Skip to main content

Magnetization to Morphogenesis: A Brief History of the Glazier-Graner-Hogeweg Model

  • Chapter
Single-Cell-Based Models in Biology and Medicine

Abstract

This chapter discusses the history and development of what we propose to rename the Glazier-Graner-Hogeweg model (GGH model), starting with its ancestors, simple models of magnetism, and concluding with its current state as a powerful, cell-oriented method for simulating biological development and tissue physiology. We will discuss some of the choices and accidents of this development and some of the positive and negative consequences of the model’s pedigree.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, and P. Walter. Molecular biology of the cell. Garland, New York, 2002.

    Google Scholar 

  2. H. Ando, Y. Sawada, H. Shimizu, and T. Sugiyama. Pattern formation in hydra tissue without developmental gradients. Dev. Biol., 133:405, 1989.

    Article  Google Scholar 

  3. P. B. Armstrong and M. T. Armstrong. A role for fibronectin in cell sorting out. J. Cell. Sci., 69:179, 1984.

    Google Scholar 

  4. P. B. Armstrong and D. Parenti. Cell sorting in the presence of cytochalasin B. J. Cell Biol., 55:542, 1972.

    Article  Google Scholar 

  5. J. Ashkin and E. Teller. Statistics of two-dimensional lattices with four components. Phys. Rev., 64:178, 1943.

    Article  Google Scholar 

  6. S. G. Brush. History of the Lenz-Ising model. Rev. Mod. Phys., 39:883, 1967.

    Article  Google Scholar 

  7. R. Chaturvedi, J. A. Izaguirre, C. Huang, T. Cickovski, P. Virtue, G. L. Thomas, G. Forgacs, M. S. Alber, S. A. Newman, and J. A. Glazier. Multi-model simulations of chicken limb morphogenesis. Lect. Notes Comput. Sci., 2659:39, 2003.

    Article  Google Scholar 

  8. D. Dan, C. Mueller, K. Chen, and J. A. Glazier. Solving the advection-diffusion equations in biological contexts using the Cellular Potts model. Phys. Rev. E, 72:041909, 2005.

    Article  Google Scholar 

  9. G. Forgacs, R. A. Foty, Y. Shafrir, and M. S. Steinberg. Viscoelastic properties of living embryonic tissues: a quantitative study. Biophys. J., 74:2227, 1998.

    Google Scholar 

  10. G. Forgacs and S. A. Newman. Biological physics of the developing embryo. Cambridge Univ. Press, Cambridge, 2005.

    Google Scholar 

  11. R. A. Foty, G. Forgacs, C. M. Pfleger, and M. S. Steinberg. Liquid properties of embryonic tissues: measurement of interfacial tensions. Phys. Rev. Lett., 72:2298, 1994.

    Article  Google Scholar 

  12. R. A. Foty, C. M. Pfleger, G. Forgacs, and M. S. Steinberg. Surface tensions of embryonic tissues predict their mutual envelopment behavior. Development, 122:1611, 1996.

    Google Scholar 

  13. J. A. Glazier. Dynamics of cellular patterns. PhD thesis, University of Chicago, 1989.

    Google Scholar 

  14. J. A. Glazier. Grain growth in three dimensions depends on grain topology. Phys. Rev. Lett., 70:2170, 1993.

    Article  Google Scholar 

  15. J. A. Glazier, M. P. Anderson, and G. S. Grest. Coarsening in the two-dimensional soap froth and the large-q Potts model: a detailed comparison. Philos. Mag. B, 62:615, 1990.

    Article  Google Scholar 

  16. J. A. Glazier and F. Graner. Simulation of the differential adhesion driven rearrangement of biological cells. Phys. Rev. E, 47:2128, 1993.

    Article  Google Scholar 

  17. F. Graner and J. A. Glazier. Simulation of biological cell sorting using a two-dimensional extended Potts model. Phys. Rev. Lett., 69:2013, 1992.

    Article  Google Scholar 

  18. P. Hogeweg. Evolving mechanisms of morphogenesis: on the interplay between differential adhesion and cell differentiation. J. Theor. Biol., 203:317, 2000.

    Article  Google Scholar 

  19. P. Hogeweg. Computing an organism: on the interface between informatic and dynamic processes. Biosystems, 64:97, 2002.

    Article  Google Scholar 

  20. P. Hogeweg. Computing an organism: on the interface between informatic and dynamic processes. In S. Kumar and P. J. Bentley, editors, On growth, form and computers, page 444. Elsevier, London, 2003.

