Mathematical modeling of cell adhesion and its applications to developmental biology and cancer invasion

Cell Mechanics: From Single Scale-Based Models to Multiscale Modeling

Volumn , Issue , 2010, Pages 319-344

  Gerisch, Alf ^a   Painter, Kevin J ^b  

^a MARTIN LUTHER UNIVERSITY HALLE WITTENBERG   (Germany)

^b HERIOT WATT UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85055375613     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1201/9781420094558     Document Type: Chapter

References (81)

1. B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, and P. Walter (2002). Molecular Biology of the Cell, 4th edition. Garland Science, Taylor & Francis Group.
2. A.R.A. Anderson (2005). A hybrid mathematical model of solid tumour invasion: the importance of cell adhesion. IMA J. Math. Med. Biol. 22:163-186.
3. A.R.A. Anderson, M.A.J. Chaplain, E.L. Newman, R.J.C. Steele, and A.M. Thompson (2000). Mathematical modelling of tumour invasion and metastasis. Comput. Math. Meth. Med. (formerly J. Theor. Med.) 2:129-154.
4. A.R.A. Anderson, A.M. Weaver, P.T. Cummings, and V. Quaranta (2006). Tumor morphology and phenotypic evolution driven by selective pressure from the microenvironment. Cell 127:905-915.
5. K. Anguige and C. Schmeiser (2009). A one-dimensional model of cell diffusion and aggregation, incorporating volume filling and cell-to-cell adhesion. J. Math. Biol. 58(3):395-427.
6. N.J. Armstrong, K.J. Painter, and J.A. Sherratt (2006). A continuum approach to modelling cell-cell adhesion. J. Theor. Biol. 243:98-113.
7. N.J. Armstrong, K.J. Painter, and J.A. Sherratt (2009). Adding adhesion to a chemical signaling model for somite formation. Bull. Math. Biol. 71:1-24.
8. K.M. Bagnall, S.J. Higgins, and E.J. Sanders (1989). The contribution made by cells from a single somite to tissues within a body segment and assessment of their integration with similar cells from adjacent segments. Development 107:931-943.
9. A.L. Bauer, T.L. Jackson, and Y. Jiang (2007). A cell-based model exhibiting branching and anastomosis during tumor-induced angiogenesis. Biophys. J. 92:3105-3121.
10. A.L. Berrier and K.M. Yamada (2007). Cell-matrix adhesion. J. Cell. Physiol. 213:565-573.
11. W. Birchmeier (1994). Molecular aspects of the loss of cell adhesion and gain of invasiveness in carcinomas. Int. Symp. Princess Takamatsu Cancer Res. Fund 24:214-232.
12. H.M. Byrne and M.A.J. Chaplain (1996). Modelling the role of cell-cell adhesion in the growth and development of carcinomas. Math. Comput. Modelling 24:1-17.
13. R.W. Carthew (2007). Pattern formation in the Drosophila eye. Curr. Opin. Genet. Dev. 17:309-313.
14. U. Cavallaro and G. Christofori (2004). Cell adhesion and signalling by cadherins and Ig-CAMs in cancer. Nat. Rev. Cancer 4:118-132.
15. U. Cavallaro and G. Christofori (2004). Multitasking in tumor progression: signaling functions of cell adhesion molecules. Ann. N.Y. Acad. Sci. 1014:58-66.
16. C.M. Cheney and J.W. Lash (1984). An increase in cell-cell adhesion in the chick segmental plate results in a meristic pattern. J. Embryol. Exp. Morphol. 79:1-10.
17. G. Christofori (2003). Changing neighbours, changing behaviour: cell adhesion molecule-mediated signalling during tumour progression. EMBO J. 22:2318-2323.
