Lecture 6 Fluid for skeletons - University of Toronto Mississauga

Lecture 6 Sept. 24
My cow ramble of last lecture actually means something. Close, careful, thoughtful,
observation of behaviour and form is the way to infer function.
Naturally selected for running; artificially selected for milk production.
Thomson’s Gazelle
Alert posture of a gazelle signals to conspecifics
‘be ready to run’.
Coelom as fluid skeleton: hydrostatic skeleton with antagonistic
muscles: stress (force per unit area) translocated by fluid
Observe an annelidan, a
segmented worm (Phylum
Annelida) and query its
A tube within a tube, the body
wall two layers of muscle with
fibres running 90 degrees to
each other, chaetae (pointy
things indeed) protruding
from the wall: can be
protracted and retracted;
septa bulkheads invested with
transverse muscle etc.
Ask questions: why
segments?, why a fluid
space?, why chaetae, why a
kidney pair in each segment?
Why muscle on septa?etc.
What is a coelom?
It is defined as a fluidfilled cavity forming
during development
within the early
differentiated tissue
Animals with a coelom
(segmented worms) are
called coelomate; animals
without one (flatworms) are
acoelomate. Some animals
(nematodes) have a fluidfilled cavity that is not
homologous with the
coelom: called a
Why chaetae? Think about where an earthworm lives. Within soil, burrowing, searching out
softer places and crevices, going around roots & rocks. The worm needs to twist and turn and
push its body. For push you need purchase. For this it has the chaetae, functioning as
hobnails or crampons. For burrowing you need a cylindrical body – no corners.
Gaining ground occurs all along the body, at each
constriction (yellows) ahead of the anchored
(greens). Peristalsis is a term applied to guts as
well as worm body walls: a dilation followed by a
constriction: peristalsis in the worm’s gut pushes
boluses of food (being digested) along the tubular
Kier on annelid locomotion, p1250. Why segments, why septa?
Circular vs longitudinal muscles, peristalsis (waves) – features of a number of
‘worm-like’ (vermiform) animals: includes holothurian echinoderms (sea
“In annelids such as the earthworm, the coelom is divided into segments by
muscular septa, which prevent movement of the hydrostatic fluid from one
segment to the other during normal locomotion…subdivision of the coelom allows
individual segments to operate independently, thereby facilitating localized
“Septa are likely crucial in allowing large lateral forces to be exerted during
‘Kier’s Law’ “at a given [coelomic fluid] pressure [internally expressed stress] the
stresses in the circumferential direction are twice those in the longitudinal
direction.” Yet the volume devoted to circular muscle is not greater: “…the area of
the longitudinal muscles is …greater [than that of the circular]. Because there is
relatively more longitudinal muscle “the resulting pressures produced by the
longitudinal muscles may be as much as 5 to 20 times greater than those produced
by the circular muscles.”
“at a given pressure, the stresses in the circumferential direction {hoop stress of
McCurley} are twice those in the longitudinal direction.” “...the volume of the
longitudinal muscles is greater [than the circular]” “...the resulting pressure
produced by the longitudinal muscles may be as much as 5-20 times greater than
those produced by the circular muscles” This is adaptive in obtaining purchase,
i.e., less force is needed to contract circulars and reach a part of the body forward
or backward.
“The septa are thought to allow the pressure to be different in one
…compartment… compared with another (without septa [imagine it as isn’t] an
increase in pressure would be transmitted along the entire length of the body);
thus the high pressure of a localized maximal contraction of the longitudinal
muscle (perhaps required to enlarge the burrow*) will not be transmitted down
the length of the worm and overwhelm the circular muscle in another part of the
body” (Kier p.1251)
*or better just to get the purchase for normal movement through soil
We then come to Nematode worms:
“…example of the importance of connective tissues [inextensible collagen fibres
are major components of connective tissue] for the hydrostatic skeleton
Nematodes possess robust longitudinal muscle bundles, but they lack the circular
muscle fibres that typically serve as antagonists in other hydrostatic animal
skeletons. How then, can the longitudinal musculature be antagonized?” –
especially by a fibre, collagen, that is inextensible.
Hydrostatic skeletons of Nematoda
Pseudocoelom locomotion
CFHCTA and adaptive volume of a fluid-filled cavity
Speciose: 20000 described
More than a million to go.
What is the most famous nematode
and what is it most famous for?
