REVIEW
Tissue Cells Feel and Respond to the
Stiffness of Their Substrate
Dennis E. Discher,
1
*
Paul Janmey,
1
Yu-li Wang
2
Normal tissue cells are generally not viable when suspended in a fluid and are
therefore said to be anchorage dependent. Such cells must adhere to a solid, but a
solid can be as rigid as glass or softer than a baby’s skin. The behavior of some cells
on soft materials is characteristic of important phenotypes; for example, cell growth
on soft agar gels is used to identify cancer cells. However, an understanding of how
tissue cells—including fibroblasts, myocytes, neurons, and other cell types—sense
matrix stiffness is just emerging with quantitative studies of cells adhering to gels
(or to other cells) with which elasticity can be tuned to approximate that of tissues.
Key roles in molecular pathways are played by adhesion complexes and the actin-
myosin cytoskeleton, whose contractile forces are transmitted through transcellular
structures. The feedback of local matrix stiffness on cell state likely has important
implications for development, differentiation, disease, and regeneration.
Anchorage dependence refers to a cell_s need
for adhesion to a solid. Most tissue cells are
simply not viable upon dissociation and sus-
pension in a fluid, even if soluble proteins are
added to engage cell adhesion molecules Ee.g.,
integrin-binding RGD peptide (1, 2)^.Fluids
are clearly distinct from solids in that fluids
will flow when stressed, whereas solids have
the ability to resist sustained pushing and pull-
ing. In most soft tissues—skin, muscle, brain,
etc.—adherent cells plus extracell ular matr ix
contribute together to establish a relatively
elastic microenvironment. At the macro scale,
elasticity is evident in a solid tissue_s ability to
recover its shape within seconds after mild pok-
ing and pinching, or even after sustained com-
pression, such as sitting.
At the cellular scale, normal tissue cells
probe elasticity as they anchor and pull on
their surroundings. Such processes are de-
pendent in part on myosin-based contractility
and transcellular adhesions—centered on in-
tegrins, cadherins, and perhaps other adhesion
molecules—to transmit forces to substrates. A
normal tissue cell not only applies forces but
also, as reviewed here, responds through
cytoskeleton organization (and other cellular
processes) to the resistance that the cell senses,
regardless of whether the resistance derives
from normal tissue matrix, synthetic substrate,
or even an adjacent cell. Furthermore, physical
properties of tissues can change in disease Eas
imaged now by magnetic resonance imaging
(MRI) or ultrasound elastography (3–5)^,and
cellular responsiveness to matrix solidity can
likewise change, as i llustrated by the growth of
cancer cells on soft agar Ee.g., (6)^.
Contractile forces in cells are generated by
cross-bridging interactions of actin and myosin
filaments. For adherent cells, some of these
forces are transmitted to the substrate (referred
to as traction forces) and cause wrinkles or
strains when the substrate consists of a thin
film or a soft gel (7–12) (Fig. 1A). The cell, in
turn, is shown to respond to the resistance of
the substrate, by adjusting its adhesions, cyto-
skeleton, and overall state. Although con-
siderable attention has been directed at the
responsiveness of individual cells to external
forces (outsideYin) that range from fluid flow
to direct stretching and local twisting (13), we
are now beginning to understand that cellular
responses to cell-exerted forces involve a
feedback loop of insideYoutsideYin that
couples to the elasticity of the extracellular
microenvironment. An analogy to muscle
building is perhaps useful: A bicep is not built
by passive flexing; the muscle must do active
work against a load. Moreover, a load of 1 kg
clearly feels different from a load of 2 kg.
Similar sensitivity, growth, and remodeling
principles seem to apply to most anchored
cells.
On ligand-coated gels of varied stiffness,
epithelial cells and fibroblasts (14)werethe
first cells reported to detect and respond dis-
1
School of Engineering and Applied Science and Cell
and Molecular Biology Graduate Group, University of
Pennsylvania, Philadelphia, PA 19104–6315, USA.
2
Departments of Physiology and Cell Biology, Uni-
versity of Massachusetts, Worcester, MA 01655, USA.
*To whom correspondence should be addressed.
