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Shear thickening of F-actin networks crosslinked with non-muscle myosin IIB

Melanie Norstromaand Margaret L. Gardel*ab

Received 13th October 2010, Accepted 21st December 2010

DOI: 10.1039/c0sm01157f

The material properties of cytoskeletal F-actin networks facilitate a broad range of cellular behaviors,

whereby in some situations cell shape is preserved in the presence of force and, at other times, force

results in irreversible shape change. These behaviors strongly suggest that F-actin networks can

variably deform elastically or viscously. While a significant amount is known about the regulation of

the elastic stiffness of F-actin networks, our understanding of the regulation of viscous behaviors of

F-actin networks islargely lacking. Here, we study the rheological behavior of F-actin networks formed

with heavy meromyosin non-muscle IIB (NMMIIB). We show that NMMIIB quenched with ADP

crosslinks F-actin into networks that, for sufficient densities, display stress stiffening behavior. By

performing a series of creep tests, we show that densely crosslinked actin/NMMIIB–ADP networks

undergo viscous deformation over a wide range of stresses, ranging from 0.001 to 10 Pa. At high

stresses, networks that stress stiffen are also observed to shear thicken, whereby the effective viscosity

increases as a function of stress. Shear thickening results in a reduction in the extent of irreversible,

viscous deformation in actin/NMMIIB–ADP networks at high stresses compared to that expected for

a linear viscoelastic material. Thus, viscous deformation contributes less to the overall mechanical

response at high levels of applied force. Our results indicate mechanisms by which the fluid-like nature

of the actomyosin cytoskeleton can be reduced under high load.

1Introduction

The actin cytoskeleton plays an essential role in numerous

physical behaviors of animal cells including mediating shape

changes during cell division and migration and maintaining

a stable shape in response to external forces.1,2These diverse

physical behaviors strongly suggest that the actin cytoskeleton

can variably behave either fluid-like, to accommodate structural

rearrangements, or solid-like, to preserve shape. The mechanical

behaviors of the actin cytoskeleton are largely determined by

a myriad of actin-binding proteins, to regulate the assembly of

actin into dynamic, force-generating networks and bundles.3In

non-muscle cells, non-muscle myosin II motors play essential

roles in building contractile actin networks and bundles that

support both movement, or flow, of the actin cytoskeleton and

provide an elastic framework for cytoskeletal force trans-

mission.4,5Thus, understanding the viscoelastic behaviors of the

actomyosin cytoskeleton is essential for an understanding of cell

mechanics.

In the presence of permanent and incompliant crosslinking

proteins, F-actin networks form soft elastic gels with a well-

defined, zero frequency plateau modulus that is sharply sensitive

to small variations in the F-actin concentration and crosslink

density.6,7Due to non-linearity in the entropic spring constant of

the semi-flexible F-actin at high extensions, the magnitude of the

elastic modulus increases at high stresses, a phenomenon known

as stress stiffening.6–8Permanently crosslinked F-actin networks

are elastic at long time scales; in the presence of a constant

applied stress, the networks deform to a certain strain but no

significant change in the strain, or creep, is observed and the

strain recovers quickly to zero after the stress is removed.9Thus,

while the elastic response of permanently crosslinked F-actin

networks is well understood, these studies do not explore the

viscous behaviors of the actin cytoskeleton.

Nearly all physiological F-actin binding proteins have a finite

binding affinity to actin, which facilitates dynamic crosslinks

between F-actins. Previous studies on the rheology of dynami-

cally crosslinked F-actin networks have focused primarily on the

elastic response of F-actin networks formed with heavy mero-

myosin skeletal muscle II10–12and a-actinin.13–15The contribu-

tions of thermalized unbinding of transient crosslinks can

capture the frequency dependent, linear viscoelastic properties of

these actin networks.10,15However, the extent to which non-

linear effects occur in the viscous behavior of transiently cross-

linked F-actin networks is unknown.

