0
Research Papers

Probing the Instability of a Cluster of Slip Bonds Upon Cyclic Loads With a Coupled Finite Element Analysis and Monte Carlo Method

[+] Author and Article Information
Xiaofeng Chen

Department of Engineering Mechanics,
Zhejiang University,
Hangzhou 310027, China

Bin Chen

Department of Engineering Mechanics,
Zhejiang University,
Hangzhou 310027, China
e-mail: chenb6@zju.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received June 17, 2014; final manuscript received August 20, 2014; accepted manuscript posted August 28, 2014; published online September 17, 2014. Editor: Yonggang Huang.

J. Appl. Mech 81(11), 111002 (Sep 17, 2014) (7 pages) Paper No: JAM-14-1261; doi: 10.1115/1.4028437 History: Received June 17, 2014; Revised August 20, 2014; Accepted August 28, 2014

Cells are subjected to cyclic loads under physiological conditions, which regulate cellular structures and functions. Recently, it was demonstrated that cells on substrates reoriented nearly perpendicular to the stretch direction in response to uni-axial cyclic stretches. Though various theories were proposed to explain this observation, the underlying mechanism, especially at the molecular level, is still elusive. To provide insights into this intriguing observation, we employ a coupled finite element analysis (FEA) and Monte Carlo method to investigate the stability of a cluster of slip bonds upon cyclic loads. Our simulation results indicate that the cluster can become unstable upon cyclic loads and there exist two characteristic failure modes: gradual sliding with a relatively long lifetime versus catastrophic failure with a relatively short lifetime. We also find that the lifetime of the bond cluster, in many cases, decreases with increasing stretch amplitude and also decreases with increasing cyclic frequency, which appears to saturate at high cyclic frequencies. These results are consistent with the experimental reports. This work suggests the possible role of slip bonds in cellular reorientation upon cyclic stretch.

