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  • J. R. Soc. Interface (2011) 8, 12171232

    on August 20, 2018 from

    doi:10.1098/rsif.2011.0157Published online 1 June 2011


    *Author for cPresent addGeorgia Instit

    Received 21 MAccepted 10 M

    Probing mechanical principles of focalcontacts in cellmatrix adhesion witha coupled stochasticelastic modelling

    frameworkHuajian Gao1,*, Jin Qian1, and Bin Chen2

    1School of Engineering, Brown University, Providence, RI 02912, USA2Institute of High Performance Computing, A*STAR 138632, Singapore

    Cellmatrix adhesion depends on the collective behaviours of clusters of receptorligandbonds called focal contacts between cell and extracellular matrix. While the behaviour of asingle molecular bond is governed by statistical mechanics at the molecular scale, continuummechanics should be valid at a larger scale. This paper presents an overview of a series ofrecent theoretical studies aimed at probing the basic mechanical principles of focal contactsin cellmatrix adhesion via stochasticelastic models in which stochastic descriptions ofmolecular bonds and elastic descriptions of interfacial tractionseparation are unified in asingle modelling framework. The intention here is to illustrate these principles using simpleanalytical and numerical models. The aim of the discussions is to provide possible clues tothe following questions: why does the size of focal adhesions (FAs) fall into a narrow rangearound the micrometre scale? How can cells sense and respond to substrates of varied stiffnessvia FAs? How do the magnitude and orientation of mechanical forces affect the bindingdynamics of FAs? The effects of cluster size, cellmatrix elastic modulus, loading directionand cytoskeletal pretension on the lifetime of FA clusters have been investigated by theoreti-cal arguments as well as Monte Carlo numerical simulations, with results showing thatintermediate adhesion size, stiff substrate, cytoskeleton stiffening, low-angle pulling and mod-erate cytoskeletal pretension are factors that contribute to stable FAs. From a mechanisticpoint of view, these results provide possible explanations for a wide range of experimentalobservations and suggest multiple mechanisms by which cells can actively control adhesionand de-adhesion via cytoskeletal contractile machinery in response to mechanical propertiesof their surroundings.

    Keywords: cell adhesion; focal adhesion; receptorligand bond; adhesion lifetime;size effect; stiffness effect


    There have been growing research activities towards theunderstanding and control of cell adhesion in the pastdecades. The feature that distinguishes cell adhesionfrom conventional adhesive contact in engineeringsystems is the specific binding between cell surfaceproteins (receptors) and complementary molecules(ligands) on other cells or extracellular matrix (ECM).The specific receptorligand recognition is often con-sidered a lock-and-key mechanism, while the variousnon-specific interactions including electrostatic and vander Waals forces are usually negligible owing to a layer

    orrespondence ( Coulter Department of Biomedical Engineering,ute of Technology, Atlanta, GA 30332, USA.

    arch 2011ay 2011 1217

    of polymer brush surrounding the cell surface called gly-cocalyx [1]. There are literally hundreds of receptors thatparticipate in cell adhesion, which are grouped into sev-eral main families: integrin, immunoglobulin, selectinand cadherin. Each of these families is accompanied byan equally diverse family of ligands [2,3]. This biologicalcomplexity is far beyond the scope of this paper and hasbeen thoroughly reviewed elsewhere [26]. Receptorligand bonds function as transmembrane linkers betweenthe cytoskeleton and ECM, where both mechanical cuesand regulatory signals are transmitted in both directionsacross the plasma membrane for a wide range of cellularprocesses such as cell spreading, migration, proliferationand differentiation [7].

    The aim of this paper is to outline some of the recentstudies exploring the mechanical principles that may be

    This journal is q 2011 The Royal Society


  • adhesion plaque

    actin bundle(a) (b)

    1218 Review. Stochasticelastic modelling framework H. Gao et al.

    on August 20, 2018 from

    possibly involved in cellmatrix adhesion. Only some ofthe key ideas and results are highlighted in the discus-sions given here. The reader is encouraged to consultvarious references given in the paper for more details.



