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• W2021884668 abstract "Most animal cell types sensitively react to the stiffness of their environment, with dramatic consequences for essential cellular processes such as adhesion, migration, differentiation, and cell fate. For example, many cell types migrate toward stiffer regions in their environment (durotaxis) (1Lo C.-M. Wang H.-B. Wang Y.-L. et al.Cell movement is guided by the rigidity of the substrate.Biophys. J. 2000; 79: 144-152Abstract Full Text Full Text PDF PubMed Scopus (2535) Google Scholar). During the last decade, cell-matrix contacts based on the transmembrane adhesion receptors from the integrin family (focal adhesions) have emerged as the mechanosensitive organelles that collect, process, and integrate the information on extracellular stiffness (2Geiger B. Spatz J.P. Bershadsky A.D. Environmental sensing through focal adhesions.Nat. Rev. Mol. Cell Biol. 2009; 10: 21-33Crossref PubMed Scopus (1876) Google Scholar); their mechanosensory function is thought to be an integral part of stiffness-dependent cellular processes. By actively pulling on the substrate through actomyosin contractility and focal adhesions, the cells are able to sense its stiffness. With >180 different components being reported in the literature (where this collection of components is collectively known as the “adhesome”), the molecular complexity of focal adhesions is overwhelming (3Zaidel-Bar R. Geiger B. The switchable integrin adhesome.J. Cell Sci. 2010; 123: 1385-1388Crossref PubMed Scopus (260) Google Scholar). Recent proteomic studies have not only found many more components, but also have revealed that many of them are recruited to focal adhesions in a force-dependent manner (4Kuo J.-C. Han X. Waterman C.M. et al.Analysis of the myosin-II-responsive focal adhesion proteome reveals a role for β-Pix in negative regulation of focal adhesion maturation.Nat. Cell Biol. 2011; 13: 383-393Crossref PubMed Scopus (437) Google Scholar, 5Schiller H.B. Hermann M.-R. Fässler R. et al.β1- and αv-class integrins cooperate to regulate myosin II during rigidity sensing of fibronectin-based microenvironments.Nat. Cell Biol. 2013; 15: 625-636Crossref PubMed Scopus (309) Google Scholar), supporting the view that focal adhesions harbor a network of mechanosensitive processes (6Schwarz U.S. Gardel M.L. United we stand: integrating the actin cytoskeleton and cell-matrix adhesions in cellular mechanotransduction.J. Cell Sci. 2012; 125: 3051-3060Crossref PubMed Scopus (256) Google Scholar). Despite the molecular complexity of focal adhesions, however, one expects that regulation of the integrin receptors through force would be at the core of the mechanosensitive function of focal adhesions. For focal adhesions of cultured tissue cells, the two most relevant of the 24 known integrin variants in humans are the α5β1- and αvβ3-integrins. Recently it has been shown with single molecule force spectroscopy that the bonds mediated by α5β1-integrins are so-called “catch bonds” (7Kong F. García A.J. Zhu C. et al.Demonstration of catch bonds between an integrin and its ligand.J. Cell Biol. 2009; 185: 1275-1284Crossref PubMed Scopus (489) Google Scholar). In contrast to the standard case of slip bonds, catch bonds possess the unusual physical property that at intermediate forces their lifetimes increase rather than decrease with increasing force (at high forces, they usually become slip bonds again). Other important examples for catch bonds are the bonds mediated by the selectin receptors capturing leukocytes in shear flow and the binding of myosin II to an actin filament during its motor cycle. In an article appearing in this issue of the Biophysical Journal, Novikova and Storm (8Novikova E.A. Storm C. Contractile fibers and catch bond clusters: a biological force sensor?.Biophys. J. 2013; 105: 1336-1345Abstract Full Text Full Text PDF PubMed Scopus (41) Google Scholar) present an elegant mathematical analysis of how stiffness-sensing at focal adhesions might arise from the interplay of catch-bond dynamics in the integrin layer and intracellular force generation through contractile fibers. To put the analysis by Novikova and Storm into context, it is instructive to recall the classical treatment by Bell, who mathematically analyzed the statistics of an ensemble of Nt parallel slip bonds, each of which can be either open or closed (9Bell G.I. Models for the specific adhesion of cells to cells.Science. 1978; 200: 618-627Crossref PubMed Scopus (3414) Google Scholar, 10Erdmann T. Schwarz U.S. Stability of adhesion clusters under constant force.Phys. Rev. Lett. 2004; 92: 108102Crossref PubMed Scopus (150) Google Scholar). If we denote the number of closed bonds at time t by N(t) (0 ≤ N(t) ≤ Nt), it dynamically evolves according to the following kinetic equation:dNdt=−NeF/N+γ(Nt−N).