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Reference:
Bid. Bull.
182: 424-434. (June, 1992)
Causes and Consequences of Fluctuating
Coelomic Pressure in Sea Urchins
OLAF ELLERS’ AND MALCOLM TELFORD2
‘Department of Zoology, University of California, Davis, California 956 16 and
‘Department of Zoology, University
of
Toronto, Toronto, Ontario M5S lA1, Canada
Abstract. We measured coelomic pressure in sea urchins
to determine whether it was high enough to support a
pneu hypothesis of growth. In Strongylocentrotus purpur-
atus the pressure was found to fluctuate rhythmically
about a mean of -8 Pa, and was negative for 70% of the
time. This is at variance with the theoretically required
positive pressures of the pneu hypothesis. Furthermore,
there were no sustained significant differences between
the pressure patterns of fed and starved urchins, presumed
to be growing and not growing, respectively. The rhyth-
mical fluctuations in pressure were caused by movements
of the lantern which changed the curvature and tension
of the peristomial membrane. We developed a mathe-
matical and morphological model relating lantern move-
ments, membrane tension, and pressure, that correctly
predicts the magnitude of the fluctuations. Pressures pre-
dicted by the model depend also on coelomic volume
changes. In Lytechinus variegatus simultaneous retraction
of the podia, which causes expansion of the ampullae,
resulted in an 8.8 Pa increase in coelomic pressure, relative
to the pressure during simultaneous podial protraction.
Introduction
For some seventy-five years, the growth and shape of
sea urchins have, with few exceptions, been attributed to
a similarity with internally pressurized tensile structures.
D’Arcy Thompson ( 19 17) remarked on the similarity of
shape between sea urchins and water droplets on a glass
plate. A water-filled balloon resting on a table (Fig. 1)
provides an analogous form. This basic idea has been in-
voked repeatedly to explain both growth and form. Moss
and Meehan ( 1968) suggested that growth of the gut and
gonads increased coelomic pressure and this caused
Received 2 I October 199 1; accepted 27 March 1992.
growth in the test. Likening echinoids to inflated structures
(pneus), Seilacher ( 1979) argued that variations in shape
among regular and irregular echinoids could be explained
by forces from the tube feet and by the occurrence of
internal “tethers” of calcite or collagen. Dafni and Erez
(1982) Dafni (1983, 1985, 1986) and Baron (1988), all
assumed the existence of positive internal pressure in sea
urchins, and explained morphogenesis in terms of the re-
sulting stress patterns and the action of forces from other
sources such as podia, internal muscles, and mesenteries.
Although internal fluid pressure is usually not relevant
in the functional analysis of solid structures, there are
engineering designs in which it does play an important
role. While designing underwater storage vessels that re-
quire a minimum of wall materials, Royles et a/. (1980)
were impressed by the similarity of their theoretically de-
rived shapes and some sea urchins (most notably Echinus
esculentus). The design of such “constant strength” or
“buckle-free” structures involves balancing pressure dif-
ferences (positive or negative) across the vessel wall with
forces in the wall. It is tempting to interpret the conver-
gence on an echinoid form as indicative of an underlying
similarity in the balance of forces. Royles et al. ( 1980)
actually coined the expression of “Echinodome” for these
structures.
The obvious and crucial question-what is the mag-
nitude of the internal pressure in echinoids-has not been
answered. Dafni (1985, 1986) attempted to manipulate
forces acting on the growing test and isolated plates, but
provided no measurements of pressure. Reporting the only
pressure measurements, Baron ( 199 1) recorded fluctuating
coelomic pressures in an echinoid. With the aid of a finite
element method he developed a complicated tensile
growth model which, although elegantly refined, is still
fundamentally a pneu hypothesis. According to his model,
424
COELOMIC PRESSURE IN URCHINS
425
a
b
c
Figure 1. (a) A balloon filled with water in water; (b) a balloon filled
with water in air; and (c) an urchin test. Note the similarity of shape
between the (b) and (c). The difference in shape between (a) and (b)
illustrates the importance of self-weight forces. There are no self-weight
forces on a water-filled balloon in water since the water inside and outside
are equally dense. In urchins, the internal volume also has no effective
weight; thus the downward forces result only from the underwater weight
of the calcite or the pull of tube feet. The weight forces are balanced by
internal pressure resulting from tension in the membrane. None of these
structures are pneus because they are not air-filled, but (a) and (b) cer-
tainly, and (c) possibly, form their shape as a result of forces analogous
to those in a pneu, including internal pressurization.
growth can occur only during periods of positive internal
pressure.
In this paper we describe a technique for measuring
coelomic pressure in sea urchins and report the results of
two series of experiments. The first series was undertaken
to determine whether there was sufficient positive pressure
to support the pneu hypothesis of growth. For this, we
compared pressures in sea urchins (Stronglyocentrotus
purpurutus)
fed
ad libitum
and presumed to be actively
growing, with pressures in starved animals, presumably
not growing (Ebert, 1968). After measuring the fluctuating
pressures, we investigated the possible morphological and
physical causes of the pressure patterns. This led to de-
velopment of a model relating pressure changes to alter-
ations in curvature in the peristomial membrane during
protraction and retraction of the lantern. In the second
series of experiments we examined the effect of volume
changes, resulting from the alternate extension and re-
traction of podia, on coelomic pressure in
Lytechinus vur-
iegatus.
