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Received February 4, 2015
Accepted April 7, 2015
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Modeling and simulation of biopolymer networks: Classification of the cytoskeleton models according to multiple scales
The Department of Chemical and Biochemical Engineering, Missouri University of Science and Technology, Rolla, MO 65409, USA
parkjoon@mst.edu
Korean Journal of Chemical Engineering, July 2015, 32(7), 1207-1217(11), 10.1007/s11814-015-0071-5
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Abstract
We reviewed numerical/analytical models for describing rheological properties and mechanical behaviors of biopolymer networks with a focus on the cytoskeleton, a major component of a living cell. The cytoskeleton models are classified into three categories: the cell-scale continuum-based model, the structure-based model, and the polymerbased model, according to the length scales of the phenomena of interest. The criteria for classification of the models are modified and extended from those used by Mofrad [M. R. K. Mofrad, Annual Rev. Fluid Mech. 41, 433 (2009)]. The main principles and characteristics of each model are summarized and discussed by comparison with each other. Since the stress-deformation relation of cytoskeleton is dependent on the length scale of stress elements, our model classification helps systematic understanding of biopolymer network modeling.
References
Discher D, Dong C, Fredberg JJ, Guilak F, Ingber D, Janmey P, Kamm RD, Schimd-Scho GW, Weinbaulam S, Ann. Biomed. Eng., 37, 847 (2009)
Stehn JR, Haass NK, Bonello T, Desouza M, Kottyan G, Treutlein H, Zeng J, Nascimento PRBB, Sequeira VB, Butler TL, Allanson M, Fath T, Hill TA, McCluskey A, Schevzov G, Palmer SJ, Hardeman EC, Winlaw D, Reeve VE, Dixon I, Weninger W, Cripe TP, Gunning PW, Cancer Res., 73, 5169 (2013)
Bernal SD, Baylin SB, Shaper JH, Gazdar AF, Chen LB, Cancer Res., 43, 1798 (1983)
Ramaekers FCS, Bosman FT, J. Pathol., 201, 351 (2004)
Geiger B, Spatz J, Bershadsky A, Nat. Rev. Mol. Cell Biol., 10, 21 (2009)
Mehrbod M, Mofrad MRK, PLoS ONE, 6, 10, e25627 (2011).
Huisman EM, in Introduction, Simulation of biopolymer networks under shear, Leiden University, Leiden (2011).
Chicurel ME, Chen CS, Ingber DE, Curr. Opin. Cell Biol., 10, 232 (1998)
Wang N, Naruse K, Stamenovic D, Fredberg JJ, Mijailovich SM, Tolic-Norrelykke IM, P. Natl. Acad. Sci. USA, 98, 7765 (2001)
Ingber DE, J. Cell Sci., 116, 1157 (2003)
Galli C, Guizzardi S, Passeri G, Macaluso GM, Scandroglio R, Acta Biomedica., 76, 5 (2005)
Chen TJ, Wub CC, Su FC, Med. Eng. Phys., 34, 1375 (2012)
Mofrad MRK, Annu. Rev. Fluid Mech., 41, 433 (2009)
Lodish H, Berk A, Zipursky SL, Matsudaira P, Baltimore D, Darnell D, Molecular Cell Biology, W. H. Freeman Co., Publications, New York (1999).
Gittes F, Mickey B, Nettleton J, Howard J, J. Cell Biol., 120, 923 (1993)
Kim T, Hwang W, Kamm RD, Exp. Mech., 49, 91 (2009)
Gardel ML, Shin JH, MacKintosh FC, Mahadevan L, Matsudaira PA, Weitz DA, Science, 304, 1301 (2004)
Gardel ML, Shin JH, MacKintosh FC, Mahadevan L, Matsudaira PA, Weitz DA, Phys. Rev. Lett., 93, 188102 (2004)
MacKintosh FC, Kas J, Janmey PA, Phys. Rev. Lett., 75, 4425 (1995)
Storm C, Pastore JJ, MacKintosh FC, Lubensky TC, Janmey PA, Nature, 435, 191 (2005)
Xu J, Tseng Y, Wirtz D, J. Biol. Chem., 275, 35886 (2000)
Lieleg O, Claessen MMAE, Bausch AR, Soft Matter, 6, 218 (2010)
Alberts B, Bray D, Johnson A, Lewis J, Raff M, Roberts K, Walter P, in Essential cell biology: An introduction to the molecular biology of the cell, Garland Publishing, New York (1998).
