The modulus of elasticity of fibrillin-containing elastic fibres in the mesoglea of the hydromedusa Polyorchis penicillatus
1 Department of Zoology, University of British Columbia, Vancouver, BC, V6T
1Z4, Canada
2 Bamfield Marine Sciences Centre, Bamfield, BC, V0R 1B0, Canada
3 Centre for Biomimetic and Natural Technologies, Mechanical Engineering
Department, University of Bath, Bath, BA2 7AY, UK
* Author for correspondence (e-mail: megillw{at}cerf.bc.ca)
Accepted 23 June 2005
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Summary |
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Key words: microfibril, modulus of elasticity, mechanical property, mesoglea, jellyfish, extracellular matrix, fibrillin, elastic fibre, Polyorchis penicillatus
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Introduction |
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Polyorchis penicillatus (Fig.
1), also known as P. montereyensis
(Rees and Larson, 1980), is a
small (
15 cm long) hydrozoan jellyfish, found along the Pacific
coast of North America from southern California to the Queen Charlotte Islands
(Arai and Brinckmann-Voss,
1980
) and southeast Alaska
(Rees and Larson, 1980
). The
geometry of Polyorchis is shown in
Fig. 1. The animal was
described by Skogsberg (1948
)
as generally cylindrical in shape, slightly longer from apex to margin than it
is in diameter, with an average fineness ratio of 1.2. The conical, nearly
hemispherical, apex of the bell consists of a large mass of mesoglea called
the peduncle. The remainder of the animal is arranged cylindrically. In
longitudinal section, the bell wall is tapered, radially thicker at the
shoulder than at the margin. The swimming muscle is striated and consists of a
layer of modified epithelial cells arranged circumferentially on the
subumbrella. In Polyorchis, the muscle layer is only one cell thick
(Gladfelter, 1972
;
Singla, 1978
;
Satterlie and Spencer, 1983
;
Spencer, 1995
;
Lin and Spencer, 2001
),
although in other species there can be extra folding of the muscle sheet to
increase the cross-sectional area
(Gladfelter, 1973
). On the
inside edge of the margin, there is a shelf (the velum) that extends radially
inward to form a nozzle. A circumferentially arranged muscle on the
subumbrellar side of the velum improves thrust generation by focussing the
expelled jet of water and also allows the animal to steer
(Gladfelter, 1972
;
Singla, 1978
;
Spencer, 1979
). Tentacles
extend radially off the outer edge of the margin, and a manubrium (digestive
organ) extends from the base of the peduncle to the centre of the velar
nozzle.
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The passive mechanics of swimming, including energy storage and release,
are determined by the properties of the mesoglea. Hydrozoan mesoglea is a
hydrogel that contains mucopolysaccharides, collagen fibrils and other
structural proteins, including microfibrils rich in a protein homologous to
mammalian fibrillin (Bouillon and
Vandermeerssche, 1957; Bouillon
and Coppois, 1977
; Gladfelter,
1972
; Weber and Schmid,
1985
; Reber-Müller et
al., 1995
). Fibrillar collagen type IV, fibronectin and
heparansulfate proteoglycan have been reported from the mesoglea of
Hydra sp. (Sarras et al.,
1991
), and laminin was identified in Podocoryne carnea
(Beck et al., 1989
) and
Hydra sp. (Sarras et al.,
1994
). The collagen fibrils and fibrillin microfibrils are
arranged in two intertwined fibrillar networks. Gladfelter
(1972
) describes the collagen
network as `a loose, three-dimensional lattice of cross-linked fibres
enclosing pockets of both bound and free water'. Weber and Schmid
(1985
) show a similar geometry
for the microfibrillar network.
The bell of Polyorchis penicillatus is divided into two concentric
layers of mesoglea separated by a sheet of cells called the gastrodermal
lamella (Gladfelter, 1972). In
the outer layer the so-called `bell mesoglea' there is a
radially arranged array of larger diameter fibres, which extend from the
gastrodermal lamella to the exumbrellar epithelium
(Chapman, 1959
;
Gladfelter, 1972
;
Weber and Schmid, 1985
;
DeMont, 1986
;
Reber-Müller et al.,
1995
,
1996
). The fibres are multiply
branched at each end and intertwine with the tissue layers to provide solid
connections. Weber and Schmid
(1985
) showed these fibres to
be microfibril bundles, and Reber-Müller et al.
(1995
) showed them to be rich
in fibrillin. These fibres are reported to be 1.51.8 µm in diameter
in fixed Polyorchis tissue samples
(Gladfelter, 1972
;
Weber and Schmid, 1985
),
0.031 µm in Limnocnida and 23 µm in
Pelagia and Aurelia
(Bouillon and Vandermeerssche,
1957
).
The inner layer of mesoglea, called the `joint mesoglea', is located
between the gastrodermal lamella and the subumbrellar epithelium. It is less
stiff and lacks the radially oriented elastic reinforcing fibres. There are
thick fibres present (Gladfelter,
1972; Weber and Schmid,
1985
), but these are sparsely distributed and arranged randomly.