Here, we measure the stress-dependent viscoelasticity in an in

vitro model of the actomyosin cortex of non-muscle cells

comprised of a network of F-actin crosslinked with heavy

aInstitute for Biophysical Dynamics, University of Chicago, Gordon Center

for Integrative Science, E233, 929 E 57th St, Chicago, IL, 60637, USA.

E-mail: gardel@uchicago.edu; Fax: +1 773-834-0406; Tel: +1 773-834-

5871

bJames Franck Institute and Physics Department, University of Chicago,

Chicago, IL, 60637, USA

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meromyosin non-muscle IIB (NMMIIB). We show that

NMMIIB saturated with ADP, to promote a high affinity to

actin, can efficiently crosslink F-actin into viscoelastic networks.

The elastic properties are similar to those observed previously

with moderate stress stiffening observed in densely crosslinked

networks. Here, we demonstrate that these networks also exhibit

shear thickening, whereby the effective viscosity increases by

over ten-fold as the applied stress increased from 0.01 to 4 Pa.

This increased viscosity is a result of both increased elastic

modulus and stress relaxation time at high stresses. A significant

consequence of shear thickening is that the extent of irreversible,

viscous deformation of the networks saturates at high stresses.

Consequently, we find that the relative contribution of viscous

deformations of the network is reduced under applied load.

These results have significant implications for the role of applied

stresses in the modulation of the fluid-like behaviors of the

actomyosin cytoskeleton.

2Experimental procedures

2.1 Protein preparation

Heavy meromyosin non-muscle IIB is prepared as previously

described16and consists of dimeric constructs of non-muscle

myosin IIB containing two enzymatically active heads. Myosin

activity is confirmed using a gliding filament assay.16Actin is

prepared from acetone powder as previously described and is

stored in G-buffer (2 mM Tris–HCl, 0.2 mM CaCl2, 0.2 mM

ATP, 0.2 mM b-mercaptoethanol and 0.01% Na–azide).17All

samples contain either 2 mM ADP or 2 mM ATP (Calbiochem),

which we previously determined to be saturating concentrations

of nucleotide. In the presence of saturating ADP, the release of

myosin heads from actin is inhibited.18Saturating ATP shortens

the myosin dwell time on actin by causing the catalytic heads to

cycle and release from the actin at their maximal rate.16,19

2.2 Rheology

Rheological experiments are performed on a Bohlin Gemini

HRnano (Malvern Instruments) using a 40 mm acrylic plate and

100 mm gap. Experiments are performed in F-actin polymeriza-

tion buffer containing 25 mM KCl, 25 mM imidazole–HCl pH

7.5, 1 mM EGTA, 4 mM MgCl2and 1 mM DTT. To form

isotropic networks, nucleotide, myosin and G-actin are added

sequentially to F-buffer at appropriate concentrations. After

mixing, the solution is placed on the sample plate and incubated

for 1 hour before measurements were made. Network polymer-

ization is assessed by monitoring the elastic modulus for five

minutes at a single frequency to confirm that no change in the

modulus is observed. Effects of ATP depletion are not observed

over a 3 hour measurement window.

3Results and discussion

3.1

with ADP

Non-muscle myosin IIB crosslinks actin when saturated

To serve as a mimimal model of the actomyosin cortex in non-

muscle cells, we chose to form networks of F-actin crosslinked

with heavy meromyosin non-muscle IIB (NMMIIB) motors

(Fig. 1). Full length non-muscle myosin IIB is widely expressed in

non-muscle cells, with important roles in establishing cell

polarity, cell division and cell adhesion.4,5Similar to other

myosin motors, NMMIIB undergoes a mechanochemical cycle

in the presence of ATP that facilitates both translocation of F-

actin and force generation within the actomyosin bond. Within

this cycle, NMMIIB has a weak affinity to F-actin when com-

plexed with ATP (koffz 1 s?1)16and a significantly higher affinity

when complexed with ADP (koffz 0.0003 s?1).19The binding

affinity between F-actin and ADP–myosin shows rich force-

dependence which can lead to enhanced lifetimes under applied

load.20Within cells, full-length non-muscle myosin IIB assembles

into minifilaments comprised of ?20 myosin motors.21To isolate

the mechanical impact of the actomyosin bond and minimize the

effect of structural rearrangements that can occur with the fila-

mentous myosin,22,23we chose to work with heavy meromyosin

non-muscle IIB (NMMIIB), which assembles into dimers.

