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Nature Reviews | Cancer
Primary tumourVascularization Detachment
Circulating
tumour cell
Adhesion to
blood vessel wall Extravasation
Growth of
secondary tumour
Intravasation
In the series of steps that comprise the
metastatic process, cancer cells migrate or flow
through vastly different microenvironments,
including the stroma, the blood vessel
endothelium, the vascular system and the
tissue at a secondary site1,2 (FIG. 1). The ability
to successfully negotiate each of these steps
and advance towards the formation and
growth of a secondary tumour is dependent,
in part, on the physical interactions and
mechanical forces between cancer cells
and the microenvironment. For example, the
physical interactions between a cell and
the extracellular matrix — the collagen-rich
scaffold on which it grows — have a key role
in allowing cells to migrate from a tumour to
nearby blood vessels. During intravasation
and extravasation, cells must undergo large
elastic deformations to penetrate endothelial
cell–cell junctions. In the vascular system,
the interplay between cell velocity and
adhesion influences the binding of cancer
cells to blood vessel walls and hence the
location of sites where a secondary tumour
can form and grow. A clearer understanding
of the role of physical interactions and
mechanical forces, and their interplay with
biochemical changes, will provide new and
important insights into the progression of
cancer and may provide the basis for new
therapeutic approaches.
Physical interactions in invasion
Following the growth of a primary tumour,
the combination of continued tumour pro-
liferation, angiogenesis, accumulated genetic
transformations and activation of complex
signalling pathways trigger the metastatic
cascade (FIG. 2). In particular, the detachment
of carcinoma cells from the epithelium and
the subsequent invasion of the underlying
stroma resembles, at both the cellular and
molecular levels, the well-characterized
epithelial-to-mesenchymal transition (EMT) in
embryogenesis3. The role of EMT in cancer
metastasis is being actively explored4,5.
Critical to EMT is the loss of E-cadherin
(an intercellular adhesion molecule) and
cytokeratins, which leads to dramatic changes
in the physical and mechanical properties
of cells: specifically, reduced intercellular
adhesion and a morphological change from
cuboidal epithelial to mesenchymal6. One
consequence of these changes is detachment
from the primary tumour and the acquisition
of a motile phenotype5. These cells also
begin to express matrix metalloproteinases
(MMPs) on their surface, which promote
the digestion of the laminin- and collagen
IV-rich basement membrane7. After leaving
the tumour microenvironment, motile
tumour cells encounter the architecturally
complex extracellular matrix (ECM), which
is rich in collagen I and fibronectin8 (BOX 1).
In the vicinity of a mammary tumour, the
matrix is often stiffer than in normal tissue
owing to enhanced collagen deposition9 and
lysyl-oxidase-mediated crosslinking of
the collagen fibres by tumour-associated
fibroblasts10. Collagen crosslinking enhances
integrin signalling as well as the bundling
of individual fibres11. Such changes in the
physicochemical properties of the matrix can
enhance cell proliferation and invasion in a
positive feedback loop9. Whether stiffening
of the stromal matrix occurs in other solid
tumours, besides mammary tumours, remains
to be determined. However, despite recent
technological advances (TABLE 1), remarkably
little is known about the molecular and
physical mechanisms that drive motile
cancer cells away from primary tumour
and into the stromal space, especially at the
subcellularlevel.
Motility in three dimensions. Much of what
we have learned about the physical and
molecular mechanisms driving normal
and cancer cell motility has come from
invitro studies using two-dimensional (2D)
substrates12–14. However, the dimensionality
of the system used to study cancer invasion
can have a key role in dictating the mode
of cell migration. This is not entirely
surprising as the three-dimensional (3D)
microenvironment of the ECM invivo is
characterized by many features, including the
pore size and fibre orientation, features that
are not found in conventional ECM-coated
OPINION
The physics of cancer: the role
of physical interactions and
mechanical forces in metastasis
Denis Wirtz, Konstantinos Konstantopoulos and Peter C.Searson
Abstract | Metastasis is a complex, multistep process responsible for >90% of
cancer-related deaths. In addition to genetic and external environmental factors,
the physical interactions of cancer cells with their microenvironment, as well as
their modulation by mechanical forces, are key determinants of the metastatic
process. We reconstruct the metastatic process and describe the importance of
key physical and mechanical processes at each step of the cascade. The emerging
insight into these physical interactions may help to solve some long-standing
questions in disease progression and may lead to new approaches to developing
cancer diagnostics and therapies.
Figure 1 | The metastatic process. In this complex process, cells detach from a primary, vascularized
tumour, penetrate the surrounding tissue, enter nearby blood vessels (intravasation) and circulate in
the vascular system. Some of these cells eventually adhere to blood vessel walls and are able to extrav-
asate and migrate into the local tissue, where they can form a secondary tumour.
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2D substrates15. In turn, many features that are
thought to be crucial for 2D motility, such as
focal adhesions, stress fibres, wide lamellipodia
and lamella, multiple filopodial protrusions at
the leading edge and apical polarization, are
either drastically reduced in size or entirely
missing from motile carcinoma or sarcoma
cells in a 3D matrix16–20. Similarly, several
cellular features that are important in 3D
cell motility have little or no role in 2D cell
motility, including nuclear deformation,
MMP production and major reorganization
of theECM.
Recent work suggests that focal adhesions,
composed of clustered integrins that physically
and dynamically connect the cellular actin
network to ECM fibres on 2D substrates,
are altered when cells are embedded inside
a 3D matrix16. Focal adhesions, which are
readily visible by microscopy in human breast
cancer cells, colon carcinoma cells and
fibrosarcoma cells plated on 2D substrates,
rapidly decrease both in size and number as
a function of the distance between the cells
in the matrix and the substrate that supports
thematrix.
The absence of prominent focal adhesions
and the associated reduction and relocalization
of stress fibres that join these focal adhesions is
in large part due to the 3D architecture of the
ECM. In general, a cell is much larger than
the diameter of the fibres of the ECM, which
are typically on the order of 100 nm. Therefore,
from a cellular perspective, the collagen fibres
in the ECM appear quasi-one-dimensional
(1D); similarly, a human hair does not
appear to have significant width and hence is
quasi-1D to the eye. Focal adhesions formed
on 2D substrates are typically 1–10 m in size,
much larger than the fibre diameter of the
ECM21–23. This finite size effect limits the size of
focal adhesions and the associated clusters
of integrins and focal adhesion proteins that can
be formed in cells embedded in a 3D matrix.
