Effects of domain unfolding and catch-like dissociation on the collective behavior of integrin–fibronectin bond clusters


To gain more understanding of cell–matrix adhesion, we consider an idealized theoretical model of a cluster of integrin–fibronectin bonds at the cell–matrix interface subjected to a dynamic ramping. The distributions of bond traction and interfacial deformation are assumed to obey classical elastic equations, whereas the dissociation/association of individual bonds as well as unfolding/refolding of fibronectin domains are described by stochastic equations. Through stochastic-elasticity coupling, we perform Monte Carlo simulations to investigate how the collective behavior and adhesion performance of the integrin–fibronectin-mediated interface are influenced by two characteristics newly incorporated in the modeling, i.e., catch-like dissociation between integrin and fibronectin, and unfolding of repeated domains in fibronectin. The probable unfolding of fibronectin domains is found to have profound effects on the resultant adhesion energy of the integrin–fibronectin-mediated interface, and governs the failure model transiting between uniform decay and catastrophic crack-like rupture.

Graphic abstract

Focal adhesions containing integrin–fibronectin bond clusters play a vital role in a wide variety of cellular processes or functions. We develop a stochastic-elasticity modeling framework for such specific interaction at cell–matrix interface, by unifying the elastic descriptions of force distribution and deformation, and the stochastic descriptions of bond dissociation/association and domain unfolding/folding. The present modeling reveals a rich array of out-of-equilibrium behaviors of the integrin–fibronectin-mediated interface, and may provide clues for the development of artificial domain-containing structures and functional surfaces to modulate the collective behavior of bond-mediated cell–matrix adhesion.

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  1. 1.

    Li, N., Lu, S., Zhang, Y., et al.: Mechanokinetics of receptor–ligand interactions in cell adhesion. Acta Mech. Sin. 31, 248–258 (2015)

    Article  Google Scholar 

  2. 2.

    Chen, Y., Ju, L., Rushdi, M., et al.: Receptor-mediated cell mechanosensing. Mol. Biol. Cell 28, 3134–3155 (2017)

    Article  Google Scholar 

  3. 3.

    Huang, G., Xu, F., Genin, G.M., et al.: Mechanical microenvironments of living cells: a critical frontier in mechanobiology. Acta Mech. Sin. 35, 265–269 (2019)

    Article  Google Scholar 

  4. 4.

    Chen, C.S., Mrksich, M., Huang, S., et al.: Geometric control of cell life and death. Science 276, 1425–1428 (1997)

    Article  Google Scholar 

  5. 5.

    Ridley, A.J., Schwartz, M.A., Burridge, K., et al.: Cell migration: integrating signals from front to back. Science 302, 1704–1709 (2003)

    Article  Google Scholar 

  6. 6.

    He, S., Li, X., Ji, B.H.: Mechanical force drives the polarization and orientation of cells. Acta Mech. Sin. 35, 275–288 (2019)

    Article  Google Scholar 

  7. 7.

    Xu, G.K., Li, B., Feng, X.Q., et al.: A tensegrity model of cell reorientation on cyclically stretched substrates. Biophys. J. 111, 1478–1486 (2016)

    Article  Google Scholar 

  8. 8.

    Lin, S.Z., Xue, S.L., Li, B., et al.: An oscillating dynamic model of collective cells in a monolayer. J. Mech. Phys. Solids 112, 650–666 (2018)

    MathSciNet  Article  Google Scholar 

  9. 9.

    Liu, H., Fang, C., Gong, Z., et al.: Fundamental characteristics of neuron adhesion revealed by forced peeling and time-dependent healing. Biophys. J. 118, 1811–1819 (2020)

    Article  Google Scholar 

  10. 10.

    Florin, E.L., Moy, V.T., Gaub, H.E.: Adhesion forces between individual ligand-receptor pairs. Science 264, 415–417 (1994)

    Article  Google Scholar 

  11. 11.

