Gametes of free-spawning invertebrates are exposed to physical stresses both before and after release from the adult. Gametes released into the water column are exposed to shear stresses (force per unit area) present in the adult habitat. These stresses are the result of shear experienced by gametes within velocity gradients between eddies in the turbulent water column and between the moving water and the surfaces of solid objects in the environment. Recent research has demonstrated that shear stresses in the range experienced by gametes in some marine habitats can reduce fertilization success and may cause some egg damage (Mead and Denny, 1995; Thomas et al., 1999). In addition to the shear stresses experienced in the external environment, gametes are exposed to shear during spawning as they are extruded through a gonoduct and pore. As the gametes travel along the duct and through the pore, a velocity gradient develops within the fluid. This gradient develops because the fluid directly in contact with the wall of a pipe, such as a gonoduct, has a velocity of zero, and the velocity increases to some mainstream value at the center of the duct (for discussion, see Kays and Crawford, 1993; Vogel, 1993). This velocity gradient imposes a shear stress on the gametes within the duct. Depending on the rate of gamete release and the size of the duct, gametes may be exposed to shear stresses that far exceed those in the adult habitat. Shear stresses imposed on eggs during spawning may therefore cause damage to gametes and potentially act in the selection of gamete traits that minimize such damage.
One of the major factors contributing to the magnitude of
the shear stress in the gonoduct is the viscosity of the spawned material. The higher the viscosity of the material, the greater the force experienced by the gametes. Thomas (1994) determined that the viscosity of gametes of three species of sea urchin declines with increasing shear rate (i.e. they exhibit shear-thinning). Shear-thinning reduces the power required to extrude the gametes from the oviduct and probably reduces the shear stress experienced by the gametes during spawning. Therefore, shear-thinning of sea urchin gametes has the potential to reduce the incidence of gamete damage due to high shear stress as the gametes travel through the gonoduct.
It is also possible that the extracellular layers surrounding the eggs have the capacity to reduce damage caused by shear stress. These layers play some role in the fertilization processes (e.g. Vaquier and Moy, 1977; Tilney et al., 1978; SeGall and Lennarz, 1979; Garbers and Kopf, 1980; Nomura and Isaka, 1985; Miller and Ax, 1990) yet they are not required for fertilization (Strathmann, 1987; Bolton and Thomas, 1999). Consequently, it is possible that these extracellular layers have some additional role in the reproduction of free-spawning invertebrates. One such role might be the protection of eggs from the shear stresses experienced in the adult habitat and as they pass through the oviduct. In echinoderms, extracellular layers (jelly coats) are composed of polysaccharides and glycoproteins (Kidd, 1978; Segall and Lennarz, 1979; Crawford and Abed, 1986) that swell considerably after exposure to sea water (Bonnell et al., 1994). The jelly coat consists of several concentric layers of complex fibrous JEB2036
Shear stresses experienced by eggs in the oviduct of the echinoid Arbacia punctulata during spawning were calculated using engineering equations that describe laminar flow through pipes. Shear stresses in the oviduct ranged from 0 to 58.7 Pa. Two properties of eggs were identified that have the potential either to minimize the shear stress in the oviduct or to reduce the damage experienced by eggs exposed to high shear stress. These properties are the viscosity of the eggs and the presence of extracellular layers on eggs of A. punctulata. The viscosity of eggs decreases with increasing shear rates, which
reduces the magnitude of shear stress experienced in the oviduct, while the extracellular layers mitigate the effect of shear stress on the eggs. Eggs with intact extracellular layers were damaged less frequently than were those with the extracellular layers removed. The results of this research indicate that physical stresses may be important selective factors in the evolution of gamete properties.
Key words: echinoid, Arbacia punctulata, shear stress, gamete, spawning, evolution, fertilization, invertebrate life history.
Summary
Introduction
SHEAR STRESS EXPERIENCED BY ECHINODERM EGGS IN THE OVIDUCT
DURING SPAWNING: POTENTIAL ROLE IN THE EVOLUTION OF EGG PROPERTIES
FLORENCE I. M. THOMAS* ANDTOBY F. BOLTON
Department of Biology, University of South Florida, 4202 East Fowler Avenue, Tampa, FL 33620-5150, USA
*e-mail: fthomas@chuma1.cas.usf.edu
networks within a polysaccharide matrix (Kidd, 1978; Holland, 1980; Crawford and Abed, 1986; Sousa et al., 1993; Bonnell et al., 1993, 1994). In at least one species, Strongylocentrotus
purpuratus, the coats consist of globular glycoproteins
interspersed in a fibrous fucose sulphate superstructure (Bonnell et al., 1994). Fibrous structures embedded in composite materials often provide mechanical strength to that material (e.g. Sastry et al., 1998). If the shear stresses experienced by eggs in the gonoduct during spawning are relatively high, the mechanical strength provided by the jelly coats may protect the eggs from this shear stress.
