Mathematical modelling and numerical simulations of actin dynamics in the eukaryotic cell

Journal of Mathematical Biology

Volumn 66, Issue 3, 2013, Pages 547-593

  George, Uduak Z ^a   Stéphanou, Angélique ^b   Madzvamuse, Anotida ^a  

^a UNIVERSITY OF SUSSEX   (United Kingdom)

^b LABORATOIRE TIMC IMAG   (France)

Author keywords

Actin dynamics; Cell deformation; Lagrangian kinematics; Moving grid finite element

Indexed keywords

EUKARYOTA;

EID: 84872299597     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-012-0521-1     Document Type: Article

References (61)

1. Abramowitz M, Stegun IA (1968) Handbook of mathematical functions with formulas, graphs, and mathematical tables. US Government Printing Office, Washington, DC.
2. Alt W, Tranquillo RT (1995) Basic morphogenetic system modeling shape changes of migrating cells: How to explain fluctuating lamellipodial dynamics. J Biol Syst 3: 905-916.
3. Ambrosio L, Fusco N, Pallara D (2000) Functions of bounded variation and free discontinuity problems. Clarendon Press, Oxford.
4. Ananthakrishnan R, Ehrlicher A (2007) The forces behind cell movement. Int J Biol Sci 3: 303-317.
5. Ananthakrishnan R, Gusk J, Käs J (2006) Cell mechanics: recent advances with a theoretical perspective. Recent Res Dev Biophys 5: 39-69.
6. Barnhart EL, Lee KC, Keren K, Mogilner A, Theriot J (2011) An adhesion-dependent switch between mechanisms that determine motile cell shape. PLoS Biol 9(5): e1001059.
7. Bausch AR, Ziemann F, Boulbitch AA, Jacobson K, Sackmann E (1998) Local measurements of viscoelastic parameters of adherent cell surfaces by magnetic bead microrheometry. Biophys J 75: 2038-2049.
8. Binamé F, Pawlak G, Roux P, Hibner U (2010) What makes cells move: requirements and obstacles for spontaneous cell motility. Mol BioSyst 6: 648-661.
9. Bischofs I, Klein F, Lehnert D, Bastmeyer M, Schwarz U (2008) Filamentous network mechanics and active contractility determine cell and tissue shape. Biophys J 95: 3488-3496.
10. Brebbia CA (1981) Boundary element methods. Springer, Berlin, Heiddberg, New York.
11. Chen H, Bernstein BW, Bamburg JR (2000) Regulating actin-filament dynamics in vivo. Trends Biochem Sci 25: 19-23.
12. Clark RAF (1996) The molecular and cellular biology of wound repair. Plenum Press, New York.
13. Cross MC, Hohenberg PC (1993) Pattern formation outside of equilibrium. Rev Mod Phys 65: 851-1112.
14. Crouch SL, Starfield AH (1983) Boundary element methods in solid mechanics. George Allen and Unwin, London.
15. Dayel MJ, Akin O, Landeryou M, Risca V, Mogilner A, et al (2009) In silico reconstitution of actin-based symmetry breaking and motility. PLoS Biol 7: e1000, 201. doi: 10. 1371/journal. pbio. 1000201.
16. Dziuk G, Elliott CM (2007) Finite elements on evolving surfaces. IMA J Numer Anal 27: 262-292.
17. Edelstein-Keshet L (2005) Mathematical models in Biology. Society for Industrial and Applied Mathematics, Philadelphia.
18. Fleischer F, Ananthakrishnan R, Eckel S, Schmidt H, Käs J, Svitkina V, Michael B (2007) Actin network architecture and elasticity in lamellipodia of melanoma cells. New J Phys 9: 420.
19. George U (2011) A numerical approach to studying cell dynamics. PhD thesis, University of Sussex.
20. Gupton LS, Anderson KL, Kole TP, Fischer RS, Ponti A, Hitchcock-DeGregori SE, Danuser G, Fowler VM, Wirtz D, Hanein D, Waterman-Storer CM (2005) Cell migration without a lamellipodium: translation of actin dynamics into cell movement mediated by tropomyosin. J Cell Biol 168: 619-631.
21. Hestenes MR, Stiefel E (1952) Methods of conjugate gradients for solving linear systems. J Res Natl Bur Stand 49: 409-436.
22. Hofreither C, Langer U, Tomar S (2010) Large-scale scientific computing, 7th international conference, LSSC 2009. In: Lirkov I, Margenov S, Waśniewski J (eds) Boundary element simulation of linear water waves in a model basin. Springer-Verlag, Berlin, Heidelberg.
23. Johnson C (1987) Numerical solution of partial differential equations by the finite element method. Cambridge University Press, Cambridge.
24. Keren K, Theriot JA (2008) Biophysical aspects of actin-based cell motility in fish epithelial keratocytes. In: Lenz P (ed) Cell motility; biological and medical physics, biomedical engineering. Springer Science + Business Media, LLC, New York.
25. LaForce T (2006) Pe281 boundary element method course notes. http://www. stanford. edu/class/energy281/BoundaryElementMethod. pdf. Accessed May 2011.
26. Lanni F, Ware BR (1984) Detection and characterization of actin monomers, oligomers, and filaments in solution by measurement of fluorescence photobleaching recovery. Biophys J 46: 97-110.
27. Lauffenburgery DA, Horwitz AF (1996) Cell migration: a physically integrated molecular process. Cell 84: 359-369.
