HYPOTHESIS SUBJECT COLLECTION: ADHESION

Dynamic cell–cell adhesion mediated by pericellular matrixinteraction – a hypothesisRudolf Winklbauer

ABSTRACTCell–cell adhesion strength, measured as tissue surface tension,spans an enormous 1000-fold range when different cell types arecompared. However, the examination of basic mechanical principlesof cell adhesion indicates that cadherin-based and relatedmechanisms are not able to promote the high-strength adhesionexperimentally observed in many late embryonic or malignanttissues. Therefore, the hypothesis is explored that the interaction ofthe pericellular matrices of cells generates strong adhesion by amechanism akin to the self-adhesion/self-healing of dynamicallycross-linked hydrogels. Quantitative data from biofilm matricessupport this model. The mechanism links tissue surface tension topericellular 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 classicalcell sorting experiments, as expressed in Steinberg’s differentialadhesion hypothesis: that quantitative differences in adhesionenergies between cells are sufficient to drive sorting.

KEY WORDS: Adhesion, Cortical tension, Surface tension,Pericellular matrix, Hydrogel, Self-healing

IntroductionTo withstand heavy mechanical loads, many animal tissues areformed from covalently cross-linked, fibrillar extracellular matrixscaffolds that are populated by individual cells. Connective tissuessuch as tendon or bone are extreme examples. Shape changes in suchtissues during growth or regeneration are slow and depend on matrixremodeling (Frantz et al., 2010). A different tissue type permits rapidcell rearrangement. Here, tissue cohesion is based on cell–celladhesion mediated by dynamic, non-covalent molecular interactions(Gumbiner, 2005; Harris and Tepass, 2010; Winklbauer and Parent,2016). The tissues imitate viscous fluids, as arbitrarily shapedexplants round up spontaneously, and cells from different tissues sortout when mixed (Foty et al., 1996; Beysen et al., 2000; Jakab et al.,2008). The time scale of these movements, ranging from minutes tohours, is similar to that of early animal development, where celladhesion-based tissues indeed predominate.The behavior of these tissues allows one to borrow concepts from

the mechanics of liquids to describe multicellular assemblies. Inparticular, for a liquid body, surface tension is defined by thereversible work required to increase its surface area. By analogy,tissue surface tension quantifies the surface free energy of cellaggregates (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 atfree cell surfaces (see Glossary for commonly used symbols), or tothe reversible work needed to separate aggregated cells, and thusmeasures the strength of cell–cell adhesion in a tissue (Fig. 1A) (Fotyet al., 1996; Foty and Steinberg, 2005; Winklbauer, 2015).

Surface tension has been determined for numerous cell types,which provides us with a large sample to compare adhesionstrengths. A striking finding from the data is that adhesion strengthsspan 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 thescale (Hegedüs et al., 2006). This raises the question of howadhesion strengths of such different magnitudes are generated. Inthis Hypothesis, I argue that the range of adhesion strengthsattainable by cadherin adhesion or similar mechanisms is severelylimited, but that the interaction of pericellular matrices can produceall observed levels of adhesion.

The range of tissue surface tensionsDuring the separation of adherent cells by an applied force, most ofthe work is dissipated in a transient deformation of cells andadhesion molecules (Décavé et al., 2002; Gonzalez-Rodriguezet al., 2013), but some is stored as free energy that is able to drive there-adhesion of cells. This free energy per unit area, or tissue surfacetension σ, is a suitable indicator of adhesion strength as it does notdepend on the specifics of the separation process, for example onits rate. It is measured when a cell aggregate is at equilibrium, byquantifying the static deformation of spherical cell aggregatesor tissue fragments under a known force (Steinberg, 1978;Winklbauer, 2015). Commonly, test aggregates are compressedbetween two parallel plates. Tracing applied force and aggregateshape until all changes have ceased allows one to determine whendissipative processes have vanished. To exclude confoundingelastic forces, it is usually shown that the inferred surface tensionis independent of the degree of deformation (Foty et al., 1996).

Examination of data available for 47 cell types indicates that thesurface tension σ values range from 0.05 to 56 mJ/m2, that is theyvary ∼1000-fold (Fig. 2; Table S1). At the low end of thedistribution, values for Xenopus (David et al., 2014), Rana (Daviset 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) andmammalian tissues (e.g. Hegedüs et al., 2006) cover the remainingrange of the distribution (Fig. 2; Table S1). Here, large differencesin surface tension are documented by single laboratories using asingle method of measurement. The Foty laboratory measuredvalues 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 theartificial expression of adhesion molecules, among the 17 cell linesgenerated, surface tensions ranged from 0.8 mJ/m2 (Foty andSteinberg, 2005) to 13.4 mJ/m2 (Jia et al., 2012) (Fig. 2; Table S1).

