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PAPERSamuelI.Stuppet al.Micropatterningofbioactiveself-assemblinggels

ISSN1744-683X

REVIEWDimitrijeStamenovićandDonaldE.IngberTensegrity-guidedselfassembly:frommoleculestolivingcells

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Self-assembly

REVIEW www.rsc.org/softmatter | Soft Matter

Tensegrity-guided self assembly: from molecules to living cells†

Dimitrije Stamenovica and Donald E. Ingber*bc

Received 18th April 2008, Accepted 12th June 2008

First published as an Advance Article on the web 29th August 2008

DOI: 10.1039/b806442c

One of the wonders of life is that all cells undergo continual turnover, and sustain their structure and

function through continuous molecular self assembly. However, this dynamic renewal process is

commonly viewed from the ‘bottom-up’, by focusing on the properties and interaction functions of

individual molecular components. In reality, all cells form from other cells using preexisting structures,

such as the cytoskeleton, as orienting scaffolds that guide replication and formation of new cellular

components. In this article, we take a ‘top-down’ approach and describe how living cells may use

hierarchical tensegrity principles to stabilize the shape and structure of their internal subcomponents at

multiple size scales. We also explain how use of this form of architecture that depends on tensional

prestress for shape stability could provide a mechanism to focus mechanical forces on the molecular

components that comprise these structures, and thereby control their biochemical activities and self

assembly behavior in living cells. In this manner, self assembly of load-bearing structures in cells

proceeds in particular patterns that precisely match the forces they need to bear. This also explains how

cells seamlessly integrate structure and function at all size scales, a process that is fundamental to all

living materials.

Dimitrije Stamenovi�c

Dimitrije Stamenovic is an

Associate Professor of Biomed-

ical Engineering at Boston

University. He received his

Ph.D. degree in mechanics from

the University of Minnesota

(Minneapolis). Prior to joining

Boston University, he worked as

a postdoctoral fellow and

a Research Associate at Har-

vard School of Public Health.

His research interests are in the

areas of biomechanics and bio-

rheology of soft tissues and

cells, respiratory mechanics,

mechanics of foam-like structures and continuum mechanics.

aDepartment of Biomedical Engineering, Boston University, Boston, MA,USAbVascular Biology Program, KFRL 11.127, Departments of Surgery andPathology, Children’s Hospital & Harvard Medical School, 300Longwood Ave, Boston, MA 02115-5737, USA. E-mail: donald.ingber@childrens.harvard.edu; Fax: +1 617-730-0230; Tel: +1 617-919-2223cHarvard Institute for Biologically Inspired Engineering, Cambridge, MA,USA

† This paper is part of a Soft Matter theme issue on Self-Assembly. Guesteditor: Bartosz Grzybowski.

This journal is ª The Royal Society of Chemistry 2009

1. Introduction

Exactly one hundred and fifty years ago, Rudolf Virchow1 first

published his observation that all living cells form from preex-

isting cells—Omnis cellula e cellula. Although this is true, every

time a cell replicates and divides it must form a new cell through

self assembly of a vast number of different molecular compo-

nents. This does not occur in solution, but rather the parent cell

builds its daughter using a preexisting subcellular molecular

framework—the cytoskeleton (CSK)—as a guiding scaffold. The

Donald Ingber

Donald Ingber is the Judah

Folkman Professor of Vascular

Biology in the Department of

Pathology at Harvard Medical

School, as well as Interim Co-

Director of both the Vascular

Biology Program, Departments

of Surgery and Pathology at

Children’s Hospital Boston, and

the Harvard Institute of Bio-

logically Inspired Engineering.

He received his B.A., M.A.,

M.Phil., M.D. and Ph.D. from

Yale University, and completed

his postdoctoral training at

Harvard. His research combines approaches from molecular cell

biology, biochemistry, physics, engineering, nanotechnology and

computer science to address fundamental questions relating to the

relation between structure and function in biology, with a particular

focus on how mechanical forces and physicality influence cell and

tissue development. He also pioneered the application of tensegrity

theory to biological systems.

Soft Matter, 2009, 5, 1137–1145 | 1137

Fig. 1 Continuous tensional integrity in the actin cytoskeleton within,

and between, living cells. This fluorescence micrograph shows the tensed

actin cytoskeleton visualized with fluorescent Alexa488-phalloidin within

a high density culture of mouse embryonic fibroblasts. Note that the

brightly stained actin filaments map out tension field lines and delineate

geodesic (shortest distance) paths as they extend in the form of central

triangulated networks and peripheral linear bundles. This continuous

contractile cytoskeletal network transmits mechanical forces to molecular

elements throughout the cytoplasm, including the nucleus, in addition to

interlinking neighboring tensed cells into a larger prestressed collective

tissue-like structure. Thus, mechanical forces can induce molecular

distortion and associated changes in biochemical activities at multiple sites

throughout the cell simultaneously (image kindly provided by Julia Sero).

CSK is responsible for control of the shape and mechanical

properties of cells, as well as nuclei and mitotic spindles, which

govern cell growth, movement and other behaviors that are

critical for life. It also orients most of the cell’s metabolic

machinery,2 and mediates mechanotransduction, the process by

which cells sense and respond to mechanical cues by altering

intracellular biochemistry and gene expression.3,4 The CSK itself

is a dynamic structure that undergoes continual turnover and

sustained self assembly of individual molecular components over

periods of seconds to minutes,5–8 yet the cell is able to maintain

the structural integrity of most of its load-bearing cytoskeletal

filaments, stabilize overall cell shape, and carry out robust

mechanical behaviors over hours to days.7,9,10 Thus, under-

standing how molecules self assemble into dynamic cytoskeletal

structures that exhibit these novel mechanical properties, and at

the same time alter the rate and pattern of their assembly in

response to mechanical and chemical cues, is one of the most

fundamental challenges in cellular biophysics.

In this article, we describe how cells control their shape and

mechanics through use of an architectural mechanism known as

‘tensegrity’11–13 to structurally integrate thousands of different

molecular components, and focus forces on these structures that

alter their self assembly. Tensegrities self stabilize by imposing an

internal tensional prestress that places the entire molecular

framework in a state of isometric tension. By stabilizing these

molecular scaffolds in place in three dimensions (3D), robust

forms and structural configurations are established in cells, which

are then maintained and remodeled through continuous molec-

ular self assembly. Because these scaffolds bear physical loads in

living cells and tissues, and mechanical stresses can alter molec-

ular shape and biochemistry,3,10 self assembly reactions are

promoted in some regions and inhibited in others. In this manner,

cytoskeletal microarchitecture focuses forces on particular

structures and molecules, and thereby governs molecular self

assembly and remodeling in 3D. As a result, structure and func-

tion are seamlessly integrated in living cells, while individual

subcomponents can be continuously removed and replaced to

ensure short term adaptability as well as long term survival.