In this paper, shear stresses in the oviduct of the sea urchin
Arbacia punctulata during spawning are estimated using
equations describing shear stress in laminar pipe flow (see Kays and Crawford, 1993; Vogel, 1994). The effects of shear-thinning on the magnitude of shear stresses are then investigated by comparing stresses calculated using parameters measured for eggs that shear-thin with those calculated when the viscosity of the eggs is held constant at its highest value. In addition, the hypothesis that extracellular layers on eggs act to protect them from damage caused by shear stresses in the oviduct is examined by exposing eggs with and without intact jelly coats to a known shear stress.
It should be noted that the equations used in this paper to estimate shear stress in the oviduct are a simplification and probably do not represent the exact shear regime experienced by eggs in the oviduct. The equations describe the velocity gradient and resultant shear produced by laminar flow of a viscous fluid through a section of pipe. The factors contributing to the velocity profile and shear gradient experienced by the eggs as they pass through the oviduct and gonopore are likely to be much more complex than those described by these simple equations. The eggs are highly deformable spheres surrounded by jelly coats that, as a whole, behave as a fluid. As the eggs move through the oviduct, it is likely that the eggs and jelly coats are deformed by the shear developed in the fluid and that the shear stress experienced by an egg is distributed over the deformed sphere. In addition, as the eggs are spawned, they pass from the oviduct into the gonopore, where the diameter
of the duct decreases from 900 to 300µm. This reduction in
diameter is likely further to deform the eggs as they pass out of the gonopore. Thus, the equations used here are unlikely to be a complete representation of the velocity profile and shear stress experienced by eggs within the oviduct. Nonetheless, the use of simple engineering equations describing laminar flow through a pipe provides a logical starting point from which to initiate an analysis of shear within the oviduct and provides some insight into the shear stresses experienced by echinoderm eggs during spawning. Future research will address the specific details of shear stress on individual eggs within the oviduct.
Materials and methods
Collection and maintenance
Arbacia punctulata Lamarck were collected from the
subtidal zone on marina walls at Panama City, Florida, USA,
during July 1998. Measurements of the release rates of eggs were made at the time of collection from some of these specimens (see below). Other specimens were transported to the Dauphin Island Sea Laboratory, Alabama, USA, in aerated sea water kept at ambient water temperature (27–30 °C). These specimens were maintained in filtered aquaria and fed periodically with lettuce and dried dog food. Salinity in the aquaria varied between 29 and 33 ‰, and temperature varied between 25 and 30 °C.
Calculation of shear stress
The shear stress experienced in the oviduct was estimated by assuming that flow characteristics within it are similar to those of laminar flow through a pipe, which is well described by engineering studies (e.g. Kays and Crawford, 1993). In general, the shear stresses (σ) within the fluid can be described using the following equations (see Vogel, 1994):
σ= µ(du/dr) = ∆pr/2l , (1) where µ is the viscosity of the fluid, du/dr is the shear rate, ∆p
is the pressure drop over a length (l) of pipe and r is the radius measured from the center of the pipe. The pressure drop in the pipe can be calculated from the flow rate through the pipe (Q.), the viscosity of the fluid and the length and diameter (d) of the pipe as follows (Vogel, 1994):
∆p = 128Q.µl/πd4, (2) In the case described above, the fluid within the pipe is Newtonian. For Newtonian fluids, viscosity remains the same no matter how fast the fluid is sheared (i.e. regardless of the flow rate through the pipe, Q.). Data available for echinoids, however, indicate that the viscosity of material spawned by females decreases with increasing shear rate (i.e. shear-thins; Thomas, 1994). Thus, the shear stress (σ) in the oviduct must be described as a function of shear rate, as follows:
σ= k(du/dr)n= ∆pr/2l , (3) where k is the apparent viscosity of the fluid and n is the exponent from the power regression. In addition, because the viscosity of the material spawned by females is not constant, the pressure drop within the oviduct cannot be calculated using the equations describing shear stress in a pipe for Newtonian fluids (equations 1 and 2 above). Instead, an equation accounting for the shear-thinning characteristics of the gametes is used as follows (see Thomas, 1994):
∆p = (Q./{2π[n/(n + 1)] ×{1/2 −[n/(3n + 1)]} ×
a(3n+1)/n}n) ×2lk . (4) where a is the radius of the duct.
chosen as the value for d. Setting r=0.25d is an arbitrary choice and represents the shear stress experienced midway between the center of the duct and the outer wall.