Department of Cell and Systems Biology, University of Toronto, 25 Harbord Street,Toronto, Ontario, M5S 3G5, Canada.

*Author for correspondence (r.winklbauer@utoronto.ca)

R.W., 0000-0002-0628-0897

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© 2019. Published by The Company of Biologists Ltd | Journal of Cell Science (2019) 132, jcs231597. doi:10.1242/jcs.231597

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Conversely, different groups have found similar tensions for similartissues. Values for 6- or for 9-day-old chick neural retinae differedby only 2.5-fold (Foty et al., 1996; Mombach et al., 2005), and limbbud values by only 1.5-fold when tissue fragments (Damon et al.,2008) were compared to dissociated and reaggregated cells (Forgacset al., 1998) (Table S1). Differences of several-fold were found forHydra tissues, but in that study, unconventional methods based onmicropipette aspiration were compared (Cochet-Escartin et al.,2017). Taken together, the data clearly document the existence of awide range of adhesion strengths.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-mediatedadhesion 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 proposehere that a mechanism based on the self-adhesion of thepericellular matrices of cells can generate the entire range oftissue surface tensions.

Membrane-receptor-based cell–cell adhesionTwo kinds of surface energy contribute to tissue surface tension(Manning et al., 2010). First, bond formation between molecules atcell–cell interfaces releases binding energy. Expressed as energy perunit contact area, this adhesion tension Γ promotes cell attachment(Fig. 1B). Considering that two cells contribute to Γ, the adhesiontension component of the tissue surface tension is σΓ=Γ/2 (seeGlossary for commonly used symbols). The second mechanism toprovide surface energy is less intuitive. In animal cells, a corticaltension (β) minimizes the cell surface and leads to isolated cells‘rounding up’ (Fig. 1C.) It is largely due to the contractility of thecortical cytoskeleton, and maintained by the expenditure ofmetabolic energy in the form of ATP hydrolysis. As contractilityis kept at a constant level when the cell surface is stretched orshrunken, it mimics a cell level surface tension (Evans and Yeung,1989; Winklbauer, 2015). Cortical tensions at free and at contactsurfaces, βs and βc, can differ (Fig. 1C), and thus the separation ofcells generates a tissue surface tension component, σβ=βs–βc(Brodland and Chen, 2000; Amack and Manning, 2012).Altogether, the total tissue surface tension equates to

s ¼ sG þ sb ¼ G=2þ bs–bc: ð1Þ

Eqn 1 describes the adhesion strength for all adhesion mechanismsdiscussed here.

Cells can adhere via membrane-integral molecules that interact ina narrow zone between membranes through a specific binding sitepresent on each molecule (Fig. 1B). Examples of respectivemembrane 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).

GlossaryFrequent subscriptsc cell–cell contacts free cell surface

List of symbolsβ cortical tension, mostly due to contractility of a cell’s cortical

cytoskeletonβel elastic tension in the PCM, due to the deformation of the PCM

during cell–cell attachmentγ free energy per unit cell surface area that can drive cell–cell

adhesionΓ adhesion tension, energy per unit contact area set free by

adhesion molecule interactionEeff effective Young’s modulus describing the elasticity of the PCMλ link tension balances the cell-separating effect of cortical tensionλcrit critical link tension at which cell separation by peeling occursr radius of cell–cell contact area in cell pairsReff effective cell/PCM radiusρ ratio r/Reff indicates the degree of cell–cell attachmentσ tissue surface tensionσβ cortex modulation component of tissue surface tensionσΓ adhesion tension component of tissue surface tensionσpcm tissue surface tension due to PCM adhesionθ contact angle between two mutually attached cells

2γc

γsγs

γsγs

β β

+

βs≈β

βc

Free surface Contact interfaceΓ=Γc−Γs

A

B C

Potential binding site Trans binding Cis binding

σ≈γs−γc

Key

Fig. 1. Tissue surface tension. (A) Schematic tissuesection indicating the reversible work of separating atissue in two parts. New surface area (bold outline) isgenerated from former cell–cell interfaces when cells(hexagons) are separated and free cell surfaces ‘roundup’. Tensions at tissue surface are compared to those incell pair. (B) Adhesion molecules at free surface releasebinding energy when interacting in cis (left) or at cell–cellcontacts (right), giving rise to tensions Γs and Γc,respectively. (C) Cell cortex (gray) and cortical tensionare downregulated at cell–cell contacts to allow for cellattachment. β, cortical tension of isolated cells; βs and βc,cortical tensions at free and contact surfaces ofadherent cells; γs and γc, free energy per unit cell surfacearea at free and contact surfaces; Γ, adhesion tension;σ, tissue surface tension.

