Skip to main content
Log in

Model for the alignment of actin filaments in endothelial cells subjected to fluid shear stress

  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

Cultured vascular endothelial cells undergo significant morphological changes when subjected to sustained fluid shear stress. The cells elongate and align in the direction of applied flow. Accompanying this shape change is a reorganization at the intracellular level. The cytoskeletal actin filaments reorient in the direction of the cells' long axis. How this external stimulus is transmitted to the endothelial cytoskeleton still remains unclear. In this article. we present a theoretical model accounting for the cytoskeletal reorganization under the influence of fluid shear stress. We develop a system of integro-partial-differential equations describing the dynamics of actin filaments, the actin-binding proteins, and the drift of transmembrane proteins due to the fluid shear forces applied on the plasma membrane. Numerical simulations of the equations show that under certain conditions, initially randomly oriented cytoskeletal actin filaments reorient in structures parallel to the externally applied fluid shear forces. Thus, the model suggests a mechanism by which shear forces acting on the cell membrane can be transmitted to the entire cytoskeleton via molecular interactions alone.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Ando, J. and A. Kamiya 1993. Blood flow and vascular endothelial cell function.Front. Med. Biol. Eng. 5, 245–264.

    Google Scholar 

  • Burridge, K., G. Nuckolls, C. Otey, F. Pavalko, K. Simon and C. Turner. 1990. Actin-membrane interaction in focal adhesions.Cell Diff. Dev. 32, 337–342.

    Article  Google Scholar 

  • Civelekoglu, G. and L. Edelstein-Keshet. 1994. Modeling the dynamics of F-actin in the cell.Bull. Math. Biol. 56, 587–616.

    MATH  Google Scholar 

  • Cooper, J. A. 1991. The role of actin polymerization in cell motility.Ann. Rev. Physiol. 53, 585–605.

    Article  Google Scholar 

  • Davies, P. F. and S. C. Tripathi. 1993. Mechanical stress mechanisms and the cell (an endothelial paradigm).Circ. Res. 72, 239–245.

    Google Scholar 

  • Dewey, C. F., S. R. Bussolari, M. A. Gimbrone and P. F. Davies. 1981. The dynamic response of vascular endothelial cells to fluid shear stress.J. Biomech. Eng.,103, 177–185.

    Article  Google Scholar 

  • Doi, M. and S. F. Edwards. 1986.The Theory of Polymer Dynamics. Oxford: Clarendon Press.

    Google Scholar 

  • Dufort, P. A. and C. J. Lumsden. 1993. Cellular automaton model of the actin cytoskeleton.Cell Motil. Cytoskel. 25, 87–104.

    Article  Google Scholar 

  • Edelstein-Keshet, L. and G. B. Ermentrout. 1990. Models for contact-mediated pattern formation: cells that form parallel arrays.J. Math. Biol.,29, 33–58.

    Article  MATH  MathSciNet  Google Scholar 

  • Franke, R. P., M. Gräfe, H. Schnittler and D. Drenckhahn. 1984. Induction of human vascular endothelial stress fibers by fluid shear stressNature 307, 648–649.

    Article  Google Scholar 

  • Fry, D. L. 1976. Hemodynamic forces in atherogenesis. InCerebrovascular Diseases, P. Scheinberg (Ed). New York: Raven Press, pp. 77–95.

    Google Scholar 

  • Geiger, B. 1989. Cytoskeleton-associated cell contacts.Curr. Opin. Cell Biol. 1, 103–109.

    Article  Google Scholar 

  • Girard, P. R., G. Helmlinger and R. M. Nerem. 1993. Shear stress effects on the morphology and cytomatrix of cultured vascular endothelial cells. InPhysical Forces and the Mammalian Cell, J. A. Frangos (Ed.), San Diego, CA: Academic Press pp.193–222.

    Google Scholar 

  • Helmlinger, G., R. V. Geiger, S. Schreck and R. M. Nerem. 1991. Effects of pulsatile flow on cultured vascular endothelial cell morphology.J. Biomech. Eng. 113, 123–131.

    Google Scholar 

  • Ishihara, A. and K. Jacobson. 1993. A closer look at how membrane proteins move.Biophys. J. 65, 1754–1755.

    Google Scholar 

  • Jammey, P. A., S. Hvidt, J. Käs, A. M. D. Lerche, E. Sackmann, M. Schliwa and T. P. Stossel. 1994. The mechanical properties of actin gel.J. Biol. Chem.,269, 32503–32513.

    Google Scholar 

  • Käs, J., H. Strey, M. Bärmann and E. Sackmann. 1993. Direct measurement of the wave-vector-dependent bending stiffness of freely flickering actin filaments.Europhys. Lett.,21, 865–870.

    Google Scholar 

  • Kaufmann, S., J. Käs, W. H. Goldmann, E. Sackmann and G. Isenberg. 1992. Talin anchors and nucleates actin filaments at lipid membranes.FEBS Lett.,314, 203–205.

