Contribution of intermediate filaments to cell stiffness,
stiffening, and growth
Ning
Wang1 and
Dimitrije
Stamenovi
2
1 Physiology Program, Department of Environmental Health,
Harvard School of Public Health, Boston 02115; and 2 Department
of Biomedical Engineering, Boston University, Boston, Massachusetts
02215
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ABSTRACT |
It has been shown previously that
intermediate filament (IF) gels in vitro exhibit stiffening at
high-applied stress, and it was suggested that this stiffening property
of IFs might be important for maintaining cell integrity at large
deformations (Janmey PA, Evtenever V, Traub P, and Schliwa M, J
Cell Biol 113: 155-160, 1991). In this study, the contribution of
IFs to cell mechanical behavior was investigated by measuring cell
stiffness in response to applied stress in adherent wild-type and
vimentin-deficient fibroblasts using magnetic twisting cytometry. It
was found that vimentin-deficient cells were less stiff and
exhibited less stiffening than wild-type cells, except at the lowest
applied stress (10 dyn/cm2) where the difference in the
stiffness was not significant. Similar results were obtained from
measurements on wild-type fibroblasts and endothelial cells after
vimentin IFs were disrupted by acrylamide. If, however, cells were
plated over an extended period of time (16 h), they exhibited a
significantly greater stiffness before than after acrylamide, even at
the lowest applied stress. A possible reason could be that the
initially slack IFs became fully extended due to a high degree of cell
spreading and thus contributed to the transmission of mechanical stress
across the cell. Taken together, these findings were consistent with
the notion that IFs play important roles in the mechanical properties
of the cell during large deformation. The experimental data also showed
that depleting or disrupting IFs reduced, but did not entirely abolish,
cell stiffening. This residual stiffening might be attributed to the
effect of geometrical realignment of cytoskeletal filaments in the
direction of applied load. It was also found that vimentin-deficient
cells exhibited a slower rate of proliferation and DNA synthesis than
wild-type cells. This could be a direct consequence of the absence of
the intracellular IFs that may be necessary for efficient mediation of
mechanical signals within the cell. Taken together, results of this
study suggest that IFs play important roles in the mechanical properties of cells and in cell growth.
vimentin; cytoskeleton; cellular mechanics; magnetic twisting
cytometry; deoxyribonucleic acid synthesis
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INTRODUCTION |
IT HAS BEEN
SHOWN previously that mechanical properties of adherent cells
reside mostly in the cytoskeleton (CSK). Numerous mechanical
measurements on living cells show that a selective disruption of three
major CSK filament systems, actin microfilaments (MFs), microtubules
(MTs), and intermediate filaments (IFs) results in a decrease of cell
stiffness (13-15, 17, 23,
24). Although those studies have provided insight into the
distinct roles of MFs and MTs as mechanical-supporting structures of
the CSK, the role of IFs remains elusive. Although their abundance,
intracellular architecture, and contribution to cell stiffness suggest
an important mechanical role, IFs appear not to be critical for cell
viability. We have recently shown that vimentin, a major structural
protein of IFs in fibroblasts and endothelial cells, plays important
roles in deformability, migration, and contractility of fibroblasts; vimentin-deficient cells are more compliant, less contractile, and less
motile than wild-type cells (5).
Further information about the mechanical role of IFs in living cells
are inferred from in vitro rheological measurements on vimentin and
keratin gels (keratin IFs are prominent in epithelial cells). These
gels exhibit highly nonlinear stress-strain behaviors, characterized by
a very low initial stiffness and a relatively high stiffness at large
strains (9, 12). This positive dependence of
stiffness on stress or strain is known as a strain-hardening or
stiffening behavior. If this in vitro stiffening behavior of IF
polymers would persist in living cells, then one would predict that the
contribution of IFs to cell stiffness would be minor during small
deformation of the cell and would increase progressively with
increasing cell deformation.
In this study, we hypothesized that in vitro stiffening behavior
of IF polymers persists in living cells. We tested this hypothesis directly, using magnetic cell twisting to apply varying mechanical stress through integrin receptors to wild-type and vimentin-deficient fibroblasts and to wild-type fibroblasts and endothelial cells in which
the vimentin IF network was chemically disrupted. We found that only a
portion of cell-stiffening behavior could be accounted for by the
rheological properties of vimentin. We also showed that
vimentin-deficient fibroblasts had much slower growth rate compared
with the wild-type cells. Taken together, these data indicate that
compromising mechanical capabilities of the cells by depleting IFs have
a significant effect on cell growth.