(1) The first term represents dissociation of the closed bonds and the second term describes rebinding of the open bonds with a dimension-less rebinding rate γ. For dissociation, it is assumed that the total force F (in units of an internal force scale of the order of pN) is shared equally between all closed bonds, and that single bonds dissociate more rapidly under larger force. For such slip bonds, the exponential relation between force and dissociation rate can be rationalized with Kramer’s theory for thermally activated escape over a transition state barrier (11Evans E. Ritchie K. Dynamic strength of molecular adhesion bonds.Biophys. J. 1997; 72: 1541-1555Abstract Full Text PDF PubMed Scopus (2061) Google Scholar). Setting the time derivate in Eq. 1 to zero and solving for the steady-state number of closed bonds N as a function of force F reveals that the adhesion cluster is only stable up to a critical force Fc = Nt plog (γ/e), where the product logarithm x = plog(a) solves the equation xex = a (linear for small arguments). Thus, a finite rebinding rate γ ensures that the adhesion cluster is stable under not-too-large values of mechanical loading. Mathematically, the critical force Fc corresponds to a saddle-node bifurcation, where a stable and an unstable branch annihilate each other. As shown in Fig. 1 a, the stable branch for the number of closed bonds N is a relatively weak and decreasing function of force F. To extend this classical slip-bond analysis to the α5β1-integrin catch-bond cluster, Novikova and Storm fitted its experimentally determined dissociation rate as a function of force to the two-pathway model for catch bonds (12Pereverzev Y.V. Prezhdo O.V. Thomas W.E. et al.The two-pathway model for the catch-slip transition in biological adhesion.Biophys. J. 2005; 89: 1446-1454Abstract Full Text Full Text PDF PubMed Scopus (154) Google Scholar). The resulting dissociation rate has a minimum at intermediate forces and can be used to appropriately modify the slip-bond dissociation term in Eq. 1. The kinetic equation then becomesdNdt=−2Ncosh(F/N−ϕmax)α+γ(Nt−N),(2) and can be analyzed with the same methods as Eq. 1 (here ϕmax = 5.9 and α = 6.55 are dimensionless numbers resulting from the data fit). One again finds a saddle-node bifurcation, thus also in this case the cluster is stable only up to a critical force Fc (this reflects the actual catch-slip bond character). However, in marked contrast to the slip-bond case first analyzed by Bell (9Bell G.I. Models for the specific adhesion of cells to cells.Science. 1978; 200: 618-627Crossref PubMed Scopus (3414) Google Scholar), now the steady-state number N of closed bonds is a strongly increasing function of force, as shown in Fig. 1 b. Thus, in the catch-bond case the number of closed bonds N is a clear internal measure for the force F acting on the adhesion cluster, in contrast to the slip-bond case, where N is only weakly dependent on force and decays rather than increases with force. From Fig. 1 b, we also note that the number of closed bonds in the unstressed case is very low due to the large value of the unstressed dissociation rate, whereas the number of closed bonds reaches its maximum very close to the critical force. Novikova and Storm report that similar behavior can be found also for other catch-bond systems, suggesting that catch bonds have evolved to provide reinforcement mainly when acting in clusters. How do these findings relate to stiffness-sensing through focal adhesions? To answer this question, the authors consider the composite system of an elastic environment with stiffness K, a focal adhesion of fixed size (Nt parallel catch bonds), and a contractile fiber pulling on it (with a linearized force-velocity relation for the myosin II motors). This model can be solved analytically and shows that the stiffer the environment, the faster the buildup of the force (13Schwarz U.S. Erdmann T. Bischofs I.B. Focal adhesions as mechanosensors: the two-spring model.Biosystems. 2006; 83: 225-232Crossref PubMed Scopus (136) Google Scholar). Novikova and Strom show that if one assumes that the cells invest a constant amount of work W into pulling on the substrate through a given focal adhesion, it reaches the force level F = (2WK)1/2. Because the number of closed bonds N in the catch-bond cluster increases roughly linearly with force (compare Fig. 1 b), this formula implies that it increases roughly as the square-root of external stiffness. In summary, the authors have shown that the number of closed bonds N in the catch-bond cluster not only provides an internal measure of the force acting on the cluster, but also of the stiffness of the elastic environment. Their focus on the dynamical process of force generation agrees well with the recent finding that the correlation between force and size of focal adhesions is strongest during their growth phase (14Stricker J. Aratyn-Schaus Y. Gardel M.L. et al.Spatiotemporal constraints on the force-dependent growth of focal adhesions.Biophys. J. 2011; 100: 2883-2893Abstract Full Text Full Text PDF PubMed Scopus (152) Google Scholar). It also agrees with the finding that it is mainly the fibronectin-α5β1-integrin bonds that support force in focal adhesions (15Roca-Cusachs P. Gauthier N.C. Sheetz M.P. et al.Clustering of α(5)β(1) integrins determines adhesion strength whereas α(v)β(3) and talin enable mechanotransduction.Proc. Natl. Acad. Sci. USA. 2009; 106: 16245-16250Crossref PubMed Scopus (309) Google Scholar). The elegant and transparent analysis by Novikova and Storm nicely complements an earlier computational analysis of this situation (16Sun L. Cheng Q.H. Zhang Y.W. et al.Effect of loading conditions on the dissociation behavior of catch bond clusters.J. R. Soc. Interface. 