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Adhesion tension generated by this mechanism depends on theenergy that is released upon binding of the factors, and their densityin 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 500molecules/μm2 (Table S3), and if all molecules would engage inbinding, the adhesion tensions (Γ/2) would be between 0.0002 and0.01 mJ/m2. These values are far below the measured tissue surfacetensions. To achieve substantial cell–cell attachment with σ=βs–βc+Γ/2 (Eqn 1) and a negligible Γ/2, cortical tension at contactsmust be reduced to βc<βs by an attachment-triggereddownregulation of the cell cortex in the contact zone (Fig. 3A). Amajor function of adhesion molecules is thus regulatory: cellscontrol each other’s cortical cytoskeleton to generate differenttensions at free and contacting surfaces. These actively maintained

differences mimic the surface tensions of liquids in cell aggregates(Amack and Manning, 2012; Winklbauer, 2015).

With reduced cortical tension at contacts, two cells can flattentheir contact interface, and the degree of this ‘spreading’ of cells oneach other determines how tightly packed a tissue will be. Atequilibrium, the ratio between γc and βs defines a contact angle θbetween two cells as cosθ=γc/βs (Fig. 3A), and high contact anglescorrespond to large relative contact areas, the absence of gapsbetween cells in aggregates, and smooth aggregate surfaces(Winklbauer, 2015; Parent et al., 2017). Thus, the cell attachmentgeometry depends on the ratio of tensions, not on their absolutevalues. With this dimensionless ‘shape factor’ (cosθ), tissue surfacetension can be written as:

s ¼ ð1–cosuÞbs: ð2Þ

Below, a corresponding shape factor for pericellular matrixadhesion will be derived.

Limits of membrane receptor adhesionAs discussed above, surface tension is generated by adownregulation of the cortex tension at contacts. With β being thecortical tension of single cells from which downregulation canproceed, it is obvious that σ<β. However, the upper limit of the σrange is not lower, but much higher than that of β (Fig. 2), whichranges from 0.02 to 4.1 mJ/m2 (Table S4). Cortex tensions above4 mJ/m2 would produce hydraulic pressures beyond 100–500 Pa, atwhich the cell surface becomes unstable (Stewart et al., 2011).Tensions close to this limit are seen in amoeba, while the metazoanmaximum in the investigated set is 2.5 mJ/m2 (Table S4). Withthese cortical tensions, only the lower part of the surface tensionrange 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 λexceeds a critical value, λcrit, determined by the maximum strengthof 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 byexpressing different amounts of cadherins reached tissue surfacetensions of 5.6 mJ/m2 at most (Fig. 2) (Foty and Steinberg, 2005). Inconclusion, adhesion strengths of σ<β≈5 mJ/m2 can be generatedthrough membrane receptor adhesion. Higher surface tensions,which were observed in half of the tissues examined (Fig. 2), have to

100.10.01 1

5.6

4.1

56.0

[mJ m−2]100

Surface tension

Cortical tension

Integrin

Cadherin

Fig. 2. Range ofmeasured tissue surface tensions and cortical tensions. The range ofmeasured surface tension values (rows above horizontal axis line) andcortical tensions (row below line) are all shown on the same logarithmic scale. The two top rows show surface tension of cell lines ectopically expressingcadherins and integrins (blue), the third row from the top displays surface tension of untreated tissues or cell aggregates (blue), or for gastrula tissues fromXenopus, Rana and zebrafish (green). Values for surface tension are taken from Table S1 and those for cortical tension from Table S4. Dashed vertical linesindicate the limits of cadherin-mediated tissue surface tension as suggested by either maximal cortical tension (4.1 mJ/m2) or by maximal cadherin-inducedsurface tension (5.6 mJ/m2). Both approaches yield very similar limits.

wabwam

wbwb

ww

Δλ

A

B

γc=βc−Γ/2βc

Γ/2

γc

λ λ

β

θ

Fig. 3. Tissue surface tension in membrane adhesion. (A) Balance oftensions 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 adhesionbonds, as well as the bending of membrane and cortex at the periphery of acell–cell contact. β, cortical tension at free cell surface, βc at contact; γc, freeenergy per unit cell surface area, i.e. overall tension, at contact; Γ/2, adhesiontension per cell; λ, link tension; θ, contact angle; Wam, Wab, work expended tostretch adhesion molecule and adhesion bond, respectively, by length Δl;Wb, membrane- or cortex-bending energy.

