ABSTRACT

Cell–cell adhesion strength, measured as tissue surface tension, spans an enormous 1000-fold range when different cell types are compared. However, the examination of basic mechanical principles of cell adhesion indicates that cadherin-based and related mechanisms are not able to promote the high-strength adhesion experimentally observed in many late embryonic or malignant tissues. Therefore, the hypothesis is explored that the interaction of the pericellular matrices of cells generates strong adhesion by a mechanism akin to the self-adhesion/self-healing of dynamically cross-linked hydrogels. Quantitative data from biofilm matrices support this model. The mechanism links tissue surface tension to pericellular matrix stiffness. Moreover, it explains the wide, matrix-filled spaces around cells in liquid-like, yet highly cohesive, tissues, and it rehabilitates aspects of the original interpretation of classical cell sorting experiments, as expressed in Steinberg's differential adhesion hypothesis: that quantitative differences in adhesion energies between cells are sufficient to drive sorting.

Introduction

To withstand heavy mechanical loads, many animal tissues are formed from covalently cross-linked, fibrillar extracellular matrix scaffolds that are populated by individual cells. Connective tissues such as tendon or bone are extreme examples. Shape changes in such tissues during growth or regeneration are slow and depend on matrix remodeling (Frantz et al., 2010). A different tissue type permits rapid cell rearrangement. Here, tissue cohesion is based on cell–cell adhesion mediated by dynamic, non-covalent molecular interactions (Gumbiner, 2005; Harris and Tepass, 2010; Winklbauer and Parent, 2016). The tissues imitate viscous fluids, as arbitrarily shaped explants round up spontaneously, and cells from different tissues sort out when mixed (Foty et al., 1996; Beysen et al., 2000; Jakab et al., 2008). The time scale of these movements, ranging from minutes to hours, is similar to that of early animal development, where cell adhesion-based tissues indeed predominate.

The behavior of these tissues allows one to borrow concepts from the mechanics of liquids to describe multicellular assemblies. In particular, for a liquid body, surface tension is defined by the reversible work required to increase its surface area. By analogy, tissue surface tension quantifies the surface free energy of cell aggregates (Steinberg, 1978; Graner, 1993; Brodland and Chen, 2000; Manning et al., 2010; Winklbauer, 2015). It corresponds to the difference between tension γc at cell–cell contacts and tension γs at free cell surfaces (see Glossary for commonly used symbols), or to the reversible work needed to separate aggregated cells, and thus measures the strength of cell–cell adhesion in a tissue (Fig. 1A) (Foty et al., 1996; Foty and Steinberg, 2005; Winklbauer, 2015).

Fig. 1.

Tissue surface tension. (A) Schematic tissue section indicating the reversible work of separating a tissue in two parts. New surface area (bold outline) is generated from former cell–cell interfaces when cells (hexagons) are separated and free cell surfaces ‘round up’. Tensions at tissue surface are compared to those in cell pair. (B) Adhesion molecules at free surface release binding energy when interacting in cis (left) or at cell–cell contacts (right), giving rise to tensions Γs and Γc, respectively. (C) Cell cortex (gray) and cortical tension are downregulated at cell–cell contacts to allow for cell attachment. β, cortical tension of isolated cells; βs and βc, cortical tensions at free and contact surfaces of adherent cells; γs and γc, free energy per unit cell surface area at free and contact surfaces; Γ, adhesion tension; σ, tissue surface tension.

Fig. 1.

Tissue surface tension. (A) Schematic tissue section indicating the reversible work of separating a tissue in two parts. New surface area (bold outline) is generated from former cell–cell interfaces when cells (hexagons) are separated and free cell surfaces ‘round up’. Tensions at tissue surface are compared to those in cell pair. (B) Adhesion molecules at free surface release binding energy when interacting in cis (left) or at cell–cell contacts (right), giving rise to tensions Γs and Γc, respectively. (C) Cell cortex (gray) and cortical tension are downregulated at cell–cell contacts to allow for cell attachment. β, cortical tension of isolated cells; βs and βc, cortical tensions at free and contact surfaces of adherent cells; γs and γc, free energy per unit cell surface area at free and contact surfaces; Γ, adhesion tension; σ, tissue surface tension.

Surface tension has been determined for numerous cell types, which provides us with a large sample to compare adhesion strengths. A striking finding from the data is that adhesion strengths span a 1000-fold range, with frog gastrula cells at the low end (David et al., 2014) and various tumor cells at the upper end of the scale (Hegedüs et al., 2006). This raises the question of how adhesion strengths of such different magnitudes are generated. In this Hypothesis, I argue that the range of adhesion strengths attainable by cadherin adhesion or similar mechanisms is severely limited, but that the interaction of pericellular matrices can produce all observed levels of adhesion.

The range of tissue surface tensions

During the separation of adherent cells by an applied force, most of the work is dissipated in a transient deformation of cells and adhesion molecules (Décavé et al., 2002; Gonzalez-Rodriguez et al., 2013), but some is stored as free energy that is able to drive the re-adhesion of cells. This free energy per unit area, or tissue surface tension σ, is a suitable indicator of adhesion strength as it does not depend on the specifics of the separation process, for example on its rate. It is measured when a cell aggregate is at equilibrium, by quantifying the static deformation of spherical cell aggregates or tissue fragments under a known force (Steinberg, 1978; Winklbauer, 2015). Commonly, test aggregates are compressed between two parallel plates. Tracing applied force and aggregate shape until all changes have ceased allows one to determine when dissipative processes have vanished. To exclude confounding elastic forces, it is usually shown that the inferred surface tension is independent of the degree of deformation (Foty et al., 1996).