E-mail: discher@seas.upenn.edu
Fig. 1. Substrate strain and tissue stiffness. (A) Strain distribution computed in a soft matrix
beneath a cell. The circular cell has a uniform and sustained contractile prestress from the edge to
near the nucleus (81). (B) Stress versus strain illustrated for several soft tissues extended by a force
(per cross-sectional area). The range of slopes for these soft tissues subjected to a small strain gives the
range of Young’s elastic modulus, E, for each tissue (24, 28, 30). Measurements are typically made on
time scales of seconds to minutes and are in SI units of Pascal (Pa). The dashed lines (- --) are those for
(i) PLA, a common tissue-engineering polymer (89); (ii) artery-derived acellularized matrix (90); and (iii)
matrigel (42).
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S PECIAL S ECTION
tinctly to soft versus stiff substrates. Although
molecular pathways are still only partially
known, muscle cells, neurons, and many other
tissue cells have since been shown to sense
substrate stiffness (15–17). Unlike cells on soft
gels or in tissues, cells cultured on tissue-
culture plastic or glass coverslips are attached
(often via adsorbed matrix protein) to essen-
tially rigid materials. The question therefore
arises: Do cells perceive and respond to the
rigidity of these conventional materials in
ways that contrast with their behavior in
much more compliant tissues, gels, or sub-
layers of cells? The increasingly clear, af-
firmative answer to this question appears
important in its impact not just on standard
cell culture but also, perhaps, in understand-
ing disease processes, morphogenesis, and
tissue-repair strategies.
Soft Tissue Benchmarks
Cells adhere to solid substrates that range in
stiffness from soft to rigid and that also vary in
topography and thickness (e.g., basement mem-
brane). Regardless of geometry, the intrinsic
resistance of a solid to a stress is measur ed by
the solid’s elast ic modulus E, which is most
simply obtained by applying a force—such
as hanging a weight—to a section of tissue
or other ma terial and then measuring the
relative change in length or strain (Fig. 1B, inset).
Another common method to obtain E involves
controlled poking by macro- and micro-indenters,
including atomic force microscopes (AFMs)
(18, 19). Many tissues and biomaterials exhibit a
relatively linear stress versus strain relation up to
small strains of about 10 to 20%. The slope E of
stress versus strain is relatively constant at the
small strains exerted by cells (20), although
stiffening (increased E) at higher strains is the
norm (21, 22). Nonetheless, microscopic views
of both natural and synthetic matrices [e.g.,
collagen fibrils and polymer-based mimetics
(23)] suggest that there are many subtleties to
tissue mechanics, particularly concerning the
length and time scales of greatest relevance to
cell sensing. Sample preparation or state is
another obvious issue; for example, elastic
moduli of whole brain in macroscopic mea-
surements can vary by a factor of 2 or more,
depending on specifics of preparation, tissue
perfusion, etc. (24). In addition, with cells as
well as tissues, many probing methods involve
high-frequency stressing (25), whereas relevant
time scales for cell-exerted strains seem likely
to range from seconds to hours, motivating long
time studies of cell rheology [recent cell me-
chanics references (26, 27)]. Regardless, com-
parisons of three diverse tissues that contain a
number of different cell types show that brain
tissue is softer than muscle (28, 29), and muscle
is softer than skin (30) (Fig. 1B). Although
mapping soft tissue micro-elasticities at a
resolution typical in histology seems impor-
tant, the implication here is that there are dis-
tinct elastic microenvironments for epithelial
cells and fibroblasts in skin, for myotubes in
fiber bundles, and for neurons in brain.
Correlations have long been made between
increased cell adhesion and increased cell
contractility [e.g., (31)], but it now seems
clear that tactile sensing of substrate stiffness
feeds back on adhesion and cytoskeleton, as
well as on net contractile forces, for many cell
types. Seminal studies on epithelial cells and
fibroblasts exploited inert polyacrylamide gels
with a thin coating of covalently attached
collagen (14). This adhesive ligand allows the
cells to attach and—by controlling the extent
of polymer cross-linking in the gels—E can
be adjusted over several orders of magnitude,
from extremely soft to stiff. Images of adhe-
sion proteins such as vinculin are revealing
(Fig. 2, top): Soft, lightly cross-linked gels
(E È 1 kPa) show diffuse and dynamic adhesion
complexes. In contrast, stiff, highly cross-
linked gels (E È 30 to 100 kPa) show cells
with stable focal adhesions, typical of those
seen in cells attached to
glass. Similarly, rigidifi-
cation of cell-derived
three-dimens ional (3D)
matrices alters 3D-matrix
adhesions, because the
adhesions are replaced
by large, nonfibrillar fo-
cal adhesions similar to
those found on fixed 2D
substrates of fibronectin
(32). Consistent with a
role for signaling in stiff-
ness sensing, tyrosine
phosphorylation on mul-
tiple proteins (including
paxillin) appears broad-
ly enhanced in cells on
stiffer gel substrates (14),
whereas pharmacologi-
cally induced, nonspecif-
ic hyperphosphorylation
drives focal adhesion for-
mation on soft materials.
