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Abstract
In this study, the connective tissue sheaths in the tube
feet of Pisaster ochraceous were studied. The role played
by the spiral fibers in the inner layer of this sheath
during extension of the tube foot was also examined. This
was done by fixing the tube feet at various states of
extension, and by measuring the external dimensions and
the fiber angle of the fibers. These spiral fibers were
found to be extensible when the tube foot was extended or
contracted, and the value of strain for the extended tube
foot was very large. (1.84) The fibers were also found
to provide adequate hoop stiffness during the contracted
state to prevent circumferential deformation of the tube
foot.
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Introductio
Asteroid movement is primarily due to the operation of
tube feet. The tube feet are extended, attached to the
substratum, and then contracted, pulling the animal along
the substratum. The extension of the tube feet is accomplished
by the contraction of the ampulla, which forces the fluid
into the lumen of the tube foot. In order for there to be
an effective translation of this increase in volume to an
actual elongation of the tube foot, there must be some
structure preventing circumferential deformation of the tube
foot as the fluid volume inside the foot increases. At the
same time, this structure must allow the tube foot to extend.
In this study, the possibility is examined that the connective
tissue of the tube foot provides such a structure in
Pisaster ochraceous.
Tube foot morphology has been studied in detail by Smith
(1946), and the biomechanics of ophiuroid tube feet has been
analyzed by Woodley. (1979) However, no direct biomechanical
study has been done on asteroid tube feet. Clark and Cowey
have analyzed the fiber wound system in the basement
membrane of turbellarian worms and nemertean worms, (Clark,
1958) and the applicability of their findings to asteroid
tube feet will be examined.
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Materials and Methods
I. Preparation of specimens
The tube feet of Pisaster ochraceous were in 3 states of
extention : (1) maximally stretched; (2) relaxed, and
(3) maximally contracted. For the stretehed and relaxed
tube feet, the starfish arm was relaxed in Mgol», and the
tube feet were amputated as close to the base as possible.
The extended tube feet were manually stretched to a point
where further extension would break the tube feet. They
were then pinned down and fixed with formaldehyde (37% in
sea water). The relaxed tube feet were pinned down and
fixed at their original lengths. Maximally contracted
tube feet were amputated from unrelaxed animals and fixed
without being pinned down.
Fixed tube feet were carefully dissected to expose their
layers. Dissection was made easier by soaking the tube feet
in a solution of 1M KOH mixed 1:1 by volume with glycerol.
(Woodley, 1967) After this treatment, the cuticle layer
and the internal longitudinal muscle layer were removed by
tearing them away with a pair of fine forceps. The outer
layer of connective tissue (composed of longitudinal
fibers) can also be partly removed by this manner,
II. Measurements
The tube foot, with the sucker removed, was slit along
its longitudinal axis, spread out, and mounted on a slide.
The specimens were viewed under the polarizing light
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microscope. The crossed fibers of the inner layer of
connective tissue were seen under careful examination, and
the fiber angle was measured as the angle rotated by the
stage between each set of fibers being at extinction.
In addition, the external dimensions of the tube foot
were measured with the use of vernier calipers. The thick-
ness of the sucker was similarly estimated, and the length
of the cylindrical portion of the tube foot obtained by
subtracting the sucker thickness from the overall length.
Since the tube feet were flat in the relaxed and extended
specimens, the diameters of them were estimated by squeezing
them between the calipers until the tube foot cross-section
was approximately circular. These measurements of radius
were confirmed by cross-sectioning tube feet of various
states with a freezing microtome; thickness of cuticle,
muscular layer, and connective tissue were measured from
these cross-sections.
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Results
Examination of cross-sections of tube foot stem under
the compound light microscope revealed 4 distinct layers.
Taken from the outside, these are:
(1) an outermost layer of cuticle;
(2) a layer of connective tissue sheath;
(3) a layer of longitudinally arranged muscular fibers
(4) a thin layer of ciliated epithelium that rests on
the lumen side of the muscle layer.
(fig. 1)
The thicknesses of layers 1-3, and the total wall thick-
ness of tube feet in the three states of extension were
estimated. (fig.1)
Examination with the polarizing light microscope (Aus
Jena, low power) showed the connective tissue sheath to
be composed of an outer and an inner layer. The fibers in
the outer layer have the same orientation as the fibers in
the muscular layer, and thus longitudinal. The fibers in