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MATERIALS AND METHODS |
Cell culture.
Primary fibroblasts were obtained from homozygous wild-type or mutant
mouse embryos in which vimentin alleles were deleted as described
previously (5). Cells were used between passages 6-12 for all experiments. Bovine capillary endothelial cells
were cultured as described previously (24). Cells were
used between passages 10-14.
Mechanical measurements.
Ferromagnetic beads (4.5-µm diameter) were coated with a
synthetic RGD (Arg-Gly-Asp)-containing peptide (Peptide 2000, Telios; 50 µg peptide/mg beads), a known ligand that binds
specifically to cell integrin receptors. The beads were stored in
carbonate buffer at 4°C overnight to facilitate protein
absorption onto the beads (24, 25).
Wild-type or vimentin-deficient fibroblasts or normal endothelial
cells were plated in a serum-free medium onto collagen I-coated wells
(Removawells, Immulon II, Dynatech; 30,000 cells/well) 4 h before
experiments. RGD-coated beads were added to the wells (on the average
1-2 beads/cell), and after 15 min, unbound beads were washed away with
a serum-free medium. One well was placed into the magnetic cell
twisting device each time, and the mechanical measurements were
performed as described previously (26). Briefly, the beads
were first magnetized by a strong magnetic pulse (1,000 gauss
over 10 µs) in the horizontal direction. As a consequence, the beads
became oriented in the horizontal plane. A twisting torque was then
applied to these beads by a weak vertical magnetic field (0-25
gauss over 60 s), causing the beads to rotate in the vertical
plane as compass needles. Bead rotation was transmitted directly to the
CSK through a series of linking proteins, generating in that way a
mechanical stress in the CSK (5, 24). The
stress was defined as the ratio of the applied mechanical torque to the volume of the bead and was calibrated with a viscous standard. Bead
angle of twist (angular strain) was measured by a magnetometer (25). The apparent stiffness was determined from
the steady-state response as the ratio of applied stress to
corresponding angle of twist. The range of applied stress was
10-80 dyn/cm2.
Statistically significant differences between the mechanical properties
of wild-type and vimentin-deficient cells were assessed by the
Student's t-test. Differences with P < 0.05 were considered significant.
Proliferation and DNA synthesis measurements.
Wild-type and vimentin-deficient confluent fibroblasts were
synchronized by being placed in 0.1% serum for 48 h before being trypsinized and plated on collagen I (5 µg/ml) in the presence of
10% serum. The cell number was counted 4, 24, and 48 h after plating. To find out at what phase of cell cycle cell growth was slowed
down, DNA synthesis was measured as follows. Bromodeoxyuridine (BrDU)
incorporation was quantified in wild-type and vimentin-deficient cells
that were synchronized, then trypsinized and plated in the presence of
serum as described above. After 4 h of plating, BrDU was incubated
with the cells. After 20 and 24 h of plating, the cells were fixed
and stained with an antibody to BrDU. Positively stained cells were
expressed as a percentage of total cells, as described previously
(2).
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RESULTS AND DISCUSSION |
Magnetic twisting measurements.
Angle of twist vs. applied stress relationships for both wild-type and
vimentin-deficient cells exhibited nonlinear dependences, with the
beads undergoing a smaller rotation in the former than in the
latter for a given stress (Fig.
1A). Consequently, the wild-type cells were stiffer and exhibited greater stiffening than the
vimentin-deficient cells over the observed range of stress (Fig.
1B). At all but the lowest applied stress (10 dyn/cm2), the stiffness of wild-type cells was
significantly greater than the stiffness of vimentin-deficient cells;
at 10 dyn/cm2 those stiffnesses were not significantly
different (Fig. 1B). Taken together, these results suggest
that the greater stiffness and stiffening in the wild-type cells than
in the vimentin-deficient cells may be attributed to the rheological
properties of vimentin IFs that were shown previously to exhibit a
prominent stiffening behavior in vitro (9). On the other
hand, it is also possible that this difference in the mechanical
properties of the wild-type and vimentin-deficient cells may be
primarily due to a difference in their CSK architecture.