    Alon, R., Hammer, D.A., Springer, T.A.: Lifetime of the P-selectin-carbohydrate bond and its response to tensile force in hydrodynamic flow. Nature 374, 539–542 (1995)

    Article  Google Scholar 

  12. 12.

    Leckband, D., Israelachvili, J.: Intermolecular forces in biology. Q. Rev. Biophys. 34, 105–267 (2001)

    Article  Google Scholar 

  13. 13.

    Evans, E., Ritchie, K.: Dynamic strength of molecular adhesion bonds. Biophys. J. 72, 1541–1555 (1997)

    Article  Google Scholar 

  14. 14.

    Evans, E.: Probing the relation between force-lifetime and chemistry in single molecular bonds. Annu. Rev. Biophys. Biomol. Struct. 30, 105–128 (2001)

    Article  Google Scholar 

  15. 15.

    Chesla, S.E., Selvaraj, P., Zhu, C.: Measuring two-dimensional receptor–ligand binding kinetics by micropipette. Biophys. J. 75, 1553–1572 (1998)

    Article  Google Scholar 

  16. 16.

    Dettmann, W., Grandbois, M., Andre, S., et al.: Differences in zero-force and force-driven kinetics of ligand dissociation from beta-galactoside-specific proteins (plant and animal lectins, immunoglobulin G) monitored by plasmon resonance and dynamic single molecule force microscopy. Arch. Biochem. Biophys. 383, 157–170 (2000)

    Article  Google Scholar 

  17. 17.

    Zhu, C., Long, M., Chesla, S.E., et al.: Measuring receptor/ligand interaction at the single-bond level: experimental and interpretative issues. Ann. Biomed. Eng. 30, 305–314 (2002)

    Article  Google Scholar 

  18. 18.

    Marshall, B.T., Long, M., Piper, J.W., et al.: Direct observation of catch bonds involving cell-adhesion molecules. Nature 423, 190–193 (2003)

    Article  Google Scholar 

  19. 19.

    Sarangapani, K.K., Yago, T., Klopocki, A.G., et al.: Low force decelerates L-selectin dissociation from P-selectin glycoprotein ligand-1 and endoglycan. J. Biol. Chem. 279, 2291–2298 (2004)

    Article  Google Scholar 

  20. 20.

    Kong, F., Garcia, A.J., Mould, A.P., et al.: Demonstration of catch bonds between an integrin and its ligand. J. Cell Biol. 185, 1275–1284 (2009)

    Article  Google Scholar 

  21. 21.

    Guo, B., Guilford, W.H.: Mechanics of actomyosin bonds in different nucleotide states are tuned to muscle contraction. Proc. Natl. Acad. Sci. USA 103, 9844–9849 (2006)

    Article  Google Scholar 

  22. 22.

    Li, W., Wong, W.J., Lim, C.J., et al.: Catch-bond behavior of DNA condensate under tension. Chin. Phys. B 24, 128704 (2015)

    Article  Google Scholar 

  23. 23.

    Litvinov, R.I., Kononova, O., Zhmurov, A., et al.: Regulatory element in fibrin triggers tension-activated transition from catch to slip bonds. Proc. Natl. Acad. Sci. USA 115, 8575–8580 (2018)

    Article  Google Scholar 

  24. 24.

    Li, L., Kang, W., Wang, J.Z.: Mechanical model for catch bond mediated cell adhesion in shear flow. Int. J. Mol. Sci. 21, 584 (2020)

    Article  Google Scholar 

  25. 25.

    Bell, G.I.: Models for specific adhesion of cells to cells. Science 200, 618–627 (1978)

    Article  Google Scholar 

  26. 26.

    Erdmann, T., Schwarz, U.S.: Stochastic dynamics of adhesion clusters under shared constant force and with rebinding. J. Chem. Phys. 121, 8997–9017 (2004)

    Article  Google Scholar 

  27. 27.

    Erdmann, T., Schwarz, U.S.: Stability of adhesion clusters under constant force. Phys. Rev. Lett. 92, 108102 (2004)

    Article  Google Scholar 

  28. 28.