The joint mesoglea is divided into eight regions by the longitudinal
interconnection of the subumbrella and gastrodermal lamella
(Spencer, 1979
). The regions
are triangularly shaped in cross-section
(Fig. 1), and their lower
stiffness allows the bell mesoglea to fold around them during deflation
(Gladfelter, 1972
;
Weber and Schmid, 1985
;
DeMont, 1986
). Most hydrozoans
are similarly constructed (Gladfelter,
1973
), although the thick-fibre array is less developed or absent
in the bell mesoglea of species that do not actively swim
(Gladfelter, 1973
;
Reber-Müller et al.,
1996
).
Modelling jellyfish mesoglea therefore as a fibre-reinforced soft tissue,
we consider first the radially oriented fibres. Bouillon and Coppois
(1977) showed that they could
be made to stain for elastin, which led them to conclude that they are
analogous in structure to vertebrate elaunin fibres, described by Kielty et
al. (2002
) as consisting of an
outer microfibrillar sheath and an inner core of amorphous crosslinked
elastin. However, since elastin seems to be limited to the vertebrates
(Faury, 2001
),
Reber-Müller et al.
(1995
,
1996
) speculated that there
might well be an as yet unidentified elastic protein in the radial fibres.
Similar speculation led Shadwick and Gosline
(1985
) to their discovery of
octopus arterial elastomer (OAE), an analogous elastin-like protein
in the circumferential fibres of octopus aorta.
There are, however, highly elastic fibres (oxytalan fibres) in vertebrates
that lack the elastin core (Keene et al.,
1991), such as mammalian zonular filaments (Sherratt et al., 2003)
and the elastic fibres in foetal membranes
(Malak and Bell, 1994
). To
stretch, these must rely either on the reorientation of a priori
unaligned microfibrils (Lillie et al.,
1994
; McConnell et al.,
1997
) or on the inherent elasticity of the microfibrils
themselves. Baldock et al.
(2001
) and Kielty et al.
(2003
) present a model of
microfibril elasticity in which the fibrillin molecules unfold and refold,
mediated by the level of Ca2+
(Wess et al., 1998
;
Eriksen et al., 2001
).
It is possible that invertebrate elastic fibres are oxytalan-like in their
construction that is, they can be modelled simply as bundles of
microfibrils. Indeed, Schmid et al.
(1999) suggest that the
elasticity in jellyfish radial fibres could be accounted for solely by the
fibrillin microfibrils without the need for an elastin analogue. However,
Sherratt et al. (2003) used a molecular combing technique to measure the
stiffness of individual fibrillin microfibrils to be 7896 MPa, nearly
two orders of magnitude greater than the stiffness of the microfibril-rich
fibres studied to date (
1 MPa). If their measurement is correct, and if
the assumption can be made that invertebrate microfibrils are similar to those
of vertebrate, then the low stiffness must be due to higher-order structure.
The low relative stiffnesses of pig
(Lillie et al., 1994
) and
lobster aorta (Davison et al.,
1995
), as well as sea cucumber dermis
(Thurmond and Trotter, 1996
),
are all explained by the reorientation of the microfibril network present in
the tissue. However, as pointed out by Wright et al.
(1999
), no similar explanation
can be valid in the axially arranged microfibril bundles in the zonular
filaments, nor in the jellyfish fibres discussed here. In jellyfish, the
elastic fibres are oriented radially, parallel to (and, as we show in this
paper, pre-tensioned in) the direction of applied stress. This geometry is
similar to that in the vertebrate eye, and Wright et al.
(1999
) reported a non-linear
(J-shaped) stressstrain behaviour for the zonular filaments in bovine
eyes, with initial moduli between 0.07 and 0.27 MPa and final moduli between
0.47 and 1.88 MPa. Direct measurements of the mechanical properties of
jellyfish fibres have not yet been made, but DeMont and Gosline
(1988a
) used Gladfelter's data
on the density and cross-sectional area of Polyorchis fibres
(Gladfelter, 1972
) to predict,
on the basis of energy storage arguments, that the modulus of the fibres
should be approximately 1 MPa. This is well within the range of subsequent
authors' measurements of the elastic modulus of similar fibres in other
animals (Table 4). In this
paper, we find the modulus of elasticity of jellyfish fibres to be
approximately 0.9 MPa. The similarity of the results, coupled with the
homology of their protein composition, suggests that invertebrate and
vertebrate microfibrils are indeed similar.
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The second component of the jellyfish bell is the gel, or mesogleal matrix.
Several studies have been conducted on the chemical composition of the
material (Chapman, 1966;
Bouillon and Coppois, 1977
;
Weber and Schmid, 1985
;
Reber-Müller et al.,
1995
,
1996
), but there are few
measurements of its mechanical properties. Alexander
(1962
) studied the creep
behaviour of mesoglea, but over long time frames (hours), by his own admission
of little relevance to the animal's swimming behaviour (
1 Hz). DeMont and
Gosline (1988a
) studied the
mechanical behaviour of mesoglea, both in isolated samples and in a novel
intact animal preparation. They concluded that the overall tensile stiffness
of mesoglea was between 400 and 1000 Pa but did not separate the contributions
of the fibres and matrix. We present in this paper the first compression tests
of jellyfish mesoglea and find the compressive stiffness, and hence stiffness
of the extracellular matrix, of the joint mesoglea to be approximately 50 Pa.
The bell mesoglea is stiffer in compression, approximately 0.35 kPa, and the
tensile stiffness along the fibre axis is approximately 1.2 kPa.