Hence, although when in 2D culture a cell is in
contact with a contiguous substrate, a cell
in a 3D matrix has confined local contact with
quasi-1Dfibres.
Nevertheless, collagen fibres in a 3D matrix
could support the formation of small and
highly dynamic integrin clusters, with sizes on
the order of tens of nanometres and lifetimes
shorter than a few seconds, which may still
be crucial to 3D cell motility. Moreover, cells
invivo could promote the bundling of collagen
fibres through the generation of contractile
forces produced by cellular protrusions. Such
collagen bundles would enhance the surface
area available and potentially promote the
formation of larger adhesions24.
Actomyosin stress fibres, containing
bundled actin filaments, have an important
role in 2D cell motility as they provide the
contractile forces required for the regulated
detachment of the rear of a cell from the
substratum and establish actin flow at
the leading edge of the cell23,25. By contrast,
cells display few stress fibres inside a 3D
matrix and these are either localized to
the cell cortex or radiate from the nucleus
towards the plasma membrane to form
pseudopodial protrusions26. Inhibition
of actomyosin contractility is often
substantially less effective in blocking 3D
cell motility than in blocking 2D cell
motility26, suggesting that the role of stress
fibres is dependent on dimensionality25,27.
Hence, eliminating the apical polarization of
cells in 2D culture reduces the number
of focal adhesions and stress fibres, and
therefore fundamentally changes the role of
components such as focal adhesion proteins
and proteins highly enriched in stress
fibres, such as the F-actin binding proteins
α-actinin, myosin II and tropomyosins.
In addition to having fewer focal adhesions
and stress fibres when in a 3D matrix,
cancer cells and epithelial or endothelial
cells inside a 3D matrix typically do not
form the characteristic wide lamellipodium
and associated filopodial protrusions at the
periphery. Instead, they display a limited
number of pseudopodial protrusions, typically
of 10–20 m thickness, which is intermediate
between a lamellipodium and filopodia16.
Traction microscopy suggests that in 2D
Glossary
Amoeboid migration
A mode of three-dimensional cell migration in a matrix that
involves dynamic cell-shape changes through actomyosin
assembly and contractility, and adhesion to the
extracellular matrix.
Epithelial-to-mesenchymal transition
(EMT). A morphological change that epithelial cells
undergo, from a cubical to an elongated shape, following
oncogenic transformation, which is often accompanied by
loss of expression of the adhesion molecule E-cadherin.
Post-EMT, cells adopt a high-motility phenotype.
Filopodia
Narrow projections of the cytoplasm extended beyond the
lamellipodia of migrating cells. Filopodia are associated with
the formation of nascent focal adhesions with a substratum.
Focal adhesions
Integrin clusters located at the basal surface of adherent
cells that connect the extracellular matrix to the
cytoskeleton through focal adhesion proteins.
Interstitial flow
Fluid flow in the extracellular matrix, often associated with
lymphatic drainage of plasma back to the vascular system.
Intravital microscopy
A microscopy technique used for the observation of
biological responses, such as leukocyte–endothelial cell
interactions, in living tissues in real time. Translucent tissues
are commonly used, such as the mesentery or cremaster
muscle, which can be easily exteriorized for microscopic
observation.
Lamellipodia
Large cytoplasmic projects found primarily at the leading
edge of migrating cells, particularly on two-dimensional
substrates.
Mechanosensing
The ability of cells to sense and respond to changes in the
mechanical compliance of a substrate. Mechanosensing is
mediated by focal adhesions and the cytoskeleton in
two-dimensional cell culture.
Mesenchymal migration
A mode of three-dimensional cell migration in a matrix that
involves integrin-based adhesion. Mesenchymal migration
occurs when the pore size of the matrix is much smaller
than the cell nucleus.
Pseudopodia
Bulges of constantly changing shape observed in the
plasma membrane of migrating cells during amoeboid
migration on two-dimensional substrates and
mesenchymal migration through three-dimensional
matrices.
Shear rate
The relative velocities of adjacent layers of fluid under shear
force in conditions of laminar flow.
Shear stress
The magnitude of the tangential force applied onto the
surface of an object per unit area. Shear stress is expressed
in units of force per unit area (Newtons m–2 in metres
kilograms seconds (MKS) units or dynes cm–2 in
centimetres grams seconds (CGS) units).
Stiffness
(Also known as elasticity or elastic modulus). A measure of
the ability of a material to resist shear forces similarly to a
solid. Rubber is elastic and shows little viscosity. A
crosslinked collagen matrix is elastic, but not viscous as it
does not flow. The cytoplasm of cells is both elastic and
viscous (viscoelastic) depending on the rate of deformation.
Stress fibres
Contractile actin filament bundles that contain myosin II,
which serves both as an F-actin bundling protein and as a
force generator. Stress fibres terminate at focal adhesions
at the basal surface of cells on substrates.
Surface tangential velocity
The velocity at the surface of a spinning object.
Translational velocity
The velocity of an object in space.
Viscosity
A measure of the ability of a material to flow like a liquid.
Water, glycerol and honey are liquids of increasing
viscosity; they are only viscous and show no elasticity.
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Nature Reviews | Cancer
Primary
tumour
Intravasation
Basement
membrane
EMT
↓ E-cad
↑ N-cad
↑ Integrins
↑ MMPs
↑ LOX
Invasion
Endothelial cells
ECMPseudopodial
protrusion
E-cad E-cad E-cad
N-cad
culture, a lamellipodium actively pulls the rest
of the cell through nascent focal adhesions
positioned at the edge of the lamellipodium28.
By contrast, 3D traction microscopy reveals
that cells inside a 3D matrix never push
the surrounding matrix and only pull on
surrounding fibres26,29. Substantial matrix
traction only occurs in the vicinity of
productive pseudopodial protrusions, which
typically number between only one and five
per cell at any time26. Interestingly, in a 3D
matrix, pseudopodial protrusions pull with
approximately equal forces at the leading and
trailing cell edges. However, the timing of
release of the pseudopodia from the collagen
fibres is asymmetric, often creating a defect
in the matrix in the wake of the cell. These
results suggest a model for 3D cancer cell
motility in which pseudopodial protrusions at
the trailing edge of the cell release first, pulling
the rear of the cell forwards. The partial
digestion of the ECM in the wake of the cell
results in biased motion, analogous to a biased
ratchet. This defect does not allow the cell to
retrace the tunnel formed during migration
and, therefore, promotes highly persistent
migration in a 3D matrix, compared to less
persistent migration of the same cell on a
2D substrate20.