Immunofluorescent labeling of fibrillar actin revealed that in the
wild-type cells, actin stress fibers and focal structures
("geodomes") are two dominant forms of polymerized actin, whereas
in vimentin-deficient cells, the stress fibers are prevailing
(5). To investigate whether this difference in the CSK
architecture could be a primary cause of the different mechanical
properties of wild-type and vimentin-deficient cells, we measured
stiffness of wild-type cells before and after disrupting chemically the
cell vimentin IF network.

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Fig. 1.
Angle of twist vs. stress relationships (A)
and corresponding stiffness vs. stress relationships (B) for
adherent wild-type and vimentin-deficient fibroblasts. Stresses ranging
from 10 to 80 dyn/cm2 were applied through Arg-Gly-Asp
(RGD)-coated ferromagnetic beads. Cells were plated on collagen
I-coated dishes for 4 h before mechanical measurements.
Means ± SE (n = 5 wells); * significantly
greater values (P < 0.05).
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We used acrylamide, a chemical that selectively disrupts the vimentin
IF network but leaves the MF and MT networks intact (6,
16). Our rationale was that if the stiffening behavior of
vimentin IFs was the key contributor to the greater stiffening of the
wild-type cells (Fig. 1, A and B), then
disrupting IFs in wild-type cells should cause decreases in stiffness
and stiffening similar to those observed in vimentin-deficient cells.
Magnetic twisting measurements were done on wild-type fibroblasts and
on bovine capillary endothelial cells, before and after acrylamide
(4 × 10
3 M) was added, using the same protocol as
described above. In our previous experience, the dose of acrylamide of
4 × 10
3 M produces maximum
effects on CSK mechanics (24). Measurements were performed
1 h after acrylamide was administered to the cells to allow a
complete disruption of the IF network (24). We used endothelial cells in addition to fibroblast to see if the effect of
vimentin IFs on cell stiffening also existed in other cell types. It
was found that cell stiffness and stiffening decreased after adding
acrylamide in both fibroblasts and endothelial cells (Figs.
2 and 3).
These results were consistent with those obtained from the measurements
on wild-type and vimentin-deficient fibroblasts (Fig. 1B).
Although we could not entirely exclude the possibility of an altered
CSK architecture playing a role, our data suggest that the rheological
properties of vimentin IFs contribute greatly to stiffening behavior of
fibroblasts and endothelial cells.

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Fig. 2.
Stiffness vs. stress relationships for wild-type
fibroblasts before and after treatment with acrylamide. Stresses
ranging from 10 to 40 dyn/cm2 were applied through
RGD-coated ferromagnetic beads. Cells were plated on collagen I-coated
dishes for 4 h before mechanical measurements. Means ± SE
(n = 7 wells); * significantly greater values
(P < 0.05).
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Fig. 3.
Stiffness vs. stress relationships for adherent
endothelial cells before and after treatment with acrylamide. Stresses
ranging from 10 to 60 dyn/cm2 were applied through
RGD-coated ferromagnetic beads. Cells were plated on collagen I-coated
dishes for 4 h before mechanical measurements. Means ± SE
(n = 5 wells); * significantly greater values
(P < 0.05).
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Our data also revealed that the stiffening was not totally abolished in
the cell where vimentin IFs were either genetically depleted or
chemically disrupted. This finding suggests that mechanisms other than
the rheological properties of vimentin may also contribute to cell
stiffening. We have shown previously using tensegrity models of the CSK
that cell stiffening may be also attributed to the effect of
realignment of CSK filaments in the direction of applied load, a
phenomenon known as "kinematic stiffening" (20,
24). However, this behavior of cells could be also
mimicked by other types of models (e.g., a simple model in which IFs,
MFs, and MTs would be viewed as elastic springs arranged in parallel), suggesting that one need not invoke tensegrity to explain the observed
features of the cell. Nevertheless, tensegrity architecture, which has
been shown to incorporate some basic structural and mechanical features
of the CSK of adherent cells (cf. 8), could provide a mechanistic
explanation for cell stiffening by identifying the rheological
properties of IFs and kinematic stiffening of the CSK as key
mechanisms. An example of this particular feature of tensegrity is
given in the APPENDIX. We would like to point out that
kinematic stiffening is a result of temporary changes in CSK geometry
for duration of applied forces. These changes are different from
alterations of CSK geometry due to CSK remodeling that are more
permanent in nature.