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be generated by different mechanisms. In the following sections, Iwill argue that adhesion via the pericellular matrices of cells cangenerate such high adhesion tensions, allowing for σ≈Γ/2>β.

Adhesion mediated by pericellular matrix interactionsIn a seemingly paradoxical manner, tissues in the classical cell-sorting experiments combine high surface tensions with loose cellpacking. In chick embryonic heart, neural retina and neural tubeaggregates, 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), cellsare surrounded by micrometer-wide matrix-filled space (Thorogoodand Hinchliffe, 1975; Singley and Solursh, 1980; Damon et al.,2008). The possibility that those cells are embedded in a covalentlycross-linked, fibrillar extracellular matrix (ECM) is excluded by theliquid-like behavior of the tissues – they round up under surfacetension, engulf each other, and show cell sorting like immisciblefluids (Steinberg, 1962, 1963; Foty et al., 1996; Jakab et al., 2008).Matrix-dwelling cells can remodel their ECM and generate residualtensions within it, but when relieved from constraints, respectivetissues shrink without rounding up (Legant et al., 2009; Kural andBilliar, 2013; Simon et al., 2014; Eyckmans and Chen, 2017). Onthe other hand, loose packing is also inconsistent with membranereceptor adhesion, which requires cell–cell distances of nomore than30 nm (Tepass et al., 2000).

The combination of fast rearrangement, sorting and loose packingcould be explained if cells were individually wrapped in an adhesivelayer of cell-type-specific matrix that determined their spacing, yetmoved with the cells as they rearrange. Such a structure is thepericellular matrix (PCM) (Clarris and Fraser, 1968; Cohen et al.,2003). Although difficult to visualize, PCMs have beendemonstrated in many cell types. In chondrocytes, their thicknessreaches several micrometers and their mechanical properties areessential to cartilage function (e.g. Clarris and Fraser, 1968; Cohenet al., 2003; Evanko et al., 2007; McLane et al., 2013; Chang et al.,2016). PCMs consist of hyaluronan, collagens, proteoglycans, suchas aggrecan or versican, and glycoproteins, like fibronectin (Evankoet al., 2007; Müller et al., 2014). Some PCM components aredirectly attached to the cell, whereas others are indirectly attached,and together they form a coherent meshwork (Fig. 4A).

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

PCMs can also promote dynamic cell–cell adhesion, asdocumented in sponges. Here, cell sorting-compatible adhesionuses multimeric proteoglycan-like molecules that attach to lectinmembrane receptors and bind to identical complexes on adjacentcells through carbohydrate–carbohydrate interactions (Fernandez-Busquets and Burger, 2003; Vilanova et al., 2016). In the closestrelatives to the metazoans, the choanoflagellates, a type of colonyformation depends on a secreted lectin in a cell surface matrix that iscompatible with cell rearrangement (Brunet and King, 2017). Thus,dynamic adhesion through a cell surface matrix is an ancientmechanism in metazoans (Vilanova et al., 2016).

Box 1. Some tension components in cell–cell adhesionThe critical link tensionThe link tension λ balances the component of βs normal to thecontact area (Winklbauer, 2015). With sinθ=λ/βs (Fig. 3A) and fromσ=(1–cosθ)βs (Eqn 3), it follows that λ=σ√((1+cosθ)/(1–cosθ)). If λexceeds 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 theelastic deformation of adhesion molecules, adhesion bonds and thecell membrane at the periphery of the contact area (Evans, 1985)(Fig. 3B). Here, adhesion molecules experience a tangential force toaccumulate at the margin. Maximum cadherin packing is exemplified indesmosomes with 1.7×1016 molecules/m2 (Al-Amoudi et al., 2007). Atthis density, essentially all molecules will be in a trans-bound state, theaverage 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 arupture force (fr) of 50×10−12 N per cadherin pair (Leckband and deRooij, 2014), a maximal link tension of the order of λcrit≈5 mN/m isestimated.