    Figure 1. A schematic of focal contacts in cellECM adhesionbased on specific binding between receptors and complementaryligands. (a) CellECM adhesion localized to discrete focalcontacts. (b) Actin bundles anchored into an adhesion plaquethat connects ECM through transmembrane molecular bonds.Focal adhesions can be exposed to cytoskeletally generatedcontractile forces in actin bundles, as well as externally appliedloads outside of the cell.


    The adhesion between cell and ECM is often localizedto discrete contact regions called focal adhesions(FAs) [8], as illustrated in figure 1a. FAs usuallyevolve from small dot-like adhesions, commonly referredto as focal complexes (FXs), which are continuouslyformed and turned over under the protruding lame-llipodia [9]. Mature and stable FAs depend on theclustering of molecular bonds, creating an adhesionplaque of complex macromolecular assemblies in whichmany cytoskeletal filaments are anchored (figure 1b).The recruitment of actin filaments and integrin receptorsto the contact regime is essential to FAs, and artificiallymutated integrins that lack an ability to connect withcytoskeletal filaments often fail to cluster and areunable to form stable adhesions [1]. Experimentally,the adhesion clusters between cell and matrix werefound to have a characteristic length scale in the orderof a few micrometres [10,11].

    The elastic properties of cytoskeleton and ECM playan essential role in the maintenance and development ofFAs. One striking example is that stem cells will differ-entiate into different lineage cell types on substrates ofdifferent elastic rigidity [12]. Experiments have shownthat many cell types spread and exhibit more polarizedFAs on stiffer than on softer matrices [1315], and cellstend to actively migrate towards stiffer regions whencultured on an elastically non-homogeneous substrate,a process known as durotaxis [16]. In vitro studies ofcross-linked networks of actin bundles and other biopo-lymer networks showed that their elastic modulus canincrease over several orders of magnitude in responseto different levels of applied stress owing to the entropicelasticity of filaments [17,18]. Moreover, some cells suchas fibroblasts can tune the stiffness of their cytoskeletonto match that of the substrate [19]. Other studies haveshown that a contracting cytoskeleton can be used tosense mechanical properties of the ECM and in turnaffect cell behaviours [20]; whether stiffness tuning ofthe cytoskeleton is the most important factor remainsunclear.

    Serving as the mechanical anchorage between celland matrix, FAs are usually exposed to forces inducedby external physical interactions such as blood flow,as well as those generated by the cells own contractilemachinery as stress fibres made of bundles of actin fila-ments and myosin II motors actively pull FAs towardsthe inside of the cell. The growth or shrinkage of FAsis strongly influenced by the magnitude of forcesapplied on it. Inhibition of the cytoskeletal contractilityleads to dissolution of cytoskeleton and decrease of FAs[21], resulting in small, diffraction-limited spots withlow traction stress near the cell periphery at the baseof the lamellipodia. When myosin II activity is sup-pressed, application of an external force, irrespective

    J. R. Soc. Interface (2011)

    of its physical origin, is found to stimulate growth ofFAs in the direction of the force [22,23]. In the case ofcell-generated tension, experiments have also shownthat the size of mature FAs can reversibly increase ordecrease in response to the magnitude of the appliedforce, with force per unit area (stress) maintainednear a constant value around 5.5 kPa, which is remark-ably similar for stationary cells of different types[24,25], although exceptional cases in which somesmall adhesions may produce non-proportionally highforces were also revealed [25,26]. Possible mechanismsby which externally applied forces and cytoskeleton-generated forces could exert changes in cell adhesioninclude force-induced protein unfolding with exposureor protection of binding sequences and conformationalchange of integrins (a more extended conformation isthought to enhance binding to ECM) [2729]. Despitethis line of studies demonstrating that forces affectprotein structure and cellular function, it remainsunclear whether mechanotransduction sharescommon mechanisms from physics or mechanics pointof views.


    Quantitative analysis and modelling of dynamic cellattachment are crucial for advancing conceptualinsights along with technological applications. Anearly theory for describing cell adhesion was establishedby Bell [30] in a thermodynamic framework. Theprocess of adhesion or de-adhesion of cells from sub-strates was subsequently modelled via peeling teststhat are familiar in engineering design but is mademore complicated by the biological interface and geo-metry involved [31,32]. More recent progresses havebeen made in modelling curved biological membranesspreading on a flat substrate mediated by binder dif-fusion [33,34], as well as receptor-mediated cellularuptake and