To explore how different parameters affect shear stress in the oviduct, shear stresses were calculated for various values
of Q.and r (the distance from the center of the oviduct). In the
first case, Q. was varied over two orders of magnitude; one
order lower and one order higher than that measured for
Arbacia punctulata. This allowed examination of the effect of
Q.on shear stress. This range was chosen because it is possible
that using KCl to induce spawning produces a maximum gamete release rate and that natural rates could be lower than
those measured in this study. In addition, Q.may vary over the
reproductive season.
By examining equations 1 and 3, it can be seen that the shear stress experienced by eggs near the wall (large r) is higher than that experienced by eggs near the middle of the oviduct (small
r). To examine the gradient in shear stress that eggs at different
locations across the oviduct experience, expected shear stresses at locations spanning the oviduct (various values of r) were calculated (equations 3 and 4) using the minimum and
maximum values of Q.and oviduct radius (a).
In addition to varying the above parameters, the effect of shear-thinning of the eggs on the magnitude of shear stresses within the oviduct was examined. To do this, the shear stresses experienced half-way between the center of the oviduct and the wall (r=0.25d) were calculated (equations 1 and 2) using the
same range of Q. as above and the maximum viscosity
measured for the eggs (7.8 Pa s). This approach provided an estimate of the shear stresses that would be experienced by eggs if they did not shear-thin but remained constant at the maximum value measured for the eggs.
Measurement of parameters required to calculate shear stress
To estimate the shear stress experienced by an egg in the oviduct of Arbacia punctulata, it was necessary to measure the parameters required for the calculations described above.
These parameters include the gamete release rate (Q.), the
dimensions of the oviduct and pore (d, a and l) and the apparent viscosity (k) and power exponent (n) of the material spawned.
Determination of Q·
Thirteen females were injected with 0.25–0.50 ml of
0.53 mol l−1KCl (see Strathmann, 1987) to induce spawning
immediately after they were collected. These individuals were highly gravid and spawned profusely. For each female, a calibrated 1 ml syringe (accuracy 0.01 ml) was placed over a single gonopore, and the material released from the pore was drawn into the syringe. Once a volume of at least 0.3 ml had been obtained, the syringe was removed from the urchin surface. The time required to collect a given volume of material was recorded using a digital stopwatch (accuracy ±0.1 s), which was started when eggs became visible at the gonopore and stopped when the syringe was removed from the urchin surface. The width of the test of each urchin was measured using a vernier caliper (accuracy ±0.5 mm) to examine the
relationship between Q.and urchin size. Urchins were released
following these measurements.
Oviduct and gonopore dimensions
Measurements of the length (l) of the oviduct were made
under a dissecting microscope at 10×magnification (accuracy
±10µm). Five oviducts were prepared from each of 11 females
by dissecting the entire duct attached to the gonopore and gonad (Fig. 1). Oviducts were dissected by cutting the test of each urchin between the gonopores with a scalpel and separating the sections carefully. The test was then removed from around each gonopore, leaving the oviduct attached to the gonopore and gonad. These structures were laid out on a glass Petri dish, and the length of the oviduct was measured in the manner described above.
The gonopores of Arbacia punctulata are oval, and the depth, width and length of the pores were measured. Measurements were made under a dissecting microscope at
100× magnification (accuracy ±5µm). Five gonopores each
were dissected from the tests of 15 females in the manner described above. The oviducts were removed, and the pores were placed on a microscope slide for measurement. To determine the depth of the gonopore, the pore was cut in half, mounted sideways on a small piece of modeling clay and measured under the dissecting microscope as described above. The mean of the five measurements was used as the dimension for a given female. A grand mean for all 15 females was also calculated and used in the estimation of shear stress in the oviduct using equations 1–4.
Determination of egg size
Egg size was measured directly using a calibrated ocular
graticule in a compound microscope (100× magnification;
[image:3.609.327.558.495.711.2]accuracy ±5µm). The thickness of the jelly coat prior to and
Fig. 1. A single gonad, oviduct and gonopore complex of a female
after hydration was also measured. To measure hydrated coats, Sumi ink was added to eggs in sea water, and the thickness of the coat was measured using a calibrated ocular on a compound microscope. Jelly coats hydrate when exposed to sea water, so it was necessary to measure the thickness of the unhydrated coats without putting the eggs in sea water. The thickness of the jelly coats was inferred by measuring the distance between abutting freshly spawned eggs. The distance between two adjacent eggs was measured using a calibrated ocular graticule
in a compound microscope (100× magnification; accuracy
±5µm). These values were then divided by two to determine
the thickness of the jelly coat on a single egg. The diameter of eggs plus jelly coats was estimated as the diameter of the egg plus twice the thickness of the jelly coat. Measurements of egg diameter and jelly coat thickness were made for ten randomly chosen eggs from each of ten replicate females.
