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

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Single-Cell-Based Models in Biology and Medicine

Abstract

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.

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References

  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. P. B. Armstrong and R. Niederman. Reversal of tissue position after cell sorting. Dev. Biol., 28(3):518–527, 1972.

    Article  Google Scholar 

  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. 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.

    Article  MATH  MathSciNet  Google Scholar 

  5. L. Carroll. Through the Looking Glass. Macmillan, London, 1872.

    Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  9. S. Etienne-Manneville. Cdc42-the centre of polarity. J. Cell Sci., 117(Pt 8):1291–1300, 2004.

    Article  Google Scholar 

  10. E. Farge. Mechanical induction of Twist in the D rosophila foregut/stomodeal primordium. Curr. Biol., 13(16):1365–1377, 2003.

    Article  Google Scholar 

  11. J. Folkman and A. Moscona. Role of cell shape in growth control. Nature, 273(5661):345–349, 1978.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  13. F. Graner. Can surface adhesion drive cell-rearrangement? Part I: biological cellsorting. J. theor. Biol., 164:455–476, 1993.

    Article  Google Scholar 

  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. 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.

    Article  Google Scholar 

  16. C. Herring. Some theorems on the free energies of crystal surfaces. Phys. Rev., 82:87–93, 1951.

    Article  MATH  Google Scholar 

  17. P. Hogeweg. Evolving mechanisms of morphogenesis: on the interplay between differential adhesion and cell differentiation. J. theor. Biol., 203(4):317–333, 2000.

    Article  Google Scholar 

  18. P. Hogeweg. Shapes in the shadow: evolutionary dynamics of morphogenesis. Artif. Life, 6(1):85–101, 2000.

    Article  Google Scholar 

  19. P. Hogeweg. Computing an organism: on the interface between informatic and dynamic processes. BioSystems, 64(1–3):97–109, 2002.

    Article  Google Scholar 

  20. S. Huang and D. E. Ingber. The structural and mechanical complexity of cell-growth control. Nat. Cell Biol., 1(5):E131–E138, 1999.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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. 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. 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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  26. A. F. M. Marée. From Pattern Formation to Morphogenesis: Multicellular Coordination in Dictyostelium discoideum. PhD thesis, Utrecht University, 2000.

    Google Scholar 

  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.

    Article  Google Scholar 

  28. A. F. M. Marée and P. Hogeweg. Modelling Dictyostelium discoideum morphogenesis: the culmination. Bull. Math. Biol., 64(2):327–353, 2002.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  32. R. Meili and R. A. Firtel. Two poles and a compass. Cell, 114(2):153–156, 2003.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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. A. Mogilner and G. Oster. Cell motility driven by actin polymerization. Biophys. J., 71(6):3030–3045, 1996.

    Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  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.

    Article  Google Scholar 

  39. C. Rottman and M. Wortis. Exact equilibrium crystal shapes at nonzero temperature in two dimensions. Phys. Rev. B, 24:6274–6277, 1981.

    Article  MathSciNet  Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  41. E. Ruoslahti. Stretching is good for a cell. Science, 276(5317):1345–1346, 1997.

    Article  Google Scholar 

  42. N. J. Savill and P. Hogeweg. Modelling morphogenesis: From single cells to crawling slugs. J. theor. Biol., 184(3):229–235, 1997.

    Article  Google Scholar 

  43. I. C. Scott and D. Y. R. Stainier. Developmental biology: twisting the body into shape. Nature, 425(6957):461–463, 2003.

    Article  Google Scholar 

  44. L. A. Segel. Computing an organism. Proc. Natl. Acad. Sci. U.S.A., 98(7):3639–3640, 2001.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  51. G. Wulff. Zur Frage des Geschwindigkeit des Wachstums und der Auflö sung der Krystallflächen. Z. Kristallogr. Mineral., 34:449–531, 1901.

    Google Scholar 

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Marée, A.F.M., Grieneisen, V.A., Hogeweg, P. (2007). The Cellular Potts Model and Biophysical Properties of Cells, Tissues and Morphogenesis. 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_5

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