Pseudopodia also have a probing role
in 3D matrices but are of no functional
importance on 2D substrates, where the
extracellular environment is compositionally
and topologically uniform. The interplay
between the growth of pseudopodia along
the quasi-1D tracks provided by the collagen
fibres, the magnitude of traction and local
digestion mediated by MMPs has not been
determined but is likely to be fundamentally
different from the 2D case given the different
shapes of membrane protrusions and the
crucial importance of MMPs in 3D cell
motility. As cellular traction on collagen fibres
may activate MMPs30, the interplay among
pulling by cell protrusions, MMP activity and
net cell migration is likely to occur within a
feedbackloop.
Pseudopodial protrusion activity in
3D matrices is readily modulated by focal
adhesion components. For example, the
scaffolding protein p130CAS mediates a high
number and high growth rate of protrusions,
whereas the mechanosensing protein zyxin
represses protrusion activity and diminishes
the rate of protrusion growth along collagen
fibres. A recent study16 showed that the
number of protrusions per unit time as
well as the growth rate of protrusions,
as modulated by focal adhesion proteins,
correlated strongly with tumour cell motility
in 3D matrices, a correlation shared by
sarcoma and carcinoma cells. For instance,
the migration speed of p130CAS- and zyxin-
depleted cells correlated with the number of
protrusions generated per unit time by these
cells in 3D matrices16. However, whereas
p130CAS-depleted cells moved more slowly
(and zyxin-depleted cells more rapidly)
than control cells in 3D matrices, these
depleted cells displayed the opposite motility
phenotypes on flat substrates. Importantly,
modulation of 3D cell motility by the
depletion of specific focal adhesion proteins
does not correlate with changes in motility
on 2D substrates. For example, vinculin-
depleted cells move at a similar speed to
control cells on flat substrates, whereas they
move faster than control cells inside a 3D
matrix16. Therefore, the role of focal adhesion
proteins in 2D cell motility is not predictive of
their role in motility in more physiologically
relevant 3D matrices. Such results suggest
that high-throughput pharmacological
screens for drugs that limit motility on 2D
substrates could be misleading. Moreover,
although the rate of filopodial protrusion
does not seem to correlate with 2D cell speed,
the rate of pseudopodial protrusion correlates
with 3D cell speed16. This suggests that
protrusion dynamics is not required perse
for effective 2D motility, but may be crucial
in establishing 3D motility.
Many features observed in vivo by
intravital microscopy31 have been recapitulated
in 3D matrix constructs, including the highly
persistent migration of single cells away from
tumours, the role of actomyosin contractility
in collective migration to lymphatic vessels
and the crucial role of MMPs in cancer
cell dispersion from a primary tumour
site. Nevertheless much more needs to be
done to validate 3D models for invitro
cancerstudies.
Intravital imaging of mammary tumours
in mice suggests that only a small number
of cells leave the primary tumour sites, and
that they undergo highly directed migration
away from the tumour by travelling along
collagen fibres1,32. Intravital microscopy of
GFP-labelled breast cancer cells in mice
suggests that these cells migrate as single cells
towards blood capillaries, and as multicellular
clusters preferentially towards lymphatic
vessels33. Such collective migration requires
the suppression of actomyosin contractility at
intercellular adhesions, which is mediated by
discoidin domain receptor family, member1
(DDR1) and the polarity regulators PAR3
and PAR6 (REF.34). To establish the invivo
relevance of invitro 3D matrix-based models,
it will be important to confirm the role of
focal adhesion proteins in cancer cell motility
(suggested by the invitro 3D assays described
above) using intravital microscopy.
Signalling and motility in cancer cells. The
role of other prominent proteins that normally
localize to the lamellipodium and filopodia of
cells in 3D matrices is largely unknown. These
proteins include those that constitute the
F-actin nucleating ARP2/3 complex and its
activators neural Wiskott–Aldrich syndrome
protein (NWASP), Wiskott–Aldrich
syndrome protein family, member 1 (WASF1;
also known as WAVE1), WASF2 and WASF3
(also known as SCAR3), the expression of
which correlates with poor clinical outcomes
in several types of cancer35,36. Expression of
the F-actin bundling protein fascin, which
localizes to filopodia in 2D cell cultures,
also correlates with poor clinical outcomes
Figure 2 | The physics of invasion and intravasation. The epithelial-to-mesenchymal transition
(EMT) is associated with a loss of adhesion through downregulation of E-cadherin (E-cad) and a change
in morphology. Invasion by tumour cells of the surrounding tissue and subsequent motion is dictated
by the physicochemical properties of the extracellular matrix (ECM). By squeezing between blood
vessel endothelial cells, tumour cells can enter the vascular system. All of these steps involve physico-
chemical processes, such as adhesion and deformation, that are dependent on the local environment.
LOX, lysyl oxidase; MMPs, matrix metalloproteinases; N-cad, N-cadherin.
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in patients with breast cancer37. In addition,
the tumour suppressor protein PTEN38 has
been shown to localize at the trailing edge of
migrating cells39. Therefore, the development
of therapeutic approaches targeting
mediators of cell motility and invasion will
require a greater understanding of the role
of these proteins in the more physiological
environment of a 3D matrix or invivo.
MMP inhibition or depletion in carcinoma
and fibrosarcoma cells has been observed
to switch the mode of migration from a
predominantly integrin-based motility
to a faster amoeboid migration mode40. By
contrast, inhibition of the master mediators
of actomyosin contractility, ROCK and RHO,
forces the adoption of a mesenchymal migration
mode in cells with an intrinsic amoeboid
shape when embedded in Matrigel41. These
observations provide a possible explanation
for the failed clinical trials of MMP inhibitors.