We consider the interaction of volume changes
and behavior of the peristomial membrane in explaining
the observed pattern of coelomic pressures in sea urchins.
Materials and Methods
Experimental animals
Specimens of
Strongylocentrotus purpuratus
collected
subtidally at Bodega Bay, California, and maintained in
running seawater, were divided into two lots. The first
was fed
ad libitum
with kelp
(Macrocystis
sp.) and the
second was starved. There were no significant differences
in the size of urchins in the fed (33.0-81.4 mm, n = 27)
and unfed (4 1.9-82.6 mm, n = 25) groups. Size was es-
timated by a volume approximation which was (height
X diameter)2. Pressure measurements were performed
during a three-week period, starting two months after the
beginning of these feeding regimes.
Lytechinus variegatus
(53.9-68.1 mm diameter) was collected at Long Key,
Florida, and maintained on natural substrate with dead
leaves of
Thalassia testudinum,
for 12 to 72 h before ex-
perimental use.
Pressure measurement
Internal pressure was measured by mounting the ur-
chins on a vertical, 14 gage, hypodermic needle passing
through the peristomial membrane. The needle was con-
nected to one side of a P305D differential, moving mem-
brane, pressure transducer (Validyne Corporation,
Northridge, California) fitted with a nickel plated 3-20
membrane to read pressures up to k550 Pa. The other
side of the transducer was open to the seawater surround-
ing the experimental animal.
Calibration of pressure transducer
The system was calibrated before each series of mea-
surements. Calibrations and all experiments were per-
formed in a two-chambered Plexiglas aquarium. At the
start, seawater levels in the two chambers were equilibrated
via a connecting valve. After closure of the valve, the water
426
0. ELLERS AND M. TELFORD
level in one chamber (positive side of transducer) was
raised by increments of 1.1 mm by the gradual immersion
of a Plexiglas box propelled by a threaded drive mecha-
nism. At each step the voltage output at l-s intervals was
averaged over a 30-s period by a Dynamic Signal Analyzer
(Hewlett-Packard #356lA). Initial calibrations were con-
tinued to a total pressure head of about 22 mm of seawater
(220 Pa). Later calibrations extended only to 11 mm of
seawater, which adequately covered the range of pressures
commonly encountered. Calibration readings were taken
as pressure increased and as it decreased back to zero.
Linear regression of transducer output (mv) and pressure,
fitted by least squares, was used to convert experimental
readings to pressure. For field experiments in Florida, the
system was simplified. The Plexiglas box and threaded
drive assembly was replaced by a pipetting technique in
which 15-ml aliquots of seawater were added sequentially
and then removed from the reference chamber.
Estimate oferrors in pressure measurements
Due to uncertainty in the measurement of the pressure
head against which the transducer was calibrated, the
range of bias in the slope of the calibration curve was less
than 0.1%. The precision range of the slope was t- 10%
because of day-to-day variation. Additionally, in the worst
case, the g-bit digitizer recorded only to the nearest 1.7
Pa, and there was drift in the zero; a combined imprecision
range of 23 Pa resulted. The accuracy can be expressed
as +(lO.l% + 3) Pa.
We were concerned that urchins might leak, thus ar-
tificially relieving high positive or negative pressures. We
ruled out this possibility by injecting the urchins with food
coloring and by coloring the liquid in the transducer. We
observed no color leakage, except at very much higher
pressures than those reported in this experiment.
Internal pressure could also be artificially relieved by
flow through the needle into the tiny space vacated as the
metal membrane of the transducer shifted while making
the measurement. This possibility was minimized by use
of a “low volume” pressure transducer. To test this po-
tential error, we set up an experiment in which we could
simulate the pressure measurement and watch what hap-
pened to the pressure and volume. The urchin was re-
placed by a rubber tube filled with dyed seawater, closed
at one end, and attached to a 5 mm diameter graduated
pipet that was open to the atmosphere at the other end.
With fluid in the pipet levelled to measure 40 Pa, we in-
serted the needle through the rubber hose. There was no
detectable motion of the water level in the pipet, indicating
that volume changes due to the transducer motion were
less than 3 ~1; in a 60 mm diameter urchin, this volume
change could be accommodated by a 10 pm upward or
downward motion of the lantern involving a strain of
5
X
10e6 in the peristomial membrane, an amount that
has a negligible effect on pressure in the coelom.
Experimental procedure
Each urchin, when mounted on the needle, rested on
a small platform. The podia reached the platform but
could not reach the sides or the floor of the aquarium.
During the course of an experiment the transducer output
was sampled at 5.12 Hz and digitized. The trace was dis-
played by the signal analyzer simultaneously with a fre-
quency spectrum. The data were transferred in 200-s sec-
tions to an Apple Mac II equipped with a “LabVIEW”
GPIB interface card (National Instruments, Austin,
Texas). For each urchin, data were recorded for 10 min.