    Google Scholar 

  21. P. Hogeweg and N. Takeuchi. Multilevel selection in models of prebiotic evolution: compartments and spatial self-organization. Orig. Life Evol. Biosph., 33:375, 2003.

    Article  Google Scholar 

  22. E. A. Holm and C. C. Battaile. The computer simulation of microstructural evolution. JOM, 53:20, 2001.

    Article  Google Scholar 

  23. E. A. Holm, J. A. Glazier, D. J. Srolovitz, and G. S. Grest. Effects of lattice anisotropy and temperature on domain growth in the two-dimensional Potts model. Phys. Rev. A, 43:2662, 1991.

    Article  Google Scholar 

  24. E. Ising. Beitrag zur Theorie des Ferromagnetismus. Z. Physik., 31:253, 1925.

    Google Scholar 

  25. T. Itayama and Y. Sawada. Development of electrical activity in regenerating aggregates of hydra cells. J. Exp. Zool., 273:519, 1995.

    Article  Google Scholar 

  26. J. A. Izaguirre, R. Chaturvedi, C. Huang, T. Cickovski, J. Coffland, G. L. Thomas, G. Forgacs, M. S. Alber, H. G. E. Hentschel, S. A. Newman, and J. A. Glazier. Compucell, a multi-model framework for simulation of morphogenesis. Bioinformatics, 20:1129, 2004.

    Article  Google Scholar 

  27. Y. Jiang. Cellular pattern formation. PhD thesis, University of Notre Dame, 1998.

    Google Scholar 

  28. Y. Jiang and J. A. Glazier. Extended large-q Potts model simulation of foam drainage. Phil. Mag. Lett., 74:119, 1996.

    Article  Google Scholar 

  29. S. A. Kauffman. Metabolic stability and epigenesis in randomly constructed genetic nets. J. Theor. Biol., 22:437, 1969.

    Article  MathSciNet  Google Scholar 

  30. C. E. Krill and L. Q. Chen. Computer simulation of 3-D grain growth using a phase-field model. Acta Mater., 50:3057, 2002.

    Article  Google Scholar 

  31. A. F. M. Marée and P. Hogeweg. How amoeboids self-organize into a fruiting body: multicellular coordination in Dictyostelium discoideum. Proc. Natl. Acad. Sci. USA, 98:3879, 2001.

    Article  Google Scholar 

  32. A. F. M. Marée and P. Hogeweg. Modelling Dictyostelium discoideum morphogenesis: the culmination. Bull. Math. Biol., 64:327, 2002.

    Article  Google Scholar 

  33. R. M. H. Merks and J. A. Glazier. A cell-centered approach to developmental biology. Physica A, 352:113, 2005.

    Article  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  35. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller. Equation of state calculations by fast computing machines. J. Chem. Phys., 21:1087, 1953.

    Article  Google Scholar 

  36. J. C. 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., 75:2244, 1995.

    Article  Google Scholar 

  37. J. C. M. Mombach, R. M. C. de Almeida, and J. R. Iglesias. Mitosis and growth in biological tissues. Phys. Rev. E, 48:598, 1993.

    Article  Google Scholar 

  38. L. Onsager. Crystal statistics. I. A two-dimensional model with an order-disorder transition. Phys. Rev., 65:117, 1944.

    Article  MATH  MathSciNet  Google Scholar 

  39. N. J. Popławski, M. Swat, J. S. Gens, and J. A. Glazier. Adhesion between cells, diffusion of growth factors, and elasticity of the AER produce the paddle shape of the chick limb. Physica A, 373:521, 2007.

    Article  Google Scholar 

  40. R. B. Potts. PhD thesis, University of Oxford, 1951.

    Google Scholar 

  41. R. B. Potts. Some generalized order-disorder transformations. Proc. Camb. Phil. Soc., 48:106, 1952.

    MATH  MathSciNet  Google Scholar 

  42. 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, 2000.

    Google Scholar 

  43. E. Ruoslahti. Stretching is good for a cell. Science, 276:1345, 1997.

    Article  Google Scholar 

  44. S. A. Safran, P. S. Sahni, and G. S. Grest. Kinetics of ordering in two dimensions. I. Model systems. Phys. Rev. B, 28:2693, 1983.

    Article  Google Scholar 

  45. P. S. Sahni, G. S. Grest, M. P. Anderson, and D. J. Srolovitz. Kinetics of the q-state Potts model in two dimensions. Phys. Rev. Lett., 50:263, 1983.

    Article  Google Scholar 

  46. P. S. Sahni, D. J. Srolovitz, G. S. Grest, M. P. Anderson, and S. A. Safran. Kinetics of ordering in two dimensions. II. Quenched systems. Phys. Rev. B, 28:2705, 1983.

