A viscous two-phase model for contractile actomyosin bundles

Journal of Mathematical Biology

Volumn 68, Issue 7, 2014, Pages 1653-1676

  Oelz, Dietmar ^a  

^a JOHANN RADON INSTITUTE FOR COMPUTATIONAL AND APPLIED MATHEMATICS   (Austria)

Author keywords

Active fluid; Actomyosin; Contractility; F actin bundle; Free boundary problem

Indexed keywords

ACTIN; MOLECULAR MOTOR; MYOSIN ADENOSINE TRIPHOSPHATASE; MYOSIN II;

BIOLOGICAL MODEL; BIOMECHANICS; CHEMISTRY; HUMAN; MATHEMATICAL PHENOMENA; PHYSIOLOGY; VISCOSITY;

ACTINS; ACTOMYOSIN; BIOMECHANICAL PHENOMENA; HUMANS; MATHEMATICAL CONCEPTS; MODELS, BIOLOGICAL; MOLECULAR MOTOR PROTEINS; MYOSIN TYPE II; VISCOSITY;

EID: 84900032524     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-013-0682-6     Document Type: Article

References (40)

1. Alberts B, Johnson A, Lewis J, Raff M, Roberts K, Walter P (2002) Molecular biology of the cell. Garland Science, New York.
2. Alt W, Bock M, Möhl C (2010) Coupling of cytoplasm and adhesion dynamics determines cell polarization and locomotion. Cell mechanics: from single scale-based models to multiscale modelling. In: Chauviere A, Preziosi L, Verdier C (eds) Mathematical & computational biology. Chapman and Hall, Boca Raton.
3. Alt W, Dembo M (1999) Cytoplasm dynamics and cell motion: two-phase flow models. Mat Biosci 156 (1-2): 207-228.
4. Bentil D (1998) Modelling and simulation of motility in actomyosin systems. J Comput Biol 5(1): 73-86.
5. Besser A, Colombelli J, Stelzer EHK, Schwarz US (2011) Viscoelastic response of contractile filament bundles. Phys Rev E 83(051): 902.
6. Besser A, Schwarz US (2007) Coupling biochemistry and mechanics in cell adhesion: a model for inhomogeneous stress fiber contraction. New J Phys 9(11): 35.
7. Carvalho A, Desai A, Oegema K (2009) Structural memory in the contractile ring makes the duration of cytokinesis independent of cell size. Cell 137(5): 926-937.
8. Colombelli J, Besser A, Kress H, Reynaud EG, Girard P, Caussinus E, Haselmann U, Small JV, Schwarz US, Stelzer EHK (2009) Mechanosensing in actin stress fibers revealed by a close correlation between force and protein localization. J Cell Sci 122(Pt 10): 1665-1679.
9. Courson D, Rock R (2010) Actin cross-link assembly and disassembly mechanics for α-actinin and fascin. J Biol Chem 285(34): 26350-26357.
10. Cramer LP, Siebert M, Mitchison TJ (1997) Identification of novel graded polarity actin filament bundles in locomoting heart fibroblasts: Implications for the generation of motile force. J Cell Biol 136(6): 1287-1305.
11. Fay FS, Fujiwara K, Rees DD, Fogarty KE (1983) Distribution of alpha-actinin in single isolated smooth muscle cells. J Cell Biol 96(3): 783-795.
12. Ferrer JM, Lee H, Chen J, Pelz B, Nakamura F, Kamm RD, Lang MJ (2008) Measuring molecular rupture forces between single actin filaments and actin-binding proteins. Proc Natl Acad Sci.
13. Finer J, Simmons R, Spudich J (1994) Single myosin molecule mechanics: Piconewton forces and nanometre steps. Nature 368(6467): 113-119.
14. Footer MJ, Kerssemakers JWJ, Theriot JA, Dogterom M (2007) Direct measurement of force generation by actin filament polymerization using an optical trap. Proc Natl Acad Sci 104(7): 2181-2186.
15. Grason GM, Shin H (2011) Structural reorganization of parallel actin bundles by crosslinking proteins: incommensurate states of twist. Biophys J 100(3, Supplement 1): 34a.
16. Huxley A (1957) Muscle structure and theories of contraction. Prog Biophys Biophys Chem 7: 255-318.
17. Jayo A, Parsons M (2010) Fascin: a key regulator of cytoskeletal dynamics. Int J Biochem Cell Biol 42(10): 1614-1617.
