Quasistatic and continuous dynamic characterization of the mechanical properties of silk from the cobweb of the black widow spider Latrodectus hesperus
1 Department of Biology, University of California, Riverside, CA 92521,
USA
2 MTS Systems Corporation, 1001 Larson Drive, Oak Ridge, TN 37830,
USA
* Author for correspondence at present address: Department of Biology, University of Akron, Arkon, OH 44325-3908, USA (e-mail: blackledge{at}uakron.edu)
Accepted 14 March 2005
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Summary |
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Key words: biomechanics, continuous dynamic analysis (CDA), dynamic mechanical analysis (DMA), spider web, major ampullate silk, polymer, Theridiidae, loss tangent, viscoelasticity
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Introduction |
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Modern phylogenetic studies have demonstrated that the orb web is an
intermediate, rather than a highly derived, architecture within the
diversification of spider webs (Coddington
and Levi, 1991; Griswold et
al., 1998
). For example, spiders in the Theridiidae spin cobwebs.
Because theridiids have orb web weaving ancestors, this implies that the
seemingly chaotic architecture of the cobweb originated from the highly
stereotyped orb architecture (Agnarsson,
2004
; Coddington,
1986
,
1990
;
Griswold et al., 1998
). At
first glance, cobwebs appear to be disorganized tangles of silk. However,
cobwebs possess suites of discrete architectural elements that are common to
webs constructed by different species and even different genera of theridiid
spiders (Agnarsson, 2004
;
Benjamin and Zschokke, 2002
,
2003
;
Coddington, 1986
).
Latrodectine spiders constitute a basal clade within the Theridiidae and
their cobwebs potentially represent an ancestral architecture for the family
(Agnarsson, 2004;
Arnedo et al., 2004
;
Benjamin and Zschokke, 2002
).
These `Latrodectus-type' webs consist of a retreat that is either
suspended within the web or at the web periphery, a supporting structure of
dry silk that includes both a sheet of radiating threads and peripheral
support threads that suspend the web in space, and sticky gumfooted lines that
attach to the substrate and function as the primary capture elements of the
web (Fig. 1; Benjamin and
Zschokke, 2002
,
2003
). Cobwebs are highly
three-dimensional and lack viscid capture spirals, in contrast to ancestral
orb webs. The construction of cobwebs is also less stereotyped and cobwebs are
continuously added to over many days, in contrast to orb webs, which are
completed in a single bout of construction. Furthermore, cobwebs generally
capture pedestrian rather than aerial prey
(Hodar and Sanchez-Pinero,
2002
). Thus, theridiid spiders use silks in a very different
ecological context than did their orb-weaving ancestors. Yet, relatively
little is known about the mechanical properties of cobweb silks.
|
We chose to investigate the web silks spun by the western black widow Latrodectus hesperus to construct cobwebs. In this study, we compare the mechanical properties of silks from the two primary architectural regions of the web, the sheet and gumfooted threads, as well as silk obtained from the major ampullate gland of anaesthetized spiders. We discuss the glandular origin of web elements, compare the mechanics of cobweb silks to orb webs, and provide novel data on the dynamic material properties of spider silk.
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Materials and methods |
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Collection of silk
We collected three different types of silk samples from each of the seven
spiders. Scaffolding silk and gumfooted lines were collected directly from
webs onto `c' shaped cardboard mounts. The 10 mm gap between the arms of the
card set a standard gage length. Both arms of the `c' were first coated with
small amounts of cyanoacrylate glue (SuperglueTM). The cards were then
adhered to silk strands in the appropriate portion of the web. Finally, a hot
wire was used to cut the silk on either side of the mount, freeing the silk
thread from the web without altering the tension of the sample. We also
obtained major ampullate silk directly from spiders through forcible silking
(Work, 1976). Spiders were
first removed from webs and anaesthetized with CO2 for 2-5 min. We
then restrained the unconscious spiders, ventral side facing up, onto a petri
dish using transparent tape such that the spinnerets of the spider were
accessible. The petri dish was then placed on the stage of a stereomicroscope
and the spinneret region was illuminated with fiber optic lights. Thus, we
could see the fibers emanating from the major ampullate spigots while we
manually pulled fibers from the spider. This allowed us to be certain of the
glandular origin of the fibers. These forcibly silked threads were taped to
cardboard mounts across 21 mm diameter gaps. Samples were then securely
affixed to the mounts, at both edges of the 21 mm gap, using cyanoacrylate
glue. We collected a total of six to nine samples of each type of silk -
scaffolding, gumfoot, and manually pulled (i.e. forcibly silked) major
ampullate silk, for each of the seven black widow spiders.