Similar principles might have guided how the first living cells

spontaneously originated from progressive hierarchical assembly

of smaller chemical and molecular components.14

2. Control of cell shape and mechanics throughtensegrity

The CSK of eukaryotic cells is an intracellular network

composed of various filamentous biopolymers that determines

cell shape stability. Mechanical properties of the CSK are a direct

consequence of the material properties of the four major classes

of cytoskeletal biopolymers—actin microfilaments, contractile

actomyosin filament bundles, microtubules and intermediate

filaments—as well as how these components are arranged

structurally. Critical to cell shape stabilization is the fact that the

CSK actively generates contractile forces through an actomyosin

filament sliding mechanism and these forces appear to be trans-

mitted via the tensed cytoskeletal lattice to all of the structural

elements of the cell (Fig. 1). For example when cell substrate

adhesions are disrupted, cells retract rapidly,15 as do portions of

the cell when it is severed with a microneedle;16 individual actin

1138 | Soft Matter, 2009, 5, 1137–1145

stress fibers similarly retract spontaneously when ablated by laser

scissors (Fig. 2A), and global rearrangements of the entire CSK

result when this is done in cells adherent to flexible substrates

that mimic the compliance of living tissue.7 Taken together, these

data strongly suggest that the whole CSK is under mechanical

tension.

Although these tensed cytoskeletal elements physically give

shape to the cell, their individual molecular constituents

continuously disassemble and reassemble.5,6,17 Because cyto-

skeletal filaments can chemically depolymerize and repolymerize,

it was initially assumed that cells alter their mechanical proper-

ties via sol–gel transitions.6,18,19 However, cells can alter their

shape without altering the total amount of filamentous

biopolymers in the cell.20 For example, while one microtubule

depolymerizes, another assembles at a different location through

a process known as dynamic instability.5,21 In the case of stress

fibers, fluorescence recovery after photobleaching (FRAP) studies

of cells expressing green fluorescent protein (GFP)-labeled actin,

combined with laser nanosurgery, show that individual actin

monomers contained within these contractile actomyosin

filament bundles exhibit rapid turnover with a half time of

fluorescence recovery of �5 min, even though the mechanical

integrity of the higher order, tensed multimolecular assembly

(i.e., the whole stress fiber) is maintained for hours (Fig. 2).7

Similarly, although intermediate filaments were thought to be

low turnover structures because of their high load-bearing

capacity (e.g., they are largely responsible for the tensile strength

of epidermis), their individual subcomponents also continuously

come and go.17 A simple analogy would be a ship’s hawser woven

from many smaller cables: if only a portion of the cables is

This journal is ª The Royal Society of Chemistry 2009

Fig. 2 Mechanical roles of self assembling cytoskeletal filaments. A)

Stress fibers visualized using GFP-actin in adherent cells that were first

photobleached with a laser (Bleach), and then a single stress fiber bundle

was cut using a femtosecond laser nanoscissor (Arrow, immediately

before laser ablation). The bottom view, immediately following the laser

application, shows that the cut parts of the fiber spontaneously retract,

indicating that they carry tension. Note that FRAP analysis of these

fibers indicates that GFP-actin is continually unbinding and reassembling

on the surfaces of these stress fiber bundles with a half time of �5 min in

these same cells (see Kumar et al.7 for details). B) Microtubules visualized

over time (as indicated in s) in a beating cardiac muscle cell expressing

GFP-tubulin. Whenever the cell contracts, the microtubule (highlighted

in red) immediately buckles indicating that it carries compression in

response to contraction of the actin network. (Obtained with permission

form Brangwynne et al.9).

Fig. 3 Schematic representations of the tensegrity force balance. A) A

simple self-stabilizing tensegrity network composed of three compression

struts interconnected by a continuous series of tensed cables. B) The

complementary tensegrity force balance between tensed actin microfila-

ments (MF), compressed microtubules (MT) and traction forces at the

focal adhesion (FA) contacts. Part of the contractile tension is trans-

mitted by MFs to FAs and balanced by traction, and part is balanced

internally by compression of MTs. C) A schematic of an entire spread cell

adherent to underlying ECM (gray) with central nucleus and radially

oriented microtubules (red) that oppose the inward-directed forces

generated by the surrounding actomyosin network (geodesic black

lattice).

necessary to hold the ship at port, then it is possible to contin-

ually remove and replace individual cables without compro-

mising the mechanical integrity of the whole. Intermediate

filaments and actin stress fibers appear to act similarly, whereas

more dynamic specialized actin structures, such as lamellipodia

and filopodia, are more directly dependent on the driving force of

actin polymerization, and hence they grow and shrink as actin

monomers are added or removed, respectively.6

Based on these observations relating to the mechanical

stability, connectivity and contractility of cytoskeletal filaments,

we suggested the possibility that the CSK may be organized as

a tensionally prestressed network.3,13,22–24 This type of architec-

tural network that utilizes tension balanced by internal

compression elements to create a self-equilibrated stable

mechanical structure is known as tensegrity.11,12 An example of

a simple, single tensegrity structure that embodies many of the

key mechanical behaviors of more complex modular tensegrities,

such as those that comprise living cells, is shown in Fig. 3A. In

the tensegrity model of the cell, the prestress (pre-existing

tension) in the internal CSK is generated through establishment

of a complementary force balance between contractile microfil-

aments that actively generate tensional forces and other intra-

cellular and extracellular structures that resist and balance these

forces (Fig. 3B). Microtubules and stiffened cross-linked actin

bundles (e.g., in filopodia) can act to resist inward-directed

contractile forces inside living cells and at its surface membrane,

as can the cell’s external adhesions to extracellular matrix (ECM)

(Fig. 3C) and to neighboring cells.13,23,24 Experimental data from

This journal is ª The Royal Society of Chemistry 2009

numerous studies suggest that cells utilize this type of force

balance to self-organize and to stabilize their CSK25–36 and to

regulate its deformability37 under various experimental condi-

tions.

Cytoskeletal tensional forces are transferred to the ECM via

integrin receptor-containing focal adhesions (FAs) (Fig. 3B), and

to the opposing CSKs of neighboring cells through cadherin-

containing cell–cell adhesion complexes. The traction forces that

arise at these extracellular membrane adhesions are largely

responsible for opposing cytoskeletal tensile forces, and bringing

them into balance.28,29,37,38 However, cytoskeletal tension is also

resisted by long internal microtubules that can buckle under the

compressive loads generated by the surrounding contractile CSK

(Fig. 2B), but support surprisingly high levels of compressive

forces (100 pN) per microtubule when surrounded by a visco-

elastic cytoplasm.9 Microtubules bear even higher compressive

loads when they are cross-linked within large bundles as in nerve

cells,39 or laterally tethered to other cytoskeletal filament systems

(e.g., intermediate filaments) that can function like guy wires.40

Because of the existence of a complementary force balance, the

proportion of forces borne by microtubules versus the ECM

substrate shifts as cells form more and more ECM adhesions.