However, these invitro studies made use of
pepsin-extracted collagen I and commercially
available Matrigel, which are both largely
uncrosslinked. In particular, pepsin extraction
of collagen I results in larger pores during
gelation15 that are permissive for amoeboid
migration. The motility of cancer cells in
crosslinked collagen gels crucially requires
MMPs, primarily MMP14 (also known
as MT1-MMP)8,15,42. These seemingly
contradictory results can be reconciled if
MMP function depends on the collagen
matrix microstructure, including the collagen
concentration and crosslinking density. MMP
inhibition would be effective in reducing
cancer cell motility in highly crosslinked
and/or concentrated regions of the matrix, but
would be ineffective for poorly crosslinked
and/or low density regions. Interestingly,
recent results suggest that mechanical load
can dramatically increase the rate of collagen
proteolysis by MMP14 (REF.43). Moreover,
combined inhibition of MMPs and actomyosin
contractility reduces cell migration more
effectively than separate inhibition of MMPs
or contractility26. These results suggest an
important functional interplay between
cellular contractility and local MMP-mediated
collagen digestion that drives cell migration in
3D matrices.
There is accumulating evidence that the
physical properties of the stroma have a
crucial role in tumour initiation, progression
and metastasis through interplay between
physical forces and biochemical signals. For
example, the stiffness of the stromal matrix
and degree of orientation of matrix fibres near
primary tumour sites strongly correlate with
worse clinical outcomes. Both invitro and
invivo, these two microstructural parameters
alone greatly enhance cell proliferation and
motility9,18,44–46.
The role of cell mechanics in intravasation
During entry into, and exit from, the vascular
system, tumour cells undergo dramatic shape
changes, driven by cytoskeletal remodelling,
that enable them to penetrate endothelial
cell–cell junctions. The cytoplasm is a
complex composite system that behaves like
an elastic material (such as rubber) at high
deformation rates but more like a viscous
material (such as ketchup) that exhibits
a yield stress at low deformation rates47.
Elasticity reflects the ability of the cytoplasm
to rebound following the application of a
force, whereas viscosity measures the ability
of the cytoplasm to undergo flow under
external shear. However, as MMP-mediated
digestion of the matrix seems to be only
partial, the rate-limiting step in the migration
of cancer cells within a matrix or across an
endothelium may be the deformation of
the interphase nucleus, which is the largest
organelle in the cell48 and is approximately
ten times stiffer than the cytoplasm49,50.
The elasticity of the nucleus seems to be
determined by the nuclear lamina underlying
the nuclear envelope49 and by both chromatin
organization51 and linkers of the nucleus and
cytoskeleton (LINC) complexes52–55. LINC
complexes are protein assemblies that span
the nuclear envelope and mediate physical
connections between the nuclear lamina
and the cytoskeleton52. These connections
are mediated by interactions between SUN
domain-containing proteins (including SUN1
and SUN2) and Klarsicht homology (KASH)
domain-containing proteins at the outer
nuclear membrane (including the nesprin2
giant isoform and nesprin 3, which can bind
actin directly or indirectly)56–58. Indeed,
depletion of LINC complex components,
including nesprins and SUN proteins, leads
to nuclear shape defects and an associated
softening of the nucleus and the cytoplasm59.
The nuclear lamina and LINC complex
molecules have crucial roles in collective
2D migration54,55; however, their role in 3D
motility remains to be explored. Mutations
that occur in nesprins and lamin A/C that
have been found in breast cancer40 could
cause changes in LINC-mediated connections
between the nucleus and cytoskeleton
and, in turn, affect cancer cell 3D motility and
invasiveness.
Biophysical measurements that compare
the mechanical properties of normal
and cancer cells have consistently shown
that cancer cells are softer than normal cells
and that this cellular compliance correlates
with an increased metastatic potential60,61.
In cancer cells, a softer cytoplasm correlates
with a less-organized cytoskeleton. However,
softening of the cytoskeleton has yet to be
verified in vivo or in a 3D matrix in the
presence and absence of interstitial flow. This
is important as the physical properties of
the environment, such as ECM stiffness62
and dimensionality63–65 and the presence of
interstitial flow, regulate cell mechanics66. The
development of new methods, such as particle-
tracking microrheology47, will allow these
measurements to be carried out in animal
models, enabling a direct test of the hypothesis
that cancer cells display lower stiffness than
non-transformed cells. Such a finding could
be used as a biophysical diagnostic marker of
disease and metastatic potential60. We note that
the reason why cancer cells may be softer than
non-transformed cells is not currentlyknown.
Migration through a 3D matrix and
penetration through an endothelium is likely
to require optimal mechanical properties:
if they are too stiff or too soft, cells cannot
deform the highly crosslinked collagen
fibres of the matrix to migrate efficiently.
However, single-cell measurements have
consistently revealed that individual cells of a
particular cell type are usually heterogeneous
and display a wide range of mechanical
properties. This suggests that cells with the
optimal mechanical properties for invasion
and intravasation into blood vessels are
Box 1 | The extracellular matrix
The extracellular matrix (ECM) is a complex composite material consisting of proteoglycan
hydrogel coupled to an assembly of crosslinked collagen fibres that are typically 100 nm or less in
diameter116. The unique three-dimensional architecture provides structural support and also allows
sensing and transduction of biochemical and mechanical signals to cells117. The properties of the
ECM are tissue-dependent: for example, the elasticity of ECM varies from less than 1 kPa in the
brain to 100 kPa in skeletal tissues118. The interstitial space in the ECM is occupied by fluid that is
usually in motion and provides a dynamic environment for cells67. The permeability of the ECM
is dependent on its composition and structure. The development of invitro models of ECM that can
mimic tissue-specific physicochemical properties, molecular composition, elasticity, pore size and
local fibre orientation will be crucial to further advance our understanding of cancer cell motility in
three dimensions and how this relates to migration invivo.