Viscosity
The viscosity of the material spawned by the females of seven Arbacia punctulata females was measured at shear rates
of 0.6, 1, 1.2, 2, 3, 4, 5, 8, 10, 12, 20, 24, 40 and 60 s−1in a
cone-and-plate viscometer (Brookfield DV II). This instrument allows the measurement of the viscosity of fluids using a relatively small volume of fluid (0.5 ml). The cone is angled so that shear stress is constant across the sample and the distance
between the cone and plate varies from 135 to 216µm. The
data obtained from these measurements of viscosity include the shear stress imposed on the material and the viscosity at each shear rate. A power regression of shear stress versus shear rate yielded values of n (the exponent) and k (the slope). The mean values of n and k for the seven measurements of viscosity were used to calculate shear stress in the oviduct using equations 3–4.
Damage to eggs with and without jelly coats
Paired samples of eggs with and without jelly coats from each of five females were prepared by removing the jelly coats from half the eggs collected from a female. The coats were removed using a technique commonly employed in embryology (see Hinegarder, 1975). Eggs were poured
through a plankton screen (Nytex) with 110µm diameter
pores. This diameter is smaller than that of A. punctulata eggs
with hydrated jelly coats (approximately 127µm) but
substantially larger than that of the egg alone (approximately
69µm). Hydrated jelly coats are relatively easy to remove
from eggs in this species. To minimize the probability of damaging eggs by subjecting them to unnecessary passes through the plankton screen, the eggs were checked for the presence of jelly coats after every two passes using Sumi ink to vizualize the edges of the coat (see Strathmann, 1987). This technique does not reduce the fertilizability of eggs or result in the loss of material from the eggs (Bolton and Thomas, 1999). Alternative methods of removing the jelly coat, such as exposure to acid, were rejected because they alter the egg membrane, resulting in a reduction in fertilizability (see Strathmann, 1987).
To assess the effects of shear stress on egg survival, eggs either with or without intact jelly coats were pipetted onto the plate of the cone-and-plate viscometer and counted. Eggs with intact jelly coats were not exposed to sea water so that the jelly coats remained unhydrated. Initial counts ranged from 35 to 50 eggs. After counting the eggs, 0.5 ml of a viscous solution was added to the eggs, and they were exposed to a shear stress near 2 Pa for 2 min. At the end of the 2 min period, the fluid within the viscometer was rinsed into a Petri dish, and all intact eggs within the dish were counted. Survivorship of eggs was calculated as the initial egg count minus the final egg count.
The viscous fluid used in these trials was a mixture of sea water and hydroxyethyl cellulose to bring the viscosity to 20 Pa
s and the shear stress to 2 Pa at a shear rate of 90 s−1. The pH
of this solution was adjusted to 8.0 by adding NaOH. Hydroxyethyl cellulose (proto-slo, Carolina Biological) was chosen for the viscous fluid because it did not appear to damage eggs or their jelly coats. Eight viscous fluids were tested prior to choosing hydroxyethyl cellulose. These fluids included chlorhexidine gluconate (KY jelly), hydroxyethyl cellulose, polyvinylpyrrolidone (PVP), polyvinylpolypyrrolidone, Percoll, methylcellulose, dextran and egg homogenate. The criteria for choosing a fluid for use in the experiments was as follows: (1) jelly coats did not hydrate in the fluid; (2) after exposure to the fluid, jelly coats hydrated to normal size when exposed to sea water; (3) after exposure to the fluid, eggs both with and without jelly coats remained viable; (4) no cell leakage was detectable upon visual inspection after exposure to the fluid. Hydroxyethyl cellulose was the only fluid that met all four criteria.
To assess the viability of eggs after exposure to the fluids listed above, 1 ml samples of eggs with and without jelly coats from five sea urchins were incubated in a dilute sperm
suspension (dry sperm diluted by 10−4in fresh sea water). In
preliminary experiments, this sperm concentration was found consistently to result in 100 % fertilization success of eggs with and without jelly coats. Thus, while no attempt was made to assess the fertilizability of the eggs, incubating them in this sperm concentration provided a test of their viability. Embryos were allowed to divide to at least the four-cell stage before being recorded as viable.