FIGURES IN THIS ARTICLE
<>
Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Neidlinger-Wilke, C., Wilke, H. J., and Claes, L., 1994, “Cyclic Stretching of Human Osteoblasts Affects Proliferation and Metabolism: A New Experimental Method and Its Application,” J. Orthop. Res., 12(1), pp. 70–78. [CrossRef] [PubMed]
Dartsch, P. C., Hammerle, H., and Betz, E., 1986, “Orientation of Cultured Arterial Smooth Muscle Cells Growing on Cyclically Stretched Substrates,” Acta. Anat. (Basel), 125(2), pp. 108–113. [CrossRef] [PubMed]
Kanda, K., and Matsuda, T., 1993, “Behavior of Arterial Wall Cells Cultured on Periodically Stretched Substrates,” Cell Transplant, 2(6), pp. 475–484. [PubMed]
Wang, H., Ip, W., Boissy, R., and Grood, E. S., 1995, “Cell Orientation Response to Cyclically Deformed Substrates: Experimental Validation of a Cell Model,” J. Biomech., 28(12), pp. 1543–1552. [CrossRef] [PubMed]
Kemkemer, R., Neidlinger-Wilke, C., Claes, L., and Gruler, H., 1999, “Cell Orientation Induced by Extracellular Signals,” Cell Biochem. Biophys., 30(2), pp. 167–192. [CrossRef] [PubMed]
Greiner, A. M., Chen, H., Spatz, J. P., and Kemkemer, R., 2013, “Cyclic Tensile Strain Controls Cell Shape and Directs Actin Stress Fiber Formation and Focal Adhesion Alignment in Spreading Cells,” PLoS One, 8(10), p. e77328. [CrossRef] [PubMed]
Wang, J. H., Goldschmidt-Clermont, P., Wille, J., and Yin, F. C., 2001, “Specificity of Endothelial Cell Reorientation in Response to Cyclic Mechanical Stretching,” J. Biomech., 34(12), pp. 1563–1572. [CrossRef] [PubMed]
Kaspar, D., Seidl, W., Neidlinger-Wilke, C., Beck, A., Claes, L., and Ignatius, A., 2002, “Proliferation of Human-Derived Osteoblast-Like Cells Depends on the Cycle Number and Frequency of Uniaxial Strain,” J. Biomech., 35(7), pp. 873–880. [CrossRef] [PubMed]
Liu, B., Qu, M. J., Qin, K. R., Li, H., Li, Z. K., Shen, B. R., and Jiang, Z. L., 2008, “Role of Cyclic Strain Frequency in Regulating the Alignment of Vascular Smooth Muscle Cells In Vitro,” J. Biophys., 94(4), pp. 1497–1507. [CrossRef]
Jungbauer, S., Gao, H., Spatz, J. P., and Kemkemer, R., 2008, “Two Characteristic Regimes in Frequency-Dependent Dynamic Reorientation of Fibroblasts on Cyclically Stretched Substrates,” J. Biophys., 95(7), pp. 3470–3478. [CrossRef]
Iba, T., and Sumpio, B. E., 1991, “Morphological Response of Human Endothelial Cells Subjected to Cyclic Strain In Vitro,” Microvasc. Res., 42(3), pp. 245–254. [CrossRef] [PubMed]
Hayakawa, K., Sato, N., and Obinata, T., 2001, “Dynamic Reorientation of Cultured Cells and Stress Fibers Under Mechanical Stress From Periodic Stretching,” Exp. Cell Res., 268(1), pp. 104–114. [CrossRef] [PubMed]
Dartsch, P. C., and Betz, E., 1989, “Response of Cultured Endothelial Cells to Mechanical Stimulation,” Basic Res. Cardiol., 84(3), pp. 268–281. [CrossRef] [PubMed]
Buck, R. C., 1980, “Reorientation Response of Cells to Repeated Stretch and Recoil of the Substratum,” Exp. Cell Res., 127(2), pp. 470–474. [CrossRef] [PubMed]
Neidlinger-Wilke, C., Grood, E. S., Wang, J. C., Brand, R. A., and Claes, L., 2001, “Cell Alignment is Induced by Cyclic Changes in Cell Length: Studies of Cells Grown in Cyclically Stretched Substrates,” J. Orthop. Res., 19(2), pp. 286–293. [CrossRef] [PubMed]
De., R., Zemel, A., and Safran, S. A., 2007, “Dynamics of Cell Orientation,” Nat. Phys., 3(9), pp. 655–659. [CrossRef]
Wei, Z., Deshpande, V. S., McMeeking, R. M., and Evans, A. G., 2008, “Analysis and Interpretation of Stress Fiber Organization in Cells Subject to Cyclic Stretch,” ASME J. Biomech. Eng., 130(3), p. 031009. [CrossRef]
Kaunas, R., Hsu, H., and Deguchi, S., 2011, “Sarcomeric Model of Stretch-Induced Stress Fiber Reorganization,” Cell Health Cytoskeleton, 3, pp. 13–22 [CrossRef].
Goldyn, A. M., Rioja, B. A., Spatz, J. P., Ballestrem, C., and Kemkemer, R., 2009, “Force–Induced Cell Polarization is Linked to RhoA-Driven Microtubule-Independent Focal-Adhesion Sliding,” J. Cell Sci., 122(20), pp. 3644–3651. [CrossRef] [PubMed]
