Departments of Surgery and Pathology, Children's Hospital and Harvard Medical School, Enders 1007, 300 Longwood Avenue, Boston, MA 02115, USA
(e-mail: donald.ingber{at}tch.harvard.edu)
"...The fact that the germ-cell develops into a very complex structure is no absolute proof that the cell itself is structurally a very complicated mechanism: nor yet does it prove, though this is somewhat less obvious, that the forces at work or latent within it are especially numerous and complex..."
D'Arcy W. Thompson (Growth and Form, 1917)
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Summary |
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Key words: Cytoskeleton, Microfilaments, Microtubules, Intermediate filaments, Integrins, Cell shape, Cell mechanics
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Introduction |
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So how do the distinct molecular components of the cytoskeleton contribute
to cell mechanics, cell shape control and cellular mechanochemistry?
Unfortunately, although great advances have been made in our understanding of
the polymerization behavior and physical properties of isolated cytoskeletal
filaments and gels, material properties measured in vitro cannot predict
mechanical behaviors observed in living cells
(Janmey et al., 1991;
Gittes et al., 1993
). Those
biologists who do study mechanical behavior at the whole cell level generally
focus on the load-bearing function of the cortical (submembranous)
cytoskeleton and ignore the internal cytoskeletal lattice
(Albrecht-Buehler, 1987
).
Mechanical models of the cell similarly depict the cell as an elastic membrane
or cortex surrounding a homogeneous cytoplasm that is viscous, viscoelastic or
elastic, sometimes with a nucleus in its center
(Evans and Yeung, 1989
;
Dong et al., 1991
;
Fung and Liu, 1993
;
Schmid-Schönbein et al.,
1995
). This view of the cell as a `tensed balloon filled with
molasses or jello', however, is of little use when one tries to understand how
mechanical forces regulate cell behavior, because it ignores internal
microstructure. We must therefore search for a model of the cell that will
allow us to relate mechanics to chemistry at the molecular level and to
translate this description of the cell into mathematical terms. The former
will permit us to define how specific molecular components contribute to
complex cell behaviors. The latter will allow us to develop computational
approaches to address levels of complexity and multi-component interactions
that exist in living cells but cannot be described by current approaches. The
long-term goal is to understand biological processes responsible for cell
behavior as integrated, hierarchical systems rather than as isolated
parts.
In this two-part Commentary, I discuss a model of the cell based on
`tensegrity architecture' that appears to meet these goals
(Ingber et al., 1981;
Ingber and Jamieson, 1982
;
Ingber and Jamieson, 1985
;
Ingber, 1993b
). Here, in Part
I, I examine the evidence that the cytoskeleton that mechanically stabilizes
the cell is a tensed tensegrity framework composed of molecular struts, ropes
and cables on the nanometer scale and examine the utility of computational
models based on this theory. I also explore the implications of this theory
for how molecules function as elements within more complex hierarchical
structures composed of systems within systems within systems (i.e. cells,
tissues and organs). In Part II, which appears in the next issue of JCS
(Ingber, 2003
), I discuss the
implications of the cellular tensegrity model and biocomplexity for our
understanding of mechanobiology and biological pattern formation, with a
particular focus on how cells harness complex molecular networks, such as gene
and protein networks, for information processing.
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Cellular tensegrity |
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According to Fuller's more general definition, tensegrity includes two
broad structural classes prestressed and geodesic which would
both fail to act like a single entity or to maintain their shape stability
when mechanically stressed without continuous transmission of tensional forces
(Fuller, 1961;
Fuller, 1979
;
Ingber, 1998
;
Chen and Ingber, 1999
). The
former hold their joints in position as the result of a `prestress'
(pre-existing tensile stress or isometric tension) within the structure
(Fig. 1). The latter
triangulate their structural members and orient them along geodesics (minimal
paths) to geometrically constrain movement. Our bodies provide a familiar
example of a prestressed tensegrity structure: our bones act like struts to
resist the pull of tensile muscles, tendons and ligaments, and the shape
stability (stiffness) of our bodies varies depending on the tone (prestress)
in our muscles. Examples of geodesic tensegrity structures include Fuller's
geodesic domes, carbon-based buckminsterfullerenes (Bucky Balls), and
tetrahedral space frames, which are popular with NASA because they maintain
their stability in the absence of gravity and, hence, without continuous
compression.
Some investigators use tensegrity to refer only to the prestressed `bar and
cable' structures or particular subclasses of these (e.g. unanchored forms)
(Snelson, 1996;
Heidemann et al., 2000
). Since
Fuller defined the term tensegrity, I use his more general definition here.
The existence of a common structural basis for these two different classes of
structure is also supported by recent work by the mathematician Robert
Connelly. He developed a highly simplified method to describe prestressed
tensegrity configurations and then discovered that the same fundamental
mathematical rules describe the closest packing of spheres
(Connelly and Back, 1998
),
which also delineate the different geodesic forms
(Fuller, 1965
).
The cellular tensegrity model proposes that the whole cell is a prestressed tensegrity structure, although geodesic structures are also found in the cell at smaller size scales. In the model, tensional forces are borne by cytoskeletal microfilaments and intermediate filaments, and these forces are balanced by interconnected structural elements that resist compression, most notably, internal microtubule struts and extracellular matrix (ECM) adhesions (Fig. 2B). However, individual filaments can have dual functions and hence bear either tension or compression in different structural contexts or at different size scales (e.g. rigid actin filament bundles bear compression in filopodia). The tensional prestress that stabilizes the whole cell is generated actively by the contractile actomyosin apparatus. Additional passive contributions to this prestress come from cell distension through adhesions to the ECM and other cells, osmotic forces acting on the cell membrane, and forces exerted by filament polymerization. Intermediate filaments that interconnect at many points along microtubules, microfilaments and the nuclear surface provide mechanical stiffness to the cell through their material properties and their ability to act as suspensory cables that interconnect and tensionally stiffen the entire cytoskeleton and nuclear lattice. In addition, the internal cytoskeleton interconnects at the cell periphery with a highly elastic, cortical cytoskeletal network directly beneath the plasma membrane. The efficiency of mechanical coupling between this submembranous structural network and the internal cytoskeletal lattice depends on the type of molecular adhesion complex that forms on the cell surface. The entire integrated cytoskeleton is then permeated by a viscous cytosol and enclosed by a differentially permeable surface membrane.
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Do cells use tensegrity architecture? |
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Given these observations and the finding that cells exert tensional forces
on their ECM adhesive substrate (Harris et
al., 1980), some investigators were initially receptive to the
tensegrity model; however, others remained sceptical
(Brookes, 1999
). Following
arguments for and against the model
(Heidemann et al., 2000
;
Ingber, 2000a
), it has become
clear that experimental validation of the cellular tensegrity model requires
convincing demonstration of three major behaviors of living cells. First,
cells must behave mechanically as discrete networks composed of different
interconnected cytoskeletal filaments and not as a mechanical (e.g. viscous or
viscoelastic) continuum. Second, and most critical, cytoskeletal prestress
should be a major determinant of cell deformability. And, finally,
microtubules should function as compression struts and act in a complementary
manner with ECM anchors to resist cytoskeletal tensional forces and, thereby,
establish a tensegrity force balance at the whole cell level. Below, I
describe the evidence demonstrating these behaviors that has accumulated over
the past decade.