To characterize the extent to which NMMIIB can cross-link F-

actin into networks, 10 mM G-actin is polymerized in the pres-

ence of a variety of concentrations of NMMIIB, ranging from

0 to 1 mM, such that the molar ratio of NMMIIB to G-actin, R,

varies from 0 to 0.1. We form networks either in the presence of

2 mM ATP, to facilitate the mechanochemical cycle of myosin,

or 2 mM ADP, which engages myosin into a high affinity binding

state to F-actin. Since we polymerize F-actin in the absence of

regulatory proteins, we expect the mean F-actin length to be 7–10

mm,24significantly larger than the expected mesh size of the

network, x z 0.5 mm.25

The rheological effects of NMMIIB crosslinking are observed

when actin/NMMIIB networks form in the presence of 2 mM

ADP. The elastic modulus for actin/NMMIIB–ADP networks is

constant between 1 and 0.01 Hz and is over 10-fold greater than

the magnitude of the viscous modulus (Fig. 2a); we denote the

value of the elastic modulus measured at 0.2 Hz as G00.2. G00.2is

highly dependent on the NMMIIB concentration, increasing

from 0.3 Pa to 1.5 Pa between R ¼ 0.001 and 0.1 (Fig. 2b, closed

circles). These characteristics indicate that NMMIIB–ADP can

efficiently crosslink F-actin into predominately elastic networks.

While previous electron microscopy data have speculated this

crosslinking capability of NMMIIB,18this is the first rheological

data showing the impact on the network elasticity.

Around 0.1 Hz, we observe a weak local minimum in the

viscousmodulusof theactin/NMMIIB–ADPnetworks.

Fig. 1

(pink) are crosslinked by NMMIIB dimers (green). Each dimer has

a catalytic head that can bind actin with certain on-rates (kon) and off-

rates (koff). The affinity of this bond, koff, is altered by the presence of

ATP or ADP.

Actin network crosslinked by NMMIIB dimers. Actin filaments

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Previous measurements of networks formed with the heavy

meromyosin skeletal muscle II (SkMM–ADP) observed a similar

minimum,albeitathigherfrequencies,around1Hz.10,11However,

bycontrasttotheseearliermeasurements,weobservenodecrease

in the elastic modulus down to frequencies of 0.001 Hz. This

suggests that relaxation time scales for actin/NMMIIB–ADP

networks, as measured by the linear viscoelastic response, are

significantly longer than those of actin/SkMM–ADP networks.

In the presence of 2 mM ATP, NMMIIB does not significantly

alter the viscoelasticity of actin/NMMIIB–ATP networks from

that of entangled F-actin. The magnitude of G00.2is similar to

that observed for entangled F-actin and insensitive to changes in

the concentration of NMMIIB–ATP as R varies from 0.001 to

0.1 (Fig. 2b, open circles). These results are consistent with

previous rheological measurements of F-actin networks formed

in the presence of heavy meromyosin skeletal muscle quenched

with ATP26,27and are also consistent with the idea that, in the

presence of ATP, the short-lived interactions of cycling myosin

heads16,19,28diminish the capability of myosin dimers to effi-

ciently crosslink F-actin.

3.2 Actin networks crosslinked with NMMIIB–ADP creep

To measure the viscoelastic behavior under different levels of

applied stress, a series of creep and creep recovery tests are

performed (Fig. 3a and b). Here, a constant stress is applied for

30 seconds and then removed while the strain is continuously

monitored. These creep and creep recovery measurements are

then repeated for a range of stresses, ranging from 0.001 to

4.0 Pa. For applied stresses as low as 0.01 Pa, entangled F-actin

solutions demonstrate considerable creep, with the strain

increasing from 0.05 to 0.12 within 30 seconds of applied stress

(Fig. 3a). This is consistent with previous results,9and likely

arises from the transient nature of physical entanglements in

F-actin solutions.