Examination of data available for 47 cell types indicates that the surface tension σ values range from 0.05 to 56 mJ/m2, that is they vary ∼1000-fold (Fig. 2; Table S1). At the low end of the distribution, values for Xenopus (David et al., 2014), Rana (Davis et al., 1997) and zebrafish gastrulae (Schötz et al., 2008) overlap, revealing a 30-fold range for vertebrate early embryo tissues (Fig. 2; Table S1). Chick late embryo (e.g. Forgacs et al., 1998) and mammalian tissues (e.g. Hegedüs et al., 2006) cover the remaining range of the distribution (Fig. 2; Table S1). Here, large differences in surface tension are documented by single laboratories using a single method of measurement. The Foty laboratory measured values between 0.63 mJ/m2 for mouse pancreatic (Jia et al., 2007) and 56 mJ/m2 for ependymoma cells (Hegedüs et al., 2006) (Table S1). In addition, when cells were aggregated through the artificial expression of adhesion molecules, among the 17 cell lines generated, surface tensions ranged from 0.8 mJ/m2 (Foty and Steinberg, 2005) to 13.4 mJ/m2 (Jia et al., 2012) (Fig. 2; Table S1). Conversely, different groups have found similar tensions for similar tissues. Values for 6- or for 9-day-old chick neural retinae differed by only 2.5-fold (Foty et al., 1996; Mombach et al., 2005), and limb bud values by only 1.5-fold when tissue fragments (Damon et al., 2008) were compared to dissociated and reaggregated cells (Forgacs et al., 1998) (Table S1). Differences of several-fold were found for Hydra tissues, but in that study, unconventional methods based on micropipette aspiration were compared (Cochet-Escartin et al., 2017). Taken together, the data clearly document the existence of a wide range of adhesion strengths.

Glossary

Frequent subscripts

     
  • c

    cell–cell contact

  •  
  • s

    free cell surface

List of symbols
     
  • β

    cortical tension, mostly due to contractility of a cell's cortical cytoskeleton

  •  
  • βel

    elastic tension in the PCM, due to the deformation of the PCM during cell–cell attachment

  •  
  • γ

    free energy per unit cell surface area that can drive cell–cell adhesion

  •  
  • Γ

    adhesion tension, energy per unit contact area set free by adhesion molecule interaction

  •  
  • Eeff

    effective Young's modulus describing the elasticity of the PCM

  •  
  • λ

    link tension balances the cell-separating effect of cortical tension

  •  
  • λcrit

    critical link tension at which cell separation by peeling occurs

  •  
  • r

    radius of cell–cell contact area in cell pairs

  •  
  • Reff

    effective cell/PCM radius

  •  
  • ρ

    ratio r/Reff indicates the degree of cell–cell attachment

  •  
  • σ

    tissue surface tension

  •  
  • σβ

    cortex modulation component of tissue surface tension

  •  
  • σΓ

    adhesion tension component of tissue surface tension

  •  
  • σpcm

    tissue surface tension due to PCM adhesion

  •  
  • θ

    contact angle between two mutually attached cells

Fig. 2.

Range of measured tissue surface tensions and cortical tensions. The range of measured surface tension values (rows above horizontal axis line) and cortical tensions (row below line) are all shown on the same logarithmic scale. The two top rows show surface tension of cell lines ectopically expressing cadherins and integrins (blue), the third row from the top displays surface tension of untreated tissues or cell aggregates (blue), or for gastrula tissues from Xenopus, Rana and zebrafish (green). Values for surface tension are taken from Table S1 and those for cortical tension from Table S4. Dashed vertical lines indicate the limits of cadherin-mediated tissue surface tension as suggested by either maximal cortical tension (4.1 mJ/m2) or by maximal cadherin-induced surface tension (5.6 mJ/m2). Both approaches yield very similar limits.

Fig. 2.

Range of measured tissue surface tensions and cortical tensions. The range of measured surface tension values (rows above horizontal axis line) and cortical tensions (row below line) are all shown on the same logarithmic scale. The two top rows show surface tension of cell lines ectopically expressing cadherins and integrins (blue), the third row from the top displays surface tension of untreated tissues or cell aggregates (blue), or for gastrula tissues from Xenopus, Rana and zebrafish (green). Values for surface tension are taken from Table S1 and those for cortical tension from Table S4. Dashed vertical lines indicate the limits of cadherin-mediated tissue surface tension as suggested by either maximal cortical tension (4.1 mJ/m2) or by maximal cadherin-induced surface tension (5.6 mJ/m2). Both approaches yield very similar limits.

This notion prompts the question of whether a single adhesion mechanism can generate the entire range of tissue surface tensions. A current model of tissue surface tension links cadherin-mediated adhesion to the cortical tension at cell surfaces (Brodland and Chen, 2000; Amack and Manning, 2012; Winklbauer, 2015). However, as argued below, such ‘membrane receptor adhesion’ can only explain low surface tension values. Instead, I propose here that a mechanism based on the self-adhesion of the pericellular matrices of cells can generate the entire range of tissue surface tensions.

Membrane-receptor-based cell–cell adhesion

Two kinds of surface energy contribute to tissue surface tension (Manning et al., 2010). First, bond formation between molecules at cell–cell interfaces releases binding energy. Expressed as energy per unit contact area, this adhesion tension Γ promotes cell attachment (Fig. 1B). Considering that two cells contribute to Γ, the adhesion tension component of the tissue surface tension is σΓ=Γ/2 (see Glossary for commonly used symbols). The second mechanism to provide surface energy is less intuitive. In animal cells, a cortical tension (β) minimizes the cell surface and leads to isolated cells ‘rounding up’ (Fig. 1C.) It is largely due to the contractility of the cortical cytoskeleton, and maintained by the expenditure of metabolic energy in the form of ATP hydrolysis. As contractility is kept at a constant level when the cell surface is stretched or shrunken, it mimics a cell level surface tension (Evans and Yeung, 1989; Winklbauer, 2015). Cortical tensions at free and at contact surfaces, βs and βc, can differ (Fig. 1C), and thus the separation of cells generates a tissue surface tension component, σβs–βc (Brodland and Chen, 2000; Amack and Manning, 2012). Altogether, the total tissue surface tension equates to
formula
(1)
Eqn 1 describes the adhesion strength for all adhesion mechanisms discussed here.

