Journal of Experimental Botany, Vol. 64, No. 15, pp. 4709–4728, 2013
doi:10.1093/jxb/ert254 Advance Access publication 7 September, 2013
review paper
The cellular mechanics of an invasive lifestyle
Amir Sanati Nezhad1 and Anja Geitmann2,*
1 2 McGill University and Génome Québec Innovation Centre, Biomedical Engineering Department, McGill University, Montreal, Canada
Institut de recherche en biologie végétale, Département de sciences biologiques, Université de Montréal, Montreal, Canada
* To whom correspondence should be addressed. E-mail: [email protected]
Received 8 March 2013; Revised 10 July 2013; Accepted 12 July 2013
Abstract
Invasive behaviour is the hallmark of a variety of cell types of animal, plant, and fungal origin. Here we review the
purpose and mechanism of invasive growth and migration. The focus is on the physical principles governing the process, the source of invasive force, and the cellular mechanism by which the cell penetrates the substrate. The current
experimental methods for measuring invasive force and the modelling approaches for studying invasive behaviour are
explained, and future experimental strategies are proposed.
Key words: Cancer cells, fungal hyphae, invasive growth, migrating cells, neurons, pollen tubes, root hairs, tip growth.
Introduction
Most eukaryotic cells are specialized for particular metabolic or structural functions, and to exert these functions
they occupy precisely defined positions within the organism.
Therefore, the spatial coordinates of cells relative to their
neighbouring cells and to the entire organism are typically
static. However, certain cells have functions that require
movement relative to their surroundings, be it the surrounding tissue or an abiotic matrix. To move against or invade a
matrix requires the ability to invade this substrate mechanically. Cells with invasive or intrusive behaviour thus have the
common challenge to overcome the resistance of a substrate
in order to accomplish their tasks. Invasive cell types exist
in all eukaryotic kingdoms and include root hairs, pollen
tubes, sclerenchyma fibres, laticifers, fungal hyphae, neurons, fibroblasts, and cancer cells. While the biological purpose and the mechanical principles of force exertion differ,
these diverse cell types share the ability to invade a substrate
mechanically—either by cellular growth or by migration. In
the following, we discuss the strategies used for this intrusive
activity and the mechanical challenges that are associated
with this invasive lifestyle. We describe how different cell types
adapt to the mechanical properties of the invaded substrate
and we provide an overview of the experimental techniques
and numerical methods that have been used to assess invasive force quantitatively. Emphasis in this review will be on
the invasive behaviour of walled cells (plants and fungi), but
other cell types will be referred to for comparison.
Purpose of invasive behaviour
The common aspect of invasive behaviour is the need for the
cell to elongate or migrate in a particular direction—often,
but not necessarily, in the direction of a target. However,
despite this mechanistic commonality, the biological purpose of this behaviour is highly diverse and depends on the
cell type.
Structural necessity
The invasive growth activity may not have a purpose per se
but may simply be a necessity to produce the desired cell
shape against the impedance of the surrounding tissue. An
example for this is sclerenchyma fibres in plants—highly elongated cells that serve to stabilize plant tissues against tensile
stress (Snegireva et al., 2010; Gorshkova et al., 2012). This
function relies on two structural and geometrical features:
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4710 | Sanati Nezhad and Geitmann
the cell walls of mature sclerenchyma fibres are reinforced
by significant amounts of cellulose and lignin, and the shape
of the cells extends over large distances parallel to the longitudinal axis of the plant organs thus equipped. Tissues that
typically possess such fibres include the phloem and the secondary xylem of dicotyledonous plants and the leaf vascular bundles of monocotyledonous plants (Lev-Yadun, 2010).
Importantly, since fibre length is directly related to the ability
of plant organs to resist tensile stress, fibre elongation influences the value of commercial plant raw materials extracted
from monocotyledon leaves, such as sisal, or from dicotyledon phloem such as flax, and, importantly, that of wood.
Despite their economic importance, the mechanics governing
the intrusive growth of sclerenchyma fibres is poorly understood, mainly because of the fact that it only occurs within
the depth of other tissues and the process has never been
reproduced in vitro.
For a meristematic cell with a length of 20 μm to attain
lengths of up to several centimetres, cells have to elongate
considerably and the growth process is highly anisotropic,
generating a geometry with an extreme aspect ratio. For reasons explained later in this review, most invasive cells employ
a tip growth mechanism to produce the elongated shape. Tip
growth, or apical growth, is defined as a growth activity in
which the expansion of the cellular envelope (plasma membrane and cell wall, if present) expands mostly or exclusively
at the outermost end(s) of the cell. This spatial confinement
of the expansion process is distinguished from diffuse or
intercalary growth which is characterized by an expansion of
most or the entire surface of the cell (Geitmann and Ortega,
2009). Sclerenchyma fibres initially expand over their entire
length together with the surrounding, typically parenchymatic, tissue (symplastic growth) and subsequently switch to an
intrusive growth phase during which the two ends of the cells
invade the apoplast of adjacent tissues (Fig. 1A) (Esau, 1977;
Snegireva et al., 2010; Gorshkova et al., 2012). The intruding
tips of the fibre cell generally have a smaller diameter than
the initial cell body (Ageeva et al., 2005). It has been postulated that fibre growth occurs in a diffuse manner rather than
by a tip growth mechanism (Ageeva et al., 2005). However,
a diffuse growth mechanism would require the walls of the
expanding fibre to slide against the cell walls of the neighbouring, non-growing parenchyma cells. Because of the
resulting shear forces, energetic considerations suggest that
this scenario is accompanied by mechanical challenges. Only
the quantitative analysis of cell surface expansion patterns
will provide a conclusive answer to the question of whether
intrusive fibre growth is generated by a tip growth mechanism
or whether it follows a diffuse expansion pattern.
Meeting nutritional needs
One of the possible goals of invasive behaviour is the exploration of the environment in the search for sources of water
and nutrients. The hyphae forming a fungal mycelium explore
anything ranging from other living tissues to abiotic material such as rocks in the search for substances that they
require for survival. Hyphae are formed by a diverse group
of microorganisms—mushroom-forming species and their
relatives in the Fungi, and oomycete water moulds in the
Stramenopila. Although not strictly accurate, for simplicity, the present review will use the term ‘fungal hyphae’ for
all of these. Hyphae are tubular cells with a typical diameter between 2 μm and 20 μm that expand at their tip. The
hyphae of a mycelium placed on a two-dimensional surface
will typically grow in the centrifugal direction to ensure the
most efficient exploration of the surroundings (Fig. 1C). In a
mycelium, hyphae advance individually. However, in certain
fungal structures, the hyphae aggregate in a parallel manner
to form a rhizomorph. These rhizomorphs have a diameter of
up to 7 mm and a length of up to 9 m. They have the function
to breach mechanical obstacles and penetrate soil and rotting wood, enabling them to search for new food sources and
transfer nutrients to a developing fruiting body (Shaw and
Kile, 1991; Yafetto et al., 2009) (Fig. 1D).
Similar to the centrifugal expansion of fungal hyphae from
a mycelium, plant root hairs grow radially from the surface
of plant roots. These cylindrical protuberances formed by
the root epidermis cells in the maturation region typically
grow away from the root surface in an orthogonal manner
to explore the surrounding soil optimally. Their final length
is typically 1–3 mm and the diameter varies between 5 μm
and 17 μm. Unlike fungal hyphae whose growth is indeterminate, root hair growth is characterized by distinct phases
and their tip-focused elongation stops once a certain length
is achieved (Bengough et al., 2011). The main purpose of
these hairs is the increase of the root surface that serves to
optimize the uptake of water and minerals, which are then
transported through the vascular cylinder of the root into the
other plant organs. Inorganic ions such as K+ and various
anions are pumped into the root hair by active transport, thus
generating a gradient in water potential that causes water to
be absorbed by osmosis from the soil. In addition, the root
hairs help to anchor the plant body in the ground (Gilroy and
Jones, 2000). Root hairs have been used as an effective model
system to study the principles underlying tip growth mechanism in plants (Galway, 2006) (Fig. 1B).