For 21 of the gumfooted lines sampled, we also collected a second sample
from the glue-coated `foot' portion of the line, which is covered with a
viscid aggregate gland secretion that adheres to prey. Aggregate glue plays an
essential role in the mechanical performance of orb weaver capture silk
(Vollrath and Edmonds, 1989)
and this sampling protocol allowed us to test the effects of theridiid glue
secretions on silk mechanics.
All samples were collected within the first 5-14 days after spiders were brought into the lab, and typically all three types of silk from an individual spider were collected and tested on the same day. Mechanical tests were performed at a temperature of 21-23°C and ambient humidity during testing was usually 25-40%, but was as high as 70% for one of the spiders.
We used polarized light microscopy to obtain three digital images of the
silk fibers within each sample, except for the glue-coated portions of the
gumfooted lines, and then measured the diameters of the fibers using NIH Image
1.63 (US National Institutes of Health). These diameters were then used to
calculate the cross-sectional area of each sample being tested. This method
produces highly repeatable measurements that are similar in accuracy to
measurements obtained through scanning electron microscopy, but also accounts
for variation in cross-sectional area from sample to sample
(Blackledge et al., 2005a).
Quasistatic mechanical analysis
Load-extension data were generated using a Nano Bionix tensile tester (MTS
Systems Corp., Oak Ridge, TN, USA). The Nano Bionix is capable of generating
load-extension data from very fine silk fibers, with a load resolution of 50
nN and an extension resolution of 35 nm. All fibers were extended at a
constant rate of 1% strain s-1 until the fibers failed. This strain
rate was chosen because it was within the range of many other studies on
spider silk mechanics, maximizing comparability of results. Raw load-extension
data were then transformed into stress and strain values to normalize data
across samples of silk of different sizes. Stress measures the force per
cross-sectional area applied to a fiber, allowing comparison of the relative
load applied to fibers of different diameters. We chose to calculate true
stress (tr), where load is normalized to the instantaneous
cross-sectional area of fibers, as:
![]() | (1) |
where F is the force applied to the specimen and A is the estimated cross-sectional area of the specimen calculated from the original cross-sectional area under an assumption of constant volume. Ideally, true stress would be calculated using the actual cross-sectional area of the specimen measured at each extension value. However, it is technologically difficult to visualize fiber diameters during stress-strain tests such that the cross-sectional area is typically calculated from the original cross-sectional area using an assumption of constant volume. Currently there are few data on whether or not this assumption is valid for spider silks.
Our use of true stress is distinct from much of the literature on spider silk mechanics, which often uses engineering stress where force measurements at all extension values are normalized to the initial cross-sectional areas of fibers. Our use of true stress rather than engineering stress generates more realistic values of the stress experienced by highly extensible fibers, such as spider silk. Furthermore, true stress values facilitate comparison of the mechanical properties of different kinds of silks that may vary widely in their extensibilities, and an important long-term goal of our research program is to generate comparative data on a broad range of silks spun by taxonomically diverse spiders.
Strain measures the extension of a fiber relative to its length and we
again chose to use true strain rather than engineering strain values. True
strain (tr) was calculated as:
![]() | (2) |
where L is the instantaneous length of the fiber at each extension value and Lo is the original gage length of the fiber. Again, true strain provides a more realistic measure of the stretchiness of highly extensible fibers, such as spider silk.