Data are also available to estimate λ for cadherin-mediated membraneadhesion, using themodel of Evans (1985) for cell peeling. λ expresses asurface energy density in a separation zone at the periphery of thecontact area, where cells tend to peel off each other. λcrit is related to theelastic adhesion energy density (Wa) and the cortex bending energydensity (Wb) per cell in the separation zone as λcrit=Wel=Wa+Wb (Evans,1985). Wa is composed of the energy densities of stretched adhesionbonds (Wab) and stretched adhesion molecules (Wam) (Fig. 3B). At theoutermost edge of the separation zone, the elastic energy of singlestretched adhesion bonds (Wab) about to rupture is maximal at thebinding energy per cadherin molecule of ∼5×10−20 J (Prakasam et al.,2006). It decreases approximately linearly to vanish a short distanceinward (Evans, 1985), and the average density per cell isWab=1.25×10−20 J. Cadherin molecules are similarly modeled aslinearly elastic springs. The elastic energy of a stretched cadherin(Wam-max) is also maximal just before rupturing, and a typical fr is50×10−12 N (Leckband and de Rooij, 2014). The respective lengthextension of a cadherin pair is 5×10−9 m (Sivasankar et al., 2001), andwith most of the lengthening occurring in the cadherin moleculesthemselves, the extension per molecule is lr≈2.5×10−9 m. Thus, theenergy per molecule is given by Wam-max=½fr×lr≈6.3×10−20 J. Again,stretching decreases approximately linearly to zero within the separationzone; 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 energiesto be 0.211 at maximal adhesiveness (Evans, 1985), Wb≈21×10−20 Jand Wel=Wa+Wb≈25×10−20 J. Adhesion molecules accumulate in theseparation zone (Evans, 1985), and at the maximal cadherin density of1.7×1016 molecules/m2 (Al-Amoudi et al., 2007), we assume that allmolecules are in a trans-bound state, and λcrit=Wel=4.3 mJ/m2.

Cortical tension in PCM-mediated cell–cell adhesionWhen cortical tension is negligible in PCM adhesion, adhesion tensionΓ/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 thecontact radius shrinks to reduce βel by the amount of Δβ, such that bothcontact-constricting tensions together balance again adhesion tensionΓ/2 (Fig. S1). Cortical tensions at free and contact surfaces, β and βc,both contribute to Δβ. As in membrane receptor adhesion, they define acontact angle cosθ=βc/β, which in this case is modified, however, bythe macroscopic contact angle (cosθmac) between the bulging PCMs atPCM–PCM contacts, resulting in a modified overall contact angle θm(Fig. S1). A component β′ of free surface cortical tension β will expandthe contact area, whereas tension βc at the contact will decrease it, andwith 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 canincrease or decrease the contact radius and modulate tissue structureindependently of the overall tissue surface tension.

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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 offibronectin, a protein present in both ECM and PCM, or its integrinreceptor, is consistent with dynamic PCM adhesion, given theliquid-like behavior of the resulting tissue (Robinson et al., 2003,2004). Likewise, the pericellular fibronectin on the surface of singlebreast cancer cells mediates their attachment to and invasion of lungendothelia (Cheng et al., 1998, 2003; Huang et al., 2008). Themutual adhesion of entire PCMs has not been studied yet, but asargued below, this process can be modeled as the interaction oftwo hydrogels.

PCMs as hydrogelsA central structural determinant of PCMs is hyaluronan. Individualchains of this extremely long molecule can bind to cell surfacereceptors and at the same time, stretched by negatively chargedhyaluronan-binding proteoglycans such as aggrecan, span the entirewidth of the PCM (Fig. 4A). This feature prompted the notion thatPCMs are polymer brushes (e.g. Lee et al., 1993; Chang et al.,2016). Mechanically, polymer brushes often resist interdigitationand 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-linkedmeshwork more than a polymer brush. Hyaluronan-bindingaggrecans also bind to each other (Han et al., 2008) and tocollagen fibrils (Rojas et al., 2014) to form networks (Fig. 4A),which through hyaluronan can attach to networks of non-fibrillarcollagen VI (Cescon et al., 2015). Only part of a complex PCMmeshwork needs to be directly attached to the cell surface (Fig. 4A).In chondrocytes, for example, the outer PCM can be peeled from thecell-attached inner part (Cohen et al., 2003). Pores in the PCM thatpermit the diffusion of large proteoglycans (Chang et al., 2016;Phillips et al., 2019) also argue against a dense, impenetrablepolymer brush, and the experimental finding that PCMs easilyreconfigure around penetrating probe particles (McLane et al.,2013) contradicts simulation results based on brush models(Kabedev and Lobaskin, 2018). Thus, although thesupramolecular architecture of PCMs is not well understood,available evidence suggests that PCMs are best described ascomplex hydrogels (Fig. 4A). This implies that self-adhesion and/orself-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-healingof hydrogelsSelf-adhesion and self-healing of dynamically cross-linkedsynthetic polymer gels depend on the interdiffusion and mutualbinding of polymer chains (Stukalin et al., 2013; Campanella et al.,

d

A B

C

Polymer brush Hydrogel

Aggrecan Hyaluronan receptors Link proteins Hyaloronan chainKey

Ws= 1 . d . Eeff . dP P d 2P d P Pd

2 2P_ _

d . Eeff2P_

τmax=

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 hyaluronanand aggrecan components of PCM are shown to illustrate differences. (B) Self-adhesion and/or self-healing of a polymer gel. Surfaces of two separate gelsconsisting of dynamically cross-linked (gray dots) polymer chains (gray lines) are brought into contact (vertical dashed line) (left). Dangling chain ends diffuseacross 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 areadapted 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) establishesan interpenetration zone of the depth d (dashed red lines), with the overall width of the adherent gels being 2P. Stretching the combined gels rapidly tooverall 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.

