Diab
ABSTRACT Spines of the sea urchin Strongylocentrotus fransiscanus
were deflected through varying angles and the resistive forces offered
by their ligaments were recorded. Data obtained for spines out of catch
and spines in catch show basic differences in shape as well as amplitude.
This difference in shape was also observed in the data obtained for dif¬
ferent spines in catch. The contractile force of the muscle layer at
the base of the sea urchin spines was determined and found to be sig¬
nificant in comparison to the resistive forces upon 10° deflection
offered by the spine ligaments when in a state of catch. A survey of a
population of spines, both agitated and non-agitated, was conducted to
obtain an objective definition of the state of catch versus non-catch.
An angular limit to deflection was found to exist for spines in catch,
beyond which their ligaments would become irreversibly damaged. Ex¬
perimental and mathematical calculation of Young's Modulus was done for
a spine ligament in catch, and this was found to be similar to that
given for vertebrate tendon at the same strain. The relationship be¬
tween resistive force offered and angular deflection was examined, and
it was found to be non-linear. The possibility of nervous control of
catch was considered, although results obtained make this seem unlikely.
That the setting of catch is Ca"' dependent was here confirmed. Further¬
more, the reversibility of the effects of Ca depletion were confirmed,
although the process of reversal remains unclear, for recovery time was
found to be very long. The effects of protein inhibitors on catch were
also studied, and the preliminary results provide strong evidence for
an enzymatic mechanism in the control of catch.
INTRODUCTION
The spines of the sea urchin are connected to the animal's test by
means of a ball and socket joint. Three concentric cylinders constitute
this joint: an outer epithelial layer, a middle muscular layer, and an
inner ligamental layer. The structure of this joint enables the sea
urchin to move its spines freely in all directions by contraction of the
muscular layers in the direction of deflection. This is apparently ac¬
companied by active shortening of the inner ligamental layer (Smith,
Wainwright, Baker and Cayer, 1981).
Agitation of an urchin, however, causes its spines to "freeze" and
their movement to be inhibited. This is known as "catch." Although the
mechanisms for setting and maintaining catch are not well understood,
cross-linking of the collagen fibrils which make up the inner ligamental
layer appears to be involved (Smith et al., 1981). Also involved seems
to be the ionic composition of the inter-fibrillar matrix of the col¬
lagenous tissue (Wilkie, 1978). Unfortunately, good data on the rates
at which catch can be set and released in vivo are entirely lacking.
This catch should not be confused with the superficially similar
phenomenon which occurs in the non-striated muscle of molluscs, as first
described in Pecten maximus by von Uexkull (1912) and extensively studied
in Mytilus edulis by Twarog (1954). This catch is due to neurally con¬
trolled muscle activity, whereas that of the sea urchin spine ligaments
does not involve muscle at all (Kawaguti and Kamishima, 1965), although
it would appear to be under neural control in the living urchin.
In this paper, an attempt has been made to shed light on this
non-muscular type of catch. In particular, an examination of the
biomechanical properties of the spine ligaments has been conducted, and
an exploration of possible control mechanisms, especially those involving
nervous and enzymatic processes, has been undertaken.
METHODS
Strongylocentrotus fransiscanus and S. purpuratus were obtained from
the subtidal and intertidal regions, respectively, of Monterey Bay.
Specimens were kept in running sea water (15°C) and well oxygenated
tanks.
The experimental preparation consisted of an urchin test with the
Aristotle's Lantern removed. The inside of the test was scraped out to
eliminate any participation of the internal nervous system (e.g. radial
nerves). The ligaments to be studied were stripped of their surrounding
muscle and epithelial layers. The entire preparation was held steady
by pushing a rubber stopper through that portion of the test previously
occupied by the Aristotle's Lantern and firmly mounting this on a plexi¬