Chen, B., Kemkemer, R., Deibler, M., Spatz, J., and Gao, H., 2012, “Cyclic Stretch Induces Cell Reorientation on Substrates by Destabilizing Catch Bonds in Focal Adhesions,” PLoS One, 7(11), p. e48346. [CrossRef] [PubMed]
Thomas, W., 2008, “Catch Bonds in Adhesion,” Annu. Rev. Biomed. Eng., 10(1), pp. 39–57. [CrossRef] [PubMed]
Thomas, W. E., Vogel, V., and Sokurenko, E., 2008, “Biophysics of Catch Bonds,” Annu. Rev. Biophys., 37(1), pp. 399–416. [CrossRef] [PubMed]
Kong, F., Garcia, A. J., Mould, A. P., Humphries, M. J., and Zhu, C., 2009, “Demonstration of Catch Bonds Between an Integrin and Its Ligand,” J. Cell Biol., 185(7), pp. 1275–1284. [CrossRef] [PubMed]
Kong, F., Li, Z., Parks, W. M., Dumbauld, D. W., Garcia, A. J., Mould, A. P., Humphries, M. J., and Zhu, C., 2013, “Cyclic Mechanical Reinforcement of Integrin–Ligand Interactions,” Mol. Cell, 49(6), pp. 1060–1068. [CrossRef] [PubMed]
Bell, G. I., 1978, “Models for the Specific Adhesion of Cells to Cells,” Science, 200(4342), pp. 618–627. [CrossRef] [PubMed]
Chen, B., and Gao, H., 2010, “Mechanical Principle of Enhancing Cell–Substrate Adhesion Via Pre-Tension in the Cytoskeleton,” Biophys. J., 98(10), pp. 2154–2162. [CrossRef] [PubMed]
Erdmann, T., and Schwarz, U. S., 2006, “Bistability of Cell-Matrix Adhesions Resulting From Nonlinear Receptor-Ligand Dynamics,” J. Biophys., 91(6), pp. L60–L62. [CrossRef]
Filippov, A. E., Klafter, J., and Urbakh, M., 2004, “Friction Through Dynamical Formation and Rupture of Molecular Bonds,” Phys. Rev. Lett., 92(13), p. 135503. [CrossRef] [PubMed]
Kong, D., Ji, B., and Dai, L., 2008, “Stability of Adhesion Clusters and Cell Reorientation Under Lateral Cyclic Tension,” J. Biophys., 95(8), pp. 4034–4044. [CrossRef]
Lawrence, M. B., and Springer, T. A., 1991, “Leukocytes Roll on a Selectin at Physiologic Flow Rates: Distinction From and Prerequisite for Adhesion Through Integrins,” Cell, 65(5), pp. 859–873. [CrossRef] [PubMed]
Rinko, L. J., Lawrence, M. B., and Guilford, W. H., 2004, “The Molecular Mechanics of P- and L-Selectin Lectin Domains Binding to PSGL-1,” J. Biophys., 86(1), pp. 544–554. [CrossRef]
Gao, H., Qian, J., and Chen, B., 2011, “Probing Mechanical Principles of Focal Contacts in Cell-Matrix Adhesion in a Coupled Stochastic-Elastic Modeling Framework,” J. R. Soc. Interface, 8(62), pp. 1217–1232. [CrossRef] [PubMed]
Prados, A., Brey, J. J., and Sánchez-Rey, B., 1997, “A Dynamical Monte Carlo Algorithm for Master Equations With Time-Dependent Transition Rates,” J. Stat. Phys., 89(3–4), pp. 709–734. [CrossRef]
Deguchi, S., Ohashi, T., and Sato, M., 2006, “Tensile Properties of Single Stress Fibers Isolated From Cultured Vascular Smooth Muscle Cells,” J. Biomech., 39(14), pp. 2603–2610. [CrossRef] [PubMed]
Evans, E., and Ritchie, K., 1997, “Dynamic Strength of Molecular Adhesion Bonds,” J. Biophys., 72(4), pp. 1541–1555. [CrossRef]
Seifert, U., 2000, “Rupture of Multiple Parallel Molecular Bonds Under Dynamic Loading,” Phys. Rev. Lett., 84(12), pp. 2750–2753. [CrossRef] [PubMed]
Erdmann, T., and Schwarz, U. S., 2004, “Stability of Adhesion Clusters Under Constant Force,” Phys. Rev. Lett., 92(10), p. 108102. [CrossRef] [PubMed]
Erdmann, T., and Schwarz, U. S., 2004, “Stochastic Dynamics of Adhesion Clusters Under Shared Constant Force and With Rebinding,” J. Chem. Phys., 121(18), pp. 8997–9017. [CrossRef] [PubMed]
Roca-Cusachs, P., Gauthier, N. C., Rio, A., and Sheetz, M. P., 2009, “Clustering of α5β1 Integrins Determines Adhesion Strength Whereas αvβ3 and Talin Enable Mechanotransduction,” Proc. Natl. Acad. Sci., 106(38), pp. 16245–16250. [CrossRef]
Dembo, M., Torney, D. C., Saxman, K., and Hammer, D., 1988, “The Reaction-Limited Kinetics of Membrane-to-Surface Adhesion and Detachment,” Proc. R. Soc. London. Ser. B, 234(1274), pp. 55–83. [CrossRef]
Krishnan, R., Canovic, E. P., Iordan, A. L., Rajendran, K., Manomohan, G., Pirentis, A. P., Smith, M. L., Butler, J. P., Fredberg, J. J., and Stamenovic, D., 2012, “Fluidization, Resolidification, and Reorientation of the Endothelial Cell in Response to Slow Tidal Stretches,” Am. J. Physiol. Cell Physiol., 303(4), pp. C368–C375. [CrossRef] [PubMed]