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2018) (Fig. 4B). When a gel is fractured, dangling chains and freebinding sites are created. Chain ends diffuse across the fractureinterface, and their entanglement alone (Fig. 4B) can alreadycontribute to self-healing (Yamaguchi et al., 2011). With regard tothe possible strength of entanglement effects, pulling a 200–400 nmpolystyrene chain out of an entangled meshwork requires workequivalent to 100 times the binding energy of membrane adhesionreceptors (Table S2) (Balzer et al., 2013).Chain interdiffusion also allows to re-establish electrostatic,

hydrophobic, hydrogen bond or metal coordination interactions thatdynamically cross-link chains in the various gels (Fig. 4B) (Phadkeet 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 anequilibrium 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 (Campanellaet al., 2018;Hinton et al., 2019). Thismayapply to PCMs that come incontact during in vitro cell reaggregation, but during cellmovement intissues, contacts are rapidly broken and re-established, and PCMsurfaces may not reach equilibrium. This would make self-healing asignificant process in PCM–PCMadhesion. Ideally, self-healing and/or self-adhesion continues until conditions have been restored at theinterface that resemble those within the gel (Campanella et al., 2018;Yu et al., 2018).

Mechanics of biological hydrogels – biofilmsPCM–PCM adhesion as a self-healing and/or self-adhesion processhas not been studied so far, but qualitative and quantitative featuresof biological hydrogels can be determined from the biofilm matricesof bacteria, microalgae and other microorganisms. Biofilms aredynamically cross-linked, hydrated polymer gels in which cells aresuspended (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 strikinglysimilar.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 ofcohesion from 1 to 100 mJ/m2 (Ozkan and Berberoglu, 2013), andbacterial biofilms show a similar range (Teixeira et al., 2005), whilethe highest tissue surface tension measured in metazoans is 56 mJ/m2 (Hegedüs et al., 2006). The strong adhesion maintains theintegrity of biofilms, but also attaches them to a wide variety oforganic or inorganic substrates. The molecular smoothness of somemetal or crystalline substrates indicates that penetration of polymerchains into the substratum is not always required. PCMs also adherestrongly to smooth surfaces (Cohen et al., 2004). Thus, althoughentanglement of carbohydrate chains (Yanaki and Yamaguchi,1990; Ashton et al., 2013) can contribute to PCM adhesion, it is notessential in all cases.Adhesion in biofilms is not mediated by the interaction of

receptor–ligand pairs with specific recognition sites, but due tounspecific, yet strong and densely spaced, molecular bonds, such ashydrophobic, H-bond and metal coordination interactions (Evenet al., 2017). In PCMs, the binding energies of specific protein–protein, protein–glycosaminoglycan and lectin–carbohydraterecognition sites of PCM components are as low as those ofadhesion-mediating membrane receptors (Table S2), but the samepotentially strong interactions as those in biofilms occur betweenstretches 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 throughsuch interactions, and release energies that are an order ofmagnitude 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 strengthof synthetic hydrogels were increased 10-fold by the extracellularsecretions of embedded fibroblasts (Xu et al., 2017).

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

Adhesion strength in PCM-mediated cell–cell attachmentIn tissues with PCM adhesion, surface tensions beyond themembrane receptor limit of σ<β are proposed to arise from highadhesion tensions (Γ/2), that is the adhesion energy released at theinterface between the interacting PCMs (Fig. 4B). We initiallyconsider the case where cortical tension is negligible (Fig. 5A,B)and Eqn 1 is reduced to:

spcm ¼ sG ¼ G=2: ð3ÞThis affects how an equilibrium is reached when cells spread oneach other upon contact. In membrane receptor adhesion, tensionmagnitudes at free and at contact surfaces remain constant, but the

Reff P

R

PP

λ=σpcm

σpcm=r/2=βel

βel

A

Br/2

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 generatedtissue surface tension; βel, component of elastic tension parallel to contact.