Cells can adhere via membrane-integral molecules that interact in a narrow zone between membranes through a specific binding site present on each molecule (Fig. 1B). Examples of respective membrane receptors are the cadherins (Harris and Tepass, 2010; Leckband and de Rooij, 2014; Lecuit and Yap, 2015), immunoglobulin family members (Crossin and Krushel, 2000) and selectins (González-Amaro and Sánchez-Madrid, 1999). Adhesion tension generated by this mechanism depends on the energy that is released upon binding of the factors, and their density in the membrane. This tension is strikingly low.

Binding energies vary between 0.6×10−20 J and 11×10−20 J for membrane receptors, with cadherins occupying the middle range (Table S2). Cadherin membrane densities vary from 9 to 500 molecules/μm2 (Table S3), and if all molecules would engage in binding, the adhesion tensions (Γ/2) would be between 0.0002 and 0.01 mJ/m2. These values are far below the measured tissue surface tensions. To achieve substantial cell–cell attachment with σ=βs–βc+Γ/2 (Eqn 1) and a negligible Γ/2, cortical tension at contacts must be reduced to βcs by an attachment-triggered downregulation of the cell cortex in the contact zone (Fig. 3A). A major function of adhesion molecules is thus regulatory: cells control each other's cortical cytoskeleton to generate different tensions at free and contacting surfaces. These actively maintained differences mimic the surface tensions of liquids in cell aggregates (Amack and Manning, 2012; Winklbauer, 2015).

Fig. 3.

Tissue surface tension in membrane adhesion. (A) Balance of tensions at cell–cell contacts in a cell pair or at the surface of a cell aggregate. (B) Illustrated here is the stretching of adhesion molecules and adhesion bonds, as well as the bending of membrane and cortex at the periphery of a cell–cell contact. β, cortical tension at free cell surface, βc at contact; γc, free energy per unit cell surface area, i.e. overall tension, at contact; Γ/2, adhesion tension per cell; λ, link tension; θ, contact angle; Wam, Wab, work expended to stretch adhesion molecule and adhesion bond, respectively, by length Δl; Wb, membrane- or cortex-bending energy.

Fig. 3.

Tissue surface tension in membrane adhesion. (A) Balance of tensions at cell–cell contacts in a cell pair or at the surface of a cell aggregate. (B) Illustrated here is the stretching of adhesion molecules and adhesion bonds, as well as the bending of membrane and cortex at the periphery of a cell–cell contact. β, cortical tension at free cell surface, βc at contact; γc, free energy per unit cell surface area, i.e. overall tension, at contact; Γ/2, adhesion tension per cell; λ, link tension; θ, contact angle; Wam, Wab, work expended to stretch adhesion molecule and adhesion bond, respectively, by length Δl; Wb, membrane- or cortex-bending energy.

With reduced cortical tension at contacts, two cells can flatten their contact interface, and the degree of this ‘spreading’ of cells on each other determines how tightly packed a tissue will be. At equilibrium, the ratio between γc and βs defines a contact angle θ between two cells as cosθ=γcs (Fig. 3A), and high contact angles correspond to large relative contact areas, the absence of gaps between cells in aggregates, and smooth aggregate surfaces (Winklbauer, 2015; Parent et al., 2017). Thus, the cell attachment geometry depends on the ratio of tensions, not on their absolute values. With this dimensionless ‘shape factor’ (cosθ), tissue surface tension can be written as:
formula
(2)
Below, a corresponding shape factor for pericellular matrix adhesion will be derived.

Limits of membrane receptor adhesion

As discussed above, surface tension is generated by a downregulation of the cortex tension at contacts. With β being the cortical tension of single cells from which downregulation can proceed, it is obvious that σ<β. However, the upper limit of the σ range is not lower, but much higher than that of β (Fig. 2), which ranges from 0.02 to 4.1 mJ/m2 (Table S4). Cortex tensions above 4 mJ/m2 would produce hydraulic pressures beyond 100–500 Pa, at which the cell surface becomes unstable (Stewart et al., 2011). Tensions close to this limit are seen in amoeba, while the metazoan maximum in the investigated set is 2.5 mJ/m2 (Table S4). With these cortical tensions, only the lower part of the surface tension range fulfills the requirement of σ<β.

Adhesion strength is also limited by the link tension λ (Fig. 3A,B) (Winklbauer, 2015). λ increases proportionally with σ, and if λ exceeds a critical value, λcrit, determined by the maximum strength of the molecular bridges between cells, adhesion bonds will break (Fig. 3B) (Winklbauer, 2015). For cadherin adhesion, λcrit≈5 mJ/m2 (Box 1). Consistent with this limit, cells rendered adhesive by expressing different amounts of cadherins reached tissue surface tensions of 5.6 mJ/m2 at most (Fig. 2) (Foty and Steinberg, 2005). In conclusion, adhesion strengths of σ<β≈5 mJ/m2 can be generated through membrane receptor adhesion. Higher surface tensions, which were observed in half of the tissues examined (Fig. 2), have to be generated by different mechanisms. In the following sections, I will argue that adhesion via the pericellular matrices of cells can generate such high adhesion tensions, allowing for σ≈Γ/2>β.