The increase of the plant root surface is often also achieved
by fungal hyphae living in symbiosis with a plant. These
mycorrhizal structures rely on an exchange of nutrients and
water between the plant and the fungus. Because of the indeterminate growth of the fungal hyphae, the volume of soil
explored and thus indirectly accessible to the plant is significantly greater than that penetrated by the root hairs (Bolan,
1991). In order to establish the symbiosis, the fungal hyphae
need to invade the root tissue. They do this either by invading
only the apoplast of the epidermis layer (ectomycorrhizae) or
by invading the root cortex and forming arbuscular structures
within the cells of the plant (endomycorrhizae) (Fig. 1B).
Delivery
The formation of an elongated cell can serve to deliver a cargo
to a distant location. This is the case in the pollen tube, a cellular protuberance formed by the pollen grain, the male gametophyte in the flowering plants. The sole function of the pollen
Mechanics of invasion | 4711
Fig. 1. Cell types capable of invasive behaviour. (A) Sclerenchyma fibres elongate first by symplastic growth together with the
surrounding parenchyma cells, and subsequently by intrusive growth at both ends of the cell. (B) Root hairs (green) are trichomes
formed from the root epidermis and invade the surrounding soil. Mycorrhizal fungi (brown) live in symbiosis with the host plant. They
invade both the root tissue of the host and the surrounding soil. (C) A fungal mycelium spreads out centrifugally when growing on a
flat surface. (D) A rhizomorph consists of an aggregate of fungal hyphae. The drawing is simplistic as it neglects the more complex
architecture that also comprises horizontally arranged hyphae. (E) Pollen tubes are formed by pollen grains upon contact with the stigma
of a receptive flower pistil. The tubes grow along or enter into the walls of the stigmatic papillae, and grow through the hollow canal or
4712 | Sanati Nezhad and Geitmann
tube is the delivery of the sperm cells from the pollen grain
attached to the stigma of the receptive flower to an ovule nestled deeply within the pistillar tissues. Upon successful delivery, the female gametophyte enveloped in the ovule is fertilized
and the ovule develops into a seed containing an embryo. The
diameter of the pollen tube is typically between 5 μm and
20 μm, and its length is indeterminate. In large flowers, it can
become tens of centimetres long, although the living portion
of the cytoplasm is confined to the tip region of the cell. For
this reason, the pollen tube has been likened to a migrating
cell that leaves a trail of cell wall behind (Mascarenhas, 1993).
In order to find its path to the ovule, the pollen tube has to
invade a series of tissues comprising the pistil of the receptive flower (Elleman et al., 1992; Palanivelu and Preuss, 2000;
Palanivelu and Tsukamoto, 2011) (Fig. 1E). Starting at the
stigmatic tissue on which it lands, it has to penetrate through
the transmitting tissue lining the style eventually to reach the
ovary (Erbar, 2003). Once it reaches the ovary, the pollen tube
has to invade the micropyle, an opening in the teguments
enveloping the ovule, and the nucellus, a tissue layer surrounding the female gametophyte. The final step consists of the penetration of the filiform apparatus of one of the synergids—an
elaborate cell wall structure. Here the tube bursts open at its
apex to release the two sperm cells (Berger et al., 2008). The
growth of the pollen tube thus occurs in contact with the cells
of the sporophyte (the pistillar tissues) and the cells of the
female gametophyte (synergids and egg cell), both of which
emit guidance signals to direct the pollen tube to its target
(Geitmann and Palanivelu, 2007; Palanivelu and Tsukamoto,
2011). Many aspects of pollen tube growth have been investigated to understand the principles of tip growth in plants,
ranging from the control of polarity, calcium-regulated exocytosis, vesicle trafficking, and oscillatory behaviour (Taylor and
Hepler, 1997; Geitmann and Steer, 2006; Kroeger et al., 2008).
Another cell type that might have delivery function in the
plant body are the laticifers. These elongated cells achieve
their length by growing at two or, if branched, more ends
(Wilson et al., 1976). This process is often initiated as early
as during early embryogenesis when most other cells are still
relatively undifferentiated. Similar to sclerenchyma fibres,
laticifers grow by separating the middle lamella between the
surrounding cells. The biological purpose of these cells is not
understood in all situations where they occur. They are typically coenocytic and they often contain substances that are
interpreted to be either waste or storage products, or toxic
agents for defence purposes.
Connecting distant locations within the organism
Invasive growth can be employed to establish direct connections between entities that are separated spatially. This
connectivity principle is the basic underpinning of neural
cells. Their function is to link the different parts of the animal body to the brain to allow for signals to travel both from
and towards the brain. The connections proper between individual neurons or neurons and target cells are made by synapses. Synapses are generally formed at the end of axons, long
extensions of the neural cell (Haydon, 1988). Axon elongation occurs by protrusion of the growth cone composed of
filopodia and lamellipodia (Dent and Gertler, 2003; Loudon
et al., 2006) (Fig. 1F). Lamellipodia are extended structures,
from which filopodia emerge with a finger-like shape. Invasive
activity of the growth cone therefore occurs at two different size scales. Filopodia are only hundreds of nanometres
thick and consist essentially of actin bundles wrapped by the
plasma membrane. The entire lamellipodium on the other
hand has a diameter of several micrometres and is thus of
the same order of magnitude as the width of the axon (Small
et al., 2002). Micrographs of growth cones taken from classic
2D cell culture samples typically show a fan-shaped, 2D morphology of this structure, whereas the in vivo, 3D morphology is more complex and irregularly shaped (Bovolenta and
Mason, 1987). Although axon morphogenesis and anatomy
are very different from those of plant and fungal cells because
they are not surrounded by a cell wall, many parallels can be
drawn between them and tip-growing walled cells (Palanivelu
and Preuss, 2000).
Colonization of new territory
Invasive activity is a necessary prerequisite for cells whose
purpose is the colonization of other tissues—whether it is
a process required during the development of the organism proper, or a symbiotic or pathogenic interaction with a
host organism. Invasive cell migration happens, for example,
during oogenesis in Drosophila melanogaster when somatic
cells that delaminate from the follicular epithelium of an
egg chamber invade the germline cluster (Fulga and Rørth,
2002). Cell migration within the organism can also be triggered upon certain signals generated within the context of
various physiological processes such as inflammation, wound
healing, or immune cell trafficking (Sánchez-Madrid and Del
Pozo, 1999; Luster et al., 2005; Wu et al., 2009; Zhao, 2009).
The malfunction of these migration processes can cause a
variety of diseases. A type of cell migration with particularly
dramatic consequences for the organism is cancer metastasis.
Here, the cancer cells from the primary tumour site invade
surrounding tissue to reach blood or lymph vessels through
which they disseminate to a distant organ into which they
penetrate to initiate the formation of new tumour (Condeelis
et al., 1992; Yamaguchi et al., 2005; Kumar and Weaver, 2009)
(Fig. 1G).
transmitting tissue of the style towards the ovary. Subsequently, they elongate towards the opening of an ovule, guided by the signals of
the female gametophyte. They enter the ovule, invade the filiform apparatus of one of the synergids, and then burst to release the sperm
cells, one of which fuses with the egg cell, the other with the central cell. (F) Neurites produce long axons elongating at their tip by way
of a growth cone that invades surrounding tissues. (G) Cancer metastasis requires tumour cells to penetrate basement membranes to
enter blood or lymph vessels, where they are disseminated to new locations in the body. Here the vessel walls have to be crossed again
to initiate a primary metastasis within the tissue.
Mechanics of invasion | 4713
During the colonization of new territory, pathogenic fungi
typically have to overcome the protective structures built by
the host organism. In order to invade the often extremely
stiff surfaces of plants, hyphae form specialized structures—
appressoria. An appressorium is sphere shaped and secretes
a glue to adhere the structure tightly to the plant surface. It
subsequently develops an infection peg at the contact surface
that penetrates and enters the host tissue (Bechinger et al.,
1999; Bastmeyer et al., 2002). The ability to invade is directly
correlated to the pathogenicity of fungi (Deising et al., 2000).