18. V. Cristini, J. Lowengrub, and Q. Nie (2003). Nonlinear simulation of tumor growth. J. Math. Biol. 46:191-224.
19. J.C. Dallon and H.G. Othmer (2004). How cellular movement determines the collective force generated by the Dictyostelium discoideum slug. J. Theor. Biol. 231:203-222.
20. A. Deutsch (1999). Cellular Automata and Biological Pattern Formation. Habilitation thesis, University of Bonn.
21. A. Deutsch and S. Dormann (2005). Cellular Automaton Modeling of Biological Pattern Formation: Characterization, Applications, and Analysis. Boston, Birkhäuser.
22. R. Dillon, K.J. Painter, and M.R. Owen (2008). A single-cell based model of cellular growth using the immersed boundary method. In B. Cheong Koo, Z. Li, and P. Li, Eds., Moving Interface Problems and Applications in Fluid Dynamics, Contemporary Mathematics. AMS, 1-16.
23. D. Drasdo, R. Kree, and J.S. McCaskill (1995). Monte Carlo approach to tissue-cell populations. Phys. Rev. E 52:6635-6657.
24. J.L. Duband, S. Dufour, K. Hatta, M. Takeichi, G.M. Edelman, and J.P. Thiery (1987). Adhesion molecules during somitogenesis in the avian embryo. J. Cell. Biol. 104:1361-1374.
25. D. Duguay, R.A. Foty, and M.S. Steinberg (2003). Cadherin-mediated cell adhesion and tissue segregation: qualitative and quantitative determinants. Dev. Biol. 253:309-323.
26. G.A. Dunn and J.P. Heath (1976). A new hypothesis of contact guidance in tissue cells. Exp. Cell Res. 101:1-14.
27. R.A. Foty and M.S. Steinberg (2004). Cadherin-mediated cell-cell adhesion and tissue segregation in relation to malignancy. Int. J. Dev. Biol. 48:397-409.
28. R.A. Foty and M.S. Steinberg (2005). The differential adhesion hypothesis: a direct evaluation. Dev. Biol. 278:255-263.
29. P. Friedl and K. Wolf (2003). Tumour-cell invasion and migration: diversity and escape mechanisms. Nat. Rev. Cancer 3:362-374.
30. J. Galle, G. Aust, G. Schaller, T. Beyer, and D. Drasdo (2006). Individual cell-based models of the spatial-temporal organization of multicellular systems: achievements and limitations. Cytometry Part A 69A:704-710.
31. A. Gerisch (2009). On the approximation and efficient evaluation of integral terms in PDE models of cell adhesion. In press. DOI 10.1093/imanum. IMA Journal of Numerical Analysis. drp027.
32. A. Gerisch and M.A.J. Chaplain (2006). Robust numerical methods for taxis-diffusion-reaction systems: applications to biomedical problems. Math. Comput. Modelling 43:49-75.
33. A. Gerisch and M.A.J. Chaplain (2008). Mathematical modelling of cancer cell invasion of tissue: local and non-local models and the effect of adhesion. J. Theor. Biol. 250:684-704.
34. J.A. Glazier and F. Graner (1993). Simulation of the differential adhesion driven rearrangement of biological cells. Phys. Rev. E 47:2128-2154.
35. F. Graner and J.A. Glazier (1992). Simulation of biological cell sorting using a two-dimensional extended Potts model. Phys. Rev. Lett. 69:2013-2016.
36. B.M. Gumbiner (2005). Regulation of cadherin-mediated adhesion in morphogenesis. Nat. Rev. Mol. Cell Biol. 6:622-634.
37. T. Hillen (2002). Hyperbolic models for chemosensitive movement. Math. Mod. Meth. Appl. Sci. 12:1007-1034.
38. T. Hillen, K. Painter, and C. Schmeiser (2007). Global existence for chemotaxis with finite sampling radius. Disc. Cont. Dyn. Syst. B (DCDS-B) 7:125-144.