glass base placed in a glass dish filled with sea water.
Test spines were connected to a Pixie element force transducer
(Endevco Corp.) by means of cylindrical caps made of stainless steel
hypodermic tubing fitted over their tips (Fig la). The connexion be¬
tween spine cap and force transducer was rigid stainless steel wire
which could swivel at the spine cap to maintain horizontal transducer
pull. The force transducer was attached to a micromanipulator, and
lateral movement of the transducer produced spine deflections through
desired angles. Angle was measured by a protractor attached to a second
micromanipulator and brought up immediately behind the spine. Any
resistance to deflection by a spine would bend the legs of the trans¬
ducer and thereby cause an increase in resistance in one of its semi¬
conductor elements and a decrease in resistance in the other (Fig. 1b).
The ratio of the resistances was linearly transformed into a voltage by
an operational amplifier circuit. The measurement of force was essential¬
ly isometric; that is, the transducer bending was a very small fraction
of spine deflection (O.lu/g compared to approximately 5 m.m./10°). Data
was recorded on a Brush 220 pen oscillograph.
Stress versus strain was measured by a "tensometer" (Fig. 2). The
preparation here used consisted of a ligament in catch with spine and
single ossicle attached. The preparation was held between one clamp
mounted on an anchored double cantilever beam and another clamp mounted
on a plate moved by a lead screw. Force was sensed by deflection of the
double beam and was monitored by a linearly variable differentiated
transducer (LVDT) on the anchored plate. Deformation of the sample was
monitored by an LVDT mounted on a moving plate. The voltage output of
the LVDT was registered on a chart recorder. The maximum stress measur¬
able was 0.85 N and the maximum strain 408 (cf. Tansey, 1983).
The most effective way to induce catch in the spine ligament was
found to be physical agitation. The preparation to be studied would be
placed in a glass dish filled with sea water. Through this sea water
would be bubbled a constant stream of air for ten minutues, following
which time experimentation would begin.
All chemicals used were applied in drops by means of a Pasteur
pipette directly on the stripped ligaments in 2 ml volumes per trial and
given three minutes to take effect (except DTT, NEM, dansylcadaverine
and putrescine, all of which were given ten minutes). The tests examin¬
ing the effects of acetylcholine and adrenaline were done four times,
and all other tests twice. The chemicals used were stored in opague
vessels to avoid any light-catalyzed oxidations, and were kept at a
temperature of 4°C. Finall, Ca" -free sea water was made up in the fol¬
lowing proportions (M): 0.445 Nacl, 0.060 Mgcl., 0.010 KCl, 0.015 EGTA,
and 0.010 Tris buffer (pH 7.8).
RESULTS
Typical data for spines out of catch and in catch
Figure 3 (a) shows a record of resistive force offered for a 10°
deflection (F (10) by a spine out of catch. Figure 3(b) shows the
E (10) for the same spine in catch. Figure 3(c) shows a record of
E (10) of a different spine in catch obtained from the same test.
The difference in record amplitude between the spine out of catch
and the two spines in catch is clear. Also significant is the shape
difference of the two types of record: the spine out of catch offers an
F (10) which takes the form of a step function, whereas the spines in
catch offer F (10)'s which show an initial, sharp peak followed by a
"sag" that eventually levels off to a steady state value. Finally
worthy of note is the shape difference within the catch records them¬
selves, namely, the extent of sag, in this case being more pronounced in
(c) than in (b). The basis of this sag is not completely understood,
but it seems to be characteristic of the catch state, and may well be
an indication of the quality of catch, more pronounced sag implying a
weaker state.
For all experiments resistive force was defined as the highest
point of the curve recorded. Thus, for spines in catch, resisitive
force was taken to be the amplitude of the initial, sharp peak.
Determination of the contractile force of the muscle layer surrounding
ligament.
Prior to detailed examination of the physical properties of the