Fujiwara I, Takahashi S, Tadakuma H, Funatsu T, Ishiwata S, Nat. Cell Biol., 4, 666 (2002)
Buxton GA, Clarke N, Husse PJ, Express Polym. Lett., 3, 579 (2009)
Mitchison T, Kirschner M, Nature, 312, 237 (1984)
Stamenovic D, FME Transactions, 34, 57 (2006)
Unterberger MJ, Holzapfel GA, Biomech. Model Mechanobiol., 13, 1155 (2014)
Chen J, Interface Focus, 4, 201300 (2014)
Chen TJ, Wu CC, Su FC, Med. Eng. Phys., 34, 1375 (2012)
Nava MM, Raimondi MT, Pietrabissa R, Biomech. Model Mechanobiol., 13, 929 (2014)
Moeendarbary E, Harris AR, WIREs Syst. Biol. Med., 6, 371 (2014)
Andrews SS, Phys. Biol., 11, 011001 (2014)
Roberts E, Cur. Opin. Struc. Biol., 25, 86 (2014)
Janmey PA, Schmidt C, in Cytoskeletal Mechanics - Models and Measurements in Cell Dynamics, Mofrad MRK, Kamm RD Eds., Cambridge University Press (2006).
Mofrad MRK, Karcher H, Kamm RD, in Cytoskeletal Mechanics - Models and Measurements in Cell Dynamics, Mofrad MRK, Kamm RD Eds., Cambridge University Press (2006).
Fabry B, Maksym G, Butler J, Glogauer M, Navajas D, Fredberg J, Phys. Rev. Lett., 87, 148102 (2001)
Bausch AR, Zeimann F, Boulbitch AA, Jacobson K, Sackmann E, Biophysics, 75, 2038 (1998)
Aubry D, Thiam H, Piel M, Allena R, Biomech. Model Mechanobiol., 10.1007/s10237-014-0595-3 (2014)
Pajic-Lijakovic I, Milivojevic M, Biomech. Model Mechanobiol., 13, 1097 (2014)
Guilak F, Haider MA, Setton LA, Laursen TA, Baaijens FPT, in Cytoskeletal Mechanics - Models and Measurements in Cell Dynamics, Mofrad MRK, Kamm RD Eds., Cambridge University Press (2006).
Mow VC, Kuei SC, Lai WM, Armstrong CG, J. Biomech. Eng. -Trans. ASME, 102, 73 (1980)
Lai WM, Hou JS, Mow VC, J. Biomech., 113, 245 (1991)
Gu WY, Lai WM, Mow VC, J. Biomech. Eng. -Trans. ASME, 120, 169 (1998)
Biot M, J. Appl. Phys., 12, 155 (1941)
Mak AF, J. Biomech. Eng. -Trans. ASME, 108, 123 (1986)
DiSilvestro MR, Suh JK, An. Biomed. Eng., 30, 792 (2002)
Baaijens FPT, Trickey WR, Laursen TA, Guilak F, An. Biomed Eng., 33, 494 (2005)
Cao L, Guilak F, Setton L, Cell. Mol. Bioeng., 2, 306 (2009)
Fabry B, Fredberg JJ, in Cytoskeletal Mechanics - Models and Measurements in Cell Dynamics, Mofrad MRK, Kamm RD Eds., Cambridge University Press (2006).