    Lin, J., Qian, J., Yin, J., et al.: Biointerfaces mediated by molecular bonds: cohesive behaviors. Int. J. Appl. Mech. 8, 1650040 (2016)

    Article  Google Scholar 

  29. 29.

    Wang, J.Z., Gao, H.J.: Clustering instability in adhesive contact between elastic solids via diffusive molecular bonds. J. Mech. Phys. Solids 56, 251–266 (2008)

    MathSciNet  MATH  Article  Google Scholar 

  30. 30.

    Qian, J., Wang, J.Z., Gao, H.J.: Lifetime and strength of adhesive molecular bond clusters between elastic media. Langmuir 24, 1262–1270 (2008)

    Article  Google Scholar 

  31. 31.

    Qian, J., Wang, J.Z., Lin, Y., et al.: Lifetime and strength of periodic bond clusters between elastic media under inclined loading. Biophys. J. 97, 2438–2445 (2009)

    Article  Google Scholar 

  32. 32.

    Gao, H.J., Qian, J., Chen, B.: Probing mechanical principles of focal contacts in cell–matrix adhesion with a coupled stochastic-elastic modelling framework. J. R. Soc. Interface 8, 1217–1232 (2011)

    Article  Google Scholar 

  33. 33.

    He, K., Li, L., Wang, J.: Diffusive-stochastic-viscoelastic model for specific adhesion of viscoelastic solids via molecular bonds. Acta Mech. Sin. 35, 343–354 (2019)

    MathSciNet  Article  Google Scholar 

  34. 34.

    Qian, J., Lin, J., Xu, G.K., et al.: Thermally assisted peeling of an elastic strip in adhesion with a substrate via molecular bonds. J. Mech. Phys. Solids 101, 197–208 (2017)

    MathSciNet  Article  Google Scholar 

  35. 35.

    Kaurin, D., Arroyo, M.: Surface tension controls the hydraulic fracture of adhesive interfaces bridged by molecular bonds. Phys. Rev. Lett. 123, 228102 (2019)

    Article  Google Scholar 

  36. 36.

    Oberhauser, A.F., Marszalek, P.E., Erickson, H.P.: The molecular elasticity of the extracellular matrix protein tenascin. Nature 393, 181–185 (1998)

    Article  Google Scholar 

  37. 37.

    Rief, M., Gautel, M., Oesterhelt, F., et al.: Reversible unfolding of individual titin immunoglobulin domains by AFM. Science 276, 1109–1112 (1997)

    Article  Google Scholar 

  38. 38.

    Rief, M., Fernandez, J.M., Gaub, H.E.: Elastically coupled two-level systems as a model for biopolymer extensibility. Phys. Rev. Lett. 81, 4764–4767 (1998)

    Article  Google Scholar 

  39. 39.

    Pereverzev, Y.V., Prezhdo, O.V., Sokurenko, E.V.: Regulation of catch binding by allosteric transitions. J. Phys. Chem. B 114, 11866–11874 (2010)

    Article  Google Scholar 

  40. 40.

    Lin, J., Lin, Y., Qian, J.: Concurrent rupture of two molecular bonds in series: implications for dynamic force spectroscopy. J. Appl. Mech. Trans. ASME 84, 111007 (2017)

    Article  Google Scholar 

  41. 41.

    Bustamante, C., Marko, J.F., Siggia, E.D., et al.: Entropic elasticity of lambda-phage DNA. Science 265, 1599–1600 (1994)

    Article  Google Scholar 

  42. 42.

    Gardel, M.L., Shin, J.H., MacKintosh, F.C., et al.: Elastic behavior of cross-linked and bundled actin networks. Science 304, 1301–1305 (2004)

    Article  Google Scholar 

  43. 43.

    Storm, C., Pastore, J.J., MacKintosh, F.C., et al.: Nonlinear elasticity in biological gels. Nature 435, 191–194 (2005)

    Article  Google Scholar 

  44. 44.