Since there is no muscle to open the bell, the jellyfish mesoglea must be
able to store enough energy during the thrust phase to power the refilling of
the subumbrellar cavity. This energy must be stored in elastic deformation of
the tissue. Gladfelter (1972)
first proposed a mechanism by which this might happen, noting that the
thickness of the mesogleal bell increased as the animal contracted its muscle,
thereby stretching the radial fibres.
DeMont and Gosline (1988a)
measured the energy required to refill the bell using experimental apparatus
designed to mimic as closely as possible the deformation of the bell in free
swimming. They sealed the subumbrellar cavity, then extracted water and
measured the pressure generated. An integration of a polynomial curve fit to
the resultant data gave them an estimate of the energy required to create the
deformation. The mean energy requirement for 11 animals tested in this way was
4.6 µJ. They made corrections for dynamic loading at the animals' usual 1
Hz swimming frequency and for dissipative losses in the tissue, then
calculated the required refill energy to be between 18 and 41 µJ.
To determine whether the radial elastic fibres could store the energy
required, DeMont and Gosline
(1988a) assumed the fibres to
have a linear stiffness similar to that of elastin, then used Gladfelter's
measurement of the fibre density in Polyorchis
(Gladfelter, 1972
) to
calculate the overall energy storage capacity of the fibres to be
approximately 38 µJ, which is at the upper end of the calculated energy
requirements. They concluded therefore that the fibres could store the energy
and that their assumption of a stiffness similar to elastin was correct.
Gladfelter (1972) analysed
the geometry of jellyfish bell during swimming. He showed that as the muscle
contracts, it remains circular in cross-section, while the outer perimeter
takes on a hexagonal cross-section due to the folding of the bell mesoglea
around the wedge-shaped regions of joint mesoglea. The resulting elastic
behaviour of the intact locomotor structure of the jellyfish is non-linear
(DeMont and Gosline, 1988a
;
Megill, 2002
), initially
compliant as the bell mesoglea folds around the joints, then stiff once the
fibres are stretched at the end of the contraction. The significance of this
non-linear behaviour is that, during the early part of the contraction, more
of the force generated by the muscle can go into expelling water, rather than
into deforming the bell (Gladfelter,
1972
). It also allows the muscle to power the refilling
indirectly, by storing energy in the spring during a time in the contraction
when it is still able to generate substantial tension but its ability to
generate useful thrust is diminished due to a rapidly decreasing volume of
water in the subumbrellar cavity (DeMont
and Gosline, 1988b
). The non-linearity complicates the analysis of
the dynamics of the system, but DeMont and Gosline
(1988c
), using a linear
approximation, were able to conclude that the animals were resonating, and
Megill (2002
) used a
non-linear oscillator model to generalise that observation to jellyfish of all
sizes.
In the current paper, we separate the contribution of the fibres from that of the matrix and conclude that the fibres have enough elastic energy storage capacity on their own to power the refilling of the subumbrellar cavity. We show that this enables the animal to increase the efficiency of its swimming mechanics by delaying the onset of energy storage to a later stage of the jet stage, when thrust efficiency drops off due to the decreasing volume of water in the subumbrellar cavity.
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Materials and methods |
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Microscopy
Fibre density
To prepare samples for microscopy, the apex of the bell was first removed
from the animal above the shoulder (Fig.
1). The resulting ring of muscle and mesoglea was then sliced
longitudinally along one side to lay the animal out flat. Next, the flattened
sample was laid on a pre-cooled microscope slide and quick-frozen using a
spray refrigerant (1.1.1.2-tetrafluoroethane; MG Chemicals, Toronto, ON,
Canada). Frozen samples were stored in a freezer until use. Samples were cut
into 35 mm strips with a previously unused, frozen razor blade. The
sections were then laid on a freezing microtome, sliced edges oriented down
and up, such that the radial fibres were oriented parallel to the cutting
surface, and shaven first on one side, then on the other, until the block of
mesoglea was 500 µm thick. Finally, the microtome was turned off and
allowed to warm up. As soon as the frozen sample had thawed sufficiently to
release itself from the microtome stage, it was transferred carefully to a new
microscope slide and covered with a cover slip.
Digital micrographs were taken of each sample using a video camera mounted on a Leitz (Wetzlar, Germany) Orthoplan interference contrast microscope, using 25x and 40x objectives and a first-order red filter to enhance the contrast. Images were captured on a microcomputer using a National Instruments (Austin, TX, USA) 1408 video capture board and LabView IMAQ software. Pixel dimensions were calibrated using micrographs taken at the same magnification of a stage micrometer (Bosch & Lomb, Rochester, NY, USA) with 10 µm line spacing.
Density was defined as the number of visible fibres intersecting a line across the micrograph, regardless of fibre diameter, divided by the width of the micrograph (40x objective, 640 pixels=128 µm; 25x objective, 640 pixels= 206 µm), multiplied by the original thickness of the sample (500 µm). The fibre density calculation assumes that the shrinkage of the sample in preparation and handling was due only to the loss of water and matrix and that few fibres, if any, were lost. Although it was impossible to confirm this assumption, it seems reasonable given the high degree of intertwining and consequent solid anchorage of the fibres in the exumbrellar epithelium and gastrodermal lamella.