Inhibition of actomyosin
contractions, in contrast,
largely eliminates promi-
nent focal adhesions,
whereas stimulation of
contractility drives in-
tegrin aggregation into
adhesions (33). Ad-
ditionally, although mi-
crotubules have been
proposed to act as ‘ ‘struts’’
in cells and thus limit
wrinkling of thin films
by cells (34), quantifica-
tion of their contribu-
tions to cells on gels
shows that they provide
only a minor fraction of
the resistance (14%) to contractile tensions;
most of a cell’s tension is thus resisted by
matrix (35).
Traction stresses (t, force per area) exerted
by fibroblasts on gels were the first to be
mapped by embedding fluorescent microbeads
near the gel surface and then imaging bead
displacements before and after cell detachment
(10, 20). Although larger tractions are exerted
on stiffer gels, typical tractions of btÀÈ1kPa
exceed by orders of magnitude the viscous
fluid drag on any cell crawling in culture. In
addition, mean cell tractions equate to mean
gel strains that differ very little (e
out
0 bt/EÀ;
3 to 4%) between gels that differ by twofold
in E.Thissuggeststhate
out
is sensed by cells
as a tactile set-point, perhaps analogous to
other physiological set-points such as extra-
cellular ion concentrations or optimal growth
factor concentrations. Furthermore, if matrix
strain is approximately constant, then cells
on soft gels need be less contractile than on
stiff gels, and if they are less contractile, then
Fig. 2. Substrate stiffness influences adhesion structures and dy-
namics (14), cytoskeleton assembly and cell spreading (17, 42), and
differentiation processes such as striation of myotubes (28). (Top) The
arrows point to dynamic adhesions on soft gels and static, focal
adhesions on stiff gels. [Adapted from (14)] (Middle) The actin cyto-
skeleton. (Bottom) A cell-on-cell layering in which the lower layer is
attached first to glass so that the upper layer, which fuses from
myoblasts that are added later, perceives a soft, cellular substrate.
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S PECIAL S ECTION
their adhesions need not be as strong. This is
consistent with a reduced adhesion strength
as measured by reduced forces to peel cells
from soft gels versus glass (28). This is also
consistent with more dynamic adhesions on
soft substrates (Fig. 2, top). Fluorescence
imaging also shows increasingly organized
F-actin and stress fibers on increasingly stiff
substrates in fibroblasts (Fig. 2, middle). Neu-
rons, in contrast, appear to apply very little
stress to their substrate, because they can only
deform very soft gels (36). Neurons also
branch more on softer substrates (37), perhaps
because the cytoskeleton is more pliable, if
less structured.
Differentiation and a
Cell-on-Cell Hypothesis
Cytoskeletal organization in muscle cells also
depends on substrate stiffness and reveals an
optimal substrate stiffness for striation of
actomyosin (28, 38)—the contractile element
of the myotube. On very soft gels that are
micropatterned with collagen strips so as to
generate well-separated myotubes, actomyosin
appears diffuse after weeks in culture. On very
stiff gels, as well as on glass micropatterns,
stress fibers and strong focal adhesions pre-
dominate, suggesting a state of isometric con-
traction. Notably, however, on gels with an
elasticity that approximates that of relaxed
muscle bundles (E È 10 kPa), a large fraction
of myotubes in culture exhibit definitive
actomyosin striations. Actomyosin striation is
even more prominent when cells are cultured
on top of a first layer of muscle cells (Fig. 2).
The lower myotubes attach strongly to glass
and form abundant stress fibers, whereas the
upper myotubes differentiate to the more
physiological, striated state. Although cell-cell
contact may provide additional signals, the
elasticity E of the myotubes, as measured by
atomic force microscopy, is in the same range
as that of gels optimal for differentiation
and—importantly—in the same range as that
of normal muscle tissue.