We then used true stress and true strain measurements to calculate five variables of interest. Young's modulus measures the stiffness, or ability of fibers to resist deformation, and is calculated as the slope of the linear region of the stress-strain curve prior to the yield point. The yield strain measures the point at which the mechanical behavior of fibers changes from elastic to viscous. Extensibility is the true strain at the point of failure of the fiber. Ultimate strength is the true stress at the point of failure of the fiber. Toughness (i.e. work of extension or work to fracture) is a measure of the energy necessary to rupture a fiber of a given volume and was calculated as the area under the `true stress-true strain' curve.
Continuous dynamic analysis
Traditional quasistatic tensile tests provide a measure of how much energy
is absorbed by fibers as they are extended (i.e. `toughness' as delimited by
the area under the stress-strain curve). Quasistatic analysis can measure
stiffening of fibers as an increase in the rate of energy absorption, but it
cannot determine how that energy is absorbed. For instance, a similar increase
in the stiffness of a fiber can occur both through an increase in elastic
effects such as crosslinking between silk fibroin molecules or through an
increase in viscosity caused by friction between molecules. Dynamic analysis
of material properties distinguishes itself from quasistatic analysis by
measuring how much energy is absorbed through these viscous and elastic
processes.
The Nano Bionix performs a novel continuous dynamic analysis (CDA) of silk
mechanics. It does so by imposing a slight oscillating dynamic strain upon the
silk fiber as it is extended. The Nano Bionix then measures the dynamic stress
response to this oscillating strain. The degree to which the dynamic stress
response is in phase with the dynamic strain oscillation provides a measure of
the elastic behavior of the fiber (storage modulus) while the viscous behavior
(loss modulus) is measured by the degree to which the oscillation in dynamic
stress lags behind that of the dynamic strain. In
Fig. 2A, the resulting dynamic
stress is neither completely in phase with the dynamic strain (where the two
sinusoidal curves would overlap perfectly, offset by 0°) nor completely
out of phase (where the stress response would be 90° out of phase with the
strain wave). Instead it exhibits viscoelastic behavior with a phase lag
somewhere between 0° and 90°. The amplitude of the dynamic
stress and the degree to which
is in phase with the applied dynamic
strain measures the elastic response, storage modulus (E'), and
is affected by the absorption of energy through the reversible deformation of
chemical bonds and breaking of ionic bonds within and between silk fibroins.
The amplitude of the dynamic stress and the degree to which
is out of
phase with the applied dynamic strain measures the viscous response, loss
modulus (E''), which is affected by the transformation of
kinetic energy into heat due to friction within and between fibroins, as well
as the permanent breaking of chemical bonds. A classic analogy to these two
dynamic variables is that of a dropping ball. The height to which the ball
bounces is proportional to its storage modulus while the difference between
the height of the bounce and the height from which it was dropped is
proportional to the loss modulus. Dynamic strain (
t) is
calculated as:
![]() | (3) |
|
where o is the dynamic strain amplitude,
is the
angular frequency, and t is time. Dynamic stress
(
t) is calculated as:
![]() | (4) |
where o is the dynamic stress amplitude,
is the
angular frequency, t is the time, and
is the phase lag. The
dynamic stiffness of the material (E*) is defined as:
![]() | (5) |
This allows the dynamic stress, t, to be expressed as:
![]() | (6) |
which can be rewritten as:
![]() | (7) |
The storage modulus (E') is E*cos
while the loss modulus (E'') is
E*sin
. Finally, the ratio of energy stored to
energy lost, the loss tangent (tan
), is calculated as:
![]() | (8) |
where E'' is the loss modulus and E' is the
storage modulus. It is important to note that the loss tangent (tan)
can vary as a function of changes in how fibers store energy elastically, how
fibers dissipate energy as heat, or both. In other words, an increase both in
loss and in storage modulus can result in either a decrease or increase in the
loss tangent (Fig. 2B).