For example, experimental studies show that microtubules

contribute to nearly 50% of cytoskeletal prestress in poorly

adherent cells, whereas they only contribute a few percent when

cells become extremely well spread on rigid ECM-coated

Soft Matter, 2009, 5, 1137–1145 | 1139

Fig. 4 A schematic depiction of how cells’ use of a tensegrity force

balance promotes microtubule (MT) polymerization (addition of grey

monomers on distal end), focal adhesion (FA) assembly, bundling of

microfilaments (MFs), and extension of intermediate filaments (IFs)

when tension is applied to the ECM and the MTs become decompressed.

substrates;33,38 in well spread cells, each microtubule carries

a compressive load of �30 pN.33 This is because with increasing

cell–ECM contact formation, the contribution of traction forces

at FAs that balance the contractile prestress increases at the

expense of compression in microtubules. In this manner, the cell

stabilizes its shape much as if it were a tent, using anchoring pegs

(e.g., FAs), poles (microtubules), and then winching in the cables

and membranes to tense (i.e., prestress) the entire structure, and

thereby create a stable form—this is the essence of the cellular

tensegrity model.

Cells may also use tensegrity to stabilize subcellular structures

and multi-molecular complexes at smaller size scales. The

mechanical stability of the cell membrane and underlying sup-

porting ‘cortical’ CSK (in erythrocytes) has been accurately

modeled using a tensegrity model in which spring-like spectrin

molecules organized geodesically in triangulated arrays pull

against relatively rigid actin protofilaments and non-

compressible regions of the lipid bilayer.41,42 The shape stability

of nuclei, mitotic spindles, actin stress fiber bundles, individual

actin filaments, lipid micelles, viral particles, clathrin-coated

vesicles and single molecules (e.g., proteins, DNA) all can be

effectively described using tensegrity models.10,12–14,43 Moreover,

in hierarchical tensegrities in which smaller tensegrity networks

are connected to larger ones by the same rules (maintenance of

tensional integrity), the entire system is mechanically and

harmonically coupled, and forces are channeled across different

length scales over the load-bearing elements of these discrete,

tensed, multi-component networks.10,13,23,24 Experimental studies

confirm that forces applied to the external face of trans-

membrane integrin receptors that physically couple to the CSK

transmit forces long distances in the cell and result in molecular

realignment deep inside the cytoplasm and nucleus, as well as

force concentrations at the opposite pole of the cell which

disappear when cytoskeletal prestress is dissipated.44,45

Because cells may stabilize their whole shape and linked

internal structures using tensegrity, there should be a comple-

mentary force balance between tension in the actin networks

(and linked intermediate filament system), compression of

microtubules, and traction on FAs (which strains the ECM when

each stress fiber contracts). At the level of a single FA, this force

balance is described as follows (Fig. 3B):

Ft ¼ Fc + T, (1)

where Ft is the tension vector of actin filaments, Fc is the

compression vector of microtubules and T is the traction vector

at adhesions to the ECM. Altering this force balance either

internally by stimulating actomyosin filament contraction, or

externally by applying mechanical forces to the ECM and the

cell, leads to redistribution of tension and compression in the

load-bearing components of the CSK and linked structures that

can, in turn, alter molecular shape and hence, change biochem-

ical activities at the nanometre scale.

3. Tensegrity-guided mechanochemical control ofmolecular self assembly

Cytoskeletal tension influences polymerization of actin, micro-

tubules and FAs,32,46,47 as well as the activities of many

1140 | Soft Matter, 2009, 5, 1137–1145

biochemical signaling molecules because mechanical distortion

or changes in oscillatory motion of molecules and biopolymers

can alter their chemical potential or kinetic behavior.10 For

example, thermodynamics shows that elastic stresses generated

by tensile forces applied to molecular polymers (e.g., individual

microtubules or microfilaments) or aggregates (e.g., FAs)

decrease their chemical potential relative to the molecular

reservoir of free, non-assembled monomers.3,48–52 Since

a decrease in potential is favored physically, decreasing chemical

potential through this mechanical means will drive biopolymer

assembly. In contrast, when it is compressed, polymer self

assembly is disfavored, and depolymerization is promoted. The

difference in the chemical potential (Dm) of an aggregate or

polymer relative to the molecular reservoir in response to

a tensile or a compressive force (F) can be described by the

following equation51

Dm ¼ Dm0 � Fl0 �F 2

2kl0; (2)

where Dm0 is the difference in the potential in the absence of

force, l0 is the average length of a monomer before force appli-

cation, and k is the tensile stiffness of the aggregate. The last term

in eqn (2) represents the elastic potential of the polymer per

monomer (for simplicity, we assume that the polymer behaves as

a linear elastic system). The molecular exchange between the

cytoplasm (reservoir of free monomers) and polymers depends

on the sign of Dm; if Dm < 0 free monomers will tend to join the

polymers (i.e., polymer assembly) and if Dm > 0 polymers will

lose monomers (i.e., polymer disassembly).