Box 1. Some tension components in cell-cell adhesion

The critical link tension

The link tension λ balances the component of βs normal to the contact area (Winklbauer, 2015). With sinθ=λ/βs (Fig. 3A) and from σ=(1–cosθ)βs (Eqn 3), it follows that λ=σ√((1+cosθ)/(1–cosθ)). If λ exceeds a critical value λcrit, adhesion bonds will be ruptured (Winklbauer, 2015), thus limiting the possible tissue surface tension. λcrit can be estimated for cadherin adhesion. λ is generated by the elastic deformation of adhesion molecules, adhesion bonds and the cell membrane at the periphery of the contact area (Evans, 1985) (Fig. 3B). Here, adhesion molecules experience a tangential force to accumulate at the margin. Maximum cadherin packing is exemplified in desmosomes with 1.7×1016 molecules/m2 (Al-Amoudi et al., 2007). At this density, essentially all molecules will be in a trans-bound state, the average lateral distance between cadherin molecules will be ∼10 nm, and thus a row of 108 molecules/m will delineate the periphery of a cell–cell contact area. These cadherins are close to rupturing, and with a rupture force (fr) of 50×10−12 N per cadherin pair (Leckband and de Rooij, 2014), a maximal link tension of the order of λcrit≈5 mN/m is estimated.

Data are also available to estimate λ for cadherin-mediated membrane adhesion, using the model of Evans (1985) for cell peeling. λ expresses a surface energy density in a separation zone at the periphery of the contact area, where cells tend to peel off each other. λcrit is related to the elastic adhesion energy density (Wa) and the cortex bending energy density (Wb) per cell in the separation zone as λcrit=Wel=Wa+Wb (Evans, 1985). Wa is composed of the energy densities of stretched adhesion bonds (Wab) and stretched adhesion molecules (Wam) (Fig. 3B). At the outermost edge of the separation zone, the elastic energy of single stretched adhesion bonds (Wab) about to rupture is maximal at the binding energy per cadherin molecule of ∼5×10−20 J (Prakasam et al., 2006). It decreases approximately linearly to vanish a short distance inward (Evans, 1985), and the average density per cell is Wab=1.25×10−20 J. Cadherin molecules are similarly modeled as linearly elastic springs. The elastic energy of a stretched cadherin (Wam-max) is also maximal just before rupturing, and a typical fr is 50×10−12 N (Leckband and de Rooij, 2014). The respective length extension of a cadherin pair is 5×10−9 m (Sivasankar et al., 2001), and with most of the lengthening occurring in the cadherin molecules themselves, the extension per molecule is lr≈2.5×10−9 m. Thus, the energy per molecule is given by Wam-max=½fr×lr≈6.3×10−20 J. Again, stretching decreases approximately linearly to zero within the separation zone; the average Wam=3.15×10−20 J, and total Wa=Wab+Wam=4.4×10−20 J. Finally, taking the ratio of adhesion to bending energies to be 0.211 at maximal adhesiveness (Evans, 1985), Wb≈21×10−20 J and Wel=Wa+Wb≈25×10−20 J. Adhesion molecules accumulate in the separation zone (Evans, 1985), and at the maximal cadherin density of 1.7×1016 molecules/m2 (Al-Amoudi et al., 2007), we assume that all molecules are in a trans-bound state, and λcrit=Wel=4.3 mJ/m2.

Cortical tension in PCM-mediated cell-cell adhesion

When cortical tension is negligible in PCM adhesion, adhesion tension Γ/2 at the interface is balanced by the elastic tension βel (Eqn 4) (Fig. 5B). When a tension Δβ is added, equilibrium is restored as the contact radius shrinks to reduce βel by the amount of Δβ, such that both contact-constricting tensions together balance again adhesion tension Γ/2 (Fig. S1). Cortical tensions at free and contact surfaces, β and βc, both contribute to Δβ. As in membrane receptor adhesion, they define a contact angle cosθ=βc/β, which in this case is modified, however, by the macroscopic contact angle (cosθmac) between the bulging PCMs at PCM–PCM contacts, resulting in a modified overall contact angle θm (Fig. S1). A component β′ of free surface cortical tension β will expand the contact area, whereas tension βc at the contact will decrease it, and with Δβ = βc – β′ (Fig. S1), Eqn 5 in the main text becomes:

ρ3 = ρpcm3 – (27π/16)[(βc – βcosθm)/ReffEeff].

As Δβ can take on positive or negative values, cortical tension can increase or decrease the contact radius and modulate tissue structure independently of the overall tissue surface tension.

Adhesion mediated by pericellular matrix interactions

In a seemingly paradoxical manner, tissues in the classical cell-sorting experiments combine high surface tensions with loose cell packing. In chick embryonic heart, neural retina and neural tube aggregates, the rearranging cells are separated by wide gaps (Steinberg, 1962, 1963, 1970), and in limb bud mesenchyme, which exhibits one of the highest surface tensions (Table S1), cells are surrounded by micrometer-wide matrix-filled space (Thorogood and Hinchliffe, 1975; Singley and Solursh, 1980; Damon et al., 2008). The possibility that those cells are embedded in a covalently cross-linked, fibrillar extracellular matrix (ECM) is excluded by the liquid-like behavior of the tissues – they round up under surface tension, engulf each other, and show cell sorting like immiscible fluids (Steinberg, 1962, 1963; Foty et al., 1996; Jakab et al., 2008). Matrix-dwelling cells can remodel their ECM and generate residual tensions within it, but when relieved from constraints, respective tissues shrink without rounding up (Legant et al., 2009; Kural and Billiar, 2013; Simon et al., 2014; Eyckmans and Chen, 2017). On the other hand, loose packing is also inconsistent with membrane receptor adhesion, which requires cell–cell distances of no more than 30 nm (Tepass et al., 2000).