39. T. Hillen and K.J. Painter (2009). A user’s guide to PDE models for chemotaxis. J. Math. Biol. 58:183-217.
40. G.S. Hillis and A.D. Flapan (1998). Cell adhesion molecules in cardiovascular disease: a clinical perspective. Heart 79:429-431.
41. T. Hofer, J.A. Sherratt, and P.K. Maini (1995). Dictyostelium discoideum: cellular self-organization in an excitable biological medium. Proc. Biol. Sci. 259:249-257.
42. K. Horikawa, G. Radice, M. Takeichi, and O. Chisaka (1999). Adhesive subdivisions intrinsic to the epithelial somites. Dev. Biol. 215:182-189.
43. E.F. Keller and L.A. Segel (1970). Initiation of slime mold aggregation viewed as an instability. J. Theor. Biol. 26:399-415.
44. R. Keller (2002). Shaping the vertebrate body plan by polarized embryonic cell movements. Science 298:1950-1954.
45. K.K. Linask, C. Ludwig, M.D. Han, X. Liu, G.L. Radice, and K.A. Knudsen (1998). N-cadherin/catenin-mediated morphoregulation of somite formation. Dev. Biol. 202:85-102.
46. C.M. Lo, H.B. Wang, M. Dembo, and Y.L. Wang (2000). Cell movement is guided by the rigidity of the substrate. Biophys. J. 79:144-152.
47. P. Macklin and J. Lowengrub (2007). Nonlinear simulation of the effect of microenvironment on tumor growth. J. Theor. Biol. 245:677-704.
48. A.F. Marée and P. Hogeweg (2001). How amoeboids self-organize into a fruiting body: multicellular coordination in Dictyostelium discoideum. Proc. Natl. Acad. Sci. USA 98:3879-3883.
49. M. Mareel and A. Leroy (2003). Clinical, cellular, and molecular aspects of cancer invasion. Physiol. Rev. 83:337-376.
50. J. Moreira and A. Deutsch (2005). Pigment pattern formation in zebrafish during late larval stages: a model based on local interactions. Dev. Dyn. 232:33-42.
51. T.J. Newman (2005). Modeling multicellular systems using subcellular elements. Math. Biosci. Eng. 2:613-624.
52. T.J. Newman and R. Grima (2004). Many-body theory of chemotactic cell-cell interactions. Phys. Rev. E 70:051916.
53. D. Ostrovsky, C.M. Cheney, A.W. Seitz, and J.W. Lash (1983). Fibronectin distribution during somitogenesis in the chick embryo. Cell. Differ. 13:217-223.
54. K.J. Painter, D. Horstmann, and H.G. Othmer (2003). Localization in lattice and continuum models of reinforced random walks. Appl. Math. Lett. 16:375-381.
55. E. Palsson (2008). A 3-D model used to explore how cell adhesion and stiffness affect cell sorting and movement in multicellular systems. J. Theor. Biol. 254:1-13.
56. E. Palsson and H.G. Othmer (2000). A model for individual and collective cell movement in Dictyostelium discoideum. Proc. Natl. Acad. Sci. USA 97:10448-10453.
57. S.D. Patel, C.P. Chen, F. Bahna, B. Honig, and L. Shapiro (2003). Cadherin-mediated cell-cell adhesion: sticking together as a family. Curr. Opin. Struct. Biol. 13:690-698.
58. N.J. Popawski, M. Swat, J.S. Gens, and J.A. Glazier (2007). Adhesion between cells, diffusion of growth factors, and elasticity of the AER produce the paddle shape of the chick limb. Physica A 373:521-532.
59. O. Pourquié (2001). Vertebrate somitogenesis. Annu. Rev. Cell. Dev. Biol. 17:311-350.
60. I. Ramis-Conde, D. Drasdo, A.R.A. Anderson, and M.A.J. Chaplain (2008). Modeling the influence of the E-cadherin-beta-catenin pathway in cancer cell invasion: a multiscale approach. Biophys. J. 95:155-165.