This is particularly obvious in pathogenic yeast such as
Candida albicans. This yeast can differentiate between multiple cell types, the major forms being yeast, elongated yeast
called pseudohyphae, and highly polarized hyphae. Switching
between these morphotypes provides Candida with the flexibility to optimize its efficiency by either being disseminated
in the blood stream (yeast form) or invading tissues (hyphae).
Consequently, mutants locked in one cell form are less pathogenic (Lo et al., 1997).
Driving force for invasion
Elongation or migration against mechanical impedance
requires the generation of invasive forces. The strategies
employed for this purpose differ significantly between walled
cells and cells devoid of this stiff outer envelope.
Cytoskeletal forces
Cytoskeleton-based force generation is generally associated
with animal cells, but this principle has also been proposed
to underlie the growth mechanism in some walled cell types
such as oomycete hyphae (Gay and Greenwood, 1966) and
chytridiomycete zoospores (Li and Heath, 1994). In oomycetes an implication of the cytoskeleton in amoeboid forward
movement of the hyphal tip was suspected because these cells
are able to elongate under conditions of very low or absent
turgor and the hyphal cytoplasm was observed to contract
during elongation (Heath and Steinberg, 1999).
In cells devoid of a rigid cell wall, a cytoskeleton-mediated
mechanism generates pushing and traction forces that are
used for cellular growth and invasion. The polymerization of
an individual cytoskeletal element generates a pushing force
that can be measured in vitro (Dogterom and Yurke, 1997;
Footer et al., 2007). At the leading edge of migrating cells
(Fig. 2A) or of the neural growth cone (Fig. 2B), an array of
actin filaments continuously polymerizes and thus pushes the
apical plasma membrane forward. In cells that do not possess
actin filaments such as in nematode sperm cells, other skeletal
proteins fulfil this role (Sepsenwol et al., 1989). When actin
filaments are not anchored at their base (or pointed ends),
polymerization at the barbed ends leads to an F-actin flow in
the proximal direction through pushback rather than to force
exertion forward. For polymerization to be translated into a
pushing force against the plasma membrane, actin needs to be
physically anchored to an internal structure or to the outside
of the cell. The latter is accomplished by way of adhesion
complexes that prevent pushback and transmit the resulting
force to the external substrate of the cell, causing traction
(Giannone et al., 2009). This mechanism has been termed the
actin-based motor-clutch system, analogous to the clutch of
a car engine (Mitchison and Cramer, 1996; Bard et al., 2008;
Féréol et al., 2011), and it operates in the neuronal growth
cone (Lin and Forscher, 1995; Kamiguchi, 2003; Suter and
Forscher, 2000). Achieving a pushing force therefore requires
a coordinated effort between the individual structural elements of the cell. Microtubules contribute to this by providing structural support for the axon proper. Microtubules
also protrude into the growth cone, a situation that is termed
engorgement (Fig. 2B). The extension of neurites can thus
be described as a three-step process that involves the protrusion of the leading edge, followed by the engorgement of the
growth cone by microtubules, and the consolidation of a new
segment of axon shaft behind the advancing growth cone
(Dent and Gertler, 2003). In migrating animal cells, the process is similar, with the difference that instead of consolidation, the rear end of the cell is retracted and thus the entire cell
volume moves forward (Schmidt et al., 1993; Lauffenburger
and Horwitz, 1996; Sheetz et al., 1998). This illustrates that
both protrusive and contractile forces are employed in concert
to move the cell body forward (Lauffenburger and Horwitz,
1996; Friedl and Brocker, 2000; Friedl and Wolf, 2003) and
both warrant quantification.
Hydrostatic pressure
The cytoskeleton in plant and fungal cells plays an important
role in the cellular growth process, but, rather than producing
any relevant forces, the cytoskeletal array in most walled cells
is limited to executing spatio-temporal control of cell wall
assembly (Smith and Oppenheimer, 2005). In tip-growing cells
this is likely to be mediated by the targeted delivery of soft
cell wall material to the growing apex (Geitmann and Emons,
2000; Kroeger et al., 2009; Bou Daher and Geitmann, 2011).
F-actin- and integrin-containing focal adhesions similar to
those in animal cells also exist in walled cells (Kaminskyj and
Heath, 1995; Bachewich and Heath, 1998). However, rather
than producing contractile forces, they are thought to ensure
adhesion of the plasma membrane to the cell wall (Corrêa
et al., 1996). Pushing forces necessary for growth against
mechanical impedance are generated in a manner that is very
different from the mechanical principles governing animal
cells. Because of the presence of the surrounding wall, plant
and fungal cells are able to establish high internal hydrostatic
pressures, typically in the range of 0.1–1 MPa, which corresponds to the pressure in a car or bicycle tyre. This hydrostatic
pressure, or turgor, is created by osmosis, the influx of water
driven by a concentration difference of osmotically active
substances (osmolytes) between the inside of the cell and the
surrounding medium or substrate. Turgor-generated forces
therefore operate on the principle of a hydroskeleton that
maintains cell and organ shape in herbaceous plant tissues
and fungi. In non-growing cells that are surrounded by a nonyielding wall, the internal turgor does not act on the outside
substrate. Harnessing the hydrostatic pressure to generate a
penetrative force therefore requires the wall to be compliant
4714 | Sanati Nezhad and Geitmann
Fig. 2. Force generation in invading cells. (A) Cross-sectional view of a migrating cell positioned on a flat surface. Migrating animal
cells produce a protrusion force at the leading edge based on actin polymerization and contractile forces. This necessitates contact
with a substrate surface through focal adhesions. (B) Top view of a growth cone positioned on a flat surface. The growth cone consists
of lamellipodia containing an actin network and narrow filopodia containing bundles of actin. The shape of a growth cone is extremely
dynamic and continuously probes the environment. (C) Tip-growing plant and fungal cell. The actin cytoskeleton is responsible for
transporting cell wall material to the apical cell wall (the configuration of the actin array shown here is typical for angiosperm pollen
tubes). The pushing force is generated by the turgor. Only where the cell wall is compliant is this pressure felt as effective force outside
of the cell (green arrows).
Mechanics of invasion | 4715
and yield to the pressure (Money, 1995). In tip-growing cells
such as fungal hyphae, root hairs, and pollen tubes, only the
apical cell wall is compliant (Fayant et al., 2010) and hence
here the turgor, or rather a fraction of it, is exerted against
the substrate (Fig. 2C).
The capacity of fungal and plant cells to establish turgor
depends on the mechanical properties of the cell wall and the
ability of the cell to produce osmotically active substances.
In the fungal appressorium, the cell wall is multilayered and
contains melanin, a substance that regulates the cell wall’s
permeability to water and solutes and also rigidifies the
wall by cross-linking (Howard and Ferrari, 1989; Mendgen
and Deising, 1993). Melanized structures are able to establish enormous turgor, and the reduction in melanin production due to mutation or pharmacological inhibition reduces
the pathogenicity of a fungal species (Kubo and Furusawa,
1991). In the rice blast fungus Magnaporthe grisea, melanization enables appressoria to increase glycerol concentration
as an internal osmolyte and to build turgor up to 8 MPa (de
Jong et al., 1997; Money, 1998) resulting in a driving force
that is sufficient to punch holes in the cuticle of a host plant
(Deising et al., 2000). Pressures in conventional fungal hyphae
are lower than those in appressoria, with typical values being
<1 MPa. The rhizomorphs of Armillaria were found to have
a turgor of 0.8 MPa, and spectroscopic analysis showed that
it was generated by the accumulation of erythritol, mannitol, and KCl (Yafetto et al., 2009). Forces exerted by growing
rhizomorph tips range from 1 mN to 6 mN, corresponding
to pressures of 40–300 kPa, comparable with the pressure
exerted by individual hyphae.