Fabry B, Fredberg JJ, Respir. Physiol. Neurobiol., 137, 109 (2003)
Sollich P, Lequeux F, Hebraud P, Cates M, Phys. Rev. Lett., 78, 2020 (1997)
Sollich P, Phys. Rev. E, 58, 738 (1998)
Haider M, Guilak F, J. Biomech. Eng. -Trans. ASME, 122(3), 236 (2000)
Haider M, Guilak F, J. Biomech. Eng. -Trans. ASME, 124(5), 586 (2002)
Stamenovic D in Cytoskeletal Mechanics - Models and Measurements in Cell Dynamics, Mofrad MRK, Kamm RD Eds., Cambridge University Press (2006).
Zhelev DV, Needham D, Hochmuth RM, Biophys. J., 67, 696 (1994)
Discher DE, Boal DH, Boey SK, Biophys. J., 75, 1584 (1998)
Boey SK, Boal DH, Discher DE, Biophys. J., 75, 1573 (1998)
Stoyanov NS, Ward DW, Feurer T, Nelson KA, Nat. Mater., 1(2), 95 (2002)
Coughlin MF, Stamenovi D, Biophys. J., 84, 1328 (2003)
Paul R, Heil P, Spatz JP, Schwarz US, Biophys. J., 94, 1470 (2008)
Volokh KY, Vilnay O, Int. J. Solids Struct., 34, 1093 (1997)
Ingber DE, Dike L, Hansen L, Karp S, Liley H, Manitos A, Int. Rev. Cytol., 150, 173 (1994)
Stamenovic D, Coughlin MF, J. Theor. Biol., 201, 63 (1999)
Alenghat FJ, Fabry B, Tsai KY, Goldmann WH, Ingber DE, Biochem. Biophys. Res. Commun., 277(1), 93 (2000)
Vasiliev JM, J. Cell Sci. Suppl., 8, 1 (1987)
Ingber DE, Annu. Rev. Physiol., 59, 575 (1997)
Fuller B, Portfolio ARTnews Annual, 4, 112 (1961)
Baudriller H, Maurin B, Canadas P, Montcourrier P, Parmerggiani A, Betache N, C R Mecanique, 334, 662 (2006)
Canadas P, Laurent VM, Oddou C, Isabey D, Wendling S, J. Theor. Biol., 218, 155 (2002)
Wang N, Stramenovic D, Am. J. Physiol. Cell Physiol., 279, C188 (2000)
Ingber DE, Faseb J., 20, 811 (2006)
Luo YZ, Xu X, Lele T, Kumars S, Ingber DE, J. Biomech., 41, 2379 (2008)
Satcher R, Dewey CF, Hartwig JH, Microcirculation, 4, 439 (1997)
Roy S, Qi HJ, Phys. Rev. E, 77, 061916 (2008)
Flory PJ, Rehner J, J. Chem Phys., 11, 512 (1943)
Treloar LRG, Trans. Far. Soc., 42, 83 (1946)
Arruda EM, Boyce MC, J. Mech. Phys. Solids, 41, 389 (1993)
Wu PD, Giessen E, J. Mech. Phys. Solids, 41, 427 (1993)
Palmer JS, Boyce MC, Acta Biomater., 4, 597 (2008)
Oosterwyck HV, Rodriguez JF, Doblare M, Garcia JM, Comput. Methods Biomech. Biomed. Eng., 16, 1002 (2013)
Holzapfel GA, Unterberger MJ, Ogden RW, J. Mech. Behav. Biomed. Mater., 38, 78 (2014)
Unterberger MJ, Schmoller KM, Bausch AR, Holzapfel GA, J. Mech. Behav. Biomed. Mater., 22, 95 (2013)
Unterberger MJ, Schmoller KM, Wurm C, Bausch AR, Holzapfel GA, Acta Biomater., 9, 7343 (2013)
Broederz CP, Storm C, MacKintosh FC, Phys. Rev. Lett., 101, 118103 (2008)
Chen TJ, Wu CC, Tang MJ, Huang JS, Su FC, PloS One, 5, e14392 (2010).
MacKintosh FC, in Cytoskeletal Mechanics - Models and Measurements in Cell Dynamics, Mofrad MRK, Kamm RD Eds., Cambridge University Press (2006).