Fibre lengths
To measure the length of the fibres, a collage was made of adjoining
25x micrographs. Individual fibres were traced by hand using a computer
graphics package (Corel Draw; Corel, Inc., Ottawa, ON, Canada). The tracings
were converted to pixelated bitmaps and saved to disk. Custom-written software
was then used to determine the length of the fibres by summing up the
straight-line distances between the pixels. This calculation assumes that the
fibres are lying in a plane and so must be interpreted as the minimum length.
We applied a correction (described later) to take into account the irregular
helical conformation reported by Gladfelter
(1972) of the fibres in
microscopy preparations.
Fibre diameters
Samples were prepared in a fashion similar to that used in the previous
section but without the microtome. Approximately 3 mm-thick sections of
mesoglea were sliced off the strip of mesoglea using a new razor blade. The
sections were laid sliced side down on a microscope slide and covered with a
cover slip. They were allowed to dry for 1 h before measurements were made, in
order to facilitate focusing of the microscope. Measurements of diameter were
made on the Leitz interference microscope with a 100x objective, oil
immersion lens (N.A.=1.32), and a 15x filar ocular micrometer (Wild,
Heerbrugg, Switzerland), at a total magnification of 1875x. The
micrometer was calibrated with a stage micrometer (Bausch & Lomb, USA)
with 10 µm line spacing.
Mechanical testing
Two mechanical tests were done to characterise the elastic behaviour of
jellyfish mesoglea in radial tension. The first was done in air with a slab of
isolated mesoglea, while the second was done underwater on an intact animal.
Both experiments were done using an Instron (Canton, MA, USA) mechanical
testing machine and a custom-built load cell. Morphological measurements (bell
height, shoulder height, margin diameter and wall thickness see
Fig. 1) were made using
callipers before testing.
Slabs of mesoglea were prepared and tested as follows. The apex was first removed by slicing the animal at the shoulder joint perpendicularly to its long axis. The resulting ring of muscle, skin and mesoglea was then sliced along one radial canal so that it could be laid flat on the moving stage of the testing machine (Fig. 2A). A 7x7 mm section of the stage (the lower grip) was covered with cyanoacrylate adhesive (Krazy Glue; Elmer's Products, Brampton, ON, Canada), and the mesogleal slab preparation laid over it such that one of the per-, ad- or inter-radii (Fig. 1) was centred on the grip. The dimensions of the grip and sample were selected to ensure that the edges of the sample were sufficiently distant from the grip to not interfere with the experiment. The stage was then raised until the upper surface of the mesogleal slab contacted a second, identically sized grip, itself connected to the load cell at the top of the testing machine frame. The stage was raised a little further, until 20 mN of force was applied to the mesogleal slab, to ensure that the glue set properly. The stage was lowered again after 10 s until the force returned to zero. This was set as the lower limit for the load cycles.
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The self-loading of the tissue made it impossible to make a meaningful
direct measurement of the resting thickness, 0. Furthermore,
the action of pressing the sample against the grip to set the glue forced the
joint mesoglea out of the wound at the shoulder and also caused some
irreversible compression of the bell mesoglea. (20 mN of force corresponds to
approximately 400 Pa of compressive stress on the sample, which was greater
than the yield stress of the tissue.) The value of
0 was
therefore back-calculated from the stiffness at high extension using a method
identical to that of Lillie et al.
(1994
). A linear regression
was fit to the loading curve at high extension, and the point at which the
regression line crossed the x-axis (zero stress) was taken to be
0. Once
0 had been determined, the extension
data were converted to engineering strain
(
=
/
0). Engineering stress and strain are
approximations to true stress [force (F) / instantaneous area
(A)] and strain [extension (dx) / instantaneous extension
(x)]. They are related to their true counterparts by:
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Engineering stress and strain are precise only for small extensions. The
consequence of using engineering quantities is that the stiffness in
compression will be overestimated, while that in tension will be
underestimated. However, the error introduced by using these small deformation
approximations (5%) is less than the experimental uncertainty
(
1520%) introduced due to the highly compliant, easily deformable
nature of the materials under test.
In order to measure the stiffness of the joint mesoglea, a second, intact
animal preparation was designed (Fig.
2B). A 7 mm square plate of polystyrene was glued to an L-shaped
rod suspended from the load cell. A second identical polystyrene plate was
cantilevered from a post fastened through the base of a plastic beaker to the
Instron stage. The beaker was filled with 11°C seawater to a level just
below the lower plate. Cyanoacrylate adhesive (Krazy Glue) was applied to the
plate, and the jellyfish positioned over the plate, as shown in
Fig. 2B, such that one of the
per-, ad- or inter-radii was centred on the plate. The glue was given 20 s to
set before additional seawater was added to raise the level to just below the
outer (now upper) edge of the mesogleal bell. Cyanoacrylate adhesive was
applied to the bottom of the upper plate. The stage below the beaker was then
raised until the upper plate came in contact with the exumbrellar surface of
the jellyfish. The stage was raised a little further, until 20 mN of force was
applied to the jellyfish, to ensure that the glue set properly. After 10 s,
seawater was added until the jellyfish was completely submerged. The stage was
then lowered until the force returned to zero. As before, this was set as the
lower limit for the load cycling. The resting thickness, 0,
was calculated as above for the isolated slabs.
In both cases, the sample was loaded in tension at 10 mm
min1 to various strains between 5 and 40% [to span the range
of radial strains measured by Gladfelter
(1972) in live swimming
animals], although if the latter was not enough to cause the sample to yield,
experiments were continued at increasing strains until it did yield. Stress
was defined as the load divided by the surface area of the polystyrene plates
(engineering stress), and strain was defined as the extension divided by the
resting thickness,
0 (engineering strain).