The cytoskeleton behaves like a discrete mechanical network
Established models of cell mechanics developed by biologists and engineers
assume that the dense cortical microfilament network that lies directly
beneath the cell membrane is the primary load-bearing element in the cell
(Albrecht-Buehler, 1987;
Evans and Yeung, 1989
;
Dong et al., 1991
;
Fung and Liu, 1993
;
Schmid-Schönbein et al.,
1995
). These models predict that externally applied stresses are
transmitted into the cell equally at all points on the cell surface and are
borne exclusively by the cell cortex. In contrast, the tensegrity model
predicts that mechanical loads are borne by discrete molecular networks that
span the cell surface and extend through the cytoplasm. More specifically,
transmembrane molecules that physically couple extracellular anchors (e.g. ECM
molecules or cell-cell adhesions) to the internal cytoskeletal lattice should
provide preferred paths for mechanical stress transfer into the cell, whereas
other transmembrane receptors would dissipate stress locally and thus fail to
transmit the same signals. If the cell is a prestressed tensegrity structure,
then a local stress can result in global structural rearrangements, even at a
distance. This is because the discrete structural elements within the
load-bearing network change orientation and spacing relative to one another
until a new equilibrium configuration is attained
(Fig. 4A). Thus, tensegrity
differs from conventional models of the cell in that application of local
stresses on the cell surface may result in directed deformation of structures,
both locally and deep inside the cell, depending on the molecular connectivity
across the surface membrane and through the viscous cytosol.
|
Ning Wang and I set out to discriminate between these conflicting models by
developing a micromanipulation method called magnetic twisting cytometry, in
which controlled mechanical stresses are applied directly to cell-surface
receptors by applying torque (shear stress) to receptor-bound magnetic
microbeads (1 to 10 µm diameter)
(Wang et al., 1993
;
Wang and Ingber, 1994
;
Wang and Ingber, 1995
). In
separate studies, magnetic tweezers (Bausch
et al., 1998
; Alenghat et al.,
2000
) were developed and used to apply linear tensional stresses
to cells, and optical tweezers were utilized to manipulate non-magnetic beads
that were similarly bound to cell-surface receptors
(Schmidt et al., 1993
;
Choquet et al., 1997
).
These techniques revealed that cell-surface adhesion receptors, such as
integrins, that link to the internal cytoskeleton provide a greater degree of
mechanical coupling across the cell surface than do other transmembrane
molecules, even though all connect to the submembranous cytoskeleton (i.e. the
actin-spectrin-ankyrin lattice). For example, when we used magnetic twisting
cytometry to stress transmembrane acetylated-low density lipoprotein (AcLDL)
metabolic receptors or histocompatibility antigens, there was detectable, but
minimal, resistance to mechanical distortion
(Wang et al., 1993;
Yoshida et al., 1996
). In
contrast, when ECM-ligandcoated beads bound to ß1 integrins were
similarly stressed, the cells responded by increasing their stiffness in
direct proportion to the applied stress. Importantly, we could partially
inhibit the integrin-dependent stiffening response by disrupting
microfilaments, microtubules or intermediate filaments, and completely prevent
it by disrupting all at once (Wang et
al., 1993
). Thus, although each cytoskeletal filament system
imparts mechanical stiffness, the mechanical properties of the cell are not
determined by the material properties of any single type of molecular
filament. The same finding has been obtained in studies with non-adherent,
circulating lymphocytes (Brown et al.,
2001
). Cellular mechanical behavior is therefore an emergent
property that results from collective interactions among all three filament
systems.
Differences in transmembrane mechanical coupling depend on the ability of
the receptor to form a membrane adhesion complex that physically links to the
internal cytoskeletal lattice. For example, binding of magnetic beads to
ß1 integrins induces formation of molecular links to the internal
cytoskeleton, as indicated by local assembly of focal adhesions containing
integrins, associated actin-binding proteins (e.g. vinculin, talin and
-actinin) and filamentous actin at the site of bead binding
(Plopper and Ingber, 1993
;
Wang et al., 1993
). Moreover,
cells from mice lacking vinculin exhibit a large drop in transmembrane
mechanical coupling that is independent of integrin binding and can be
restored by transfection of the cells with this focal adhesion protein
(Ezzell et al., 1997
;
Alenghat et al., 2000
). In
optical tweezer studies, beads bound to cell-surface integrins also exhibit
very little resistance to stress during the first seconds to minutes after
binding; however, once the integrins have formed focal adhesions, the beads
stiffen so that they can no longer be displaced
(Schmidt et al., 1993
;
Choquet et al., 1997
). Local
recruitment of focal adhesion proteins to integrin-binding sites also can be
induced by pulling on integrins with ECM-coated micropipettes in conjunction
with a micromanipulator (Riveline et al.,
2001
). This effect is mediated by an increase in cytoskeletal
tension, either activated internally by the GTPase Rho and its downstream
target Rho-associated kinase (ROCK) or by external application of tension to
the cytoskeleton via integrins in the presence of the active form of another
downstream Rho target, mDia1.
When larger mechanical stresses are applied to transmembrane integrin
receptors on living cells, using ligand-coated micropipettes, both local and
distant effects are observed. Application of these higher forces to integrins
and associated focal adhesions results in physical distortion of the surface
membrane and immediate repositioning of cytoskeletal filaments along the
applied tension field lines within the cytoplasm
(Fig. 5A,B), as well as
realignment of molecular elements within nucleoli deep in the center of the
nucleus (Fig. 5C-F)
(Maniotis et al., 1997a).
Application of tension to transmembrane AcLDL receptors produces no such
changes. Cells that lack intermediate filaments fail to support efficient
mechanical coupling between integrins and the nucleus; instead tension
produces cytoplasmic tearing (Maniotis et
al., 1997a
; Eckes et al.,
1998
). Intermediate filament disruption also destabilizes the
microtubule and microfilament networks
(Goldman et al., 1996
). Yet,
the intermediate filament lattice alone is sufficient to provide some
mechanical stiffness to the cell as shown, for example, when lymphocytes that
are devoid of intact microfilaments or microtubules are compressed against a
substrate by centrifugation (Brown et al.,
2001
).
|
Other studies used micropipettes to pull on microbeads bound to integrins
on living cells transfected with a construct that produces a fusion protein of
enhanced yellow fluorescent protein (EYFP) and cytochrome C oxidase to make
mitochondria fluorescent. Real-time fluorescence microscopic analysis revealed
coordinated movement of mitochondria as far as 20 µm into the cell
(Fig. 5G) (Wang et al., 2001). Again,
pulling on transmembrane AcLDL receptors that couple only to the membrane
cortex failed to produce this effect. Mitochondria directly associate with
microtubules and are excluded from the cell cortex. Thus, forces transmitted
by integrins to microfilaments in the focal adhesion apparently can be passed
to microtubules at distant sites and so these different filament networks must
be mechanically connected inside living cells. Application of fluid shear
stresses to the apical cell surface of cultured endothelium also results in
mechanical distortion of GFP-labeled intermediate filaments deep inside the
cytoplasm (Helmke et al.,
2001
).