Despite the strong crosslinking effects observed in the linear

viscoelastic response, creep is also observed in actin/NMMIIB–

Fig. 2

frequency dependent linear elastic (closed squares) and viscous (open

squares) moduli for actin/NMMIIB–ADP network formed with 10 mM

F-actin, 0.5 mM NMMIIB (R ¼ 0.05) in the presence of 2 mM ADP. (b)

The elastic modulus measured at 0.2 Hz, G00.2, for actin/NMMIIB

networks as R is varied from 0.001 to 0.1. Networks formed in the

presence of 2 mM ATP and 2 mM ADP are shown as open and closed

circles, respectively. Actin concentration is 10 mM. Error bars are stan-

dard error.

NMMIIB crosslinks F-actin in saturating ADP. (a) The

Fig. 3

stiffen. (a and b) Creep and creeprecovery tests lasting30 s are performed

over a range of stresses. The applied stress (solid black line) and resultant

strain (open circles, right axis) are shown as a function of experimental

time. Data in (a) are of an entangled F-actin solution (cA¼ 10 mM)

whereas (b) are of a actin/NMMIIB–ADP network (cA¼ 10 mM, R ¼

0.05) (c) The effective elastic modulus, G0eff, is calculated from the creep

tests at different levels of applied stress. Data shown are from an

entangled F-actin solution, R ¼ 0, (closed squares) and actin/NMMIIB–

ADP networks with R ¼ 0.025 (open circles) or R ¼ 0.05 (closed trian-

gles). For all data, cA¼ 10 mM.

Actin/NMMIIB–ADP networks show significant creep and stress

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ADP networks when a steady stress is applied for 30 s. For

relatively low stresses, on the order of 0.1 Pa, the strain increases

from 0.06 to 0.08 whereas, at a higher stress of 1 Pa, the strain

increases from 0.33 to 0.41 (Fig. 3b). Thus, the transient nature

of the NMMIIB–ADP crosslinking is apparent even at short

time scales in these creep measurements.

3.3

stiffen

Densely crosslinked actin/NMMIIB–ADP networks stress

From the series of creep tests, we examine relationships between

stress and strain or strain rate over a wide range of applied stress,

s0. The ratio of s0to the average strain measured between 15 and

30 s, gavg, provides a measure of the effective elastic modulus

during the creep measurement, G0eff¼ s0/gavg.

For entangled F-actin solutions, G0effis constant for applied

stresses below 0.1, indicative of linear elastic behavior (Fig. 3c,

squares). By contrast, as the applied stress is increased above

0.1 Pa, G0eff decreases, indicating stress weakening behavior

which is known to occur for F-actin solutions.7Sparsely cross-

linked actin/NMMIIB–ADP networks (R ¼ 0.025) also have

a constant G0efffor stresses up to 0.1 Pa, but show slight stress

stiffening behavior, with G0effincreasing from 0.3 to 0.45 Pa as

the applied stress is increased from 0.1 to 1 Pa (Fig. 3c, circles).

Bycontrast,denselycrosslinked

networks (R ¼ 0.05) show significant stress stiffening above

applied stresses of 0.1 Pa (Fig. 3c, triangles). When s0< 0.1, G0eff

is remarkably constant. However, when s0is greater than 0.1 Pa,

G0effincreases from 1.5 to 5 Pa. These results are consistent with

previously known transitions between stress weakening and

stress stiffening behavior as the crosslink density is increased.7

Furthermore, they are qualitatively consistent with other types of

measurements used to assess the non-linear elastic response.9

actin–NMMIIB–ADP

3.4

viscosity at higher stresses

Stress stiffening networks demonstrate higher effective

To further evaluate the changes in the viscoelastic nature of the

networks under applied stress, we calculate the effective

viscosity, heff, by determining the ratio between the applied

stress, s0, to the strain rate during the creep measurement. The

strain rate is calculated by finding the difference in strain between

5 and 30 s and dividing by the time to obtain, g ¼ (g(30 s) ?

