Abstract
It is well documented in literature that under plane substrate stretching adherent cells reorganize their actin cytoskeleton by reorienting their stress fibres in one or two distinct directions, depending upon the magnitude of the substrate strain and the contractile mechanism of the cell. Since the cell is a quite deformable body, previous theoretical modelling according to the principles of linear elasticity theory is not adequate. Experimental evidence such as the concurrent appearance of two distinct and symmetric directions of orientation of the stress fibres in the same cell indicates the presence of a coexistence of phases nonlinear elastic phenomenon. Moreover, the aforementioned evidence supports the assumption that the strain energy density function of the stress fibres should be nonconvex. In the present study, following finite elasticity principles, the reorientation phenomenon is treated as a nonlinear elastic stability problem adopting the global (Maxwell’s) criterion. In this way, apart from explaining thoroughly the coexistence of phases phenomenon, the contribution of other key elements, such as prestress and substrate strain, is stressed out. Further, the nonconvexity factor is correlated to the influence of the small GTPase Rho, regulator of the formation of the actin stress fibres. The predominant final stress fibres configuration, that is transverse to the maximum extracellular strain direction and appears after the coexistence of phases placement, is also clarified. The mathematical model that is proposed here for the description of adherent cell behaviour under plane substrate stretching is an extension of previous work by the authors, where the orientation of stress fibres under uniaxial substrate stretching was studied.
Similar content being viewed by others
References
Dartsch P.C., Haemmerle H.: Orientation response of arterial smooth muscle cells to mechanical stimulation. Eur. J. Cell Biol. 41, 339–346 (1996)
Takemasa T., Sugimoto K., Yamashita K.: Amplitude-dependent stress-fiber reorientation in early response to cyclic strain. Exp. Cell Res. 230, 407–410 (1997)
Neidlinger-Wilke C., Grood E.S., Wang J.H.-C., Brand R.A., Claes L.: Cell alignment is induced by cyclic changes in cell length: studies of cells grown in cyclically stretched substrates. J. Orthop. Res. 19, 286–293 (2001)
Wang J.H.-C., Goldschmidt-Clermont P., Yin F.C.-P.: Contractility affects stress-fiber remodeling and reorientation of endothelial cells subjected to cyclic mechanical stretching. Ann. Biomed. Eng. 28, 1165–1171 (2001)
Wang N., Tolić-Nørrelykke I.M., Chen J., Mijailovich S.M., Butler J.P., Fredberg J.J., Stamenović D.: Cell prestress. I. Stiffness and prestress are closely associated in adherent contractile cells. Am. J. Physiol. Cell Physiol. 282, C606–C616 (2002)
Kaunas R., Nguyen P., Usami S., Chien S.: Cooperative effects of Rho and mechanical stretch on stress-fiber organization. Proc. Natl. Acad. Sci. USA 102, 15895–15900 (2005)
Butler J.P., Tolić-Nørrelykke I.M., Fabry B., Fredberg J.J.: Traction fields, moments, and strain energy that cells exert on their surroundings. Am. J. Physiol. Cell Physiol. 282, C595–C605 (2002)
Bischofs I.B., Schwarz U.S.: Cell organization in soft media due to active mechanosensing. Proc. Natl. Acad. Sci. USA 100, 9274–9279 (2003)
Bischofs I.B., Safran S.A., Schwarz U.S.: Elastic interactions of active cells with soft materials. Phys. Rev. E 69, 021911 (2004)
Stamenović D.: Contractile torque as a steering mechanism for orientation of adherent cells. Mol. Cell Biomech. 2, 69–76 (2005)
Ericksen, J.L.: In: Knopsm R.J., Morton, K.W. (eds.) Introduction to the Thermodynamics of Solids, Chap. 3, pp. 39–61. Chapman & Hall, London (1991)
Pitteri M., Zanzotto G.: Continuum Models for Phase Transitions and Twinning in Crystals. Chapman & Hall, Boca Raton (2003)
Ogden R.W.: Non-linear Elastic Deformations. Dover, New York (1997)
Lazopoulos K., Stamenovic D.: A mathematical model of cell reorientation in response to substrate stretching. MCB 3(1), 43–48 (2006)
Lazopoulos K., Pirentis A.: Substrate stretching and reorganization of stress fibers as a finite elasticity problem. Int. J. Solids Struct. 44, 8285–8296 (2007)
Rajagopal K.R., Wineman A.S.: A constitutive equation for non-linear solids which undergo deformation induced microstructurar changes. Int. J. Plast. 8, 385–395 (1992)
Wang J.H.-C.: Substrate deformation determines actin cytoskeleton reorganization: a mathematical modeling and experimental study. J. Theor. Biol. 202, 33–41 (2000)
Gilmore R.: Catastrophe Theory for Scientists and Engineers. Wiley, New York (1981)
Wang J.H.-C., Goldschmidt-Clermont P., Wille J., Yin F.C.-P.: Specificity of endothelial cell reorientation in response to cyclic mechanical stretching. J Biomech 34, 1563–1572 (2001)
Thompson J.M.T., Hunt G.W.: A General Theory of Elastic Stability. Wiley, London (1973)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Pirentis, A.P., Lazopoulos, K.A. On stress fibre reorientation under plane substrate stretching. Arch Appl Mech 79, 263–277 (2009). https://doi.org/10.1007/s00419-008-0225-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-008-0225-6