Janmey PA, Mccormick ME, Rammensee S, Leight JL, Georges PC, Mackintosh FC, Nat. Mater., 6(1), 48 (2007)
Head DA, Levine AJ, MacKintosh FC, Phys. Rev. Lett., 91, 108102 (2003)
Head DA, Levine AJ, MacKintosh FC, Phys. Rev. E Stat. Nonlin. Soft Matter Phys., 68, 061907 (2003)
Wilhelm J, Frey E, Phys. Rev. Lett., 91, 108103 (2003)
Onck PR, Koeman T, van Dillen T, van der Giessen E, Phys. Rev. Lett., 95, 178102 (2005)
Conti E, MacKintosh FC, Phys. Rev. Lett., 102, 088102 (2009)
Abhilash AS, Purohit PK, Joshi SP, Soft Matter, 8, 7004 (2012)
Alonso R, Young J, Cheng Y, Cell. Mol. Bioeng.,, 7, 58 (2014)
Cucker F, Smale S, IEEE Trans. Autom. Control, 52(5), 852 (2007)
Fallqvist B, Kulachenko A, Kroon M, J. Theor. Biol., 350, 57 (2014)
Huisman EM, van Dillen T, Onck PR, van der Giessen E, Phys. Rev. Lett., 99, 208103 (2007)
Huisman EM, Storm C, Barkema GT, Phys. Rev. E, 78, 051801 (2008)
Huisman EM, Storm C, Barkema GT, Phys. Rev. E, 82, 061902 (2010)
Kim T, Hwang W, Lee H, Kamm RD, PLoS Comput. Biol., 5, e10004 (2009)
Kim T, in Thesis: Simulation of Actin cytoskeleton structure and rheology, Massachusetts Institute of Technology, Massachusetts (2007).
Kim T, Gardel ML, Munro E, Biophys. J., 106, 526 (2014)
Mak M, Zaman M, Kamm R, Med. Phys., 41, 164 (2014)
Cyron C, Baush AR, Muller KW, Wall WA, J. Comput. Phys., 244, 236 (2013)
Gong J, Zhang D, Tseng Y, Li B, Wirtz D, Scahfer BW, PLoS ONE, 8, e77417 (2013)
Li B, Wang Y, Gong J, Zhejiang J, Univ-Sci. A, 15, 732 (2014)
Matsushita S, Adachi T, Inoue Y, Hojo M, Sokabe M, J. Biomech., 43, 3162 (2010)
Chu JW, Voth GA, Biophys. J., 90, 1572 (2006)
Yogurtcu ON, Kim JS, Sun SX, Biophys. J., 103, 719 (2012)
Fan J, Saunders MG, Voth GA, Biophys. J., 103, 1334 (2012)
Fan J, Saunders MG, Haddadian EJ, Ffreed KF, de la Cruz EM, Voth GA, J. Mol. Biol., 425, 1225 (2013)
Ming D, Kong Y, Wu Y, Ma J, PNAS, 100, 104 (2003)
Kratky O, Porod G, Recl. Trav. Chim. Pays-Bas., 68, 1106 (1949)
Fixman M, Kovac J, J. Chem. Phys., 58, 1564 (1973)
Holzapfel GA, Ogden RW, J. Elast., 104, 319 (2011)
Blundell JR, Terentjev EM, Macromolecules, 42(14), 5388 (2009)
Lin Y, Wei X, Qian J, Sze KY, Shenoy VB, J. Mech. Phys. Soilids, 62, 2 (2014)
Wagner B, Tharmann R, Haase I, Fischer M, Bausch AR, PNAS, 103, 13974 (2006)
Hatami-Marbini H, Mofrad MRK, Stud. Mechanobiology Tissue Eng. Biomater., 4, 3 (2011)
Buxton GA, Clarke N, Hussey PJ, eXPRESS Pol. Lett., 3, 579 (2009)
Alonso R, Young J, Cheng Y, Cell. Mol. Bioeng., 7, 58 (2014)
Likhtman AE, J. Non-Newton. Fluid Mech., 157(3), 158 (2009)
Park J, Mead DW, Denn MM, J. Rheol., 56(5), 1057 (2012)
Pollack GH, in Cytoskeletal Mechanics - Models and Measurements in Cell Dynamics, Mofrad MRK, Kamm RD Eds., Cambridge University Press (2006).
