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Single-Cell-Based Models in Biology and Medicine pp 137–150Cite as

The Cellular Potts Model in Biomedicine

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Part of the book series: Mathematics and Biosciences in Interaction ((MBI))

Abstract

In this chapter we describe how the the Cellular Potts Model (CPM) has been applied to problems in the biomedical field. Examples are given in epidermal biology, cancer and vasculogenesis. They demonstrate the strength of the CPM and its rich set of extensions, in elucidating biomedically important phenomena.

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References

  1. J. C. Adams and F. M. Watt. Fibronectin inhibits the terminal differentiation of human keratinocytes. Nature, 340:307–309, 1989.

    Article  Google Scholar 

  2. J. C. Adams and F. M. Watt. Changes in keratinocyte adhesion during terminal differentiation-reduction in fibronectin binding precedes α-5-β-1-integrin loss from the cell-surface. Cell, 63:425–435, 1990.

    Article  Google Scholar 

  3. D. Ambrosi, A. Gamba, and G. Serini. Cell directional persistence and chemotaxis in vascular morphogenesis. B. Math. Biol., 66:1851–1873, 2004.

    Article  MathSciNet  Google Scholar 

  4. A. R. A. Anderson and M. A. J. Chaplain. Continuous and discrete mathematical models of tumor-induced angiogenesis. B. Math. Biol., 60:857–899, 1998.

    Article  MATH  Google Scholar 

  5. Y. Barrandon and H. Green. Cell size as a determinant of the clone forming ability of human keratinocytes. PNAS, 82:5390–5394, 1985.

    Article  Google Scholar 

  6. Y. Barrandon and H. Green. Three clonal types of keratinocytes with different capacities for multiplication. PNAS, 84:2302–2306, 1987.

    Article  Google Scholar 

  7. E. Dejana. Endothelial cell-cell junctions: Happy together. Nat. Rev. Mol. Cell Bio., 5:261–270, 2004.

    Article  Google Scholar 

  8. R. Dover and C. S. Potten. Cell cycle kinetics of cultured human epidermal keratinocytes. J. Invest. Dermatol., 80:423–429, 1983.

    Article  Google Scholar 

  9. J. F. Dye, L. Lawrence, C. Linge, L. Leach, J. A. Firth, and P. Clark. Distinct patterns of microvascular endothelial cell morphology are determined by extracellular matrix composition. Endothelium, 11:151–167, 2004.

    Article  Google Scholar 

  10. A. Gamba, D. Ambrosi, A. Coniglio, A. De Candia, S. Di Talia, E. Giraudo, G. Serini, L. Preziosi, and F. Bussolino. Percolation morphogenesis and burgers dynamics in blood vessels formation. Phys. Rev. Lett., 90:118101, 2003.

    Article  Google Scholar 

  11. H. Gerhardt, M. Golding, M. Fruttiger, C. Ruhrberg, A. Lundkvist, A. Abramsson, M. Jeltsch, C. Mitchell, K. Alitalo, D. Shima, and C. Betsholtz. VEGF guides angiogenic sprouting utilizing endothelial tip cell filopodia. J. Cell Biol., 161:1163–1177, 2003.

    Article  Google Scholar 

  12. S. Gory-Fauré, M.-H Prandini, H. Pointu, V. Roullot, I. Pignot-Paintrand, M. Vernet, and P. Huber. Role of vascular endothelial-cadherin in vascular morphogenesis. Development, 126:2093–2102, 1999.

    Google Scholar 

  13. G. Helmlinger, M. Endo, N. Ferrara, L. Hlatky, and R. K. Jain. Growth factors-formation of endothelial cell networks. Nature, 405:139–141, 2000.

    Article  Google Scholar 

  14. N. A. Hotchin, A. Gandarillas, and F. M. Watt. Regulation of cell-surface β-1 integrin levels during keratinocyte terminal differentiation. J. Cell Biol., 128:1209–1219, 1995.

    Article  Google Scholar 

  15. U. B. Jensen, S. Lowell, and F. M. Watt. The spatial relationship between stem cells and their progeny in the basal layer of human epidermis: a new view based on whole-mount labelling and lineage analysis. Development, 126:2409–2418, 1999.