The zero point of the transducer was checked after each
measurement was completed, and the needle was detached
and syringed to remove any coagulated coelomic fluid.
Diameter and height of each specimen was measured by
calipers. The water in the experimental chamber was re-
placed after each group of five specimens to minimize
changes in water temperature.
The procedure for L. variegatus was similar except that
a 10 min section of data was transferred directly into the
computer, and the light level was manipulated to induce
podial movements. For each of ten urchins, room lights
and fiber-optic microscope lights directed at the urchin
were alternately switched on and off every 2 min. When
the lights were on, the podia retracted; when the lights
were off, they extended.
Data analysis
For S. purpuratus specimens, each 200 s trace was
scanned and the following information was compiled: (i)
seconds below zero pressure; (ii) the mean pressure; (iii)
the standard deviation of pressure; (iv) the maximum
pressure; (v) the minimum pressure; (vi) the mean of pos-
itive pressures: (vii) the standard deviation of positive
pressures; (viii) the mean of negative pressures; (ix) the
standard deviation of negative pressures. Two-way anal-
yses of variance by trace and by feeding regime were per-
formed on these data. Additional t-tests were performed
to compare fed and starved animals by successive traces.
A Fourier transform of the third 200-s trace for each spec-
imen gave the amplitude and periodicity of rhythmic
pressure fluctuations. Using the first 200-s trace (during
which the needle was inserted), a discriminant functions
analysis was performed to see whether fed and unfed in-
dividuals could be identified from their initial pressure
patterns. We performed a stepwise regression to determine
which variables to include in the discriminant functions
analysis. The discriminant model is
Y = b + a,xl + a2x2 + a3x3. - -a9x9, (1)
COELOMIC PRESSURE IN URCHINS
427
unled
I
(b) -10
-20
-2 -30
E -40 400 450 500 550
t
600
(cl
v,
8
: 250
150
50
-50
-I50
led
-- I
0 ;0 lb0 150 '260
Cd) -200
-40
-60
. I I
I I I I
400 450 500 550 600
TINE (s)
Figure 2. (a) Pressure-time trace for an unfed urchin during the first
200 s of the experiment. The large negative pressure pulse, characteristic
of unfed urchins, occurred just after the needle was inserted through the
peristomial membrane. (b) Pressure-time trace for an unfed urchin 400-
600 s after the start of the experiment. This trace shows the characteristic,
rhythmic fluctuations of pressure associated with movements of the lan-
tern. (c) Pressure-time trace for a fed urchin during the first 200 s of the
experiment, showing the characteristic, positive pressure pulse as the
needle was inserted through the peristomial membrane. (d) Pressure-
time trace for a fed urchin 400-600 s after the start of the experiment,
showing rhythmical changes with lantern movements. Differences in the
traces for starved and fed urchins (a and c) were statistically significant;
during the third 200-s traces (b and d) the differences were not significant.
where y is equal to - 1 if an urchin is fed, and is equal to
fl if an urchin is unfed. The nine variables descriptive
of the pressure traces are xi to x9. The fitted slopes are a,
to a9 and b is the intercept.
For L. variegatus the average level of pressure was
measured for each 2-min segment except the first, which
was assumed to be a settling-down period. A paired t-test
was done on the average pressures to compare the lights-
off periods with the immediately ensuing lights-on periods.
Results
Description of the pressure traces
Pressure traces for S. purpuratus characteristically fluc-
tuated at a frequency of 0.055 Hz with a S.D. of 0.021
Hz (n = 167 traces). This corresponds to an average period
of 18 s, and the range of periods corresponding to the
above S.D. is 13-29 s.
When the needle was inserted through the peristomial
membrane, there was usually a negative or positive pres-
sure peak (Fig. 2) that often went off-scale on the recording
equipment, and that differed significantly from the fluc-
tuations in the second and third traces as shown by the
maxima and minima in Table I. Over several minutes
the pressure tended toward, and eventually stabilized at,
an average mean pressure of -8.2 Pa with a S.D. of 11
Pa (n = 52 urchins). According to our error estimate, zero
lies in the range ? (8.2
X
10% + 3) Pa: a t-test shows that
the worst-case zero of -3.8 Pa is significantly different
from -8.2 Pa with a S.E. of 1.4 Pa (P < 0.0 1). The average
S.D. of the pressure was 10 Pa with S.D. of 6.4 Pa (n
= 52). The pressure was below zero 70% of the time.
Urchins fed ad libitum, and those receiving food only
via occasional cannibalism, had very different initial pres-
sure responses (Fig. 2). Well-fed urchins had pressures
that tended to increase initially. Unfed urchins had pres-
sures that tended to decrease initially. All of the variables
except S.D. differed significantly in the first 200-s trace
(Table I). Step-wise regression of variables for the first
trace indicated that the mean of the positive pressures
and the minimum pressure (? = 0.41, slope significantly
non-zero, P < 0.00 1) correctly predicted whether the an-
imals were fed or unfed 83% of the time.
There were no significant correlations between urchin
volume and any of the nine descriptive variables in any
traces for fed urchins, nor in the first 200-s trace for unfed
urchins. However, in subsequent traces from unfed ur-
chins, five of the variables (mean, S.D., minimum, mean
negative, and S.D. of negative pressures) were correlated
with test size (Table II).