The combination of fast rearrangement, sorting and loose packing could be explained if cells were individually wrapped in an adhesive layer of cell-type-specific matrix that determined their spacing, yet moved with the cells as they rearrange. Such a structure is the pericellular matrix (PCM) (Clarris and Fraser, 1968; Cohen et al., 2003). Although difficult to visualize, PCMs have been demonstrated in many cell types. In chondrocytes, their thickness reaches several micrometers and their mechanical properties are essential to cartilage function (e.g. Clarris and Fraser, 1968; Cohen et al., 2003; Evanko et al., 2007; McLane et al., 2013; Chang et al., 2016). PCMs consist of hyaluronan, collagens, proteoglycans, such as aggrecan or versican, and glycoproteins, like fibronectin (Evanko et al., 2007; Müller et al., 2014). Some PCM components are directly attached to the cell, whereas others are indirectly attached, and together they form a coherent meshwork (Fig. 4A).

Fig. 4.

PCM self-adhesion and/or self-healing. (A) PCM architecture hypothetically modeled as a polymer brush (left) or as a hydrogel (right). Only hyaluronan and aggrecan components of PCM are shown to illustrate differences. (B) Self-adhesion and/or self-healing of a polymer gel. Surfaces of two separate gels consisting of dynamically cross-linked (gray dots) polymer chains (gray lines) are brought into contact (vertical dashed line) (left). Dangling chain ends diffuse across the interface (vertical dashed line) and entangle (purple chains) or form dynamic bonds by recombining free binding sites (red dots) or exchanging (‘hopping’) occupied sites (green dots) (orange and blue chains, respectively). The average interpenetration depth, d, is indicated. Chain interactions images are adapted with permission from Stukalin et al. (2013). Copyright 2013, American Chemical Society. (C) Mechanical separation of adhering PCM gels. Surfaces (dashed blue lines) of two gels of width P are brought into contact. Interdiffusion of chain ends (red arrows) across the interface (dashed blue line) establishes an interpenetration zone of the depth d (dashed red lines), with the overall width of the adherent gels being 2P. Stretching the combined gels rapidly to overall width 2P+d requires a maximal stress τmax at the final position. Slow relaxation of the gels upon the retraction of the chains spanning the interface (red arrows) separates the gels (black arrows) after the mechanical work Ws has been expended.

Fig. 4.

PCM self-adhesion and/or self-healing. (A) PCM architecture hypothetically modeled as a polymer brush (left) or as a hydrogel (right). Only hyaluronan and aggrecan components of PCM are shown to illustrate differences. (B) Self-adhesion and/or self-healing of a polymer gel. Surfaces of two separate gels consisting of dynamically cross-linked (gray dots) polymer chains (gray lines) are brought into contact (vertical dashed line) (left). Dangling chain ends diffuse across the interface (vertical dashed line) and entangle (purple chains) or form dynamic bonds by recombining free binding sites (red dots) or exchanging (‘hopping’) occupied sites (green dots) (orange and blue chains, respectively). The average interpenetration depth, d, is indicated. Chain interactions images are adapted with permission from Stukalin et al. (2013). Copyright 2013, American Chemical Society. (C) Mechanical separation of adhering PCM gels. Surfaces (dashed blue lines) of two gels of width P are brought into contact. Interdiffusion of chain ends (red arrows) across the interface (dashed blue line) establishes an interpenetration zone of the depth d (dashed red lines), with the overall width of the adherent gels being 2P. Stretching the combined gels rapidly to overall width 2P+d requires a maximal stress τmax at the final position. Slow relaxation of the gels upon the retraction of the chains spanning the interface (red arrows) separates the gels (black arrows) after the mechanical work Ws has been expended.

PCMs can mediate the non-specific, transient, yet strong, initial adhesion of cells to a substratum (Cohen et al., 2004). For example, the attached PCM of chondrocytes is torn apart by an intense shear flow of the medium, showing that in this case, PCM–substratum adhesion is stronger than PCM–PCM cohesion (Cohen et al., 2003). Eventually, as cells spread, the wide membrane–substratum separation that is due to the bulky PCM is replaced by, for instance, integrin-based focal contacts (Cohen et al., 2006), but this decrease in separation distance does not necessarily imply that adhesion itself has become stronger.

PCMs can also promote dynamic cell–cell adhesion, as documented in sponges. Here, cell sorting-compatible adhesion uses multimeric proteoglycan-like molecules that attach to lectin membrane receptors and bind to identical complexes on adjacent cells through carbohydrate–carbohydrate interactions (Fernandez-Busquets and Burger, 2003; Vilanova et al., 2016). In the closest relatives to the metazoans, the choanoflagellates, a type of colony formation depends on a secreted lectin in a cell surface matrix that is compatible with cell rearrangement (Brunet and King, 2017). Thus, dynamic adhesion through a cell surface matrix is an ancient mechanism in metazoans (Vilanova et al., 2016).

The mechanism seems to have been retained in higher metazoans. At the molecular level, lymphocyte–endothelial and keratocyte–keratocyte adhesion require the PCM component hyaluronan (DeGrendele et al., 1996; Nandi et al., 2000; Milstone et al., 1994). The experimental aggregation of cells upon the expression of fibronectin, a protein present in both ECM and PCM, or its integrin receptor, is consistent with dynamic PCM adhesion, given the liquid-like behavior of the resulting tissue (Robinson et al., 2003, 2004). Likewise, the pericellular fibronectin on the surface of single breast cancer cells mediates their attachment to and invasion of lung endothelia (Cheng et al., 1998, 2003; Huang et al., 2008). The mutual adhesion of entire PCMs has not been studied yet, but as argued below, this process can be modeled as the interaction of two hydrogels.

PCMs as hydrogels

A central structural determinant of PCMs is hyaluronan. Individual chains of this extremely long molecule can bind to cell surface receptors and at the same time, stretched by negatively charged hyaluronan-binding proteoglycans such as aggrecan, span the entire width of the PCM (Fig. 4A). This feature prompted the notion that PCMs are polymer brushes (e.g. Lee et al., 1993; Chang et al., 2016). Mechanically, polymer brushes often resist interdigitation and show little adhesion, which makes them well suited for low-friction interfaces that bear compressive loads (Milner et al., 1988; Kreer, 2016).