Thus, the cellular response to stress does depend on connectivity within
discrete molecular networks that span the cell surface and extend through the
cytoplasm, and on cooperative interactions between all three cytoskeletal
filament systems. The data discussed above therefore provide direct support
for the tensegrity model and are not consistent with models that view the cell
as an elastic membrane surrounding a viscous cytosol. These studies, however,
also reveal a caveat. Even though the internal cytoskeletal lattice is clearly
critical for the cellular response to mechanical stress, the cell may appear
to behave like an elastic cortex surrounding a viscous cytosol, if the highly
elastic, submembranous cytoskeletal network is probed independently of the
internal cytoskeletal lattice. This was observed in experiments in which
non-adhesion receptors (Wang et al.,
1993; Wang and Ingber,
1994
; Wang and Ingber,
1995
) or inactive (unligated) integrins (B. Mathews, F. Alenghat
and D.E.I., unpublished) were magnetically twisted, and when activated
integrins were pulled in the plane of the membrane
(Bausch et al., 1998
). This
caveat might also explain why only local responses are observed when
mechanical stresses are applied to cell surfaces by micropipettes coated with
laminin (Heidemann et al.,
1999
); in this study, efficient mechanical coupling between cell
surface adhesion receptors and the internal cytoskeleton (i.e. focal adhesion
formation) does not appear to occur.
Prestress is a major determinant of cell mechanics
The most fundamental feature of the cellular tensegrity model is the
importance of tensional integrity and internal tensile stress (prestress) for
cell shape stability. There is no question that mammalian cells experience
isometric tension, because this can be visualized if one plates cells on
flexible substrates (Harris et al., 1981) or quantifies cell-generated forces
(Kolodney and Wylomerski, 1992; Pelham
and Wang, 1997; Wang et al.,
2001
; Balaban et al.,
2001
). Microsurgical techniques can also demonstrate this
directly: sever the cell anywhere and the cut edges spontaneously retract
(Pourati et al., 1998
).
Engineers use a similar technique to quantify prestress (residual stress)
within whole living tissues and organs
(Fung and Liu, 1989
;
Omens and Fung, 1990
).
Altering cytoskeletal prestress by modulating actomyosin-based contractility
using drugs (Hubmayr et al.,
1996
; Wang et al.,
2001
), varying transmembrane osmotic forces
(Cai et al., 1998
),
transfecting cells with constitutively active myosin light chain (MLC) kinase
(Cai et al., 1998
) or quickly
distending a cell's adhesive substrate
(Pourati et al., 1998
) also
results in immediate changes in cell shape stability (shear modulus). Most
importantly, experimental measurement of cultured cells, using traction force
microscopy to quantify prestress within individual cells
(Pelham and Wang, 1997
;
Butler et al., 2002
) and
magnetic twisting cytometry to measure cell stiffness, reveals a linear
correlation between stiffness (elastic modulus) and cellular prestress
(Wang et al., 2002
), as
predicted a priori by the tensegrity model
(Stamenovic et al., 1996
).
Cells also exhibit a nearly linear dependence of their dynamic mechanical
behavior (dynamic modulus) on cytoskeletal prestress
(Stamenovic et al.,
2002a
).
Those who view cell mechanics as largely a function of the elastic cell
cortex might ascribe these results to the importance of tensional prestress in
the cortical cytoskeleton. However, measurements of cell mechanics using
magnetic twisting cytometry in conjunction with two different-sized magnetic
beads conflict with this interpretation; cell stiffness scales directly with
bead size for a given applied stress, which is the opposite of what would be
predicted by a prestressed membrane cortex model
(Wang and Ingber, 1994).
Moreover, no change in mechanics can be detected in round versus flat cells or
in cells expressing constitutively active MLC kinase when they are probed with
techniques that measure only the cortical cytoskeleton
(Wang and Ingber, 1994
;
Cai et al., 1998
). In
contrast, major differences are evident in the same cells when one measures
cell mechanics through integrins that couple to the internal cytoskeleton by
magnetic twisting cytometry. Differences in shape stability owing to altered
prestress therefore cannot be explained solely on the basis of changes in the
cell cortex.
Cytoskeletal prestress is also important for shape stability in the
cytoplasm and nucleus. For example, addition of ATP to membrane-permeabilized
cells results in coordinated retraction and rounding of the entire cell,
cytoskeleton and nucleus, and this response can be prevented by blocking
cytoskeletal tension generation (Sims et
al., 1992). Tensegrity models of nucleated cells composed of
struts and tensed cables (Fig.
4B) exhibit similar coordinated retraction behavior when their
anchors are dislodged. Moreover, quantification of changes in cell stiffness
in membrane-permeabilized cells using magnetic twisting cytometry confirmed
that cytoskeletal tension (prestress) is a critical determinant of cell and
nuclear shape stability independently of transmembrane osmotic forces
(Wang and Ingber, 1994
). The
stiffness of the cell, cytoskeleton and nucleus also can be altered by
disruption of the tensed intermediate filament lattice by drugs
(Wang et al., 1993
;
Maniotis et al., 1997a
;
Wang and Stamenovic, 2000
;
Brown et al., 2001
), synthetic
inhibitory peptides (Goldman et al.,
1996
) or genetic techniques [e.g. vimentin-knockout mice
(Eckes et al., 1998
;
Wang and Stamenovic, 2000
;
Brown et al., 2001
)] or by
modifying the ability of the ECM substrate to resist cell traction
(Wang and Ingber, 1994
).
Thus, as predicted by the tensegrity model, continuous transmission of tension
between different cytoskeletal filament systems, and from the cytoskeleton to
both the nucleus and ECM receptors, is critical for cell shape stability.
Interestingly, even the submembranous cytoskeleton (the cortical
actin-ankyrin-spectrin lattice) appears to require tensional prestress for its
mechanical stability (Discher et al.,
1998
; Coughlin and Stamenovic,
2003
).
