A zipper network model of the failure mechanics
of extracellular matrices
Michael C. Rittera, Rajiv Jesudasona, Arnab Majumdara, Dimitrije Stamenovic ´a, Jo Ann Buczek-Thomasb, Phillip J. Stoneb,
Matthew A. Nugentb, and Be ´la Sukia,1
aDepartment of Biomedical Engineering, Boston University, 44 Cummington Street, Boston, MA 02215; andbDepartment of Biochemistry, Boston University
School of Medicine, 715 Albany Street, Boston, MA 02118
Edited by Robert Langer, Massachusetts Institute of Technology, Cambridge, MA, and approved December 2, 2008 (received for review August 26, 2008)
Mechanical failure of soft tissues is characteristic of life-threaten-
ing diseases, including capillary stress failure, pulmonary emphy-
sema, and vessel wall aneurysms. Failure occurs when mechanical
forces are sufficiently high to rupture the enzymatically weakened
extracellular matrix (ECM). Elastin, an important structural ECM
protein, is known to stretch beyond 200% strain before failing.
However, ECM constructs and native vessel walls composed pri-
marily of elastin and proteoglycans (PGs) have been found to fail
at much lower strains. In this study, we hypothesized that PGs
significantly contribute to tissue failure. To test this, we developed
a zipper network model (ZNM), in which springs representing
elastin are organized into long wavy fibers in a zipper-like forma-
tion and placed within a network of springs mimicking PGs. Elastin
and PG springs possessed distinct mechanical and failure proper-
ties. Simulations using the ZNM showed that the failure of PGs
alone reduces the global failure strain of the ECM well below that
of elastin, and hence, digestion of elastin does not influence the
failure strain. Network analysis suggested that whereas PGs drive
the failure process and define the failure strain, elastin determines
the peak and failure stresses. Predictions of the ZNM were exper-
imentally confirmed by measuring the failure properties of engi-
neered elastin-rich ECM constructs before and after digestion with
trypsin, which cleaves the core protein of PGs without affecting
elastin. This study reveals a role for PGs in the failure properties of
engineered and native ECM with implications for the design of
elastin ? strain ? stress ? trypsin
pulmonary emphysema (2), vessel wall aneurysms (3, 4), and
prosthetic heart valve failure (5). Whereas emergency surgery
can be life saving for aneurysm patients (6), there is no cure for
emphysema (7). These diseases are caused by various changes in
the extracellular matrix (ECM) that lead to a weakening of
ECM. A better understanding of the structure of the ECM, and
how its components contribute to functional behavior (8), is
necessary to provide insight into the development and progres-
sion of these diseases and will also be important if future
tissue-engineered constructs are to be implanted in the body.
Elastin, collagen, and proteoglycans (PGs) are the principle
components that form the complex structural network of the
and collagen are fibrous proteins capable of carrying loads and
resisting tension (10, 11). PGs make up the gel in which elastin
and collagen fibers are embedded and are necessary for the
of the ECM has major effects on its mechanical (9, 13–15) and
failure properties (3, 16–21).
Independently, 2 groups have obtained similar surprising
results related to failure of tissues composed primarily of elastin
and PGs: Black et al. (17), using tissue-engineered ECM con-
structs, and Goodall et al. (22), studying the inferior mesenteric
vein of patients with abdominal aortic aneurysm. Both groups
issue failure is characteristic of several life-threatening dis-
eases, including capillary stress failure in the lung (1),
found that elastin degradation led to a significant decrease in the
maximum stress during a failure test (peak stress). Surprisingly,
independent of digestion, the strains at which these tissues failed
(failure strain) were in the range of 60–120%, much lower than
the known failure strain of elastin, which is at least 200% (9). If
elastin fibers percolate, i.e., reach uninterrupted from one end
of the tissue to the other (23), one would expect the failure strain
of the composite to be near that of elastin. Furthermore, in both
cases, elastin degradation had no effect on the failure strain.
These findings suggest that something other than elastin must
contribute to failure.
