The cellular mechanics of an invasive lifestyle

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.

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: 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.

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 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.

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 7mm 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 1–3mm 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 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).

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.

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).

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 0.1–1MPa, 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 non-yielding 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 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 8MPa (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 <1MPa. The rhizomorphs of Armillaria were found to have a turgor of 0.8MPa, 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 non-invasive 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, visco-elasticity, 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).

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). A_e, interaction surface with the invaded substrate; P, constant hydrostatic pressure in the walled cell (turgor); F_e, effective invasive force; F, constant load applied on the solid stylus; P_e, 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 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 tip-growing 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 cysteine-rich 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).

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

(1)

with

(2)

where F_e is the effective invasive force exerted by the invading cell, F_s is the resistance produced by the substrate which depends on k_t, the factor defining the degree of cohesion or adhesion between the elements (cells, soil particles) of the invaded substrate (tissue, soil, agarose), k_e, a parameter related to the intrinsic hardness of substrate, and, s, a factor indicating the surface interaction (friction) between substrate and invading cell. F_d is the potential driving force (in plant and fungal cells F_d is a result of turgor; in animal cells F_d is the sum of the polymerization and traction-based propulsion forces generated by the cytoskeleton). k_c is the factor defining how compliance of the cell wall or the plasma membrane of the invading cell limits the exertion of F_d to the outside of the cell with 0<k_c<1. This relationship indicates the following possible strategies to reduce F_s.

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 k_t and/or k_e 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 k_e 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 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.

Experimental quantification of invasive force

The quantitative comparison between F_e and F_s 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 (k_t, k_e, s). The comparison of F_e and F_d, 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.

Quantification of driving force F_d

Depending on the cell type, F_d 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 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 8MPa 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 0.1–0.4MPa for lily pollen tubes (Benkert et al., 1997), 0.4–0.5MPa for fungal hyphae (Lew et al., 2004), and 0.3–1MPa 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 effective force F_e

Quantification of the effective force F_e 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. This second point is crucial as quantitative values for F_e cannot be obtained using either a measuring tool whose stiffness is so high that the exertion of F_e 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 tip-growing 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 0.1MPa is sufficient to penetrate this substrate.

Fig. 4.

Experimental strategies to measure the effective force F_e. (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).

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 ~5MPa.

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). 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. F_e 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 F_d is available as F_e, 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 F_e 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 Lab-on-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 0.15MPa 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 F_s 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 50MPa to 80MPa (assessed with the Vicker test) were successfully penetrated by fungal hyphae with pressures not higher than 8MPa (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 fracture-inducing 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 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 F_s in pathogenic fungi with the aim of comparing it with F_e 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 rigid-lever 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 k_t and k_e, 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 F_e can be achieved by modulating either F_d or k_c. In animal cells, k_c is relatively constant and modulation of F_d requires spatial and temporal regulation in the polymerization or contractile activities of the cytoskeletal arrays. In walled cells, temporal modulation of F_e can be achieved by modulating either the turgor (F_d) or the cell wall mechanical properties (k_c). 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 k_c). 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 F_s (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 k_c to maintain F_e under decreasing F_d (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.

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. Multi-photon 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)