Statistical tests were carried out following Zar
(1984) and Dixon and Massey
(1983
). Unless otherwise
noted, results are given as means ±
S.E.M. (standard error of the mean).
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Results |
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Fibre morphology
Fibres were oriented more or less perpendicularly to the ex- and
sub-umbrellar surfaces and traversed most of the thickness of the bell,
anchored in the exumbrella by intertwining with the fibres there, as observed
by other workers (Gladfelter,
1972; Weber and Schmid,
1985
; Reber-Müller et
al., 1995
). Near the gastrodermal lamella, they branched multiply
into finer and finer fibres, presumably anchoring themselves in the lamella,
though this could not be discerned using the available microscope. Branching
began about halfway across the thickness of the bell. Because of the
preparation procedure (freezing and thawing), the sample tended to leak and
shrink substantially, with a loss of radial thickness typically of
40%.
When viewed through the microscope, the fibres were slack
(Fig. 4). Because the fibres
assume an irregular helical conformation when slack
(Gladfelter, 1972
), it was not
possible to measure their exact length from the micrograph. However, a minimum
estimate can be obtained by assuming the fibres to lie in a plane. The mean
length of the crimped planar projection of the six fibres highlighted in
Fig. 4 was 0.64±0.01 mm
(N=6). To correct for the non-planar conformation of the fibres, we
assume that they are as crimped in depth as they are in planar projection. The
radial thickness of the exumbrellar mesoglea in
Fig. 4 was approximately 0.5
mm. The ratio of the folded to unfolded length of the fibres was therefore
0.64 mm/0.5 mm=1.28. This gives a corrected mean fibre length of 0.82 mm. The
total radial thickness of the collage shown in
Fig. 4 is 1.35 mm. The animal's
measured resting wall thickness was 3.0 mm, indicating a 55% loss of radial
thickness due to water loss. Thus, if the water loss was uniform throughout
the animal, the corrected thickness of the outer mesoglea was approximately
1.11 mm, suggesting an in vivo pre-strain of the fibres of
35%.
This is obviously an educated guess, but it does partially confirm the
speculation by previous authors that the fibres were probably pre-strained
in vivo (Bouillon and
Vandermeerssche, 1957
; Chapman,
1959
; Gladfelter,
1972
; DeMont,
1986
).
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Fibre diameters
Fig. 5D is a typical
micrograph of the mesogleal fibres. 1400 measurements were made of 350 fibres
in 10 jellyfish data are presented in
Fig. 6 and summarised in
Table 1. Sections of mesoglea
were taken from inter-, per- and ad-radii, and no significant differences
(ANCOVA, F=0.012, F0.975,2,14=4.46,
P>0.05) were found between regions or animals that is, the
change in fibre diameter scaled identically with bell height in all three
regions for all animals. All measurements were therefore pooled into one
regression, given by df=1.35+0.05h
(µm). Using the pooled regression, the predicted unbranched fibre diameter
for a `standard' animal of h=20 mm [corresponding to the size of the
jellyfish used by DeMont and Gosline
(1988a) to calculate the
energy required to refill the bell] was 2.34±0.41 µm (95% confidence
intervals at h=20 mm). This is substantially larger than the 1.5
µm reported by Gladfelter
(1972
) and the 1.8 µm
reported by Weber and Schmid
(1985
). Neither reported how
the measurements were made, nor from animals of what size, nor did they give a
range. However, Gladfelter's and Weber and Schmid's measurements were made on
histological preparations, so it is most likely that the dehydration of the
fibres accounts for their smaller dimensions.
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Fibre densities
Fig. 5AC shows a
typical set of micrographs used to measure fibre densities. Samples were taken
from eight jellyfish ranging in size from 17.7 to 42.3 mm bell height. Fibre
densities were highest at the ad-radius, followed by the per- and then the
inter-radii. Consistent with Gladfelter
(1972), the density of fibres
was greatest near the gastrodermal lamella (subumbrellar side) and least near
the exumbrellar side (Fig. 4).
The higher density near the gastrodermal lamella was due to the high degree of
branching in that region. Only micrographs from the mid-thickness region of
the bell wall, where fibres were mostly unbranched, were used in the
calculation of the mean fibre densities. The distribution of fibre density
over the cylindrical section of the bell is reported in
Table 2. In all regions, the
fibre density decreased with bell height
(Fig. 7). No significant
differences were found between regions in the regression slopes of density
against bell height (ANCOVA, P>0.05), so the data were pooled, and
an overall regression slope fitted to the data. For the range of jellyfish
studied, density (n) was found to scale linearly with bell height
following the equation n=3225.5h
(mm2). For the `standard' jellyfish of 20 mm bell height,
the fibre density is predicted to be 212±34 mm2.
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Mechanical properties of mesoglea
A total of nine individual jellyfish were tested using one or both of the
protocols described earlier. Six animals were tested using the isolated slab
procedure only, two were tested using both methods, and one was tested using
the whole animal method only. We report data for the 11 tests in
Table 3.