Podial movements and pressure
When the lights were turned off, L. variegatus pro-
tracted its podia and the coleomic pressure decreased.
When the lights were turned on, podia retracted and the
coelomic pressure increased (Fig. 3). Coelomic pressure
Table I
Results oft-te.rts showing statisticuliy sign$cant differences between
@d and starved Strongylocentrotus purpuratus for the nine variables
descriptive qj’coelomic pressure during the three successive 200 s traces
Variable Trace I Trace 2 Trace 3
Seconds below zero
Mean pressure
SD. pressure
Maximum pressure
Minimum pressure
Mean fve pressure
S.D. +ve pressure
Mean -ve pressure
S.D. -ve pressure
** n.s. ns.
*** n.s. n.s.
ns. n.s. n.s.
** n.s. n.s.
*** n.s. n.s.
*** ns. n.s.
*** n.s. n.s.
** n.s. n.s.
** n.s. n.s.
(n.s. not significant; **P 5 0.01; ***P 5 0.00 I).
428
0. ELLERS AND M. TELFORD
Table II
Correlarion coeficienrs between body six and sralistical variables
descripiive ofprexwrc~ ~races,/kvn unfed Strongylocentrotus
purpuratus
Variable Trace I Trace 2 Trace 3
Seconds below zero
Mean pressure
S.D. pressure
Maximum pressure
Minimum pressure
Mean +ve pressure
SD. +ve pressure
Mean pve pressure
SD. -ve pressure
ns. n.s. - n.s.
n.s. -0.4 * -0.5 *
n.s. 0.4 * 0.4 *
ns. n.s. - n.s.
ns. -0.4 * -0.5 **
n.s. n.s. - n.s.
ns. n.s. - n.s.
n.s. -0.5 * -0.6 **
n.s. 0.4 * 0.4 *
(ns. not significant: *P 5 0.05; **P 5 0.01). Note: There were no
correlations between any of these variables and body size in fed urchins.
during the lights-on period was 8.8 Pa higher than the
mean pressure during the immediately subsequent lights-
off period (P < 0.0001; n = 20; 10 urchins, 2 paired sam-
ples each).
Discussion
The fluctuating coelomic pressures observed in this
study were predominantly negative. In the wide range of
animals surveyed by Trueman (1975) most reported
pressures are positive, the highest being 1 O4 Pa in the lug-
worm, Arenicola marina. In soft-walled pressure vessels,
the internal pressure can only be zero or positive relative
to the outside. At zero relative pressure, the body wall is
limp and any process tending to a negative internal pres-
sure will cause the membrane to collapse and fold, thus
reducing the pressure to zero (Clark and Cowey, 1958).
Negative pressures are possible in systems in which the
walls have flexural stiffness, as is the case with some skel-
etal and muscular tissues. Trueman ( 1975) reported pres-
sures of -500 Pa from underneath the foot of Pateffa sp.
during the passage of pedal waves. Negative pressures have
also been generated inside the gastropod foot (Voltzow,
1986) and by the suckers of an octopus (Kier and Smith,
1990; Smith, 1991). Many soft-bodied animals have some
hard, stiff parts, while many primarily hard-bodied or-
ganisms have some soft, flexible membranes. Sea urchins,
having a hard test and large peristomial membrane, are
examples of the latter.
There are several processes that could influence coe-
lomic pressures in sea urchins, but some of them do not
produce pressures of the observed magnitude. However,
we found two processes of great importance: the exertion
of force on the coelomic fluid (for instance, by the peri-
stomial membrane) and the movement of water into the
coelomic space (as in the simultaneous retraction of the
podia). Before considering these two in more detail, we
show why a number of the other possibilities are not sig-
nificant.
Causes
of
pressure in wchins
Pressure is a force magnitude per area. In non-accel-
erating fluids, at each point in the fluid there is a balance
of forces in all directions. Gravitational pressure, pK, at a
given depth is
(2)
where p is the density of seawater, g the acceleration due
to gravity, and d the depth (atmospheric pressure is not
included). We measured the difference between pressures
inside and outside the urchin. Because the two locations
were at the same depth, hydrostatic, gravitational pressures
are irrelevant, and the remaining discussion refers only
to relative transmural pressures.
Sound or sudden impacts from waves could also cause
internal pressure. The rhythmic, 20-s pressure patterns
we observed cannot be sound because there was no such
rhythm when the needle was removed from the urchin.
Nevertheless, in the ocean, sudden coelomic pressures
from impact forces such as waves and sound are possible
and might have implications for behavior, mechanical
functioning, or even pressure-regulated growth of urchins.
These phenomena have not been investigated.
Hydrodynamic forces are unlikely to be of importance
in explaining pressures inside urchins, because rates of
flow are very slow. Hanson and Gust (1986) measured
rhythmic flows inside urchin coeloms that have the same
periodicity (20 s) as the pressure pulses we measured.
Thus, fluid dynamic pressures cannot be immediately
ruled out in explaining the observed pressure patterns.
