The Cellular Potts Model and Biophysical Properties of Cells, Tissues and Morphogenesis

  • Athanasius F. M. Marée
  • Verônica A. Grieneisen
  • Paulien Hogeweg
Part of the Mathematics and Biosciences in Interaction book series (MBI)


In this chapter we examine the properties of the Cellular Potts Model (CPM) formalism which make it preeminently suitable for modelling biological cells. The most outstanding feature in which CPM differs from other modelling formalisms, is that a cell is modelled as a deformable object, and takes its shape from a combination of internal and external forces which act upon it. The energy minimisation based CPM formalism enables us to integrate these forces acting at different scales. We map the parameters of the basic CPM formalism to physical and biological properties of cells. We show through those mappings that the modelling formalism is a powerful tool for investigating a large range of biological questions, from those concerning biophysical properties of single cells, cell motion, tissue level properties, all the way up to understanding the full morphogenesis and life-cycle of an organism.


Cellular Potts Model Tissue Level Property 4U00 0F0U 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    V. C. Abraham, V. Krishnamurthi, D. L. Taylor, and F. Lanni. The actin-based nanomachine at the leading edge of migrating cells. Biophys. J., 77(3):1721–1732, 1999.Google Scholar
  2. [2]
    P. B. Armstrong and R. Niederman. Reversal of tissue position after cell sorting. Dev. Biol., 28(3):518–527, 1972.CrossRefGoogle Scholar
  3. [3]
    J. B. Beltman, A. F. M. Maréê, J. N. Lynch, M. J. Miller, and R. J. De Boer. Lymph node topology dictates T cell migration behavior. J. Exp. Biol., in press, 2007.Google Scholar
  4. [4]
    J. Carr and R. L. Pego. Metastable patterns in solutions of u t = ɛ 2 u xxf ( u ). Comm. Pure Appl. Math., 42(5):523–576, 1989.MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    L. Carroll. Through the Looking Glass. Macmillan, London, 1872.Google Scholar
  6. [6]
    M. A. Castro, F. Klamt, V. A. Grieneisen, I. Grivicich, and J. C. Moreira. Gompertzian growth pattern correlated with phenotypic organization of colon carcinoma, malignant glioma and non-small cell lung carcinoma cell lines. Cell Prolif., 36(2):65–73, 2003.CrossRefGoogle Scholar
  7. [7]
    C. S. Chen, M. Mrksich, S. Huang, G. M. Whitesides, and D. E. Ingber. Geometric control of cell life and death. Science, 276(5317):1425–1428, 1997.CrossRefGoogle Scholar
  8. [8]
    L. P. Cramer, T. J. Mitchison, and J. A. Theriot. Actin-dependent motile forces and cell motility. Curr. Opin. Cell Biol., 6(1):82–86, 1994.CrossRefGoogle Scholar
  9. [9]
    S. Etienne-Manneville. Cdc42-the centre of polarity. J. Cell Sci., 117(Pt 8):1291–1300, 2004.CrossRefGoogle Scholar
  10. [10]
    E. Farge. Mechanical induction of Twist in the D rosophila foregut/stomodeal primordium. Curr. Biol., 13(16):1365–1377, 2003.CrossRefGoogle Scholar
  11. [11]
    J. Folkman and A. Moscona. Role of cell shape in growth control. Nature, 273(5661):345–349, 1978.CrossRefGoogle Scholar
  12. [12]
    J. A. Glazier and F. Graner. Simulation of the differential adhesion driven rearrangement of biological cells. Phys. Rev. E, 47(3):2128–2154, 1993.CrossRefGoogle Scholar
  13. [13]
    F. Graner. Can surface adhesion drive cell-rearrangement? Part I: biological cellsorting. J. theor. Biol., 164:455–476, 1993.CrossRefGoogle Scholar
  14. [14]
    V. A. Grieneisen. Estudo do estabelecimento de configurações em estruturas celulares. Master’s thesis, Universidade Federal do Rio Grande do Sul, Porto Alegre, 2004.Google Scholar
  15. [15]