Results
The mean egg release rate (Q.) measured for 15 females was
3.4×10−9±2.2×10−9m3s−1(range 1.1×10−9to 8.1×10−9m3s−1;
Table 1). There was no significant relationship between urchin
diameter (W) and Q.(r2=0.074, P>0.36). The mean diameter of
Arbacia punctulata females used for gonopore measurements
Viscosity
The viscosity of Arbacia punctulata eggs exhibited shear-thinning behavior (Fig. 2). Viscosity was higher at low shear rates than at high shear rates. These measurements yielded good regression fits to the power function that describes the relationship between shear stress and shear rate for materials
that shear-thin (equation 3). The value of r2 for these
regressions was 0.972±0.04 (mean ± S.D., N=7; range
0.903–0.995; Table 3). The mean value of the apparent viscosity (k) was 2.9±0.9 Pa s (N=7, range 2.1–4.9 Pa s) and for the power exponent (n) was 0.41±0.03 (N=7, range 0.39–0.46; Table 3).
Estimates of shear stress
Shear stresses at a position midway between the oviduct
wall and the center of the duct increased with increasing Q.
(Fig. 3) and with decreasing oviduct radius (a). Shear stress
ranged from 3.5 to 58.7 Pa for Q.over two orders of magnitude
(10−8 to 10−10m3s−1) when oviduct radius was set at the
minimum value (a=2.25×10−4m). Using the mean value of the
radius (a=4.5×10−4m) over the same range of Q. yielded
estimated shear stresses ranging from 1.9 to 32.0 Pa. Using the
maximum radius (a=7.8×10−4m) for these calculations,
yielded shear stresses that ranged from 0.9 to 16.2 Pa (Fig. 3A).
When Q.was restricted to the order of magnitude measured for
A. punctulata (0 to 10−9m3s−1), estimates of shear stresses (Fig. 3B) ranged from 8.9 to 22.8 Pa using a minimum radius
(a=2.25×10−4m). Over this same Q.range, shear stress ranged
from 4.8 to 12.5 Pa using the mean a (a=4.5×10−4m), and from
2.4 to 6.3 Pa using the maximum a (a=7.8×10−4m). Estimated
shear stresses calculated for eggs in the absence of shear-thinning (using equations 1 and 2 with a constant viscosity of 7.8 Pa s) were a great deal higher than those estimated using the shear-thinning parameters. For maximum d, the shear
stresses ranged up to 2×103Pa; for mean d, they ranged up to
16×103Pa; for minimum d, they ranged up to 158×103Pa.
Table 1. The egg release rate (Q·) for 13 Arbacia punctulata
females of diameter (W)
W Q·×109 Female (mm) (m3s−1)
1 36.0 3.9
2 46.5 6.3
3 41.0 2.7
4 21.5 2.1
5 43.0 1.2
6 48.5 3.6
7 47.0 1.1
8 37.0 2.9
9 22.0 1.3
10 39.5 8.1
11 37.5 3.8
12 44.0 1.5
13 45.5 6.1
[image:5.609.317.561.63.262.2]Mean ±S.D. 39.1±8.6 3.4±2.2
Table 2. The dimensions of the oviduct and gonopore
measured in 15 female Arbacia punctulata
Mean Minimum Maximum
(mm) (mm) (mm)
Urchin diameter (mm) 41.0±6.6 24 48
Oviduct length (mm) 9.9±2.3 6.7 14.7
Gonopore
Depth 0.63±0.13 0.47 0.84
Outer width 0.30±0.12 0.10 0.47 Outer length 0.40±0.09 0.27 0.58 Inner width 0.90±0.27 0.51 1.27 Inner length 0.75±0.26 0.55 1.57
Values are given as means ±S.D.
Shear rate (s-1)
0 10 20 30 40 50 60
Viscosity,
µ
(Pa s)
[image:5.609.47.297.95.288.2]0 2 4 6 8
Fig. 2. Viscosity (µ) of Arbacia punctulata eggs versus shear rate measured in seven individuals represented by different symbols. Note that viscosity decreases with increasing shear rate (exhibits shear-thinning).
Table 3. Regression of shear stress versus shear rate for the
eggs of seven Arabacia punctulata
k
Female n (Pa s) r2
1 0.39 4.9 0.992
2 0.41 3.3 0.903
3 0.46 2.5 0.987
4 0.38 2.8 0.941
5 0.42 2.2 0.993
6 0.42 2.1 0.993
7 0.40 2.2 0.995
Mean ±S.D. 0.41±0.03 2.9±0.9 0.972
Shear stress = (shear rate)n.