CDA is distinguishable from more traditional dynamic mechanical analysis (DMA) of material properties because CDA measures storage and loss modulus as a continuous function of extension. In contrast, DMA measures storage and loss modulus at a constant extension but across a range of changes in oscillation frequencies or temperatures. DMA is performed at a constant static strain that is quite small, typically 1-2%, and usually within the elastic limit of polymers. However, spider silks can stretch well beyond this 1-2% during ecological function and their viscoelastic nature makes it likely that their mechanical behaviors would change as a function of extension such that spider silks would not display the same mechanical behavior at different strains. Thus, it is important to examine the mechanical behavior of silks across a wide variety of strains. For this study, we used a dynamic strain oscillation with a frequency of 20 Hz and dynamic force amplitude of 4.5 mN, resulting in a maximum dynamic displacement of 45 µm.
Statistical analysis
We used one-way analysis of variance (ANOVA) to compare thread diameter,
Young's modulus, extensibility, ultimate strength, and toughness across the
three types of silk that we sampled. We used linear regression to test for
relationships between stress and strain within each type of silk, as well for
relationships between cross-sectional area of fibers and each of the four
quasistatic parameters that we measured. One-way ANOVAs were also used to
compare the initial, final, and maximum values of loss tangent, as well as
loss tangent at the yield point and the true stress and true strain values at
the maximum loss tangent across silk types.
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Results |
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Quasistatic properties of silks
The stress-strain characteristics of all three types of silk were
qualitatively similar. These included an initially stiff modulus of 9-11 GPa
for the first 2% of strain. The fibers then reached a `yield region'
where mechanical behavior varied from only a slight strain softening
(particularly for forcibly silked samples) to a distinct drop in stress.
Subsequently, this yield region was followed by a strain hardening that was
largely linear and continued until failure of the fiber
(Fig. 4). Occasionally, sudden
slight drops in stress were sometimes exhibited by fibers near failure
(Fig. 4). The stress-strain
curves quickly recovered to their previous stiffness after these drops.
Furthermore, these drops only occurred when testing multistranded fibers.
Therefore, we interpret them as areas where fibers were snapping around one
another, suddenly loosening and then regaining stress. The mechanical
properties of fibers exhibiting this `noise' were not noticeably different
from tests where these drops did not occur.
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There was significant variation among silk types for all five quasistatic mechanical parameters (Fig. 5; one-way ANOVAs, all P<0.05). Scaffolding silk was slightly stiffer and less extensible than gumfooted silk, but did not differ in ultimate strength or toughness. Forcibly silked major ampullate fibers exhibited greater differences from the other two types of silk. These fibers were less extensible and had lower toughness than gumfooted and scaffold silks. The modulus of forcibly silked major ampullate silk was also slightly higher than that for gumfooted silk and ultimate strength was lower than that for scaffold silk.
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Extensibility and ultimate strength were positively associated with one another for both scaffold and gumfoot silk, but not for pulled major ampullate silk (Fig. 6). Variation in quasistatic mechanical properties of silk was largely independent of cross-sectional area, except for extensibility (Fig. 7). Thicker fibers had greater extensibility for both gumfooted and pulled major ampullate fibers (P<0.05). A similar positive, but non-significant trend was exhibited by the scaffold thread in relation to thread diameter.
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Dynamic properties of silks
The storage modulus of all three types of silk changed in a non-linear
fashion as fibers were strained (Fig.
8). Storage modulus was initially flat or decreased slightly to a
low around the yield point of the fiber, before increasing in a relatively
linear fashion as the fibers were subsequently strained to failure. In
contrast, the loss modulus of all fibers increased sharply during the first
2-5% of strain, exhibited a rapid drop near the yield point, and then
increased linearly at a lower slope until failure.
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Pulled major ampullate fibers exhibited a higher storage modulus and a lower loss modulus than either scaffold or gumfoot silk. For all types of silk, loss modulus was approximately one order of magnitude less than storage modulus, resulting in loss tangent values that ranged from 0.03-0.07 initially and then increased to a maximum of 0.12-0.20 before decreasing again (Figs 8, 9). The dynamic behavior of scaffold and gumfooted threads was similar to one another, while pulled major ampullate silk differed significantly from both scaffold and gumfooted silks for all parameters except strain at maximum loss tangent (Tukey's HSD tests for unequal sample sizes, P<0.05). In particular, initial loss tangent was approximately 50% lower for pulled major ampullate silk.