We hypothesized that PGs contribute significantly to tissue
failure. Specifically, if elastin does not form a percolating network,
the failure of PG bridges between the elastin fibers should reduce
the global failure strain of the ECM below that of elastin. To test
this hypothesis, we developed a spring network model, the zipper
network model (ZNM). The predictions of ZNM were then com-
pared with measurements made on engineered ECM constructs
containing mostly elastin and PGs before and after digestion with
trypsin, a protease known to cleave the core protein of PGs (24)
with little effect on elastin (5).
Sample images of the ZNM being stretched during a failure test
are shown in Fig. 1 Left. In the undeformed network, the elastin
fibers, composed of a contiguous set of elastin springs, are wavy
and arranged in a zipper-like formation. During stretch, these
in the network (see animation in supporting information (SI)
Movie S1). The individual elastin and PG springs fail when they
experience 200% and 0.5% local strain, respectively. The max-
imum strain on PGs increases first nearly linearly with global
strain (Fig. 2). Above 35% global strain, the maximum strain on
PGs fluctuates near 0.5% as more and more PGs reach failure,
whereas the fraction of failed PGs gradually increases to 45%. It
is thus the failure of the PG bridges that eventually leads to a
complete network failure at ?100% global strain.
To mimic elastin digestion, half of the elastin fibers were cut
into 2 fragments. This resulted in an elimination of 3.1% of the
elastin springs from the network. Fig. 3A compares the stress–
strain curves for a control and an elastin-digested failure simu-
lation. The tests were repeated for 7 realizations of the random
network. The peak stress significantly decreased by ?40% (P ?
0.001), whereas the failure strain of the network was 109 ? 9%
and did not change with digestion (Fig. 3B).
Author contributions: M.A.N. and B.S. designed research; M.C.R., R.J., and J.A.B.-T. per-
formed research; P.J.S. and M.A.N. contributed new reagents/analytic tools; A.M. and D.S.
analyzed data; and M.C.R. and B.S. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
1To whom correspondence should be addressed. E-mail: email@example.com.
This article contains supporting information online at www.pnas.org/cgi/content/full/
© 2009 by The National Academy of Sciences of the USA
January 27, 2009 ?
vol. 106 ?
no. 4 ?
The effects of graded digestion of PGs on the stress–strain
curves of the network are illustrated in Fig. 4. With progressive
elimination of PGs, the curves shift down and to the right. The
stiffness, defined as the local slope at 20% strain, decreased
linearly with the amount of PGs eliminated (Fig. 4 Inset). Table
1 summarizes the failure data for several digestion groups. The
model predicts that the removal of 60% of PGs decreases the
peak stress and the failure strain by only 29% and 15%,
respectively (P ? 0.05).
The ?30% decrease in peak stress at 60% PG removal is a
result of leaving dangling pieces of elastin that can no longer
contribute to the stress. This is similar to the case when the
elastin fibers are cut. Table 2 shows the total elastic energy of the
springs as well as the percentage energy carried by elastin when
the majority of the energy is carried by the elastin fibers. As PGs
are removed, the absolute energy carried by elastin decreases,
and this is the main cause of the decrease in total network energy
and peak stress. Furthermore, although the elastin digestion
results in a much larger decrease in total energy than PG
digestion, the energy carried by the elastin is still near 90%.
of the ZNM being stretched to various strains. The elastin fibers are drawn as
thick lines and the PGs as thin lines. Note that the elastin does not percolate
across the network. The color scale shows the relative forces on each spring.
(Right) Phase-contrast images of a region of a tissue sample undergoing
failure taken at strains comparable with those in the network model on the
Failure of the ZNM and an engineered ECM construct. (Left) Images
on the PGs (dashed line) as a function of global strain during a failure test of
the ZNM. Curves represent the average of 7 simulations.
of the ZNM. (A) Sample stress–strain curves for model simulations with and
without simulated elastase digestion. Peak stress and stress at failure, or
failure stress, are indicated by arrows. (B) Failure data comparing control (n ?
7) and elastase (n ? 7) digestion simulations. Digestion leads to a significant
drop in peak stress but no change in failure strain. Stress is in arbitrary units.
*, P ? 0. 001.
(Inset) Stiffness of the model evaluated at 20% strain for the various PG
digestion simulations. Stress and stiffness are in arbitrary units.
www.pnas.org?cgi?doi?10.1073?pnas.0808414106Ritter et al.