Maurin B, Canadas P, Baudriller H, Montcourrier P, Bettache N, J. Biomech. Eng. -Trans. ASME, 41, 2036 (2008)
Chen P, Shenoy VB, Soft Matter, 7, 355 (2011)
Na S, Meininger GA, Humphrey JD, J. Theor. Biol., 246, 87 (2007)
Jang Y, Park S, Char K, Korean J. Chem. Eng., 28(5), 1149 (2011)
Jeong Y, Kang IS, Korean J. Chem. Eng., 12(5), 540 (1995)
Stehn JR, Haass NK, Bonello T, Desouza M, Kottyan G, Treutlein H, Zeng J, Nascimento PRBB, Sequeira VB, Butler TL, Allanson M, Fath T, Hill TA, McCluskey A, Schevzov G, Palmer SJ, Hardeman EC, Winlaw D, Reeve VE, Dixon I, Weninger W, Cripe TP, Gunning PW, Cancer Res., 73, 5169 (2013)
Bernal SD, Baylin SB, Shaper JH, Gazdar AF, Chen LB, Cancer Res., 43, 1798 (1983)
Ramaekers FCS, Bosman FT, J. Pathol., 201, 351 (2004)
Geiger B, Spatz J, Bershadsky A, Nat. Rev. Mol. Cell Biol., 10, 21 (2009)
Mehrbod M, Mofrad MRK, PLoS ONE, 6, 10, e25627 (2011).
Huisman EM, in Introduction, Simulation of biopolymer networks under shear, Leiden University, Leiden (2011).
Chicurel ME, Chen CS, Ingber DE, Curr. Opin. Cell Biol., 10, 232 (1998)
Wang N, Naruse K, Stamenovic D, Fredberg JJ, Mijailovich SM, Tolic-Norrelykke IM, P. Natl. Acad. Sci. USA, 98, 7765 (2001)
Ingber DE, J. Cell Sci., 116, 1157 (2003)
Galli C, Guizzardi S, Passeri G, Macaluso GM, Scandroglio R, Acta Biomedica., 76, 5 (2005)
Chen TJ, Wub CC, Su FC, Med. Eng. Phys., 34, 1375 (2012)
Mofrad MRK, Annu. Rev. Fluid Mech., 41, 433 (2009)
Lodish H, Berk A, Zipursky SL, Matsudaira P, Baltimore D, Darnell D, Molecular Cell Biology, W. H. Freeman Co., Publications, New York (1999).
Gittes F, Mickey B, Nettleton J, Howard J, J. Cell Biol., 120, 923 (1993)
Kim T, Hwang W, Kamm RD, Exp. Mech., 49, 91 (2009)
Gardel ML, Shin JH, MacKintosh FC, Mahadevan L, Matsudaira PA, Weitz DA, Science, 304, 1301 (2004)
Gardel ML, Shin JH, MacKintosh FC, Mahadevan L, Matsudaira PA, Weitz DA, Phys. Rev. Lett., 93, 188102 (2004)
MacKintosh FC, Kas J, Janmey PA, Phys. Rev. Lett., 75, 4425 (1995)
Storm C, Pastore JJ, MacKintosh FC, Lubensky TC, Janmey PA, Nature, 435, 191 (2005)
Xu J, Tseng Y, Wirtz D, J. Biol. Chem., 275, 35886 (2000)
Lieleg O, Claessen MMAE, Bausch AR, Soft Matter, 6, 218 (2010)
Alberts B, Bray D, Johnson A, Lewis J, Raff M, Roberts K, Walter P, in Essential cell biology: An introduction to the molecular biology of the cell, Garland Publishing, New York (1998).