Establishment of a tensegrity force balance between microtubules,
microfilaments and ECM
The feature of the cellular tensegrity model that most troubles
investigators is the presence of compression struts inside the cell. Some
argue that the cytoskeleton is like a network of muscles, tendons and
ligaments without the bones (Brookes,
1999). So where are the compression elements? The answer depends
on the size scale and hierarchical level that one examines. From the
physiological perspective, the most relevant level relates to how the cell
controls its shape and structure within living tissues. When cells are
enzymatically dislodged from tissues, they spontaneously round up and lose
their characteristic forms. When the ECM is carefully removed from developing
tissues without disrupting cell-cell contacts, cells do not completely round
up; however, they partially retract and lose specialized tissue morphology,
such as epithelial branches and buds
(Banerjee et al., 1977
). In
other words, cells cannot stabilize their specialized shapes in the absence of
their ECM adhesions. Thus, one cannot define the critical determinants of cell
shape stability in anchorage-dependent cells without considering the mechanics
of the adhesion substrate, just as one cannot describe the stability of a
spider web without considering the tree branches to which it is tethered.
Studies of cultured cells confirm that cell shape depends on the ability of
local regions of the ECM anchoring substrate to withstand compression. Cells
are not evenly glued to their adhesive substrate, rather they are spot welded
in regions known as focal adhesions
(Burridge et al., 1988) that
contain clustered integrin receptors and cytoskeleton-coupling proteins as
well as immobilized signal transduction molecules
(Plopper and Ingber, 1993
;
Plopper et al., 1995
;
Miyamoto et al., 1995
). Focal
adhesions generally form at the base of the cell directly beneath the ends of
each contractile stress fiber (Burridge et
al., 1988
); thus, they represent discrete points of cytoskeletal
insertion on the ECM analogous to muscle-insertion sites on bone. To support
cell spreading, isolated regions of the extracellular substrate located
between focal adhesions must resist local compression produced by the
shortening of each internal stress fiber. It is for this reason that adherent
cells pull flexible substrates up into `compression wrinkles' between their
localized adhesions (Harris et al.,
1980
). Thus, these local regions of the ECM act like external
support elements to resist cytoskeletal tensional forces and thereby establish
a tensegrity force balance.
If these ECM regions were the only elements that resisted cell tension,
then all cells adherent to planar ECMs would look like fried eggs. This is not
the case, because cells also use internal compression struts to refine their
shape. During neurulation in the embryo, developing epithelial cells extend
internal microtubule struts along their vertical (apical-basal) axis to
transform themselves into columnar cells
(Burnside, 1971). One can also
induce round lymphocytes (Bailly et al.,
1991
) and erythrocytes
(Winckler and Solomon, 1991
)
to form long membrane extensions by promoting microtubule polymerization. If
microtubules did not resist compression and were tensed like rubber bands,
then these cells would not be able to create highly elongated forms, and
spherical contraction would result. In other words, these cells must contain
some internal element that resists inward-directed cytoskeletal forces in
order to extend outward; this is a key feature of tensegrity architecture.
The remaining concern that has been raised is whether long microtubules that extend throughout the cytoplasm of cultured cells actually bear compression. To envision how this might work in the tensegrity model more clearly, think of a camp tent. The surface membrane of the tent is stabilized (made stiff) by placing it under tension. This can be accomplished by various means: pushing up tent poles against the membrane, pulling the membrane against fixed tent pegs in the ground and tethering the membrane to an overlying tree branch. The internal tent poles and external tethers provide complementary load-bearing functions because both resist the inward-directed forces exerted by the tent membrane. It is through this tensegrity force balance that the tensional prestress is generated that stabilizes the tent's form.
If cells use tensegrity and the cytoskeleton is organized liked a tent,
then if you were to disrupt the microtubules (tent poles), the force they
normally carried would be transferred to the cell's adhesive anchors. This
transfer of forces would cause increased traction on the cell's adhesions
(i.e. the tent pegs would be pulled upward and closer together, and the tree
branch would be wrenched downward) (Fig.
2B). By contrast, if all CSK filaments experience tension, like a
bunch of tensed rubberbands, then if you were to break any of the filaments,
tension on the substrate would rapidly dissipate (the tree branch would leap
back up to its starting position). Importantly, many experiments have shown
that when microfilaments or intermediate filaments the tension
elements in the model are chemically disrupted, cell tractional forces
exerted on ECM adhesions decrease (Kolodney and Wyslomerski, 1992;
Eckes et al., 1998). Moreover,
when microtubules the struts in the model are disrupted,
traction on the ECM substrate rapidly increases in many cell types and
experimental systems (Danowski,
1989
; Kolodney and Wyslomerski, 1992;
Kolodney and Elson, 1995
;
Wang et al., 2001
;
Stamenovic et al.,
2002b
).
Although these results directly support the tensegrity model, there is one
potential concern: microtubule depolymerization also activates MLC kinase
(Kolodney and Elson, 1995).
This could mean that the observed increase in ECM traction is entirely
controlled through a chemical mechanism (e.g. through tubulin monomer release)
and a subsequent increase in active tension generation, rather than
mechanically through a tensegrity force balance
(Danowski, 1989
;
Kolodney and Elson, 1995
).
Other investigators have proposed that microtubule-dependent changes in
intracellular calcium levels are responsible for these effects
(Paul et al., 2000
).
Importantly, recent studies have shown that microtubule disruption results in
an increase in tractional forces exerted on the ECM substrate, even under
conditions in which MLC phosphorylation and intracellular calcium levels do
not change (Wang et al.,
2002
; Stamenovic et al.,
2002b
). Quantification of cell tractional forces and the amount of
prestress within individual cells using traction force microscopy revealed
that microtubules counterbalance
5-30% of the total cellular prestress,
depending on the cell. Thus, the ability of microtubules to bear compression
locally contributes significantly to cellular prestress and cell shape
stability. Note that both application of mechanical force to cell-ECM
adhesions (Riveline et al.,
2001
) and microtubule disruption
(Liu et al., 1987
) activate
the Rho signaling pathway that leads to MLC phosphorylation. So
tensegrity-based transfer of mechanical loads to ECM adhesion sites following
microtubule disruption could, in part, increase active contraction through a
mechanochemical mechanism [see Part II of this Commentary for more discussion
of tensegrity and mechanochemistry
(Ingber, 2003
)].
Because of complementary tensegrity-based force interactions between
microtubules, contractile microfilaments and ECM adhesions, the relative
contribution of microtubules to cellular prestress will vary depending on the
structural context. For example, the poles in the tent bear less compressive
load when the tent membrane is partially secured to the overlying tree branch.
Similarly, microtubules may bear less compression (and the ECM more) in highly
spread cells on rigid substrates, whereas more compression will be transferred
from the ECM onto these internal struts when the ECM is compliant or when the
cell's ECM adhesions are dislodged. Experiments analyzing the effects of ECM
adhesion and mechanical forces on microtubule polymerization in various
adherent cells (Joshi et al.,
1985; Dennerll et al.,
1988
; Dennerll et al.,
1989
; Lamoureux et al.,
1990
; Mooney et al.,
1994
; Putnam et al.,
1998
; Putnam et al.,
2001
; Kaverina et al.,
2002
) and a thermodynamic model of microtubule regulation
(Buxbaum and Heidemann, 1988
)
support this notion. This may explain why microtubules did not appear to
contribute significantly to smooth muscle cell mechanics in a study in which
these cells were held under external tension
(Obara et al., 2000
), whereas
in other studies they were found to play an important mechanical role in both
smooth muscle cells (Wang et al.,
2001
; Stamenovic et al., 2002) and cardiac muscle cells
(Tagawa et al., 1997
).