According to eqn (2), tensile forces (F > 0) cause Dm to

decrease, whereas compressive forces (F < 0) cause Dm to

increase, but in both cases the elastic potential decreases Dm. This

contribution of the elastic potential may be negligible in the case

of actin filaments that have relatively high tensile stiffness. But it

may be important in the case of stress fibers,53 which are more

This journal is ª The Royal Society of Chemistry 2009

extensible than individual actin filaments,54 and of microtubules

which buckle under compression, and then have a relatively low

effective compressive stiffness.33 Conversely, microtubule poly-

merization can be induced by tensing cell surface ECM receptors

and thereby, decompressing microtubules (Fig. 4).22,55–57

Using the complementary force balance (eqn (1)) and the

mechanically-induced change in the chemical potential (eqn (2)),

we can predict assembly of various molecular structures of the

CSK in response to modulation of cytoskeletal tension. For

example, because cell traction forces are focused on the cell’s

adhesions to the ECM within FAs, some of the molecular

components of the FA anchoring complexes experience high

levels of mechanical stress. If myosin motor activity increases and

actin tension rises, then compression on microtubules and trac-

tion on FAs will increase. Consequently, actin filaments and FAs

will assemble,8,46,58–61 whereas microtubules will buckle and

disassemble, as observed in living cells.28,62 If on the other hand,

cytoskeletal tension is increased by straining the ECM or by

spreading of the cell, traction on FAs will increase while

compression of microtubules will diminish. Consequently, FAs

and microtubules will grow, and this is again precisely what is seen

in cells.32,39,48,56,57,60,63 During cell spreading, growing microtu-

bules that come into close juxtaposition to FAs also may bear

some compressive load, and thereby reduce the tension exerted on

FAs;24,64 this can cause FAs to disassemble and become smaller.65

The complementary force balance appears to provide a way to

shift forces between these various load-bearing molecular

elements in the cell, and thus it may have a direct impact on their

self assembly. However, through evolution, nature has enhanced

this form of regulation by overlaying other mechano-chemical

modulation schemes. This complexity has sometimes obscured

the fundamental role that complementary force balances

contribute to cell regulation. For example, the finding that

depolymerizing microtubules increases ECM traction when cells

are cultured on flexible substrates provided evidence in support

of the existence of a tensegrity force balance in cells: the

compressive force originally borne by microtubules was trans-

ferred to external ECM adhesions.66 But then another study

discovered that much of this response (�85%) is mediated by

activation of myosin light chain phosphorylation and tension

generation, hence suggesting that it is controlled chemically.67

However, later experiments demonstrated similar force transfer

from microtubules to ECM adhesions when the microtubules

were depolymerized even under conditions where myosin motors

were optimally stimulated.28 Finally, it was discovered that

increased tension on integrin receptors in ECM adhesions

increases cytoskeletal tension by activating the small GTPase

Rho, which stimulates Rho-associated kinase (ROCK) to

enhance myosin light chain phosphorylation, while promoting

actin polymerization through another effector, mDia.61 The

point is that because of the existence of a complementary force

balance, compressive forces borne by microtubules are shifted to

ECM adhesions when these biopolymers are disassembled, and

then the enhanced traction on integrins feeds back to activate

Rho-dependent contractility, thereby amplifying this response. A

reproducible and statistically significant increase in force transfer

occurs using the tensegrity mechanism alone, but through

mechanochemistry, a five to ten times higher level of traction can

be generated.

This journal is ª The Royal Society of Chemistry 2009

Another example is the finding that forming ECM adhesions,

and thereby transferring compressive loads off microtubules and

onto FAs, promotes microtubule assembly and neurite

outgrowth in nerve cells,39,49,56 as predicted by eqn (1) and (2).

However, the total levels of microtubule monomer and polymer

generally remain constant in epithelial cells, even when they vary

their ECM adhesions and change shape.21,68 Tubulin monomer

concentrations are thought to remain relatively constant because

of tubulin ‘autoregulation’: when tubulin monomer levels

increase, they feed back to inhibit tubulin protein synthesis by

selectively destabilizing tubulin mRNA.68 At first glance, this

would suggest that these cells do not utilize a tensegrity balance

because decreasing ECM adhesions and rounding cells should

compress microtubules and induce their disassembly, if tubulin

monomer levels remained constant. But then it was discovered

that steady-state tubulin monomer levels actually increase in

rounded cells with fewer ECM adhesions to compensate for the

change in chemical potential of the monomers within the

compressed microtubules, thereby maintaining a constant

amount of microtubule polymer in the cell.20 In this mechano-

chemical mechanism, tubulin autoregulation (which decreases

tubulin monomer synthesis) is offset by a specific slowing of

tubulin protein degradation. How these force shifts between

ECM and microtubules produce these complex, but finely

balanced, effects remains unknown; however, it demonstrates

that cellular regulation is not a question of chemistry or physics,

but a tight coupling between both that may be facilitated through

use of tensegrity principles.

Self assembly of FAs may be similarly regulated directly by

forces shifted to cell–ECM adhesions via the tensegrity force

balance, and indirectly through force-dependent mechano-

chemical mechanisms as different structural molecules within the

same FA respond differently when traction is increased on

integrins in these ECM adhesions. For example, mechanical

stress application to integrins leads to mechanical unfolding of

the FA protein, p130Cas, which may further influence FA self

assembly by altering protein phosphorylation.69 Mechanical

tension applied to integrins also directly activates stress-sensitive

ion channels on the cell surface,70 which will change various

calcium-dependent self assembly processes in the cell, including

gene transcription. Force application to integrins and the cyto-

skeletal linker proteins of the FA also can activate numerous

intracellular signaling molecules, including small and large G

proteins, protein kinases, and adenylyl cyclase (i.e., cAMP

production) by modulating protein conformation and molecular

assembly dynamics in the FA.3,71

Shifting forces onto FAs also increases self assembly of the

cytoskeletal proteins that form the backbone of the FA, and the

FA disassembles when tension is dissipated (Fig. 5). For

example, decreasing cytoskeletal tension alters the binding

kinetics of the FA protein, zyxin, by increasing its unbinding

constant (koff), whereas vinculin in the same FAs does not change

its kinetics.8 Interestingly, when zyxin is released from FAs, it can

travel to the nucleus and alter gene transcription.72 But these

effects appear to be indirect because force-dependent FA

assembly requires activation of Rho and associated stimulation

of its downstream effectors ROCK and mDia, which again

feedback to stimulate enhanced tension generation and increased

actin assembly, respectively.61

Soft Matter, 2009, 5, 1137–1145 | 1141

Fig. 5 Mechanical control of focal adhesion self assembly. A) Fluo-

rescence micrographs of endothelial cells expressing GFP-zyxin which

localizes primarily in streak like focal adhesions before (Control) and

after 15 or 30 min treatment with the ROCK inhibitor, Y27632, to

dissipate cytoskeletal prestress. Note that tension dissipation promotes

zyxin disassembly over this time course. B) Recovery curve for zyxin in

control (open circles) versus Y27632-treated cells (closed triangles)

measured using FRAP analysis; the solid lines are curves fit to the data

(solid lines) using the method of least squares. C) Measurements of the

koff of zyxin during the time of exposure to Y27632 (error bars indicate

SEM). The koff measured in each of the Y27632-treated cells was

significantly increased relative to the koff measured in control cells (see

Lele et al.8 for details).