Sensitivity analysis demonstrates that both the peak stress and
the failure strain of the network linearly increase with the failure
strain of the PG springs (see Fig. S1) while all other model
parameters were held constant. These failure parameters also
linearly depend on the spring constant k of the PG springs (see
Microscopic images of a region of an engineered ECM sheet
during failure test are compared with the failure of the model in
Fig. 1. The quantitative predictions of the model (Fig. 4) are
compared with experimentally measured stiffness and failure
parameters in Fig. 5. Compared with controls, the stiffness
After 30 min, the control samples did not change, whereas the
stiffness in trypsin-digested samples dropped significantly to
?75–80% of baseline. The trypsin digestion led to 31% and 29%
drop in peak stress and failure strain (Fig. 5 Inset; P ? 0.05).
Biochemical analysis showed that the trypsin digestion elimi-
nated 65% of chondroitin sulfate and 45% of heparan sulfate
from the samples.
We have developed a network model, the ZNM, to account for
the structural roles PGs play in the mechanical and failure
properties of elastin-rich ECM. The main findings are as follows.
(i) The ZNM reproduces the essential stress–strain and failure
properties of the ECM, such that the network fails at ?100%
strain while keeping elastin at its known failure strain of 200%.
(ii) The ZNM also accounts for the previously reported effects
of elastin digestion on the failure properties of engineered ECM
sheets (17) and native vessels (22). (iii) The predictions of the
ZNM were tested by using mechanical and biochemical assays
after PG digestion. Of particular importance is the fact that,
whereas in the above studies, elastin digestion did not alter the
failure strain, PG digestion in this study did reduce the failure
strain both in the experiment and the simulations. (iv) Finally, an
important result of the network analysis is that elastin carries the
load and determines the peak stress, whereas PGs reduce the
failure strain of the network. Although many models have been
proposed to mimic ECM mechanics (25–28), and the importance
of PGs and their interaction with fibers have been recognized
(29–31), these models have not been used to account for the
can be attributed to 2 features: its inclusion of separate failure
elastin fibers into a particular formation in which fibers overlap
The mechanism of failure of the ZNM is a gradual straight-
ening of the elastin fibers, followed by pulling them out of the
matrix by successively breaking the PG bridges, a previously
uncharacterized network phenomenon. In an attempt to relate
the ZNM to the composition and structure of the ECM, we
fibers per ?m2) from electron microscopic images (32). We also
measured the total glycosaminoglycan (GAG) content of 3 ECM
constructs (?1 ?g/cm2) using elastase digestion (33), followed by
dimethylmethylene blue assay (34). Although various PGs have
very different numbers of GAG chains (35), for simplicity, we
assume that on average, there are 10 GAGs on each PG. Taking
area is ?1,300 PGs per ?m2. This calculation is, however, based
on dry weight without taking hydration into account. Elastin is
not sensitive to hydration (36), whereas PGs in solution inflate,
and we estimated that hydration can increase their volume at
least by a factor of 10 (37). Therefore, an elastin fiber would be
surrounded by ?10–100 hydrated PGs, which is the same order
of magnitude used in the ZNM.
Although there are no simple ways to selectively eliminate all
of the various PGs from the ECM without altering the levels of
other proteins, we chose trypsin digestion because trypsin is
known to digest the protein core of PGs (24). Trypsin cleaves
after arginine and lysine residues (38), also found in elastin. To
ensure that elastin was not degraded by trypsin, we measured the
amount of elastin in the ECM samples with an ELISA after
trypsin digestion at increasing concentrations up to 33 times that
used in the mechanical tests. We found no effect of trypsin on
elastin levels, suggesting that the mechanical changes in Fig. 5
were not the result of elastin digestion but were instead due to
elimination of PGs.
To compare the modeling results of PG digestion (Table 1) to
experimental data (Fig. 5), we determined the relative amounts
of the various GAGs in these ECM sheets using35SO4radiola-
beling and cationic nylon filtration (39) and found that ?85% of
the GAGs in these ECM sheets is chondroitin sulfate. Thus, the
total amount of GAGs eliminated during trypsin digestion was
time for control (n ? 11) and trypsin-digested (n ? 13) engineered ECM
constructs. Values are normalized to the baseline at time 0. (Inset) Peak stress
and failure strain for the control and trypsin digested groups.*, P ? 0.05.
