough to detect
gradients across individual layers. With the chorion and trabecular layers
eliminated as candidates, the resistance must lie in one or more subchoral
layers. Two observations implicate a wax layer specifically. First, extraction
of eggs with chloroform:methanol (which extracts a broad range of lipids) led
to markedly higher rates of water loss, suggesting that eggs of M.
sexta are indeed waterproofed by wax. This conclusion does not exclude a
role for the crystalline chorionic layer, which may also be destroyed by
organic solvents. Second, from laying to hatching, rates of metabolism and
water loss were strongly correlated. It appears that as metabolic rate
increases embryos obtain adequate O2 only by increasing the
conductance of one or more layers, leading to higher rates of water loss. See
Schmidt-Nielsen (1984
) for a
discussion of this tradeoff in bird eggs.
What remains is to develop a mechanistic view of how an oxygenwater
tradeoff is manifest in subchoral layers. Previous work on waxes suggests the
problem will not be trivial even the problem of waterproofing alone
has been controversial (Lockey,
1988). Beament
(1945
,
1961
,
1968
) championed the idea that
resistance to water flux through thin wax layers stems not from the properties
bulk wax but from a single monolayer of polar lipid molecules interacting with
and organized by a substrate, i.e. the cuticle. The monolayer hypothesis,
however, has since been criticized on a number of fronts
(Gilby and Cox, 1963
;
Lockey, 1976
;
Toolson et al., 1979
;
Machin, 1980
). More recent
work (Gibbs, 1998
,
2002
) has focused on the
effects of lipid chain length and structure on phase transitions, finding that
phase behaviour is a major factor influencing cuticular permeability. These
latter results suggest that bulk properties of wax layers, rather than
interaction with a substrate, determine their permeability to water.
Complications in this model arise from the behaviour of `bulk waxes'
which if they contain many different lipid species can exist in multiple
alternative packing arrangements or as separate, coexisting solid and liquid
phases (Gibbs, 1998
). How
O2 moves across such heterogeneous material is of particular
interest.
In insect eggshells specifically, interactions between waxes and the
crystalline chorionic layer may also occur
(Margaritis et al., 1980).
Major structural units in the crystalline layer are arranged periodically at
intervals of 810 nm and smaller units at 3.55.5 nm
(Margaritis, 1985
); the open
distances between units appear to be as low as 1 or 2 nm
(Margaritis et al., 1984
;
Margaritis and Mazzini, 1998
).
The scale of these features is of the same order as the physical dimensions of
individual wax molecules. For comparison, a straight-chain alkane containing
n carbon atoms has a length of (n1)*1.27
Å (1 nm=10 Å) between terminal carbons
(Ocko et al., 1997
). Thus a
C-27 alkane would have a length of about 33 Å (3.3 nm), long enough to
bridge spaces within the crystal lattice. It would also be narrow enough to
intercalate into the crystal. Alternatively, polar lipids could be organized
by interaction with polar sites on the surface of the crystalline layer
(à la Beament). A still more radical hypothesis is that the
crystalline layer itself is responsible for most of the waterproofing
and most of the resistance to O2 flux. Evaluating this
last idea will require more detailed information, presently unavailable, on
the sequences and arrangement of crystalline proteins.
Our work has both ecological and evolutionary implications. First, the wax
layer and possibly also the vitelline envelope and crystalline chorionic
layers, are the physical locus of a tradeoff between oxygen influx and water
vapour efflux. Studies examining the physiological ecology of insect eggs
(i.e. relationships among geographic distributions, eggshell structure,
desiccation resistance and temperature-associated oxygen shortage) should
focus explicitly on these subchoral layers. Second, the division of labor
among eggshell layers the chorion functioning to protect subchoral
layers and embryo from mechanical threats
(Hinton, 1981) and the
subchoral layers controlling the fluxes of water, oxygen and carbon dioxide
indicates that the two sets of layers may be functionally and
genetically decoupled over evolutionary time and likely are shaped by distinct
sets of selection pressures.
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Acknowledgments |
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