However, most PCMs will resemble a dynamically cross-linked meshwork more than a polymer brush. Hyaluronan-binding aggrecans also bind to each other (Han et al., 2008) and to collagen fibrils (Rojas et al., 2014) to form networks (Fig. 4A), which through hyaluronan can attach to networks of non-fibrillar collagen VI (Cescon et al., 2015). Only part of a complex PCM meshwork needs to be directly attached to the cell surface (Fig. 4A). In chondrocytes, for example, the outer PCM can be peeled from the cell-attached inner part (Cohen et al., 2003). Pores in the PCM that permit the diffusion of large proteoglycans (Chang et al., 2016; Phillips et al., 2019) also argue against a dense, impenetrable polymer brush, and the experimental finding that PCMs easily reconfigure around penetrating probe particles (McLane et al., 2013) contradicts simulation results based on brush models (Kabedev and Lobaskin, 2018). Thus, although the supramolecular architecture of PCMs is not well understood, available evidence suggests that PCMs are best described as complex hydrogels (Fig. 4A). This implies that self-adhesion and/or self-healing processes of polymer gels (Campanella et al., 2018; Diba et al., 2018) can serve as models for PCM adhesion.

PCM–PCM adhesion as self-adhesion and/or self-healing of hydrogels

Self-adhesion and self-healing of dynamically cross-linked synthetic polymer gels depend on the interdiffusion and mutual binding of polymer chains (Stukalin et al., 2013; Campanella et al., 2018) (Fig. 4B). When a gel is fractured, dangling chains and free binding sites are created. Chain ends diffuse across the fracture interface, and their entanglement alone (Fig. 4B) can already contribute to self-healing (Yamaguchi et al., 2011). With regard to the possible strength of entanglement effects, pulling a 200–400 nm polystyrene chain out of an entangled meshwork requires work equivalent to 100 times the binding energy of membrane adhesion receptors (Table S2) (Balzer et al., 2013).

Chain interdiffusion also allows to re-establish electrostatic, hydrophobic, hydrogen bond or metal coordination interactions that dynamically cross-link chains in the various gels (Fig. 4B) (Phadke et al., 2012; Stukalin et al., 2013; Campanella et al., 2018; Diba et al., 2018; Hinton et al., 2019; Cao and Forest, 2019). When left separated, free binding sites on fracture surfaces gradually recombine until an equilibrium is reached. Nevertheless, when brought into contact, bond formation across equilibrium surfaces can still occur (Fig. 4B). The resulting attachment is referred to as self-adhesion (Campanella et al., 2018; Hinton et al., 2019). This may apply to PCMs that come in contact during in vitro cell reaggregation, but during cell movement in tissues, contacts are rapidly broken and re-established, and PCM surfaces may not reach equilibrium. This would make self-healing a significant process in PCM–PCM adhesion. Ideally, self-healing and/or self-adhesion continues until conditions have been restored at the interface that resemble those within the gel (Campanella et al., 2018; Yu et al., 2018).

Mechanics of biological hydrogels – biofilms

PCM–PCM adhesion as a self-healing and/or self-adhesion process has not been studied so far, but qualitative and quantitative features of biological hydrogels can be determined from the biofilm matrices of bacteria, microalgae and other microorganisms. Biofilms are dynamically cross-linked, hydrated polymer gels in which cells are suspended (Mazza, 2016; Even et al., 2017). Like in PCMs, carbohydrate chains and proteins are the main building blocks, and, although they differ molecularly from metazoan PCM constituents, the mechanical properties of biofilms and PCMs are strikingly similar.

Most importantly, the range of biofilm surface energies encompasses that of metazoan tissue surface tensions (Table S1). Microalgae lawns from different species feature free energies of cohesion from 1 to 100 mJ/m2 (Ozkan and Berberoglu, 2013), and bacterial biofilms show a similar range (Teixeira et al., 2005), while the highest tissue surface tension measured in metazoans is 56 mJ/m2 (Hegedüs et al., 2006). The strong adhesion maintains the integrity of biofilms, but also attaches them to a wide variety of organic or inorganic substrates. The molecular smoothness of some metal or crystalline substrates indicates that penetration of polymer chains into the substratum is not always required. PCMs also adhere strongly to smooth surfaces (Cohen et al., 2004). Thus, although entanglement of carbohydrate chains (Yanaki and Yamaguchi, 1990; Ashton et al., 2013) can contribute to PCM adhesion, it is not essential in all cases.

Adhesion in biofilms is not mediated by the interaction of receptor–ligand pairs with specific recognition sites, but due to unspecific, yet strong and densely spaced, molecular bonds, such as hydrophobic, H-bond and metal coordination interactions (Even et al., 2017). In PCMs, the binding energies of specific protein–protein, protein–glycosaminoglycan and lectin–carbohydrate recognition sites of PCM components are as low as those of adhesion-mediating membrane receptors (Table S2), but the same potentially strong interactions as those in biofilms occur between stretches of interpenetrating carbohydrate chains (e.g. Scott, 1992; Scott and Heatley, 1999; Han et al., 2008; Vilanova et al., 2016). Single aggrecan molecules bind to each other or to collagen through such interactions, and release energies that are an order of magnitude higher than those for single cadherin pairs (Han et al., 2008; Rojas et al., 2014) (Table S2). Consistent with strong, dynamic PCM component interactions, the healing rate and strength of synthetic hydrogels were increased 10-fold by the extracellular secretions of embedded fibroblasts (Xu et al., 2017).