It remains difficult for some to envision how a single molecular filament,
such as a microtubule, could withstand compressive forces. The ability of
individual microtubules to resist buckling when compressed could be greatly
enhanced, however, by the presence of lateral tensile connections that would
function as molecular guy wires. On the basis of the frequency of lateral
connections along microtubules, engineers have calculated that intermediate
filaments could provide this function
(Brodland and Gordon, 1990).
However, electron microscopy reveals many types of lateral molecular linkage
that could act in this manner (Heuser and
Kirschner, 1980
; Fey et al.,
1984
).
Importantly, microscopic visualization of the dynamics of green fluorescent
protein (GFP)-labeled microtubules provides direct evidence of end-on
compressive buckling of individual microtubules in living cells
(Fig. 6). Buckled microtubules
also immediately straighten when they slip by an obstacle in the cytoplasm
(Kaech et al., 1996;
Wang et al., 2001
).
Furthermore, the curvature of individual microtubules (a readout of
compressive buckling) decreases when drugs are used to decrease cytoskeletal
tension, whereas buckling increases when agents are added that increase
contraction, such as thrombin in endothelial cells
(Waterman-Storer and Salmon,
1997
; Wang et al.,
2001
). Disruption of microtubules also significantly reduces the
stiffness (shear modulus) of the cell
(Wang et al., 1993
;
Stamenovic et al., 2002) and induces retraction of long processes in various
cell types (Tomasek and Hay,
1984
; Domnina et al.,
1985
; Vasiliev,
1987
; Madreperla and Adler,
1989
; Bailly et al.,
1991
; Ingber et al.,
1995
).
|
Taken together, these studies indicate that at least a subset of
microtubules function as compression struts within the cytoplasm and act in a
complementary manner with ECM adhesions to resist microfilament-based
tensional forces in the cytoskeleton of adherent cells. In this manner, a
tensegrity force balance is established. Moreover, microtubules appear to
provide a similar compression-bearing function in the mitotic spindle:
Pickett-Heaps and co-workers severed a single microtubule within the spindle
with a UV microbeam, and the remaining microtubules buckled as if the total
compressive load was distributed among a decreased number of semiflexible
compression struts (Pickett-Heaps et al.,
1997). However, microtubules have a dual function in that some
(kinetochore) microtubules experience tension when they shorten and pull the
chromosomes apart and toward the spindle poles during anaphase at the end of
mitosis (Zhou et al.,
2002
).
Mathematical formulation of the tensegrity theory
The cellular tensegrity theory was initially an intuitive model, and
prestressed tensegrity structures constructed out of sticks and elastic
strings were used to visualize the concept
(Ingber and Jamieson, 1985;
Ingber, 1993b
;
Wang et al., 1993
).
Nevertheless, these simple models closely mimicked living cells. For example,
the cell and nucleus of a round tensegrity model spread in a coordinated
manner, and the nucleus moves to the base (polarizes) when it attaches to a
rigid substrate (Fig. 4B),
which is just like living cells in culture
(Ingber et al., 1986
;
Ingber, 1990
). Also, like
cultured cells, the models contract and wrinkle flexible substrates, and they
take on a round form when detached
(Ingber, 1993b
). In addition,
the models exhibit the linear stiffening behavior (strain hardening) displayed
by cultured cells (Wang et al.,
1993
) and whole living tissues
(McMahon, 1984
), apparently
because increasing numbers of the struts realign along the applied tension
field lines (Fig. 4A). Another
model, composed of multiple soda straws tensionally linked by elastic string,
kinematically transforms into three-dimensional forms that closely resemble
structures observed within actin geodomes and stress fibers of living cells by
light (Fig. 3B) and electron
microscopy (Osborn et al.,
1978
), including strut-for-strut and vertex-for-vertex identity on
the nanometer scale (Ingber,
1993b
).
Although these conceptual models were impressive, further advance in this
field required the development of a mathematical formulation of the cellular
tensegrity model. A theoretical formulation of the model starting from first
mechanistic principles was developed by Dimitrije Stamenovic working with my
group (Stamenovic et al.,
1996) and by others (Wendling
et al., 1999
; Wendling et
al., 2002
; Volokh et al.,
2000
; Volokh et al.,
2002
). In this model, actin microfilaments and intermediate
filaments carry the prestress that is balanced internally by microtubules and
externally by focal adhesions to the ECM substrate. Work on variously shaped
models revealed that even the simplest prestressed tensegrity sculpture
embodies the key mechanical properties of all members of this tensegrity
class. Thus, for simplicity, we used a symmetrical cell model in which the
tensed filaments are represented by 24 cables and the microtubules by six
struts organized as shown in the structure in
Fig. 1B. The cytoskeleton and
substrate together were assumed to form a self-equilibrated, stable mechanical
system; the prestress carried by the cables was balanced by the compression of
the struts.
A microstructural analysis of this model using the principle of virtual
work led to two a priori predictions: (1) the stiffness of the model (or cell)
will increase as the prestress (pre-existing tensile stress) is
raised; and (2) at any given prestress, stiffness will increase linearly with
increasing stretching force (applied stress). The former is
consistent with what we know about how muscle tone alters the stiffness of our
bodies, and it closely matches data from experiments with living cells
(Wang et al., 2002;
Stamenovic et al., 2002a
;
Stamenovic et al., 2003
). The
latter meshes nicely with the mechanical measurements of stick-and-string
tensegrity models, cultured cells and whole living tissues, although it also
can be explained by other models
(Heidemann et al., 2000
). This
mathematical approach strongly supported the idea that the architecture (the
spatial arrangement of support elements) and prestress (the level of isometric
tension) in the cytoskeleton are key to a cell's ability to stabilize its
shape.
Largely through the work of Stamenovic and co-workers, this oversimplified
micromechanical model continues to be progressively modified and strengthened
over time (Coughlin and Stamenovic,
1997; Coughlin and Stamenovic,
1998
; Stamenovic and
Coughlin, 1999
; Stamenovic
and Coughlin, 2000
;
Stamenovic and Ingber, 2002
).
A more recent formulation of the model includes, for example, semiflexible
struts analogous to microtubules, rather than rigid compression struts, and
incorporates values for critical features of the individual cytoskeletal
filaments (e.g. volume fraction, bending stiffness and cable stiffness) from
the literature (Coughlin and Stamenovic,
1997
; Stamenovic and
Coughlin, 1999
). This more refined model is qualitatively and
quantitatively superior to that containing rigid struts. Another formulation
of the tensegrity model includes intermediate filaments as tension cables that
link the cytoskeletal lattice and surface membrane to the cell center
(Wang and Stamenovic, 2000
).