Expected pressures from flow are less than or equal to the
dynamic pressure, pd, which is
pd = ; u2, (3)
where p is the density of seawater, and u is the velocity
of flow (Vogel, 198 1). In our experimental observations,
-4 ‘, !. i
I I I I I
0 IO0 200 300 400 500 600
TINE (seconds)
Figure 3. The pressure pattern in L~~fechinzrs variegam when lights
are alternately turned on and off at 2-min intervals (black bar indicates
lights on). The podia protracted when the light was off and retracted
when the light was turned on.
COELOMIC PRESSURE IN URCHINS
429
the standard deviation of pressure was 10 Pa. This would
correspond to a minimum flow of 100 mm s-‘. Because
Hanson and Gust ( 1986) observed a maximum flow of
1.5 mm ss’, we conclude that the pressures we observed
were not due to flow.
Tension in a curved, stretched membrane can be an-
other cause of pressure differentials. According to La-
place’s law (see Popov, 1976; Wainwright et al., 1976;
Vogel, 1988; or Ellers and Telford, 199 l), the pressure
drop across such a membrane or a flexible body wall de-
pends on its tension and radius of curvature. The pressure
inside the membrane will be positive with respect to ex-
ternal pressure when the membrane is inwardly concave.
In a cylinder the pressure difference, Ap, across the mem-
brane is
where r is the radius of curvature and T the tension in
the membrane. The tension, T, is the stress times the
thickness of the material. More generally, in a three-di-
mensional shape such as a sphere or ellipsoid, two radii
of curvature are involved, so that at every point on the
surface
Ap++>, r2
(5)
where T, is the tangential tension in one direction with
radius of curvature rl , and Tz is the tangential tension in
an orthogonal direction, with radius of curvature r2
(modified from Timoshenko and Woinowsky-Krieger,
1959, p. 435). Both negative and positive differences can
occur across a membrane, depending on whether its radii
of curvature are positive or negative.
If the several coelomic compartments in echinoids (so-
matocoels, hydrocoel, axocoel, and peripharyngeal coe-
lom) (Hyman, 1955; Smith, 1984) are bounded by
stretched membranes, there is potential for a diversity of
pressure relationships between them. We found no reason
to suspect that there are more than two functionally pres-
surized spaces, the water-vascular system and the coelom
proper. Injection of red dye confirmed a separate peri-
pharyngeal space, but the membrane is flaccid and flimsy
and could not support separate pressurization. The only
stretched membranes are found in the peristome, peri-
proct, and water vascular system.
Prcwrre and peristomial membrane
The peristomial membrane is a circular sheet composed
of cross-fiber collagen arrays and circular and radial mus-
cles (Hyman, 1955). In some species, it contains calcite
plates or spicules (Smith, 1984; Candia Carnevali et a/.,
1990). It is joined to the test at the distal edge, and to the
lantern centrally. Thus the shape of the membrane is like
a washer: flat, with a hole in the middle. No one has stud-
ied the deformation of this membrane as the lantern pro-
tracts and retracts, but from our pressure measurements
and the general rules about membranes given above, we
can make predictions about its curvature.
Curvature of the membrane depends on the relative
pressure difference across it. As the lantern protracts, the
pressure inside becomes negative relative to ambient.
From Laplace’s law, we know that a negative internal
pressure implies that the membrane is convex on the coe-
lomic side. Conversely, a positive internal pressure would
imply that the membrane is concave on the coelomic side.
The same is true for the periproctal membrane. In species
in which the periproct is flexible, its shape might indicate
a positive or negative internal pressure. These predictions
hold only if the membranes have low flexural stiffness.
Often flexural stiffness may be conferred by catch-collagen
or ossicles. If the membranes are flexurally very stiff, then
they may produce negative or positive pressures regardless
of their curvature, just as the test does not reverse its cur-
vature as internal pressure changes from positive to neg-
ative. It should be a goal of future studies to determine
the flexural stiffness of such membranes.
Regardless of the membrane curvature and tlexural
stiffness, protractor and retractor muscles controlling the
motion of the lantern exert forces that cause tension in
the peristomial membrane and thus a pressure drop across
it. We observed the lantern moving in and out during our
pressure measurements, and the 20-s pressure rhythm ap-
peared to match its protraction and retraction. Jensen
(1985) suggests that the role of such lantern movements
is to stir the coelomic fluid, thus facilitating distribution
of nutrients and respiratory gases.
Pressure and podial movements
When many podia simultaneously retract, water pre-
viously in the podia will be stored in the ampullae, thus
effectively moving water into the coelomic space. If the
peristomial membrane and periproct do not move com-
pensatorily outward, and if there is negligible flow via the
madreporite, the pressure in the coelom must rapidly in-
crease. In fact, because of the incompressibility of water,
if there is no volume regulation the urchin must either
spring a leak or the pressure would become so great that
the podia could not retract. Fechter (1965) recognized
this problem. He calculated that the volume made avail-
able when the peristomial membrane moves outward is
sufficient to compensate for the volume of water moved
into the coelomic space when all podia simultaneously
contract. Further, he showed that the size of the peristo-
mial membrane was more closely correlated with the
number of podia than with test size. Finally, he demon-
430
0. ELLERS AND M. TELFORD
strated only very small flows via the madreporite during
simultaneous podial retraction. We observed that simul-
taneous podial retraction caused an 8.8 Pa pressure in-
crease in the coelom. Fechter (1965) working with
Echinus esculentus, reported an increase of 200 Pa.