Fujiwara I, Takahashi S, Tadakuma H, Funatsu T, Ishiwata S, Nat. Cell Biol., 4, 666 (2002)
Buxton GA, Clarke N, Husse PJ, Express Polym. Lett., 3, 579 (2009)
Mitchison T, Kirschner M, Nature, 312, 237 (1984)
Stamenovic D, FME Transactions, 34, 57 (2006)
Unterberger MJ, Holzapfel GA, Biomech. Model Mechanobiol., 13, 1155 (2014)
Chen J, Interface Focus, 4, 201300 (2014)
Chen TJ, Wu CC, Su FC, Med. Eng. Phys., 34, 1375 (2012)
Nava MM, Raimondi MT, Pietrabissa R, Biomech. Model Mechanobiol., 13, 929 (2014)
Moeendarbary E, Harris AR, WIREs Syst. Biol. Med., 6, 371 (2014)
Andrews SS, Phys. Biol., 11, 011001 (2014)
Roberts E, Cur. Opin. Struc. Biol., 25, 86 (2014)
Janmey PA, Schmidt C, in Cytoskeletal Mechanics - Models and Measurements in Cell Dynamics, Mofrad MRK, Kamm RD Eds., Cambridge University Press (2006).
Mofrad MRK, Karcher H, Kamm RD, in Cytoskeletal Mechanics - Models and Measurements in Cell Dynamics, Mofrad MRK, Kamm RD Eds., Cambridge University Press (2006).
Fabry B, Maksym G, Butler J, Glogauer M, Navajas D, Fredberg J, Phys. Rev. Lett., 87, 148102 (2001)
Bausch AR, Zeimann F, Boulbitch AA, Jacobson K, Sackmann E, Biophysics, 75, 2038 (1998)
Aubry D, Thiam H, Piel M, Allena R, Biomech. Model Mechanobiol., 10.1007/s10237-014-0595-3 (2014)
Pajic-Lijakovic I, Milivojevic M, Biomech. Model Mechanobiol., 13, 1097 (2014)
Guilak F, Haider MA, Setton LA, Laursen TA, Baaijens FPT, in Cytoskeletal Mechanics - Models and Measurements in Cell Dynamics, Mofrad MRK, Kamm RD Eds., Cambridge University Press (2006).
Mow VC, Kuei SC, Lai WM, Armstrong CG, J. Biomech. Eng. -Trans. ASME, 102, 73 (1980)
Lai WM, Hou JS, Mow VC, J. Biomech., 113, 245 (1991)
Gu WY, Lai WM, Mow VC, J. Biomech. Eng. -Trans. ASME, 120, 169 (1998)
Biot M, J. Appl. Phys., 12, 155 (1941)
Mak AF, J. Biomech. Eng. -Trans. ASME, 108, 123 (1986)
DiSilvestro MR, Suh JK, An. Biomed. Eng., 30, 792 (2002)
Baaijens FPT, Trickey WR, Laursen TA, Guilak F, An. Biomed Eng., 33, 494 (2005)
Cao L, Guilak F, Setton L, Cell. Mol. Bioeng., 2, 306 (2009)
Fabry B, Fredberg JJ, in Cytoskeletal Mechanics - Models and Measurements in Cell Dynamics, Mofrad MRK, Kamm RD Eds., Cambridge University Press (2006).
Fabry B, Fredberg JJ, Respir. Physiol. Neurobiol., 137, 109 (2003)
Sollich P, Lequeux F, Hebraud P, Cates M, Phys. Rev. Lett., 78, 2020 (1997)
Sollich P, Phys. Rev. E, 58, 738 (1998)
Haider M, Guilak F, J. Biomech. Eng. -Trans. ASME, 122(3), 236 (2000)
Haider M, Guilak F, J. Biomech. Eng. -Trans. ASME, 124(5), 586 (2002)
Stamenovic D in Cytoskeletal Mechanics - Models and Measurements in Cell Dynamics, Mofrad MRK, Kamm RD Eds., Cambridge University Press (2006).