18. Katoh K, Kano Y, Masuda M, Onishi H, Fujiwara K (1998) Isolation and contraction of the stress fiber. Mol Biol Cell 9(7): 1919-1938.
19. Kozlov MM, Mogilner A (2007) Model of polarization and bistability of cell fragments. Biophys J 93(11): 3811-3819.
20. Kruse K, Jülicher F (2000) Actively contracting bundles of polar filaments. Phys Rev Lett 85: 1778-1781.
21. Kruse K, Jülicher F (2003) Self-organization and mechanical properties of active filament bundles. Phys Rev E 67(051): 913.
22. Langanger G, Moeremans M, Daneels G (1986) The molecular organization of myosin in stress fibers of cultured cells. J Cell Biol 102(1): 200-209.
23. Lenz M, Gardel ML, Dinner AR (2012) Requirements for contractility in disordered cytoskeletal bundles. New J Phys 14(3): 033-037.
24. Mackintosh F, Levine A (2008) Nonequilibrium mechanics and dynamics of motor-activated gels. Phys Rev Lett 100(1).
25. Mogilner A, Edelstein-Keshet L (2002) Regulation of actin dynamics in rapidly moving cells: a quantitative analysis. Biophysl J 83(3): 1237-1258.
26. Oelz D, Schmeiser C (2010) Derivation of a model for symmetric lamellipodia with instantaneous cross-link turnover. Arch Ration Mech Anal 198(3): 963-980.
27. Peskin C, Odell G, Oster G (1993) Cellular motions and thermal fluctuations: the brownian ratchet. Biophys J 65(1): 316-324.
28. Peterson LJ, Rajfur Z, Maddox AS, Freel CD, Chen Y, Edlund M, Otey C, Burridge K (2004) Simultaneous stretching and contraction of stress fibers in vivo. Mol Biol 15(7): 3497-3508.
29. Prass M, Jacobson K, Mogilner A, Radmacher M (2006) Direct measurement of the lamellipodial protrusive force in a migrating cell. J Cell Biol 174(6): 767-772.
30. Rossier O, Gauthier N, Biais N, Vonnegut W, Fardin MA, Avigan P, Heller E, Mathur A, Ghassemi S, Koeckert M, Hone J, Sheetz M (2010) Force generated by actomyosin contraction builds bridges between adhesive contacts. EMBO J 29(6): 1055-1068.
31. Rubinstein B, Fournier MF, Jacobson K, Verkhovsky A, Mogilner A (2009) Actin-myosin viscoelastic flow in the keratocyte lamellipod. Biophys J 97(7): 1853-1863.
32. Sedeh RS, Fedorov AA, Fedorov EV, Ono S, Matsumura F, Almo SC, Bathe M (2010) Structure, evolutionary conservation, and conformational dynamics of homo sapiens fascin-1, an f-actin crosslinking protein. J Mol Biol 400(3): 589-604.
33. Svitkina TM, Verkhovsky AB, McQuade KM, Borisy GG (1997) Analysis of the actin-myosin ii system in fish epidermal keratocytes: mechanism of cell body translocation. J Cell Biol 139(2): 397-415.
34. Thoresen T, Lenz M, Gardel M (2011) Reconstitution of contractile actomyosin bundles. Biophys J 100(11): 2698-2705.
35. Tseng Y, Fedorov E, McCaffery J, Almo SC, Wirtz D (2001) Micromechanics and ultrastructure of actin filament networks crosslinked by human fascin: a comparison with α-actinin. J Mol Biol 310(2): 351-366.
36. Tseng Y, Schafer B, Almo S, Wirtz D (2002) Functional synergy of actin filament cross-linking proteins. J Biol Chem 277(28): 25609-25616.
37. Verkhovsky A, Svitkina T, Borisy G (1997) Polarity sorting of actin filaments in cytochalasin-treated fibroblasts. J Cell Sci 110(15): 1693-1704.
38. Wachsstock D, Schwarz W, Pollard T (1994) Cross-linker dynamics determine the mechanical properties of actin gels. Biophys J 66(3, Part 1): 801-809.
39. Weihing RR (1985) The filamins: properties and functions. Can J BiochemCell Biol 63(6): 397-413.
40. Xu JQ, Harder B, Uman P, Craig R (1996) Myosin filament structure in vertebrate smooth muscle. J Cell Biol 134(1): 53-66.