spine ligament, it was necessary to obtain a measure of the contractile
force (F.) of which its surrounding muscle was capable. A comparison
of this force with that offered upon 10° deflection of a spine in catch
would determine whether the preparation was to consist of a stripped
ligament or whether the muscular layer around the ligament could be
left intact.
A test spine with muscle intact was connected to the force trans¬
ducer as shown in Fig. la. F was measured by using a probe to mechan¬
ically stimulate the portion of the test immediately before that region
of the muscle layer facing away from the transducer. This caused the
muscle to contract and attempt deflection of the spine, thereby pulling
against the transducer and yielding discreet peaks on the chart re¬
corder (Fig. 4, top arrows). The test spine was subsequently stripped
of its muscle and set into catch. Fy(10) was recorded (Fig. 4, bottom
arrow) and this was compared with the F
The results showed that
2/3 F, a force too great to be ignored. All experiments were
therefore run on ligaments stripped of their surrounding muscle.
Definition of catch and non-catch in a population of spines.
F (10)'s were measured for 88 spines, some agitated and some not,
to obtain an objective definition of catch versus non-catch. Spine
length for all trials was relatively constant (approximately 2.5 cm) and
so no normalization of results by lever arm was considered necessary.
Nor was ligament cross-sectional area taken into account for the same
reasons.
The forces recorded and the number of spines offering each force
were plotted in the form of a histogram (Fig. 5). It was observed that
most spines fell into two categories, one having a range for F (10) of
0.00—0.10g, the other of 0.34—-064g. The former category was deemed
characteristic of spines out of catch, the latter of spines in catch.
Any F (10)'s recorded which were greater than 0.64g were also considered
characteristic of spines in catch. Whether these larger values might
have resulted from slight errors in angular deflection measurements
(which would have resulted in large differences in resistive forces
recorded-see next two sections), differences in spine length, or some
other variable is unclear.
Critical deflection angle for irreversible damage.
Having defined the state of catch, it was now possible to look more
closely at its mechanical properties. First to come to light was that
there seemed to be a limit to the extent a ligament in catch could be
stretched before its constitution was unalterably changed. It was
observed that repeated spine deflections of 10° or less yielded re¬
sistive forces of similar magnitude (Fig. 6a), whereas repeated
deflections beyond this (in this case 20° and 30°--Fig. 6b) yielded
resistive forces of decreasing magnitude. These results suggest that a
ligament in catch begins to be damaged at spine deflections of between
10° and 20°.
Computation of Young's Modulus (E) for a ligament in catch.
Young's Modulus is a measure of the tensile stiffness of a material.
Measurement of stress (force/cross-sectional area) at varying strain
(change in ligament length/original ligament length) was done by using
the "tensometer" of Figure 2 (see Methods), and the data obtained were
plotted in the form of a stree-strain curve (Fig. 7). From the slope
of this curve at 0.58 strain, Young's Modulus (stress/strain) was calcu¬
lated to be 2.8 x 10° N/m", a value similar to that given for vertebrate
tendon at the same strain, namely, 3.5 x 10° N/m (Wainwright, Biggs,
Currey and Gosline, 1976).
Young's Modulus was also calculated theoretically by a mathematical
derivation of E based on a schematic diagram of the spine-ligament
system (Fig. 8). The value obrained was 1.1 x 10° N/m", which, consider¬
ing the potential sources of error in ligament dimension measurements,
is certainly consistent with that obtained experimentally (see
Appendix A).
Relationship between resistive force and angular deflection for a spine
in catch.
A spine in catch was deflected incrementally to different angles and
the resistive force offered at each angle was recorded (Fig. 9). It was
found that the relationship between these two variable was not linear.
Below deflections of approximately 8°, the curve resembled that obtained
for stress versus strain (Fig. 7). Above deflections of 8°, however,