    Google Scholar 

  16. Y. Jiang, J. A. Pjesivac-Grbovic, C. Cantrell, and J.P. Freyer. A multiscale model for avascular tumour growth. Biophys. J., 89:3884–3894, 2005.

    Article  Google Scholar 

  17. P. H. Jones, S. Harper, and F. M. Watt. Stem cell patterning and fate in human epidermis. Cell, 80:83–93, 1995.

    Article  Google Scholar 

  18. E. F. Keller and L. A. Segel. Initiation of slime mold aggregation viewed as an instability. J. Theor. Biol., 26:399–415, 1970.

    Article  Google Scholar 

  19. M. A. Knewitz and J. C. M. Mombach. Computer simulation of the influence of cellular adhesion on the morphology of the interface between tissues of proliferating and quiescent cells. Comp. Biol. Med., 36:59–69, 2006.

    Article  Google Scholar 

  20. L. Lamalice, F. Houle, G. Jourdan, and J. Huot. Phosphorylation of tyrosine 1214 on VEGFR2 is required for VEGF-induced activation of Cdc42 upstream of SAPK2/p38. Oncogene, 23:434–445, 2004.

    Article  Google Scholar 

  21. S. Lowell, P. Jones, I. Le Roux, J. Dunne, and F. M. Watt. Stimulation of human epidermal differentiation by Delta-Notch signalling at the boundaries of stem-cell clusters. Curr. biol., 10:491–500, 2000.

    Article  Google Scholar 

  22. S. Lowell and F. M. Watt. Delta regulates keratinocyte spreading and motility independently of differentiation. Mech. Dev., 107:133–140, 2001.

    Article  Google Scholar 

  23. D. Manoussaki, S. R. Lubkin, R. B. Vernon, and J. D. Murray. A mechanical model for the formation of vascular networks in vitro. Acta Biotheor., 44:271–282, 1996.

    Article  Google Scholar 

  24. S. R. McDougall, A. R. A. Anderson, M. A. J. Chaplain, and J. A. Sherratt. Mathematical modelling of flow through vascular networks: implications for tumourinduced angiogenesis and chemotherapy strategies. B. Math. Biol., 64:673–702, 2002.

    Article  Google Scholar 

  25. R. M. H. Merks, S. V. Brodsky, M. S. Goligorksy, S. A. Newman, and J. A. Glazier. Cell elongation is key to in silico replication of in vitro vasculogenesis and subsequent remodeling. Dev. Biol., 289(1):44–54, 2006.

    Article  Google Scholar 

  26. R. M. H. Merks and J. A. Glazier. Dynamic mechanisms of blood vessel growth. Nonlinearity, 19:C1–C10, 2006.

    Article  MATH  MathSciNet  Google Scholar 

  27. R. M. H. Merks, S. A. Newman, and J. A. Glazier. Cell-oriented modeling of in vitro capillary development. In Peter M.A. Sloot, Bastien Chopard, and Alfons G. Hoekstra, editors, Cellular Automata. 6th international conference on Cellular Automata for Research and Industry, volume 3305 of Lect. Notes Comput. Sc., pages 425–434, Berlin, 2004. Spinger Verlag.

    Google Scholar 

  28. R. M. H. Merks, Erica D. Perryn, and James A. Glazier. Contact-inhibited chemotactic motility: Role in de novo and sprouting blood vessel growth. arXiv:q-bio.TO/0505033, 2005.

    Google Scholar 

  29. T. M. Moore, G. H. Brough, P. Babal, J. J. Kelly, M. Li, and T. Stevens. Storeoperated calcium entry promotes shape change in pulmonary endothelial cells expressing Trp1. Am. J. Physiol., 275:L574–L582, 1998.

    Google Scholar 

  30. J. D. Murray, D. Manoussaki, S. R. Lubkin, and R. B. Vernon. A mechanical theory of in vitro vascular network formation. In C. D. Little, V. Mironov, and E. Helene Sage, editors, Vascular morphogenesis: in vivo, in vitro, in mente, pages 173–188. Birkhauser, Boston, MA, 1998.

