Polarization and movement of keratocytes: A multiscale modelling approach

Bulletin of Mathematical Biology

Volumn 68, Issue 5, 2006, Pages 1169-1211

  Marée, Athanasius F M ^a   Jilkine, Alexandra ^b   Dawes, Adriana ^b   Grieneisen, Verônica A ^a   Edelstein Keshet, Leah ^b  

^a UTRECHT UNIVERSITY   (Netherlands)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

2D cell motility model; Actin cytoskeleton; Cdc42 Rac Rho; Cellular Potts Model; Chemotaxis; Mathematical model; Small G proteins

Indexed keywords

ACTIN; GUANINE NUCLEOTIDE BINDING PROTEIN;

ANIMAL; ARTICLE; BIOLOGICAL MODEL; CELL MOTION; CELL POLARITY; CYTOLOGY; EPITHELIUM CELL; FISH; MATHEMATICS; PHYSIOLOGY;

ACTINS; ANIMALS; CELL MOVEMENT; CELL POLARITY; EPITHELIAL CELLS; FISHES; GTP-BINDING PROTEINS; MATHEMATICS; MODELS, BIOLOGICAL;

EID: 33745608331     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-006-9131-7     Document Type: Article

References (108)

1. Abercrombie, M., 1980. The Croonian Lecture, 1978: The crawling movement of metazoan cells. Proc. R. Soc. Lond. Ser. B 207, 129-147.
2. Abraham, V.C., Krishnamurthi, V., Taylor, D.L., Lanni, F., 1999. The actin-based nanomachine at the leading edge of migrating cells. Biophys. J. 77(3), 1721-1732.
3. Allen, W.E., Zicha, D., Ridley, A.J., Jones, G.E., 1998. A role for Cdc42 in macrophage chemotaxis. J. Cell Biol. 141(5), 1147-1157.
4. Amann, K.J., Pollard, T.D., 2001. Direct real-time observation of actin filament branching mediated by Arp2/3 complex using total internal reflection fluorescence microscopy. Proc. Natl. Acad. Sci. U.S.A. 98(26), 15009-15013.
5. Asano, Y., Mizuno, T., Kon, T., Nagasaki, A., Sutoh, K., Uyeda, T.Q.P., 2004. Keratocyte-like locomotion in amiB-null Dictyostelium cells. Cell Motil. Cytoskeleton 59(1), 17-27.
6. Baird, D., Feng, Q., Cerione, R.A., 2005. The Cool-2/α-Pix protein mediates a Cdc42-Rac signaling cascade. Curr. Biol. 15(1), 1-10.
7. Benard, V., Bohl, B.P., Bokoch, G.M., 1999. Characterization of Rac and Cdc42 activation in chemoattractant-stimulated human neutrophils using a novel assay for active GTPases. J. Biol. Chem. 274(19), 13198-13204.
8. Borghans, J.A.M., De Boer, R.J., Segel, L.A., 1996. Extending the quasi-steady state approximation by changing variables. Bull. Math. Biol. 58(1), 43-63.
9. Bottino, D., Mogilner, A., Roberts, T., Stewart, M., Oster, G., 2002. How nematode sperm crawl. J. Cell Sci. 115(Pt 2), 367-384.
10. Boukharov, A.A., Cohen, C.M., 1998. Guanine nucleotide-dependent translocation of RhoA from cytosol to high affinity membrane binding sites in human erythrocytes. Biochem. J. 330, 1391-1398.
11. Burridge, K., Wennerberg, K., 2004. Rho and Rac take center stage. Cell 116(2), 167-179.
12. Cameron, L.A., Svitkina, T.M., Vignjevic, D., Theriot, J.A., Borisy, G.G., 2001. Dendritic organization of actin comet tails. Curr. Biol. 11(2), 130-135.
13. Carlsson, A.E., 2001. Growth of branched actin networks against obstacles. Biophys. J. 81(4), 1907-1923.
14. Carlsson, A.E., 2003. Growth velocities of branched actin networks. Biophys. J. 84(5), 2907-2918.
15. Caron, E., 2003. Rac signalling: A radical view. Nat. Cell Biol. 5(3), 185-187.