the curve began to rise sharply, an increase in resistive force coincid¬
ing with the region of angular deflection in which the critical angle
for damage has been found to lie. The increase in resistive force is
probably due to the application of deflective force directly on to the
inter-fibrillar cross-links which cause catch in the collagenous ligament.
Consequently, excessive force applied here would tend to break these
cross-links and thereby abolish catch. Hence the occurence of the
critical angle for damage in this region.
Consideration of possible nervous control of catch.
Takahashi (1967) reported that the tonus of an isolated strip of
ligament connected to spine and single ossicle was increased by the
addition of 10 Macetylcholine (ACh) and decreased by the addition of
10 "M adrenalin (Adr). Tonus was assessed by the rate of isotonic
lengthening of ligament preparations under a constant load. The rate
decreased upon the addition of ACh and increased upon the addition of
Adr, although the extent of length change is unclear, for his figure has
no vertical scale bar (cf. Boolootian, 1966).
An attempt to verify these results was made here by measuring the
F (10)'s offered by ligaments before and after chemical treatment: sim¬
ilar pre- and post-treatment Fy(10)'s constituted negative results and
indicated that the chemicals had been ineffective, whereas dissimilar
Fy(10)'s (a post-treatment increase showing the setting of catch, a
post-treatment decrease showing the releasing of catch) constituted
positive results and indicated that the chemicals had been effective.
For all chemical analysis, the following control was used. Methylene
blue was applied by Pasteur pipette to a stripped ligament. The ques¬
tion to be addressed was whether chemical solutions applied to a lig¬
ament could penetrate it and thus exhibit their maximum effect, or
whether the density of the ligament prevented their diffusion and
restricted them to the ligament's outer surface, thereby dampening their
potential effects. After one minute, the ligament was cut open to re¬
veal its inner surface. This was found to be blue in colour, showing
that the ligament was indeed permeable to liguids.
ACh was used in 10 'M concentrations and Adr in 10 M concentra¬
tions. ACh was applied to both ligaments out of catch, to see if catch
could be induced, and ligaments in catch, to see if some extreme state
of catch, otherwise unattainable by mere physical agitation, could be
induced. Adr was applied to ligaments in catch to see if it could
abolish this state. The results obtained in all cases were negative.
As another test of cholinergic control of catch, curare was applied
in concentrations of 10 "M to a ligament in catch to see if this catch
could be abolished. If catch were ACh dependent, then curare, by
blocking any ACh recepors present within the ligament, might abolish
catch. The results obtained were again negative, lending further
testimony to the catch state's independence of ACh.
Other catecholamines were also tested, namely, serotonin and
dopamine. These are known to release catch in the non-straiated muscle
of molluscs (Florey, 1966). Concentrations used were 10 M and
10
application was to ligaments in catch to see if effects similar to
those in molluscs could occur in the sea urchin, that is, the release
of catch. Once more, the results obtained were negative (all chemical
analysis results are summarized in Table I).
The effects of Ca on catch.
Wilkie (1978) proposed that the ionic composition of the matrix sur¬
rounding the collagen fibrils in echinoderm connective tissue is re¬
sponsible for the maintenance of catch. A variation in inter-fibrillar
ionic composition might, therefore, influence catch in the spine liga¬
ments of sea urchins. Smith et al. (1981) have demonstrated that the
absence of divalent cation prevents the setting of catch in these liga¬
ments. This has been confirmed in this study for the divalent cation
Ca". A ligament in a state of non-catch was bathed in Ca -free sea
water (see Methods) for five minutes and then bubbled in the same medium
for a further ten minutes to see if the physical agitation which normal¬
ly sets catch in regular sea water could do so here, in the absence of
Ca". Positive results were obtained, indicating that the setting of