The mean and SD of stiffness measured at 20% strain as a function of
Table 1. Failure data for control networks and networks with
SimulationPeak stressFailure strain, %
PGs digested, 30%
PGs digested, 40%
PGs digested, 50%
PGs digested, 60%
3.96 ? 0.14
3.36 ? 0.19*
3.08 ? 0.14*†
2.97 ? 0.20*†
2.80 ? 0.35*†
108.6 ? 9.0
93.6 ? 5.6*
94.3 ? 7.3*
93.6 ? 6.9*
92.6 ? 6.4*
For all simulations, the number of random networks used was 7.*, signif-
digested (P ? 0.05).
Table 2. Mean total elastic energy of the springs in the network
for various simulations and the percentage of contribution
of elastin to the total energy
PGs removed, 30%
PGs removed, 60%
The total energy (in arbitrary units) does not include bond bending (more
details in Table S1).
Ritter et al.
January 27, 2009 ?
vol. 106 ?
no. 4 ?
61%, and hence the experimental data should be compared with
the simulation results in Table 1 at 60% PG removal. Note that
during simulated digestion, the 60% is removed randomly,
whereas during stretch (Fig. 2), 45% of PGs break in a correlated
manner as a result of avalanching (see Methods).
The elastin-related model parameters were chosen based on
literature (9) and our previous study (19). The failure properties
after elastin digestion (17). These model parameters were then
used to a priori predict the effects of trypsin digestion. The drop
in peak stress (Table 1) is in excellent agreement with experi-
ments (Fig. 5). However, the failure strain and its drop after
trypsin digestion are lower in the model. The likely reason is that
the failure strain in our previous study (17) was higher than in
this study because of the variability between different batches of
the cell culture-based ECM sheets. Nevertheless, the peak stress
and failure strain of the model are linearly related to the failure
strain (see Fig. S1) and the spring constant of the PG springs
(Fig. S2). Hence, it is possible to find parameter combinations
such that the model simultaneously matches all of the measured
properties reported here.
The PG failure threshold used in this study may seem unre-
alistically low. Redaelli et al. (40) suggest a much higher failure
strain for PGs in tendons. However, there are several mecha-
nisms that can contribute to an increased network failure strain.
For example, one can find another ratio of the spring constants
for elastin and PGs such that the PG failure threshold can be
much higher. Because these parameters are interdependent, it is
difficult to predict the precise physiological values for each
because of the lack of relevant experimental data.
Elastin fibers in the ZNM are organized, much more so than in
real tissue. Because of this organization, the model produces
realistic failure mechanics only when stretched in the direction
of the fibers. The elastin fibers do not percolate, and there is no
vertical cross-section composed only of PGs. Hence, failure
occurs by pulling the elastin fibers out of the PG matrix.
However, if the ZNM was stretched in the direction perpendic-
ular to the fibers, its failure strain would be equal to that of the
PG’s, because there are horizontal cross-sections composed
purely of PGs. It is therefore expected that if the fibers had
random orientation, the failure strain of the PGs would have to
be between their current value of 0.5% and the failure of the
whole network, ?100%, which would provide more realistic
estimates of PG failure.
Fiber alignment was further investigated through additional
simulations that include 2 elastin fibers initially not aligned with
the PG network does not percolate (Fig. 6A). As the network is
stretched, the PGs begin to break, and the elastin fibers show
increasing alignment with the direction of strain (Fig. 6B). This
network has a failure strain of ?70% (see animation in Movie
S2). The decrease from the 100% failure strain of the ZNM is
due to several factors. First, because PGs are initially more
aligned with the direction of strain, they will also experience a
larger local strain for any given global strain. This again could
indicate that the actual failure strain of PGs is higher than the
one chosen for the ZNM. Second, this simulation possesses a
much smaller elastin-to-PG ratio and, hence, more springs in the
in this simulation were longer than those in the original ZNM,
they are directly connected by fewer PGs. Hence, fewer PGs
share the same load, and hence, there is an increased strain on
individual PGs. Thus, an important limitation of the ZNM is the
lack of random orientation of fibers, which leads to an under-
estimation of the failure strain of PGs. The ZNM was con-
structed as a 2D model because the thickness-to-width ratio of
the ECM sheets that we used was ?0.005. It is difficult to
construct a network with random orientation of fibers in 2D, a
limitation that can be overcome in 3D models. Thus, apart from
the limitation of fiber orientation, the ZNM is a realistic model
of the failure process, and the model’s results suggest a previ-
ously uncharacterized role for PGs: Because it is the PGs that fail
The model also suggests that elastin plays an important role
structurally and in the mechanics of elastin-rich constructs or
native tissue. Elastin fibers carry the bulk of the load when
tension is applied, and thus elastin determines the maximum
stress that the tissue can carry before failure. This conclusion is
also based on the fact that removing only 3.1% of the elastin
springs produced the greatest decrease in peak energy of all of
the model simulations (Table 2).