    Gong, B., Lin, J., Wei, X., et al.: Cross-linked biopolymer networks with active motors: mechanical response and intra-network transport. J. Mech. Phys. Solids 127, 80–93 (2019)

    Article  Google Scholar 

  45. 45.

    Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (1987)

    Google Scholar 

  46. 46.

    Erdmann, T., Schwarz, U.S.: Impact of receptor–ligand distance on adhesion cluster stability. Eur. Phys. J. E 22, 123–137 (2007)

    Article  Google Scholar 

  47. 47.

    Li, L., Yao, H.M., Wang, J.Z.: Dynamic strength of molecular bond clusters under displacement- and force-controlled loading conditions. J. Appl. Mech. Trans. ASME 83, 021004 (2016)

    Article  Google Scholar 

  48. 48.

    Li, L., Zhang, W.Y., Wang, J.Z.: A viscoelastic-stochastic model of the effects of cytoskeleton remodelling on cell adhesion. R. Soc. Open Sci. 3, 160539 (2016)

    MathSciNet  Article  Google Scholar 

  49. 49.

    Xu, G.K., Yang, C., Du, J., et al.: Integrin activation and internalization mediated by extracellular matrix elasticity: a biomechanical model. J. Biomech. 47, 1479–1484 (2014)

    Article  Google Scholar 

  50. 50.

    Huang, Q., Wang, J.: Use of loading devices with low stiffness may cause uncertainty in measuring the strength of cellular adhesion. J. Mech. Phys. Solids 142, 103970 (2020)

    MathSciNet  Article  Google Scholar 

  51. 51.

    Qian, J., Gao, H.J.: Soft matrices suppress cooperative behaviors among receptor–ligand bonds in cell adhesion. PLoS ONE 5, e12342 (2010)

    Article  Google Scholar 

  52. 52.

    Qin, Y., Li, Y., Zhang, L.Y., et al.: Stochastic fluctuation-induced cell polarization on elastic substrates: a cytoskeleton-based mechanical model. J. Mech. Phys. Solids 137, 103872 (2020)

    MathSciNet  Article  Google Scholar 

  53. 53.

    Chung, J., Kushner, A.M., Weisman, A.C., et al.: Direct correlation of single-molecule properties with bulk mechanical performance for the biomimetic design of polymers. Nat. Mater. 13, 1055–1062 (2014)

    Article  Google Scholar 

  54. 54.

    Mashaghi, A., Bezrukavnikov, S., Minde, D.P., et al.: Alternative modes of client binding enable functional plasticity of Hsp70. Nature 539, 448–451 (2016)

    Article  Google Scholar 

  55. 55.

    Zhu, F.B., Cheng, L.B., Wang, Z.J., et al.: 3D-printed ultratough hydrogel structures with titin-like domains. ACS Appl. Mater. Interfaces 9, 11363–11367 (2017)

    Article  Google Scholar 

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This work was supported by the National Natural Science Foundation of China (Grants 11672268 and 91748209) and the Fundamental Research Funds for Central Universities of China (Grant 2020XZZX005-02).

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Correspondence to Jin Qian.

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Executive Editor: Xi-Qiao Feng



Two-state model for catch bond between integrin and fibronectin

The two-state model assumes that there are two binding sites for \({\alpha_{5} }\beta_{1}\)-fibronectin bond, with the following ordinary kinetic equations that govern the evolution of states in these two allosteric sites:

$${{\frac{{{\text{d}}P_{{1}} \left( {t,f} \right)}}{{{\text{d}}t}} = - k_{{{12}}} \left( f \right)P_{{1}} \left( {t,f} \right) + k_{{{21}}} \left( f \right)P_{{2}} \left( {t,f} \right)},\,\frac{{{\text{d}}P_{{2}} \left( {t,f} \right)}}{{{\text{d}}t}} = - k_{{{21}}} \left( f \right)P_{{2}} \left( {t,f} \right) + k_{{{12}}} \left( f \right)P_{{1}} \left( {t,f} \right)},$$