“…if all the matter in the universe except the
nematodes were swept away, our world would still be
dimly recognizable, and if, as disembodied spirits, we
could then investigate it, we should find its mountains,
hills, vales, rivers, lakes and oceans represented by a
film of nematodes. The location of towns would be
decipherable, since for every massing of human beings
there would be a corresponding massing of certain
nematodes. Trees would still stand in ghostly rows
representing our streets and highways. The location of
the various plants and animals would still be
decipherable, and had we sufficient knowledge, in
many cases even their species could be determined by
an examination of their erstwhile nematode
from "Nematodes and Their Relationships", 1915
Nathan Augustus Cobb, father of American
See next slide: C. elegans: for being the first animala whose genome was entirely sequenced.
Pseudocoelom as fluid skeleton Caenorhabditis elegans*
Phylum Nematoda Roundworms
pinworms: most too small (<2mm) to leave
any casual impression on laypeople.
Most free-living in soil; some parasitic.
Nematodes in the ocean? They are
parasites of whales but are they in the sea
Unsegmented, i.e., not metameric
Circular body in transverse section, pointed
Remarkably high internal pressure of
pseudocoel fluid.
Locomotes lying on
Its side and thrashing
Its body about.
Jon Eisenback
Uniformity of body design
Though the number of nematode species is so great, they are unusually uniform in
body design. “characteristic features …are largely independent of size, of diet and
of stage of development [of free-living or parasitic existence].” “…the elementary
student may be forgiven …for thinking …there is only one nematode but that the
model comes in different sizes and with a great variety of life histories. (Harris &
Crofton 1957)”. (Flatworms and corals are much more diverse in morphology – so
the uniformity of the nematode ‘body plan’ cannot be explained as because these
worms are simpler organisms.)
A D’Arcy Thompson (the diagram of forces man) is associated with the idea that
mechanical principles constrain form. “A bridge, a ship, an aeroplane are
recognizable at once because their design is based necessarily and largely on the
mechanical forces which play such a predominant part in their economy” (Harris &
Crofton 1957). The features of an animal or plant available for evolution to act
upon are limited or constrained by the mechanically possible. Natural selection
constrains what evolves -- but so also do physical laws.
Nematode shape is dictated by mechanical considerations. Being an elongated
unsegmented cylinder is key to its locomotion. Every soil-living nematode needs
to have this pointed-end cylindrical in the middle shape.
Fluid skeleton locomotion with only one set of muscles:
More sources for fluid skeletons:
*Shadwick R.E. 2008. Foundations of animal hydraulics: geodesic fibres control the
shape of soft bodied animals. J. exp. Biol. 211: 289-291.
Discussion of the importance of a classic paper:
Clark R.B., Cowey J.B. 1958. Factors controlling the change of shape of certain
nemertean and turbellarian worms. J. exp. Biol. 731-748.
Harris J.E., Crofton H.D. 1957. Structure and Function in the nematodes: internal
pressure and cuticular structure in Ascaris. J. exp. Biol. 34: 116-130.
*Assigned for reading. Just Shadwick, other references for background reading.
Worm as a fibre-reinforced cylinder
Clark-Cowey model “one of the key design principles of structural systems in biology”
(Shadwick 2008)
From the 1950s the concept has existed of a hydrostatic skeleton: “a system in
which muscles shorten to act against a contained volume of fluid, rather than rigid
skeletal elements [sclerites, bones] to maintain shape and effect movement” (op.
cit.) The important role of collagen helices is more recent and begins with Clark &
“…a structure composed of inextensible fibres [can] accommodate large
extensibility” is the basic idea of the Clark & Cowey paper (Shadwick 2008).
“…how [did a pseudocoelomate]… move if it had only one set of muscles as in the
case of nematodes” (op. cit.)
“…the geometry of the reinforcing fibres in the body wall was the key to the
solution…”. An antagonist of the longitudinal muscles of nematodes is a collagen
fibre helix in the cuticle.
[ memonic device ‘CFHCTA’ Canadians For Happy Carefree TAs : crossed fibre
helical connective tissue arrays (Kier).]
The Clark-Cowey model as explained by Kier, but see also Shadwick
A: imagine the worm
a segment of a model worm, represented as a cylinder (radius r, length l) wrapped
(A) A unit
one unit
full turn of an inextensible fibre having length D; fibres with the opposite sense are
fluid-filled cylinderbyone
long, its wall stiffened by
one turn of a collagen fibre
There is a (helical) fibre
angle ø: as the segment
lengthens, cylinder diameter
and ø both decrease [at 0° a
thread]; as the segment
shortens, its diameter and ø
both increase [at 90° flat
If one plots the volume of
the cylinder (y axis) vs fibre
angle ø (x axis), V will vary
following this curve, its
cylindrical body remaining
circular in transverse
Shadwick R E J Exp Biol 2008;211:289-291
B represents
the unit length of the worm cut along the top
©2008 by The Company of Biologists Ltd
and laid open, D being the fibre length.