Data from proliferation and DNA synthesis measurements.
Although our previous studies have shown that in the absence of
vimentin, fibroblasts exhibit impaired motility and wound healing
(5), it is not clear what is the effect of vimentin on
cell growth. In this study, we measured cell proliferation in
synchronized cells and found that it was slower in the
vimentin-deficient cells than in the wild-type cells (Fig.
4). Our measurements of DNA synthesis
indicated that it was much greater in the wild-type cells than in the
vimentin-deficient cells; 20 h after plating, 25% of
vimentin-deficient cells and 75% of wild-type cells showed BrDU
incorporation, whereas 24 h after plating, 50% of
vimentin-deficient and 90% of wild-type cells showed BrDU
incorporation (Fig. 5). Thus in addition
to what we found earlier, that vimentin-deficient cells have impaired
mechanical stability, migration, and contractility (5),
here we presented evidence that cell proliferation was also impaired
due to a slower rate of DNA synthesis. At the present time we do not
know the exact mechanism of the slower rate of DNA synthesis for
vimentin-deficient cells. One possibility could be that in the absence
of the IF network, the transfer of mechanical stress from the cell
surface to the nucleus is impaired. This may not be an unreasonable
explanation because previous studies have shown that DNA synthesis is
directly correlated with the extent of cell distension (i.e.,
spreading) and, therefore, with the corresponding distending stress
(18). The assumption is that the distending stress
regulates DNA synthesis in a dose-dependent fashion. Because the
ability of the cell to efficiently transfer mechanical stress depends
critically on the ability of the CSK to stabilize cell shape and
prevent excessive cell deformation by utilizing the stiffening
mechanism, IFs, which provide a significant portion of this stiffening
during large cell deformation (e.g., spreading, locomotion), are
essential for normal cell function. An alternative explanation is that
in the absence of IFs, the active component of CSK tension is decreased
(5), which, in turn, leads to a decrease in cell stiffness
and DNA synthesis. This possibility is supported by the recent finding
that DNA synthesis is blocked when CSK tension is completely inhibited
(7).

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Fig. 4.
Synchronized wild-type and vimentin-deficient fibroblast
proliferation as a function of plating time. Cells were plated on
collagen I-coated dishes. Means ± SE (n = 4 wells); * significantly different values (P < 0.05).
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Fig. 5.
DNA synthesis of synchronized wild-type and
vimentin-deficient fibroblasts as a function of plating time. Cells
were serum deprived for 48 h and plated on collagen I dishes.
Positively bromodeoxyuridine-stained cells are presented as a
percentage of all cells 20 and 24 h after plating. Means ± SE (n = 3 wells; 5 randomly chosen counting areas per
well).
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Critique.
Despite similarities between data obtained from magnetic twisting
measurements on wild-type and vimentin-deficient cells on one hand, and
wild-type cells before and after IF disruption by acrylamide on the
other hand, there are some salient differences that need to be
addressed. First, at low applied stress (10 dyn/cm2) there
was very little difference in stiffness between wild-type and
vimentin-deficient cells (Fig. 1B). Similar observations
were made in endothelial cells before and after the treatment with acrylamide (Fig. 3). On the other hand, data for wild-type fibroblasts showed that at 10 dyn/cm2, the stiffness was greater,
although not significantly, before than after acrylamide (Fig. 2).
This, in turn, suggests that besides disrupting the vimentin IF
network, acrylamide might have other effects that could cause a further
reduction in cell stiffness. Because the intracellular IF, MF, and MT
networks appear to be physically interconnected
(21-23), disruption of the IF network may cause
geometric rearrangements of the other two. It is also possible that
during 1 h from the time acrylamide was added to the cells until
the magnetic twisting measurements were performed, the CSK underwent a
significant remodeling. Finally, acrylamide may decrease cell stiffness
through decreasing the active CSK tension by inhibiting metabolic
activities of the cell.
We explained impaired DNA synthesis in the vimentin-deficient cells
relative to the wild-type cells by the absence of IFs in the former to
mediate efficient transfer of mechanical stress from the cell surface
to the nucleus. On the other hand, it has been shown previously that
the IFs of living cells appear slack (cf. 1, 8). This would imply that
IFs do not affect transfer of mechanical stress across the CSK unless
the cell is highly spread and the IFs are fully extended. To explore
this possibility, we performed the mechanical measurements in
endothelial cells that were plated over an extended period of time (16 h). The measurements were done before and after acrylamide was added.