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contact angle between cells increases during spreading untiltensions are balanced (Fig. 3A). In PCM adhesion, tension Γ/2 thatdrives the progressive attachment of adjacent PCMs remainsconstant, not only in amount, but also in direction, and eventuallyhas to be balanced by a counter tension other than the negligiblecortical tension (Fig. 5B). This tension is provided by the elasticityof the PCM (Table S5). Just as cells are flattened at contacts duringmembrane receptor adhesion, PCMs are deformed as the contactzone expands (Fig. 5), and binding energy is transformed intoelastic energy in the PCM. The elastic tension increases withincreasing deformation of the PCM during attachment until iteventually balances the adhesion tension (Fig. 5B).The three-dimensional pattern of the elastic stresses is likely to be

complex (Han et al., 2011), but for simplicity, the followingassumes that deformations are small and the PCM is sufficientlyextended such that stresses are essentially balanced within the PCM.The elastic stresses are projected onto the PCM–PCM interactionsurface as an elastic tension βel (Fig. 5B), and PCM-mediatedattachment is viewed as the adhesion of spheres of effective radiusReff (Fig. 5B) (see Glossary for symbols). A single effective elasticmodulus Eeff is taken to capture PCM elasticity. With theseassumptions, the Johnson–Kendall–Roberts theory (JKR) forthe adhesion of elastic spheres (Johnson et al., 1971; see articleby Gay at http://www.msc.univ-paris-diderot.fr/~cgay/homepage/doku.php?id=diffusion:jkr) can be applied. In JKR, free andcontacting surfaces meet perpendicularly (Fig. 5B) (Hui et al.,2000). For tensions parallel to the interface, adhesion tension Γ/2 isbalanced by the respective component (βel) of the elastic tensiongenerated 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:

spcm ¼ G=2 ¼ bel ¼ l: ð4ÞWith the contact angle being fixed at 90°, it no longer describescontact geometry. Instead, the ratio (ρ) of contact area radius r toeffective cell radius Reff can be used to describe the degree of mutualcell attachment (Fig. 5B). In JKR, r3=9R*2γπ/2E*, and with γ=Γ/2,R*=Reff/2, E*=Eeff/2(1–ν

2) with ν=0.5 (Ladam et al., 2003), weobtain:

r3 ¼ ð27p=16ÞððG=2Þ=ReffEeff Þ: ð5ÞThus, ρ depends on (Γ/2)/Reff Eeff, where the product of effectivesize and PCM elasticity, Reff Eeff, defines a characteristic elastictension. With Eqn 3 and Eqn 5, it follows that

spcm ¼ ð16=27pÞr3Reff Eeff ; ð6Þindicating 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 adimension-less ‘shape’ factor, cosθ or (16/27π)ρ3, respectively, anda tension; this is cortical tension in membrane receptor adhesion, butan elastic tension in PCM adhesion that is generated by thedeformation 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 aninterpenetration depth, d, when conditions at the interpenetrationzone and outside are the same (Fig. 4C). Separating the PCMsrequires them to be pulled apart by a length, d, which at a PCMthickness (P), corresponds to a strain of ε=d/2P. Pullinginstantaneously to the end position, assuming linear elasticity

(Parada and Zhao, 2018), and with pulling being followed by a slowcreeping of the stretched PCMs leading to eventual separation(Fig. 4C), the reversible work of separation per PCM surface, andhence the surface energy, is

spcm ¼ 1=4Eeff d2=2P: ð7Þ

The dependence of σpcm on Eeff allows us to ask whethermeasured elasticities of PCMs are compatible with observed tissuesurface tensions. First, an upper limit for the shape factor ρ isestimated. In JKR, the adhesion force between elastic spheres, F=(3/2)π2γR*=(3/2)πΓ(Reff/2), is concentrated at the rim of the contactarea, suggesting an approximate link tension of:

l � ð3=4Þspcm=r, ð8Þand 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 generatethe range of observed tissue surface tensions from 0.05 to 56 mJ/m2

with Reff=10 μm would thus require elastic moduli of PCMsbetween 0.065 and 72 kPa. This is well within the range of themeasured values of 0.0005 to 361 kPa (Table S5), supporting theplausibility of a PCM adhesion mechanism.

The PCM mechanism was introduced here to explain highadhesion strengths, but as it can also mediate low-strength adhesionin the range of cortical tensions observed, the effect of the cortex onPCM adhesion must be considered (Fig. S1). The PCM can screencortex-modulating membrane receptors, such as cadherins, fromeach other, leaving cells with uniform cortical tension β at free andcontacting surfaces. However, even cells separated by PCMs canestablish 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 andWinklbauer, 2017); this potentially combines contact-inducedcytoskeletal control with PCM adhesion.