the inner connective tissye layer are oriented obliquely to
the longitudinal fibers in a right and left-hand double
spiral lattice.
The connective tissue layer is reported to be collagenous
by other authors. (Smith, 1946; Woodley, 1967) This is
consistent with the finding here that this layer stains with
Alcian blue.
Taking the relaxed specimens as the standard, the
measured radii and the observed fiber angles (6) can be used
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to calculate the length of 1 turn of fiber (L): L= 2wr/tano
(fig, 3) The number of turns of fiber (N) per relaxed tube
foot was estimated by N=length/L (fig. 2), N= 1.33.
The length of the fiber, D, was estimated by D-L/cos 6
(fig. 2) D=4.08mm.
If the fiber is assumed to be inextensible (D stays
constant at 4.08 mm when the tube foot is stretched or
contracted), the fiber angle can be predicted for the extended
and contracted tube feet by the relationship e-Sin" (2wr/D)
using 4.08 mm as D and the measured radius for each state as
r. (fig. 3) The predicted values of e did not agree well
with those observed (fig.4), indicating that D does not
stay constant. The new values of D which are consistent
with the observed e in the extended and contracted states
can be calculated using the observed 6 andr for each state.
(fig. 5) The strain on these fibers can also be calculated
as ln D'/D. (fig. 5)
Using the measured radii, lengths, and wall thicknesses
of tube feet, the lumen volume for each state of extension
can be calculated. (fig. 6) The lumen volume was observed
to have decreased when the tube foot was extended from a
value of 0.34mm2 to 0.25mm2. (fig. 6)
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Discussion
The fiber angles in the inner layer of connective tissue were
observed to change when the tube foot was extended or
contracted, inconsistent with Smith's observation for
Astropecten irregularis that the fibers are circular.
(Smith, 1946) (fig.6) If the fibers were circular, the
fiber angles should not change as a function of extension.
and should remain at 90' to the longitudinal axis.
The presence of spiral fibers presents two problems
regarding the mechanism of tube foot extension:
(1) Clark And Cowey (1958), based on an analysis of
turbellarian and nemertean worms, show that the volume
enclosed by an inextensible spiral fiber wound cylinder
is defined by the equation:
Da sin e cos e
V=
(fig.7)
4 T
Thus, the volume is maximum when 6=54 44', and decreases
as 6 departs from this value. The relaxed tube feet of
P. ochraceous have a mean 6 of 42, whereas in the contracted
feet, 6=75, and in the extended ones, 6=6. Therefore,based
on this analysis, the volume of the tube foot will decrease
from the relaxed to the extended state. The lumen volume of
the tube foot was indeed observed to have decreased as the
tube foot is extended. (fig.6) However, this is inconsistent
with the accepted mechanism of the operation of the ampulla/
tube foot system. Tube foot extension is accomplished by
the contraction of the ampulla, forcing fluid into thelumen
Since fluid is incompressible, the lumen
of the tube foot.
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volume of the foot must increaseduring extension.
This seeming discrepancy can be explained in 2 ways:
(a) The fibers may be extensible to an extent greater than
expected, and the equation proposed by Clark and Cowey
therefore does not apply to this system. The strain on
the spiral fibers was calculated for extended and contracted
states, and was shown to be non-zero. (fig.5) The reported
value for vertebrate collagenous fibers is about 10%.
(Wainwright, et al., 1976) This agrees well with the strain
calculated for the contracted specimens of about 0.07. The
strain calculated for the extended tube feet (1.21) is
substantially larger than 102. The basis for this exten-
sibility is not clear. It may be conjectured however that
the fibers are kinked similarly to those in vertebrate
arteries (Wainwright, et al, 1976), and therefore allow
much more entension than expected. Further studies involving
electron microscopy are needed to verify this hypothesis.
(b) Although the actual measurements show that the lumen
volume does decrease, this could be entirely due to an
artifact introduced by the sample preparation. The tube
feet were extended by manually stretching them, whereas in live
animals, the tube feet areextended by pumping fluid in.
Thus, in a live animal, the cross-section stays circular as
the tube foot is extended, and the radius in the extended
tube foot is conceivably larger than the ones measured
in the fixed specimens. Indeed, observations in live
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animals show the radius of extended tube feet to be approxi¬
mately 0.46 mm., as oppose to 0.24mm in the prepared
specimens. The lumen volume calculated (3.5mm2) using this
value for ris actually larger than that of the relaxed
specimens, as required to be consistent with the classic view
of the operation of the tube foot.
Using the measured value of r-0.46 mm for the extended
foot, the strain calculated for the spiral fibers is 1.84,
Again, no explanation for this large extensibility is
immediately forthcoming.
Another artifact that could be present in this method