61. K.A. Rejniak (2007). An immersed boundary framework for modelling the growth of individual cells: an application to the early tumour development. J. Theor. Biol. 247:186-204.
62. N.J. Savill and J.A. Sherratt (2003). Control of epidermal stem cell clusters by Notch-mediated lateral induction. Dev. Biol. 258:141-153.
63. G. Schaller and M. Meyer-Hermann (2005). Multicellular tumor spheroid in an off-lattice Voronoi-Delaunay cell model. Phys. Rev. E 71:051910.
64. J.A. Sherratt, S. Gourley, N.A. Armstrong, and K.J. Painter (2009). Boundedness of solutions of a nonlocal reaction-diffusion model for cellular adhesion. Eur. J. Appl. Math. 20:123-144.
65. M.S. Steinberg (1962). Mechanism of tissue reconstruction by dissociated cells. II. Time course of events. Science 137:762-763.
66. M.S. Steinberg (1962). On the mechanism of tissue reconstruction by dissociated cells, I. Population kinetics, differential adhesiveness, and the absence of directed migration. Proc. Natl. Acad. Sci. USA 48:1577-1582.
67. M.S. Steinberg (1962). On the mechanism of tissue reconstruction by dissociated cells. III. Free energy relations and the reorganization of fused, heteronomic tissue fragments. Proc. Natl. Acad. Sci. USA 48:1769-1776.
68. M.S. Steinberg (2007). Differential adhesion in morphogenesis: a modern view. Curr. Opin. Genet. Dev. 17:281-286.
69. M.S. Steinberg and M. Takeichi (1994). Experimental specification of cell sorting, tissue spreading, and specific spatial patterning by quantitative differences in cadherin expression. Proc. Natl. Acad. Sci. USA 91:206-209.
70. C.D. Stern and R.J. Keynes (1987). Interactions between somite cells: the formation and maintenance of segment boundaries in the chick embryo. Development 99:261-272.
71. M. Takeichi (1988). The cadherins: cell-cell adhesion molecules controlling animal morphogenesis. Development 102:639-655.
72. M. Takeichi (1995). Morphogenetic roles of classic cadherins. Curr. Opin. Cell Biol. 7:619-627.
73. U. Tepass, D. Godt, and R. Winklbauer (2002). Cell sorting in animal development: signalling and adhesive mechanisms in the formation of tissue boundaries. Curr. Opin. Genet. Dev. 12:572-582.
74. P.L. Townes and J. Holtfreter (1955). Directed movements and selective adhesion of embryonic amphibian cells. J. Exp. Zool. 128:53-120.
75. S. Turner and J.A. Sherratt (2002). Intercellular adhesion and cancer invasion: a discrete simulation using the extended Potts model. J. Theor. Biol. 216:85-100.
76. S. Turner, J.A. Sherratt, and D. Cameron (2004). Tamoxifen treatment failure in cancer and the nonlinear dynamics of TGFβ. J. Theor. Biol. 229:101-111.
77. S. Turner, J.A. Sherratt, K.J. Painter, and N.J. Savill (2004). From a discrete to a continuous model of biological cell movement. Phys. Rev. E 69:021910.
78. R. Weiner, B.A. Schmitt and H. Podhaisky (1997). ROWMAP: a ROWcode with Krylov techniques for large stiff ODEs. Appl. Numer. Math. 25:303-319.
79. M.J. Wheelock, Y. Shintani, M. Maeda, Y. Fukumoto, and K. Johnson (2008). Cadherin switching. J. Cell. Sci. 121:727-735.
80. S.M. Wise, J.S. Lowengrub, H.B. Frieboes, and V. Cristini (2008). Three-dimensional multispecies nonlinear tumor growth: I. Model and numerical method. J. Theor. Biol. 253:524-543.
81. W. Wood and P. Martin (2002). Structures in focus: filopodia. Int. J. Biochem. Cell Biol. 34:726-730.