Mathematical Modeling of Cell Migration

Methods in Cell Biology

Volumn 84, Issue , 2008, Pages 911-937

  Carlsson, Anders E ^a   Sept, David ^b  

^a WASHINGTON UNIVERSITY   (United States)

^b WASHINGTON UNIVERSITY IN ST LOUIS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACTIN; MYOSIN;

BIOLOGICAL MODEL; CELL ADHESION; CELL MOTION; CYTOLOGY; FINITE ELEMENT ANALYSIS; LISTERIA; METABOLISM; PSEUDOPODIUM; REVIEW;

ACTINS; CELL ADHESION; CELL MOVEMENT; FINITE ELEMENT ANALYSIS; LISTERIA; MODELS, BIOLOGICAL; MYOSINS; PSEUDOPODIA;

EID: 35448981763     PISSN: 0091679X     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0091-679X(07)84029-5     Document Type: Review

References (72)

1. Abraham V.C., Krishnamurthi V., Taylor D.L., and Lanni F. The actin-based nanomachine at the leading edge of migrating cells. Biophys. J. 77 (1999) 1721-1732
2. Ahmadi A., Liverpool T.B., and Marchetti M.C. Nematic and polar order in active filament solutions. Phys. Rev. E Stat. Nonlin. Soft. Matter Phys. 72 (2005) 060901
3. Alberts J.B., and Odell G.M. In silico reconstitution of Listeria propulsion exhibits nano-saltation. PLoS Biol. 2 (2004) 2054-2066
4. Alt W., and Dembo M. Cytoplasm dynamics and cell motion: Two-phase flow models. Math. Biosci. 156 (1999) 207-228
5. Atilgan E., Wirtz D., and Sun S.X. Morphology of the lamellipodium and organization of actin filaments at the leading edge of crawling cells. Biophys. J. 89 (2005) 3589-3602
6. Atilgan E., Wirtz D., and Sun S.X. Mechanics and dynamics of actin-driven thin membrane protrusions. Biophys. J. 90 (2006) 65-76
7. Bernheim-Groswasser A., Prost J., and Sykes C. Mechanism of actin-based motility: A dynamic state diagram. Biophys. J. 89 (2005) 1411-1419
8. Bershadsky A.D., Ballestrem C., Carramusa L., Zilberman Y., Gilquin B., Khochbin S., Alexandrova A.Y., Verkhovsky A.B., Shemesh T., and Kozlov M.M. Assembly and mechanosensory function of focal adhesions: Experiments and models. Eur. J. Cell Biol. 85 (2006) 165-173
9. Bottino D., Mogilner A., Roberts T., Stewart M., and Oster G. How nematode sperm crawl. J. Cell Sci. 115 (2002) 367-384
10. Burroughs N.J., and Marenduzzo D. Three-dimensional dynamic Monte Carlo simulations of elastic actin-like ratchets. J. Chem. Phys. 123 (2005) 174908
11. Carlsson A.E. Force-velocity relation for growing biopolymers. Phys. Rev. E 62 (2000) 7082-7091
12. Carlsson A.E. Growth of branched actin networks against obstacles. Biophys. J. 81 (2001) 1907-1923
13. Carlsson A.E. Growth velocities of branched actin networks. Biophys. J. 84 (2003) 2907-2918
14. Carlsson A.E. The effect of branching on the critical concentration and average filament length of actin. Biophys. J. 89 (2005) 130-140
15. Dawes A.T., Bard Ermentrout G., Cytrynbaum E.N., and Edelstein-Keshet L. Actin filament branching and protrusion velocity in a simple 1D model of a motile cell. J. Theor. Biol. 242 (2006) 265-279
16. Dawes A.T., and Edelstein-Keshet L. Phosphoinositides and Rho proteins spatially regulate actin polymerization to initiate and maintain directed movement in a 1D model of a motile cell. Biophys. J. 92 3 (2007) 744-768
17. De Lozanne A., and Spudich J.A. Disruption of the Dictyostelium myosin heavy chain gene by homologous recombination. Science 236 (1987) 1086-1091
18. Dickinson R.B., Caro L., and Purich D.L. Force generation by cytoskeletal filament end-tracking proteins. Biophys. J. 87 (2004) 2838-2854
19. Dickinson R.B., Caro L., and Purich D.L. Force generation by cytoskeletal filament end-tracking proteins. Biophys. J. 88 (2005) 757-758 (Vol. 87, p. 2838, 2004)
20. Dickinson R.B., and Purich D.L. Clamped-filament elongation model for actin-based motors. Biophys. J. 82 (2002) 605-617
21. Dickinson R.B., Southwick F.S., and Purich D.L. A direct-transfer polymerization model explains how the multiple profilin-binding sites in the actoclampin motor promote rapid actin-based motility. Arch. Biochem. Biophys. 406 (2002) 296-301