Zhelev DV, Needham D, Hochmuth RM, Biophys. J., 67, 696 (1994)
Discher DE, Boal DH, Boey SK, Biophys. J., 75, 1584 (1998)
Boey SK, Boal DH, Discher DE, Biophys. J., 75, 1573 (1998)
Stoyanov NS, Ward DW, Feurer T, Nelson KA, Nat. Mater., 1(2), 95 (2002)
Coughlin MF, Stamenovi D, Biophys. J., 84, 1328 (2003)
Paul R, Heil P, Spatz JP, Schwarz US, Biophys. J., 94, 1470 (2008)
Volokh KY, Vilnay O, Int. J. Solids Struct., 34, 1093 (1997)
Ingber DE, Dike L, Hansen L, Karp S, Liley H, Manitos A, Int. Rev. Cytol., 150, 173 (1994)
Stamenovic D, Coughlin MF, J. Theor. Biol., 201, 63 (1999)
Alenghat FJ, Fabry B, Tsai KY, Goldmann WH, Ingber DE, Biochem. Biophys. Res. Commun., 277(1), 93 (2000)
Vasiliev JM, J. Cell Sci. Suppl., 8, 1 (1987)
Ingber DE, Annu. Rev. Physiol., 59, 575 (1997)
Fuller B, Portfolio ARTnews Annual, 4, 112 (1961)
Baudriller H, Maurin B, Canadas P, Montcourrier P, Parmerggiani A, Betache N, C R Mecanique, 334, 662 (2006)
Canadas P, Laurent VM, Oddou C, Isabey D, Wendling S, J. Theor. Biol., 218, 155 (2002)
Wang N, Stramenovic D, Am. J. Physiol. Cell Physiol., 279, C188 (2000)
Ingber DE, Faseb J., 20, 811 (2006)
Luo YZ, Xu X, Lele T, Kumars S, Ingber DE, J. Biomech., 41, 2379 (2008)
Satcher R, Dewey CF, Hartwig JH, Microcirculation, 4, 439 (1997)
Roy S, Qi HJ, Phys. Rev. E, 77, 061916 (2008)
Flory PJ, Rehner J, J. Chem Phys., 11, 512 (1943)
Treloar LRG, Trans. Far. Soc., 42, 83 (1946)
Arruda EM, Boyce MC, J. Mech. Phys. Solids, 41, 389 (1993)
Wu PD, Giessen E, J. Mech. Phys. Solids, 41, 427 (1993)
Palmer JS, Boyce MC, Acta Biomater., 4, 597 (2008)
Oosterwyck HV, Rodriguez JF, Doblare M, Garcia JM, Comput. Methods Biomech. Biomed. Eng., 16, 1002 (2013)
Holzapfel GA, Unterberger MJ, Ogden RW, J. Mech. Behav. Biomed. Mater., 38, 78 (2014)
Unterberger MJ, Schmoller KM, Bausch AR, Holzapfel GA, J. Mech. Behav. Biomed. Mater., 22, 95 (2013)
Unterberger MJ, Schmoller KM, Wurm C, Bausch AR, Holzapfel GA, Acta Biomater., 9, 7343 (2013)
Broederz CP, Storm C, MacKintosh FC, Phys. Rev. Lett., 101, 118103 (2008)
Chen TJ, Wu CC, Tang MJ, Huang JS, Su FC, PloS One, 5, e14392 (2010).
MacKintosh FC, in Cytoskeletal Mechanics - Models and Measurements in Cell Dynamics, Mofrad MRK, Kamm RD Eds., Cambridge University Press (2006).