Cell-cell contact appears to induce similar
cell-on-gel effects for systems other than
muscle. Astrocytes growing on glass, for ex-
ample, appear to provide a soft cell ‘‘stroma’’
adequate for neuronal branching that is simi-
lar to gels having brainlike E (39). Cell-cell
contact may have a similar effect when cells
are grown at a high density. When endo-
thelial cells are confluent, the cells have
indistinguishable morphologies on soft versus
stiff substrates (40), whereas cells attached
only to an underlying stiff surface differ in
their spreading and cytoskeletal organization
(Fig. 2). Related results are also emerging
with epithelial cells and fibroblasts, as well as
cardiomyocytes that show a tendency to ag-
gregate and form cell-cell contacts in pref-
erence to contact with soft gels (41). Such
studies may set the stage for a better un-
derstanding of mechanosensitivity in cell-cell
interactions during embryogenic and tissue
regeneration processes.
Materials ranging from fibrin gels and
microfabricated pillars to layer-by-layer poly-
mer assemblies (41–45) all suggest a similar
trend of more organized cytoskeleton and
larger, more stable adhesions with increasing
E as outlined here, despite likely differences
in adhesive ligand density and long-time
elasticity. However, the responses appear to
be specific to anchorage-dependent and/or
relatively contractile cells. Highly motile amoe-
boid cells such as human neutrophils are
perfectly viable in blood (a fluid) and do not
appear to be sensitive to substrate stiffness;
neutrophils spread on soft gels just as much as
they do on stiff gels and glass, whether activated
or not (46–48). Although additional study is
needed and could prove ligand dependent, the
initial contrast with cells derived from solid
tissue highlights the compelling need for
insights into molecular pathways of stiffness
sensing in relation to anchorage dependence
and contractility. Variation with cell type
implies an active, regulated response, rather
than a universal need of cells to exert traction
forces on a stiff matrix. Differences no doubt
depend in part on expression and engagement
of adhesion molecules. Integrins reportedly
undergo adhesion-modulating conforma-
tional changes in response to force (49), and
they also appear to be down-regulated on
soft gels [e.g., a
5
-integrin (40)]. However, over-
expression of a
5
-integrin does not override
the limited spreading of cells on soft gels,
whereas overexpression of actin drives cyto-
skeletal assembly and strongly promotes
spreading (17).
Nonlinear Response to Compliance
Signals and Molecular Effectors
Myosin inhibitors—including a potent non-
muscle myosin II inhibitor, blebbistatin
(50)—have provided key evidence for the crit-
ical role of contractility in substrate sensing
(14, 38). Important roles are also reported for
integrating activator proteins of the Ras
superfamily, especially Rho subfamily mem-
bers that are broadly known to regulate the
cytoskeleton, cell growth, and transcription. In
cellssuchasfibroblasts,itiswellestablished
that Rho-stimulated contractility drives stress
fiber and focal adhesion formation and that
up-regulation of a smooth m uscle actin
correlates with contractility on rigid substrates
(33, 51). Rac1 is another Rho family protein
that when activated in macrophages, promotes
engulfment of antibody-bearing soft beads,
which otherwise are not engulfed (48). RhoA,
Fig. 3. Substrate stiffness influences contractility, motility, and spreading. (A) Interplay of physical and
biochemical signals in the feedback of matrix stiffness on contractility and cell signaling as extended from
(91). (B) Cells exert less tension on softer, collagen-coated gels but crawl faster (20), causing an
accumulation of cells toward the stiff end of a soft-to-stiff gradient gel (54). Curves are schematic. [Image
adapted from (54)] (C) Spread area, a, of smooth muscle cell versus ligand density and matrix stiffness,
based on measurements fitted by a thermodynamic model (17). Similar nonlinear responses are also seen
for adhesions, cytoskeleton organization, tractions exerted on the substrate, and other cellular processes.
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in contrast, has no observable effect in these
measurements. Current views of signaling
pathways, especially various physical signals
(Fig. 3A), clearly implicate Rac in cell mo-
tility (versus contractility)—indeed, myosin
inhibition activates Rac (52). The involvement
of contractile-effector proteins in sensing im-
plies that cell crawling is also likely to be
sensitive to substrate stiffness (Fig. 3B), as
demonstrated in studies of the ‘‘cell on gel’’
effect with epithelial cells (14), fibroblasts
(20), and smooth muscle cells (53, 54). With
the latter cell type, crawling speed appears
maximal at an intermediate stiffness. The re-
sult is reminiscent of a bell-shaped curve of
crawling speed versus the concentration of
adhesive ligand (55), which has been mathe-
matically modeled as a shift in the balance
between ligand-mediated traction and ligand-
mediated anchorage (56). Additionally, smooth
muscle cells on gels are slowed by inhibition
of Rho kinase, suggesting that RhoA activity
contributes to the tensions needed to detach
any established adhesions at the rear of a
motile cell (a process not needed in engulf-
ment) (57). The dependence of cell crawling
speed and direction on substrate stiffness,
particularly gradients in stiffness, is now re-
ferred to as ‘ ‘ durotaxis’’ (20).