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Structure and properties of gumfooted lines
Gumfooted lines consisted of two pairs of fibers, one of which was
approximately 25% thicker than the other
(Fig. 3). Gumfooted lines were
coated with aggregate glue secretions along their lower 5-10 mm and the
thinner pair of fibers was joined to the thicker pair of fibers approximately
1-3 cm above this gluey foot (Fig.
10). This connection consisted of many fine fibers and the thinner
pair of gumfooted fibers was cut just about this connection. The remaining
portion of these thinner fibers could be seen curled up at the connection of
the thicker fiber pair to the scaffolding of the web.
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Two juvenile L. hesperus were observed while constructing gumfoots in the field (Riverside, CA, USA). In each instance, the spider rapidly descended to the substrate upon a dragline. The spider then turned around so that it was facing up toward the web and set an attachment to the substrate, while grasping the initial dragline in its front leg. Then it moved its spinnerets along the distal portion of the gumfoot, presumably laying the second fatter dragline and aggregate glue. With its hindleg still on the substrate, the spider briefly touched its chelicerae to the original dragline, cutting the original dragline. The spider then rapidly ascended the thread.
The gluey region of the gumfooted fiber had a greater extensibility, ultimate strength, and toughness relative to the adjacent region of dry gumfooted fiber (Fig. 11; paired t-tests, t=3.6-6.2, d.f.=20, P<0.0025-0.00001). Young's modulus was much lower (t=8.3, d.f.=20, P<0.000001) for the viscid region of the gumfooted thread. The dynamic characteristics of the viscid and dry portions of the gumfooted fibers differed most dramatically from one another during the first 20% of strain and then tended to converge with each other (Fig. 12). Storage modulus of the viscid portion of the fiber was initially four times lower than that of the dry portion and subsequently increased steadily rather than showing the drop in storage modulus over the first 2-3% of strain that characterized dry fibers. Loss modulus was similar between the wet and dry gumfooted samples, except within the initial elastic region. Dry portions of gumfooted fibers exhibited a rapid increase in loss modulus up to the yield point while wet portions had a higher initial loss modulus that resulted in a relatively linear increase in loss modulus throughout fiber extension.
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Discussion |
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Our mechanical data contrast with those obtained for scaffolding silk of
L. hesperus webs by Moore and Tran
(1999). They reported that
silk from the sheet and supporting structure of L. hesperus webs was
mechanically distinct from orb weaver major ampullate silk because it had a
`j' shaped stress-strain curve with an extremely high compliance over the
first 3-5% of strain, rather than the high stiffness initially exhibited by
orb weaver major ampullate silk (see Fig.
4). We never found silk with the initial high compliance behavior
described by Moore and Tran
(1999
), despite sampling
fibers from all regions of the cobwebs from the same species of spider from
the same geographic region. Both studies tested silks of similar ages (3-14
days) and used similar strain rates (
1-2% s-1) so that
methodological differences per se seem unlikely to account for the
discordance between our studies. Instead, one potential difference is in how
we interpreted when fibers were fully tensed, which delimits the beginning of
the tensile test (i.e. the zero point of strain). Moore and Tran's fibers may
not have been fully tensed at the start of their data collection, such that
the initial 5% of strain with high compliance in their study actually
represented data taken from fibers that were only partially under tension. In
fact, Moore and Tran's stress-strain curves qualitatively resemble those of
our study, and most other mechanical analyses of major ampullate silk from
orb-weaving spiders, if the tests began at `5% strain', where they seem to
show the initially stiff elastic region that characterizes major ampullate
silk.
Casem et al. (1999) also
argued that L. hesperus scaffolding silk was a unique material. They
found that silk collected directly from cobwebs had an amino acid composition
that did not correspond to any previously characterized silk composition,
while the amino acid composition of dragline silk obtained through forcible
silking of black widows was similar to that of orb weavers. Yet, for 10 of the
11 amino acids Casem et al.