16. Cramer, L.P., Mitchison, T.J., Theriot, J.A., 1994. Actin-dependent motile forces and cell motility. Curr. Opin. Cell Biol. 6(1), 82-86.
17. Dawes, A.T., Edelstein-Keshet, L., 2006. Phosphoinositides and Rho proteins spatially regulate actin polymerization to initiate and maintain directed movement in a 1D model of a motile cell. submitted.
18. DiMilla, P.A., Barbee, K., Lauffenburger, D.A., 1991. Mathematical model for the effects of adhesion and mechanics on cell migration speed. Biophys. J. 60(1), 15-37.
19. Ehrengruber, M.U., Deranleau, D.A., Coates, T.D., 1996. Shape oscillations of human neutrophil leukocytes: Characterization and relationship to cell motility. J. Exp. Biol. 199(Pt 4), 741-747.
20. Etienne-Manneville, S., 2004. Cdc42 - the centre of polarity. J. Cell Sci. 117(Pt 8), 1291-1300.
21. Falet, H., Hoffmeister, K.M., Neujahr, R., Italiano, J.E. Jr, Stossel, T.P., Southwick, F.S., Hartwig, J.H., 2002. Importance of free actin filament barbed ends for Arp2/3 complex function in platelets and fibroblasts. Proc. Natl. Acad. Sci. U.S.A. 99(26), 16782-16787.
22. Fashena, S.J., Einarson, M.B., O'Neill, G.M., Patriotis, C., Golemis, E.A., 2002. Dissection of HEF1-dependent functions in motility and transcriptional regulation. J. Cell Sci. 115(Pt 1), 99-111.
23. Firtel, R.A., Chung, C.Y., 2000. The molecular genetics of chemotaxis: Sensing and responding to chemoattractant gradients. BioEssays 22(7), 603-615.
24. Fischer, R.S., Fritz-Six, K.L., Fowler, V.M., 2003. Pointed-end capping by tropomodulin3 negatively regulates endothelial cell motility. J. Cell Biol. 161(2), 371-380.
25. Fleming, I.N., Elliott, C.M., Exton, J.H., 1996. Differential translocation of Rho family GTPases by lysophosphatidic acid, endothelin-1, and platelet-derived growth factor. J. Biol. Chem. 271(51), 33067-33073.
26. Funamoto, S., Meili, R., Lee, S., Parry, L., Firtel, R.A., 2002. Spatial and temporal regulation of 3-phosphoinositides by PI 3-kinase and PTEN mediates chemotaxis. Cell 109(5), 611-623.
27. Galbraith, C.G., Sheetz, M.P., 1999. Keratocytes pull with similar forces on their dorsal and ventral surfaces. J. Cell Biol. 147(6), 1313-1324.
28. Gamba, A., De Candia, A., Di Talia, S., Coniglio, A., Bussolino, F., Serini, G., 2005. Diffusion-limited phase separation in eukaryotic chemotaxis. Proc. Natl. Acad. Sci. U.S.A. 102(47), 16927-16932.
29. Gardner, T.S., Cantor, C.R., Collins, J.J., 2000. Construction of a genetic toggle switch in Escherichia. Coli. Nature 403(6767), 339-342.
30. Giniger, E., 2002. How do Rho family GTPases direct axon growth and guidance? A proposal relating signaling pathways to growth cone mechanics. Differentiation 70(8), 385-396.
31. Glazier, J.A., Graner, F., 1993. Simulation of the differential adhesion driven rearrangement of biological cells. Phys. Rev. E 47(3), 2128-2154.
32. Goodwin, J.S., Drake, K.R., Remmert, C.L., Kenworthy, A.K., 2005. Ras diffusion is sensitive to plasma membrane viscosity. Biophys. J. 89(2), 1398-1410.
33. Gracheva, M.E., Othmer, H.G., 2004. A continuum model ofmotility in ameboid cells. Bull. Math. Biol. 66(1), 167-193.
34. Graner, F., 1993. Can surface adhesion drive cell-rearrangement? Part I: Biological cell-sorting. J. Theor. Biol. 164, 455-476.