Molecular mechanisms involved in cellu-
lar responses to matrix stiffness are still open
to investigation, but it seems important to
consider close relation ships (or not) be-
tween ‘‘insideYoutsideYin’’ pathways and
‘‘outsideYin’’ pathways (Fig. 3A). Adhe-
sions on stiff materials are multifaceted mech-
anosensors [for a review, see, e.g., (5)], and,
on the one hand, contractility does appear to
regulate the formation and dynamics of
adhesion structures (14). Indeed, myosin II
has a well-established role on rigid substrates
in adhesion and cytoskeletal organization (33),
as well as spreading (58)andcelltension(13 ).
On the other hand, applying external forces
to cells (outsideYin) leads to growth of
focal adhesions on rigid materials, with or
without myosin contractile forces (59). None-
theless, insideYoutside activity can trigger
outsideYin path ways such as the opening
of stress-activated channels (60), with induc-
tion of calcium transients and activation of
calmodulin and myosin II.
Additional work from the outsideYin
perspective has shown that stretching well-
spread cells leads to deactivation of Rac (for
G30 min) without affecting Rho activity (52).
Stretching can also create new cytoskele-
tal binding sites for activator and adapter
proteins (61) and thus alter the balance be-
tween protrusion and contractility. The mech-
anism may involve conformational changes
to uncover scaffold binding sites or other
activities; for example, one key focal adhe-
sion protein, talin, must unfold for vinculin
binding (62–64), and although the unfolding
forces are not yet clear, similar helical bundle
cytoskeletal proteins unfold at forces that just
a few myosin molecules can generate. On the
other hand, fluid shearing of endothelial cells
activates Rho and also increases cell traction
forces (65), but h ow such stimulation—
transient or sustained—depends on myosin ac-
tivity and compares with substrate-mediated
pulling forces or substrate compliance effects
remains unknown.
The effects and effectors of contractility
can be transient as well as nonlinear, but are
nonetheless essential to clarify. The tempo-
rary deactivation of Rac with stretch may have
to be integrated over time to understand its
place in signaling (66), and although myosin
II activity is crucial for stiffness sensing, on
rigid substrates it only delays the earliest
phase of cell spreading (by È2 hours), ap-
parently through stiffening of the cell cortex
(67). Overstimulation of myosin, like over-
stimulation of most motors, is also likely to
slow and eventually stall cell migration. The
effect may be related to the formation of less
dynamic myosin assemblies on progressively
stiffer substrates, fostering larger, more stable
focal adhesions. Reconstitution experiments
with mixtures of actin, myosin, adenosine 5¶-
triphosphate (ATP), and cross-linkers might
lend important insight into motor-driven self-
assembly processes.
Varied responses to mechanical signals at
the cellular and molecular scales are increas-
ingly in need of multivariate analyses. More
data are needed to define coupled responses
to substrate stiffness, contractile state, ligand
density, and activator levels, as well as ef-
fects such as growth factor stimulation. A
number of studies have already revealed
nonlinear response maps, as illustrated by
the spread area of cells on gels (Fig. 3C).
Modeling efforts to date have been thermo-
dynamic (17, 68), kinetic (56), and—for cell-
cell interactions—purely mechanical (69),
but all generally yield nontrivial responses,
saturable or even bell-shaped in E and other
inputs. A major challenge in all such mod-
eling is to clarify the principal enigma: how
contractile traction forces exerted by a cell
tend to increase with stiffness of the cell’s
substrate.
Do Cells Feel Their Way in
Organogenesis?
Cell type–dependent increases in contractility
with increasing substrate stiffness may offer
partial answers to some long-standing ques-
tions of cell-cell organization. Random mix-
tures of two cell types often lead to shell-core
cell aggregates (Fig. 4), as first observed when
heart cells segregated into the interior of a
mass of retinal cells after 1 day in culture (70).
Individual cell clusters form by ‘‘pulling’’
away from each other (71). Such observations
are now being used to manipulate aggregate
morphologies through printing of cell masses
into gels as toroids and other shapes (72).