    Article  Google Scholar 

  • Ku, D. N., D. P. Giddens, C. K. Zarins and S. Glagov. 1985. Pulsatile flow and atherosclerosis in the human carotid bifurcation.Arteriosclerosis,5, 293–302.

    Google Scholar 

  • Kusumi, A., Y. Sako and M. Yamamoto. 1993. Confined lateral diffusion of membrane receptors as studied by single particle tracking (nanovid microscopy): effects of calcium-induced differentiation in cultured epithelial cells.Biophys. J. 65, 2021–2040.

    Article  Google Scholar 

  • Langille, B. L. and S. L. Adamson. 1981. Relationship between blood fow direction and endothelial cell orientation at arterial branch sites in rabbits and mice.Circ. Res.,48, 481–488.

    Google Scholar 

  • Levesque, M. J. and R. M. Nerem. 1985. The elongation and orientation of cultured endothelial cells in response to shear stress.J. Biomech. Eng. 107, 341–347.

    Article  Google Scholar 

  • Luby-Phelps, K., D. L. Taylor and F. Lanni. 1986. Probing the structure of cytoplasm.J. Cell Biol. 102, 2015–2022.

    Article  Google Scholar 

  • Luna, E. J. and A. L. Hitt. 1992. Cytoskeleton-plasma membrane interactions.Science 258, 955–964.

    Google Scholar 

  • Meyer, R. K. and U. Aebi. 1990. Bundling of actin filaments by alpha-actin depends on its molecular length.J. Cell Biol. 110, 2013–2024.

    Article  Google Scholar 

  • National Institutes of Health-United States. 1981.Arteriosclerosis 1981. Bethesda, MD: National Heart, Lung and Blood Institute, National Institutes of Health.

    Google Scholar 

  • Ookawa, K., M. Sato and N. Ohshima 1993. Time course changes in cytoskeletal structures of cultured endothelial cellsFront. Med. Biol. Eng. 5, 121–125.

    Google Scholar 

  • Otey, C. A., F. M. Pavalko and K. Burridge. 1990. An interaction between alpha-actinin and the β-1-integrin subunit in vitro.J. Cell Biol. 111, 721–729.

    Article  Google Scholar 

  • Pavalko F. M. and C. A. Otey. 1994. Role of adhesion molecule cytoplasmic domains in mediating interactions with the cytoskeleton.Proceedings of the Society for Experimental Biology & Medicine 205, 282–293.

    Google Scholar 

  • Pollard, T. D. and J. A. Cooper. 1986. Actin and actin-binding proteins: a critical evaluation of mechanisms and functions.Ann. Rev. Biochem. 55, 987–1035.

    Article  Google Scholar 

  • Press, W. H., B. P. Flannery, S. A. Teukolsky and W. T. Vetterling. 1987.Numerical Recipes: The Art of Scientific Computing. Cambridge: Cambridge University Press.

    Google Scholar 

  • Satcher, R. L. 1993. A mechanical model of vascular endothelium. Ph. D. thesis, MIT, Cambridge, MA.

    Google Scholar 

  • Sherratt, J. A. and J. Lewis, 1993. Stress-induced alignment of actin filaments and the mechanics of cytogel.Bull. Math. Biol. 55, 637–654.

    MATH  Google Scholar 

  • Stossel, T. P., C. Chaponnier, R. M. Ezzell,et al. 1985. Nonmuscle actin-binding proteins.Annu. Rev. Cell Biol. 1, 353–402.

    Article  Google Scholar 

  • Wang, N., J. P. Butler and D. E. Ingber. 1993. Mechanotransduction across the cell surface and through the cytoskeleton.Science 260, 1124–1127.

    Google Scholar 

  • Wechezak, A. R., R. F. Viggers and L. R. Sauvage. 1985. Fibronectin and F-actin redistribution in cultured endothelial cells exposed to shear stress.Lab. Invest. 53, 639–647.

    Google Scholar 

  • Weeds, A. 1982. Actin-bonding proteins: regulators of cell architecture and motility.Nature 296, 811–816.

    Article  Google Scholar 

  • Wegner, A. 1976. Head to tail polymerization of actin.J. Mol. Biol. 108, 139–150.

    Google Scholar 

  • Wong, A. J., T. D. Pollard and I. M. Herman. 1983. Actin filament stress fibers in vascular endothelial cells in vivo.Science 167, 867–869.

    Google Scholar 

  • Zhao, S., A. Suciu, T. Ziegler, J. E. Moore, E. Bürki, J.-J. Meister and H. R. Brunner. 1995. Synergistic effects of fluid shear stress and cyclic circumferential stretch on vascular endothelial cell morphology and cytoskeleton.Arterioscler. Thromb. Vasc. Biol. 15, 1781–1786.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Suciu, A., Civelekoglu, G., Tardy, Y. et al. Model for the alignment of actin filaments in endothelial cells subjected to fluid shear stress. Bltn Mathcal Biology 59, 1029–1046 (1997). https://doi.org/10.1007/BF02460100

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02460100

Keywords

Navigation