catch is Ca dependent.
Smith et al. also state that the prevention of catch in their ex¬
-free and Ca" -Mg -free sea waters was reversible, but
periments by Ca
they give no indication of the time course for these reversals. Follow¬
ing the above described experiment, the preparation was bathed in
regular sea water to determine the extent of time required for the
recovery of catch. It was found that bubbling the preparation in this
new medium after 30 minutes could not induce catch-indeed, the F (10)
recorded was equal to that recorded when the preparation was bubbled
in Ca"'-free sea water (0.05g). A similar result was obtained upon
bubbling after one hour in the regular sea water. Bubbling after three
hours yielded an F.(10) of twice the amplitude of that yielded after one
hour, yet it was still in the force range previously deemed to be char¬
acteristic of spines out of catch (0.lg). Finally, the preparation was
left in the regular sea water overnight (nine hours) after which time an
F.(10) characteristic of spines in catch (cf. Fig. 5) was yielded:
O.38g. Thus, the spine had recovered.
Ca'-free sea water was then applied to a ligament in catch to see
if it could abolish catch. The results obtained were negative, showing
that the maintenance of the catch state was not Ca dependent.
Are disulphide bonds involved in catch?
Ascaris collagen contains 27/1000 residues of 4 cystine and is
known to form cross-links by means of disulphone bonds between these
residues (Wainwright et al., 1976). The possibility of the occurence of
such disulphide cross-linking between the collagen fibrils in the spine
ligaments of sea urchins was here considered. The chemicals used to
test for this were ditiothreitol (DTT) and N—-ethyl maleimide (NEM).
These were used in 5 x 10 'M concentrations. DTT breaks disulphide
linkages, and was therefore applied to ligaments in catch to see if it
could abolish this catch. NEM prevents the formation of disulphide
linkages, and was therefore applied to ligaments out of catch; sub¬
sequent bubbling and recording of F (10) would determine whether it had
prevented the setting of catch. F (10)'s offered before and after
12
treatment with DTT were similar, showing that this chemical had had no
effect on the maintenance of catch. F (10)'s offered upon bubbling after
NEM had been added were considerably greater than those offered before
bubbling (having an amplitude, 0.43g, characteristic of spines in catch),
showing that NEM had not prevented the setting of catch. Both these sets
of results suggest that disulphide cross-linking is not involved in the
setting or maintenance of catch in the spine ligaments of sea urchins.
The effects of protein inhibitors on catch.
Dansylcadaverine and putrescine act as substrates for the enzyme
transglutaminase, and thereby inhibit its biological functions when
added to a system in excess. Transglutaminase will catalyze, for ex¬
ample, the incorporation of dansylcadaverine into a convenient protein
receptor such as casein, and measurement of the protein bound fluores¬
cence of this reaction has been used to ascertain the potency of this
enzyme (Lorand, 1976). In vertebrates, transglutaminase is known to
catalyze the cross-linking of the fibrin clot during haemostasis, and
the production of the vaginal plug by postejaculatory clotting of rodent
seminal plasma (Folk, 1980). It is also known to catalyze the in vitro
formation of cross-links between fibronectin and collagen in cultured
fibroblasts of rat kidney (Folk, 1980).
In light of these observations, it seemed possible that trans¬
glutaminase or a transglutaminase-like enzyme (TGL) might be involved
in the cross-linking of collagen fibrils which constitutes the state
of catch. Dansylcadaverine and putrescine were applied to both lig¬
aments out of catch. The application to ligaments already in catch
was a control for any reactions other than the suspected enzymatic one,
The control application gave negative results, showing that the in¬
hibitors did not abolish catch. On the other hand, the application to
ligaments out of catch produced positive results, for post-treatment
bubbling could not induce catch in these ligaments. This showed that
the inhibitors could prevent the setting of catch, and in so doing
presented evidence for a potential enzymatic mechanism for the control
