Viscoelasticity of cross-linked actin networks: Experimental tests, mechanical modeling and finite-element analysis

Acta Biomaterialia

Volumn 9, Issue 7, 2013, Pages 7343-7353

  Unterberger, Michael J ^a   Schmoller, Kurt M ^b,d   Wurm, Christine ^b   Bausch, Andreas R ^b   Holzapfel, Gerhard A ^a,c  

^a GRAZ UNIVERSITY OF TECHNOLOGY   (Austria)

^b TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^c ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

^d STANFORD UNIVERSITY   (United States)

Author keywords

Actin network; Continuum mechanics; Microsphere; Viscoelasticity; Worm like chain

Indexed keywords

CHAINS; CONTINUUM MECHANICS; FINITE ELEMENT METHOD; LIPID BILAYERS; MICROSPHERES; PROTEINS;

ACTIN NETWORKS; CORTEXES; CROSSLINKED NETWORKS; EUKARYOTIC CYTOSKELETON; EXPERIMENTAL TEST; FINITE ELEMENT ANALYSE; MECHANICAL FORMULATION; MECHANICAL MODELING; SINGLE FILAMENTS; WORMLIKE CHAIN;

VISCOELASTICITY;

F ACTIN; G ACTIN;

ARTICLE; EXPERIMENTAL TEST; FINITE ELEMENT ANALYSIS; MODEL; PRIORITY JOURNAL; PROTEIN CROSS LINKING; TENSILE STRENGTH; VISCOELASTICITY;

EUKARYOTA;

EID: 84878280409     PISSN: 17427061     EISSN: 18787568     Source Type: Journal    
DOI: 10.1016/j.actbio.2013.03.008     Document Type: Article

References (74)