Forces that are preferentially transferred across integrins in

FAs and channeled through the CSK (Fig. 1) can also alter

signaling activities and molecular assembly reactions deep inside

the cell.3,10,13 For example, pulling on integrins with micropi-

pettes results in immediate realignment of molecular cytoskeletal

filaments in the cytoplasm and of nucleoli inside the nuclei of

living cells.44 This raises the possibility that assembly and func-

tion of intranuclear structures, such as chromatin protein

complexes and nuclear matrix scaffolds involved in gene tran-

scription, RNA processing, DNA replication and other nuclear

functions, could potentially be regulated directly by mechanical

stresses channeled from the cell surface over discrete prestressed

cytoskeletal elements.3,23,73 Although direct mechanical effects on

gene transcription have not been demonstrated, it is known that

the nucleus must physically expand before DNA replication can

proceed.74,75 Stresses channeled through the CSK can also acti-

vate stress sensitive calcium channels on the nuclear membrane,

which may modulate gene transcription by altering molecular

self assembly processes inside the nucleus.76 Forces transferred to

the huge cytoskeletal protein, titin, can also regulate gene tran-

scription as a result of physical unfolding of its peptide back-

bone, which modulates self assembly of a protein signaling

complex at its protein kinase domain that controls nuclear

translocation of MuRF2, a ligand of the transactivation domain

of the serum response transcription factor (SRF).77

Cell–cell contacts mediated by cadherins also mediate trans-

membrane force transfer to the CSK78 and thereby influence the

1142 | Soft Matter, 2009, 5, 1137–1145

tensegrity force balance. These contacts enable load transfer

between adjacent cells and shift part of the cytoskeletal tension

from integrin-containing FAs to cadherin-based cell–cell

contacts, such that when FAs disassemble, cell–cell junctions

strengthen and grow.79 These changes in molecular self assembly

within cell junction complexes that could be mediated via ten-

segrity-based force transfer between FAs, CSK filaments and

cell–cell contacts are of great physiological importance because

they regulate vascular permeability in vitro and in vivo.36

Complementary force balances also influence the actin poly-

merization that drives formation of protrusive lamellipodia and

filopodia that extend from the leading edge of cells and mediate

cell migration. The proximal ends of these structures are linked to

regions of the actin CSK that are stiffened through triangulation

within geodesic regions of the network,80,81 or to underlying FAs

at the cell base that indirectly or directly anchor them to the

substrate. These actin filaments polymerize and form stiffened

bundles or planar networks (in filopodia or lamellipodia,

respectively) that push against the upper tensed plasma

membrane of the cell and against proximal linkages to the tensed

actomyosin filament networks at the leading edge (Fig. 6); this

creates another tensegrity force balance on a smaller scale.24,64

However, the basal anchoring points of the actin filament bundles

and planar networks act like flexible hinges and thus, these

structures wave up and down as the cell moves forward. Changes

in this force-balance due to elevation of cytoskeletal contractile

forces or external mechanical signals control cell migration.82–86

Moreover, although these actin rich protrusions push the

membrane outward through the force of actin polymerization,

they are also simultaneously under tension. For instance, as soon

as a growing filopodium (which uses cross-linked bundles of actin

filaments as internal compression struts) comes into contact with

an ECM-coated micropipette or substrate, traction can be

detected that feeds back to regulate tubulin self assembly.87,88

The above examples describe a potential connection between

the force balance inside the cell and intracellular biochemical

signaling. While this relationship is relevant regardless of the

mechanisms by which forces are transmitted through the CSK,

the tensegrity model offers a plausible description of how the

complementary force balance may be used by the cell to alter

cellular biochemical activities. More specifically, if cells used

a prestress-based tensegrity mechanism to structure themselves,

then these discrete networks will preferentially channel and focus

forces over long distances in the cell at faster rates than via

chemical diffusion. In addition, tensegrity predicts that varying

prestress will alter mechanical signal transfer and associated

mechanochemistry; these predictions are not consistent with

long-range force transfer across rigid elements. Most impor-

tantly, there are now numerous studies that experimentally

demonstrate prestress dependence of long range force transfer in

cells and nuclei, as well as of associated biochemical signaling

events at these distant sites.45,89–91

Changes in the complementary force-balance between these

stiffened actin structures, cytoskeletal contractile forces and

external mechanical stresses conveyed over integrins and FAs

control cell migration.82–86 This is because cell motility relies on

the stabilization of FA–CSK contacts and the local generation of

force, which overcomes the resistance to migration. The strength

of FA contacts depends on substrate rigidity (i.e., its ability to

This journal is ª The Royal Society of Chemistry 2009

Fig. 6 Tension-based control of actin polymerization during cell spreading and motility. A) The continuous actin CSK tensionally stiffens and

remodels into basal stress fibers and an apical dome as a result of transmitting force across the cell’s basal FA sites and to the compression-resistant

ECM. Increased binding of cell surface integrin receptors at the leading edge of the cell results in increased inositol lipid (PIP2) synthesis and subsequent

release of free actin monomer (not shown). Vertices on the dome that are free of tropomyosin and myosin act as nucleation sites for actin polymerization

and result in extension of MF bundles that form the core of a newly formed filopodium. Contraction of loose MF nets that interconnect this MF bundle

with basal stress fibers and the rear-lying apical dome cause the filopodium to move down and up. B) Greater tension within the basal CSK pulls the

filopodium downward, using its point of attachment to the tensionally-stiffened dome as a fulcrum. Fixation of the tip of the exploring filopodium to the

rigid ECM substratum due to ECM receptor binding shifts the CSK force balance. The trailing CSK lattice is pulled downward and slightly forward due

to continuous tension molding. Downward motion of the actin dome results in exposure of new vertices and self assembly of a second filopodium begins.

C) Tension molding of the continuous prestressed lattice continues and the surrounding actin nets within the lamellopodium are pulled forward along

the stiffened filopodial microfilament core. Actin microfilaments within these nets also tend to align and interconnect with the rear-lying basal stress

fibers. Flattening and forward movement of the actin dome continues as does growth and extension of the newly forming filopodium. D) The flattened

filopodial core merges with the rear basal stress fiber, a new FA forms closer to the new leading edge, transferring traction force from the old FA which

subsequently disassembles. The system is recocked and the second filopodium begins its own exploration of the substratum. Reiteration of this process

promotes cell spreading and net forward motion (see Ingber et al.64 for details). Note that only the actin CSK is depicted; ECM, extracellular matrix;

solid black rectangles, FAs. (Obtained with permission from Ingber et al.64).

resist cell contraction) and thus, cells use it to direct their

migration.83 Cells probe substrate stiffness using their contractile

apparatus through their filopodia and lamellipodia. Those

protrusions that land on stiff substrate regions receive strong

feedback, anchor to the substrate, and redistribute tensile forces

such that the entire CSK and cell pull themselves forward

(Fig. 6), whereas those that land on soft substrate regions receive

weak feedback, have mobile anchorages and become

unstable.22,60 This creates a bias that guides cell movement from

softer towards stiffer substrate regions, through a process known

as durotaxis.84,85,92–94

As described above, a similar tensegrity force balance may also

provide shape stability to the erythrocyte membrane,42 which

closely resembles the cortical submembranous CSK of eukary-

otic cells. The basic structural unit of the submembranous skel-

etal network is composed of a geodesic tessellation of ‘‘spoked’’

hexagons formed by six tension-bearing spectrin dimers that

radiate from a central strut-like actin protofilament towards six

suspension complexes that anchor the molecules to the lipid

bilayer membrane that surrounds the cell.41,42 Mechanical

deformations of the erythrocyte membrane induce changes in

spectrin tension and protofilament orientation, thereby trans-

ducing mechanical signals into biochemical events at the bilayer

and submembranous CSK.42 It is likely that similar force

balances exist in the plasma membranes of all eukaryotes, which

may similarly control the rate and pattern of molecular self

assembly.