    Google Scholar 

  31. P. Namy, J. Ohayon, and P. Tracqui. Critical conditions for pattern formation and in vitro tubulogenesis driven by cellular traction fields. J. Theor. Biol., 227:103–120, 2004.

    Article  MathSciNet  Google Scholar 

  32. A. Rangarajan, C. Talora, R. Okuyama, M. Nicolas, C. Mammucari, H. Oh, J. C. Aster, S. Krishna, D. Metzger, P. Chambon, L. Miele, M. Aguet, F. Radtke, and G. P. Dotto. Notch signalling is a direct determinant of keratinocyte growth arrest and entry into differentiation. EMBO J., 20:3427–3436, 2001.

    Article  Google Scholar 

  33. J. P. Rieu, A. Upadhyaya, J. A. Glazier, N. B. Ouchi, and Y. Sawada. Diffusion and deformations of single hydra cells in cellular aggregates. Biophys. J., 79:1903–1914, 2000.

    Article  Google Scholar 

  34. W. Riseau. Mechanisms of angiogenesis. Nature, 386:671–674, 1997.

    Article  Google Scholar 

  35. P. A. Rupp, A. Czirók, and C. D. Little. αvβ3 integrin-dependent endothelial cell dynamics in vivo. Development, 131:2887–2897, 2004.

    Article  Google Scholar 

  36. N. J. Savill and P. Hogeweg. Modelling morphogenesis: from single cells to crawling slugs. J. Theor. Biol., 184:229–235, 1997.

    Article  Google Scholar 

  37. N. J. Savill and J. A. Sherratt. Control of epidermal stem cell clusters by Notchmediated lateral induction. Dev. Biol., 258:141–153, 2003.

    Article  Google Scholar 

  38. G. Serini, D. Ambrosi, E. Giraudo, A. Gamba, L. Preziosi, and F. Bussolino. Modeling the early stages of vascular network assembly. EMBO J., 22:1771–1779, 2003.

    Article  Google Scholar 

  39. E. L. Stott, N. F. Britton, J. A. Glazier, and M. Zajac. Stochastic simulation of benign avascular tumour growth using the Potts model. Math. Comp. Model., 30:183–198, 1999.

    Article  Google Scholar 

  40. S. Turner and J. A. Sherratt. Intercellular adhesion and cancer invasion: A discrete simulation using the extended Potts model. J. theor. Biol., 216:85–100, 2002.

    Article  MathSciNet  Google Scholar 

  41. S. Turner, J. A. Sherratt, and D. Cameron. Tamoxifen treatment failure in cancer and the nonlinear dynamics of TGFβ. J. Theor. Biol., 229:101–111, 2004.

    Article  MathSciNet  Google Scholar 

  42. G. M. Walker, J. Sai, A. Richmond, M. Stremler, C. Y. Chung, and J. P. Wikswo. Effects of flow and diffusion on chemotaxis studies in a microfabricated gradient generator. Lab Chip, 5:611–618, 2005.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Centre for Infectious Disease, University of Edinburgh, Ashworth Laboratories Kings Buildings, West Mains Road, Edinburgh, EH9 3JF, Scotland

    Nicholas J. Savill

  2. Department of Plant Systems Biology, VIB Technologiepark 927, B-9052, Ghent, Belgium

    Roeland M. H. Merks

  3. Department of Molecular Genetics, Ghent University, Ghent, Belgium

    Roeland M. H. Merks

Authors
  1. Nicholas J. Savill
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  2. Roeland M. H. Merks
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Editor information

Editors and Affiliations

  1. Division of Mathematics, University of Dundee, 23 Perth Road, Dundee, DD1 4HN, UK

    Alexander R. A. Anderson , Mark A. J. Chaplain  & Katarzyna A. Rejniak ,  & 

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© 2007 Birkhäuser Verlag Basel/Switzerland

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Savill, N.J., Merks, R.M.H. (2007). The Cellular Potts Model in Biomedicine. In: Anderson, A.R.A., Chaplain, M.A.J., Rejniak, K.A. (eds) Single-Cell-Based Models in Biology and Medicine. Mathematics and Biosciences in Interaction. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8123-3_6

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