Janmey PA, Mccormick ME, Rammensee S, Leight JL, Georges PC, Mackintosh FC, Nat. Mater., 6(1), 48 (2007)
Head DA, Levine AJ, MacKintosh FC, Phys. Rev. Lett., 91, 108102 (2003)
Head DA, Levine AJ, MacKintosh FC, Phys. Rev. E Stat. Nonlin. Soft Matter Phys., 68, 061907 (2003)
Wilhelm J, Frey E, Phys. Rev. Lett., 91, 108103 (2003)
Onck PR, Koeman T, van Dillen T, van der Giessen E, Phys. Rev. Lett., 95, 178102 (2005)
Conti E, MacKintosh FC, Phys. Rev. Lett., 102, 088102 (2009)
Abhilash AS, Purohit PK, Joshi SP, Soft Matter, 8, 7004 (2012)
Alonso R, Young J, Cheng Y, Cell. Mol. Bioeng.,, 7, 58 (2014)
Cucker F, Smale S, IEEE Trans. Autom. Control, 52(5), 852 (2007)
Fallqvist B, Kulachenko A, Kroon M, J. Theor. Biol., 350, 57 (2014)
Huisman EM, van Dillen T, Onck PR, van der Giessen E, Phys. Rev. Lett., 99, 208103 (2007)
Huisman EM, Storm C, Barkema GT, Phys. Rev. E, 78, 051801 (2008)
Huisman EM, Storm C, Barkema GT, Phys. Rev. E, 82, 061902 (2010)
Kim T, Hwang W, Lee H, Kamm RD, PLoS Comput. Biol., 5, e10004 (2009)
Kim T, in Thesis: Simulation of Actin cytoskeleton structure and rheology, Massachusetts Institute of Technology, Massachusetts (2007).
Kim T, Gardel ML, Munro E, Biophys. J., 106, 526 (2014)
Mak M, Zaman M, Kamm R, Med. Phys., 41, 164 (2014)
Cyron C, Baush AR, Muller KW, Wall WA, J. Comput. Phys., 244, 236 (2013)
Gong J, Zhang D, Tseng Y, Li B, Wirtz D, Scahfer BW, PLoS ONE, 8, e77417 (2013)
Li B, Wang Y, Gong J, Zhejiang J, Univ-Sci. A, 15, 732 (2014)
Matsushita S, Adachi T, Inoue Y, Hojo M, Sokabe M, J. Biomech., 43, 3162 (2010)
Chu JW, Voth GA, Biophys. J., 90, 1572 (2006)
Yogurtcu ON, Kim JS, Sun SX, Biophys. J., 103, 719 (2012)
Fan J, Saunders MG, Voth GA, Biophys. J., 103, 1334 (2012)
Fan J, Saunders MG, Haddadian EJ, Ffreed KF, de la Cruz EM, Voth GA, J. Mol. Biol., 425, 1225 (2013)
Ming D, Kong Y, Wu Y, Ma J, PNAS, 100, 104 (2003)
Kratky O, Porod G, Recl. Trav. Chim. Pays-Bas., 68, 1106 (1949)
Fixman M, Kovac J, J. Chem. Phys., 58, 1564 (1973)
Holzapfel GA, Ogden RW, J. Elast., 104, 319 (2011)
Blundell JR, Terentjev EM, Macromolecules, 42(14), 5388 (2009)
Lin Y, Wei X, Qian J, Sze KY, Shenoy VB, J. Mech. Phys. Soilids, 62, 2 (2014)
Wagner B, Tharmann R, Haase I, Fischer M, Bausch AR, PNAS, 103, 13974 (2006)
Hatami-Marbini H, Mofrad MRK, Stud. Mechanobiology Tissue Eng. Biomater., 4, 3 (2011)
Buxton GA, Clarke N, Hussey PJ, eXPRESS Pol. Lett., 3, 579 (2009)
Alonso R, Young J, Cheng Y, Cell. Mol. Bioeng., 7, 58 (2014)
Likhtman AE, J. Non-Newton. Fluid Mech., 157(3), 158 (2009)
Park J, Mead DW, Denn MM, J. Rheol., 56(5), 1057 (2012)
Pollack GH, in Cytoskeletal Mechanics - Models and Measurements in Cell Dynamics, Mofrad MRK, Kamm RD Eds., Cambridge University Press (2006).
Maurin B, Canadas P, Baudriller H, Montcourrier P, Bettache N, J. Biomech. Eng. -Trans. ASME, 41, 2036 (2008)
Chen P, Shenoy VB, Soft Matter, 7, 355 (2011)
Na S, Meininger GA, Humphrey JD, J. Theor. Biol., 246, 87 (2007)
Jang Y, Park S, Char K, Korean J. Chem. Eng., 28(5), 1149 (2011)
Jeong Y, Kang IS, Korean J. Chem. Eng., 12(5), 540 (1995)