Although a hydrostatic pressure-based mechanism is
generally accepted to provide the explanation for invasive
growth in walled cells (Howard and Ferrari, 1989; Peterson
and Farquhar, 1996; Bechinger et al., 1999; Deising et al.,
2000; Lew, 2011), and calculations have demonstrated that
cytoskeleton-based forces would be trivial compared with
the turgor (Money, 2007), the role of the cytoskeleton for
invasion may be more complex than just the delivery of cell
wall components. In pollen tubes, low concentrations of
actin-depolymerizing drugs compromise the tubes’ ability to
invade an agarose-stiffened substrate (Gossot and Geitmann,
2007). The fungal tips of the oomycetes Achlya bisexualis
and Phytophthora cinnamomi display an F-actin-depleted
zone in most of the invasive but only in a few of the noninvasive hyphae (Walker et al., 2006; Suei and Garrill, 2008).
Moreover, the size of the apical actin-depleted zone is dose
dependent and becomes larger with an increasingly stiffened
agarose medium (Suei and Garrill, 2008). Interestingly, the
hyphae of some oomycetes are unable to regulate or control
turgor (Lew et al., 2004; Lew, 2011) and they can grow at
very low turgor (Money and Harold, 1993). Together with
the fact that the disruption of the F-actin cap in oomycete
hyphae promotes cell bursting (Jackson and Heath, 1990),
this has led to the hypothesis that actin is directly involved
in controlling tip yielding and thus invasive growth. To carry
out this function, F-actin would be required to retain cell
growth against the pressure of the turgor by linking to the
cell wall. Molecules with epitopes similar to those of integrin
do indeed localize closely with F-actin in oomycetes, making this a plausible concept (Kaminskyj and Heath, 1995;
Chitcholtan and Garrill, 2005; Suei and Garrill, 2008).
Physics of invasion
Unless liquefied by enzymatic or other means, the substrate
through which the invading cell has to penetrate poses a steric
hindrance. While softer substrates may not present mechanical resistance that limits the invasive activity, harder substrates do. This can be deduced from experiments in which a
stiff substrate or obstacle either stalls the growing cell (Wright
et al., 2007; Sanati Nezhad et al., 2013a), redirects its growth
direction (Bibikova et al., 1997; Gossot and Geitmann, 2007),
or causes it to split into multiple branches (Held et al., 2011).
Depending on the microstructure of the substrate, different
types of mechanical resistance and forces are likely to oppose
the advancement of the invading cell: resistance against fracture formation, resistance against compression or displacement, and friction. Depending on the cell type and the type of
invaded substrate, establishing the magnitude of mechanical
impedance therefore requires information about the geometry and dimensions of both the invading cell and the material
forming the substrate. This may involve physical principles
such as the elasticity of thin shells, plasticity, viscosity, viscoelasticity, visco-plasticity, adhesion theory, hardness of materials, and fracture mechanics.
Fracture mechanics
For an object to invade a substrate it must displace the
material that is present at this location. Depending on the
mechanical properties of the substrate, this invasion causes
a fracture into which the invading object advances (Fig. 3A).
In polycarbonate materials, fracture formation induced by
deep penetration of a stylus reduces the force required for
penetration (Wright et al., 1992). The behaviour of relatively
soft, biological materials in terms of penetration and fracture formation is only poorly understood (Stevenson and Ab
Malek, 1994; Shergold and Fleck, 2004). The typically inhomogenous structure of substrates penetrated by invasive cells
makes this even more complicated. If the invaded substrate
is a living tissue, invasion typically occurs by separating two
neighbouring cells from each other. Therefore, the adhesion
forces between these neighbours determine the mechanical
impedance to this process. In animal tissues, cell–cell adhesion is ensured by molecules such as integrins, cadherins, and
selectins, whereas the cells in a plant tissue are glued together
by the middle lamella, a pectinaceous material. The role
of the middle lamella as a limiting factor for invasion was
illustrated, for example, by the finding that in aspen plants
with altered expression of pectin methyl esterase the invasive
growth of fibres was affected. High pectin methyl esterase
activity was found to inhibit, while low activity stimulated
fibre elongation. This can be explained by a stiffening of the
middle lamella in the invaded tissues caused by increased calcium gelation of pectins resulting from their de-esterification
by the enzyme (Siedlecka et al., 2008).
4716 | Sanati Nezhad and Geitmann
Fig. 3. Forces generated during invasive activity. (A) Forces generated by a tip-growing, walled cell. (B) Effect of diameter modulation
on the effective invasive force and pressure in a walled cell (at constant turgor) compared with a solid stylus (at constant load applied
at the base of the shank). Ae, interaction surface with the invaded substrate; P, constant hydrostatic pressure in the walled cell (turgor);
Fe, effective invasive force; F, constant load applied on the solid stylus; Pe, effective invasive pressure at the interaction surface with the
invaded substrate.
Mechanical properties of the invaded substrate
Deep penetration of a cylindrical object into a substrate
requires the radial expansion of the substrate at the tip of the
penetrating object. Two material properties that help describe
the behaviour of a penetrated substrate are the yield strain
(hardness) and the fracture resistance (toughness) of material
(Fig. 3). Hardness is defined as the resistance of a material to
the localized deformation that would be required to achieve the
radial dilation or cavity formation. Depending on the nature
of the material, this deformation can be plastic (irreversible)
or elastic (reversible). Toughness, on the other hand, is the
resistance of the material to fracture formation. It is determined by the adhesion or cohesion between the molecules
forming the substrate. Fracture formation can be either brittle—that is, the material is not deformed significantly before a
crack appears (like glass)—or ductile—when plastic deformation precedes crack formation (like clay). Fracture formation
is not limited to hard material, as can easily be demonstrated
with an agar gel that forms cracks while being a relatively soft
material. A viscous material, on the other hand, is unlikely to
form cracks and will rather flow around the invading object.
The independence of the two properties hardness and toughness can be illustrated by examining the behaviour of living
tissues that are subject to penetration by invasive cells. The
mucous membranes in animals are relatively soft while being
tough due to the presence of cell–cell connections. Once these
connections are severed (and thus a ‘crack’ between cells is
formed), a pathogenic fungus easily deforms the tissue to generate the cavity for the hypha. The cells of a plant tissue on the
other hand are turgid and exert hydrostatic pressure to resist
cavity formation even once a crack between the cells is formed.
To invade a plant tissue, an advancing pollen tube or fungal
hyphae will have to exert a dilating pressure that is higher than
that posed by the invaded tissue.
Given that the amount of substrate material that needs to
be compressed or displaced is directly related to the size of the
cross-section of the invading cell, a smaller diameter would
be expected to facilitate invasion by reducing the amount of
dilation that has to be achieved. It is important to emphasize in this context that a walled cell under pressure operates
differently from a penetrating solid stylus. The locally acting invasive pressure of a solid object such as a needle can
be increased by reducing the diameter of the stylus while
maintaining the applied load (force) constant. Consequently,
sharpening of a needle tip focuses the load applied onto the
shank onto a smaller surface at the invading tip. The locally
acting invasive pressure of a pressurized cell on the other hand
Mechanics of invasion | 4717
is constant (at constant turgor) and consequently the overall
invasive force is reduced in smaller tubes (Fig. 3B). While cell
size has in fact been related to pathogenicity in a variety of
fungi (Wang and Lin, 2012), many other factors contribute
to the determination of optimal cell size. For example, the
yeast Cryptococcus significantly increases its cell size during later stages of infection to evade phagocytosis and better tolerate oxidative and nitrosative stresses (Crabtree et al.,
2012). The size of pollen tubes varies significantly between
species. Comparison of a few species leads to the speculation that smaller tube diameters (5–12 μm) occur in species
in which the tube has to penetrate a solid transmitting tissue
(e.g. Arabidopsis or Nicotiana), whereas larger tube diameters
(12–20 μm) dominate in species were tubes grow through a
hollow, mucus-filled canal that might pose less of a mechanical challenge (Lilium and Camellia). Whether the correlation
holds over a wider range of species remains to be investigated. The biological function of the pollen tube certainly
poses a minimum requirement for the size of the tube, since it
must allow the transport and delivery of the male germ unit
comprising the vegetative nucleus and the two sperm cells.
Extremely narrow tube diameters such as those encountered
in certain fungal hyphae, although advantageous in terms of
invasive behaviour, might therefore be prohibitive in pollen
tubes. This has been demonstrated in vitro by blocking the
forward movement of the male germ unit by a mechanical
constriction (Sanati Nezhad et al., 2013a).