g(5 s)/25 s. For entangled F-actin solutions, heffis approximately

10 Pa s and independent of the applied stress below 0.1 Pa,

(Fig. 4a, squares). At stresses larger than 0.1 Pa, heffdecreases,

consistent with large deformation rates that occur prior to

breaking. For networks which are weakly stress stiffening (R ¼

0.025), the effective viscosity is remarkably constant between

0.01 and 1 Pa (Fig. 4a, open circles).

For densely crosslinked samples, the effective viscosity

increasesmoderately,from10Pasto30Pasastheappliedstressis

increased from 0.001 Pa to 0.1 Pa. At stresses above 0.3 Pa, the

effectiveviscosityincreasessharply,from30Pastonearly1000Pa

s as the stress is increased up to 4 Pa (Fig. 4a, triangles). Thus, the

effective viscosity is proportional to the applied stress, heffz s0,

and indicates that the viscosity is strongly divergent at a critical

strain rate. Thus, densely crosslinked actin/NMMIIB–ADP

networks demonstrate significant shear thickening whereby the

effective viscosity increases as a function of applied stress.

In a simplified Maxwell model, the viscosity is equal to the

product of the elastic modulus and a time constant characterizing

the stress relaxation, s, such that: h z G0s. Thus, samples that

have stress-dependent changes in G0would be expected to yield

stress-dependent changes in h without any changes to s.

However, by calculating s ¼ heff/G0eff, we find that s is not

constant but rather increases from 10 s to nearly 100 s as the

applied stress is increased from 0.01 to 4 Pa (Fig. 4b, triangles).

Thus, the increase in the effective viscosity at high stresses likely

occurs, in part, from both the increased elastic modulus at high

stresses as well as increased stress relaxation time scales.

Fig. 4

viscosity, heff, as a function of applied stress, s0for entangled F-actin

solution, R ¼ 0 (closed squares), and actin/NMMIIB–ADP networks

with R ¼ 0.025 (open circles) and R ¼ 0.05 (closed triangles). (b) Stress

relaxation time scale, s, as a function of applied stress, s0for actin/

NMMIIB–ADP networks with R ¼ 0.05. (c) The unrecovered strain after

a creep measurement, defined as the difference in the strain prior to

a creep measurement and after the recovery phase, as a function of

applied stress. Entangled actin solutions (solid squares) and actin/

NMMIIB–ADP networks formed with R ¼ 0.025 (open circles) and R ¼

0.05 (closed triangles).

Actin/NMMIIB–ADP networks shear thicken. (a) Effective

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3.5Shear thickening samples preserve shape at high stresses

A second metric by which to characterize the viscous, irreversible

flow is to determine the extent to which the materials regain their

shape after the applied stress is removed during the creep

recovery phase. For a perfectly elastic sample, the strain quickly

returns back to zero after removal of the applied stress whereas

for a purely viscous material, the strain remains unchanged.

Thus, the extent of the unrecovered strain, measured by the

difference between the strain measured at the end of the creep

recovery and the strain prior to application of the applied stress,

characterizes the extent of viscous flow of the network.

The total sample deformation can be deconstructed into the

sum of two modes of deformation reflecting the reversible, elastic

deformation, ge, and the irreversible, viscous deformation, gv,

such that g ¼ ge+ gv. If the strains are additive, the total applied

stress, s0, is equal to both the stress resulting in viscous defor-

mation, sv,and the stress resulting in elastic deformation,se, such

that: s0¼ se¼ sv.9For a sample with a constant viscosity, then

gvz s0and the unrecoverable strain should be linear with the

magnitude of applied stress.

Both entangled F-actin solutions and actin/NMMIIB–ADP

networks show incomplete recovery of strain, consistent with an

irrecoverable viscous flow. For entangled F-actin solutions, the

unrecovered strain increases linearly with applied stresses below

0.08 Pa (Fig. 4c, solid squares). At higher stresses, the unrecov-

ered strain increases faster than the changes in the stress,

consistent with the decreased effective viscosity shown in Fig. 4a.