The Clark-Cowey model as explained by Kier, but see also Shadwick
So the area under the
(A) A unit length segment of a model worm, represented as a cylinder (radius r, length l) wrapped
curve depicts volume
by one full turn of an inextensible fibre having length D; fibres with the opposite sense are
change with ø change in a
cylindrical worm. “A worm
with a volume equal to the
maximum that could be
enclosed by the fiber
Curve peaks at about
system at [55°] would be
unable to elongate or
shorten significantly
because any length change
would entail a decrease in
volume of an essentially
incompressivle fluid…”
Kier, p. 1249.
to ‘pick’ a volume and live
Shadwick R E J Exp Biol 2008;211:289-291
with it.
©2008 by The Company of Biologists Ltd
(A) A unit length segment of a model worm, represented as a cylinder (radius r, length l) wrapped
by one full turn of an inextensible fibre having length D; fibres with the opposite sense are
Volume of the
cylindrical fibre system
changing with fibre
angle. A worm is longer
and thinner at lower
angles (F) and shorter
and fatter at higher
angles (G). A worm
species ‘chooses’ a
constant volume, i.e., a
horizontal line
somewhere along the y
axis e.g. FG. This gives
the range over which its
fibres can contribute to
length change: for FG it
is from 25 to ~82 helix
inclination angle.
“The system can always
contain less than this
volume if the cross
section becomes
elliptical instead of
circular. Allowing a
worm to adopt a
flattened elliptical
cross-section as it
changes length.“ Only
where the horizontal
line intersects the
curve will the worm be
circular in cross
©2008 by The Company of Biologists Ltd
Shadwick R E J Exp Biol 2008;211:289-291
I don’t follow this, gkm.
The fluid cavity of a
nematode can evolve to an
adaptive range of
extensibility that depends
upon the relationship
between the possible
range of helical fibre
angles and the fixed
volume of the species.
Pick a particular fixed
volume (up the y axis) – a
larger volume – and the
range of helix angles
available for shape change
(involving flattening as the
circular body goes to an
elliptical cross section) is
more constrained. More
extensible species (e.g.,
Lineus) will evolve to use a
volume that is giving the
helix a greater range of
The relationship between volume and fibre angle θ as in Fig. 1C, on which are superimposed the
actual volumes of various nemerteans and turbellarians (fine horizontal lines).
Shadwick R E J Exp Biol 2008;211:289-291
©2008 by The Company of Biologists Ltd
In nematodes “…the body wall provides a passive elastic antagonist to muscle
contraction, even though there are no elastic (i.e., stretchy) elements. Furthermore
since the fibres are loaded in tension this sets up the possiblility of elastic energy storage
to aid in the recoil and extension of the relaxing muscle.” (Shadwick 2008)
I would have thought this is more than a
possibility. The CFHCTA can act as antagonist
to the return of the longitudinals to their
precontracted state – at least in part – and the
longitudinals on the left side can also stretch
those of the right and vice versa.
So helical collagen fibres can provide an antagonist to longitudinal muscles,
and the volume of a nematode’s pseudocoel can be an adaptation for
optimal extensibility. But the issue would seem still to be: how do
nematodes actually move through the soil? How do they obtain purchase
without chaetae? Is obtaining purchase an explanation for the pointed
anterior and posterior body?
More attempts to understand the Clark-Cowey worm-volume curve
Suppose a nematode worm with a fixed volume of fluid skeleton and its helical
collagen fibre array moving between 25 and 80˚. Over this range of angles the
worm’s shape varies from longer and thinner at the ‘25-end’ to shorter and fatter
at the ’80-end’. But the fluid cavity (pseudocoel) must stay the same volume over
this range of angles [in a way the curve shape no longer matters, i.e., there is
nothing special about 55˚as the high point] but the worm does lengthen or
shorten via the helix, this involving flattening of its circular (section) shape to an
ellipse. The worm’s helix can thus act as a means of affecting body shape in
opposition to the longitudinal muscles.
The lengthening of the helix (via energy derived from the longitudinal muscles) can
act to antagonize those muscles over a range of ‘extensibility’.
Where the worm species has ‘chosen’ its volume on the angle-volume curve can
be adaptive or maladaptive depending on selection for better or worse

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