We found that the cells exhibited a significantly greater stiffness
before than after acrylamide even at the lowest applied stress of 10 dyn/cm2 (Fig. 6). This result
is consistent with the possibility that in highly spread cells, IFs are
fully extended and thus participate in stress transmission across the
CSK even at very low-applied stress. Because our DNA synthesis
measurements were done 20 and 24 h after plating, there was
sufficient time for the cells to fully spread and for IFs of the
wild-type cells to be fully extended during both measurements. This is
consistent with the fact that the DNA synthesis in wild-type cells
increased by only 20% between 20 and 24 h after plating (Fig. 5),
suggesting that IFs were involved in the stress transfer.

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Fig. 6.
Stiffness vs. stress relationships for adherent
endothelial cells before and after treatment with acrylamide. Stresses
ranging from 10 to 60 dyn/cm2 were applied through
RGD-coated ferromagnetic beads. Cells were plated on collagen I-coated
dishes for 16 h before mechanical measurements. Means ± SE
(n = 5 wells); * significantly greater values
(P < 0.05).
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CONCLUSIONS |
An important question about the mechanical behavior of adherent
cells is what is the mechanism of the observed stiffening response.
Janmey et al. (9) and Ma et al. (12) have
demonstrated that IF gels exhibit stiffening in vitro. Results of our
study suggested that this mechanical behavior of IF polymers could also persist in the complex CSK network of living cells and could account for the part of the cell-stiffening behavior. This was the first direct
evidence for the mechanical role of IFs in living cells exposed to
varying applied stress. Our study also demonstrated that in the absence
of vimentin, cells exhibited slower rates of proliferation and DNA
synthesis. We speculated that these effects were a direct consequence
of the absence of the intracellular IF network that might be necessary
to efficiently mediate the transfer of mechanical signals from the cell
surface to the nucleus.
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APPENDIX |
We used a six-strut tensegrity model as a representative of
cellular tensegrity. This particular model was very useful in our
previous studies, in which we analyzed the microstructural basis of
various aspects of cell mechanical behavior (3,
4, 19, 20). In this study, we
added the contribution of IFs to the model.
The model is composed of three types of elements: 1)
tension-bearing peripheral cables that play the role of MFs,
2) compression-bearing struts that play the role of MTs, and
3) tension-bearing radial cables that play the role of IFs
(Fig. 7). This arrangement is consistent
with the intracellular distribution of the CSK filamentous structures;
MFs are concentrated in the peripheral cortical region, whereas MTs and
IFs occupy a more central region, extending from the nucleus to the
cell surface (cf. 1).

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Fig. 7.
Six-strut tensegrity model. Microtubule struts: AA, BB, CC;
microfilament cables AB, AC, BC; intermediate filament (radial) cables
OA, OB, OC. Stretching force T/2 (thick arrows) is applied at the strut
endpoints A in the x direction.
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The model was stretched uniaxially by pulling apart a pair of parallel
struts (Fig. 7), and its stiffness was calculated using methods of
engineering mechanics as described below. To mimic the behavior of the
IF-deficient and IF-disrupted cells, the stiffness was calculated for
the case where the IF elements were not included in the model. All
relevant equations are given below.
From the geometry of the six-strut tensegrity model (Fig. 7) it follows
that
where lAB, lAC,
and lBC are lengths of cables AB, AC, and BC;
LAA, LBB, and
LCC are lengths of struts AA, BB, and CC;
rOA, rOB, and
rOC are lengths of radial cables OA, OB, and OC;
and sx, sy, and
sz are distances between the pairs of parallel
struts along x, y, and z axes,
respectively. At the reference state (before stretching force T was
applied), LAA = LBB = LCC
L0,
sx = sy = sz
s0 = L0/2, lAB = lAC = lBC
l0 =
L0,
rOA = rOB = rOC
r0 =
L0/4. For simplicity, it was assumed
that L0 was of unit length
(L0 = 1).
Equilibrium equations, obtained by considering force balance at nodes
A, B, and C, are the following
where T is external stretching force, FAB,
FAC, and FBC are forces in cables AB, AC, and
BC, and NOA, NOB, and NOC are
forces in radial cables OA, OB, and OC, respectively.