The unrecovered strain in weakly crosslinked actin/NMMIIB–

ADP networks varies linearly with the applied stress over the

entire range of measurement, from 0.008 to 0.8 Pa s (Fig. 4c,

open circles).

For densely crosslinked actin/NMMIIB–ADP networks (R ¼

0.05), the extent of the unrecovered strain increases linearly with

an applied stress below 0.1 Pa, consistent with the constant

effective viscosity over this range (Fig. 4c, closed triangles).

However, at higher stresses, the unrecovered strain approaches

a plateau such that increased stress does not result in higher

amounts of the unrecovered strain. Thus, shear thickening

samples have enhanced shape preservation at higher stresses than

one would expect for linear viscoelastic samples.

3.6

elastic at high stresses

Densely crosslinked actomyosin networks become more

The nature of the viscous relaxation in actin networks formed

with transient crosslinkers is likely to arise from numerous

processes involving a broad spectrum of relaxation time scales.15

Indeed, during a 30 s creep experiment, we observe that the strain

resembles a power law, such that g(t) z g0ta(Fig. 5a). Similar

power law behavior is observed for creep measurements over

much longer times, on the order of 30 min (data not shown). The

magnitude of a reflects the viscoelastic nature of the network,

with a ¼ 0 reflective of a pure elastic solid and a ¼ 1 reflecting

a viscous fluid. For stresses between 0.001 and 0.01 Pa, entangled

F-actin solutions and actin/NMMIIB–ADP networks have

similar values of a, approximately 0.12 (Fig. 5b). For stresses

above 0.04, a begins to increase for solutions of entangled

F-actin, a further indication of the fluidization of these networks

at higher stresses (Fig. 5b, squares). By contrast, as stresses are

increased from 0.01 to 1 Pa, a decreases for actin/NMMIIB–

ADP networks, reflecting the solidification of these networks at

higher stresses (Fig. 5b, triangles). Interestingly, at higher

stresses, a begins to increase again prior to network breaking.

Thus, under a range of increased stresses, actin/NMMIIB–ADP

networks behave more solid-like.

4 Conclusions

Here we have explored the viscoelastic properties of F-actin

networks formed with heavy meromyosin non-muscle IIB.

Similar to what has been found for heavy meromyosin skeletal

muscle II (SkMM),10–12heavy meromyosin non-muscle IIB can

efficiently crosslink F-actin into elastic networks when quenched

in the high affinity ADP-binding state. Interestingly, the linear

viscoelasticity of actin/NMMIIB–ADP networks has striking

differences from actin/SkMM–ADP networks that may reflect

differences in the nature of these two crosslinkers. For similar

network compositions, actin/NMMIIB–ADP networks appear

to have a lower elastic modulus, suggesting that the efficiency of

crosslinking by NMMIIB–ADP may be impaired. Furthermore,

the viscous relaxation time scales of the actin/SkMM–ADP occur

within 0.1–1 Hz; by contrast, no such relaxation is observed for

actin/NMMIIB–ADP networks down to 0.001 Hz. These results

are consistent with the higher affinity of NMMIIB–ADP to

Fig. 5

stresses. (a) The strain as a function of time for an entangled 10 mM actin

solution (R ¼ 0) is shown at two applied stresses 0.04 Pa (squares)and 0.2

Pa (circles). A scaling exponent, a, is measured by fitting a power law

between1 and30 s. (b)The scaling exponent,a, for anactinsolution(R¼

0, squares) and an actin/NMMIIB–ADP network (R ¼ 0.05, triangles) as

a function of applied stress.