Besides the role identified for PGs in tissue failure, our results
have implications for tissue engineering. In designing tissue-
engineered materials, it is important to match the mechanical
properties of the native tissue if the replacement tissue is to
function properly in the body. However, the replacement tissue
should also be able to withstand the naturally occurring stresses
and strains even during diseases with proteolytic activity. Our
results now provide an understanding of what components and
organizational features of the ECM determine these properties
and hence may offer a rational basis for future design of
engineered materials with target functional properties.
Network Model. The model consists of 286 linear springs accounting for the
stiffness of elastin and PGs combined into a hexagonal lattice, with pin joints
connecting the springs. The network also contains torsional springs, which
resist angular rotation of the springs around the pin joints. The total elastic
energy, E, of the network is given by E ? 1/2 ? ?k?l2? b??2?, where ?l
is the change in length of the spring from its stress-free initial length, k is the
spring constant, b is the angular spring or bond bending constant, and ?? is
the change in angle between 2 springs from the stress-free initial angle. The
summation runs through all linear and bond-bending springs. Bond bending
resists the springs from aligning with the direction of strain and is related to
the compressibility of the PGs and possibly the bending stiffness of elastin
During the simulations, the left boundary was fixed; the right boundary
was moved in small steps to mimic stretching, whereas the top and bottom
boundaries together with internal nodes were free to move. The network
configuration was found by minimizing E by using simulated annealing (41).
amount. If the change in total energy (?E) was negative, the new configura-
tion was accepted, otherwise it was accepted based on the probability P ?
until ?E/E remained lower than a threshold for 10 iterations. Stress was
calculated at each strain by numerical differentiation of E (42).
of 0% and 65% strains. Note that at 0% strain, the fibers are not aligned with
the direction of strain.
Images of a network that contains 2 elastin fibers at network strains
www.pnas.org?cgi?doi?10.1073?pnas.0808414106Ritter et al.
ZNM. In the ZNM, elastin and PG springs have k values of 6 and 2 and strain
failure thresholds of 200% and 0.5%, respectively. The bond-bending con-
of the ZNM, these constants have arbitrary units. The springs are arranged
such that there are long fibers of elastin springs that are embedded in a
network of PG springs (Fig. 1). Note that the elastin fibers do not percolate
across the tissue; instead, they reach ?3/4 of the way across and overlap from
opposite sides creating a ‘‘zipper-like’’ formation. This topology, selected
after preliminary testing with various configurations, was the simplest that
allowed the largest number of fibers in the network without reaching per-
‘‘cell’’ size of ?30%. The resulting node locations were saved and loaded into
place for the ZNM. The new spring lengths were then set as the initial
conditions of the network, and k was reassigned as above. This procedure
allows for an initial heterogeneity of the model mimicking intersample vari-
ability in the experiments.
Testing the ZNM. The ZNM was stretched in steps of 5% strain until failure. At
eters that produced failure parameters of the network similar to data from
actual experiments (17). Next, the ZNM was used to test a phenomenon
referred to as avalanching. This occurs when the breaking of one spring leads
to a condition that causes other springs to break without the network being
further stretched. We found that without avalanching, increasing strain step
sizes led to increasing values of peak stress and failure strain. During ava-
lanching, however, the model was insensitive to step size. Because the peak
stress and failure strain should not depend on how the stress–strain curve is
recorded, the more realistic avalanching was kept throughout. To examine
but no change in failure strain. The effects of enzymatic degradation were
certain amino acids and does not completely dissolve the protein (43). This
digestion of PGs was simulated in 2 ways. First, because of their negative
charges, GAGs draw water into the tissue (44), and they help to fill volume,
thus keeping ECM proteins from easily aligning with the direction of strain
(42). This is precisely the role of bond bending. Thus, simulations with and
without bond bending were compared. Second, PGs should also play a role in
transferring shear stress during stretch. To test this, increasing percentages of
the PG springs were removed from the network. Eliminating the PG springs
had a stronger effect on the failure properties than eliminating bond bend-
ing, and hence, only the former was used in subsequent simulations.