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Fig. 8A shows a typical result of a radial test of an isolated slab of mesoglea. Negative strains indicate that the sample is being tested in compression, while positive strains indicate tension. Because the joint mesoglea was forced out of the sample during the glue-setting step at the beginning of the experiment, the compressive stiffness measured was that of the dense fibre-reinforced bell mesoglea. In the plane transverse to the fibres, the tissue is isotropic, so the compressive stiffness of the mesoglea is also the tensile stiffness of the bell mesogleal matrix. The mean modulus of elasticity of the bell mesoglea, Em, was 344±52 Pa. The stiffness of the material was higher in tension, reflecting the fibre-reinforcement of the mesoglea in the radial direction. Data for the six jellyfish tested in this manner are presented in Table 3 (animals 1924). The mean stiffness of the mesoglea in radial tension, EL, was 974±162 Pa.
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Two animals (25, 27) were tested both ways. After the intact animal test, slabs of mesoglea were cut from the animals and tested in isolation. Neither the compressive stiffness, Em, nor the radial tensile stiffness, EL, were different from those of previously tested animals, so all data were combined to give overall averages of Em=352±39 Pa and EL=1186±159 Pa.
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Discussion |
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Scaling
We have shown that the wall thickness of Polyorchis scales
linearly with bell height (i.e. the ratio of wall thickness to bell height is
constant over the range of sizes studied;
Fig. 3). The polyp of
Polyorchis, if it exists, remains undiscovered
(Brinckmann-Voss, 2000) but, by
comparison with other species, it can be assumed that young medusae are of the
order of 12 mm in bell height when they first appear. We found medusae
whose bell height exceeded 45 mm. If the geometric scaling assumption is true,
then the outer mesogleal thickness increases from a few dozen microns to more
than 5 mm. We did not make measurements of the fibres in very small medusae,
but it seems reasonable to assume that the fibres extend from the gastrodermal
lamella to the exumbrella as they do in larger individuals, particularly as
this is the case in other hydromedusae
(Reber-Müller et al.,
1995
). The implication of all of this is that the fibres increase
in length by 10100-fold as the animal grows, which implies that they
must grow, rather than simply stretch, which in turn implies that additional
fibrillin microfibrils must be added to the radial fibres as the medusa grows.
The decrease in fibre density with size
(Fig. 7) suggests that new
fibres are not added, but rather that the existing fibres grow. The additional
microfibrils might come from the three-dimensional fine microfibrillar network
in the surrounding mesoglea, rather than be laid down de novo.
The alternative explanation is that the fibrillin scaffolding is laid down first, and not added to. The extra fibre length would then be postulated to come from the addition of some jellyfish mesogleal elastomer. The prediction in this case would be that the stiffness of the fibres should decrease with size. Owing to practical constraints imposed by our testing apparatus, we did not make any measurements of the stiffness of small or large animals, but it would be interesting to do so.
Stiffness of the joint mesoglea
Due to the watery composition of jellyfish joint mesoglea, we were not able
to make a direct measurement of its stiffness. However, we were able to derive
an estimate of the stiffness of this highly compliant material by proceeding
as follows. We measured the compressive stiffness of intact combined joint and
bell mesoglea and found it to be 131±11 Pa. The thickness of the joint
mesoglea is not constant around the circumference of the bell, but rather
wedge-shaped, thinner near the radial canal (per-radius) and inter-radius than
in the adradial region (Fig.
1). The triangular shape of the joint mesogleal wedge has the
effect of increasing the effective stiffness measured during the experiment
(since the resting thickness, 0, is not constant). The value
we measured was therefore an upper limit. An exact correction factor would
depend on the shape of the wedge, which we did not measure, but, based on
Gladfelter's drawing (Gladfelter,
1972
) and the relative sizes of the jellyfish and testing plate
(Fig. 2, inset), we can
estimate that the stiffness of the joint mesoglea, Ejm, is
about one-third of the combined stiffness, or approximately 50 Pa. This is a
factor of seven less than the stiffness of the bell mesoglea
(Em=352 Pa), which helps to explain how the buckling is
controlled during the thrust phase of locomotion.
Radial fibre stiffness
The stiffness of the radial fibres can be calculated from the tensile
stiffness of the bell mesoglea by accounting separately for contributions by
the fibres and matrix to the overall elasticity
(McConnell et al., 1997).
Because the radial fibres traverse the entire bell wall
(Fig. 4), the mesoglea can be
modelled as a continuous parallel composite (sensu
Lillie et al., 1998
):
![]() | (2) |
![]() | (3) |
![]() | (4) |
Towards a model of fibre elasticity
Elastic fibres such as those in jellyfish mesoglea play an important role
in the mechanical behaviour of biological soft tissues. The factor of seven
greater stiffness of (fibre-reinforced) bell mesoglea over (fibre-free) joint
mesoglea highlights this role, as do the serious cardiovascular, ocular and
skeletal consequences of genetic disruption of the structure of elastic fibres
in humans (Marfan's syndrome; for reviews, see
Robinson and Godfrey, 2000;
Milewicz et al., 2000
). It is
important therefore to understand the origin of elasticity of the fibres. To
do this, we must understand the fibre structure and material properties of its
constituent components.
A jellyfish radial fibre is itself a fibre-reinforced composite. Scanning
electron micrographs presented by Weber and Schmid
(1985) show the structure of
the radial fibres of Polyorchis penicillatus
(Fig. 9). It is evident from
the figure that the radial fibres consist of a bundle of axially oriented,
high aspect ratio, parallel microfibrils. The cross section shows that the
bundle is densely packed with a volume fraction of microfibrils between 70 and
80%. Reber-Müller et al.