Friction and shear at the interaction surface
Friction is an interaction between two surfaces that prevents
or limits their relative tangential movement. The presence of
friction causes shear forces in the two objects that are moved
against each other. When a solid needle or punch is forced into
a substrate, the entire surface of the invading object experiences friction and hence shear forces against the invaded substrate, thus representing a source of energy loss (Wright et al.,
1992). Friction over the entire surface would, for example, be
experienced by the stylet of an aphid piercing into plant tissue in its search for the phloem. Tip-growing cells minimize
this effect by reducing the surface potentially exposed to friction. In tip-growing cells, only the hemisphere-shaped apical region of the cell moves forward by expansion, whereas
the cellular envelope of the distal, cylindrical region remains
stationary relative to the surrounding substrate (Fig. 3). This
applies to both neurites (Lamoureux et al., 2009) and tipgrowing plant and fungal cells (Bernal et al., 2007; Fayant
et al., 2010; Rojas et al., 2011). Interestingly, it was shown
that the maximum of cell wall assembly and expansion does
not seem to occur at the extreme apex of tip-growing cells,
but in an annular region surrounding the apical pole of pollen tubes (Geitmann and Dumais, 2009; Zonia and Munnik,
2009), root hairs (Dumais et al., 2004), and the rhizomorphs
formed from fungal hyphae (Yafetto et al., 2009) (Fig. 3).
This raises a question about the mechanism of the process
and whether an annulus-shaped friction zone may perhaps
ensure that the pole of the cell is less exposed to potentially
damaging friction forces.
While friction in the rear end of migrating animal cells is
a prerequisite for the generation of traction forces, the front
ends of these cells are probably exposed to friction that might
limit the invasive activity (Fig. 3). However, in classical 2D
cell culture set-ups, these forces are negligible and the question has not been addressed in detail in 3D experimental
devices or in vivo. Due to the very small size of filopodia (a
diameter of a few hundred nanometres) friction is likely to be
extremely small and minimized by local exocytosis of phospholipids to the plasma membrane.
Pushback
The exertion of an invasive force requires the cell body to be
fixed in space; otherwise the pushback will cause the rear end
of the cell to move away from the obstacle rather than the
front end advancing into the substrate. This effect can easily be observed in vitro when pollen tubes growing in a liquid environment are presented with a mechanical obstacle
(Agudelo et al., 2013). To exert invasive forces, migrating animal cells, therefore, build connections to their neighbours and
then exert traction forces to push themselves forward relative
to these neighbouring cells (Fournier et al., 2010; Koch et al.,
2012).
Plant cells do not form focal adhesions in the same way
as animal cells. Therefore, they also rarely adhere to a dish
used for in vitro cell culture. In the TipChip, a microfluidic
platform conceived to study tip-growing cells, pushback
is therefore prevented by building a kink into the microchannel through which the tube grows (Agudelo et al.,
2013). In vivo, plant and fungal cells rely on glue-like substances that allow the cells to adhere to their neighbours.
Once a walled, tip-growing cell such as a pollen tube or a
fungal hypha has invaded the tissue, the distal portions of
the cell wall in contact with the invaded substrate generate sufficient friction force to prevent pushback. Among
the molecules that have been suggested to be involved in
the adhesion of pollen tubes to the transmitting tissue
are arabinogalactan proteins (Cheung and Wu, 1999),
pectic polysaccharides, and SCA (stigma/stylar cysteinerich adhesin) (Lord, 2000). The critical phase, therefore,
is the first step of the invasive process, when the pollen
grain or the fungal spore is at the surface of the substrate
and needs to establish the first entry. In the Brassicaceae,
pollen grains attach to the papillae of the stigma forming an adhesion foot, and subsequently emit a tube that
elongates at the papilla surface (Chapman and Goring,
2010). Once the tube reaches the base of the papilla, it
invades the stigmatic tissue (Kandasamy et al., 1994).
The surface along which the tube adheres to the papillae
is apparently sufficient to provide adhesion and friction
forces to enable the apex to exert an invasive force. The
appressoria formed by pathogenic fungi secrete glue-like
substances that ensure tight adherence to the host tissue
surface (Braun and Howard, 1994). Mechanical modelling
has been used to predict the strength of the adhesion of
appressorium anchored to the rice leaf surface (Goriely
and Tabor, 2006).
4718 | Sanati Nezhad and Geitmann
Supplemental tools for invasion
Brute force is not the only strategy used by invading cells to
pave their way. This is illustrated by experiments that compare the mechanical properties of the invaded substrate with
the measured invasive force of fungal hyphae and find that
the mechanical force is not sufficient to overcome the hardness of the tissue (Bastmeyer et al., 2002). Hence invasion
will only occur if
Fe > Fs (kt , ke , s )
(1)
with
Fe = Fd × kc
(2)
where Fe is the effective invasive force exerted by the invading cell, Fs is the resistance produced by the substrate which
depends on kt, the factor defining the degree of cohesion
or adhesion between the elements (cells, soil particles) of
the invaded substrate (tissue, soil, agarose), ke, a parameter
related to the intrinsic hardness of substrate, and, s, a factor
indicating the surface interaction (friction) between substrate
and invading cell. Fd is the potential driving force (in plant
and fungal cells Fd is a result of turgor; in animal cells Fd is
the sum of the polymerization and traction-based propulsion
forces generated by the cytoskeleton). kc is the factor defining
how compliance of the cell wall or the plasma membrane of
the invading cell limits the exertion of Fd to the outside of
the cell with 0<kc<1. This relationship indicates the following
possible strategies to reduce Fs.
Lysis of the substrate
An efficient way to soften the living tissue posing mechanical impedance to invasion is the digestion by enzymatic or
other biochemical means. Cancer cells (Mason and Joyce,
2011), neurons (Seeds et al., 1997), fungal hyphae (Mendgen
et al., 1996; Money, 2007), laticifers (Wilson et al., 1976),
and pollen tubes (Hiscock et al., 1994 Greenberg, 1996) are
known to rely on this mechanism. They produce a series of
enzymes and proteins that help to reduce kt and/or ke by
breaking down the molecules responsible for cell adhesion in
the invaded tissue or by degenerating the tissue in its entirety.
The extracellular matrix through which migrating and growing animal cells have to move consists of structural proteins
and thus the enzymatic tools required for animal tissue invasion are typically proteolytic enzymes (Seeds et al., 1997). An
example is the membrane-type-1 matrix metalloproteinase
(Wolf et al., 2007) whose pharmacological inhibition prevents
tumour cells from blazing their trail, instead forcing them to
squeeze significantly when moving through the collagen fibre
network. To do so, the cells display dramatic changes in cell
shape and nuclear deformations (Kumar and Weaver, 2009).
Evidence for the importance of enzymatic lysis for fungal
infection was provided based on enzyme-deficient mutants
which typically display lowered pathogenicity (Rogers et al.,
1994; Tonukari et al., 2000). Lytic enzymes such as cutinase
seem to be the primary mechanism particularly in those
pathogenic fungi that do not form specialized infection structures such as appressoria (Mendgen et al., 1996; Bastmeyer
et al., 2002). Pollen tubes also produce cutinases (Hiscock
et al., 1994), a requirement that may be particularly relevant
in species whose stigmatic papillae are covered by a cuticle.
Pollination was found to affect the structure of the stigmatic
papillae visibly in Arabidopsis and Brassica. In these species,
the pollen tube grows within the wall of the papilla towards
the transmitting tissue (Elleman et al., 1992). Among the
other proteins that have been invoked to be responsible for
the facilitation of pollen tube penetration, some are produced
by the pollen tube and secreted to act on the pistillar apoplast; others are produced by the pistil itself, their expression and/or release being triggered by pollination. These
include the expansins (Cosgrove et al., 1997; Cosgrove, 2000;
Pezzotti et al., 2002), polygalacturonase (Dearnaley and
Daggard, 2001), glucanase (Kotake et al., 2000; Doblin et al.,
2001), endoxylanase (Bih et al., 1999), pectinase (Konar and
Stanley, 1969), and pectin esterases (Mu et al., 1994; Micheli,
2001; Jiang et al., 2005). A very elegant way to soften a biotic
substrate is to trigger it to undergo programmed cell death.