where \({P_{{1}} \left( {t,f} \right)}\), \({P_{{2}} \left( {t,f} \right)}\) denote the probability for the allosteric sites subjected to force \(f\) to exist in states 1 and 2 at time \(t\), respectively. \({k_{{{12}}} \left( f \right) = k_{{{12}}}^{{0}} {\text{exp}}\left[ {{{x_{{{12}}} f} \mathord{\left/ {\vphantom {{x_{{{12}}} f} {(k_{{\text{B}}} T}}} \right. \kern-\nulldelimiterspace} {(k_{{\text{B}}} T}})} \right]}\) and \({k_{{{21}}} \left( f \right) = k_{{{21}}}^{{0}} {\text{exp}}\left[ { - {{x_{{{21}}} f} \mathord{\left/ {\vphantom {{x_{{{21}}} f} {(k_{{\text{B}}} T)}}} \right. \kern-\nulldelimiterspace} {(k_{{\text{B}}} T)}}} \right]}\) are the rates for the reversible transition between the two states, with \({k_{{{12}}}^{{0}} }\), \({k_{{{21}}}^{{0}} }\) being the rate constants in the absence of force and \({x_{{{12}}} }\), \({x_{{{21}}} }\) being the widths of the activation barrier for the corresponding transition to occur. It is natural to assume that when \({f = {0}}\) at the beginning of evolution, the two probabilities are in thermodynamic equilibrium, thus the right-sides in Eq. (A1) can be set to zero. Therefore, the initial values of probability at two sites should be \({P_{{1}} \left( {0,0} \right) = {{k_{{{21}}}^{{0}} } \mathord{\left/ {\vphantom {{k_{{{21}}}^{{0}} } {\left( {k_{{{12}}}^{{0}} + k_{{{21}}}^{{0}} } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {k_{{{12}}}^{{0}} + k_{{{21}}}^{{0}} } \right)}}}\) and \({P_{{2}} \left( {0,0} \right) = {{k_{{{12}}}^{{0}} } \mathord{\left/ {\vphantom {{k_{{{12}}}^{{0}} } {\left( {k_{{{12}}}^{{0}} + k_{{{21}}}^{{0}} } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {k_{{{12}}}^{{0}} + k_{{{21}}}^{{0}} } \right)}}}\), respectively. Using these two initial conditions, the solution to Eq. (A1) for \(f \ne 0\) is given by

$${P_{{1}} \left( {t,f} \right) = q\left( f \right) + \left[ {q\left( {0} \right) - q\left( f \right)} \right]{\text{exp}}\left[ { - {t \mathord{\left/ {\vphantom {t {\tau_{r} \left( f \right)}}} \right. \kern-\nulldelimiterspace} {\tau_{r} \left( f \right)}}} \right],\quad P_{{2}} \left( {t,f} \right) = {1} - P_{{1}} \left( {t,f} \right),}$$


$${\tau_{{\text{r}}} \left( f \right) = {{1} \mathord{\left/ {\vphantom {{1} {\left[ {k_{{{12}}} \left( f \right) + k_{{{21}}} \left( f \right)} \right]}}} \right. \kern-\nulldelimiterspace} {\left[ {k_{{{12}}} \left( f \right) + k_{{{21}}} \left( f \right)} \right]}}}$$

