Skip to main content
SpringerLink
Log in

Mathematical Modeling of the Dynamic Mechanical Behavior of Neighboring Sarcomeres in Actin Stress Fibers

  • Published:
Cellular and Molecular Bioengineering Aims and scope Submit manuscript

Abstract

Actin stress fibers (SFs) in live cells consist of series of dynamic individual sarcomeric units. Within a group of consecutive SF sarcomeres, individual sarcomeres can spontaneously shorten or lengthen without changing the overall length of this group, but the underlying mechanism is unclear. We used a computational model to test our hypothesis that this dynamic behavior is inherent to the heterogeneous mechanical properties of the sarcomeres and the cytoplasmic viscosity. Each sarcomere was modeled as a discrete element consisting of an elastic spring, a viscous dashpot and an active contractile unit all connected in parallel, and experiences forces as a result of actin filament elastic stiffness, myosin II contractility, internal viscoelasticity, or cytoplasmic drag. When all four types of forces are considered, the simulated dynamic behavior closely resembles the experimental observations, which include a low-frequency fluctuation in individual sarcomere length and compensatory lengthening and shortening of adjacent sarcomeres. Our results suggest that heterogeneous stiffness and viscoelasticity of actin fibers, heterogeneous myosin II contractility, and the cytoplasmic drag are sufficient to cause spontaneous fluctuations in SF sarcomere length. Our results shed new light to the dynamic behavior of SF and help design experiments to further our understanding of SF dynamics.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7

Similar content being viewed by others

References

  1. Amato, P. A., and D. L. Taylor. Probing the mechanism of incorporation of fluorescently labeled actin into stress fibers. J. Cell Biol. 102:1074–1084, 1986.

    Article  Google Scholar 

  2. Besser, A. S. & Schwarz, U. S. Coupling biochemistry and mechanics in cell adhesion: a model for inhomogeneous stress fiber contraction. J. New Phys. 9:425 (2007).

    Google Scholar 

  3. Burridge, K., and J. R. Feramisco. Non-muscle alpha actinins are calcium-sensitive actin-binding proteins. Nature 294:565–567, 1981.

    Article  Google Scholar 

  4. Burridge, K., and E. S. Wittchen. The tension mounts: stress fibers as force-generating mechanotransducers. J. Cell Biol. 200:9–19, 2013.

    Article  Google Scholar 

  5. Cai, Y., et al. Cytoskeletal coherence requires myosin-IIA contractility. J. Cell Sci. 123:413–423, 2010.

    Article  Google Scholar 

  6. Cavnar, P. J., S. G. Olenych, and T. C. Keller, 3rd. Molecular identification and localization of cellular titin, a novel titin isoform in the fibroblast stress fiber. Cell Motil Cytoskeleton 64:418–433, 2007.

    Article  Google Scholar 

  7. Chapin, L. M., E. Blankman, M. A. Smith, Y. T. Shiu, and M. C. Beckerle. Lateral communication between stress fiber sarcomeres facilitates a local remodeling response. Biophys. J. 103:2082–2092, 2012.

    Google Scholar 

  8. Charras, G. T., and M. A. Horton. Determination of cellular strains by combined atomic force microscopy and finite element modeling. Biophys. J. 83:858–879, 2002.

    Article  Google Scholar 

  9. Colombelli, J., et al. Mechanosensing in actin stress fibers revealed by a close correlation between force and protein localization. J. Cell Sci. 122:1665–1679, 2009.

    Article  Google Scholar 

  10. Cramer, L. P., M. Siebert, and T. J. Mitchison. Identification of novel graded polarity actin filament bundles in locomoting heart fibroblasts: implications for the generation of motile force. J. Cell Biol. 136:1287–1305, 1997.

    Article  Google Scholar 

  11. Decker, B., and M. S. Kellermayer. Periodically arranged interactions within the myosin filament backbone revealed by mechanical unzipping. J. Mol. Biol. 377:307–310, 2008.

    Article  Google Scholar 

  12. Deguchi, S., T. Ohashi, and M. Sato. Tensile properties of single stress fibers isolated from cultured vascular smooth muscle cells. J. Biomech. 39:2603–2610, 2006.

    Article  Google Scholar 

  13. Discher, D. E., P. Janmey, and Y. L. Wang. Tissue cells feel and respond to the stiffness of their substrate. Science 310:1139–1143, 2005.

    Article  Google Scholar 

  14. Endlich, N., C. A. Otey, W. Kriz, and K. Endlich. Movement of stress fibers away from focal adhesions identifies focal adhesions as sites of stress fiber assembly in stationary cells. Cell Motil Cytoskeleton 64:966–976, 2007.