Though unspecific in origin, adhesiveness in biofilms varies strongly between cells types or for different substrates. For example, the adhesion energy of Pseudomonas aeruginosa varies between strains from strongly adhesive to strongly repellent (Teixeira et al., 2005). This suggests that a wide range of adhesion strengths can be easily generated, presumably through simple, yet critical variations of matrix components. For example, a reduced binding of interacting sites, entropy debts due to increased stretching or compression of polymer coils (Milner et al., 1988), or increased bending or torsion of matrix elements, which all can be induced by a slightly altered spatial arrangement of sites, will diminish adhesion and favor repulsion. This feature of biological polymer gels can explain the strong sorting tendencies of PCM-coated metazoan cells from sponges (Wilson, 1907) to chick embryos (Foty et al., 1996).

Adhesion strength in PCM-mediated cell–cell attachment

In tissues with PCM adhesion, surface tensions beyond the membrane receptor limit of σ<β are proposed to arise from high adhesion tensions (Γ/2), that is the adhesion energy released at the interface between the interacting PCMs (Fig. 4B). We initially consider the case where cortical tension is negligible (Fig. 5A,B) and Eqn 1 is reduced to:
formula
(3)
This affects how an equilibrium is reached when cells spread on each other upon contact. In membrane receptor adhesion, tension magnitudes at free and at contact surfaces remain constant, but the contact angle between cells increases during spreading until tensions are balanced (Fig. 3A). In PCM adhesion, tension Γ/2 that drives the progressive attachment of adjacent PCMs remains constant, not only in amount, but also in direction, and eventually has to be balanced by a counter tension other than the negligible cortical tension (Fig. 5B). This tension is provided by the elasticity of the PCM (Table S5). Just as cells are flattened at contacts during membrane receptor adhesion, PCMs are deformed as the contact zone expands (Fig. 5), and binding energy is transformed into elastic energy in the PCM. The elastic tension increases with increasing deformation of the PCM during attachment until it eventually balances the adhesion tension (Fig. 5B).
Fig. 5.

Tissue surface tension in PCM adhesion. (A) Initial contact of PCMs (pink) of thickness P; R, cell radius; Reff=R+P. (B) Equilibrium state of PCM-mediated adhesion, with balance of tensions at PCM-PCM contact. Γ/2, adhesion tension per cell; λ, link tension; σpcm, pericellular matrix generated tissue surface tension; βel, component of elastic tension parallel to contact.

Fig. 5.

Tissue surface tension in PCM adhesion. (A) Initial contact of PCMs (pink) of thickness P; R, cell radius; Reff=R+P. (B) Equilibrium state of PCM-mediated adhesion, with balance of tensions at PCM-PCM contact. Γ/2, adhesion tension per cell; λ, link tension; σpcm, pericellular matrix generated tissue surface tension; βel, component of elastic tension parallel to contact.

The three-dimensional pattern of the elastic stresses is likely to be complex (Han et al., 2011), but for simplicity, the following assumes that deformations are small and the PCM is sufficiently extended such that stresses are essentially balanced within the PCM. The elastic stresses are projected onto the PCM–PCM interaction surface as an elastic tension βel (Fig. 5B), and PCM-mediated attachment is viewed as the adhesion of spheres of effective radius Reff (Fig. 5B) (see Glossary for symbols). A single effective elastic modulus Eeff is taken to capture PCM elasticity. With these assumptions, the Johnson–Kendall–Roberts theory (JKR) for the adhesion of elastic spheres (Johnson et al., 1971; see article by Gay at http://www.msc.univ-paris-diderot.fr/~cgay/homepage/doku.php?id=diffusion:jkr) can be applied. In JKR, free and contacting surfaces meet perpendicularly (Fig. 5B) (Hui et al., 2000). For tensions parallel to the interface, adhesion tension Γ/2 is balanced by the respective component (βel) of the elastic tension generated by cell attachment (Fig. 5B). Since σpcm=Γ/2 (Eqn 3), σpcm also equals the link tension λ perpendicular to the interface (Fig. 5B), and:
formula
(4)
With the contact angle being fixed at 90°, it no longer describes contact geometry. Instead, the ratio (ρ) of contact area radius r to effective cell radius Reff can be used to describe the degree of mutual cell attachment (Fig. 5B). In JKR, r3=9R*2γπ/2E*, and with γ=Γ/2, R*=Reff/2, E*=Eeff/2(1–ν2) with ν=0.5 (Ladam et al., 2003), we obtain:
formula
(5)
Thus, ρ depends on (Γ/2)/Reff Eeff, where the product of effective size and PCM elasticity, Reff Eeff, defines a characteristic elastic tension. With Eqn 3 and Eqn 5, it follows that
formula
(6)
indicating that surface tension is proportional to this elastic tension. In membrane receptor adhesion (Eqn 2), as in PCM adhesion (Eqn 6), tissue surface tension can be expressed as the product of a dimension-less ‘shape’ factor, cosθ or (16/27π)ρ3, respectively, and a tension; this is cortical tension in membrane receptor adhesion, but an elastic tension in PCM adhesion that is generated by the deformation of the PCM during cell–cell attachment.
The proportionality of tissue surface tension and PCM elasticity can also be derived by assuming that self-adhesion and/or self-healing of two PCMs has reached an equilibrium at an interpenetration depth, d, when conditions at the interpenetration zone and outside are the same (Fig. 4C). Separating the PCMs requires them to be pulled apart by a length, d, which at a PCM thickness (P), corresponds to a strain of ε=d/2P. Pulling instantaneously to the end position, assuming linear elasticity (Parada and Zhao, 2018), and with pulling being followed by a slow creeping of the stretched PCMs leading to eventual separation (Fig. 4C), the reversible work of separation per PCM surface, and hence the surface energy, is
formula
(7)
The dependence of σpcm on Eeff allows us to ask whether measured elasticities of PCMs are compatible with observed tissue surface tensions. First, an upper limit for the shape factor ρ is estimated. In JKR, the adhesion force between elastic spheres, F=(3/2)π2γR*=(3/2)πΓ(Reff/2), is concentrated at the rim of the contact area, suggesting an approximate link tension of:
formula
(8)

and with λ=σpcm and λ<λcrit, it follows that ρ<(3/4). Second, according to Eqn 5, ρ<3/4 entails that σ/(ReffEeff)<1/13. To generate the range of observed tissue surface tensions from 0.05 to 56 mJ/m2 with Reff=10 μm would thus require elastic moduli of PCMs between 0.065 and 72 kPa. This is well within the range of the measured values of 0.0005 to 361 kPa (Table S5), supporting the plausibility of a PCM adhesion mechanism.