Although the madreporite is not involved in volume-
related pressure regulation, Fechter (1965) concluded that
it was involved in non-volume-related changes due to
gravitational, hydrostatic pressure. We believe that Fech-
ter’s conclusion must be wrong, but first we will present
his experimental evidence. Fechter glued the madreporite
shut and performed two manipulations. (1) He increased
the hydrostatic, gravitational pressure by increasing the
depth at which the urchin was kept. When the external
pressure increased the podia collapsed. (2) He pulled the
lantern outward, decreasing the pressure in the coelom,
and again the tube feet collapsed.
In the second case, the madreporite could not relieve
the induced pressure change because, according to Fech-
ter’s own results, it allows insufficient flow. We argue,
instead, that pulling the peristomial membrane outwards
causes a volume flow from the podia into the ampullae.
In the first case, when hydrostatic pressure increases, it
does so with negligible volume change. Therefore, al-
though the increase in hydrostatic pressure may be suf-
ficient to cause the podia to collapse, it would do so only
if the pressure was being relieved by a flow from the podia
into the ampullae. But because this pressure change is
gravitational, it is not associated with a volume change,
and therefore even the tiniest flow from the podia into
the ampullae will immediately relieve the pressure differ-
ence.
The only way we can explain Fechter’s results is if there
was an air bubble in the coelom that would have dimin-
ished in size with increasing gravitational pressure, there-
fore causing flow from the podia into the ampullae. Such
air bubbles sometimes form in urchins that have been in
air for some time. Fechter dried the madreporite with a
stream of hot air, before gluing it shut. Perhaps this pro-
cedure explains his results. We suggest that, contrary to
Fechter’s conclusion, his experiments do not show that
the madreporite functions to accommodate hydrostatic
gravitational pressures. Furthermore, such a function is
unnecessary because volume changes caused by hydro-
static pressure would be accommodated by miniscule
flows and deformation of tissues.
Although accommodation of hydrostatic, gravitational
pressure is unnecessary, there are other types of pressure
that might require the coelomic pressure to be maintained
independent of the water-vascular system, and perhaps
the madreporite has such a role. For instance, the pressure
fluctuations we observed (+ 10 Pa) could have caused the
podia to malfunction because these pressures would be
exerted on the ampullae inside the coelom. But such fluc-
tuations can only cause podia to extend or retract if they
cause the ampullae to expand or contract, which would
happen only if volume changes were associated with the
pressure fluctuations. Additionally, the deformation of a
membrane depends on its stiffness and on radius of cur-
vature [as in equations (4) and (5) above]. The radius of
curvature of the ampullae is much smaller than that of
the peristomial membrane, and therefore we expect much
smaller deformations in the ampullae. That the ampullae
have a smaller radius of curvature than the peristomial
membrane may be a design requirement of echinoderm
water-vascular systems.
The digestive tract is another potential source of pres-
sure change. When full, the stomach will take up more
room in the coelom, and the peristomial membrane must
move outwards to relieve the volume increase. Similarly,
flows into and out of the mouth, or in the siphon, may
cause volume fluctuations that could cause pressure
changes if the peristomial membrane does not move
compensatorily. Further, without compensation by the
peristomial membrane, defecation may lower coelomic
pressure because it tends to reduce the volume of gut con-
tents.
Finally, several authors have described ruffled sacs
hanging externally from the peristomial membrane (Hy-
man, 1955; Smith, I 984) the supposed function of which
is either as gills or pressure regulators for the peripharyn-
geal coelom. However, no experimental data about their
function have been presented. We saw no evidence that
these sacs expanded or contracted while the coelomic
pressure fluctuated. Furthermore, their openings are far
too small to allow sufficient flow to regulate coelomic
volume.
A model yf.f;,rces causing a pressure drop across the
peristomial membrane
The forces causing protraction of the lantern, and thus
tension in the peristomial membrane, come from lantern
protractor and retractor muscles and from the submerged
weight of the lantern. These forces must be estimated.
Andrietti et al. (1990) report 3 g (0.03 N) for lantern weight
minus buoyancy in a specimen of Paracentrotus lividus.
They also report forces of 40 g (0.4 N) exerted by lantern
protractors and forces of 10 g (0.1 Iv’) exerted by lantern
retractor muscles. Because P. lividus rarely exceeds 70
mm diameter (Mortensen, 1977) it is similar in size to
S. purpuratus and L. variegatus, and the forces should be
comparable.
The assumed geometry of the lantern, test and peristo-
mial membrane are shown in Figure 4a. The forces on
the peristomial membrane are: ( 1) a vertical force, f,, ex-
erted by the lantern weight and the lantern muscles; (2)
forces from the pressure difference across the membrane;
and (3) the reactive, tensile force exerted on the membrane
COELOMIC PRESSURE IN URCHINS
431
AP membmna
(W
Figure 4. (a) Location of the peristomial membrane in an urchin.