In summary, maintenance and renewal of the load-bearing

structural elements of the entire cell and CSK that self renew

through continuous molecular self assembly appear to be gov-

erned by the tensegrity force balance principle. Tensional forces

borne by the actin cytoskeletal network and intermediate fila-

ments are balanced internally by compression of microtubules

and externally by tethering forces of adhesion to the ECM

This journal is ª The Royal Society of Chemistry 2009

(Fig. 3) and cell–cell contacts.9,28,29,33,34,38,79 Similar forces are

balanced between the surface membrane and internal contractile

CSK as when cells are osmotically swollen,95 and between the

nucleus and the surrounding cytoskeleton.15,44

The existence of this complementary balance may explain how

external mechanical signals can propagate a long distance

through the cell and be sensed by intracellular signaling molecules

and structures that are distributed throughout the cell, including

mitochondria, nuclei, and nucleoli, as demonstrated in the

past.44,45,96 Even more importantly, these forces may govern the

pattern of molecular assembly, for example, actomyosin filament

bundles and stress fibers map out tension field lines within the

cytoplasm.44,97,98 Moreover, the efficiency of force transmission

through the cell appears to depend on the level of the prestress in

the cytoskeletal filaments. While mechanical signals can be

transferred over long distances along a solid structure whether or

not it is prestressed, experimental data from living cells show that

an increase in tensile prestress increases long distance propagation

of external mechanical signals through the cell, whereas inhibition

of tension results in only a localized effect at the cell

periphery.45,91,96 This, in turn, suggests that mechanical signal

transmission through the cell demands that the CSK be organized

as a solid network structure in which stability and rigidity are

conferred by cytoskeletal prestress.

Thus, the shape and biological function of a cell may be more

a manifestation of the hierarchical self organization of its CSK,

than a result of generalized chemical self assembly. It is the

cytoskeletal lattice, which maintains its shape stability through

the agency of tensile prestress and the formation of a comple-

mentary force balance, that may provide a physical mechanism

to direct its own continuous self assembly in distinct 3D patterns

that maintains cell form and function. This same tensegrity-

based stabilization mechanism may provide a way to transduce

mechanical signals into changes in intracellular biochemistry and

Soft Matter, 2009, 5, 1137–1145 | 1143

alterations of molecular polymerization throughout the cell and

nucleus, and thereby integrate structure and function.

4. Summary

Living cells maintain their structure and function through

continuous molecular self assembly; however, this does not occur

in isolation or through solution chemistry. In this article, we

described how cells may stabilize the shape of their CSK, nuclei

and other specialized structures at smaller length scales using the

tensegrity principle in which prestress conveys shape stability in

3D. Most importantly, these tensionally-stabilized networks may

provide a conduit for preferential force channeling across the cell

and over various length scales so that stresses applied at the

macroscale can result in molecular conformational alterations at

the nanoscale. In this manner, tensegrity may facilitate mechano-

chemical transduction and may convert mechanical forces into

changes in molecular biochemistry. Some of these changes feed

back to control the self assembly of these very same cytoskeletal

structures that both generate tension and resist stresses borne by

these shape stabilizing networks.

Because molecular assembly events are influenced by force,

and mechanical loads are distributed in specific patterns across

cytoskeletal elements, biochemical reactions can be induced to

proceed in specific patterns that precisely match the needs of the

cell to resist those applied stresses. Due to the existence of

a complementary force balance between microtubules, contrac-

tile microfilaments, intermediate filaments and membrane

adhesion complexes, forces can be shifted back and forth

between complementary load-bearing elements and thereby alter

their orientation and self assembly. This simple mechanical

balance has important physiological relevance for cells, tissues,

and organs. One simple example is how transferring forces off

microtubules and onto ECM adhesions decompresses microtu-

bules and thereby promotes their assembly and nerve growth. In

fact, nerves will extend new processes in whatever direction

tension is applied to their surfaces through ECM adhesions,39,55

and nerve fiber patterns map out minimal paths that correspond

to tension field lines in whole organs, including the brain, which

appear to be driven by mechanical energy minimization.99,100

Another example is the observation that internal microtubules

become compressed and buckle when beating heart cells

contract, and they undergo elastic recoil and help the cell restore

its extended shape when they relax.9 Moreover, abnormal

increases in self assembly of microtubules in heart cells impairs

contraction (due to increased internal resistance) and leads to

heart failure in whole animals.101,102

The challenge for the future is to develop more complex hier-

archical tensegrity models of cell structure and mechanics, and to

couple them to equally quantitative descriptions of molecular self

assembly that can incorporate shape, orientation and pattern as

well as total polymer mass. In short, we need to integrate ‘physi-

cality’ into systems biology, and tensegrity may greatly facilitate

this unification of biology, chemistry and physics.

5. Acknowledgements

This work was supported by grants from NIH, NSF, DARPA

and Coulter Foundation. Dr Ingber is a recipient of a DoD

1144 | Soft Matter, 2009, 5, 1137–1145

Breast Cancer Innovator Award. We thank Julia Sero for

allowing us to use her microscopic image.

6. References

1 R. Virchow, Die Cellularpathologie in ihrer Begrundung aufphysiologische und pathologische Gewebelehre, August Hirschwald,Berlin, 1858.

2 D. E. Ingber, Cell, 1993, 75, 1249–1252.3 D. E. Ingber, Annu. Rev. Physiol., 1997, 59, 575–599.4 P. A. Janmey, Physiol. Rev., 1998, 78, 763–781.5 T. Mitchison and M. Kirschner, Nature, 1984, 312, 237–242.6 T. P. Stossel, Science, 1993, 260, 1086–1094.7 S. Kumar, I. Z. Maxwell, A. Heisterkamp, T. R. Polte, T. P. Lele,

M. Salanga, E. Mazur and D. E. Ingber, Biophys. J., 2006, 90,3762–3773.

8 T. P. Lele, J. Pendse, S. Kumar, M. Salanga, J. Karavitis andD. E. Ingber, J. Cell. Physiol., 2006, 207, 187–194.

9 C. P. Brangwynne, F. C. MacKintosh, S. Kumar, N. A. Geisse,J. Talbot, L. Mahadevan, K. K. Parker, D. E. Ingber andD. A. Weitz, J. Cell Biol., 2006, 173, 733–741.