35. Grimm, H.P., Verkhovsky, A.B., Mogilner, A., Meister, J.-J., 2003. Analysis of actin dynamics at the leading edge of crawling cells: Implications for the shape of keratocyte lamellipodia. Eur. Biophys. J. 32(6), 563-577.
36. Hall, A., 1998. Rho GTPases and the actin cytoskeleton. Science 279(5350), 509-514.
37. Haugh, J.M., Codazzi, F., Teruel, M., Meyer, T., 2000. Spatial sensing in fibroblasts mediated by 3′ phosphoinositides. J. Cell Biol. 151(6), 1269-1280.
38. Higgs, H.N., Pollard, T.D., 1999. Regulation of actin polymerization by Arp2/3 complex and WASp/Scar proteins. J. Biol. Chem. 274(46), 32531-32534.
39. 2 of Wiskott-Aldrich syndrome protein (WASp) stimulates actin nucleation by Arp2/3 complex. J. Cell Biol. 150(6), 1311-1320.
40. Huang, M., Yang, C., Schafer, D.A., Cooper, J.A., Higgs, H.N., Zigmond, S.H., 1999. Cdc42-induced actin filaments are protected from capping protein. Curr. Biol. 9(17), 979-982.
41. Jilkine, A., 2005. Modelling the interactions of small GTPases. Master's thesis, University of British Columbia, Canada.
42. Jilkine, A., Marée, A.F.M., Edelstein-Keshet, L., 2006. Mathematical model for spatial segregation of the Rho-family GTPases based on inhibitory crosstalk. submitted.
43. Jiménez, C., Portela, R.A., Mellado, M., Rodríguez-Frade, J.M., Collard, J., Serrano, A., Martínez-A, C., Avila, J., Carrera, A.C., 2000. Role of the PI3K regulatory subunit in the control of actin organization and cell migration. J. Cell Biol. 151(2), 249-262.
44. Kaibuchi, K., Kuroda, S., Amano, M., 1999. Regulation of the cytoskeleton and cell adhesion by the Rho family GTPases in mammalian cells. Annu. Rev. Biochem. 68, 459-486.
45. Kiosses, W.B., Daniels, R.H., Otey, C., Bokoch, G.M., Schwartz. M.A., 1999. A role for p21-activated kinase in endothelial cell migration. J. Cell Biol. 147(4), 831-844.
46. Kole, T.P., Tseng, Y., Jiang, I., Katz, J.L., Wirtz, D., 2005. Intracellular mechanics of migrating fibroblasts. Mol. Biol. Cell 16(1), 328-338.
47. Kraynov, V.S., Chamberlain, C., Bokoch, G.M., Schwartz, M.A., Slabaugh, S., Hahn, K.M., 2000. Localized Rac activation dynamics visualized in living cells. Science 290(5490), 333-337.
48. Krewson, C.E., Chung, S.W., Dai, W.G., Saltzman, W.M., 1994. Cell-aggregation and neurite growth in gels of extracellular-matrix molecules. Biotechnol. Bioeng. 43(7), 555-562.
49. Kurokawa, K., Itoh, R.E., Yoshizaki, H., Nakamura, Y.O.T., Matsuda, M., 2004. Coactivation of Rac1 and Cdc42 at lamellipodia and membrane ruffles induced by epidermal growth factor. Mol. Biol. Cell 15(3), 1003-1010.
50. Landau, L.D., Lifshitz, E.M., 1976. Mechanics, Volume 1 of Course of Theoretical Physics, 3rd edition. Butterworth-Heinemann, Oxford.
51. Lauffenburger, D.A., 1989. A simple model for the effects of receptor-mediated cell-substratum adhesion on cell migration. Chem. Eng. Sci. 44(9), 1903-1914.
52. Laurent, V.M., Kasas, S., Yersin, A., Schäffer, T.E., Catsicas, S., Dietler, G., Verkhovsky, A.B., Meister, J.-J., 2005. Gradient of rigidity in the lamellipodia of migrating cells revealed by atomic force microscopy. Biophys. J. 89(1), 667-675.
53. Lee, J., Jacobson, K., 1997. The composition and dynamics of cell-substratum adhesions in locomoting fish keratocytes. J. Cell Sci. 110, 2833-2844.