being a characteristic relaxation time of the two-state allosteric site and \({q\left( f \right) = k_{{{21}}} \left( f \right)\tau_{{\text{r}}} \left( f \right)}\) being a normalized quantity that represents the transition rate \({k_{{{21}}} }\), subjected to external force \(f\). Using Bell’s model, the escape rates of integrin–fibronectin bond from the two binding sites are determined by \({k_{{1}} = k_{{1}}^{{0}} {\text{exp}}\left[ {{{x_{{1}} f} \mathord{\left/ {\vphantom {{x_{{1}} f} {(k_{{\text{B}}} T)}}} \right. \kern-\nulldelimiterspace} {(k_{{\text{B}}} T)}}} \right]}\), \({k_{{2}} = k_{{2}}^{{0}} {\text{exp}}\left[ {{{x_{{2}} f} \mathord{\left/ {\vphantom {{x_{{2}} f} {(k_{{\text{B}}} T)}}} \right. \kern-\nulldelimiterspace} {(k_{{\text{B}}} T)}}} \right]}\), respectively. Here, \({k_{{1}}^{{0}} }\), \({k_{{2}}^{{0}} }\) are the rate constants in the absence of force, and \({x_{{1}} }\), \({x_{{2}} }\) are the widths of the corresponding activation barrier. Combining two dissociation rates with the probabilities at two allosteric sites in Eq. (A2), we obtain the dissociation rate of the catch bond as

$${k_{{{\text{off}}}}^{{{\text{catch}}}} \left( {t,f} \right) = k_{{1}} \left( f \right)P_{{1}} \left( {t,f} \right) + k_{{2}} \left( f \right)P_{{2}} \left( {t,f} \right)}.$$

Extracting \({{\varvec{\upalpha}}}_{5}{{\varvec{\upbeta}}}_{1}\)-fibronectin dissociation kinetics by excluding the effect of anchoring protein

We should notice that in the original atomic force microscopy (AFM) experiments on \({\alpha_{{5}} \beta_{{1}} }\)-fibronectin dissociation [20], the integrin molecules were immobilized on the substrate surface through anchoring protein GG-7, adding an extra slip bond with a dissociation coefficient \({k_{{{\text{off}}}}^{{{\text{slip}}}} = k_{{\text{s}}}^{{0}} {\text{exp}}\left[ {{{x_{{\text{s}}} f} \mathord{\left/ {\vphantom {{x_{{\text{s}}} f} {(k_{{\text{B}}} T)}}} \right. \kern-\nulldelimiterspace} {(k_{{\text{B}}} T)}}} \right]}\). Here, \({k_{{\text{s}}}^{{0}} }\) is the rate constant at zero force, and \({x_{{\text{s}}} }\) is the width of the energy barrier. The values of slip bond parameters (for GG-7) are found to be \({k_{{\text{s}}}^{{0}} = {0}{\text{.016 s}}^{{ - 1}} }\) and \({x_{{\text{s}}} = {0}{\text{.27 nm}}}\) [39], which means a quite strong linking between integrin and GG-7. In the presence of sequential chain of the allosteric and slip contacts, the survival probability of GG-7-\({\alpha_{{5}} \beta_{{1}} }\)-fibronectin chain, \({P_{{{\text{all}}}} \left( {t,f} \right)}\), should obey the following kinetic equation:

$${\frac{{{\text{d}}P_{{{\text{all}}}} \left( {t,f} \right)}}{{{\text{d}}t}} + \left[ {k_{{{\text{off}}}}^{{{\text{catch}}}} \left( {t,f} \right) + k_{{{\text{off}}}}^{{{\text{slip}}}} \left( f \right)} \right]P_{{{\text{all}}}} \left( {t,f} \right) = {0}}.$$

This equation can be solved by combining Eqs. (A2) to (A4) together with the initial condition that the bond is intact at \({t = {0}}\) (\({P_{{{\text{all}}}} \left( {{0},f} \right) = {1}}\))

$${P_{{{\text{all}}}} \left( {t,f} \right) = {\text{exp}}\left\{ { - {t \mathord{\left/ {\vphantom {t {\tau_{{{\text{all}}}} \left( f \right)}}} \right. \kern-\nulldelimiterspace} {\tau_{{{\text{all}}}} \left( f \right)}} + h\left( f \right)\left\{ {{\text{exp}}\left[ { - {t \mathord{\left/ {\vphantom {t {\tau_{{\text{r}}} \left( f \right)}}} \right. \kern-\nulldelimiterspace} {\tau_{{\text{r}}} \left( f \right)}}} \right] - {1}} \right\}} \right\}},$$