2012; 9: 928-937Crossref PubMed Scopus (21) Google Scholar) and shows that the α5β1-integrin catch-bond cluster in combination with a contractile fiber leads to an effective response that resembles the mechanosensory function of single focal adhesions. In the future, this simple model could be extended, with regard to several important aspects. On the one hand, a complete mathematical description of cellular mechanosensing through focal adhesions should go beyond a single focal adhesion in a stationary state and describe a population of dynamically growing, moving, and shrinking focal adhesions (17Walcott S. Sun S.X. A mechanical model of actin stress fiber formation and substrate elasticity sensing in adherent cells.Proc. Natl. Acad. Sci. USA. 2010; 107: 7757-7762Crossref PubMed Scopus (176) Google Scholar). On the other hand, the model for a catch-bond cluster should be extended to include more aspects of the molecular complexity of focal adhesions. For example, it remains to be seen whether the other most prominent integrin in the focal adhesions of tissue cells, αvβ3, is also a catch bond, as suggested by a recent cellular study (5Schiller H.B. Hermann M.-R. Fässler R. et al.β1- and αv-class integrins cooperate to regulate myosin II during rigidity sensing of fibronectin-based microenvironments.Nat. Cell Biol. 2013; 15: 625-636Crossref PubMed Scopus (309) Google Scholar). As it is obvious from Fig. 1 b, the α5β1-integrin catch-bond cluster performs very badly in the unstressed situation, thus other adhesion receptors seem to be required to establish initial contacts. The exact spatiotemporal coordination of the different integrins is an open but very important issue (18Rossier O. Octeau V. Giannone G. et al.Integrins β1 and β3 exhibit distinct dynamic nanoscale organizations inside focal adhesions.Nat. Cell Biol. 2012; 14: 1057-1067Crossref PubMed Scopus (266) Google Scholar). It is also clear that the mechanism studied here has to interact with many other mechanosensitive processes at focal adhesions, including recruitment of additional components under force, and signaling, e.g., through the small GTPases from the Rho-family (4Kuo J.-C. Han X. Waterman C.M. et al.Analysis of the myosin-II-responsive focal adhesion proteome reveals a role for β-Pix in negative regulation of focal adhesion maturation.Nat. Cell Biol. 2011; 13: 383-393Crossref PubMed Scopus (437) Google Scholar, 5Schiller H.B. Hermann M.-R. Fässler R. et al.β1- and αv-class integrins cooperate to regulate myosin II during rigidity sensing of fibronectin-based microenvironments.Nat. Cell Biol. 2013; 15: 625-636Crossref PubMed Scopus (309) Google Scholar). Irrespective of these future developments, however, the generic analysis presented here provides a very useful conceptual framework for the investigator to think about the way adhesion receptors under force collectively act together during stiffness sensing. The author thanks Thorsten Erdmann for helpful discussions and critical comments. The author is a member of the CellNetworks cluster of excellence at Heidelberg and is supported by the EU-program MEHTRICS. Contractile Fibers and Catch-Bond Clusters: a Biological Force Sensor?Novikova et al.Biophysical JournalSeptember 17, 2013In BriefCatch bonds are cellular receptor-ligand pairs whose lifetime, counterintuitively, increases with increasing load. Although their existence was initially pure theoretical speculation, recent years have seen several experimental demonstrations of catch-bond behavior in biologically relevant and functional protein-protein bonds. Particularly notable among these established catch-bond formers is the integrin α5β1, the primary receptor for fibronectin and, as such, a crucial determinant for the characteristics of the mechanical coupling between cell and matrix. Full-Text PDF Open ArchiveCorrection et al.Biophysical JournalOctober 15, 2013In Brief2013. Catch Me Because You Can: A Mathematical Model for Mechanosensing. Ulrich S. Schwarz. Biophys J. 105(6): 1289–1291 Full-Text PDF Open Archive" @default.
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• W2021884668 title "Catch Me Because You Can: A Mathematical Model for Mechanosensing" @default.
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