28. Le Clainche C, Carlier MF (2008) Regulation of actin assembly associated with protrusion and adhesion in cell migration. Physiol Rev 88: 489-513.
29. Lewis MA, Murray JD (1991) Analysis of stable two-dimensional patterns in contractile cytogel. J Nonlinear Sci 1: 289-311.
30. Lewis MA, Murray JD (1992) Analysis of dynamic and stationary pattern formation in the cell cortex. J Biol Syst 31: 25-71.
31. Madzvamuse A (2000) A numerical approach to the study of spatial pattern formation. PhD thesis, Exeter college, University of Oxford.
32. Madzvamuse A, Wathern AJ, Maini PK (2003) A moving grid finite element method applied to a model biological pattern generator. J Comput Phys 190: 478-500.
33. Maeda YT, Inose J, Matsuo MY, Iwaya S, Sano M (2008) Ordered patterns of cell shape and orientational correlation during spontaneous cell migration. PLoS ONE 3: e3734.
34. Moreo P, Gaffney EA, Garca-Aznar JM, Doblaré M (2010) On the modelling of biological patterns with mechanochemical models: insights from analysis and computation. Bull Math Biol 72: 400-431.
35. Murray JD (1993) Mathematical Biology. Springer-Verlag, Berlin.
36. Okeyo KO, Adachi T, Sunaga J, Hojo M (2009) Actomyosin contractility spatiotemporally regulates actin network dynamics in migrating cells. J Biomech 42(15): 2540-2548.
37. Paluch E, Piel M, Prost J, Bornens M, Sykes C (2005) Cortical actomyosin breakage triggers shape oscillations in cells and cell fragments. Biophys J 89: 724-733.
38. Paluch E, Sykes C, Prost J, Bornens M (2006) Dynamic modes of the cortical actomyosin gel during cell locomotion and division. Trends Cell Biol 16: 5-10.
39. Pullarkat PA, Fernández A (2007) Rheological properties of the eukaryotic cell cytoskeleton. Phys Rep 449: 29-53.
40. Purcell E (1977) Life at low reynolds number. Am J Phys 45: 1-11.
41. Reddy JN (1993) An introduction to the finite element method. McGraw-Hill, New York.
42. Ridley AJ, Schwartz MA, Burridge K, Firtel RA, Ginberg MH, Borisy G, Parsons JT, Horwitz AR (2003) Cell migration: Integrating signal from front to back. Science 302: 1704-1709.
43. Saad Y (2003) Iterative methods for sparse linear systems. Society for Industrial and Applied Mathematics, Philadelphia.
44. Sadd MH (2005) Elasticity: theory, applications and numerics, vol 2. Elsevier, North Holland.
45. Sadd Y, Schultz MH (1986) Gmres: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Stat Comput 7: 856-869.
46. Senju Y, Miyata H (2009) The role of actomyosin contractility in the formation and dynamics of actin bundles during fibroblast spreading. J Biochem 145(2): 137-150.
47. Sethian JA (1996) Level set methods: evolving interfaces in geometry, fluid mechanics, computer vision and materials sciences. Cambridge University Press, Cambridge.
48. Simon JR, Gough A, Urbank E, Wang F, Lanni F (1988) Analysis of rhodamine and fluorescein-labeled f-actin diffusion in vitro by flourescence photobleaching recovery. Biophys J 54: 801-815.
49. Stephanou A (2010) Spatio-temporal dynamics of the cell: characterization from images and computer simulations. Lambert Academic Publishing, Victoria.
50. Stephanou A, Chaplain M, Tracqui P (2004) A mathematical model for the dynamics of large membrane deformations of isolated fibroblasts. Bull Math Biol 66: 1119-1154.
51. Stéphanou A, Mylona E, Chaplain M, Tracqui P (2008) A computational model of cell migration coupling the growth of focal adhesions with oscillatory cell protrusions. J Theor Biol 253: 701-716.
52. Strang G, Fix G (1988) An analysis of the finite element method, vol 2. Cambridge Press, Wellesley.
53. Watanabe N (2010) Inside view of cell locomotion through single-molecule: fast f-/g-actin cycle and g-actin regulation of polymer restoration. Proc Jpn Acad 86: 62-83.
54. Xue F, Janzen DM, Knecht DA (2010) Contribution of filopodia to cell migration: a mechanical link between protrusion and contraction. Int J Cell Biol 2010(2010): 13. doi: 10. 1155/2010/507821.
55. Yang L, Dolnik M, Zhabotinsky AM, Epstein IR (2002) Pattern formation arising from interactions between turing and wave instabilities. J Chem Phys 117: 7259-7265.
56. Zachmanoglou EC, Thoe DW (1986) Introduction to partial differential equations with applications. Dover Publications, Inc., New York.
57. Zaman MH, Kamm RD, Matsudaira P, Lauffenburgery DA (2005) Computational model for cell migration in three-dimensional matrices. Biophys J 89: 1389-1397.
58. Zhu C, Bao G, Wang N (2000) Cell mechanics: mechanical response, cell adhesion and molecular deformation. Annu Rev Biomed Eng 2: 189-226.
59. Zienkiewicz OC (1977) The finite element method. McGraw-Hill, North Holland.
60. Zienkiewicz OC, Taylor RL, Zhu JZ (2005) The finite element method: its basis and fundamentals. Butterworth, Heinemann, Elsevier.
61. Zill DG, Cullen MR (2000) Advanced engineering mathematics. Jones and Bartlett Publishers International, Inc, London.