54. Levchenko, A., Iglesias, P.A., 2002. Models of eukaryotic gradient sensing: Application to chemotaxis of amoebae and neutrophils. Biophys. J. 82(1 Pt 1), 50-63.
55. Maly, I.V., Borisy, G.G., 2001. Self-organization of a propulsive actin network as an evolutionary process. Proc. Natl. Acad. Sci. U.S.A. 98(20), 11324-11329.
56. Marée, A.F.M., Hogeweg, P., 2001. How amoeboids self-organize into a fruiting body: Multicellular coordination in Dictyostelium discoideum. Proc. Natl.Acad. Sci. U.S.A. 98(7), 3879-3883.
57. Marion, J.B., Thornton, S.T., 1995. Classical Dynamics of Particles and Systems, chapter 7, 4th edition. Harcourt Brace, Fort Worth.
58. Matozaki, T., Nakanishi, H., Takai, Y., 2000. Small G-protein networks: Their crosstalk and signal cascades. Cell. Signal. 12(8), 515-524.
59. Meili, R., Firtel, R.A., 2003. Two poles and a compass. Cell 114(2), 153-156.
60. Meinhardt, H., 2003. Complex pattern formation by a self-destabilization of established patterns: Chemotactic orientation and phyllotaxis as examples. C. R. Biol. 326(2), 223-237.
61. Metropolis, N., Rosenbluth, A.E., Rosenbluth, M.N., Teller, A.H., Teller, E., 1953. Equation of state calculations by fast computing machines. J. Chem. Phys. 21, 1087-1092.
62. Michaelson, D., Silletti, J., Murphy, G., D'Eustachio, P., Rush, M., Philips, M.R., 2001. Differential localization of Rho GTPases in live cells: Regulation by hypervariable regions and RhoGDI binding. J. Cell Biol. 152(1), 111-126.
63. Mogilner, A., Edelstein-Keshet, L., 2002. Regulation of actin dynamics in rapidly moving cells: A quantitative analysis. Biophys. J. 83(3), 1237-1258.
64. Mogilner, A., Oster, G., 1996a. Cell motility driven by actin polymerization. Biophys. J. 71(6), 3030-3045.
65. Mogilner, A., Oster, G., 1996b. The physics of lamellipodial protrusion. Eur. Biophys. J. 25(1), 47-53.
66. Mogilner, A., Oster, G., 2003. Force generation by actin polymerization II: The elastic ratchet and tethered filaments. Biophys. J. 84(3), 1591-1605.
67. Mombach, J.C.M., Glazier, J.A., Raphael, R.C., Zajac, M., 1995. Quantitative comparison between differential adhesion models and cell sorting in the presence and absence of fluctuations. Phys. Rev. Lett. 75(11), 2244-2247.
68. Mullins, R.D., Heuser, J.A., Pollard, T.D., 1998. The interaction of Arp2/3 complex with actin: Nucleation, high affinity pointed end capping, and formation of branching networks of filaments. Proc. Natl. Acad. Sci. U.S.A. 95(11), 6181-6186.
69. Mullins, R.D., Stafford, W.F., Pollard, T.D., 1997. Structure, subunit topology, and actin-binding activity of the Arp2/3 complex from Acanthamoeba. J. Cell Biol. 136(2), 331-343.
70. Nalbant, P., Hodgson, L., Kraynov, V., Toutchkine, A., Hahn, K.M., 2004. Activation of endogenous Cdc42 visualized in living cells. Science 305(5690), 1615-1619.
71. Narang, A., 2006. Spontaneous polarization in eukaryotic gradient sensing: A mathematical model based on mutual inhibition of frontness and backness pathways. J. Theor. Biol. 240(4), 538-553.
72. Neely, M.D., Nicholls, J.G., 1995. Electrical activity, growth cone motility and the cytoskeleton. J. Exp. Biol. 198(Pt 7), 1433-1446.