In certain plant species, the transmitting tissue in the path
ahead of the pollen tube is triggered into an autodigestion
mechanism that, albeit not leading to complete liquefaction,
certainly reduces the turgor in the cells forming the path of
the pollen tubes and may also provide additional nutrients
to the advancing pollen tube (Herrero and Dickinson, 1979;
Cheung, 1995; Wang et al., 1996).
Lubrication
Friction forces can be significantly reduced if the surfaces that
slide against each other are lubricated. The breakdown products
of many of the enzymatic activities listed above may have the
side effect of lubricating the interface between the invading cell
and the substrate. However, the distinction between the effect
of enzymatic activities on ke or s is difficult to make experimentally, and further research is warranted to assess this biological
relevance and the biochemical basis of this effect. Analysis of
mutants that show unaffected pollen tube growth in vitro but
reduced performance in vivo or in an in vitro assay that exposes
them to friction could be informative in that regard.
Lubrication would seem particularly important if the
invading cell does not grow by tip growth but in a diffuse or
intercalary manner, as has been suggested for sclerenchyma
fibres (Ageeva et al., 2005). A minimal prerequisite for this
mode of elongation would be the absence or breakage of
plasmodesmata (cell–cell links) between the growing fibre
and surrounding parenchymatic cells. Moreover, it would
help if the contact surface (Lev-Yadun, 2010), namely the.
middle lamella, had lubricating properties that allowed the
two cell walls to slide against each other.
Adaptation of cell shape
While invading plant and fungal cells generally maintain their
overall cylindrical shape, the strategy of invading animal cells
Mechanics of invasion | 4719
to overcome obstacles is often a repeated change in cell shape
(Friedl and Wolf, 2003). This strategy is called amoeboid
migration and is typical for leucocytes and some types of
tumour (Farina et al., 1989; Friedl et al., 2001). It can be compared with a ‘chimneying’ mechanism in which propulsion is
generated by pushing-off of the surrounding surfaces. The
high flexibility of wall-less cells thus allows them to invade
extremely small spaces by forming narrow protuberances.
Amoeboid migration does not rely on the formation of focal
adhesions or on proteolytic activity but aims at circumnavigating, rather than degrading, the physical barriers.
The overall cell shape is much less flexible in walled cells,
although moderate changes in diameter or shape of the
usually circular cross-section of tip-growing cells has been
observed in an in vitro assay that challenges growing pollen
tubes to invade slit-shaped gaps (Sanati Nezhad et al., 2013a).
On the other hand, obstacle avoidance is frequently encountered in tip-growing walled cells. While these cells typically
maintain their geometrically simple shape characterized by
axial symmetry and a strictly convex profile, they are able to
change their growth direction and thus avoid obstacles and
choose the path of least resistance in a heterogeneous substrate (Bibikova et al., 2002; Gossot and Geitmann, 2007;
Wright et al., 2007). A heterogeneous substrate can thus represent a mechanical guidance cue to direct invasive growth
towards a target simply by reducing the degree of freedom
with which the cell is able to move. This seems to be the case
in pollen tubes growing through the transmitting tract of a
receptive flower. Because of the elongated shape of the cells
comprising the transmitting tissue, the geometry of the network of mucus-filled intracellular spaces has a bias in the longitudinal direction (Lennon et al., 1998; Lush et al., 2000).
This geometry is likely to favour the tube growth in one direction—on the fastest way to the ovary.
The quantitative comparison between Fe and Fs in Equation
(1) is an important approach in the investigation of invasive
growth, since the difference between the two reveals the need
for strategies other than brute force that are employed for
invasive activities (kt, ke, s). The comparison of Fe and Fd, on
the other hand, reveals how the cell modulates its own properties to control the invasive activity. All three forces thus
warrant experimental quantification, which poses various
degrees of technical difficulty.
et al., 2007). Even for this seemingly simple concept, certain assumptions need to be made (or ideally experimentally
determined), for example the degree of bundling between
actin filaments since this critically influences buckling behaviour (Mogilner and Rubinstein, 2005).
The pushing action in migrating cells relies on the simultaneous generation of myosin-mediated traction forces that
are transferred to the outside through integrin–extracellular
matrix linkages. In artificial 2D matrices, the traction force
has been measured using high-density arrays of elastomeric
micro-pillars as force sensors. Based on the bending of the
pillars and taking into account their mechanical properties,
the traction force was quantified (Du Roure et al., 2005).
Another approach was to correlate the displacement of beads
embedded within the elastomer with the deformations generated by cells (Dembo et al., 1996). The situation is more
complex for cells growing in a 3D substrate, although bead
displacement is useful here as well (Legant et al., 2010). The
displacement of collagen fibrils and the motility of focal
adhesion proteins were also used as indicative of the traction
force (Petroll and Ma, 2003; Fraley et al., 2010). The strain
energy concept was used to compare traction forces in different cancer cell types with different degrees of invasive behaviour (Koch et al., 2012).
The role of turgor as a driving force for plant and fungal
cells is easily illustrated by exposure of these cells to altered
osmotic conditions. The drop of cellular turgor in appressoria resulting from osmotic stress prevents the penetration of
infection hyphae into the plant surface (Howard et al., 1991).
The value of 8 MPa for the turgor in the fungal appressoria
observed by these authors was determined by osmotically collapsing the appressorium and deducing the pressure from the
osmotic pressure of the solution required to achieve this collapse. This is one of the classical methods to determine turgor,
but it does not allow monitoring turgor over time (Geitmann,
2006). A dynamic albeit invasive method to determine hydrostatic pressure in cells is the pressure probe, which is based on
the insertion of a micropipette into the cellular lumen. The
needle pressure required to prevent the cytosol from entering the micropipette corresponds to the intracellular turgor.
This technique has been used to determine a pressure of
0.1–0.4 MPa for lily pollen tubes (Benkert et al., 1997), 0.4–
0.5 MPa for fungal hyphae (Lew et al., 2004), and 0.3–1 MPa
for root hairs (Lew, 1996). Semi-quantitative monitoring of
pollen tube turgor has been done using a compression technique that allows for comparison over time, but requires complex modelling for the extraction of absolute values (Zerzour
et al., 2009; Vogler et al., 2013).
Quantification of driving force Fd
Quantification of effective force Fe
Depending on the cell type, Fd is of very diverse nature. In
the lamelliapodia and filopodia of migrating animal cells, the
polymerization activities of the cytoskeletal array pushing
the apical plasma membrane can be estimated by establishing
the density and total number of actin filaments at the leading edge or within a filopodium, and multiplying this number
by the forces measured in vitro for single filaments (Footer
Quantification of the effective force Fe requires challenging
the invading cell with an obstacle of calibrated mechanical
properties (Fig. 4). To obtain values that are physiologically
relevant, this method has to fulfil two criteria: (i) the measuring tool proper should not significantly alter the growth
behaviour of the cell; and (ii) the force exerted by the invading cell should be in the dynamic range of the measuring tool.
Experimental quantification of
invasive force
4720 | Sanati Nezhad and Geitmann
Fig. 4. Experimental strategies to measure the effective force Fe. (A) Substrates with calibrated stiffness (e.g. agarose). (B) A bead held
using an optical trap is placed in front of an advancing cell. (C) Fungal appressorium attached to a waveguide. (D) Cantilever placed
perpendicularly to the growth direction of the elongating cell. (E) A narrow, wedge-shaped opening made from material with calibrated
elasticity (e.g. PDMS).
This second point is crucial as quantitative values for Fe cannot be obtained using either a measuring tool whose stiffness
is so high that the exertion of Fe on the tool is below its detection limit, or so low that the invading cell is not challenged by
its mechanical properties. This can be illustrated by the most
low-tech approach to measurement—the exposure of tipgrowing cells to agar-stiffened media with calibrated properties (Fig. 4A). While these were found to be useful to test the
dependence of the invasive capacity of the fungal hyphae of
the pathogen Wangiella dermatitidis on cell wall mechanical
properties (Brush and Money, 1999; Walker et al., 2006; Suei
and Garrill, 2008), even the hardest agar (8%, w/v) would not
provide sufficient resistance to the invasive force of appressoria since a pressure of 0.1 MPa is sufficient to penetrate this
substrate.