1. G.B. Nash, E. O'Brien, E.C. Gordon-Smith, and J.A. Dormandy Abnormalities in the mechanical properties of red blood cells caused by Plasmodium falciparum Blood 74 1989 855 861
2. S.S. An, B. Fabry, X. Trepat, N. Wang, and J.J. Fredberg Do biophysical properties of the airway smooth muscle in culture predict airway hyperresponsiveness? Am J Respir Cell Mol Biol 35 2006 55 64
3. W.R. Trickey, G.M. Lee, and F. Guilak Viscoelastic properties of chondrocytes from normal and osteoarthritic human cartilage J Orthop Res 18 2000 891 898
4. T. Ohashi, and M. Sato Remodeling of vascular endothelial cells exposed to fluid shear stress: experimental and numerical approach Fluid Dyn Res 37 2005 40 59
5. D. Zeng, T. Juzkiw, A.T. Read, D.W.-H. Chan, M.R. Glucksberg, and C.R. Ethier Young's modulus of elasticity of schlemm's canal endothelial cells Biomech Model Mechanobiol 9 2010 19 33
6. J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, and M. Romeyke Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence Biophys J 88 2005 3689 3698
7. S. Suresh Biomechanics and biophysics of cancer cells Acta Biomater 3 2007 413 438
8. G.Y.H. Lee, and C.T. Lim Biomechanics approaches to studying human diseases Trends Biotechnol 25 2007 111 118
9. O. Lieleg, M.M.A.E. Claessens, and A.R. Bausch Structure and dynamics of cross-linked actin networks Soft Matter 6 2010 218 225
10. J. Stricker, T. Falzone, and M.L. Gardel Mechanics of the F-actin cytoskeleton J Biomech 43 2010 9 14
11. Y. Luan, O. Lieleg, B. Wagner, and A.R. Bausch Micro- and macrorheological properties of isotropically cross-linked actin networks Biophys J 94 2008 688 693
12. K.M. Schmoller, O. Lieleg, and A.R. Bausch Cross-linking molecules modify composite actin networks independently Phys Rev Lett 101 2008 118102
13. K.M. Schmoller, O. Lieleg, and A.R. Bausch Structural and viscoelastic properties of actin/filamin networks: cross-linked versus bundled networks Biophys J 97 2009 83 89
14. J.H. Shin, M.L. Gardel, L. Mahadevan, P. Matsudaira, and D.A. Weitz Relating microstructure to rheology of a bundled and cross-linked F-actin network in vitro PNAS 101 2004 9636 9641
15. P.A. Janmey, S. Hvidt, J. Käs, D. Lerche, A. Maggs, and E. Sackman Elastic modulus and filament motions J Bio Chem 269 1994 503 513
16. C.P. Broedersz, K.E. Kasza, L.M. Jawerth, S. Munster, D.A. Weitz, and F.C. MacKintosh Measurement of nonlinear rheology of cross-linked biopolymer gels Soft Matter 6 2010 4120 4127
17. R. Tharmann, M.M. Claessens, and A.R. Bausch Viscoelasticity of isotropically cross-linked actin networks Phys Rev Lett 98 2007 088103
18. D.A. Head, F.C. MacKintosh, and A.J. Levine Nonuniversality of elastic exponents in random bond-bending networks Phys Rev E Stat Nonlin Soft Matter Phys 68 2003 025101
19. T. Kim, W. Hwang, H. Lee, and R.D. Kamm Computational analysis of viscoelastic properties of crosslinked actin networks PLoS Comput Biol 5 2009 e1000439
20. O. Lieleg, K.M. Schmoller, C.J. Cyron, Y. Luan, W.A. Wall, and A.R. Bausch Structural polymorphism in heterogeneous cytoskeletal networks Soft Matter 5 2009 1796 1803
21. R.H. Ewoldt, G.H. McKinley, and A.E. Hosoi New measures for characterizing nonlinear viscoelasticity in large amplitude oscillatory shear J Rheol 52 2008 1427 1458
22. C. Semmrich, R.J. Larsen, and A.R. Bausch Nonlinear mechanics of entangled F-actin solutions Soft Matter 4 2008 1675 1680
23. J. Xu, Y. Tseng, and D. Wirtz Strain hardening of actin filament networks J Bio Chem 275 2000 35886 35892
24. D.A. Head, A.J. Levine, and F.C. MacKintosh Distinct regimes of elastic response and deformation modes of cross-linked cytoskeletal and semiflexible polymer networks Phys Rev E Stat Nonlin Soft Matter Phys 68 2003 061907
25. E.M. Huisman, T. van Dillen, P.R. Onck, and E. Van der Giessen Three-dimensional cross-linked F-actin networks: relation between network architecture and mechanical behavior Phys Rev Lett 99 2007 208103
26. C.J. Cyron, and W.A. Wall Finite-element approach to Brownian dynamics of polymers Phys Rev E Stat Nonlin Soft Matter Phys 80 2009 066704
27. D.C. Morse Viscoelasticity of concentrated isotropic solutions of semiflexible polymers. 1. Model and stress tensor Macromolecules 31 1998 7030 7043
28. J.S. Palmer, and M.C. Boyce Constitutive modeling of the stress-strain behavior of F-actin filament networks Acta Biomater 4 2008 597 612
29. Unterberger MJ, Schmoller KM, Bausch AR, Holzapfel GA. A new approach to model cross-linked actin networks: multi-scale continuum formulation and computational analysis. J Mech Behav Biomed Mat, in press.
30. C. Bustamante, J.F. Marko, E.D. Siggia, and St. B. Smith Entropic elasticity of λ-phage DNA Science 265 1994 1599 1600
31. J.F. Marko, and E.D. Siggia Stretching DNA Macromolecules 28 1995 8759 8770
32. T. Odijk Stiff chains and filaments under tension Macromolecules 28 1995 7016 7018
33. F.C. MacKintosh, J. Käs, and P.A. Janmey Elasticity of semiflexible biopolymer networks Phys Rev Lett 75 1995 4425 4428
34. C. Storm, and P.C. Nelson Theory of high-force DNA stretching and overstretching Phys Rev E Stat Nonlin Soft Matter Phys 67 2003 051906
35. J.R. Blundell, and E.M. Terentjev Stretching semiflexible filaments and their networks Macromolecules 42 2009 5388 5394
36. G.A. Holzapfel, and R.W. Ogden On the bending and stretching elasticity of biopolymer filaments J Elast 104 2011 319 342
37. H.M. James, and E. Guth Theory of the elastic properties of rubber J Chem Phys 11 1943 455 481
38. P.J. Flory, and J. Rehner Jr. Statistical mechanics of cross-linked polymer networks J Chem Phys 11 1943 512 526