The star in both figures marks the point of attachment to the edge of
the peristome. (b) Geometric model of the peristomial membrane. The
angle 8, and the radius of curvature ofthe membrane are not independent.
Zero vertical displacement occurs when the membrane is horizontal.
by the test. The vertical force, f,, exerts a force, f,, in the
membrane,
f, = AL
cos (e) ’
where 0 is the angle between the vertical and a tangent at
the central margin of the membrane (at the point of at-
tachment of the peristomial membrane to the teeth) (Fig.
4b). The force, f,,,, on the membrane corresponds to a
tension, T, (force per length) in the membrane of
f
“=& (7)
where ri is the radius of the central margin of the peristo-
mial membrane. From Laplace’s equation (4)
(8)
where r,, is the radius of curvature of the membrane. In
using equation (4) rather than (5) we make two simplifying
assumptions: that a second horizontal radius of curvature
can be ignored, and that the curve formed by a vertical
cross section of the peristomial membrane has a single
radius of curvature at every point. In reality this curve
may have variable radii of curvature. A more realistic
model would add an unjustifiable degree of complexity
for the present context. The two-dimensional approach
used here should give results of the correct order of mag-
nitude.
The radius of curvature of the peristomial membrane,
rpm, for a given protraction of the lantern, v, and a given
horizontal, peristomial radius, h, can be derived from the
geometry shown in Figure 4b. The radius of curvature is
h
rpm = 2 cos (arctan (v/h)) cos (0 + arctan (v/h)) * (9)
Substituting through equations 6, 7 and 8,
Ap = f, cos (arctan (v/h)) cos (13 + arctan (v/h))
rhr; cos (0) 7 (10)
which is shown in Figure 5. This graph shows that many
possible combinations of pressure, protraction, and 0 are
possible when only the force balance on the membrane
is considered. Initially, this may seem counterintuitive.
Intuition suggests that as the lantern protracts, the internal
pressure should get more and more negative relative to
outside as the membrane pulls more and more on the
constant volume of water inside the urchin. That this
pressure pattern is not implied in Figure 5 reflects the fact
8
6
x14
membrane angle, 8
Figure 5. Contour plot of theoretical predictions from the geometric,
force balance model of the peristomial membrane (see Fig. 4 and text
for details). Elongation ofthe peristomial membrane and pressure across
it are functions of the membrane angle at the central edge, 8, and pro-
traction, v, given a downward force of the teeth and lantern muscles on
the membrane, f,. This graph shows that many combinations of 0 and
v are possible at a given pressure across the membrane. Which 0, v path
the membrane follows as the lantern protracts depends on the volume
of the urchin and the properties of the peristomial membrane.
432
0. ELLERS AND M. TELFORD
that the force balance makes no assumption about the
volume of water inside the urchin, nor about the material
properties of the peristomial membrane.
To understand a fluctuating pattern of pressure be-
coming increasingly negative as the lantern protracts, ex-
amine the change in length of the peristomial membrane.
The length of the membrane, the distance along its vertical
arc from the attachment point at the test to its attachment
point at the teeth, is
Lprn = r&r - 2(fl + 4))
(the angle 4 is shown in Fig. 4b). (1 I>
By examining the contour plots of pressure drop, and
peristomial membrane length (Fig. 5) it is possible to
imagine what is happening as the lantern moves. As it
protracts, the peristomial membrane elongates, and, as-
suming constant coelomic volume, the internal pressure
must decrease. Initially, assume that the membrane starts
at the point, B = s radians (the membrane is straight and
horizontal). As the lantern protracts, the line representing
the motion of the lantern must move towards higher v
(protraction) and towards lower 0 on the graph, to stay
in the region of negative pressure and simultaneously to
increase the length of the peristomial membrane. Increase
in the length of the peristomial membrane helps to com-
pensate for volume changes that would otherwise occur
because it can arch upward, effectively compensating for
the volume of the lantern pulled downward.
According to Figure 5, the tendency to decrease 0 while
increasing v, initially causes Ap to become negative
quickly because many pressure contour lines must be
crossed, but, after even a little protraction, it is possible
for the lantern to protract and follow an isobar. This may
be an explanation for the plateaus often observed at the
peaks of fluctuations in the pressure trace. A path followed
by the lantern could be specified by two functions of time,
fl(time) and v(time), which we call a “0, v” path. This
path, represented by an imaginary line in Figure 5, will
depend on the constraints imposed by the degree of con-
stancy of the coelomic volume and the material properties
of the peristomial membrane. We plan to develop this
theoretical model further in the future and obtain mea-
surements of the motion of the lantern, the constancy of
the coelomic volume, and the material properties of the
peristomial membrane.
This crude, initial model serves to explain some aspects
of the relationship between pressure and the behavior of
the structures that cause it. The pressures are ofthe correct
order of magnitude to have been caused by lantern mus-
cles. The mean negative pressure observed (-8 Pa) is small
enough that it could have been caused by the weight of
the lantern. If the podia simultaneously retract, or if the
stomach is full, thus raising the coelomic volume, this
model shows that the lantern can still protract with only
a change in the 0, v path. Finally, it is reasonable to cal-
culate the pressure based solely on what the peristomial
membrane is doing, because the pressure inside the ur-
chin’s coelom is the same everywhere, and thus if any
other structure were contributing, it would have to be
balanced by tension in the peristomial membrane.