22. Edelstein-Keshet L. A mathematical approach to cytoskeletal assembly. Eur. Biophys. J. Biophys. Lett. 27 (1998) 521-531
23. Edelstein-Keshet L., and Ermentrout G.B. A model for actin-filament length distribution in a lamellipod. J. Math. Biol. 43 (2001) 325-355
24. Friedl P. Prespecification and plasticity: Shifting mechanisms of cell migration. Curr. Opin. Cell Biol. 16 (2004) 14-23
25. Gerbal F., Chaikin P., Rabin Y., and Prost J. An elastic analysis of Listeria monocytogenes propulsion. Biophys. J. 79 (2000) 2259-2275
26. Gov N.S., and Gopinathan A. Dynamics of membranes driven by actin polymerization. Biophys. J. 90 (2006) 454-469
27. Gracheva M.E., and Othmer H.G. A continuum model of motility in ameboid cells. Bull. Math. Biol. 66 (2004) 167-193
28. Grimm H.P., Verkhovsky A.B., Mogilner A., and Meister J.J. Analysis of actin dynamics at the leading edge of crawling cells: Implications for the shape of keratocyte lamellipodia. Eur. Biophys. J. Biophys. Lett. 32 (2003) 563-577
29. Gupton S.L., Anderson K.L., Kole T.P., Fischer R.S., Ponti A., Hitchcock-DeGregori S.E., Danuser G., Fowler V.M., Wirtz D., Hanein D., and Waterman-Storer C.M. Cell migration without a lamellipodium: Translation of actin dynamics into cell movement mediated by tropornyosin. J. Cell Biol. 168 (2005) 619-631
30. Higgs H.N. Formin proteins: A domain-based approach. Trends Biochem. Sci. 30 (2005) 342-353
31. Hill T.L. "Linear Aggregation Theory in Cell Biology." (1987), Springer-Verlag, New York
32. Knecht D.A., and Loomis W.F. Antisense RNA inactivation of myosin heavy chain gene expression in Dictyostelium discoideum. Science 236 (1987) 1081-1086
33. Kovar D.R., and Pollard T.D. Insertional assembly of actin filament barbed ends in association with formins produces piconewton forces. Proc. Natl. Acad. Sci. USA 101 (2004) 14725-14730
34. Kruse K., Joanny J.F., Julicher F., and Prost J. Contractility and retrograde flow in lamellipodium motion. Phys. Biol. 3 (2006) 130-137
35. Kruse K., Joanny J.F., Julicher F., Prost J., and Sekimoto K. Asters, vortices, and rotating spirals in active gels of polar filaments. Phys. Rev. Lett. 92 (2004) 078101
36. Kruse K., Joanny J.F., Julicher F., Prost J., and Sekimoto K. Generic theory of active polar gels: A paradigm for cytoskeletal dynamics. Eur. Phys. J. E Soft Matter 16 (2005) 5-16
37. Kruse K., and Julicher F. Actively contracting bundles of polar filaments. Phys. Rev. Lett. 85 (2000) 1778-1781
38. Kruse K., and Sekimoto K. Growth of fingerlike protrusions driven by molecular motors. Phys. Rev. E 66 (2002) 31904-31909
39. Landau L.D., Lifshiëtìs E.M., Kosevich A.D.M., and Pitaevskiæi L.P. "Theory of Elasticity." (1986), Pergamon Press, Oxford, New York
40. Lee A., Lee H.Y., and Kardar M. Symmetry-breaking motility. Phys. Rev. Lett. 95 (2005) 138101-138104
41. Liverpool T.B., and Marchetti M.C. Instabilities of isotropic solutions of active polar filaments. Phys. Rev. Lett. 90 (2003) 138102
42. Maly I.V., and Borisy G.G. Self-organization of a propulsive actin network as an evolutionary process. Proc. Natl. Acad. Sci. USA 98 (2001) 11324-11329
43. Marcy Y., Prost J., Carlier M.F., and Sykes C. Forces generated during actin-based propulsion: A direct measurement by micromanipulation. Proc. Natl. Acad. Sci. USA 101 (2004) 5992-5997
44. Maree A.F., Jilkine A., Dawes A., Grieneisen V.A., and Edelstein-Keshet L. Polarization and movement of keratocytes: A multiscale modelling approach. Bull. Math. Biol. 68 (2006) 1169-1211
45. Miao L., Vanderlinde O., Stewart M., and Roberts T.M. Retraction in amoeboid cell motility powered by cytoskeletal dynamics. Science 302 (2003) 1405-1407
46. Mogilner A., and Edelstein-Keshet L. Regulation of actin dynamics in rapidly moving cells: A quantitative analysis. Biophys. J. 83 (2002) 1237-1258
47. Mogilner A., and Oster G. Cell motility driven by actin polymerization. Biophys. J. 71 (1996) 3030-3045