    Article  Google Scholar 

  15. Esue, O., Y. Tseng, and D. Wirtz. Alpha-actinin and filamin cooperatively enhance the stiffness of actin filament networks. PLoS ONE 4:e4411, 2009.

    Article  Google Scholar 

  16. Frank, D., and N. Frey. Cardiac Z-disc signaling network. J. Biol. Chem. 286:9897–9904, 2011.

    Article  Google Scholar 

  17. Gautel, M. Cytoskeletal protein kinases: titin and its relations in mechanosensing. Pflugers Arch. 462:119–134, 2011.

    Article  Google Scholar 

  18. Gordon, A. M., A. F. Huxley, and F. J. Julian. The variation in isometric tension with sarcomere length in vertebrate muscle fibres. J. Physiol. 184:170–192, 1966.

    Google Scholar 

  19. Guolla, L., M. Bertrand, K. Haase, and A. E. Pelling. Force transduction and strain dynamics in actin stress fibres in response to nanonewton forces. J. Cell Sci. 125:603–613, 2012.

    Article  Google Scholar 

  20. Haga, H., et al. Elasticity mapping of living fibroblasts by AFM and immunofluorescence observation of the cytoskeleton. Ultramicroscopy 82:253–258, 2000.

    Article  Google Scholar 

  21. Hall, A. Rho GTPases and the actin cytoskeleton. Science 279:509–514, 1998.

    Article  Google Scholar 

  22. Hill, A. V. Length of muscle, and the heat and tension developed in an isometric contraction. J. Physiol. 60:237–263, 1925.

    Google Scholar 

  23. Hoffman, L. M., et al. Genetic ablation of zyxin causes Mena/VASP mislocalization, increased motility, and deficits in actin remodeling. J. Cell Biol. 172:771–782, 2006.

    Article  Google Scholar 

  24. Hotulainen, P., and P. Lappalainen. Stress fibers are generated by two distinct actin assembly mechanisms in motile cells. J. Cell Biol. 173:383–394, 2006.

    Article  Google Scholar 

  25. Isenberg, G., P. C. Rathke, N. Hulsmann, W. W. Franke, and K. E. Wohlfarth-Bottermann. Cytoplasmic actomyosin fibrils in tissue culture cells: direct proof of contractility by visualization of ATP-induced contraction in fibrils isolated by laser micro-beam dissection. Cell Tissue Res. 166:427–443, 1976.

    Article  Google Scholar 

  26. Jaffe, A. B., and A. Hall. Rho GTPases: biochemistry and biology. Annu. Rev. Cell Dev. Biol. 21:247–269, 2005.

    Article  Google Scholar 

  27. Katoh, K., Y. Kano, M. Masuda, H. Onishi, and K. Fujiwara. Isolation and contraction of the stress fiber. Mol. Biol. Cell 9:1919–1938, 1998.

    Article  Google Scholar 

  28. Kaunas, R., H.-J. Hsu, and S. Deguchi. Sarcomeric model of stretch-induced stress fiber reorganization. Cell Health and Cytoskeleton 3:13–22, 2011.

    Google Scholar 

  29. Kreis, T. E., K. H. Winterhalter, and W. Birchmeier. In vivo distribution and turnover of fluorescently labeled actin microinjected into human fibroblasts. Proc. Natl Acad Sci. U.S.A. 76:3814–3818, 1979.

    Article  Google Scholar 

  30. Kumar, S., et al. Viscoelastic retraction of single living stress fibers and its impact on cell shape, cytoskeletal organization, and extracellular matrix mechanics. Biophys. J . 90:3762–3773, 2006.

    Article  Google Scholar 

  31. Lazarides, E., and K. Burridge. Alpha-actinin: immunofluorescent localization of a muscle structural protein in nonmuscle cells. Cell 6:289–298, 1975.

    Article  Google Scholar 

  32. Peterson, L. J., et al. Simultaneous stretching and contraction of stress fibers in vivo. Mol. Biol. Cell 15:3497–3508, 2004.

    Article  Google Scholar 

  33. Ponti, A., et al. Periodic patterns of actin turnover in lamellipodia and lamellae of migrating epithelial cells analyzed by quantitative Fluorescent Speckle Microscopy. Biophys. J. 89:3456–3469, 2005.

    Article  Google Scholar 

  34. Rassier, D. E. The mechanisms of the residual force enhancement after stretch of skeletal muscle: non-uniformity in half-sarcomeres and stiffness of titin. Proc. Biol. Sci. 279:2705–2713, 2012.

    Google Scholar 

  35. Reedy, M. K., G. F. Baht, and D. A. Fishman. How many myosins per cross-bridge? I. Flight muscle myofibrils from the blowfly, Sarcophaga bullata. Cold Spring Harbor Symposia Quant. Biol. 37:397–421 (1973).