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Table 1 | Tools for the study of the physics of cancer
Tool or technique Application Refs
Cellular adhesion and migration
Single-molecule force spectroscopy Measurements of cell–matrix and cell–cell adhesion at single-molecule
resolution; measurement of single ligand–receptor binding invivo
120–125
Flow chamber assays Measurement of global cell–matrix adhesion 103,126–128
Adhesive micropatterns Control of cell and nuclear shape and size; control of axis of cell division;
high-throughput drug testing
129–133
Adhesive nanopatterns Control of subcellular adhesion; integrin clustering 21
Programmed subcellular release Controlled localized detachment of cells from substrates 134–136
Deformable pillars Measurement of local traction forces generated by cells; application of localized
forces to the basal surface of cells
137,138
3D traction microscopy Measurement of cell-induced 3D matrix remodelling 26
2D traction microscopy Measurement of forces generated by cells on 2D substrates 139
Galvanotaxis Measurement of the influence of electric field on motility 140,141
Controlled cellular polarization
Flow chambers Measurements of cell polarization induced by flow and mechanotransduction 142,143
Wound-healing Measurements of migration and polarization during collective cell migration 144
Single-cell motility Measurement of motility parameters for cells on substrates and in 3D matrices 16
Micropatterns for wound-healing Measurement and control of cell polarization during collective cell migration 145–147
Cellular and nuclear mechanics
Atomic force microscopy Measurement of cellular and single-molecule mechanics; imaging of cells at the
nanoscale; application of controlled forces to the apical surface of cells
45,62,148
Particle tracking microrheology Measurement of intracellular, nuclear and extracellular matrix mechanics
invitro and invivo
50,63,149
Magnetic/optical tweezers Measurement of cellular and subcellular mechanics; application of localized
forces at the cell surface and in the cytoplasm
61,150
Calibrated microneedles Application of localized forces to the apical surface of cells and measurement of
cell mechanotransduction
151–153
Laser ablation Ablation of cytoskeletal fibres 154–156
Micropipette suction Measurement of cellular and nuclear mechanics 49,157,158
Controlled microenvironment
Substrates of controlled compliance Measurement of cellular mechanosensing; testing of the role of
microenvironment compliance on cellular functions
159,160
Substrates of controlled nanotopography Testing the role of local topography on cell functions 161–163
Stretchable substrates Measurement of subcellular and nuclear mechanotransduction 59,164
Biomimetic matrices 3D matrices of controlled pore size, compliance and distance between ligands 165
Adhesive micropatterns Control of the dimensionality of the microenvironment (1D versus 2D); control of
cell shape and size
20,131,132
Confining microchannels Measurement of cell motility in confined spaces 166
Microfluidic devices Control and measurement of cell chemotaxis and durotaxis; cell sorting;
high-throughput molecular detection
61,167–170
Imaging
Multiphoton laser scanning microscopy Real-time imaging of individual cells and extracellular matrix invivo 31,73,
171,172
Fluorescence recovery after photobleaching (FRAP) Measurement of the subcellular diffusion of molecules 173,174
Fluorescence loss in photobleaching (FLIP) Measurement of the net transport of molecules in the cytoplasm 123,173,174
Fluorescence resonance energy transfer (FRET) Protein localization and activity in live cells 175,176
Fluorescence lifetime imaging (FLIM) Fluorescence imaging in thick samples 177
Fluorescence correlation spectroscopy Dynamics of molecules in live cells 178,179
Photoactivation Activation of proteins; ultraresolution microscopy 180–182
1D, one-dimensional; 2D, two-dimensional; 3D, three-dimensional.
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Nature Reviews | Cancer
Circulating
tumour cell
Circulating tumour cell trajectory
dvessel > dcell
likely to preserve this phenotype over several
generations. If mechanical properties are
determined randomly on cell division, the
broad distribution of mechanical properties
implies that migration and intravasation
would be unlikely events. Therefore, an
important question is whether the physical
attributes of cancer cells, such as stiffness,
are passed on from generation to generation.
If these physical properties are inherited, then
it may be possible to alter them, either through
pharmacological inhibition or activation
of proteins affecting cell mechanics, so that
they are not optimal for stromal invasion and
intravasation.
Different optimal mechanical properties
are probably required for each step of the
metastatic cascade. For example, the optimal
mechanical properties for invasion into the
stromal matrix near the primary tumour
site could be different from the mechanical
properties of cells that have optimal (efficient)
intravasation. Hence the mechanical properties
of cancer cells might dynamically change
during the metastatic process to successfully
survive the harsh and changing environment
of blood vessels, lymphatic vessels and the
stromal space. These differences in mechanical
properties might also be modulated by
biochemical gradients50, interstitial flows67 and
endogenous electric fields68.
Shear stress and the circulatory system
During their transit through the circulatory
system, tumour cells are subjected to
haemodynamic forces, immunological
stress and collisions with host cells, such
as blood cells and the endothelial cells
lining the vessel wall. All of these stresses
could affect cell survival and the ability to
establish metastatic foci. Only circulating
tumour cells (CTCs) that overcome or even
exploit the effects of fluid shear (see below)
and immunosurveillance will adhere to the
vascular endothelium of distant organs, exit
the circulation and successfully enter these
tissues. A tiny fraction of CTCs survive
to generate metastases; most CTCs die or
remain dormant69.
On entering the circulatory system,
the trajectory or path of a tumour cell is
influenced by a number of physical and
mechanical parameters: the pattern of blood
flow, the diameter of the blood vessels and
the complex interplay between shear flow
and intercellular adhesion that leads to the
arrest of cell movement in larger vessels.
Shear stress (τ) arises between adjacent
layers of fluid (in this case blood) of
viscosity (μ) moving at different velocities.
The velocity of a fluid in a cylindrical tube
is maximum at the centre and zero at the
cylinder walls, and the relative velocities of
parallel adjacent layers of fluid in laminar
flow define the shear rate (dγ/dt ≡ γ
) where
γ is the amplitude of deformation and
t is the time elapsed. Shear stress is defined by
the product of fluid viscosity and shear rate,
and has units of force per unit area (Newtons
per square metre (N m–2) or dynes per square
centimetre (dyn cm–2)).
The viscosity of blood is about 4centipoise
(cP), which is considerably greater than the
viscosity of water (0.7 cP at 37 °C), primarily
owing to the presence of red blood cells.
At shear rates greater than 100 s–1 , blood
is considered a Newtonian fluid, implying
that the shear stress increases linearly with
shear rate. The normal time-averaged levels
of shear stress vary between 1–4 dyn cm–2 in
the venous circulation and 4–30 dyn cm–2
in the arterial circulation70. The maximum
shear stress is experienced at the vessel wall.
The mean blood velocity (vav ) in arteries for
a vessel of diameter d = 4 mm is 0.45 m s–1,
whereas vav = 0.1 m s–1 in a 5 mm vein. The
corresponding shear rates (dγ/dt = 8vav/d) are
900 s–1 in arteries and 160 s–1 in veins.
The interstitial fluid velocity in other
tissues, such as cartilage and bone subjected
to mechanical loading during daily activity,
induces varying levels of fluid shear stress
up to 30 dyn cm–2 (REFS 2,71). Cells in the
gastrointestinal tract are also constantly
subjected to peristalsis and fluid shear stresses
up to 30 dyn cm–2. Renal epithelial cells
normally sense stresses up to 0.5 dyn cm–2
(REF. 72), which are significantly increased
under pathological conditions such as
hypertension.