(1995
) showed the fibres to be
rich in fibrillin, and the beaded structure of fibrillin microfibrils
(Kielty et al., 2003
) is
evident in the longitudinal section. It is not clear from Weber and Schmid
(1985
) whether or not there is
a matrix material in the space between the microfibrils.
|
Material properties
To develop a mechanical model of the composite, we need information on the
material properties of the constituent components. Sherratt et al. (2003) used
molecular combing experiments to calculate a stiffness approaching 100 MPa for
the component microfibrils. They modelled the microfibrils as linear springs,
but it is certainly possible, indeed likely, that the mechanical behaviour of
fibrillin microfibrils is not linear, but quite non-linear, or J-shaped. Many
biological materials exhibit this type of behaviour. At low extensions, there
are no tight constraints and the resistance is entropy-based on orientation
and conformation, so modulus is low; at high extensions, there is much
orientation, and forces pull against the constraining molecular bonds, so
modulus is high. To illustrate this, we have drawn a J-shaped curve in
Fig. 10. The diamond
represents the single stress value (approximately 18 MPa) reported by Sherratt
et al. (2003). The 7896 MPa stiffness reported was based on the
assumption that the stress rose linearly from zero. But if our J-curve
correctly represents the fibrillin microfibril behaviour, then it actually
exhibits stiffnesses both lower and higher than their reported value.
Fibrillin is a globular protein (Kielty et
al., 2003), so it seems reasonable to think that microfibrils made
of fibrillin might behave similarly to actin filaments, which are known to
have a tensile stiffness of approximately 2.5 GPa
(Gittes et al., 1993
; Kojima
et al., 1994). This suggests that the stiffness at 18 MPa on the postulated
J-shaped stressstrain curve (Fig.
10) might be more than an order of magnitude greater than the
secant stiffness calculated by Sherratt et al. (2003). If this is true, then
the stiffness at the initial toe region of the J-curve
(Fig. 10) would be an order of
magnitude or more lower than their estimate, or
10 MPa or less.
|
A further reinterpretation of the data presented by Sherratt et al. (2003) comes in their calculation of the strain experienced by the microfibrils during their experiments. They based their calculation of the strain on the displacement of fibrillin beads, as seen with their atomic force microscope, from approximately 59 nm to approximately 70 nm. They calculate the strain in the microfibrils as (7059)/59=0.186. However, in their X-ray diffraction data (fig. 1 in Sherratt et al., 2003), they show that the zonule fibres must be stretched to a strain of 2 in order for the bead separation to reach 70 nm. Thus, there appears to be an order of magnitude difference between the whole zonule fibre strain and the microfibril inter-bead strain. If this is true, and if we consider fibrillin microfibrils to have a J-shaped curve, then it is possible that the microfibril stiffness could be as low as 1 MPa.
Although we believe each step in our reinterpretation of the data presented by Sherratt et al. (2003) is reasonable, we cannot conclude definitively whether 1 MPa or 100 MPa best represents the stiffness of the microfibrils. Therefore, we must consider both as possible, and assess what we can infer about the fibres' structure and elasticity.
Composite models
Based on the structure shown by Weber and Schmid
(1985), we model the elastic
fibre as a fibre-reinforced composite. There are three possible arrangements
of the microfibrils and matrix in the composite. The first possibility is that
the microfibrils are continuous, extending the full length of the fibre,
arranged in parallel. This is unlikely, given the 3 mm length of the elastic
fibres, but it is not impossible. The second is a variation on the first: the
microfibrils are structurally discontinuous but functionally continuous
because of direct molecular interaction in the form of crosslinks between the
microfibrils. The third is that the microfibrils are discontinuous and do not
span the full length of the fibre but instead overlap to a degree,
transferring axial load in shear through the matrix.
Since the second possibility is a variation on the first, we will consider them together. Thus, we have two hypotheses to investigate: functionally continuous microfibrils or discontinuous microfibrils in which the load is transferred through a matrix. It is clear that if there is no matrix, a discontinuous model cannot work. Considering the discussion earlier about the modulus of the microfibrils, each of the two hypotheses must be modelled with two values for the microfibril stiffness.
Test hypotheses
Case 1. Functionally continuous and 100 MPa
In this model, we consider the fibres to be a parallel composite with stiff
reinforcing fibres. Relabelling terms to represent the components of the
radial fibres (matrix and cross-linked microfibril bundles) and rearranging,
Eqn 2 becomes:
![]() | (5) |
Case 2. Functionally continuous and 1 MPa
We use the same mechanical model here as in the first case but come at the
problem from a different angle. If our measurement of the fibre stiffness is
correct (and its similarity to the stiffness of other fibrillin-rich fibres
Table 4
suggests that it is), then the requirement in Eqn 5 that
Em0 requires that the microfibrils have a maximum
modulus of 1.28 MPa (Vµf=70%). Even if the volume
fraction is assumed to be as low as 50%, the maximum
Eµf must be less than 1.8 MPa. These values are so
close to the reinterpreted value of the microfibril modulus that we cannot
reject this hypothesis.