The PCM mechanism was introduced here to explain high adhesion strengths, but as it can also mediate low-strength adhesion in the range of cortical tensions observed, the effect of the cortex on PCM adhesion must be considered (Fig. S1). The PCM can screen cortex-modulating membrane receptors, such as cadherins, from each other, leaving cells with uniform cortical tension β at free and contacting surfaces. However, even cells separated by PCMs can establish small, local membrane receptor contacts (e.g. Tickle et al., 1978; Babai and Tremblay, 1972; Caruso et al., 1997; Ewald et al., 2012; Goldenberg et al., 1969; Luu et al., 2015; Wen and Winklbauer, 2017); this potentially combines contact-induced cytoskeletal control with PCM adhesion.

The surface tension of tissues with mixed membrane receptor and PCM contacts is σ=σpcmβ (Eqn 1). As for contact geometry, the contact angle θ between PCMs remains at 90° (Fig. S1), while ρ can be altered by cortical tension. With an appropriate correction term (Box 1), Eqn 5 becomes
formula
(9)

As the additional term can be positive or negative, cortical tension can increase or decrease the contact radius independently of the overall tissue surface tension.

Cell motility, adhesion and sorting

The relative strengths of cortical and adhesion tensions must affect the migration and rearrangement of cells in tissues. Generally, cortex contractility is linked to the forces that determine the motility of a cell. Random fluctuations in contractility lead to cell dispersal and also determine tissue viscosity (Marmottant et al., 2009), and during active migration, cortex contraction pushes the cell body forward or pulls it after an advancing protrusion. In both cases, motility forces are of the order of the cortical tensions (β), and thus are limited to below 4 to 5 mJ/m2. In membrane receptor adhesion, adhesion strength is of the same magnitude, as is the case in gastrula tissues where σ/β≈¾ (David et al., 2014). PCM adhesion decouples surface tension from cortical tension and allows for σ/β≫1. In respective tissues, for example, from late embryonic organ primordia, the adhesive forces (σ) far outweigh cell motile forces (β).

This consideration explains how tissue viscosity and hence the rate of passive cell rearrangement is related to surface tension. Gastrula tissues with low surface tensions that are consistent with membrane adhesion all exhibit a cell rearrangement rate of ∼2 μm/min, consistent with σ/β≈0.75. By contrast, in high adhesion strength tissues that would require PCM adhesion, rearrangement is slower by up to an order of magnitude (David et al., 2014), as expected if σ≫β.

The ratio of σ to β also determines whether adhesion strength differences can drive cell sorting, as proposed in the differential adhesion hypothesis to explain the results of sorting experiments (Steinberg, 1963). PCM-coated cells in mixed aggregates would probe the adhesiveness of PCMs of their neighbors. At overall high-adhesion tensions, respective differences between cell types can be large owing to differences in PCM size, structure and composition, and overcome the smaller cell-dispersing effects of cortex tension fluctuations. This implies that the classic sorting experiments were carried out with cells exhibiting strong, unspecific, biofilm-like adhesion, and justifies a modified version of the differential adhesion hypothesis that includes qualitative differences between adhesion molecules, but not cortex contractility (Steinberg, 1970; Steinberg, 1978). However, for membrane receptor adhesion or when PCM adhesion strength is low, cortical tension and adhesion strengths are of similar magnitude, and cell dispersal may not be sufficiently suppressed by adhesion differentials. A lack of sorting by differential adhesion at low σ has been demonstrated in the Xenopus gastrula (Ninomiya et al., 2012), and, fittingly, cell sorting as a mechanism of boundary formation is replaced there by another process, the contact-induced, active repulsion of cells (Rohani et al., 2014).

Conclusions

Cell adhesion through viscoelastic hydrogel matrices is an ancient mechanism, with fossil biofilms dating back 3.5 billion years (Noffke et al., 2013). It can be viewed as hydrogel self-adhesion and/or self-healing that is driven by matrix-surface free energy. As proposed here, the mechanism is conserved as a mechanical principle in metazoans in the form of PCM–PCM adhesion. An additional mechanism in metazoans, the modulation of the cell cortex through membrane receptors that bind in trans promotes adhesion not by releasing binding energy, but by reducing cortical tension at contacts. The range of cortex tensions, which spans 0.02 to 4 mJ/m2, limits the contribution of this mechanism to low cell adhesion strengths, whereas hydrogel surface energies of up to 100 mJ/m2 can support the highest adhesion strengths measured. The PCM adhesion model invites the application of concepts from hydrogel mechanics to the study of tissue structure and morphogenesis, and it suggests that PCM-based tissues belong to a large class of biological, biomimetic and artificial materials with common mechanical properties.

Acknowledgements

I thank Olivia Luu for help with the figures, Martina Nagel for checking the references and Yunyun Huang for suggestions to improve the manuscript.

Footnotes

Funding

R.W. is funded by the Canadian Institutes of Health Research (PJT-15614) and the Natural Sciences and Engineering Research Council of Canada (RGPIN-2017-06667).

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Competing interests

The authors declare no competing or financial interests.

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