10 D. E. Ingber, FASEB J., 2006, 20, 811–827.11 B. Fuller, Portfolio Artnews Ann., 1961, 4, 112–127.12 D. E. Ingber, Sci. Am., 1998, 278, 48–57.13 D. E. Ingber, J. Cell Sci., 2003, 116, 1157–1173.14 D. E. Ingber, BioEssays, 2000, 22, 1160–1170.15 J. Sims, S. Karp and D. E. Ingber, J. Cell Sci., 1992, 103, 1215–1222.16 J. Pourati, J. A. Maniotis, D. Spiegel, J. L. Schaffer, J. P. Butler,

J. J. Fredberg, D. E. Ingber, D. Stamenovic and N. Wang, Am. J.Physiol.: Cell Physiol., 1998, 274, C1283–C1289.

17 K. L. Vikstrom, S. S. Lim, R. D. Goldman and G. G. Borisy, J. CellBiol., 1992, 118, 121–129.

18 P. A. Janmey, S. Hvidt, L. Lamb and T. P. Stossel, Nature, 1990,345, 89–92.

19 M. Tempel, G. Isenberg and E. Sackmann, Phys. Rev. E, 1996, 54,1802–1810.

20 D. Mooney, L. Hansen, R. Langer, J. P. Vacanti and D. E. Ingber,Mol. Biol. Cell, 1994, 5, 1281–1288; D. Mooney, R. Langer andD. E. Ingber, J. Cell Sci., 1995, 108, 2311–2320.

21 M. Kirschner and T. Mitchison, Cell, 1986, 45, 329–342.22 D. E. Ingber, J. A. Madri and J. D. Jameison, Proc. Natl. Acad. Sci.

U. S. A., 1981, 78, 3901–3905.23 D. E. Ingber and J. D. Jamieson, in Gene Expression during Normal

and Malignant Differentiation, ed. L. C. Anderson, G. C. Gahmbergand P. Ekblom, Academic Press, Orlando, FL, 1985, pp. 13–32.

24 D. E. Ingber, J. Cell Sci., 1993, 104, 613–627.25 N. Wang, J. P. Butler and D. E. Ingber, Science, 1993, 260, 1124–

1127.26 N. Wang and D. E. Ingber, Biophys. J., 1994, 66, 2181–2189.27 N. Wang and D. Stamenovic, Am. J. Physiol.: Cell Physiol., 2000,

279, C188–C194.28 N. Wang, K. Naruse, D. Stamenovic, J. J. Fredberg,

S. M. Mijailovich, I. M. Tolic-Nørrelykke, T. Polte, R. Mannixand D. E. Ingber, Proc. Natl. Acad. Sci. U. S. A., 2001, 98, 7765–7770.

29 N. Wang, I. M. Tolic-Nørrelykke, J. Chen, S. M. Mijailovich,J. P. Butler, J. J. Fredberg and D. Stamenovic, Am. J. Physiol.:Cell Physiol., 2002, 282, C606–C616.

30 D. E. Discher, P. Janmey and Y.-L. Wang, Science, 2005, 310, 1139–1143.

31 B. Eckes, D. Dogic, E. Colucci-Guyon, N. Wang, A. Maniotis,D. Ingber, A. Merckling, F. Langa, M. Aumailley, A. Delouvee,V. Koteliansky, C. Babinet and T. Krieg, J. Cell Sci., 1998, 111,1897–1907.

32 I. Kaverina, O. Krylyshkina, K. Beningo, K. Anderson, Y.-L. Wangand J. V. Small, J. Cell Sci., 2002, 115, 2283–2291.

33 D. Stamenovic, S. M. Mijailovich, I. M. Tolic-Nørrelykke, J. Chenand N. Wang, Am. J. Physiol.: Cell. Physiol., 2002, 282, C617–C624.

34 D. Stamenovic, S. M. Mijailovich, I. M. Tolic-Nørrelykke andN. Wang, Biorheology, 2002, 40, 221–225.

35 T. R. Polte, G. S. Eichler, N. Wang and D. E. Ingber, Am. J.Physiol.: Cell Physiol., 2004, 286, C518–C528.

36 A. Mammoto, S. Huang and D. E. Ingber, J. Cell Sci., 2007, 120,456–467.

This journal is ª The Royal Society of Chemistry 2009

37 D. Stamenovic, Acta Biomater., 2005, 1, 255–262.38 S. Hu, J. Chen and N. Wang, Front. Biosci., 2004, 9, 2177–2182.39 T. J. Dennerll, H. C. Joshi, V. L. Steel, R. E. Buxbaum and

S. R. Heidemann, J. Cell Biol., 1998, 107, 665–674.40 G. W. Brodland and R. Gordon, J. Biomech. Eng., 1990, 112, 319–

321.41 L. A. Sung and C. Vera, Ann. Biomed. Eng., 2003, 31, 1314–1326.42 C. Vera, R. Skelton, F. Bossens and L. A. Sung, Ann. Biomed. Eng.,

2005, 33, 1387–1404.43 Y. Luo, X. Xu, T. Lele, S. Kumar and D. E. Ingber, J. Biomech.,

2008, DOI: 10.1016/j.jbiomech.2008.05.026.44 A. J. Maniotis, C. S. Chen and D. E. Ingber, Proc. Natl. Acad. Sci.

U. S. A., 1997, 94, 849–854.45 S. Hu, J. Chen, B. Fabry, Y. Numaguchi, A. Gouldstone,

D. E. Ingber, J. J. Fredberg, J. P. Butler and N. Wang, Am. J.Physiol.: Cell Physiol., 2003, 285, C1082–C1090.

46 M. Chrzanowska-Wodnicka and K. Burridge, J. Cell Biol., 1996,133, 1403–1415.

47 T. Yeung, P. C. Georges, L. A. Flanagan, B. Marg, M. Ortiz,M. Funaki, N. Zahir, W. Ming, V. Weaver and P. A. Janmey, CellMotil. Cytoskeleton, 2005, 60, 24–34.

48 T. L. Hill, Proc. Natl. Acad. Sci. U. S. A., 1981, 78, 5613–5617.49 R. E. Buxbaum and S. R. Heidemann, J. Theor. Biol., 1988, 134,

379–390.50 A. Nicolas, B. Geiger and S. A. Safran, Proc. Natl. Acad. Sci. U. S. A.,

2004, 101, 12520–12525.51 T. Shemesh, B. Geiger, A. D. Bershadsky and M. M. Kozlov, Proc.

Natl. Acad. Sci. U. S. A., 2005, 102, 12383–12388.52 A. Basser and S. A. Safran, Biophys. J., 2006, 90, 3469–3484.53 K. A. Lazopoulos and D. Stamenovic, J. Biomech., 2008, 41, 1289–

1294.54 S. Deguchi, S. Ohashi and M. Sato, J. Biomech., 2006, 39, 2603–2610.55 D. Bray, Dev. Biol., 1984, 102, 379–389.56 S. R. Heidemann and R. Buxbaum, Neurotoxicology, 1994, 15, 95–

108.57 A. J. Putnam, K. Schultz and D. J. Mooney, Am. J. Physiol.: Cell

Physiol., 2001, 280, C556–C564.58 K. Buridge, K. Fath, T. Kelly, G. Nucko and C. Turner, Annu. Rev.