    F. Guilak, G. R. Erickson, and H. P. Ting-Beall. The effects of osmotic stress on the viscoelastic and physical properties of articular chondrocytes. Biophys. J., 82(2):720–727, 2002.CrossRefGoogle Scholar
  16. [16]
    C. Herring. Some theorems on the free energies of crystal surfaces. Phys. Rev., 82:87–93, 1951.MATHCrossRefGoogle Scholar
  17. [17]
    P. Hogeweg. Evolving mechanisms of morphogenesis: on the interplay between differential adhesion and cell differentiation. J. theor. Biol., 203(4):317–333, 2000.CrossRefGoogle Scholar
  18. [18]
    P. Hogeweg. Shapes in the shadow: evolutionary dynamics of morphogenesis. Artif. Life, 6(1):85–101, 2000.CrossRefGoogle Scholar
  19. [19]
    P. Hogeweg. Computing an organism: on the interface between informatic and dynamic processes. BioSystems, 64(1–3):97–109, 2002.CrossRefGoogle Scholar
  20. [20]
    S. Huang and D. E. Ingber. The structural and mechanical complexity of cell-growth control. Nat. Cell Biol., 1(5):E131–E138, 1999.CrossRefGoogle Scholar
  21. [21]
    M. Iwamoto, K. Sugino, R. D. Allen, and Y. Naitoh. Cell volume control in Paramecium: factors that activate the control mechanisms. J. Exp. Biol., 208(Pt 3):523–537, 2005.CrossRefGoogle Scholar
  22. [22]
    Y. Jiang, H. Levine, and J. Glazier. Possible cooperation of differential adhesion and chemotaxis in mound formation of Dictyostelium. Biophys. J., 75(6):2615–2625, 1998.Google Scholar
  23. [23]
    A. Jilkine, A. F. M. Marée, and L. Edelstein-Keshet. Mathematical model for spatial segregation of the Rho-family GTPases based on inhibitory crosstalk. Bull. Math. Biol., in press, 2007.Google Scholar
  24. [24]
    J. Käfer, P. Hogeweg, and A. F. M. Marée. Moving forward moving backward: directional sorting of chemotactic cells due to size and adhesion differences. PLoS Comput. Biol., 2(6):e56, 2006.CrossRefGoogle Scholar
  25. [25]
    V. M. Laurent, S. Kasas, A. Yersin, T. E. Schäffer, S. Catsicas, G. Dietler, A. B. Verkhovsky, and J.-J. Meister. Gradient of rigidity in the lamellipodia of migrating cells revealed by atomic force microscopy. Biophys. J., 89(1):667–675, 2005.CrossRefGoogle Scholar
  26. [26]
    A. F. M. Marée. From Pattern Formation to Morphogenesis: Multicellular Coordination in Dictyostelium discoideum. PhD thesis, Utrecht University, 2000.Google Scholar
  27. [27]
    A. F. M. Marée and P. Hogeweg. How amoeboids self-organize into a fruiting body: multicellular coordination in Dictyostelium discoideum. Proc. Natl. Acad. Sci. U.S.A., 98(7):3879–3883, 2001.CrossRefGoogle Scholar
  28. [28]
    A. F. M. Marée and P. Hogeweg. Modelling Dictyostelium discoideum morphogenesis: the culmination. Bull. Math. Biol., 64(2):327–353, 2002.CrossRefGoogle Scholar
  29. [29]
    A. F. M. Marée, A. Jilkine, A. Dawes, V. A. Grieneisen, and L. Edelstein-Keshet. Polarization and movement of keratocytes: a multiscale modelling approach. Bull. Math. Biol., 68(5):1169–1211, 2006.CrossRefGoogle Scholar
  30. [30]
    A. F. M. Marée, A. V. Panfilov, and P. Hogeweg. Migration and thermotaxis of Dictyostelium discoideum slugs, a model study. J. theor. Biol., 199:297–309, 1999.CrossRefGoogle Scholar
  31. [31]
    A. F. M. Marée, A. V. Panfilov, and P. Hogeweg. Phototaxis during the slug stage of Dictyostelium discoideum: a model study. Proc. R. Soc. Lond. Ser. B, 266:1351–1360, 1999.CrossRefGoogle Scholar
  32. [32]
    R. Meili and R. A. Firtel. Two poles and a compass. Cell, 114(2):153–156, 2003.CrossRefGoogle Scholar
  33. [33]
    N. Metropolis, A. E. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller. Equation of state calculations by fast computing machines. J. Chem. Phys., 21:1087–1092, 1953.CrossRefGoogle Scholar
  34. [34]