[image:5.609.316.566.572.706.2] [image:5.609.49.299.590.723.2]Shear stresses estimated for various distances from the center of the oviduct (calculated using equation 4 and various
values of r) were dependent on both Q. and oviduct diameter
(Fig. 4). At the highest Q.measured (8.1×10−9m3s−1), the shear
stresses in the oviduct ranged from 0 to 11.5 Pa (Fig. 4A) for
the widest radius (a=7.8×10−4m) and from 0 to 41.9 Pa for the
narrowest radius (a=2.25×10−4m). At the lowest Q.measured
for the Arbacia punctulata females (1.1×10−9m3s−1), the shear
stresses in the oviduct ranged from 0 to 5.2 Pa for the widest
diameter (a=7.8×10−4m) and from 0 to 18.5 Pa for the
narrowest (a=2.25×10−4m) (Fig. 4B).
Survival and fertilization success
When exposed to a shear stress of approximately 2 Pa, nearly 100 % of the eggs (97 %) with intact jelly coats survived. However, a significantly (paired t-test, mean difference 0.13; d.f.=4. F=6.1, P=0.0036) smaller percentage (71 %) of the eggs
without jelly coats survived exposure to this shear stress. Nearly 100 % of the eggs with and without jelly coats were viable prior to exposure to shear stress and remained viable after exposure to the viscous fluid used in the experiments.
Discussion
Shear stresses (estimated using equations 3 and 4) experienced by eggs in the oviduct of Arbacia punctulata at
the mean rate of release (mean Q.) range from 0 Pa at the center
of the oviduct to more than 41 Pa at the wall (Fig. 4). This range of shear stress far exceeds that predicted in extreme marine environments. Although shear stresses in very exposed habitats such as surf zones are predicted to reach nearly 1.9 Pa and in the boundary layer may approach 4 Pa (Denny et al., 1992), these stresses will be considerably lower in most habitats (Denny, 1988). In coastal habitats, for example, energy
dissipation rates (ε·) are estimated to be of the order of 10−1to
10−2W m−2(Rothschild and Osborn, 1988; cited in Mead and
Denny, 1995). This magnitude of energy dissipation represents
2 4 6 8 10
0 5 10 15 20 25 0 10 20 30 40 50 60
Min
Mean
Max
Shear stress (Pa)
Shear stress (Pa)
Min
Mean
Max
A
B
10 20 30 40 50 60 70 80 90 100 0
[image:6.609.316.555.69.398.2]Q.×109 (m3 s-1)
Fig. 3. Shear stress calculated using equations 3 and 4 for a position midway between the oviduct wall and the center of the duct. Calculations were made using the mean (solid line), minimum (dashed and dotted line) and maximum (dashed line) values of oviduct radius (a): (A) with gamete release rate (Q.) varied over two orders of magnitude and (B) with Q.limited to the order of magnitude measured for Arbacia punctulata (shaded region in A).
-0.75 -0.50 -0.25 0.25 0.50 0.75 0
10 20 30 40 50
0 10 20 30 40 50
Radius (mm) 0
5 10 15 20
0 5 10 15 20
Shear stress (Pa)
A
B
Shear Stress (Pa)
Maximum diameter
Minimum diameter
Maximum diameter
Minimum diameter
0
[image:6.609.50.281.72.434.2]-0.75 -0.50 -0.25 0 0.25 0.50 0.75
a shear stress of the order of 10−2to 10−3Pa (energy dissipation
rate, ε·=τ2/µ; where τ is shear stress and µ is the dynamic
viscosity of sea water). Given that shear stresses near 1.4 Pa are known to reduce egg viability (Mead and Denny, 1995), it is possible that shear stresses in the oviduct (up to 58 Pa) damage eggs. If shear stress does have the potential to cause lethal or non-lethal damage, stresses experienced in the oviduct may be a factor in the selection of egg traits that limit the impact of these stresses. Both the presence of jelly coats and the shear-thinning behavior of the material released during spawning are traits that have this potential.
There has been considerable interest in the roles of jelly coats in echinoderm biology; however, the idea that jelly coats protect eggs from shear stress in the oviduct is new. The jelly coats of echinoderm eggs have been hypothesized to have a number of potential roles in the fertilization process including: (1) species-specific egg–sperm recognition (Miller and Ax, 1990); (2) induction of the acrosomal reaction (Tilney et al., 1978; SeGall and Lennarz, 1979); (3) induction of egg–sperm binding (Vaquier and Moy, 1977; Lopez et al., 1993); (4) activation and chemotaxis of sperm (Garbers and Kopft, 1980; Nomura and Isaka, 1985; and (6) enlarging the effective size of the egg, thereby increasing the likelihood of a sperm–egg collision (Epel, 1991). Jelly coats, however, have a very complex structure that is not likely to be important to any of these hypothesized roles.