Similar problems arise with techniques based on optical trap
technology (Fig. 4B). The optical trap has been used successfully to assess the pushing force exerted by neurite filopodia
and lamellipodia by placing beads in front of the advancing
leading edge (Cojoc et al., 2007). The authors found that a
single filopodium exerts forces up to 3 pN, whereas lamellipodia exert forces of 20 pN or more. Pharmacological assays
revealed that in these cells no force can be produced in the
absence of actin polymerization and that development of
forces larger than 3 pN requires microtubule polymerization.
While the optical trap is thus adequate for force measurements in the range of those exerted by animal cells and those
produced by the hyphae of Neurospora crassa (Wright et al.,
2005, 2007), it would be inappropriate for most plant and
fungal cells as the maximum holding force of this tool is only
in the hundreds of piconewtons. Furthermore, the light used
for trapping a bead was found to interfere with the functioning of the Spitzenkörper in the hyphae of N. crassa (Wright
et al., 2005), thus raising concerns about the generation of
unspecific artefacts.
To measure the effective invasive force of walled cells, these
have been presented with elastic barriers of various materials
and in various orientations (Fig. 4). The force of the infection hypha formed from a fungal appressorium has been
measured using gold foil (Miyoshi, 1895), Mylar membranes
of various stiffness (Howard et al., 1991), and a waveguide
(Bechinger et al., 1999) (Fig. 4C). The waveguide approach is
particularly elegant, since the deformation resulting from the
formation of the infection hypha can be quantified based on
the change in the light propagated by total internal reflection.
Using the elastic constants of the waveguide, the local force
inducing the deformation was determined to be 8–25 μN
for the plant pathogenic fungus Colletotrichum graminicola
(Bechinger et al., 1999). Given that the force is applied to an
average diameter of 2 μm of the surface, this corresponds to
a pressure of ~5 MPa.
Conventional hyphae and other tip-growing cells cannot be
tested using the waveguide technique since this requires tight
adherence of the body of the cell to the surface of the waveguide. Instead, a micro-strain gauge has been used for this
purpose (Johns et al., 1999; MacDonald et al., 2002; Money
et al., 2004). To immobilize the basal part of the hyphae, these
were grown within agarose-stiffened media and only their tips
entered a volume of liquid medium where the strain gauge was
positioned perpendicularly to the growth direction (Fig. 4D).
Mechanics of invasion | 4721
The advancing hyphae cause the deflection of a silicon beam
with an electrical-resistive element, which in turn changes the
electrical resistance depending on the applied growth force.
Fe was found to be mainly dependent on the diameter of the
hyphae, which varied between 10 μm and 110 μm (Johns
et al., 1999; Bastmeyer et al., 2002). The results suggest that
only ~10–50% of the Fd is available as Fe, whereas the rest
is absorbed by the cell wall (Bastmeyer et al., 2002). Similar
results were obtained for rhizomorphs (Yafetto et al., 2009).
The disadvantage of the strain gauge consists of the fact that
it risks underestimating Fe because of a cellular shape change
upon orthogonal contact of the tip-growing cell with the flat
surface of the strain gauge (Money, 2007). Pollen tubes, for
example, easily reorient their growth direction in response to
a mechanical trigger (Gossot and Geitmann, 2007), making
the strain gauge approach difficult to use reliably. A different approach was therefore developed for these cells. Rather
than a perpendicularly placed object, the cells were presented
with wedge-shaped, narrow openings constructed using Labon-Chip technology (Sanati Nezhad et al., 2013a) (Fig. 4E).
The wedge shape of the microscopic gap in the polydimethylsiloxane (PDMS) material ensured that pollen tubes did not
avoid the obstacle. Based on the known material properties of
the elastic material PDMS, the dilating force exerted normal
to the gap wall was calculated using finite element modelling.
From this, the pressure could be deduced and was found with
0.15 MPa to be slightly below the typical turgor of pollen
tubes (Benkert et al., 1997). Whether or not this means that
pollen tubes operate with a much lower safety margin than
fungal hyphae remains to be proven, but this concept would
be consistent with the fact that these cells must eventually
burst to accomplish their biological function.
During metastasis, tumour cells penetrate the walls of lymphatic or blood vessels twice, first in order to enter the vessel
from the location of the primary tumour, then to enter the
tissue of the target organ. The basement membranes which
separate epithelial tissues from the underlying stroma are,
from a mechanical point of view, the most challenging obstacles, and various in vitro assays have used this material to test
the invasiveness of tumour cells. Among the tissues used for
this purpose are the chorioallantoic membrane of chicken
embryos (Hart and Fidler, 1978), amniotic membrane from
human placenta (Liotta et al., 1980), bovine lens capsule
(Starkey et al., 1984), and reconstituted basement membrane
matrigel (Albini et al., 1987). The tests are set up so that the
tumour cells are placed on one side of a porous filter coated
with the tissue or matrigel and a chemotactic signal is placed
on the other side. While this represents an excellent comparative assay, this approach does not provide quantitative values
for the physical force exerted by the cells.
Quantification of force Fs necessary to invade a
substrate
Assessment of the mechanical resistance to invasion presented
by the substrate requires the use of a penetrometer or similar
tool that is pressed onto the surface of the substrate using a
known load. Classical hardness tests include the Brinell test
that uses a spherical tip, and the Vicker test that employs a
pyramidal tip. The ‘hardness’ of the material is then calculated as the ratio of the load to the indented surface area. For
a homogenous and plastic material, the relationship between
the loading and shear stresses can be determined to assess the
yield stress, the stress at which a material begins to deform
plastically. However, the notion of yield stress in the context
of a penetrometer test was developed for ductile materials
such as metals that have a regular crystal lattice structure. The
bulk properties measured using this technique therefore do
not necessarily correspond quantitatively to the resistance the
material displays against a penetrating cell. This was evident
when Mylar sheets with yield strengths ranging from 50 MPa
to 80 MPa (assessed with the Vicker test) were successfully
penetrated by fungal hyphae with pressures not higher than
8 MPa (Howard et al., 1991). The situation is probably much
more complicated for the biological or abiotic substrates
encountered naturally by tip-growing cells.
The differences between the fracture mechanics of metals
and that of living tissues and other natural substrates are based
on multiple parameters. First, biological tissues are sensitive
to temperature, tissue density, and water content, and they
usually have a relatively high degree of deformability and the
behaviour may be highly non-linear (Vincent, 1983; Lucas and
Pereira, 1990; Hiller and Jeronimidis, 1996; Round et al., 2000;
Farquhar and Zhao, 2006). Moreover, some materials may
fracture easily (brittle fracture), whereas others are deformed
plastically or behave like viscous fluids. These differences complicate the application of classical fracture mechanics to living
tissues. Secondly, biological tissues and natural substrates are
usually both non-uniform and anisotropic. Non-uniformity is
created, for example, by the cellular structure of a living tissue
or the granular structure of soil, and implies the presence of
variation of the mechanical properties depending on location.
In an anisotropic material, on the other hand, the mechanical
properties vary depending on the orientation of the applied
deforming load. This can, for example, result from the presence of longitudinally oriented cells such as fibres. Fractures
develop much more easily in parallel to these fibres than perpendicular to them. Despite these complicating structural and
geometrical parameters, crack-opening tests including the
wedge penetration test and the notch tensile test have been
used successfully to estimate the fracture properties of living
tissues (Khan and Vincent, 1993). To make classical fracture
analysis applicable to living tissues, modifications have been
applied such as defining the stress intensity factor expressed in
terms of applied load, crack length, and geometry (Khan and
Vincent, 1993; Wright and Vincent, 1996; Alvarez et al., 2000).
