Research on Biomedical Engineering
Research on Biomedical Engineering
Original Article

Numeric reconstruction of 2D cellular actomyosin network from substrate displacement

Nishitani, Wagner Shin; Carbonari, Ronny Calixto; Alencar, Adriano Mesquita

Downloads: 0
Views: 494


Introduction: One of the fundamental structural elements of the cell is the cytoskeleton. Along with myosin, actin microfilaments are responsible for cellular contractions, and their organization may be related to pathological changes in myocardial tissue. Due to the complexity of factors involved, numerical modeling of the cytoskeleton has the potential to contribute to a better understanding of mechanical cues in cellular activities. In this work, a systematic method was developed for the reconstruction of an actomyosin topology based on the displacement exerted by the cell on a flexible substrate. It is an inverse problem which could be considered a phenomenological approach to traction force microscopy (TFM). Methods: An actomyosin distribution was found with a topology optimization method (TOM), varying the material density and angle of contraction of each element of the actomyosin domain. The routine was implemented with a linear material model for the bidimensional actomyosin elements and tridimensional substrate. The topology generated minimizes the nodal displacement squared differences between the generated topology and experimental displacement fields obtained by TFM. The structure resulting from TOM was compared to the actin structures observed experimentally with a GFP-attached actin marker. Results: The optimized topology reproduced the main features of the experimental actin and its squared displacement differences were 11.24 µm2, 27.5% of the sum of experimental squared nodal displacements (40.87 µm2). Conclusion: This approach extends the literature with a model for the actomyosin structure capable of distributing anisotropic material freely, allowing heterogeneous contraction over the cell extension.


Traction force microscopy, Cell mechanics, Actin, Topology optimization method, Finite element method.


Bendsøe MP, Sigmund O. Material interpolation schemes in topology optimization. Archive of Applied Mechanics. 1999; 69(9-10):635-54.

Boudou T, Ohayon J, Picart C, Tracqui P. An extended relationship for the characterization of Young’s modulus and Poisson’s ratio of tunable polyacrylamide gels. Biorheology. 2006; 43(6):721-8. PMid:17148855.

Bridgman PC, Dave S, Asnes CF, Tullio AN, Adelstein RS. Myosin IIB is required for growth cone motility. The Journal of Neuroscience. 2001; 21(16):6159-69. PMid:11487639.

Butler JP, Tolić-Nørrelykke IM, Fabry B, Fredberg JJ. Traction fields, moments, and strain energy that cells exert on their surroundings. American Journal of Physiology. Cell Physiology. 2002; 282(3):C595-605. PMid:11832345.

Chandran PL, Wolf CB, Mofrad MR. Band-like stress fiber propagation in a continuum and implications for Myosin contractile stresses. Cellular and Molecular Bioengineering. 2009; 2(1):13-27.

Das M, MacKintosh F. Poisson’s ratio in composite elastic media with rigid rods. Physical Review Letters. 2010; 105:138102.

Dembo M, Wang YL. Stresses at the cell-to-substrate interface during locomotion of fibroblasts. Biophysical Journal. 1999; 76(4):2307-16. PMid:10096925.

Fernandez P, Bausch AR. The compaction of gels by cells: a case of collective mechanical activity. Integrative Biology. 2009; 1(3):252-9. PMid:20023736.

Ghosh S, Matsuoka Y, Asai Y, Hsin K-Y, Kitano H. Software for systems biology: from tools to integrated platforms. Nature Reviews. Genetics. 2011; 12(12):821-32. PMid:22048662.

Hiremath P, Bauer M, Aguirre AD, Cheng H-W, Unno K, Patel RB, Harvey BW, Chang W-T, Groarke JD, Liao R, Cheng S. Identifying early changes in myocardial microstructure in hypertensive heart disease. PLoS One. 2014; 9(5):e97424. PMid:24831515.

Ingber DE. Cellular mechanotransduction: putting all the pieces together again. FASEB Journal: Official Publication of the Federation of American Societies for Experimental Biology. 2006; 20(7):811-27. PMid:16675838.

Lo C-M, Wang H-B, Dembo M, Wang YL. Cell movement is guided by the rigidity of the substrate. Biophysical Journal. 2000; 79(1):144-52. PMid:10866943.

Mello LAM, Lima CR, Amato MBP, Lima RG, Silva ECN. Three-dimensional electrical impedance tomography: a topology optimization approach. IEEE Transactions on Biomedical Engineering. 2008; 55(2 Pt 1):531-40. PMid:18269988.

Pelletier V, Gal N, Fournier P, Kilfoil ML. Microrheology of microtubule solutions and actin-microtubule composite networks. Physical Review Letters. 2009; 102(18):188303. PMid:19518917.

Rhee S, Grinnell F. Fibroblast mechanics in 3D collagen matrices. Advanced Drug Delivery Reviews. 2007; 59(13):1299-305. PMid:17825456.

Riedl J, Crevenna AH, Kessenbrock K, Yu JH, Neukirchen D, Bista M, Bradke F, Jenne D, Holak TA, Werb Z, Sixt M, Wedlich-Söldner R. Lifeact: a versatile marker to visualize F-actin. Nature Methods. 2008; 5(7):605-7. PMid:18536722.

Riedl J, Flynn KC, Raducanu A, Gärtner F, Beck G, Bösl M, Bradke F, Massberg S, Aszodi A, Sixt M, Wedlich-Söldner R. Lifeact mice for studying F-actin dynamics. Nature Methods. 2010; 7(3):168-9. PMid:20195247.

Sen S, Engler AJ, Discher DE. Matrix strains induced by cells: computing how far cells can feel. Cellular and Molecular Bioengineering. 2009; 2(1):39-48. PMid:20582230.

Svanberg K. A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM Journal on Optimization. 2002; 12(2):555-73.

Tomasek JJ, Gabbiani G, Hinz B, Chaponnier C, Brown RA. Myofibroblasts and mechano-regulation of connective tissue remodelling. Nature Reviews. Molecular Cell Biology. 2002; 3(5):349-63. PMid:11988769.

Tseng Q, Duchemin-Pelletier E, Deshiere A, Balland M, Guillou H, Filhol O, Théry M. Spatial organization of the extracellular matrix regulates cell--cell junction positioning. Proceedings of the National Academy of Sciences of the United States of America. 2012; 109(5):1506-11. PMid:22307605.

Zienkiewicz OC, Taylor RL. The basis. 5th ed. Oxford: Butterworth-Heinemann; 2000. (The Finite Element Method; 1).
5889fbf75d01231a018b4890 rbejournal Articles
Links & Downloads

Res. Biomed. Eng.

Share this page
Page Sections