Shear flow influences the translational
and rotational motion of CTCs (see the next
section) and hence determines the orientation
and time constant associated with receptor–
ligand interactions that lead to adhesion.
Shear flow may also induce deformation of
CTCs and margination towards the vessel
walls. However, the magnitude of these
effects and their influence on occlusion and
adhesion remain to be determined. Sur-
prisingly, little is known about the effects of
shear flow on the viability and proliferation
ofCTCs.
Extravasation of circulating tumour cells
For a circulating tumour cell to exit the
circulatory system, it must first bind to a
blood vessel wall. There are two mechanisms
of arrest, physical occlusion and cell
adhesion; the relative prevalence of these
mechanisms depends on the local blood
vessel diameter (FIG. 3).
Physical occlusion. If a circulating tumour
cell enters a vessel whose diameter is less
than the circulating tumour cell (dvessel < dcell),
then arrest can occur by mechanical trapping
(physical occlusion). As circulating tumour
cells of epithelial origin are typically >10 m in
size, physical occlusion occurs in small vessels
or capillaries of <10 m. Arrest at branches in
blood vessels in the brain, with subsequent
extravasation and metastasis formation, has
been observed by intravital microscopy in a
mousemodel73.
Adhesion. Extravasation of a tumour cell
from a large blood vessel (dcell < dvessel) requires
the adhesion of the cell to the vessel wall
through the formation of specific bonds. The
probability (P) of arrest at a large vessel can
be written as P ∝ ft, where f is the collision
frequency between membrane-bound
receptors and endothelial ligands and t
is the residence time74. The residence time is
dependent on the shear force exerted on the
cell and the adhesive forces associated with
ligand–receptor pairs between the circulating
tumour cell and the endothelial cells of the
blood vessel wall. Increasing fluid shear is
expected to increase the collision frequency
with the endothelium but decrease the
residence time of receptor–ligandpairs.
Figure 3 | Arrest of circulating tumour cells. Tumour cells with a diameter (dcell) less than the diam-
eter of the blood vessel wall (dvessel) will follow a trajectory that is determined by the local flow pattern
and by collisions with host cells and blood vessel walls. Collisions with a blood vessel wall may lead to
arrest. Tumour cells with diameter greater than the diameter of a blood vessel will be arrested owing
to mechanical trapping (physical occlusion).
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A cell moving along a vessel wall
has both translational and tangential
(angular) velocity (BOX 2). The translational
velocity of a cell is always larger than the
surface tangential velocity, resulting in a
slipping motion relative to the stationary
blood vessel wall. This slipping motion
increases the encounter rate between a
single receptor on a CTC and ligands on
the vessel wall75. For a cell undergoing
rotational motion, the rotation brings
successive receptors on the CTC surface
into contact with ligands on the vessel
wall. The total adhesion strength depends
in non-trivial ways on the tensile strength
of the individual receptor–ligand bond
and the number of the involved receptor–
ligand pairs. For example, cell adhesion
or cell aggregation assays have been used
to quantify global cell–cell adhesion76,77.
However, these assays linearly extrapolate
multiple-bond avidity to evaluate receptor–
ligand affinity, an oversimplification that
neglects possible cooperative effects. The
development of sophisticated biophysical
tools for measuring the kinetic and
micromechanical properties of single
ligand–receptor bonds have allowed single-
molecule affinity to be distinguished from
multi-molecular avidity78,79.
The probability of arrest, leading to
extravasation, is expected to be maximum
at intermediate values of shear stress. The
kinetic (ON and OFF rates) and micro-
mechanical (tensile strength) properties
of a single receptor–ligand bond dictate
whether a bond will form at a prescribed
shear stress level as well as the macro-
scopic pattern of cell adhesion (FIG.4).
For instance, the initiation of receptor-
mediated cell adhesion under shear stress
requires: a relatively fast ON rate, which
allows receptor–ligand binding at relatively
short interaction (encounter) timescales;
sufficient tensile strength to resist the
dispersive hydrodynamic force; and a
relatively slow OFF rate, which will provide
adequate bond lifetime, thereby facilitating
the formation of additional bonds.
Receptor–ligand pairs — such as the selectins
and their ligands discussed below — that
exhibit high tensile strengths, fast ON rates
and relatively fast OFF rates can initiate
binding under shear stress and mediate
transient rolling interactions. Molecules
with slower ON rates, such as integrins,
can engage only after selectin-mediated
cell binding or, in the absence of selectin-
dependent interactions, at a very low shear
stress. Integrin clustering is responsible for
the multi-bond, firm adhesion of cells onto
surfaces80. Thus, integrins are involved in the
dissemination of tumour cells, and may also
control angiogenesis and metastatic growth81.
The nature of receptor–ligand interactions
in the adhesion of CTCs. Evidence suggests
that CTCs may escape immune surveillance
and promote their egress from the circulatory
system by associating with platelets.
Direct evidence for the role of platelets in
metastasis comes from studies in a mouse
model showing the inhibition of metastasis
by either pharmacological82 or genetic83
depletion of platelets, and the restoration of
metastatic potential by platelet infusion84.
It is thought that by forming heterotypic
adhesive clusters with CTCs, platelets mask
and protect CTCs from immune-mediated
mechanisms of clearance85,86. Platelets may
also facilitate tumour cell adhesion to the
vessel wall87–89 (FIG.4) and release an array
of bioactive compounds such as vascular
endothelial growth factor (VEGF) at points
of attachment to the endothelium, thereby
promoting vascular hyperpermeability and
extravasation90. After tumour cells have
exited the circulation, factors secreted from
activated platelets can induce angiogenesis
and stimulate growth at the metastatic
site91. CTCs may also hijack polymorpho-
nuclear leukocytes (PMNs) for arrest in the
endothelium of distant organs. Microscopy
studies have shown PMNs in close
association with metastatic tumour cells
during tumour cell arrest and extravasation
invivo92.