73. Nishiura, Y., 1991. Singular limit approach to stability and bifurcation for bistable reaction diffusion-systems. Rocky Mt. J. Math. 21(2), 727-767.
74. Nobes, C.D., Hall, A., 1995. Rho, Rac, and Cdc42 GTPases regulate the assembly of multimolecular focal complexes associated with actin stress fibers, lamellipodia, and filopodia. Cell 81(1), 53-62.
75. Nobes, C.D., Hall, A., 1999. Rho GTPases control polarity, protrusion, and adhesion during cell movement. J. Cell Biol. 144(6), 1235-1244.
76. Parent, C.A., Devreotes, P.N., 1999. A cell's sense of direction. Science 284(5415), 765-770.
77. Pollard, T.D., Blanchoin, L., Mullins, R.D., 2000. Molecular-mechanisms controlling actin filament dynamics in nonmuscle cells. Annu. Rev. Biophys. Biomol. Struct. 29, 545-576.
78. Pollard, T.D., Borisy, G.G., 2003. Cellular motility driven by assembly and disassembly of actin filaments. Cell 112(4), 453-465.
79. Postma, M., Bosgraaf, L., Loovers, H.M., Van Haastert, P.J.M., 2004. Chemotaxis: Signalling-modules join hands at front and tail. EMBO Rep. 5(1), 35-40.
80. Postma, M., Van Haastert, P.J.M., 2001. A diffusion-translocation model for gradient sensing by chemotactic cells. Biophys. J. 81(3), 1314-1323.
81. Raftopoulou, M., Hall, A., 2004. Cell migration: Rho GTPases lead the way. Dev. Biol. 265(1), 23-32.
82. Ream, R.A., Theriot, J.A., Somero, G.N., 2003. Influences of thermal acclimation and acute temperature change on the motility of epithelial wound-healing cells (keratocytes) of tropical, temperate and Antarctic fish. J. Exp. Biol. 206(Pt 24), 4539-4551.
83. Redmond, T., Zigmond, S.H., 1993. Distribution of F-actin elongation sites in lysed polymorphonuclear leukocytes parallels the distribution of endogenous F-actin. Cell Motil. Cytoskeleton 26(1), 7-18.
84. Ridley, A.J., 2001a. Rho family proteins: Coordinating cell responses. Trends Cell Biol. 11(12), 471-477.
85. Ridley, A.J., 2001b. Rho GTPases and cell migration. J. Cell Sci. 114(Pt 15), 2713-2722.
86. Ridley, A.J., Paterson, H.F., Johnston, C.L., Diekmann, D., Hall, A., 1992. The small GTP-binding protein Rac regulates growth factor-induced membrane ruffling. Cell 70(3), 401-410.
87. Rubinstein, B., Jacobson, K., Mogilner, A., 2005. Multiscale two-dimensional-modeling of a motile simple-shaped cell. SIAM Multiscale Model. Simul. 3(2), 413-439.
88. Sako, Y., Hibino, K., Miyauchi, T., Miyamoto, Y., Ueda, M., Yanagida, T., 2000. Single-molecule imaging of signaling molecules in living cells. Single Mol. 1(2), 159-163.
89. Sakumura, Y., Tsukada, Y., Yamamoto, N., Ishii, S., 2005. A molecular model for axon guidance based on cross talk between rho GTPases. Biophys. J. 89(2), 812-822.
90. Sander, E.E., Ten Klooster, J.-P., Van Delft, S., Van Der Kammen, R.A., Collard, J.G., 1999. Rac downregulates Rho activity: Reciprocal balance between both GTPases determines cellular morphology and migratory behavior. J. Cell Biol. 147(5), 1009-1022.
91. Segel, L.A., 2001. Computing an organism. Proc. Natl. Acad. Sci. U.S.A. 98(7), 3639-3640.
92. Steinmetz, M.O., Stoffler, D., Hoenger, A., Bremer, A., Aebi, U., 1997. Actin: From cell biology to atomic detail. J. Struct. Biol. 119(3), 295-320.
93. Suetsugu, S., Miki, H., Takenawa, T., 2002. Spatial and temporal regulation of actin polymerization for cytoskeleton formation through Arp2/3 complex and WASP/WAVE proteins. Cell Motil. Cytoskeleton 51(3), 113-122.