Actin/NMMIIB–ADP networks become more solid-like at high

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actin,19,29which is speculated to be important for the contribu-

tion of NMMIIB in maintaining cellular tension.30

By performing a series of creep measurements over a range of

stresses, we characterized the viscoelastic nature of the actin/

NMMIIB-ADP networks at different levels of force. Similar to

previous data for densely crosslinked F-actin networks, we

observe stress stiffening at high concentrations of NMMIIB–

ADP. However, we also identify that these networks also shear

thicken, such that the effective viscosity also increases under high

stresses. The consequence of a stress-dependent viscosity is that

the extent of unrecoverable deformation is not linearly propor-

tional to applied stress, as one would expect for a linear visco-

elastic material. The net result is that these networks behave

more solid like at higher stresses, such that the extent of irre-

versible, viscous flow is diminished.

One possible mechanism for enhanced solid-like behavior at

high stress is an increased time scale of actomyosin crosslinks.

Numerous reports have shown that the binding affinity of

myosin motors to actin increases under tensile load.16,31Impor-

tantly, the bond between actin and ADP–myosin, as is studied

here, has been shown to behave as a catch bond, whereby the

bond affinity increases with applied force, for forces up to 5 pN.20

At even higher forces, a transition to slip bond behavior,

whereby the bond affinity decreases with applied force, is

observed. We can estimate the force on individual actin/ADP–

myosin bonds in our experiments by considering the length scale

between effective crosslinks within our network, x z 0.5 mm. By

multiplying the applied stress by x2z 0.25 mm2, the forces

applied to each dimer can be estimated to range from 0.25 pN to

2.5 pN as the applied stress is increased from 1 Pa to 10 Pa. Thus,

the stresses we are applying at the macroscopic scale are

consistent with the range of forces where individual actin/ADP–

myosin bonds are expected to display catch bond behavior.

Consistent with slip bond behavior at even higher loads, stresses

higher than 10 Pa cannot be sustained by our reconstituted

actomyosin networks. Thus, our results suggest rheological

consequences of single molecule behavior on viscous flows within

actomyosin networks at different levels of tension.

Recent data have shown that the extent of viscous flow of

actomyosin networks within cells is force-dependent. Nearly all

adherent cells demonstrate a ‘‘retrograde’’ flow of actomyosin

networks from the cell periphery towards the cell nucleus.32

Recently, work has shown that the rate of flow decreases as the

tension within the actomyosin network increases.33Our data

indicate that these observations in live cells could reflect shear

thickening of the actomyosin networks, such that stress relaxa-

tion time scales increase at higher amounts of tension. This

mechanism would facilitate large scale, rapid rearrangements

and deformations of the actomyosin cytoskeleton at low tension,

but facilitate efficient stress transmission through actomyosin

networks with longer stress relaxation time scales at high tension.

Thus, non-linearity in both the viscous and elastic nature of

crosslinked F-actin networks likely plays an important role in

regulating the extent and nature of cytoskeletal deformation

under different levels of tension.

Acknowledgements

M.L.G. acknowledges support from the Materials Research

Science and Engineering Consortium at the University of Chi-

cago, a Packard Fellowship, Burroughs Wellcome Career Award

at the Scientific Interface and NIH Director’s Pioneer Award.

References

1 D. A. Fletcher and R. D. Mullins, Nature, 2010, 463, 485–492.

2 J. Stricker, T. Falzone and M. L. Gardel, J. Biomech., 2010, 43, 9–14.

3 B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts and P. Walter,

Molecular Biology of the Cell, Garland Science, 4th edn, 2002.

4 M. A. Conti and R. S. Adelstein, J. Cell Sci., 2008, 121, 11–18.

5 M. Vicente-Manzanares, X. Ma, R. S. Adelstein and A. R. Horwitz,

Nat. Rev. Mol. Cell Biol., 2009, 10, 778–790.

6 F. C. MacKintosh, J. Kas and P. A. Janmey, Phys. Rev. Lett., 1995,

75, 4425–4428.