of the catch state, one which would involve possibly transglutaminase
or an enzyme similarly sensitive to dansylcadaverine and putrescine
inhibition.
DISCUSSION
This paper presents measurements of the mechanical properties of
the spine ligaments in sea urchins and considers some possible physiolog¬
ical control mechanisms. It confirms and extends, on a different urchin
genus, the basic findings of Smith et al. It also offers suggestive
preliminary evidence for a Ca dependent enzymatic mechanism of collagen
cross-linking as the basis for setting catch.
One new and important finding reported here is the occurence of
some sort of structural damaging or weakening when a spine in catch is
deflected through an angle of between 10° and 20°. A similar alteration
in ligament constitution at approximately the same amount of stretch
appears to have occured in the experiments of Smith et al. Although
they do not consider this idea per se, they do present a plot of ex¬
tension versus time for ligaments stretched vertically along the long
axes of their spines (see their Fig. 3). Extensibility at a stretch
14
(measured under constant load) of 0.3--0.4 mm in the spines they term
"movable" decreased dramatically relative to extensions on either side
of this range. This means that in this region, the ligaments were
suddenly offering an increased resistance to stretch. When extension
was carried out beyond 0.4 mm, an increased rate of extension per time
was observed, as though the ligaments had become damaged or structurally
weakened. Smith et al. do not discuss this result, but it may reflect
functional passage through the 10°--20° critical angle range described
above. By using the schematic diagram of Fig 8, the range of angular
deflection which corresponds to their "critical" 0.3--0.4 mm extension
range can be calculated. If a ligament radius (x) of 1.0 mm is taken
for the ligaments they were using, as estimated from their micrographs
(see their Fig. 4), 0.3--0.4 mm ligament extensions (1) are seen to be
equivalent to angular deflections of 16.9°--21.8°. This was precisely
the range in which the critical angle for damage was found to lie in this
study.
Exactly what happens at this angle requires a model for the liga¬
ment system and the mechanism of catch maintenance by the collagen
fibrils. According to the ideas presented by Smith et al., this
critical angle may represent the limiting amount of stretch which the
cross-links between the collagen fibrils making up the ligament can
withstand before suffering breakage. Since the breakage appears to be
largely irreversible (cf. Fig. 6), it can be concluded that the cross¬
links are not capable of reformation once broken by excessive stretch.
Another index of the stress-strain relationship of the spine liga¬
ment is given by the relationship between resistive force offered (F
and angular deflection (ad) presented in Fig. 9. At first sight, these
graphs appear not to be similar, although their variables would suggest
that they ought to be: F is directly proportional to stress (through
cross-sectional area) and ad is an indirect, but linear (for small
angles), way of measuring strain. From Fig. 8, conversion of strain to
equivalent ad is possible. This shows that the graphs are indeed simi¬
lar, and that they differ only in extent. The maximum strain to which
the spine ligament was subjected was 2.58 (Fig. 7), and this corresponds
to an ad of 5.4° (using a ligament length (L) of 4 mm and a ligament
radius (x) of 1 mm). Thus, the range of the stress-strain curve is
equivalent to that part of the F-ad curve over angles of 0°--5.4°.
Moreover, the slope of the stress-strain curve would have probably risen
steeply had more strain (that is, greater than 2.58) been applied to the
caught ligament, in harmony with the F-ad curve.
Experiments were also conducted to test possible nervous control
of the catch state. The findings of these experiments would suggest
that nervous control is either not involved, or is only a part of a
greater mechanism. On the other hand, experiments conducted to test
possible enzymatic control offer strong (although it must be emphasized
still preliminary) evidence for the role of transglutaminase or TGL in
the mechanism of catch.
Transglutaminase has been observed to play a part in several