Figures

Grahic Jump Location
Fig. 2

The flow chart of the coupled FEA and Monte Carlo method to determine the lifetime of the bond cluster upon a cyclic load

Grahic Jump Location
Fig. 1

An elastic fiber is adhered to a rigid substrate through a cluster of slip bonds. The fiber is subjected to a periodic force, F(t), on its right end. The bonds are formed between receptors and ligands, which are uniformly distributed along the fiber or on a portion of substrate surface with neighboring distance, l0. The total number of receptors is n and the total number of ligands is N. In the model, the fiber is considered as 1D elastic rod and the bonds as elastic springs.

Grahic Jump Location
Fig. 3

Variation of the lifetime of a single slip bond with stretch amplitude (a) and with cyclic frequency (b) and (c). In the calculation, A = 5 pN and k0 = 0.01s-1 for (a) and (b), and, A = 5 pN and α = 0.8 for (c).

Grahic Jump Location
Fig. 4

Variation of the lifetime of a cluster of slip bonds without rebinding with stretch amplitude (a) and with cyclic frequency (b) and (c). In the simulation, A = 200 pN and k0 = 0.01s-1 for (a) and (b) while A = 200 pN and α = 0.8 for (c).

Grahic Jump Location
Fig. 5

Two characteristic failure modes: (1) sliding mode, where a significant number of bonds rebind to the substrate after broken as shown in (a) and the fiber gradually slides forward for a relatively long time as shown in (b); (2) catastrophic failure, where only a few bonds rebind to the substrate after broken as shown in (c) and the fiber quickly detaches from the substrate as shown in (d). Each minicircle in (a) or (c) represents a bond breaking event at a specific time at a specific site on substrate surface. The vertical coordinate in (a) and (c) is the sequential number of ligands on the surface of substrate and that in (b) and (d) is the displacement of the right end of the fiber. In the simulation, A = 60 pN, α = 0.5, and f = 0.3 Hz for (a) and (b), while A = 60 pN, α = 0.5, and f = 10 Hz for (c) and (d).

Grahic Jump Location
Fig. 6

Variation of the lifetime of a cluster of slip bonds with rebinding with stretch amplitude (a) and cyclic frequency (b) and (c). In the simulation, A = 60 pN for (a) and (b), and A = 60 pN and α = 0.5 for (c).

Grahic Jump Location
Fig. 7

(a) Variation of the lifetime of a cluster of slip bonds with rebinding with stretch amplitude. (b) Bond breaking sequence versus time. Each point represents a bond breaking event on substrate surface. (c) The displacement of the right end of stress fiber versus time. In the simulation, A = 60 pN, β in Eq. (1) is set to be 1, α = 0.8, and f = 0.3Hz.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In