Effect of Stress-Fiber Inclusion on the Local Stiffness of Cell Cytoskeleton Probed by AFM Indentation: Insights from a Discrete Network Model

Document Type: Research Paper

Authors

1 Small Medical Devices, BioMEMS & LoC Lab, Department of Mechanical Engineering, University of Tehran, Tehran, Iran

2 Department of Civel & Environmental Engineering, College of Engineering, Michigan State University, East Lansing,USA

Abstract

In this paper, we analyze the effect of stress-fiber inclusion on the stiffness of an actin random network. To do this, use a discrete random network model to analyze the elastic response of this system in terms of apparent Young’s modulus. First, we showed that for a flat-ended cylindrical AFM indenter the total indentation force has a linear relation with the indentation depth and the indenter radius in a fibrous network. Using this relation, we concluded that the stiffening effect of the stress-fiber on the fibrous network has a range of effectivity and surprisingly, the stiffening is not maximum when the stress-fiber is immediately under the indenter but, when has a certain distance with it. In addition, when the stress-fiber axis has a specific distance from the loading region, it has negligible effect on the local stiffness of the network. These results shed light on some aspects of the widely used AFM stiffness measurements of cells.

Keywords

Main Subjects

[1]           B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, P. Walter, Molecular biology of the cell. Garland science, New York, pp. 1227-1242, 2007.

[2]           H. Haga, S. Sasaki, K. Kawabata, E. Ito, T. Ushiki, T. Sambongi, Elasticity mapping of living fibroblasts by AFM and immunofluorescence observation of the cytoskeleton, Ultramicroscopy, Vol. 82, No. 1-4, pp. 253-258, 2000.

[3]           S. Tojkander, G. Gateva, P. Lappalainen, Actin stress fibers–assembly, dynamics and biological roles, J Cell Sci, Vol. 125, No. 8, pp. 1855-1864, 2012.

[4]           A. Calzado-Martín, M. Encinar, J. Tamayo, M. Calleja, A. San Paulo, Effect of actin organization on the stiffness of living breast cancer cells revealed by peak-force modulation atomic force microscopy, ACS nano, Vol. 10, No. 3, pp. 3365-3374, 2016.

[5]           N. Wang, M. Zhang, Y. Chang, N. Niu, Y. Guan, M. Ye, C. Li, J. Tang, Directly observing alterations of morphology and mechanical properties of living cancer cells with atomic force microscopy, Talanta, Vol. 191, pp. 461-468, 2019.

[6]           M. R. Mofrad, Rheology of the cytoskeleton, Annual Review of Fluid Mechanics, Vol. 41, pp. 433-453, 2009.

[7]           A. Alessandrini, P. Facci, AFM: a versatile tool in biophysics, Measurement science and technology, Vol. 16, No. 6, pp. R65, 2005.

[8]           L. Lu, S. J. Oswald, H. Ngu, F. C.-P. Yin, Mechanical properties of actin stress fibers in living cells, Biophysical journal, Vol. 95, No. 12, pp. 6060-6071, 2008.

[9]           K. D. Costa, A. J. Sim, F. C. Yin, Non-Hertzian approach to analyzing mechanical properties of endothelial cells probed by atomic force microscopy, Journal of biomechanical engineering, Vol. 128, No. 2, pp. 176-184, 2006.

[10]         Y. M. Efremov, M. Velay-Lizancos, C. J. Weaver, A. I. Athamneh, P. D. Zavattieri, D. M. Suter, A. Raman, Anisotropy vs isotropy in living cell indentation with AFM, Scientific reports, Vol. 9, No. 1, pp. 5757, 2019.

[11]         Q. Li, G. Y. Lee, C. N. Ong, C. T. Lim, AFM indentation study of breast cancer cells, Biochemical and biophysical research communications, Vol. 374, No. 4, pp. 609-613, 2008.

[12]         M. J. Unterberger, K. M. Schmoller, A. R. Bausch, G. A. Holzapfel, A new approach to model cross-linked actin networks: multi-scale continuum formulation and computational analysis, Journal of the mechanical behavior of biomedical materials, Vol. 22, pp. 95-114, 2013.

[13]         C. P. Broedersz, X. Mao, T. C. Lubensky, F. C. MacKintosh, Criticality and isostaticity in fibre networks, Nature Physics, Vol. 7, No. 12, pp. 983, 2011.

[14]         E. Conti, F. C. MacKintosh, Cross-linked networks of stiff filaments exhibit negative normal stress, Physical review letters, Vol. 102, No. 8, pp. 088102, 2009.

[15]         C. Broedersz, M. Sheinman, F. MacKintosh, Filament-length-controlled elasticity in 3D fiber networks, Physical review letters, Vol. 108, No. 7, pp. 078102, 2012.

[16]         S. B. Lindström, A. Kulachenko, L. M. Jawerth, D. A. Vader, Finite-strain, finite-size mechanics of rigidly cross-linked biopolymer networks, Soft Matter, Vol. 9, No. 30, pp. 7302-7313, 2013.

[17]         G. Žagar, P. R. Onck, E. van der Giessen, Two fundamental mechanisms govern the stiffening of cross-linked networks, Biophysical journal, Vol. 108, No. 6, pp. 1470-1479, 2015.

[18]         M. J. Unterberger, G. A. Holzapfel, Advances in the mechanical modeling of filamentous actin and its cross-linked networks on multiple scales, Biomechanics and modeling in mechanobiology, Vol. 13, No. 6, pp. 1155-1174, 2014.

[19]         K. Costa, F. Yin, Analysis of indentation: implications for measuring mechanical properties with atomic force microscopy, Journal of biomechanical engineering, Vol. 121, No. 5, pp. 462-471, 1999.

[20]         E. K. Dimitriadis, F. Horkay, J. Maresca, B. Kachar, R. S. Chadwick, Determination of elastic moduli of thin layers of soft material using the atomic force microscope, Biophysical journal, Vol. 82, No. 5, pp. 2798-2810, 2002.

[21]         R. Vargas-Pinto, H. Gong, A. Vahabikashi, M. Johnson, The effect of the endothelial cell cortex on atomic force microscopy measurements, Biophysical journal, Vol. 105, No. 2, pp. 300-309, 2013.

[22]         J. Humphrey, H. R. Halperin, F. C. Yin, Small indentation superimposed on a finite equibiaxial stretch. Implications for cardiac mechanics, Journal of Applied Mechanics, Transactions ASME, Vol. 58, No. 4, pp. 1108-1111, 1991.

[23]         M. Beatty, S. Usmani, On the indentation of a highly elastic half-space, The Quarterly Journal of Mechanics and Applied Mathematics, Vol. 28, No. 1, pp. 47-62, 1975.

[24]         R. Batra, Quasistatic indentation of a rubberlike layer by a rigid cylinder, in Proceeding of, 345-357.

[25]         J. C. Maxwell, L. on the calculation of the equilibrium and stiffness of frames, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 27, No. 182, pp. 294-299, 1864.

[26]         D. Stauffer, A. Aharony, 2018, Introduction to percolation theory, Taylor & Francis,

[27]         V. Abaqus, 6.14 Documentation, Dassault Systemes Simulia Corporation, Vol. 651, 2014.

[28]         N. Zolfaghari, M. Moghimi Zand, and R. Dargazany. "Local Response of Actin Networks is Controlled by Tensile Strains in The Stress-Fibers: Insights from a Discrete Network Model." International Journal of Applied Mechanics, In press.


Volume 50, Issue 2
December 2019
Pages 289-294
  • Receive Date: 26 August 2019
  • Revise Date: 15 October 2019
  • Accept Date: 16 October 2019