This model generates predictions of mechanical behavior in the absence of
intermediate filaments that closely mimic results obtained in studies of
living cells in which vimentin has been knocked out genetically or
intermediate filaments have been disrupted by pharmacological approaches.
Moreover, all of these tensegrity models yield elastic moduli (stiffness)
that are quantitatively similar to those of cultured adherent cells
(Stamenovic and Coughlin,
1999; Stamenovic and
Coughlin, 2000
). Importantly, although models of the cytoskeleton
that incorporate only tensile elements (i.e. they lack internal compression
struts) can mimic the cell's response to generalized membrane deformation
(e.g. owing to poking of a cell with an uncoated micropipette), they cannot
explain many other cell mechanical behaviors, especially those that are
measured through cell-surface receptors that link to the internal cytoskeleton
(Coughlin and Stamenovic,
2003
).
Stamenovic has also carried out an energy analysis using quantitative
results from traction force microscopy studies of living cells
(Stamenovic et al., 2002b).
An energy analysis is independent of microstructural geometry and, thus, it
circumvents potential limitations of using a specific tensegrity configuration
(network architecture) in the theoretical calculations. This analysis revealed
that microtubules contribute significantly to the contractile energy budget of
the cell and, thus, it provides independent support for the concept that
compression-bearing microtubules play an important role in the determination
of mechanical behavior within adherent cells. In contrast, the amount of
contractile energy stored in extension of actin microfilaments was found to be
negligible. These results are therefore consistent with the tensegrity model,
because they suggest that the primary mechanical role of microfilaments is to
carry prestress and to transfer tensional forces throughout the cell, whereas
microtubules carry compression and balance a substantial fraction of the
contractile prestress within the actin network. Stamenovic's analysis also
provided evidence for the notion that intermediate filaments provide a lateral
mechanical support to microtubules and thus enhance their ability to carry
compression without buckling, as predicted previously
(Brodland and Gordon,
1990
).
Taken together, these results show that, although the current formulation
of the tensegrity theory relies on the use of a highly simplified architecture
(six struts and 24 cables), it nevertheless effectively predicts many static
mechanical behaviors of living mammalian cells. Most critically, the a priori
prediction of the tensegrity model that cell stiffness will increase in
proportion with the prestress has been confirmed in various experimental
studies (Wang et al., 2002;
Stamenovic et al., 2002a
;
Stamenovic et al., 2003
).
However, what is more surprising is that this model also leads to predictions
of dynamic behavior. For example, it predicts that at a given frequency of
loading, both the elastic (storage) and frictional (loss) moduli should
increase with increasing prestress, whereas the fraction of the frictional
energy loss relative to the elastic energy storage should be independent of
prestress. Recent experiments again confirm these predictions
(Wang et al., 2001
;
Stamenovic et al.,
2002a
).
Interestingly, recent work suggests that the dynamic mechanical behavior of
mammalian cells depends on generic system properties, as indicated by a
spectrum of time constants when the cells are stressed over a wide range of
force application frequencies (Goldmann
and Ezzell, 1996; Fabry et
al., 2001
). This work suggests that these dynamic behaviors
reflect a non-deterministic property of the cell at some higher system level
of molecular interaction. It is not consistent with the notion of a single
type of cytoskeletal filament or molecular interaction (e.g. actin
crosslinking) being responsible for cell dynamic behavior. It is also not
consistent with standard ad hoc models of cell mechanics that assume that the
elastic and frictional behaviors of the cell originate from two distinct
compartments (the elastic cortex and the viscous cytoplasm). Importantly,
computer simulations suggest that dynamic mechanical behaviors exhibited by
living cells, including the dependence of both their elastic and frictional
moduli on prestress, are natural consequences of their use of tensegrity
(Canadas et al., 2002
) (C.
Sultan, N. Liang, D. Stamenovic and D.E.I., unpublished). In other words,
tensegrity could provide a common structural basis for both the elastic and
viscous behaviors of living cells.
Other micromechanical models of the cell have been proposed over the past
decade; these are based on porous cellular solids
(Satcher and Dewey, 1996),
filament dynamics [i.e. thermal fluctuations (MacKintosh and Janmey, 1995)]
and percolation theory (Forgacs,
1995
). As in the tensegrity theory, these models incorporate
microstructure and assume that the cytoskeleton is organized as a porous
network composed of discrete structural elements. However, these models differ
from tensegrity in that they do not take into account contributions from
collective interactions among different cytoskeletal filament systems (or the
ECM) and do not explain how highly organized structures [e.g. actin geodomes
(Lazarides, 1976
)] appear in
the cytoskeleton. More importantly, they do not include a role for
cytoskeletal prestress in cell shape stability or lead to a priori predictions
of complex mechanical behaviors in whole living cells. Thus, although these or
other models of the cell may be able to describe particular cell behaviors
(Heidemann et al., 2000
), they
cannot explain many others (Ingber,
2000a
). Only the tensegrity theory provides all these features
and, thus, it appears to be the most unified and robust model of the cell
available at present.
Incorporating structural complexity: multimodularity
Although the simple six-strut tensegrity model of the cell has been very
useful, the reality is that the living cell is more complex because it is a
`multimodular' tensegrity structure. By multimodularity, I mean that the cell
is composed of multiple smaller, self-stabilizing tensegrity modules that are
linked by similar rules of tensional integrity (see the structures in
Fig. 7 and the sculpture in
Fig. 1A). As long as these
modules are linked by tensional integrity, then the entire system exhibits
mechanical coupling throughout and an intrinsic harmonic coupling between part
and whole (Ingber and Jamieson,
1985; Pienta et al.,
1991
; Pienta and Coffey,
1991a
). Destruction of one unit in a multimodular tensegrity,
however, results only in a local response; that particular module will
collapse without compromising the rest of the structure. This is similar to
cutting the Achilles tendon: foot stability is lost, but control of the
remainder of the body remains intact. This point is critical because some have
ruled out the relevance of tensegrity as a model for living cells on the basis
that, if cells used tensegrity, then disruption of one molecular support
element would produce total cellular collapse, as in a single tensegrity
module (Forgacs, 1995
). The
fact that individual fragments of cells continue to exhibit specialized
behaviors, including movement
(Albrecht-Buehler, 1980
), after
mechanical disruption of the cell confirms that multiple structural modules
exist in the cytoplasm, even though they exhibit spatially coordinated
behavior in the whole cell. Use of a multimodular tensegrity arrangement
provides another important advantage: subsystems or small groups of modules
can be repaired and replaced without disruption of higher-order structure.