(1999
) studied, including all
amino acids constituting more than 1.5% of the silk proteins, L.
hesperus scaffolding silk and L. hesperus dragline silk were
more similar to one another than either was to dragline silk of orb weavers.
Thus, it does not appear that the amino acid composition of black widow
scaffold silk differs substantially from black widow dragline or orb weaver
major ampullate silk. Instead, the similarity in amino acid composition seems
to support the conclusion that L. hesperus cobweb silk and dragline
silk are identical materials. This is also congruent with our finding that the
mechanical behavior of sheet/supporting threads and forcibly silked major
ampullate fibers from L. hesperus were mechanically similar. We
therefore feel secure in concluding that the origin of most fibers within the
sheet and supporting structure of L. hesperus cobwebs is the major
ampullate gland.
It should be noted that Casem et al.
(1999) found that solubilized
proteins from black widow dragline and scaffolding silk migrated differently
on an SDS-PAGE gel. This suggests that perhaps there might be differences that
persist through the electrophoresis process in how the major ampullate silk
molecules from draglines and scaffolds amalgamate with one another.
Alternatively, the different banding patterns may be due to the presence of
silk from other glands, such as from the pyriform glands, which are used to
affix the network of major ampullate fibers to one another and would have been
included with the major ampullate fibers in the scaffold/sheet of the
cobweb.
The orb-weaving ancestors of theridiids constructed webs using a framework
of major ampullate threads and a capture spiral of flagelliform fibers coated
with aggregate glue droplets (Coddington
and Levi, 1991; Griswold et
al., 1998
). Thus, as the adhesive capture element of the cobweb,
the sticky gumfooted thread is functionally similar to orb web capture spiral
(Blackledge et al., 2005b
).
However, the glandular origin of the silk used to construct the gumfooted
capture threads of cobwebs has been uncertain and hypotheses have included
major ampullate, minor ampullate, and flagelliform glands
(Benjamin and Zschokke, 2002
;
Coddington, 1986
). We found
that sticky gumfooted lines are clearly not mechanically equivalent to
flagelliform silk because even the viscid regions of sticky gumfooted threads
(Fig. 11) lack the 400% or
greater extensibility exhibited by orb weaver capture fibers
(Denny, 1976
;
Köhler and Vollrath,
1995
; Opell and Bond,
2001
). Other researchers have suggested that gumfooted threads are
composed of one thicker pair of major ampullate fibers and a second thinner
pair of minor ampullate threads (Benjamin
and Zschokke, 2002
). We did find that one pair of fibers within
the gumfooted thread was always thicker than the other. However, that
difference was within the range of variation for black widow major ampullate
silk as suggested by scaffolding and forcibly silked fibers
(Fig. 3), while the diameter of
12 minor ampullate fibers that we obtained from L. hesperus using the
same forcible silking technique described above were all much smaller than
either gumfooted fibers or forcibly silked major ampullate fibers (mean
± S.E.M. = 1.1±0.1 µm for
minor ampullate fibers compared with Fig.
3). Our mechanical data also suggest that the gumfooted fibers are
all composed of major ampullate silk because the dry region of the gumfooted
threads was virtually identical to that of the rest of the cobweb. In
contrast, the mechanical performance of the 12 minor ampullate fibers that we
obtained through forcibly silking was strikingly different. In particular,
Young's modulus for minor ampullate fibers (mean ±
S.E.M. = 6.3±0.4 GPa) was about 40%
lower than that for gumfooted threads and other major ampullate fibers
(Table 1), indicating that the
crystalline structure of minor ampullate fibers was unlike that of cobweb
silks. Finally, there was little difference in the mechanical performance
between paired samples of the upper, two fiber, and lower, four fiber, dry
regions of the gumfoots (paired t-tests, P>0.05 for all
variables except tensile strength, which was significantly higher for the
upper region at P<0.05, N=15). This suggests that all
four threads are spun from the same silk proteins. Therefore, we conclude that
gumfooted threads are constructed from major ampullate silk fibers, like the
scaffolding support elements of the cobweb (see also
Blackledge et al., 2005b
).