Such phenomena have been explained by a
‘‘differential adhesion hypothesis’’ in which
different cell types bear different numbers and
types of adhesion proteins (e.g., cadherins),
giving rise to an effective surface tension, g,at
interfaces with cell layers (73). Although pos-
sible contributions of cytoskeleton and cell
tension have not yet been reported, studies of
zebrafish embryos (74) have shown that (i)
disruption of actin filaments dissociates cells
entirely, even though cadherins remain at the
cell surface; and (ii) the effect is potentiated
by at least one drug that inhibits actomyosin
contractility.
Quantitative estimates of g for the spherical
aggregates of cadherin-expressing cells (73)
exceed the rate-dependent cohesive strength of
lipid bilayers [as low as 2 to 3 mN/m (75)] and
suggest adhesion energies per cadherin that are
orders of magnitude larger than would be
expected of individual cadherin bonds. Such
large g values could be due to the cytoskele-
ton or even contractility (because g/btÀ;1to
10 mm is a stress fiber length scale), especially
because there is growing evidence of common
RhoGTPas e-cytoskeleton signaling among
integrin- and cadherin-mediated adhesion
(76–79). A major role for contractility in cell
sorting was speculated long ago (80), but
results reviewed here make it clear that
contractile state can be strongly influenced by
Fig. 4. Sorting of two cell types into a 3D shell-core aggregate (È300 mm in diameter) in which low
expressers of N-cadherin (labeled in red) surround high expressers of N-cadherin (labeled in green)
(73). Scanning electron micrograph of a typical spheroid’s surface shows well-spread cells. [Adapted
from (73) with permission from Elsevier. Image courtesy of G. Forgacs, University of Missouri]
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the stiffness of the anchoring substrate. Heart
cells pulling on equally stiff heart cells can
generate a positive and steady feedback on
their cytoskeleton that may not occur when
these cells pull on other tissue cell types. Cell
aggregation of less differentiated cells such as
some stem cells that assemble into ‘‘embryoid
bodies’’ has yet to be studied with myosin
inhibitors or related methods, but the principles
may extend to stem cell differentiation, partic-
ularly because at least some stem cells express
nonmuscle myosin II at levels similar to those
of myoblasts (81).
Added Facets and Prospects
Mechanobiology is a broad field. Emphasized
here is the recent recognition that most tissue
cells not only adhere to but also pull on their
microenvironment and thereby respond to its
stiffness in ways that relate to tissue elasticity.
Many emerging topics are not dealt with ad-
equately in this brief review of substrate
stiffness effects. These include in vitro models
of fibrotic stiffening and related disease pro-
cesses (82, 83); perturbed secretion and uptake
(84, 85); 2D versus 3D responses (32, 86); de-
formations of fibronectin and other matrix
molecules (87); structure formation such as
capillary development (15, 88); deeper aspects
of cell differentiation such as with stem cells
(81); the relative sensitivity and contractility of
some cells relative to others; and broader
effects of matrix elasticity, as well as fluidity
(i.e., matrix rheology), on cells in tissue de-
velopment, remodeling, and regeneration. For
the cell biologist, this review may suggest the
need for a better unders tanding of mechano-
chemical pathways and the benefit of more
biologically relevant elastic substrates than
rigid coverslips and polystyrene for in vitro
studies. For the applied biologist or bio-
engineer, modified strategies for tissue repair
and cell scaffolding may emerge, such as the
development of fibrous scaffolds for cell
seeding (23), where careful attention can be
given to fiber flexibility. All of these topics
seem likely to add to our rapidly growing
recognition that tissue cells feel and respond to
the mechanics of their substrate in many
contexts.
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1/2
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S PECIAL S ECTION
![Fig. 3. Substrate stiffness influences contractility, motility, and spreading. (A) Interplay of physical and biochemical signals in the feedback of matrix stiffness on contractility and cell signaling as extended from (91). (B) Cells exert less tension on softer, collagen-coated gels but crawl faster (20), causing an accumulation of cells toward the stiff end of a soft-to-stiff gradient gel (54). Curves are schematic. [Image adapted from (54)] (C) Spread area, a, of smooth muscle cell versus ligand density and matrix stiffness, based on measurements fitted by a thermodynamic model (17). Similar nonlinear responses are also seen for adhesions, cytoskeleton organization, tractions exerted on the substrate, and other cellular processes.](/figures/fig-3-substrate-stiffness-influences-contractility-motility-1g73hy5k.webp)