Tissue Culture. The ECM constructs containing elastin and proteoglycans were
from neonatal rat aortic smooth muscle cells (NNRSMC) isolated from Spra-
gue–Dawley rats, 1–3 days of age. The NNRSMCs were then grown in culture
and streptomycin (DV3.7), and 20% FBS. The samples were maintained for 6
solution was then added to the cultures that allowed the constructs to be
that described by Black et al. (17). Tissue strips, with dimensions 15 ? 5 mm,
were attached to metal plates by using cyanoacrylate glue. The plates were
then attached to steel wires connected to a force transducer (model 403A;
Aurora Scientific) and a dual force transducer and lever arm (model 300B;
Aurora Scientific). The larger-scale transducer was required for failure test
data, whereas the more sensitive transducer was used to obtain stress–strain
curves for lower strains. The 22-ml sample bath was filled with PBS, and the
at 37 °C.
Samples were preconditioned by stretching up to 25% strain 3 times,
followed by 5 min of equilibration. Baseline stress–strain curves were taken,
and 66 ?g (2.6 nmol) of porcine pancreatic trypsin (type IX; Sigma) was added
to the baths of the digestion groups. The trypsin was treated with succinyl
alanyl prolyl valyl chloromethyl ketone to inactivate any elastase contami-
nant. This trypsin preparation exhibited undiminished activity against the
synthetic trypsin substrate, tosyl arginine methyl ester (26). Stress–strain
curves from each sample were then collected every 5 min for up to 30 min.
Separate control and trypsin-treated groups were prepared in a similar fash-
ion and were stretched to failure after 30 min of digestion.
To obtain stress–strain data, samples were stretched uniaxially by using a
triangular wave, up to 25% strain at a rate of 0.75% strain per second. Strain
is defined as the displacement divided by the initial length of the sample, and
at 20% strain.
Imaging. Thickness of the samples was determined by using a laser scanning
confocal microscope (FV-1000; Olympus). Because elastin autofluoresces, no
specific labeling was necessary. The emission spectrum was mapped by using
a 488-nm argon laser excitation, and images were collected from emission
between 500 and 600 nm. Multiple stacked images with varying Z-position
were collected, and the thickness of the samples was determined as the
half-width of the mean intensity profile in the Z-direction. Thickness data
0 and 40%, at 10 locations in 1 sample per group. At 20% strain, the thickness
of the control and trypsin-digested sample was 21 ? 3 ?m and 10 ? 2 ?m,
respectively. These values were used in the calculation of stress.
Proteoglycan ELISA. NNRASMC cultures were subject to trypsin and GAGase
95% methanol and 3.7% formaldehyde. For heparan sulfate detection, con-
trol and Heparinase III-treated cells were incubated with a 1 ?g/ml solution of
heparan sulfate stub antibody (clone F69-3G10) and a 0.16 ?g/ml solution of
peroxidase-conjugated goat anti-mouse IgG. For chondroitin sulfate (CS)
detection, control and chondroitinase ABC-treated cells were incubated with
ness Corporation) and 0.4 ?g/ml solution of peroxidase-conjugated goat
anti-mouse IgG. The reactions were developed by using the TMB Microwell
Peroxidase Substrate System (KPL) and stopped with the addition of 0.5 M
sulfuric acid. The absorbance was read at 450 nm and at 570 nm (background
the signal observed with the relative enzyme lyase treatment minus that
observed without lyase.
Statistical Analysis. All data are presented as the mean ? standard deviation.
Different groups were tested with 1- and 2-way ANOVA, and a significant
difference was defined as P ? 0.05.
ACKNOWLEDGMENTS. This work was supported by National Institutes of
Health Grants HL59215 and HL088572.
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