In order to characterize the anisotropy of tissues, tests such as
the induced crack formation were applied in different directions. This has been done, for example, on apple parenchyma
tissue (Khan and Vincent, 1993) and wood (Samarasinghe and
Kulasiri, 2000). However, in these experiments, the fractureinducing testing instrument was of macroscopic size, namely
the blades of a microtome or a saw. Because of the microstructured biotic substrate whose structural features (cells) are
at the same scale as the penetrating object (the invading cell),
mechanical testing in the context of invasive growth studies
4722 | Sanati Nezhad and Geitmann
should ideally be done using a penetrometer of similar size
scale and a shape that resembles that of the invading cell. This
approach was chosen for the determination of Fs in pathogenic fungi with the aim of comparing it with Fe determined
using a strain gauge. The resistance strength of cutaneous and
subcutaneous tissue samples from fresh human cadavers and
for skin strips from slaughtered horses was quantified using
glass microprobes attached to silicon bridge strain gauges or
steel needles attached to spring-loaded strain gauges and rigidlever force transducers. The measured forces were compared
with the invasive forces of the mammalian pathogen Pythium
insidiosum (Ravishankar et al., 2001). While the penetrometer
test may provide a good indication for kt and ke, it is likely
to neglect the role of s, since imitating the friction conditions
seems to be nearly impossible unless the penetrometer is fabricated from the same material as that of which the invading
cell is composed.
Modulation of the effective force
An invasive cell may need to switch between invasive and
non-invasive phases over its lifetime, thus requiring temporal control, and successful invasion towards a target is likely
to require spatial adjustments in the direction of invasion.
Moreover, the substrates through which tip-growing cells
have to penetrate are typically heterogeneous, such as granular soil, or the cellular structure of various types of plant tissues. It can therefore be suspected that the invading cells are
able to perceive the degree of substrate stiffness and that they
respond by adjusting their invasive force. These spatio-temporal adjustments of Fe can be achieved by modulating either Fd
or kc. In animal cells, kc is relatively constant and modulation
of Fd requires spatial and temporal regulation in the polymerization or contractile activities of the cytoskeletal arrays. In
walled cells, temporal modulation of Fe can be achieved by
modulating either the turgor (Fd) or the cell wall mechanical
properties (kc). Spatial regulation, on the other hand, relies
solely on the cell wall, since turgor is scalar and pressure is
exerted in all directions equally. A spatial reorientation of the
invasive activity therefore requires the spatial re-definition of
the surface area that is most prone to yield to the turgor (i.e.
non-uniform spatial distribution of kc). In pollen tubes, this
is achieved by redirection of the secretory activity, mediated
by the actin cytoskeleton (Bou Daher and Geitmann, 2011).
Whether temporal regulation relies on modulation of the cell
wall or the turgor is largely unknown, and may differ between
cell types, with turgor modulation being posited for fibres
(Gorshkova et al., 2012) and cell wall regulation favoured for
pollen tubes (Winship et al., 2010, 2011; Sanati Nezhad et al.,
2013a). Adaptation to stress conditions occurs very rapidly,
as can be observed when these are changed in vitro. Using
calibrated microscopic openings made from elastic PDMS
material revealed that pollen tubes of Camellia japonica maintained a constant growth speed despite a continuously narrowing opening and thus continuously increasing Fs (Sanati
Nezhad et al., 2013a). That the maintenance of growth speed
at increasing impedance was ensured by increasing softness
of the apical cell wall was confirmed by the fact that the pollen tubes had an altered diameter or burst once they grew past
the area of physical constraint. In oomycete hyphae, the presence or absence of an actin cap depends on the stiffness of the
surrrounding matrix, clearly demonstrating the adaptability
of this cell to the mechanical properties of the environment
(Walker et al., 2006). It was shown that oomycetes sustain
growth despite reduced turgor by softening their cell walls
(Money and Harold, 1992). This means essentially increasing
kc to maintain Fe under decreasing Fd (Money, 2008).
The short-term modulation of cell wall properties is possibly employed for a more systematic approach to invasion—
the sledge hammer mechanism. Pollen tubes are known to
display regular oscillations in growth rate, with periods in the
range of 30 s to a few minutes (Chebli and Geitmann, 2007).
These regular changes in growth rate are temporally correlated with changes in the mechanical properties of the apical
cell wall (Zerzour et al., 2009; Kroeger and Geitmann, 2013).
The biological function of these oscillations has not been
proven, but the analogy of a sledge hammer principle that
facilitates invasion does not seem too far fetched (Geitmann,
1999). Similar, albeit less regular, oscillations were observed
in fungal hyphae (Lopez-Franco et al., 1994; Johns et al.,
1999) and seem to be measurable even in the coordinated
multihyphal structure of the rhizomorph (Yafetto et al.,
2009). The variations in force exertion associated with this
behaviour warrant more detailed research and temporal correlation with other cellular parameters to understand fully
the regulatory mechanism and the putative mechanical role
(Kroeger and Geitmann, 2011, 2012).
Future research
Investigation of invasive growth has always profited from
ingenious and creative experimental approaches, such as the
use of gold foil as substrate more than a hundred years ago
(Miyoshi, 1895). The availability of sophisticated methods
such as Lab-on-a-Chip and MEMS (microelectro-mechanical systems) will enhance our ability to test tip-growing and
migrating cells with precisely calibrated measuring tools, and
with micro-structured environments that resemble those the
cell encounters in nature (Held et al., 2009, 2010, 2011; Brand
and Gow, 2012; Sanati Nezhad et al., 2013a). These technical
developments on the experimental side are paralleled by the
advancement on the computation side. Finite element modelling will allow calculation of the forces present in geometrically
more complex situations, for example a tip-growing cell that
encounters an obstacle that is not radially symmetric (Sanati
Nezhad et al., 2013a). MEMS-based devices will also be used
to determine the cellular parameters that are important for the
understanding of invasive force generation such as the interplay between turgor and the mechanical properties of the cell
wall (Sanati Nezhad et al., 2013b; Vogler et al., 2013). Both
technical and computational advancement in concert will
hopefully allow quantification of the forces that are elusive so
far, such as friction, and to better understand the mechanical
challenges posed by complex and heterogeneous substrates.
Mechanics of invasion | 4723
One of the challenges of studying invasive growth is inherent to the nature of the problem: microscopic observation of
cellular behaviour in natural growth conditions is often compromised by the very substrate or obstacle the cell is growing
through. The development of methods that allow for live cell
imaging deep into tissues will therefore make an important
contribution to the field. One of the techniques already successfully employed is multi-photon excitation microscopy
that exploits localized non-linear excitation to excite fluorescence only within a thin raster-scanned plane. Since there is
no absorption in out-of-focus areas of the specimen, more
of the excitation light penetrates through the specimen to
the plane of focus, and deeper regions can be imaged. Multiphoton excitation microscopy has been used to monitor nerve
development in brain slices or living animals (Svoboda et al.,
1996), pollen tubes growing within pistillar tissues (Cheung
et al., 2010), and tumour cells in the act of invading a tissue
(Gatesman Ammer et al., 2011). Other emerging deep tissue
imaging methods such as light sheet microscopy are likely to
play an equally important role in the development of in situ
observation strategies.
Finally, invasive growth cannot be fully understood without considering closely associated processes such as guidance
mechanisms that orient growth. Invasive growth in many of
the cell types discussed above is targeted and follows chemical
and mechanical guidance cues provided either by the target
proper or by the invaded substrate (Palanivelu and Preuss,
2000; Kramer, 2006; Chebli and Geitmann, 2007; O’Donnell
et al., 2009; Brand and Gow, 2012). How the mechanical constraints of invasion are integrated with the targeting mechanism provides a series of open questions that need to be
addressed in future experimental and modelling approaches.
Acknowledgements
The authors appreciate the extremely helpful suggestions
by editor Bruno Moulia and the two anonymous reviewers,
as well as discussions with Alexandra Brand. Research in
the Geitmann lab is supported by grants from the Natural
Sciences and Engineering Research Council of Canada
(NSERC) and the Fonds Québécois de la Recherche sur la
Nature et les Technologies (FQRNT)
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