7 M. L. Gardel, J. H. Shin, F. C. MacKintosh, L. Mahadevan,

P. Matsudaira and D. A. Weitz, Science, 2004, 304, 1301–1305.

8 C. Storm, J. J. Pastore, F. C. MacKintosh, T. C. Lubensky and

P. A. Janmey, Nature, 2005, 435, 191–194.

9 C. P. Broedersz, K. E. Kasza, L. M. Jawerth, S. Muenster,

D. A. Weitz and F. C. MacKintosh, Soft Matter, 2010, 6, 4120–4127.

10 O. Lieleg, M. M. Claessens, Y. Luan and A. R. Bausch, Phys. Rev.

Lett., 2008, 101, 108101.

11 O. Lieleg, K. M. Schmoller, M. M. Claessens and A. R. Bausch,

Biophys. J., 2009, 96, 4725–4732.

12 R. Tharmann, M. M. Claessens and A. R. Bausch, Phys. Rev. Lett.,

2007, 98, 088103.

13 D. H. Wachsstock, W. H. Schwarz and T. D. Pollard, Biophys. J.,

1994, 66, 801–809.

14 S. M. Ward, A. Weins, M. R. Pollak and D. A. Weitz, Biophys. J.,

2008, 95, 4915–4923.

15 C. P. Broedersz, M. Depken, N. Y. Yao, M. R. Pollack, D. A. Weitz

and F. C. MacKintosh, Phys. Rev. Lett., 2010, 105, 238101.

16 M. F. Norstrom, P. A. Smithback and R. S. Rock, J. Biol. Chem.,

2010, 285, 26326–26334.

17 J. A. Spudich and S. Watt, J. Biol. Chem., 1971, 246, 4866–4871.

18 M. Kovacs, K. Thirumurugan, P. J. Knight and J. R. Sellers, Proc.

Natl. Acad. Sci. U. S. A., 2007, 104, 9994–9999.

19 F. Wang, M. Kovacs, A. Hu, J. Limouze, E. V. Harvey and

J. R. Sellers, J. Biol. Chem., 2003, 278, 27439–27448.

20 B. Guo and W. H. Guilford,Proc. Natl. Acad.Sci. U. S. A., 2006, 103,

9844–9849.

21 R. Niederman and T. D. Pollard, J. Cell Biol., 1975, 67, 72–92.

22 A. B. Verkhovsky, T. M. Svitkina and G. G. Borisy, J. Cell Biol.,

1995, 131, 989–1002.

23 P. M. Bendix, G. H. Koenderink, D. Cuvelier, Z. Dogic,

B. N. Koeleman, W. M. Brieher, C. M. Field, L. Mahadevan and

D. A. Weitz, Biophys. J., 2008, 94, 3126–3136.

24 P. A. Janmey, J. Peetermans, K. S. Zaner, T. P. Stossel and

T. Tanaka, J. Biol. Chem., 1986, 261, 8357–8362.

25 C. F. Schmidt, M. Barmann, G. Isenberg and E. Sackmann,

Macromolecules, 1989, 22, 3638.

26 D. Humphrey, C. Duggan, D. Saha, D. Smith and J. Kas, Nature,

2002, 416, 413–416.

27 Y. Luan, O. Lieleg, B. Wagner and A. R. Bausch, Biophys. J., 2008,

94, 688–693.

28 S. S. Rosenfeld, J. Xing, L. Q. Chen and H. L. Sweeney, J. Biol.

Chem., 2003, 278, 27449–27455.

29 S. B. Marston, Biochem. J., 1982, 203, 453–460.

30 M. Vicente-Manzanares, J. Zareno, L. Whitmore, C. K. Choi and

A. F. Horwitz, J. Cell Biol., 2007, 176, 573–580.

31 C. Veigel, J. E. Molloy, S. Schmitz and J. Kendrick-Jones, Nat. Cell

Biol., 2003, 5, 980–986.

32 M.L.Gardel,I. C. Schneider,

C. M. Waterman, Annu. Rev. Cell Dev. Biol., 2010, 26, 3.1–3.19.

33 Y. Aratyn-Schaus and M. L. Gardel, Curr. Biol., 2010, 20, 1145–1153.

Y.Aratyn-Schaus and

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