The jelly coat consists of several concentric layers of complex fibrous networks (Kidd, 1978; Holland, 1980; Crawford and Abed, 1986; Sousa et al., 1993; Bonnell et al., 1993, 1994). The inner layer consists of a dense network of fibers (Kidd, 1978; Bonnell et al., 1994) that are resistant to mechanical and chemical disruption in some species (Kidd, 1978). The middle layer is composed of a network of thicker fibers and is surrounded by a dense outer layer (Kidd, 1978; Crawford and Abed, 1986; Bonnell et al., 1994). These layers are reminiscent of networks that provide mechanical strength to numerous engineering materials (e.g. Sastry et al., 1998).
The idea that extracellular layers protect eggs from shear stress raises some interesting points for conjecture. For example, the primary force driving selection of extracellular layers may be protection of eggs from shear stress experienced in the oviduct during egg release. In addition, roles for jelly coats in the fertilization processes (such as those listed above) may drive secondary selection for specific attributes of extracellular layers common to both invertebrate and vertebrate animals.
Further evidence in support of the idea that extracellular layers may be the result of selection is that they represent a substantial portion of the energy invested in each egg (3–11 %; Bolton and Thomas, 1999). Assuming that the energy available for reproduction is finite, investment in an extracellular layer may reduce the number of eggs that can be produced and/or the amount of energy invested in each egg. In evolutionary terms, for a trait to have a selective advantage, benefits accrued by the presence of the trait must exceed the costs of producing the trait. Therefore, it is likely that extracellular layers play a
role either in ensuring the survival of the egg to fertilization or in fertilization itself.
It is interesting to note that shear stresses lower than those estimated for eggs within the oviducts of Arbacia punctulata can influence fertilization in the sea urchin Strongylocentrotus
purpuratus (Mead and Denny, 1995). In this study, shear
stresses up to 1.4 Pa decreased both fertilization success in the presence of shear and the fertilizability of the eggs. Presumably, the eggs in this study sustained non-lethal damage that affected their fertilizability at shear stresses below those experienced in most of the oviduct during spawning. Most eggs, however, are capable of fertilization after release from the gonopore despite the fact that they have been exposed to shear stresses that exceed those that caused the damage reported by Mead and Denny (1995). In addition, the results of the present study indicate that eggs remained nearly 100 % fertilizable even after exposure to shear stresses up to 2 Pa.
A possible explanation for these somewhat contradictory results is the effect of the hydration state of the jelly coats on resistance to shear. In the research of Mead and Denny (1995), the jelly coats were hydrated. However, as in the oviduct, the coats of eggs in the present study were not hydrated. It is possible, therefore, that hydrated jelly coats are more susceptible to damage than are unhydrated coats. Jelly coats go through considerable changes in structure as they hydrate. Upon hydration, the thickness of the jelly coat increases nearly sixfold (Table 4) and the volume increases by approximately 10-fold (Bolton and Thomas, 1999). As the jelly coat swells, the fibers in the coat are stretched and decrease in diameter from 50–60 nm to 5–25 nm (Bonnell et al., 1993). While the angles between fibers have not been measured, it is reasonable to assume that they become larger as the jelly coat swells. The observation that hydrated coats fail under lower stress than unhydrated coats is consistent with observed failure progression in engineered fiber-reinforced materials. The fibers in the hydrated jelly coats are under shear loads much as are the fibers in engineered composite materials (e.g. Sastry et al., 1993). They are also loaded in what might reasonably be approximated as tri-axial tension by the expansion of the jelly coating. This expansion probably affects the angle between fibers in the network and would explain the reduction in cross-sectional area of the fibers. Engineering analyses of such Table 4. Effects of hydration on the thickness of the jelly coat
of Arbacia punctulata eggs
Unhydrated (µm) Hydrated (µm)
J E EJ J E EJ
10±4 68±3 78±2 57±10 69±2 127±10
J, jelly coat thickness; E, egg diameter after jelly coat removal; EJ, diameter of egg with intact jelly coat.
Values are means ±S.D. (N=10).
networks also support the notion that the internal stresses attendant on hydration would initiate sequential failure of the network of fibers (Sastry et al., 1998), and thus the egg has a weaker coating after hydration.