of sample preparation is again due to the fact that the
tube foot is stretched while there is no fluid in the lumen.
This could result in the detachment of the connective
tissue sheaths from the tube feet wall. If this is the case,
the radii measured on the prepared samples have no bearing
on the actual radii of the sheaths.
The second problem presented by the spiral fibers is:
(2) When a cylinder is pressurized, the hoop stress on the
cylinder wall is twice the longitudinal stress. (Wainwright
et al., 1976) (fig. 8) Consequently, for a cylinder
constructed from an isotropic material, the radius increases
at twice its rate of the length as the cylinder is pressurized.
Thus, if a cylinder such as a tube foot is to increase in
length rather than in girth, its circumferential (hoop)
stiffness must be at least twice that of its longitudinal
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stiffness.
For a fiber wound cylinder where the fibers are the only
elements resisting the internal pressure, the hoop stiffness
(Eg) and the longitudinal stiffness (Ep) are related to
the fiber angle (0):
EH= Ef sin e
E- Ef cos 0
Er=modulus of fiber along its axis
EH/E =2 if 0= 63° 26:
Eu/Er is larger than 2 if 0 is larger than 63° 26'.
The Eg and Ey, theoretical values for different extensional
states of tube feet are shown in figure 8. The contracted
tube feet exhibit fiber angles corresponding to a hoop
stiffness that is more than two times the longitudinal
stiffness. This indicates that the spiral fibers effectively
revent circumferential deformation only in the contracted
tube feet. Other structures must play this role in the
extended and relaxed tube feet, but the identity of these
structures is uncertain.
To summarize, this study has shown that the spiral
fibers allow the tube foot in P. ochraceous to extend by
being able to tolerate a large strain. Their role in the
prevention of circumferential deformation as the tube foot
is extended is only apparent in the contracted tube foot.
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Acknowledgement
MAny thanks to my advisor, Dr. Mark Denny, for providing
answers to all questions, and for the careful revision
of the paper.
Thanks to Freya Sommer for inputs and providing numerous
glass slides and cover slips.
Thanks to Dr. W.H. Magruder for assistance in microscopy
and photography.
Thanks to Janet Vogelzang for encouragement and moral
support all along the way.
Finally, thanks to all the Pisasters for selflessly
sacrificing tube feet for the study. Also, gratitude is
warranted to the Pycnopodia for being the villain all
quarter.
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References
Clark, R.B. 1964 Dynamics in Metazoan Evolution. London:
Oxford University Press.
Clark, R.B. and Cowey, J.B. 1958 Factors controlling the
change of shape of certain nemertean and turbellarian
worms. J. exp. Biol. 35, 731-48.
Cowey, J.B. 1952 The structure and function of the basement
membrane muscle system in Amphiporus lactifloreus
(Nemertea). Quart. J.micr.Scl. 93, 1-13.
Smith, J.E. 1946 The mechanics and innervation of the
starfish tube foot-ampulla system. Philos. Trans. B,
232, 279-310.
Woodley, J.D. 1967 Problems in the Ophiuroid water vascular
system. Symp. zool. Soc. Lond. 20, 75-104.
Woodley, J.D. 1979 The biomechanics Ophiuroid tube-feet.
Proceedings of the European Colloquium on Echinoderms.
3-8 September, 293-299.
Wainwright, S.A. et al. 1976 Mechanical Design in Organisms.
London: Edward Arnold (Publishers) Limited.
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Figure Legends
Figure 1: Cross-section of tube foot, showing different
tissue layers and their dimensions at different
states of extension.
Figure 2
Schematic representation of an amputated tube foot
with the sucker removed.
Diagram only shows one
set of fiber in a double spiral system.
Figure 3:
A unit length of tube foot slit along the longitudinal
axis and unrolled out.
D-length of fiber
0=fiber angle
reradius
length of tube foot for 1 turn of fiber
(Clark and Cowey, 1958)
Figure 4:
Plot of radius vs. fiber angle of extended and
contracted tube feet. Solid line represents the pre¬
dicted values, assuming D remains constant at
4.08 mm; whereas the crosses, the observed values.
Figure 5:
Calculated D and strain for extended and contracted
tube feet.
Values reported are mean values in
units of mm.
extended tube feet: n-9, standard deviation (S.D.)
for D=2.36
contracted tube feet : n-10; S.D. for D-0.384
Figure 6:
Dimensions measured for tube feet at different
lengths.
Reported values are means in mm.
L=length for 1 turn of fiber
r-radius
0=fiber angle
V=volume=r (length)
thickness)2(length)
LV=7(r-wall
Relaxed Extended Contracted
0.18
S.D. for L
0.18
1.9
S.D. for r
0.039
o.018
0.035
3.16
S.D. for 6
2.0
0.85
0.47
S.D. for V
0.31
0.31
0.18
S.D. for LV
0.13
0.09
volume enclosed by inextensible fiber wound
Figure 7:
cylinder. Volume is in arbitrary units
(Clark and Cowey, 1958)
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Figure 8:
Theoretical hoop stiffness and longitudinal stiffness
for different states of extension.
6-= longitudinal stress
OH-hoop stress
- pressure
Reradius
t-wall thickness
Er=longitudinal stiffness
E-hoop stiffness
Ef=modulus of fiber along its axis
O
gre 1