    Google Scholar 

  36. Rossier, O. M., et al. Force generated by actomyosin contraction builds bridges between adhesive contacts. EMBO J. 29:1055–1068, 2010.

    Article  Google Scholar 

  37. Russell, B., M. W. Curtis, Y. E. Koshman, and A. M. Samarel. Mechanical stress-induced sarcomere assembly for cardiac muscle growth in length and width. J. Mol. Cell. Cardiol. 48:817–823, 2010.

    Article  Google Scholar 

  38. Russell, R. J., S. L. Xia, R. B. Dickinson, and T. P. Lele. Sarcomere mechanics in capillary endothelial cells. Biophys. J. 97:1578–1585, 2009.

    Article  Google Scholar 

  39. Satcher, Jr., R. L., and C. F. Dewey, Jr. Theoretical estimates of mechanical properties of the endothelial cell cytoskeleton. Biophys. J. 71:109–118, 1996.

    Article  Google Scholar 

  40. Schillers, H., M. Walte, K. Urbanova, and H. Oberleithner. Real-time monitoring of cell elasticity reveals oscillating myosin activity. Biophys. J. 99:3639–3646, 2010.

    Google Scholar 

  41. Schoenberg, R. J. P. a. M. Force generation and shortening in skeletal muscle. Comprehensive Physiology Supplement 27: Handbook of Physiology, Skeletal Muscle, 173–187, 2011.

  42. Smith, M. A., et al. A zyxin-mediated mechanism for actin stress fiber maintenance and repair. Dev. Cell 19:365–376, 2010.

    Google Scholar 

  43. Stachowiak, M. R., and B. O’Shaughnessy. Recoil after severing reveals stress fiber contraction mechanisms. Biophys. J. 97:462–471, 2009.

    Google Scholar 

  44. Turnacioglu, K. K., J. W. Sanger, and J. M. Sanger. Sites of monomeric actin incorporation in living PtK2 and REF-52 cells. Cell Motil Cytoskeleton 40:59–70, 1998.

    Google Scholar 

  45. Vogel, V., and M. Sheetz. Local force and geometry sensing regulate cell functions. Nat. Rev. Mol. Cell Biol. 7:265–275, 2006.

    Google Scholar 

  46. Wang, N., et al. Mechanical behavior in living cells consistent with the tensegrity model. Proc. Natl Acad Sci. U.S.A. 98:7765–7770, 2001.

    Google Scholar 

  47. Weber, K., and U. Groeschel-Stewart. Antibody to myosin: the specific visualization of myosin-containing filaments in nonmuscle cells. Proc. Natl Acad. Sci. U.S.A. 71:4561–4564, 1974.

    Google Scholar 

  48. Yam, P. T., and J. A. Theriot. Repeated cycles of rapid actin assembly and disassembly on epithelial cell phagosomes. Mol. Biol. Cell 15:5647–5658, 2004.

    Google Scholar 

Download references

Acknowledgments

This work was supported in part by grants from the National Institutes of Health (R01GM50877), the Huntsman Cancer Foundation, and shared resources from the Cancer Center Support Grant (2 P30 CA42014-21) to MCB. YTS is supported in part by grants from the National Institutes of Health (R01HL67646 and R01DK088777).

Author information

Authors and Affiliations

  1. Huntsman Cancer Institute, University of Utah, Salt Lake City, UT, USA

    L. M. Chapin, E. Blankman & M. C. Beckerle

  2. The Departments of Biology, University of Utah, Salt Lake City, UT, USA

    M. C. Beckerle

  3. Oncological Sciences, University of Utah, Salt Lake City, UT, USA

    L. M. Chapin, E. Blankman & M. C. Beckerle

  4. Bioengineering, University of Utah, Salt Lake City, UT, USA

    L. T. Edgar

  5. The Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT, USA

    L. T. Edgar

  6. Department of Medicine Division of Nephrology, University of Utah, Salt Lake City, UT, USA

    Y. T. Shiu

Authors
  1. L. M. Chapin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. T. Edgar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. E. Blankman
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. C. Beckerle
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Y. T. Shiu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to M. C. Beckerle or Y. T. Shiu.

Additional information

Associate Editor Michael R. King oversaw the review of this article.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chapin, L.M., Edgar, L.T., Blankman, E. et al. Mathematical Modeling of the Dynamic Mechanical Behavior of Neighboring Sarcomeres in Actin Stress Fibers. Cel. Mol. Bioeng. 7, 73–85 (2014). https://doi.org/10.1007/s12195-013-0318-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12195-013-0318-3

Keywords

Search

Navigation