We found that forcibly silked fibers of major ampullate silk were stiffer
and less extensible that naturally spun fibers from scaffolds and gumfoots.
This difference between forcibly silked fibers and native silks has also been
seen in orb-weaving spiders (Madsen et
al., 1999;
Pérez-Rigueiro et al.,
2003
). There are at least two potential explanations.
Anaesthetizing spiders with CO2 may alter the pH of the bodies of
spiders, thereby affecting assembly of silk polymers
(Madsen and Vollrath, 2000
). A
second possible explanation is that spiders can actively control the flow of
the silk fiber through the major ampullate spigot using an internal friction
brake. With such a mechanism, spiders may increase the amount of stress
applied to the fiber during forcible silking, which could enhance the
formation of ß-sheet crystalline regions and increase the orientation of
the amorphous fibers (Ortlepp and Gosline,
2004
). This hypothesis is supported in part by our dynamic data.
Forcibly silked fibers had a higher storage modulus and a lower loss modulus
than native silks. Both of these differences are consistent with an increased
orientation of molecules within the fiber.
Dynamic material properties
Spider silk exhibits an extraordinary capacity to dissipate energy,
relative to many other materials (Denny,
1976). Table 2 presents comparative data from a variety of natural and synthetic materials.
These data were extracted from DMA studies, which were conducted across a
range of temperatures and dynamic oscillation frequencies at very low,
constant static strains. Because these DMA data are most comparable to the
data that we obtained for spider silk during the initial Hookean region, we
chose to present the storage modulus and loss tangent at 1% strain.
Temperature can greatly influence the dynamic performance of materials such
that we present dynamic data from these other studies only at temperatures
near 20°C, because that is the temperature at which we tested our spider
silk. It is readily apparent from Table
2 that black widow major ampullate spider silk has a storage
modulus that is much higher than most other materials. Moreover, the loss
tangent for spider silk is approximately an order of magnitude higher than
other materials, except for rubber and elastin, both of which have very low
dynamic stiffness. Thus, spider silk has a unique combination of high storage
modulus and high loss tangent that results in an immense capacity to dissipate
kinetic energy.
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The dynamic mechanical behavior of black widow silk is congruent with
existing hypotheses about the structure of major ampullate spider silk at the
molecular level. Structural studies of major ampullate spider silk suggest
that it consists primarily of a matrix of amorphous polypeptide chains with
small crystals, formed from ß-pleated sheets, embedded within that matrix
(Gosline et al., 1999;
Xu and Lewis, 1990
). Molecular
models of major ampullate spider silk suggest that these crystals play an
essential role in providing spider silk with its enormous strength by
producing thin regions of locally high modulus that crosslink amino acid
chains within the amorphous matrix
(Termonia, 1994
). This locally
high modulus ensures that the crystalline ß-sheets undergo little
extension as silk fibers are strained. Therefore, it is the amorphous region
of the fiber in which most conformational changes are expected to take place
as silks are stretched (Warwicker,
1960
). It is hypothesized that the initial high stiffness of silk
fibers during the first 2% of extension (
10 GPa) is caused by the
presence of hydrogen (H) bonds that form between polypeptide chains within the
amorphous region. The ability of H-bonds to reform accounts for the high
elasticity of this Hookean region. After approximately 2% strain, these
H-bonds rapidly break thereby greatly increasing the mobility of polypeptide
chains within the amorphous region, which produces a rapid decrease in
stiffness (i.e. `yield'). Subsequent to that yield point, the amorphous chains
gradually extend until they are aligned with the fiber axis and the covalent
bonds within individual silk fibroins ultimately fail. Atomic force microscopy
has corroborated this hypothetical increase in orientation of fibrils during
fiber extension for L. hesperus scaffolding silk
(Gould et al., 1999
).
Throughout fiber extension, the ß-sheets are thought never to strain
beyond 2-3% such that the covalent bonding between alanine residues that forms
those sheets do not break (Termonia,
1994
).