94. Svitkina, T.M., Borisy, G.G., 1999. Arp2/3 complex and actin depolymerizing factor/cofilin in dendritic organization and treadmilling of actin filament array in lamellipodia. J. Cell Biol. 145(5), 1009-1026.
95. Svitkina, T.M., Verkhovsky, A.B., McQuade, K.M., Borisy, G.G., 1997. Analysis of the actin-myosin II system in fish epidermal keratocytes: Mechanism of cell body translocation. J. Cell Biol. 139(2), 397-415.
96. Takai, Y., Sasaki, T., Matozaki, T., 2001. Small GTP-binding proteins. Physiol. Rev. 81(1), 153-208.
97. Takubo, T., Tatsumi, N., 1997. Distribution of myosin and actin in moving human neutrophils detected by double-fluorescence staining. Anal. Quant. Cytol. Histol. 19(3), 233-238.
98. Tsuji, T., Ishizaki, T., Okamoto, M., Higashida, C., Kimura, K., Furuyashiki, T., Arakawa, Y., Birge, R.B., Nakamoto, T., Hirai, H., Narumiya, S., 2002. ROCK and mDia1 antagonize in Rho-dependent Rac activation in Swiss 3T3 fibroblasts. J. Cell Biol. 157(5), 819-830.
99. Vallotton, P., Gupton, S.L., Waterman-Storer, C.M., Danuser, G., 2004. Simultaneous mapping of filamentous actin flow and turnover in migrating cells by quantitative fluorescent speckle microscopy. Proc. Natl. Acad. Sci. U.S.A. 101(26), 9660-9665.
100. Van Leeuwen, F.N., Kain, H.E.T., Van Der Kammen, R.A., Michiels, F., Kranenburg, O.W., Collard, J.G., 1997. The guanine nucleotide exchange factor Tiam1 affects neuronal morphology: Opposing roles for the small GTPases Rac and Rho. J. Cell Biol. 139(3), 797-807.
101. Verkhovsky, A.B., Chaga, O.Y., Schaub, S., Svitkina, T.M., Meister, J.-J., Borisy, G.G., 2003. Orientational order of the lamellipodial actin network as demonstrated in living motile cells. Mol. Biol. Cell 14(11), 4667-4675.
102. Verkhovsky, A.B., Svitkina, T.M., Borisy, G.G., 1999. Self-polarization and directional motility of cytoplasm. Curr. Biol. 9(1), 11-20.
103. Wells, A., Gupta, K., Chang, P., Swindle, S., Glading, A., Shiraha, H., 1998. Epidermal growth factor receptor-mediated motility in fibroblasts. Microsc. Res. Tech. 43(5), 395-411.
104. Wittmann, T., Waterman-Storer, C.M., 2001. Cell motility: Can Rho GTPases and microtubules point the way? J. Cell Sci. 114(Pt 21), 3795-3803.
105. Xu, J., Wang, F., Van Keymeulen, A., Herzmark, P., Straight, A., Kelly, K., Takuwa, Y., Sugimoto, N., Mitchison, T., Bourne, H.R., 2003. Divergent signals and cytoskeletal assemblies regulate self-organizing polarity in neutrophils. Cell 114(2), 201-214.
106. Zebda, N., Bernard, O., Bailly, M., Welti, S., Lawrence, D.S., Condeelis, J.S., 2000. Phosphorylation of ADF/cofilin abolishes EGF-induced actin nucleation at the leading edge and subsequent lamellipod extension. J. Cell Biol. 151(5), 1119-1128.
107. Zhang, B., Zheng, Y., 1998. Regulation of RhoA GTP hydrolysis by the GTPase-activating proteins p190, p50RhoGAP, Bcr, and 3BP-1. Biochemistry 37(15), 5249-5257.
108. Zondag, G.C.M., Evers, E.E., Ten Klooster, J.-P., Janssen, L., Van Der Kammen, R.A., Collard, J.G., 2000. Oncogenic Ras downregulates Rac activity, which leads to increased Rho activity and epithelial-mesenchymal transition. J. Cell Biol. 149(4), 775-782.