48. Mogilner A., and Oster G. The polymerization ratchet model explains the force-velocity relation for growing microtubules. Eur. Biophys. J. Biophys. Lett. 28 (1999) 235-242
49. Mogilner A., and Oster G. Cell biology. Shrinking gels pull cells. Science 302 (2003) 1340-1341
50. Mogilner A., and Oster G. Polymer motors: Pushing out the front and pulling up the back. Curr. Biol. 13 (2003) R721-R733
51. Mogilner A., and Rubinstein B. The physics of filopodial protrusion. Biophys. J. 89 (2005) 782-795
52. Noireaux V., Golsteyn R.M., Friederich E., Prost J., Antony C., Louvard D., and Sykes C. Growing an actin gel on spherical surfaces. Biophys. J. 78 (2000) 1643-1654
53. Novak I.L., Slepchenko B.M., Mogilner A., and Loew L.M. Cooperativity between cell contractility and adhesion. Phys. Rev. Lett. 93 (2004) 268109
54. Peskin C.S., Odell G.M., and Oster G.F. Cellular motions and thermal fluctuations-the Brownian Ratchet. Biophys. J. 65 (1993) 316-324
55. Rubinstein B., Jacobson K., and Mogilner A. Multiscale two-dimensional modeling of a motile simple-shaped cell. Multisc. Model. Simul. 3 (2005) 413-439
56. Sambeth R., and Baumgaertner A. Autocatalytic polymerization generates persistent random walk of crawling cells. Phys. Rev. Lett. 86 (2001) 5196-5199
57. Satyanarayana S.V.M., and Baumgaertner A. Shape and motility of a model cell: A computational study. J. Chem. Phys. 121 (2004) 4255-4265
58. Shemesh T., Bershadsky A.D., and Kozlov M.M. Force-driven polymerization in cells: Actin filaments and focal adhesions. J. Phys.-Condens. Matter 17 (2005) S3913-S3928
59. Shemesh T., Geiger B., Bershadsky A.D., and Kozlov M.M. Focal adhesions as mechanosensors: A physical mechanism. Proc. Natl. Acad. Sci. USA 102 (2005) 12383-12388
60. Shemesh T., Otomo T., Rosen M.K., Bershadsky A.D., and Kozlov M.M. A novel mechanism of actin filament processive capping by formin: Solution of the rotation paradox. J. Cell Biol. 170 (2005) 889-893
61. Small J.V., and Resch G.P. The comings and goings of actin: Coupling protrusion and retraction in cell motility. Curr. Opin. Cell Biol. 17 (2005) 517-523
62. Upadhyaya A., Chabot J.R., Andreeva A., Samadani A., and van Oudenaarden A. Probing polymerization forces by using actin-propelled lipid vesicles. Proc. Natl. Acad. Sci. USA 100 (2003) 4521-4526
63. van der Gucht J., Paluch E., Plastino J., and Sykes C. Stress release drives symmetry breaking for actin-based movement. Proc. Natl. Acad. Sci. USA 102 (2005) 7847-7852
64. van Oudenaarden A., and Theriot J.A. Cooperative symmetry-breaking by actin polymerization in a model for cell motility. Nat. Cell Biol. 1 (1999) 493-499
65. Vavylonis D., Kovar D.R., O'Shaughnessy B., and Pollard T.D. Model of formin-associated actin filament elongation. Mol. Cell 21 (2006) 455-466
66. Vidali L., Chen F., Cicchetti G., Ohta Y., and Kwiatkowski D.J. Rac1-null mouse embryonic fibroblasts are motile and respond to platelet-derived growth factor. Mol. Biol. Cell 17 (2006) 2377-2390
67. Vogel V., and Sheetz M. Local force and geometry sensing regulate cell functions. Nat. Rev. Mol. Cell Biol. 7 (2006) 265-275
68. Wolgemuth C.W. Lamellipodial contractions during crawling and spreading. Biophys. J. 89 (2005) 1643-1649
69. Wolgemuth C.W., Miao L., Vanderlinde O., Roberts T., and Oster G. MSP dynamics drives nematode sperm locomotion. Biophys. J 88 (2005) 2462-2471
70. Wolgemuth C.W., Mogilner A., and Oster G. The hydration dynamics of polyelectrolyte gels with applications to cell motility and drug delivery. Eur. Biophys. J. 33 (2004) 146-158
71. Zeile W.L., Zhang F.L., Dickinson R.B., and Purich D.L. Listeria's right-handed helical rocket-tail trajectories: Mechanistic implications for force generation in actin-based motility. Cell Motil. Cytoskeleton 60 (2005) 121-128
72. Zhu J., and Carlsson A.E. Growth of attached actin filaments. Eur. Phys. J. E Soft Matter 21 (2007) 209-222