CTCs may also mimic the behaviour
of neutrophils by directly binding to the
vascular endothelium through selectin-
mediated tethering and by cell rolling
followed by strong adhesion87,93. Indeed,
P-, L- and E-selectins facilitate cancer metastasis
and tumour cell arrest in the microvasculature
by mediating specific interactions between
selectin-expressing host cells and ligands
on tumour cells. The most direct evidence
for the involvement of P-selectin (which
is present on activated platelets and the
endothelium) in the metastatic process
is the marked inhibition of metastasis in
P-selectin-knockout mice compared to
wild-type controls in a colon carcinoma
xenograft model94,95. Similarly, mice
deficient in L-selectin, which is expressed
only by leukocytes, have reduced levels
of metastasis95. The extent of metastasis is
further reduced in P- and L-selectin double-
deficient mice95, thereby suggesting that
P- and L-selectins have synergistic effects
in the facilitation of metastatic spread.
It is thought that tumour cells can form
multicellular complexes with platelets and
leukocytes (via P- and L-selectin-dependent
mechanisms96,97, respectively). These
multicellular complexes can then arrest in
the microvasculature of distant organs, and
can eventually extravasate and establish
metastatic colonies. Interestingly, leukocyte
L-selectin can also enhance metastasis by
interacting with endothelial L-selectin
ligands that are induced adjacent to
established intravascular colon carcinoma
cell emboli98. Endothelial E-selectin has also
been shown to support metastatic spread
invivo99,100.
Selectins bind to sialofucosylated oligo-
saccharides, such as sialyl Lewisx (sLex) and
its isomer sLea, which are present mainly
on cell surface glycoproteins. Various
metastatic tumour cells, such as colon
and pancreatic carcinoma cells, express
sialofucosylated glycoproteins such as
Box 2 | Fluid shear stress and slipping velocity
For a moving spherical object with translational velocity (vcell), the angular velocity (ω) describes
the rate of spinning about its rotational axis, and the surface tangential velocity (vtg) describes the
velocity at the surface. For example, the translational velocity of the earth (about 30 km s–1) results
in one rotation around the sun in one year. The angular velocity results in one rotation around the
polar axis in one day (about 2π radians per day) and is independent of longitude. The surface
tangential velocity is highest at the equator and is about 465 ms–1. For a spherical object in contact
with a surface in a low viscosity fluid, such as air, the translational velocity is synchronized with the
angular velocity. This situation can be envisioned as a ball rolling along the floor where
vtg/vcell = 1. Numerical solutions of vtg/vcell (REF. 119) show that for a spherical cell touching the
surface in a viscous fluid, vtg/vcell = 0.57. Therefore, both translational motion and rotation along a
vessel wall contribute to receptor–ligand interactions. In the absence of a slipping motion, each
cell receptor can only interact with a limited number of immobilized counter-receptors located
within its reactive zone. Binding occurs only when the separation distance between a receptor and
a ligand is sufficiently small, within the reactive radius around a receptor. Thus, when a free ligand
is brought inside this reactive zone, the complex will react. By contrast, when a cell moves with
a finite slipping velocity, each cell receptor can potentially bind to any counter receptor
present within its reactive zone. Thus, the slipping velocity has been reported to enhance the
receptor–ligand encounter rate75.
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Nature Reviews | Cancer
Circulating tumour cell
Extravasation
Circulating tumour cell
a
b
Capture
Capture
RollingArrest
Endothelial cell
Basement
membrane
Ligand
Receptor
Endothelial cell
Tumour cell
CD44, CEA,
PODXL
E-selectin,
P-selectin
Ligand
Receptor
Endothelial cell
Tumour cell
Integrins
ICAM1, VCAM1
Receptor–ligand binding
Platelet
Nucleation Platelet-mediated captur
eG
rowth
CD44 variant isoforms, carcinoembryonic
antigen (CEA) and podocalyxin (PODXL),
all of which are recognized by selectins101–103.
As overexpression of these moieties on
tumour cells correlates with poor prognosis
and tumour progression104, it appears
that selectin-mediated adhesion to these
sialofucosylated target molecules on
tumour cells may represent an important
determinant for metastatic spread. Thus, the
intravascular phase of the metastatic process
represents a key step in which therapeutic
intervention may be successful105. We
note that additional molecules, such as
glycoprotein Iba (GPIba) and GPVI106,107,
integrins and their counter receptors,
intercellular adhesion molecule1 (ICAM1)
and vascular cell adhesion molecule1
(VCAM1), may be involved in tumour
cell–host cell interactions104 (FIG. 4).
The location of metastatic sites. The location
of metastatic sites with respect to a primary
tumour has been the subject of intense
investigations for many years2,108–110. Analysis
of autopsy data revealed that metastatic sites
are not colonized randomly108,111. Although
primary tumours are found to metastasize
to many different sites, there is a higher
probability of metastasis at certain sites. For
example, prostate cancer tends to metastasize
to bone marrow and the liver, whereas breast
cancer tends to metastasize to bone marrow
and the lungs. Pancreatic cancer and colon
cancer tend to metastasize to the liver and
thelungs.
The patterns of metastasis have been
explained in terms of two hypotheses.
The ‘seed and soil’ hypothesis states that
a tumour cell will metastasize to a site
where the local microenvironment is
favourable112, just as a seed released by
a plant will only grow if it lands at a site
where the soil is fertile. The ‘mechanical’
hypothesis states that metastasis is likely to
occur at sites based on the pattern of blood
flow108. Both blood flow (the mechanical
hypothesis) and local microenvironment (the
seed and soil hypothesis) are thought to
have complementary roles in influencing the
location of a metastatic site2,108.
Based on the preceding discussion of the
arrest of circulating tumour cells, we can
elaborate on the physics of the location of
metastatic sites. Blood is circulated from most
organs to the heart and then the lungs by the
venous system, and is subsequently returned
to the heart and circulated to the organs by
the arterial system. The organ capillary beds
are characterized by a network of small blood
vessels. If a tumour cell encounters a capillary
of diameter smaller than the size of the cell
(dcell > dvessel) then the probability of
cell trapping by physical occlusion at that
site is very high. For a metastasis to occur,
the tumour cell must still extravasate and
colonize the local tissue. In one study, more
than 50% of metastases could be explained
by the blood flow pattern between the
primary and secondary site111. As cell
trapping, extravasation and colonization
occur in series, we can speculate that
the probability of a metastasis occurring
at a specific site in accordance with the
mechanical hypothesis can be expressed as
P ∝ Pt · Pe,i · Pc,i, where Pt is the probability
of encountering a vessel with diameter less
than the cell diameter, Pe,i is the probability
of extravasation at that site and Pc,i is the
probability of colonization. The probability of
extravasation and colonization is expected to
be dependent on the local microenvironment.