Implications of the observed pressures for the pneu
theory
In keeping with the pneu hypothesis, we expected con-
tinuously positive internal pressure in sea urchins. Instead
we found fluctuating positive and negative pressures, with
an overall mean below zero. Clearly, the original version
of the pneu hypothesis must be rejected on the basis of
these measurements.
Baron (199 1) also recognized the problem for the pneu
hypothesis when he found fluctuating pressures. He de-
veloped a modified version of the hypothesis that preserves
the spirit of the original (Thompson, 19 17) but incorpo-
rates new rules for growth of the skeleton. Baron (1991)
proposed that skeletal plates grow at their margins when-
ever they are in tension, and that growth is directly pro-
portional to tensile stress. Instead of the term “pneu,” he
called this a “tensile growth model.” These growth rules
necessitated development of a finite element analysis to
determine the expected stresses in the skeleton caused by
internal pressure and other forces, such as those from tube
feet. From these analyses Baron (199 1) was able to gen-
erate urchin-like shapes using a computer. Making several
alternative assumptions about internal pressure, he ex-
amined their effect on the shapes produced by his model.
In these simulations, he found that a pressure fluctuating
about a mean of 30 Pa, with a S.D. of 30 Pa, generated a
shape indistinguishable from that produced with a con-
stant pressure of 30 Pa. Based on this finding, he thereafter
simulated urchin shapes using constant pressures.
Baron’s (199 1) assumptions can be compared with our
more extensive pressure measurements. For his standard
growth situation he assumed a pressure of 30 Pa, and the
other pressure used was 15 Pa. We observed an average
pressure of -8 Pa. Under fluctuating pressure regimes he
assumed a negative pressure for at most 17% of the time,
whereas we observed it for 70% of the time. Baron’s (199 1)
model allowed growth whenever the skeleton was in ten-
sion due to internal pressure. This implies that during
periods of no growth, the pressure must be lower. But we
found that in well-fed, growing (Ebert, 1968) and starved,
possibly shrinking, urchins (Levitan, 1988; 1989) the
mean pressures were equal after the initial pressure surges
in the first 200-s traces (Table I).
The discrepancies between our observations and Bar-
COELOMIC PRESSURE IN URCHINS
433
on’s ( 199 1) assumptions have two possible implications:
that our specimens were abnormal, or that his assump-
tions do not reflect the pressure patterns in real urchins.
In the latter case, it may be that the spirit of the pneu
hypothesis is wrong, or that Baron’s ( 199 1) version does
not incorporate exactly the right assumptions. These pos-
sibilities can only be resolved by further experiments and
more refined theories.
At present, the most detailed predictions of urchin
shape, based on Baron’s ( 199 1) tensile growth model, deal
only with regular urchins. A challenge to all models is the
great diversity of forms that must be generated, including
flattened sand dollars (Clypeasteroida), heart urchins
(Spatangoida), and the bizarre flask-shaped pourtalesiids
(Holectypoida).
Acknowledgments
This work was supported by University of California,
Davis, Agricultural Experiment Station Project no. 5 134-
H and a U. C. Davis, Bodega Marine Laboratory Travel
Grant to 0. Ellers; and a Natural Sciences and Engineering
Research Council of Canada Grant (#A4696) to M. Tel-
ford. We thank Bodega Marine Laboratory for use of their
facilities. We specially thank K. Brown for her organi-
zational help and H. Fastenau for diving to collect the
urchins and subsequently caring for and feeding them.
We thank J. Swanson and the staff of Keys Marine Lab-
oratory, Florida, for the use of their facilities and help in
collecting urchins. Thanks also to M. Martinez and K.
Driver who assisted in some of the experiments and to
D. Levitan who critically read the manuscript.
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434
0. ELLERS AND M. TELFORD
Appendix 1
List of theoretical variables
Ap, pressure drop across a membrane
T, tension in the membrane
r, radius of curvature
T, , tangential tension in one direction in the membrane,
rl , radius of curvature associated with T,
T2, tangential stress in the direction perpendicular to T,
r2, radius of curvature associated with T2
pn, gravitational pressure, (not including atmospheric
pressure)
d, water depth
p, density of seawater
g, acceleration due to gravity
pd, dynamic pressure
u, speed of flow
f,, vertical force exerted on the membrane by the lantern
weight and muscles
f,,,, is the tangential force in the membrane at the mem-
brane’s attachment to the teeth
0, angle of membrane’s attachment to the lantern (see Fig.
5b), same as tangential angle defined by f,
T, tension in the membrane
ri, radius of the central margin of the peristomial mem-
brane
r
,,,,,, radius of curvature of the peristomial membrane
v, lantern protraction distance
h, horizontal distance from the central margin to the distal
margin of the peristomial membrane.
IL, arc length of the peristomial membrane
4, see diagram in Figure 5b.
0, v path-the combination of 8 and v used by the mem-
brane as it protracts