Case 3. Discontinuous and 100 MPa
It is possible that the radial fibres are structured more like a series
composite. That is to say, the stress is transferred from one microfibril to
the next in shear through a soft matrix. It is obvious that the microfibrils
overlap to a great degree, so the strict series (Reuss) model is not likely to
be applicable. However, we can use Cox's model of an aligned discontinuous
fibre composite (Cox, 1952).
Given the data we have about the morphology of the fibre, we choose to
formulate Cox's model following Jackson et al.
(1988
):
![]() | (6) |
Case 4. Discontinuous and 1 MPa
We use the same mechanical model as in Case 3 but with much more compliant
microfibrils. Using our reinterpreted microfibril modulus of approximately 1
MPa, a matrix shear modulus of 1 kPa is required to obtain an overall fibre
modulus of 0.9 MPa. This is well within the realms of possibility, so we
cannot reject this hypothesis.
Although we cannot reject Case 4, we think it unlikely, as there does not
appear to be any matrix material between the fibres
(Fig. 9; Weber and Schmid, 1985). It is
however possible that there is a matrix material present in the elastic
fibres, which did not stain in Weber and Schmid's preparation.
Reber-Müller et al.
(1995
,
1996
) suggested this
possibility, although Schmid et al.
(1999
) suggested that the
microfibrils alone were responsible for the observed elasticity of the fibres.
It seems more likely that the functionally continuous model is correct,
particularly given the high volume fraction and high degree of overlap of the
microfibrils in the fibre and observations by several authors of irreversible
transglutaminase-derived crosslinks between fibrillin-rich microfibrils in
several systems (Thurmond and Trotter,
1996
; Qian and Granville, 1997;
Schittny et al., 1997
;
Kielty et al., 2002
). In
either case, however, we conclude that the modulus of the microfibrils must be
much less than the 7896 MPa reported by Sherratt et al. (2003) and that
it should be of the order of 1 MPa.
Low modulus behaviour of fibres
Evidence that the jellyfish fibres are showing rubber-like entropic
elasticity can be extracted from a comparison of Wright et al.
(1999) and Sherratt et al.
(2003). The extremely low initial stiffness behaviour for zonule fibres
reported by Wright et al.
(1999
) and the initial part of
the zonule strain vs bead periodicity data (3050% zonule
strain with no change in bead periodicity) reported by Sherratt et al. (2003)
could arise from the microfibrils being slack and wavy and as a consequence of
exhibiting conformational entropy on their own. For this to happen, the only
requirement is that the persistence length of the microfibrils must be less
than the total contour length between junction points. If this is the case,
then the microfibrils can act as an entropic chain and give low stiffness
elasticity. That this is possible, indeed probable, is documented in the AFM
(atomic force microscope) figure presented by Sherratt et al. (2003), which
shows the contour of a single microfibril from their combing experiments. The
control sample, presumably a microfibril that was just allowed to bind to the
mica surface without the flow-induced `combing', is strongly coiled,
indicating that it is very flexible. From this we can only conclude that the
persistence length of microfibrils is much less than their contour lengths,
and hence that they can act as entropic chains.
At very low extension, then, jellyfish fibres are likely to be extremely compliant. However, when extended further (30% or more), it is likely that the component microfibrils are becoming extended in the direction of the applied strain, and the fibre stiffness rises due to a non-Gaussian stiffening of the coiled microfibrils. As the fibres are stretched further, we suggest that the microfibrils themselves are being stretched. The role of the substantial pre-strain we calculate for fibres in vivo would therefore be to straighten the microfibrils and hence increase the stiffness to a level useful for storing energy.
Energetics
Whatever the source of the elasticity, with the measured stiffness of the
fibres it is possible to determine whether the fibres alone are sufficient to
account for the energy required to refill the bell. Elastic energy
(W) is the integral of the elastic restoring force (F) over
the distance stretched (x):
![]() | (7) |
![]() | (8) |
![]() | (9) |
![]() | (10) |
![]() | (11) |
The resilience of the mesogleal bell was calculated by DeMont and Gosline
(1988a) to be 0.58, so the
total energy that can be released from the fibres is 20 µJ, which is
sufficient to meet the 17 µJ of energy estimated by DeMont and Gosline
(1988b
) to be required to
refill the bell of a similarly sized animal (bell height = 2 cm). The model
assumes that all of the fibres are aligned perfectly with the local stress
axis and that they are all strained maximally. This will, of course, not be
the case generally, so the total energy available will be somewhat less.
However, the resilience value of 0.58 was probably an underestimate of the
true resilience of the intact structure since it was calculated from isolated
tissue preparations whose properties will have been affected by water leakage
from the sample.
In his analysis of the deformation of the animal, Gladfelter
(1972) showed that the
presence of the joint mesoglea substantially reduced the radial strain
relative to a hypothetical unjointed animal of otherwise identical resting
dimensions. He concluded that the joints existed to allow the animal to make a
contraction of given magnitude for less input force. DeMont and Gosline
(1988a
) measured the
non-linear stiffness of the intact mesogleal bell. They took Gladfelter's
argument further, suggesting that the non-linear elasticity allowed the muscle
to power the refilling stage by storing energy at a time in the jet phase when
it is not useful for generating thrust
(DeMont and Gosline, 1988b
).
We have shown that the radial fibres are stiff enough on their own to store
the energy required to refill the bell. This allows the joint mesoglea to be
much more compliant, which reduces the cost of locomotion by reducing the
opposition to thrust development.
![]() |
Acknowledgments |
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