Our dynamic data are consistent with this molecular model of silk
(Termonia, 1994). We found
that the loss tangent rapidly increases during the first 2-3% strain and
reaches a maximum at the yield point (Fig.
8). This was due to an initial drop in storage modulus that was
followed by a rapid increase in loss modulus. This decrease in storage modulus
is predicted by the breaking of H-bonds during fiber extension within the
elastic region, while the increase in loss modulus is consistent with the
frictional heat generated as the mobility of the amorphous chains increases
during yield. After the yield point, storage modulus increases as amorphous
chains begin to align along the axis of extension while loss modulus increases
due to frictional forces. The loss tangent then decreases as individual
amorphous chains are strained beyond their maxima and the covalent bonds
holding those peptide chains together then rupture.
The change in dynamic behavior of gumfooted lines coated with aggregate
glue is also consistent with hypothesized molecular models of major ampullate
silk. Aggregate glue contains water molecules that hydrate silk fibers
(Vollrath and Edmonds, 1989;
Vollrath et al., 1990
). This
hydration disrupts the hydrogen bonding between amorphous chains thereby
decreasing the stiffness of hydrated fibers. Disruption of hydrogen bonding is
consistent with the reduced storage modulus that we found for viscid gumfoot
silk relative to dry gumfoot (Fig.
12). Furthermore, viscid regions of the gumfooted lines lack the
steep increase in loss modulus exhibited by dry fibers because the amorphous
chains can already move more freely prior to the yield point. This results in
a loss tangent that is initially 400% higher for viscid silk than for dry silk
(Fig. 12). Subsequently, loss
tangent then rapidly converges for the two types of silk after 15-20% as
energy absorption is affected primarily by the physical extension of amorphous
chains and the permanent breaking of covalent bonds, which is unaffected by
hydration.
Broader implications
We found that the material properties of the silk used to construct cobwebs
are strikingly similar to those for orb-weaving spiders
(Table 1). Recent analysis of
silk cDNA and gene sequences has shown that Latrodectus geometricus,
a widow that is closely related to L. hesperus
(Garb et al., 2004), has
coding sequences for proteins that resemble the two primary constituents of
major ampullate silk from orb-weaving spiders
(Gatesy et al., 2001
).
Furthermore, cDNAs generated from L. hesperus major ampullate silk
glands (Lawrence et al., 2004
)
show strong congruence with both the L. geometricus and orb weaver
major ampullate silk cDNAs.
Current phylogenetic hypotheses for relationships within the Araneae
suggest that cobweb spiders are derived from orb-weaving spiders
(Coddington and Levi, 1991;
Griswold et al., 1998
). Thus,
the simplest explanation as to why orb web and cobweb weaving spiders share
mechanical and biochemical similarities in major ampullate silk is because of
their common ancestry. But the question then arises as to what could underlie
the stabilizing selection that has maintained the silk characteristics of
these taxa that are ecologically diverse and last shared a common ancestor
>130 million years ago (Penney,
2002
; Selden,
1990
). There are several potential explanations for this
conservation. One possibility is that despite significant differences in web
architecture and the physical challenges of capturing pedestrian versus aerial
prey, there may be similar selection acting upon the mechanical function of
cobweb and orb web silks. Recent empirical studies have shown that the
mechanical properties of orb weaver major ampullate silk may be closely tuned
to their function as lifelines for spiders as they fall
(Garrido et al., 2002
;
Osaki, 1996
). Because all true
spiders (suborder Araneomorphae) have major ampullate spigots
(Platnick et al., 1991
) and
typically spin draglines when moving through the environment, this suggests
that selection for a functional dragline may have played a greater role in
shaping the mechanical properties of major ampullate silk than the demands of
capturing prey in silken nets. Future studies should examine the quasistatic
and dynamic mechanical properties of major ampullate silk from diverse true
spiders to discover the phylogenetic and ecological limits to the similarities
that we found between the silks spun by cobweb and orb web-weaving
spiders.
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Acknowledgments |
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