clotting-type processes in a wide variety of organisms, and in particu¬
lar in the cross-linking of collagen fibres in both vertebrates and in¬
vertebrates (Folk, 1980). Therefore, it is reasonable to suspect that
it might also play a part in the cross-linking of collagen fibrils in
the spine ligaments in sea urchins.
Now it has been demonstrated that the setting of catch is Ca
dependent. Ca could participate in at least two important control
processes: the conduction of nervous activity, especially neurosecretion,
and the activation of an enzymatic reaction chain. Concerning the
latter, it is known that transglutaminase requires Ca' to convert it
from its zymogen form to its active state (Lorand, 1976). Thus, if
catch were controlled by transglutaminase or TGL, then the absence of
Ca"' should block its setting by preventing the activation of this
enzyme.
An important question which must now be addressed concerns the
whereabouts of the transglutaminase or TGL store. Smith et al. state
that in the ligament, "axons contain large numbers of opaque secretory
droplets." Could the contents of these vesicles be the enzyme, and
therefore these vesicles the enzyme store? If so, then the following
mechanism could be conceived: Ca" ions trigger the neurosecretory
release of transglutaminase or TGL and their subsequent activation,
enabling them to catalyze the cross-linking of the collagen fibrils and
thereby set catch. This would explain the requirement of Ca" for the
setting of catch. However, this model would not be able to explain the
observed long recovery time (many hours) for a ligament when its Ca
supply is depleted and then replenished. It would seem that once the
Ca" supply had been replenished, the ligament should immediately
regain its ability to catch.
Bearing this problem in mind, a more satisfactory mechanism is the
following. Ca" again permits neurosecretory activity of the nerve
fibres which run through the ligament, but the released substance is
not enzyme, rather, it is an essential cofactor. This cofactor
activates the enzyme which is already present in the medium surrounding
the collagenfibrils. Ca must play one further role, however: it must
somehow prevent the loss of the enzyme by diffusion in a stripped liga¬
ment surrounded by regular sea water. One possibility is that Ca
mediates or stabilizes the binding of the enzyme to some extracellular
structure, such as the collagen fibrils themselves or the external sur¬
face of the nerve endings. The latter of these two seems the more
likely, for it would give the ligament system more control of the catch
mechanism by bringing the point of release and the point of action of
the cofactor closer. It would also for the same reason tend to conserve
cofactor and avoid any spontaneous cross-linking of the collagen fibrils
resulting in spontaneous catch. Taking the surface of the nerve endings
then as a likely place for the location of the transglutaminase of TGL,
released factor might thus "activate" the Ca -enzyme complex by causing
its release from its anchoring structures, allowing it then to cross¬
link the collagen fibrils and set catch.
This mechanism clearly incorporates the observation that the
setting of catch id Ca dependent. In addition, it also explains the
long recovery time after treatment with Ca" -free sea water. Removal
of Ca" from the medium surrounding a ligament would not only prevent
the neurosecretion of cofactor, it would also result in the release of
inactive enzyme into the inter-fibrillar matrix. Within a short time,
this inactive enzyme would diffuse out of the ligament and be lost to
the surrounding medium. Resupply of Ca would immediately reestablish
the ability of the neurosecretory vesicles to release cofactor,
but would not immediately reestablish the ability of the ligament to
catch; rather, a considerably longer time would be required to regenerate
the lost enzyme.
ACKNOWLEDGMENTS
First and foremost, endless gratitude is due Professor William
Frank Gilly. His seemingly indefatigable drive and attention, which
would pick up my spirits when all else was crumbling, his sharp-edged
wit, which at the best of times was only just bearable, and his acute
but truly constructive criticism, which would restrain the energy of an
oftentimes overzealous undergraduate and firmly warn him against im¬