The surface tension of tissues with mixed membrane receptor andPCM contacts is σ=σpcm+σβ (Eqn 1). As for contact geometry, thecontact angle θ between PCMs remains at 90° (Fig. S1), while ρ canbe altered by cortical tension. With an appropriate correction term(Box 1), Eqn 5 becomes

r3 ¼ r3pcm–ð27p=16Þððbc–bcosumÞ=ReffEeff Þ: ð9ÞAs the additional term can be positive or negative, cortical tension

can increase or decrease the contact radius independently of theoverall tissue surface tension.

Cell motility, adhesion and sortingThe relative strengths of cortical and adhesion tensions must affectthemigration and rearrangement of cells in tissues. Generally, cortexcontractility is linked to the forces that determine the motility of acell. Random fluctuations in contractility lead to cell dispersal andalso determine tissue viscosity (Marmottant et al., 2009), and duringactive migration, cortex contraction pushes the cell body forward orpulls it after an advancing protrusion. In both cases, motility forcesare of the order of the cortical tensions (β), and thus are limited tobelow 4 to 5 mJ/m2. In membrane receptor adhesion, adhesionstrength is of the same magnitude, as is the case in gastrula tissueswhere σ/β≈¾ (David et al., 2014). PCM adhesion decouples surfacetension from cortical tension and allows for σ/β≫1. In respectivetissues, for example, from late embryonic organ primordia, theadhesive forces (σ) far outweigh cell motile forces (β).

This consideration explains how tissue viscosity and hence therate of passive cell rearrangement is related to surface tension.

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Gastrula tissues with low surface tensions that are consistent withmembrane adhesion all exhibit a cell rearrangement rate of ∼2 μm/min, consistent with σ/β≈0.75. By contrast, in high adhesionstrength tissues that would require PCM adhesion, rearrangement isslower by up to an order of magnitude (David et al., 2014), asexpected if σ≫β.The ratio of σ to β also determines whether adhesion strength

differences can drive cell sorting, as proposed in the differentialadhesion hypothesis to explain the results of sorting experiments(Steinberg, 1963). PCM-coated cells in mixed aggregates wouldprobe the adhesiveness of PCMs of their neighbors. At overall high-adhesion tensions, respective differences between cell types can belarge owing to differences in PCM size, structure and composition,and overcome the smaller cell-dispersing effects of cortex tensionfluctuations. This implies that the classic sorting experiments werecarried out with cells exhibiting strong, unspecific, biofilm-likeadhesion, and justifies a modified version of the differentialadhesion hypothesis that includes qualitative differences betweenadhesion molecules, but not cortex contractility (Steinberg, 1970;Steinberg, 1978). However, for membrane receptor adhesion orwhen PCM adhesion strength is low, cortical tension and adhesionstrengths are of similar magnitude, and cell dispersal may not besufficiently suppressed by adhesion differentials. A lack of sortingby differential adhesion at low σ has been demonstrated in theXenopus gastrula (Ninomiya et al., 2012), and, fittingly, cell sortingas a mechanism of boundary formation is replaced there by anotherprocess, the contact-induced, active repulsion of cells (Rohani et al.,2014).

ConclusionsCell adhesion through viscoelastic hydrogel matrices is an ancientmechanism, with fossil biofilms dating back 3.5 billion years (Noffkeet al., 2013). It can be viewed as hydrogel self-adhesion and/or self-healing that is driven bymatrix-surface free energy. As proposed here,the mechanism is conserved as a mechanical principle in metazoansin the form of PCM–PCM adhesion. An additional mechanism inmetazoans, the modulation of the cell cortex through membranereceptors that bind in trans promotes adhesion not by releasingbinding energy, but by reducing cortical tension at contacts. The rangeof cortex tensions, which spans 0.02 to 4 mJ/m2, limits thecontribution of this mechanism to low cell adhesion strengths,whereas hydrogel surface energies of up to 100 mJ/m2 can support thehighest adhesion strengths measured. The PCM adhesion modelinvites the application of concepts from hydrogel mechanics to thestudy of tissue structure and morphogenesis, and it suggests thatPCM-based tissues belong to a large class of biological, biomimeticand artificial materials with common mechanical properties.

AcknowledgementsI thank Olivia Luu for help with the figures, Martina Nagel for checking the referencesand Yunyun Huang for suggestions to improve the manuscript.

Competing interestsThe authors declare no competing or financial interests.

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

Supplementary informationSupplementary information available online athttp://jcs.biologists.org/lookup/doi/10.1242/jcs.231597.supplemental

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