39. E.M. Arruda, and M.C. Boyce A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials J Mech Phys Solids 41 1993 389 412
40. P.D. Wu, and E. van der Giessen On improved network models for rubber elasticity and their applications to orientation hardening in glassy polymers J Mech Phys Solids 41 1993 427 456
41. M.F. Beatty An average-stretch full-network model for rubber elasticity J Elast 70 2003 65 86
42. C. Storm, J.J. Pastore, F.C. MacKintosh, T.C. Lubensky, and P.A. Janmey Nonlinear elasticity in biological gels Nature 435 2005 191 194
43. M. Tkachuk, and C. Linder The maximal advance path constraint for the homogenization of materials with random network microstructure Philos Magn 92 2012 2779 2808
44. C. Miehe, S. Göktepe, and F. Lulei A micro-macro approach to rubber-like materials - Part I: the non-affine micro-sphere model of rubber elasticity J Mech Phys Solids 52 2004 2617 2660
45. P.A. Janmey, M.E. McCormick, S. Rammensee, J.L. Leight, P.C. Georges, and F.C. MacKintosh Negative normal stress in semiflexible polymer gels Nat Mater 6 2007 48 51
46. Holzapfel GA, Ogden RW. Elasticity of biopolymer filaments. Acta Biomater, in press.
47. X. Liu, and G.H. Pollack Mechanics of F-actin characterized with microfrabicated cantilevers Biophys J 83 2002 2705 2715
48. G.A. Holzapfel Nonlinear solid mechanics. A continuum approach for engineering 2000 John Wiley & Sons Chichester
49. C. Miehe, and S. Göktepe A micro-macro approach to rubber-like materials. Part II: the micro-sphere model of finite rubber viscoelasticity J Mech Phys Solids 53 2005 2231 2258
50. A.B. Mathur, A.M. Collinsworth, W.M. Reichert, W.E. Krauss, and G.A. Truskey Endothelial, cardiac muscle and skeletal muscle exhibit different viscous and elastic properties as determined by atomic force microscopy J Biomech 34 2001 1545 1553
51. E. Zhou, S. Quek, and C. Lim Power-law rheology analysis of cells undergoing micropipette aspiration Biomech Model Mechanobiol 9 2010 563 572
52. W.R. Jones, H.P. Ting-Beall, G.M. Lee, S.S. Kelley, R.M. Hochmuth, and F. Guilak Alterations in the Young's modulus and volumetric properties of chondrocytes isolated from normal and osteoarthritic human cartilage J Biomech 32 1999 119 127
53. J.A. Spudich, and S. Watt The regulation of rabbit skeletal muscle contraction. I. Biochemical studies of the interaction of the tropomyosin-troponin complex with actin and the proteolytic fragments of myosin J Bio Chem 246 1971 4866 4871
54. S. MacLean-Fletcher, and T.D. Pollard Identification of a factor in conventional muscle actin preparations which inhibits actin filament self-association Biochem Biophys Res Commun 96 1980 18 27
55. J. Uhde, M. Keller, E. Sackmann, A. Parmeggiani, and E. Frey Internal motility in stiffening actin-myosin networks Phys Rev Lett 93 2004 268101
56. MATLAB. R2010b, The Math Works, Inc., USA.
57. Mezger TG. The rheology handbook, 2nd ed. Hannover: Vincentz Network; 2006.
58. T. van Dillen, P.R. Onck, and E. Van der Giessen Models for stiffening in cross-linked biopolymer networks: a comparative study J Mech Phys Solids 56 2008 2240 2264
59. Z.P. Bažant, and B.H. Oh Efficient numerical integration on the surface of a sphere Z Angew Math Mech 66 1986 37 49
60. G.A. Holzapfel, and T.C. Gasser A viscoelastic model for fiber-reinforced composites at finite strains: continuum basis, computational aspects and applications Comput Methods Appl Mech Eng 190 2001 4379 4403
61. L. Le Goff, O. Hallatschek, E. Frey, and F. Amblard Tracer studies on F-actin fluctuations Phys Rev Lett 89 2002 258101
62. P. Fernández, P.A. Pullarkat, and A. Ott A master relation defines the nonlinear viscoelasticity of single fibroblasts Biophys J 90 2006 3796 3805
63. A.R. Payne The dynamic properties of carbon black-loaded natural rubber vulcanizates. Part I J Appl Polym Sci 6 1962 57 63
64. K.M. Schmoller, P. Fernández, R.C. Arevalo, D.L. Blair, and A.R. Bausch Cyclic hardening in bundled actin networks Nat Commun 1 2010 134 140
65. O. Lieleg, and A.R. Bausch Cross-linker unbinding and self-similarity in bundled cytoskeletal networks Phys Rev Lett 99 2007 158105
66. A.S. Abhilash, Prashant K. Purohit, and Shailendra P. Joshi Stochastic rate-dependent elasticity and failure of soft fibrous networks Soft Matter 8 2012 7004 7016
67. O. Lieleg, K.M. Schmoller, M.M.A.E. Claessens, and A.R. Bausch Cytoskeletal polymer networks: viscoelastic properties are determined by the microscopic interaction potential of cross-links Biophys J 96 2009 4725 4732
68. Taylor RL, FEAP - a finite element analysis program. Version 8.2, University of California at Berkeley, USA.
69. R.M. Hochmuth Review: micropipette aspiration of living cells J Biomech 33 2000 15 22
70. D.E. Discher, D.H. Boal, and S.K. Boey Simulations of the erythrocyte cytoskeleton at large deformation. II. Micropipette aspiration Biophys J 75 1998 1584 1597
71. F.P.T. Baaijens, W.R. Trickey, T.A. Laursen, and F. Guilak Large deformation finite element analysis of micropipette aspiration to determine the mechanical properties of the chondrocyte Ann Biomed Eng 33 2005 494 501
72. M. Herant, W.A. Marganski, and M. Dembo The mechanics of neutrophils: synthetic modeling of three experiments Biophys J 84 2003 3389 3413
73. E. Monteiro, J. Yvonnet, Q.-C. He, O. Cardoso, and A. Asnacios Analyzing the interplay between single cell rheology and force generation through large deformation finite element models Biomech Model Mechanobiol 10 2011 813 830
74. CUBIT. Version 12.1, Sandia Corp., USA.