It is probable that the shear stresses in the viscometer are not exactly the same as those experienced in vivo. Thus, these experiments may not provide direct data on the survivorship of eggs in the oviduct. However, because the experimental results are internally consistent (both those with and without jelly coats were exposed to the same shear regime), the experiments do provide data on the relative survival of eggs with and without extracellular layers. Furthermore, the estimates are conservative because the highest shear stress obtainable in the viscometer represents only 1/30 of the highest stresses calculated for the gonoduct.
It is evident that shear-thinning (a decrease in viscosity with increasing shear rate) of the eggs decreases the shear stress experienced in the oviduct. In the absence of shear-thinning,
the shear stress experienced by eggs can be between 103and
105times higher than that experienced when eggs shear-thin.
The mechanisms responsible for shear-thinning of echinoderm eggs are not known; however, other biological fluids such as blood exhibit this characteristic. Shear-thinning of fluids may be the result either of a physical property of the fluid or of the interactions between particles suspended within the fluid. For example, blood cells are suspended in a Newtonian fluid (plasma). Shear-thinning of blood is the result of a decrease in the volume fraction of cells as the blood moves into narrow capillaries and the positioning of cells one behind the other as the space for them to pass narrows (e.g. Fung, 1981, 1990). It is unlikely that changes in the volume fraction of eggs accounts for their shear-thinning. Eggs are not a suspension of semi-solid spheres in a viscous fluid such as blood. In contrast, there is virtually no extracellular fluid associated with the eggs. Therefore, it is likely that shear-thinning in eggs is the result either of a specific physical property of the eggs or of a tendency for them to be aligned behind one another parallel to the direction of flow.
Whether properties that result in shear-thinning of eggs are a consequence of selection for specific egg traits or the result of passive alignment of eggs (spheres) within the oviduct is not known. As noted above, fluids that consist of particles can exhibit shear-thinning (e.g. Fung, 1981, 1990). However, it is possible that some property of the egg produces the shear-thinning behavior observed in echinoderms. For example, at high shear, the fibers in the jelly coat may be aligned parallel to the direction of flow, thereby decreasing the viscosity of the jelly. This alignment may allow the eggs to elongate in the oviduct, which could affect the shear gradient experienced by the egg. This interaction between egg properties and shear gradients could be an interesting subject for further study.
It is possible that our techniques account for the damage observed in eggs without jelly coats. The eggs were exposed to shear in a viscous solution that contained hydroxyethyl cellulose. This compound may weaken the egg in some way.
However, eggs both with and without intact jelly coats remained fertilizable after exposure to the fluid and the shear. Furthermore, the coats remained intact and hydrated normally after exposure to the solution. Thus, it is assumed that the solution caused minimal damage.
The estimates of shear stress reported in this paper are
dependent on both the release rate of eggs (Q.) and the
dimensions of the oviduct. It is possible that the mode of spawning used in this paper (injection of KCl) produces
maximum values of Q.. Shear rates during natural spawning
may be less than those reported here. Measurements of natural rates of gamete release are necessary to estimate naturally occurring shear stress. In addition, the diameter of the inner region of the gonopore was used as the diameter of the oviduct in our calculations of shear stress using equations 1–4. The gonopore and gonoduct complex in sea urchins, however, is not a straight pipe and widens and narrows as eggs progress from the ovary to the gonopore (Fig. 1). In fact, the outer opening of the gonopore is the narrowest portion of the duct complex and may be the location where local shear stresses are maximal.
The factors contributing to the shape of the velocity profile of the eggs within the oviduct are complex and are unlikely to be entirely represented by the equations used here. These equations describe a shear gradient across a continuous fluid. However, eggs are relatively large compared with the diameter of the tube. Therefore, in the oviduct, the shear stresses may be distributed unevenly across the egg, resulting in a discontinuous shear gradient. While the approach used here is a simplification, it provides a logical starting point for research into this complex issue. Future research should examine the properties of eggs and how this affects the distribution of shear within the oviduct.
Despite these simplifying assumptions, it is evident that eggs passing through the gonoduct complex during spawning are exposed to high shear. The evidence reported here indicates that Arbacia punctulata eggs possess at least two properties that may decrease either the damage caused by shear (jelly coats) or the magnitude of shear experienced in the oviduct (shear-thinning of the eggs). In addition, the trends in egg damage (eggs with hydrated coats are more susceptible to damage than those with nonhydrated coats) observed in this paper, in Mead and Denny (1995) and in Thomas et al. (1999) reflect trends predicted from engineering analysis of composite materials containing a fiber network (Sastry et al., 1998). Thus, there is some evidence that gamete traits ameliorate the damage caused by shear stress.
undergraduate assistants was provided by an NSF PECASE award to F.I.M.T. (OCE-9701434).
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