This is critical because the molecules that comprise living cells undergo
continuous turnover.
|
Computer simulations of complex multimodular tensegrity arrangements depict
subtle mechanical behaviors that are reminiscent of those of living cells. For
example, a simulation of a prestressed fabric composed of multiple
interconnected tensegrity modules displays coordinated retraction of all the
support elements throughout the depth of the material when it is released from
its anchors (Fig. 8A). This
response is similar to what happens to the cell, cytoplasm and nucleus
following addition of trypsin to cleave ECM anchors
(Fig. 8B) or to whole living
tissues (e.g. skin or muscle) following a surgical incision. Another computer
simulation revealed that, when physically extended, a fabric comprised of
multiple (36) interconnected tensegrity modules (each containing 6 struts and
24 cables, as in Fig. 1B)
displayed undulating movements (Fig.
8C) that are similar to those exhibited by extending lamellipodia
in living cells (Fig. 8D). This
observation raises the possibility that the actin filaments that rapidly
polymerize (elongate) within a newly forming lamellipodium push out against
the surrounding actin filament network and surface membrane and thereby
prestress the entire structure. It also may explain why lamellipodia generally
exhibit a similar morphology in all cells: their form is a manifestation of
the underlying force balance that stabilizes their three-dimensional
architecture and not a direct property of any one of its individual
components. The observations that directional movement of the cytoplasm is
controlled through a balance between cytoskeleton-based protrusive and
retractive forces (Verkhovsky et al.,
1999), decreasing the tension (stiffness) in the surface membrane
accelerates lamellipodia extension
(Raucher and Sheetz, 2000
),
and rapid linear extension of acrosomal processes is based on a dynamic
balance between extension of rigid actin struts and resisting membrane
elements (Tilney and Inoue,
1982
) also support the generality of this model for movement of
subcellular microdomains.
|
Implications for the hierarchical nature of biological systems
Importantly, the cellular tensegrity model also takes into account the
hierarhical features of living cells as well as those of the tissues and
organs in which they normally reside
(Ingber and Jamieson, 1985;
Ingber, 1993b
;
Ingber et al., 1994
;
Ingber, 1998
). This level of
complexity is commonly ignored in cell biology. Fuller was the first to note
that tensegrity systems can be constructed as structural hierarchies in which
the tension or compression elements that comprise the structure at one level
are themselves tensegrity systems composed of multiple components on a smaller
scale (Fuller, 1961
). The
tensegrity model of the nucleated cell, in which the entire nuclear tensegrity
lattice is itself a tension element in the larger structure
(Fig. 4B), illustrates this
concept.
Living organisms are similarly constructed as tiers of systems within
systems within systems. The bones and muscles of our bodies use a tensegrity
force balance to stabilize themselves
(Levin, 1997;
Chen and Ingber, 1999
). Whole
organs, such as the heart and lung, are also prestressed structures
(Omens and Fung, 1990
), owing
to tension generation within their constituent cells and the existence of
larger-scale distending forces (e.g. hemodynamic forces and air pressure).
Neural architecture in the brain (Van
Essen, 1997
) and retina
(Galli-Resta, 2002
) are also
governed by internal tissue forces, in this case generated within the
cytoskeletons of their constituent cells. The forces in these tissues and
organs are resisted by stiffened ECMs (e.g. crosslinked collagen bundles,
elastin bundles and basement membranes), by the non-compressibility of
proteoglycan-rich ECMs and other cells, and by opposing contractile forces
generated by neighboring cells (e.g. mesenchyme versus epithelium). It is for
this reason that the edges of the wound spontaneously retract when a tissue or
organ is incised with a scalpel (Liu and
Fung, 1989
; Omens and Fung,
1990
).
A counterintuitive feature of hierarchical tensegrity structures is that a tensed member on one size scale can act locally to resist compression on a smaller size scale. A simple analogy is how rats can climb up a ship's mooring rope by compressing it locally between their front and rear feet, but only when the rope is tensionally stiffened. Similarly, the existence of a stabilizing prestress in a whole organ or tissue stiffens internal tension elements, such as basement membranes, which, in turn, may resist compression applied locally by individual adherent cells (i.e. between their isolated focal adhesions) and thereby stabilize cell shape on the microscale.
But the tensegrity hierarchy does not end at the level of the cell. The
internal cytoskeleton that behaves like a tensegrity structure also connects
to the elastic submembranous cytoskeleton at the cell periphery and to the
nuclear scaffold at the cell center (Fey
et al., 1984; Georgatos and
Blobel, 1987
; Maniotis et al.,
1997a
; Zhen et al.,
2002
). At the molecular level, the submembranous cytoskeleton is
another tensegrity structure: it is a discrete network composed of actin,
ankryin and spectrin molecules that is both prestressed
(Discher et al., 1998
), owing
to transmembrane osmotic forces, and organized geodesically within a hexagonal
network (Liu et al., 1987
).
The entire network and attached membrane undergo expansion and contraction in
response to changes in osmotic pressure. Although this is mediated by
elongation of individual molecules in the network, such as spectrin, the
geodesic arrangement might also facilitate this process by permitting these
large-scale shape changes without disruption of network continuity (e.g.
breakage of individual struts). This capability of geodesic structures is
visualized in Fig. 9, which
shows a geodesic sphere created by the designer Chuck Hoberman that undergoes
large-scale expansion and contraction by using a kinematic mechanism to
produce elongation of individual network members, rather than molecular
distortion as in living cells. In fact, as described by Caspar, it may be
because of tensegrity that geodesic viral capsids can similarly expand and
contract without loss of structural integrity
(Caspar, 1980
).
|
The nucleus may represent yet another tensegrity structure
(Ingber and Jamieson, 1985;
Ingber, 1993b
;
Ingber et al., 1994
), because
it is prestressed and exhibits shape stability even when isolated from the
cell (e.g. during nuclear transplantation). During mitosis, microtubule struts
polymerize from two centrosomes oriented at opposite poles of the cell and
push out against a mechanically continuous network of chromatin
(Maniotis et al., 1997b
),
thereby creating the `mitotic spindle' that holds the chromosomes in position.
Laser microbeam experiments have confirmed that this tensionally stiffened
spindle is a prestressed tensegrity cage
(Pickett-Heaps et al., 1997
).
What maintains nuclear shape in interphase cells is less clear; however, there
is no doubt that the nucleus is prestressed: cleave the protein lattice that
makes up the nuclear matrix and the tightly packaged (compressed) DNA explodes
outward. Nuclear shape stability in the living cell, however, also depends on
the presence of tensed intermediate filaments that connect the nucleus to
cell-surface adhesions and thus act like molecular guy wires at the level of
the whole cell (Maniotis et al.,
1997a
). These different subcellular tensegrity structures (e.g.
the internal cytoskeleton, submembranous cytoskeleton and nucleus) may act
independently, but when mechanically coupled they function as one integrated,
hierarchical tensegrity system.