Every collision between a circulating
tumour cell and a blood vessel wall, where
dcell < dvessel, has the potential to result in
adhesion. If the residence time is sufficiently
long, then the tumour cell may adhere to
the blood vessel wall and then extravasate.
The probability that the residence time is
sufficiently long for eventual extravasation
to occur is related to the local shear stress.
A further complexity is that the expression
levels for adhesion proteins are different in
different organs and hence the strength of the
receptor–ligand adhesion may also be organ-
specific113. For the seed and soil hypothesis, we
write the probability of metastasis occurring
at a specific site i as Pi ∝ Pa,i · Pe,i · Pc,i, where
Pa,i is the probability that a collision at site i
leads to adhesion and Pe,i and Pc,i are the same
as defined above. From these considerations
it is evident that the probability of metastasis
occurring in a specific organ in both the
Figure 4 | Capture and arrest of circulating tumour cells. a | A collision between a cell and a
vessel wall may lead to transient and/or persistent (firm) adhesion as a result of ligand–receptor
interactions. Transient adhesion is characterized by weaker bonds involving ligands such as CD44,
carcino embryonic antigen (CEA) or podocalyxin (PODXL) binding with selectin receptors. Persistent
adhesion either follows transient binding or is initiated at very low shear stress and involves interac-
tions between integrins and their receptors, such as intercellular adhesion molecule 1 (ICAM1) and
vascular cell adhesion molecule 1 (VCAM1). For consistency we designate the adhesion molecules
on the surface of endothelial cells as receptors and the interacting molecules on the circulating
tumour cells as ligands. We note that in the literature, integrins participating in receptor–ligand
pairs are usually identified as receptors. b | The association of tumour cells with platelets may
enhance arrest through platelet-mediated capture, a process analogous to nucleation and growth.
The growth process is achieved by a platelet-bridging mechanism, whereby platelets adherent to
an endothelium-bound carcinoma cell serve as a ‘nucleus’ to capture free-flowing cells that subse-
quently attach to the blood vessel wall downstream or next to the already adherent cell. This nuclea-
tion mechanism, which is primarily dependent on P-selectin, results in the formation of growing
clusters of adherent cells.
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mechanical hypothesis and the seed and soil
hypothesis have common elements related to
extravasation and colonization, both of which
are dependent on the local microenvironment.
As described above, it is likely that
there is an optimal range of shear stress,
corresponding to values found in the
venous system, to achieve a sufficiently
long residence time. For example, invitro
adhesion assays reveal that metastatic tumour
cells bind to the vascular endothelium
under venous but not arterial levels of shear
stress87,93,97. Furthermore, high shear stresses
(12dyn cm–2) similar to those encountered in
the arterial circulation have been reported to
result in cell cycle arrest of metastatic tumour
cells, which facilitates their eradication by
the immune system114. By contrast, evidence
suggests that low levels of shear stress, typical
of the venous system, may have opposite
effects on intracellular signalling and
tumour cell function. For example, venous
shear stress has been suggested to induce
an EMT, as shown by the shear-mediated
internalization of E-cadherin in metastatic
oesophageal OC-1 tumour cells115. Moreov er,
exposure of free-flowing OC-1 cells to a shear
rate of 200 s–1 increased their mobility and
invasive capacity invitro115. However, further
studies are needed to establish whether
these observations can be extended beyond
the OC-1 tumour cell line, and whether
fluid shear stress can increase the invasive
potential of tumour cells invivo.
Conclusions
The physical interactions of cancer cells
with the diverse microenvironments
encountered during the metastatic process
have a key role in the spread of cancer.
Mechanical forces modulate cell motility
in the architecturally complex extracellular
matrix during invasion and in the
vascular system during intra-vasation and
extravasation. Shear flow in the vascular
system dictates the trajectory of circulating
tumour cells and has a role in regulating
adhesion at blood vessel walls, a key step in
extravasation. The emerging insight into the
role of physical and mechanical processes
in metastasis should contribute to the
development of new approaches for cancer
diagnosis and treatment. For instance, it is
noteworthy that several drug candidates
show potential when examined invitro but
fail in clinical trials. This failure may stem
at least in part from the use of conventional
invitro systems that fail to replicate the
physiological microenvironment in humans
as well as the lack of cell-phenotypic
measurements. Specifically, the effects of key
microenvironmental physical properties on
cancer and stromal cell responses to drug
candidates have yet to be explored in a
systematic fashion. These physical properties
include mechanical forces, ECM stiffness and
the ECM pore size and tortuosity. Moreover,
current cutting-edge ‘-omic’ measurements
conducted on patient specimens need to be
complemented with state-of-the-art physical
measurements of, for example, cell and tissue
microrheology, cell and nuclear shape and
cell–cell and cell–matrix adhesion (TABLE 1).
Such a holistic approach could drastically
reduce the divergent effects of potential
drug candidates on cell responses in animal
models and in patients, and could help us
to identify the appropriate and efficacious
targets for treatment.
The authors are at the Departments of Materials
Science and Engineering, Chemical and Biomolecular
Engineering and Oncology, the Institute for
Nanobiotechnology, Johns Hopkins Center of Cancer
Nanotechnology Excellence, Johns Hopkins Physical
Sciences in Oncology Center, Johns Hopkins University,
3400 North Charles Street, Baltimore,
Maryland 21218, USA.
e-mails: wirtz@jhu.edu; kk@jhu.edu; searson@jhu.edu
doi:10.1038/nrc3080
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Acknowledgements
The authors gratefully acknowledge support from the
US National Institutes of Health (grants U54CA143868,
U54CA151838 and RO1CA101135).
Competing interests statement
The authors declare no competing financial interests.
FURTHER INFORMATION
Denis Wirtz’s homepage: http://www.jhu.edu/chembe/wirtz
Konstantinos Konstantopoulos’s homepage:
http://web1.johnshopkins.edu/kostaslab
Peter C. Searson’s homepage: http://www.jhu.edu/searson
Johns Hopkins Center of Cancer Nanotechnology
Excellence: http://ccne.inbt.jhu.edu
Johns Hopkins Engineering in Oncology Center:
http://psoc.inbt.jhu.edu
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