-CUTICLE
OUTER
CONN.TISSU
INNER
-LONG.MUSCLE
-EPITHELIUM
LUMEN

THICKNESS (in mm.)
CUTICLE CON.TIS. MUSCLE TOTAL
RELAXED O.105 0.045 O.20 O.270
EXTENDED O.O6O 0.030
O.075 O.165
CONTRACTED O.105 0.045
O.300 0.450
O
Hgre a



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L= 27r/tane
n= length/L
n=1.33
n: number of turns of fiber
O
C
C
Kgore 3
271
99
ANG
. .
O=On (2T7/D)
D=L/eose
(C
80
60
c
40

4
20
Fgure 4

extended
..*

.4.5
3
2
radius (in mm)
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contracted
—
.6 .7
C


e 5
Extended Contracted
Relaxed
4.38
3.64
4.08








O.O7
.2
Strain
O











Forr-O.46, Strain-.84


Strain= In D/D


27r
—
D¬
sine
C
relaxed
4.0
43
420
2.4
LV
.34
V= VOLUME
LV - LUMEN VOLUME
extended
12.8
.24
6°
2.3
.25
contracted
2.5
66
75
.35
(C
H
C
L
10
D'sin?0 cos 9
41
—

30 50
70
fiber angle (9)
(0
Figure 1
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States
contracted
relaxed
extended
..
PR
2t
8
Ht
- 26
0
E-Efsie
O.96Ef
42°
O.67Ef
6
O.OEf
E, -Efcose
O.26Ef
O.74Ef
O.OOET
Hgure g
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