On a smaller scale, cells also use a tensegrity force balance to stabilize
the elongated forms of specialized membrane projections. Stiffened bundles of
crosslinked actin filaments push out on the tensed surface membrane to create
filopodia that extend from the cell surface at the leading edge of migratory
cells (Sheetz et al., 1992)
and to form acrosomal extensions in sperm
(Tilney and Inoue, 1982
).
Crosslinking of any type of flexible molecular filament into larger bundles
greatly increases its ability to resist compression because the fixed lateral
connections prevent filament buckling or bending, just as a metal hoop
stiffens wood struts in a barrel. Thus, microfilaments, which normally bear
tension in the cell, have a dual function in that they can act as compression
struts when organized in this manner. Crosslinked bundles of microtubules
similarly stabilize cilia as well as long cell processes, as in neurites
(Joshi et al., 1985
).
Prestressed and geodesic forms of tensegrity also occur at the molecular
level. The most impressive example of a geodesic form is the finding that
actin microfilaments self-organize into well developed geodesic domes (actin
geodomes) in the cytoskeletons of certain cells in vitro
(Fig. 3B)
(Lazarides, 1976;
Osborn et al., 1978
) as well
as in vivo (Rafferty and Scholtz, 1985). Other examples of geodesic structures
include hexagonal arrangements of basement membrane proteins
(Yurchenco and Schittny,
1990
), polyhedral enzyme complexes
(Wagenknecht et al., 1991
),
clathrin-coated transport vesicles
(Vigers et al., 1986
) and all
viral capsids (Caspar, 1980
).
Biological polymers, such as microfilaments
(Schutt et al., 1997
), lipid
micelles (Butcher and Lamb,
1984
; Farrell et al.,
2002
), and individual proteins, RNA and DNA molecules all have
been depicted as prestressed tensegrity structures
(Ingber, 1998
;
Ingber, 2000b
; Farell et al.,
2002) because at this scale no components `touch' and, hence, all structural
stability must depend on continuous tensional (attractive) forces. For
example, in proteins, stiffened peptide elements (e.g.
-helices and
ß-strands) act locally to resist inwardly directed forces generated by
attractive (tensile) intramolecular binding forces. Thus, three-dimensional
models of the shape of a protein, such as a membrane channel, are not unlike
tensegrity models (Fig. 7A,B)
composed entirely of springs that have different elasticities (as in
Fig. 1C); the major difference
is that that intramolecular binding forces obviate the need for physical
tensile connections in the proteins. The prestressed nature of proteins can be
visualized if a single peptide bond is cleaved: immediate loss of shape
stability results. Moreover, studies with optical tweezers reveal that
individual DNA molecules exhibit linear stiffening behavior
(Smith et al., 1992
) similar
to that of living cells, tissues and tensegrity models.
For these reasons, the cellular tensegrity model has come to include the
concept that cells, tissues and other biological structures at smaller and
larger size scales exhibit integrated mechanical behavior because of
tensegrity architecture (Ingber and
Jamieson, 1985; Ingber,
1993b
; Ingber,
1998
; Pienta and Coffey, 1991; Pienta et al., 1991a;
Ingber et al., 1994
). The
recognition that nature uses both prestressed and geodesic structures at
smaller size scales in the cell also provides further evidence to suggest that
these different classes of structure are manifestations of a common
"design" principle. Geodesic tensegrity forms (e.g. tetrahedra,
octahedra and icosahedra) similarly predominate in the inorganic world of
crystals and atoms and thus, this principle may have contributed to how life
first emerged on this planet (Ingber,
2000b
).
![]() |
Conclusion |
---|
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---|
The power of the tensegrity theory to predict complex cell behaviors from first principles, to mimic pattern formation within the cytoskeleton on the nanoscale and to translate cell shape control into molecular terms speaks for itself. Yet, for many molecular cell biologists, there is still little value in this knowledge. They do not need to take into account the contributions of physical forces or supramolecular assemblies in studies that focus on individual molecules or signaling mechanisms. However, at some point, we all will have to translate what we have learned from our simplified systems in order to predict, manipulate and control cellular function in vivo. Then physical factors, tissue structure and understanding of hierarchical systems biology how molecular processes function within living multicellular organisms will become important.
For those interested in cell and tissue physiology, cell context is already
critical. Pursuit of the tensegrity model has led to new insights into cell
mechanics and to the recognition that mechanical stresses can be transferred
through the viscous cytosol and to the nucleus in living cells through
discrete molecular networks. It also has helped to explain how living
organisms can function as integrated mechanical systems, even though they are
complex hierarchical structures (molecules within cells within tissues within
organs). Indeed, the tensegrity principle has been invoked by investigators to
explain an unusually wide range of unexplained phenomena in many different
systems and species, including: lipid micelle formation
(Butcher and Lamb, 1984),
protein folding in milk globules (Farrell
et al., 2002
), protein organization within viral capsids
(Caspar, 1980
), the structure
of actin microfilaments (Schutt et al.,
1997
), pattern formation in paramecium (Kaczanowska et al., 1995),
hyphal morphology in fungi (Kaminsky and
Heath, 1996
), neurite outgrowth
(Joshi et al., 1985
;
Buxbaum and Heidemann, 1988
),
endothelial permeability barrier function
(Moy et al., 1998
), vascular
tone (Northover and Northover,
1993
), dystrophin function in muscular dystrophy
(Gillis, 1999
),
choriocarcinoma differentiation (Hohn et
al., 1996
), control of apoptosis
(Ciesla, 2001
), morphogenesis
of mammalian cells and tissues (Ingber et
al., 1981
; Ingber and
Jamieson, 1985
; Pienta and
Coffey, 1991a
; Pienta et al.,
1991
; Huang and Ingber,
1999
; Ingber, 1993; Ingber et
al., 1994
), the structure of the skin
(Ryan, 1989
), lens
(Yamada et al., 2000
),
cartilage (Malinin and Malinin,
1999
), retina (Galli-Resta,
2002
) and brain (Van Essen,
1997
), the mechanics of the human skeleton
(Levin, 1997
), tumor formation
and metastasis (Ingber et al.,
1981
; Ingber and Jamieson,
1985
; Pienta and Coffey,
1991b
; Huang and Ingber,
1999
), as well as gravity sensing in both animals and plants
(Ingber, 1999; Yoder et al.,
2001
). In addition, it has helped to elucidate the molecular basis
of cellular mechanotransduction and has revealed previously unrecognized roles
of the ECM, cytoskeletal structure and cytoskeletal tension (prestress) in the
control of cellular information processing, as I will describe in Part II of
this Commentary (Ingber,
2003
).
The cellular tensegrity model remains a work in progress that will continue
to be refined as more information emerges. However, the ability of the
tensegrity theory to predict and explain complex cell behaviors is a testament
to the notion posed by D'Arcy Thompson in the quote that opens this article
(Thompson, 1952): although
the living cell is a complicated structure, it still may be governed by simple
rules.
![]() |
Acknowledgments |
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References |
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