pulsiveness and the dangers of getting "too big for one's boots," all
contributed tremendously to my development as a thoughtful, cautious
and honest scientist.
Thanks must also go to Mark Denny, without whose insight and warm
encouragement I may never have ventured into the wild world of
biomechanics, and to David Epel, whose marksmanship may have hit the
bull even "in the dark." Let me also express appreciation to Stuart
Thompson for his valuable feedback on directions for further research
and to all those who had the courage to inquire, the patience to
listen, and the interest to criticize.
Finally, let me thank the sea urchin itself for providing me with
such an exciting but at the same time accessible system to study, a
system which I find more baffling now than when I started and which I
hope to come back to soon.
APPENDIX A
From a schematic diagram of the spine-ligament system (Fig. 8), a mathematical derivation
of Young's Hodulus (E) is possible:
1/y - X cos
1 2 y x cos V
Strain = 1/L cos
where V - 15
yost/os
where stress - F/A
E a stress/strain
where A =x dx d
2 F L cos/1 A
F = E (x dx df) y x cosd/L cos y
Moment (M)= Fx cos
-E (x dx do) yx cos 9/Y L cos
Hotal - 4 e t eosh 2 00 40
E/V L cost) 26/4 (1/2 + 1/4 sin 209
Motal
(1/2 + 1/4 sin 29)
F a (y E/V2 L CoS 4
C
A simple rearrangement then gives the final equation for f.
E - F 21 cos 4/ 2/ (1/2 t 1/4 sin 20
When one considers that working with physically measured ligamental radius means working with
numbers taken to the fourth power, one can appreciate that the mathematically calculated
Value for Young's Modulus is quite consistent with that obtained experimentally.
REFERENCE
BOOLOOTIAN, R.A., editor, 1966. Physiology of echinodermata, Inter¬
science Publishers, pp. 521-524.
FLOREY, E., 1966. An introduction to general and comparative animal
physiology, W.B. Saunders Company, pp. 590-594.
FOLK, J.E., 1980. Transglutaminases. Ann. Rev. Biochem. 49: 517-531.
KAWAGUTI, S. and KAMISHIMA, Y., 1965. Electron microscopy on the spine
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FIGURE LEGENDS
Fig, la: Diagram of the apparatus used to measure resistive forces
offered by spines in catch and spines out of catch when
deflected to desired angles.
The functional core of the force transducer shown above.
Fig. 1b:
The "tensometer" used to measure stress at varying strains
Fig. 2:
exerted longitudinally on a ligament in catch.
Typical chart recordings of F (10) offered by a spine out of
Fig. 3:
catch (a), the same spine in catch (b), and a different spine
obtained from the same test in catch (c).
F of the muscle layer surrounding a spine ligament measured
Fig. 4:
m
by mechanical stimulation (top arrows) compared to F (10)
offered by the same ligament after it was stripped of its
muscle and set into catch (bottom arrow).
Histogram of the F (10)'s offered by a population of spines,
Fig. 5:
some agitated, some not, giving an objective definition of
catch versus non-catch.
F (10) recorded repeatedly from a spine in catch showing a
Fig. 6a:
relatively constant amplitude per deflection.
F (20) (bottom arrows) and F (30) (top arrows) recorded
Fig. 65:
répeatedly from the same spine in catch showing a gradual
decrease in amplitude per deflection.
Stress-strain curve for a spine ligament in catch, as measured
Fig. 7:
by the tensometer in Fig. 2.
Schematic diagram of spine-ligament system (a) and cross¬
Fig. 8:
sectional area of a spine ligament (b) used in the calculation
of strain equivalence of angular deflection and mathematical
computation of Young's Modulus.
The relationship between resistive force offered and angular
Fig. 9:
deflections over a range of 0°--11.5°.
The results of chemical analysis carried out on spine ligaments
Table I
in catch and out of catch.
24
SPINE -
LIGAMENT
TEST
TRANSDUCER
(a)
SILICON
V
BRASS
(b)
AMPLIFIER
CHART RECORDER.
EPOXY
—
STARFISH SKELETON
STRETCHING MACHINE
LVDT
ANCHORED
LEVER PLATE
MOVING PLATE
LVDT
Fig. 2
DOUBLE
CANTILEVER
O
CLAMP
.........
- . . . .
J.

§
O
CLAMPS
0.50
0.2.
0.50
0.25

(b)
8 0.50
025
—
100
ata

—
50
100 150
TME (sec)

300
200
TIE (sec)

——
200
100
TIME (sec)
—
400
Fig. 3
—


—
S
—
10
(5) aouo
—
—
—

—

SANIdS 40 AZGWON
—


(6) oo
9
—

—

—

(5) oo
8
0
300
50
Fig. 7
0.5
1.5
1.0
% STRAIN
2.0
2.5
0

+
O.3
S O.
L
O.

8
ANGULAR DEFLECTION (degrees)
—
10
SPINE —
LIGAMENT

(a)
Fig. 8
0


(b)