where \({\tau_{{{\text{all}}}} \left( f \right) = k_{{2}} \left( f \right) + \frac{{k_{{{21}}} \left( f \right)\left[ {k_{{1}} \left( f \right) - k_{{2}} \left( f \right)} \right]}}{{k_{{{12}}} \left( f \right) + k_{{{21}}} \left( f \right)}} + k_{{{\text{off}}}}^{{{\text{slip}}}} \left( f \right)}\) is a combination of rate coefficients, and

$${h\left( f \right) = \left[ {q\left( {0} \right) - q\left( f \right)} \right]\left[ {k_{{1}} \left( f \right) - k_{{2}} \left( f \right)} \right]\tau_{{\text{r}}} \left( f \right)},$$

The average lifetime \({T_{{{\text{all}}}} }\) of this sequential chain is given by integration of the survival probability over time

$$T_{{{\text{all}}}} = \int\limits_{0}^{\infty } {P_{{{\text{all}}}} \left( {t,f} \right){\text{d}}t} .$$

Choosing appropriate parameters for the two-state model in Eq. (A4) as follow, \({x_{{1}} = x_{{2}} = {0}{\text{.15 nm}}}\)\({x_{{{12}}} = x_{{{21}}} = {0}{\text{.6 nm}}}\), \({k_{{1}}^{{0}} = {\text{3 s}}^{{ - 1}} }\), \({k_{{2}}^{{0}} = {0}{\text{.003 s}}^{{ - 1}} }\), \({k_{{{12}}}^{{0}} = {\text{2 s}}^{{ - 1}} }\), \({k_{{{21}}}^{{0}} = {\text{20 s}}^{{ - 1}} }\), we can theoretically reproduce the experimental data. Neglecting the \({k_{{{\text{off}}}}^{{{\text{slip}}}} \left( f \right)}\) term in Eq. (A5), we can derive a new force dependence of lifetime for the integrin–fibronectin bonding

$$T_{{{\text{catch}}}} = \int\limits_{0}^{\infty } {P_{{{\text{catch}}}} \left( {f,t} \right){\text{d}}t},$$

with the survival probability of catch bond being

$${P_{{{\text{catch}}}} \left( {t,f} \right) = {\text{exp}}\left\{ { - {t \mathord{\left/ {\vphantom {t {\tau_{{{\text{catch}}}} \left( f \right)}}} \right. \kern-\nulldelimiterspace} {\tau_{{{\text{catch}}}} \left( f \right)}} + h\left( f \right)\left\{ {{\text{exp}}\left[ { - {t \mathord{\left/ {\vphantom {t {\tau_{{\text{r}}} \left( f \right)}}} \right. \kern-\nulldelimiterspace} {\tau_{{\text{r}}} \left( f \right)}}} \right] - {1}} \right\}} \right\}},$$

where \({\tau_{{{\text{catch}}}} = k_{{2}} + \frac{{k_{{{21}}} \left( {k_{{1}} - k_{{2}} } \right)}}{{k_{{{12}}} + k_{{{21}}} }}}\) and the expressions for \({\tau_{{\text{r}}} \left( f \right)}\) and \({h\left( f \right)}\) are shown in Eqs. (A3) and (A7). Therefore, the probability of catch bond dissociation is

$${P_{{{\text{off}}}} = {1} - P_{{{\text{catch}}}}}.$$

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Lin, J., Wang, Y. & Qian, J. Effects of domain unfolding and catch-like dissociation on the collective behavior of integrin–fibronectin bond clusters. Acta Mech. Sin. (2021). https://doi.org/10.1007/s10409-020-01039-x

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  • Integrin–fibronectin complex
  • Cell–matrix adhesion
  • Domain unfolding
  • Catch bond
  • Rate dependence
  • Modulus effect