The MF cables lAB, lAC,
and lBC were assumed to be linearly elastic
(Hookean) of stiffness k and of resting length
lr, based on the observed behavior of isolated
actin filaments (11) and actin gels (9) and
that they support only tensile forces. Thus the force in those cables
is given as
For simplicity, it was assumed that k was of unit
stiffness (k = 1).
The radial IF cables rOA,
rOB, and rOC were assumed
to be nonlinear (quadratic) elastic, and thus exhibited stiffening,
based on similar behavior of vimentin gels (9) and that
they support only tensile forces. Thus the force in those
cables is given as
where k1 and k2
are constants and rr is the resting length. To
mimic the in vitro stress-strain behavior of vimentin gels (9), it was assumed that k1 = 0.1 and that k2 = 1.0.
The MT struts were assumed to be rigid, and thus transmit forces but do
not directly contribute to the model deformability. Our previous
modeling studies showed that this assumption of rigid struts was
reasonable for obtaining good qualitative simulations of cell
mechanical behavior (4, 20).
It was also assumed that the MF cables were initially tensed (i.e.,
lr
l0) and that the IF
cables were initially slack (i.e., rr
r0). The former assumption was based on the
evidence that the actin CSK is initially tensed ("prestressed")
even before external forces are applied to the cell (cf. 15), whereas
the latter assumption was based on the slack appearance of IFs in living cells (cf. 1, 8).
The above equations were simultaneously solved for
sx, sy, and
sz for a given T (ranging from 0 to 2 units of
force), lr
0.90l0,
and rr
1.05r0 using a
numerical procedure (TK Solver Plus software). In the case where the IF
elements were not present in the model, the above equations were solved
by setting NOA = NOB = NOC
0 (cf. 20). The applied stress was computed as
8T/5L02, and the
corresponding strain as (sx
s0)/s0 (19).
The stiffness was defined as the ratio of stress to strain.
Model predictions.
The model predicted several features that were consistent with the data
obtained from magnetic cell twisting (Fig. 1B and Figs. 2
and 3). First, at a given stress, the stiffness was greater in the case
where the IF elements (i.e., radial cables in Fig. 7) were present than
when they were absent from the model (Fig. 8). This difference was minor at low
stress, and it increased progressively with increasing stress. Second,
the stiffening was greater when the IF elements were present in the
model than when they were not (Fig. 8). The above differences were
primarily due to the nonlinear (stiffening) properties of the IF
elements. Third, the model exhibited stiffening even when the IF
elements were absent. This was entirely due to the effect of kinematic
stiffening (Fig. 8). Because the absence of IF elements from the model
produced changes in its mechanical
properties that were similar to the changes caused by the
absence or disruption of vimentin IFs in living cells, we concluded
that the mechanisms that determined the model stiffening behavior might
also be present in the cell, i.e., that the cell stiffening was partly
due to the rheological properties of IFs and partly due to the
kinematic stiffening of the CSK.

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Fig. 8.
Stiffness vs. stress relationships predicted by the model
for the cases where the intermediate filament (IF) cables are present
and when they are not present in the model; stiffness and stress are
given in units force per length square. Note that in the presence of IF
elements, the model exhibits greater stiffening and greater stiffness
than when the IF elements are not present. This behavior is consistent
with the observations in living cells (Fig. 1B and Figs. 2
and 3).
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ACKNOWLEDGEMENTS |
We thank Dr. Victor Koteliansky for providing wild-type and
vimentin-deficient fibroblasts and Jianxin Chen and In Lim for technical assistance.
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FOOTNOTES |
This work was supported by National Heart, Lung, and Blood Institute
Grant HL-33009.
Address for reprint requests and other correspondence: N. Wang,
Physiology Program, Dept. of Environmental Health, Harvard School of
Public Health, 665 Huntington Ave., Boston, MA 02115 (E-mail:
nwang{at}hsph.harvard.edu) or D. Stamenovi
, Dept. of Biomedical Engineering, Boston Univ., 44 Cummington St., Boston, MA 02215 (E-mail: dimitrij{at}engc.bu.edu).
The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
"advertisement"
in accordance with 18 U.S.C. §1734 solely to indicate this fact.
Received 29 November 1999; accepted in final form 28 January 2000.
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