    A. Mogilner and L. Edelstein-Keshet. Regulation of actin dynamics in rapidly moving cells: a quantitative analysis. Biophys. J., 83(3):1237–1258, 2002.Google Scholar
  35. [35]
    A. Mogilner and G. Oster. Cell motility driven by actin polymerization. Biophys. J., 71(6):3030–3045, 1996.Google Scholar
  36. [36]
    J. C. M. Mombach, J. A. Glazier, R. C. Raphael, and M. Zajac. Quantitative comparison between differential adhesion models and cell sorting in the presence and absence of fluctuations. Phys. Rev. Lett., 75(11):2244–2247, 1995.CrossRefGoogle Scholar
  37. [37]
    N. B. Ouchi, J. A. Glazier, J.-P. Rieu, A. Upadhyaya, and Y. Sawada. Improving the realism of the cellular Potts model in simulations of biological cells. Physica A, 329(3–4):451–458, 2003.MATHCrossRefMathSciNetGoogle Scholar
  38. [38]
    R. A. Ream, J. A. Theriot, and G. N. Somero. 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, 2003.CrossRefGoogle Scholar
  39. [39]
    C. Rottman and M. Wortis. Exact equilibrium crystal shapes at nonzero temperature in two dimensions. Phys. Rev. B, 24:6274–6277, 1981.CrossRefMathSciNetGoogle Scholar
  40. [40]
    B. Rubinstein, K. Jacobson, and A. Mogilner. Multiscale two-dimensional modeling of a motile simple-shaped cell. SIAM Multiscale Model. Simul., 3(2):413–439, 2005.MATHCrossRefMathSciNetGoogle Scholar
  41. [41]
    E. Ruoslahti. Stretching is good for a cell. Science, 276(5317):1345–1346, 1997.CrossRefGoogle Scholar
  42. [42]
    N. J. Savill and P. Hogeweg. Modelling morphogenesis: From single cells to crawling slugs. J. theor. Biol., 184(3):229–235, 1997.CrossRefGoogle Scholar
  43. [43]
    I. C. Scott and D. Y. R. Stainier. Developmental biology: twisting the body into shape. Nature, 425(6957):461–463, 2003.CrossRefGoogle Scholar
  44. [44]
    L. A. Segel. Computing an organism. Proc. Natl. Acad. Sci. U.S.A., 98(7):3639–3640, 2001.CrossRefGoogle Scholar
  45. [45]
    M. S. Steinberg. Reconstruction of tissues by dissociated cells: some morphogenetic tissue movements and the sorting out of embryonic cells may have a common explanation. Science, 141:401–408, 1963.CrossRefGoogle Scholar
  46. [46]
    M. S. Steinberg. Adhesion-guided multicellular assembly: a commentary upon the postulates, real and imagined, of the differential adhesion hypothesis, with special attention to computer simulations of cell sorting. J. theor. Biol., 55(2):431–443, 1975.CrossRefMathSciNetGoogle Scholar
  47. [47]
    T. M. Svitkina and G. G. Borisy. 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, 1999.CrossRefGoogle Scholar
  48. [48]
    W. A. Thomas, J. Thomson, J. L. Magnani, and M. S. Steinberg. Two distinct adhesion mechanisms in embryonic neural retina cells. III. Functional specificity. Dev. Biol., 81(2):379–385, 1981.CrossRefGoogle Scholar
  49. [49]
    W. R. Trickey, F. P. T. Baaijens, T. A. Laursen, L. G. Alexopoulos, and F. Guilak. Determination of the Poisson’s ratio of the cell: recovery properties of chondrocytes after release from complete micropipette aspiration. J. Biomech., 39(1):78–87, 2006.CrossRefGoogle Scholar
  50. [50]
    A. B. Verkhovsky, T. M. Svitkina, and G. G. Borisy. Self-polarization and directional motility of cytoplasm. Curr. Biol., 9(1):11–20, 1999.CrossRefGoogle Scholar
  51. [51]
    G. Wulff. Zur Frage des Geschwindigkeit des Wachstums und der Auflö sung der Krystallflächen. Z. Kristallogr. Mineral., 34:449–531, 1901.Google Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  • Athanasius F. M. Marée
    • 1
  • Verônica A. Grieneisen
    • 1
  • Paulien Hogeweg
    • 1
  1. 1.Theoretical Biology and BioinformaticsUtrecht UniversityUtrechtthe Netherlands

Personalised recommendations