Cell Biol., 1988, 4, 487–525.59 N. Q. Balaban, U. S. Schwarz, D. Riveline, P. Goichberg, G. Tzur,

I. Sabanay, D. Mahalu, S. Safran, A. Bershadsky, L. Addadi andB. Geiger, Nat. Cell Biol., 2001, 3, 466–472.

60 B. Geiger and A. Bershadsky, Curr. Opin. Cell Biol., 2001, 13, 584–592.

61 D. Riveline, E. Zamir, N. Q. Balaban, U. S. Schwarz, T. Ishizaki,S. Narumiya, Z. Kam, B. Geiger and A. D. Bershadsky, J. CellBiol., 2001, 153, 1175–1186.

62 C. M. Waterman-Storer and E. D. Salmon, J. Cell Biol., 1997, 139,417–434.

63 R. Kaunas, P. Nguyen, P. Usaml and S. Chien, Proc. Natl. Acad. Sci.U. S. A., 2005, 102, 15895–15900.

64 D. E. Ingber, L. Dike, L. Hansen, S. Karp, H. Liley, A. Maniotis,H. McNamee, D. Mooney, G. Plopper, J. Sims and N. Wang, Int.Rev. Cytol., 1994, 150, 173–224.

65 J. V. Small and I. Kaverina, Curr. Opin. Cell Biol., 2003, 15, 40–47.66 B. A. Danowski, J. Cell Sci., 1989, 93, 255–266.67 M. S. Kolodney and E. L. Elson, Proc. Natl. Acad. Sci. U. S. A.,

1995, 92, 10252–10256.68 A. Ben-Ze’ev, S. R. Farmer and S. Penman, Cell, 1979, 17, 319–325.69 Y. Sawada and M. P. Sheetz, J. Cell Biol., 2002, 156, 609–615.

This journal is ª The Royal Society of Chemistry 2009

70 B. D. Matthews, D. R. Overby, R. Mannix and D. E. Ingber, J. CellSci., 2006, 119, 508–518.

71 A. D. Bershadsky, N. Q. Balaban and B. Geiger, Annu. Rev. CellDev. Biol., 2003, 19, 677–695.

72 D. A. Nix and M. C. Beckerle, J. Cell Biol., 1997, 138, 1139–1147.73 D. E. Ingber, Curr. Opin. Cell Biol., 1991, 3, 841–848.74 D. E. Ingber, Proc. Natl. Acad. Sci. U. S. A., 1990, 87, 3579–3583.75 A. Yen and A. B. Pardee, Science, 1979, 204, 1315–1317.76 N. Itano, S. Okamoto, D. Zhang, S. A. Lipton and E. Ruoslahti,

Proc. Natl. Acad. Sci. U. S. A., 2003, 100, 5181–5186.77 S. Lange, F. Xiang, A. Yakovenko, A. Vihola, P. Hackman,

E. Rostkova, J. Kristensen, B. Brandmeier, G. Franzen,B. Hedberg, L. G. Gunnarsson, S. M. Hughes, S. Marchand,T. Sejersen, I. Richard, L. Edstrom, E. Ehler, B. Udd andM. Gautel, Science, 2005, 308, 1599–1603.

78 U. S. Potard, J. P. Butler and N. Wang, Am. J. Physiol.: CellPhysiol., 1997, 272, C1654–C1663.

79 C. M. Nelson, D. M. Pirone, J. L. Tan and C. S. Chen, Mol. Biol.Cell, 2004, 15, 2943–2953.

80 E. Lazarides, J. Cell Biol., 1976, 68, 202–219.81 P. C. Rathke, M. Osborn and K. Weber, Eur. J. Cell Biol., 1979, 19,

40–48.82 T. J. Mitchison and L. P. Cramer, Cell, 1996, 84, 371–379.83 M. P. Sheetz, D. P. Felsenfeld and C. G. Galbraith, Trends Cell Biol.,

1998, 8, 51–54.84 R. J. Pelham, Jr. and Y.-L. Wang, Proc. Natl. Acad. Sci. U. S. A.,

1997, 94, 13661–13665.85 C.-M. Lo, H.-B. Wang, M. Dembo and Y.-L. Wang, Biophys. J.,

2000, 79, 144–152.86 S. R. Heidemann and R. Buxbaum, J. Cell Biol., 1998, 141, 1–4.87 P. Lamoureux, J. Zheng, R. E. Buxbaum and S. R. Heidemann, J.

Cell Biol., 1992, 118, 655–661.88 J. Zheng, R. E. Buxbaum and S. R. Heidemann, J. Cell Biol., 1994,

127, 2049–2060.89 S. Hu, J. Chen, J. P. Butler and N. Wang, Biochem. Biophys. Res.

Commun., 2005, 329, 423–428.90 S. Hu and N. Wang, Mol. Cell. Biomech., 2006, 3, 49–60.91 S. Na, O. Collin, F. Chowdhury, B. Tay, M. Ouyang, Y. Wang and

N. Wang, Proc. Natl. Acad. Sci. U. S. A., 2008, 105, 6626–6631.92 J. Y. Wong, A. Velasco, P. Rajagopalan and Q. Pham, Langmuir,

2003, 19, 1908–1913.93 I. B. Bischofs and U. S. Schwarz, Proc. Natl. Acad. Sci. U. S. A.,

2003, 100, 9274–9279.94 U. S. Schwarz and I. B. Bischofs, Med. Eng. Phys., 2005, 27, 763–

772.95 S. Cai, L. Pestic-Dragovich, M. E. O’Donnell, N. Wang,

D. E. Ingber, E. Elson and P. de Lanerolle, Am. J. Physiol.: CellPhysiol., 1998, 275, C1349–C1356.

96 N. Wang and Z. Suo, Biochem. Biophys. Res. Commun., 2005, 328,1133–1138.

97 H. Greenspan and J. Folkman, J. Theor. Biol., 1977, 65, 397–398.98 J. Bereiter-Hahn, M. Luck, T. Miebach, H. K. Stelzer and M. Voth,

J. Cell Sci., 1990, 96, 171–188.99 C. Cherniak, Biol. Cybern., 1992, 66, 503–510.

100 C. Cherniak, Z. Mokhtarzada, R. Rodriguez-Esteban andK. Changizi, Proc. Natl. Acad. Sci. U. S. A., 2004, 101, 1081–1086.

101 H. Tagawa, N. Wang, T. Narishige, D. E. Ingber, M. R. Zile andG. Cooper, Circ. Res., 1997, 80, 281–289.

102 H. Tsutsui, K. Ishihara and G. Cooper, 4th, Science, 1993, 260, 682–687.

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