    Article  Google Scholar 

  47. M. Sato, H. R. Bode, and Y. Sawada. Patterning processes in aggregates of hydra cells visualized with the monoclonal antibody, Ts19. Dev. Biol., 141:412, 1990.

    Article  Google Scholar 

  48. M. Sato and Y. Sawada. Regulation in the numbers of tentacles of aggregated hydra cells. Dev. Biol., 133:119, 1989.

    Article  Google Scholar 

  49. M. Sato, H. Tashiro, A. Oikawa, and Y. Sawada. Patterning in hydra cell aggregates without the sorting of cells from different axial origins. Dev. Biol., 151:111, 1992.

    Article  Google Scholar 

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

    Article  Google Scholar 

  51. N. J. Savill and J. A. Sherratt. Control of epidermal stem cell clusters by Notch-mediated lateral induction. Dev. Biol., 258:141, 2003.

    Article  Google Scholar 

  52. 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, 2003.

    Article  Google Scholar 

  53. H. Shimizu, Y. Sawada, and T. Sugiyama. Minimum tissue size required for hydra regeneration. Dev. Biol., 155:287, 1993.

    Article  Google Scholar 

  54. M. S. Steinberg. Reconstruction of tissues by dissociated cells. some morphogenetic movements and the sorting out of embryonic cells may have a common explanation. Science, 141:401, 1963.

    Article  Google Scholar 

  55. M. S. Steinberg. The problem of adhesive selectivity in cellular interactions. In M. Locke, editor, Cellular membranes in development, page 321. Academic, New York, 1964.

    Google Scholar 

  56. M. S. Steinberg. Does differential adhesion govern self-assembly processes in histogenesis? equilibrium configurations and the emergence of a hierarchy among populations of embryonic cells. J. Exp. Zool., 173:395, 1970.

    Article  Google Scholar 

  57. M. S. Steinberg and M. Takeichi. Experimental specification of cell sorting, tissue spreading and specific spatial patterning by quantitative differences in cadherin expression. Proc. Natl. Acad. Sci. USA, 91:206, 1994.

    Article  Google Scholar 

  58. A. Szolnoki and G. Szabo. Vertex dynamics during domain growth in three-state models. Phys. Rev. E, 70:027101, 2004.

    Article  Google Scholar 

  59. U. Technau and T. W. Holstein. Cell sorting during the regeneration of hydra from reaggregated cells. Dev. Biol., 151:117, 1992.

    Article  Google Scholar 

  60. G. L. Thomas, R. M. C. de Almeida, and F. Graner. Coarsening of three-dimensional grains in crystals, or bubbles in dry foams, tends towards a universal, statistically scale-invariant regime. Phys. Rev. E, 74:021407, 2006.

    Article  Google Scholar 

  61. V. Tikare, E. A. Holm, D. Fan, and L. Q. Chen. Comparison of phase-field and Potts models for coarsening processes. Acta Mater., 47:363, 1998.

    Article  Google Scholar 

  62. S. Turner and J. A. Sherratt. Intercellular adhesion and cancer invasion: a discrete simulation using the extended Potts model. J. Theor. Biol., 216:85, 2002.

    Article  MathSciNet  Google Scholar 

  63. S. Turner, J. A. Sherratt, K. J. Painter, and N. J. Savill. From a discrete to a continuous model of biological cell movement. Phys. Rev. E, 69:021910, 2004.

    Article  MathSciNet  Google Scholar 

  64. A. Upadhyaya. Thermodynamic and fluid properties of cells, tissues and membranes. PhD thesis, University of Notre Dame, 2000.

    Google Scholar 

  65. J. von Neumann. Metal interfaces. American Society for Metals, Cleveland, 1952.

    Google Scholar 

  66. D. Weaire and J. A. Glazier. Modelling grain growth and soap froth coarsening: past, present and future. Mater. Sci. Forum, 94–96:27, 1992.

    Article  Google Scholar 

  67. D. Weaire and J. P. Kermode. Computer simulation of a two-dimensional soap froth. I. method and motivation. Phil. Mag. B, 48:245, 1983.

    Article  Google Scholar 

  68. D. Weaire and J. P. Kermode. Computer simulation of a two-dimensional soap froth. II. analysis of results. Phil. Mag. B, 50:379, 1984.

    Article  Google Scholar 

  69. J. Wejchert, D. Weaire, and J. P. Kermode. Monte Carlo simulation of the evolution of a two-dimensional soap froth. Phil. Mag. B, 53:15, 1986.

    Google Scholar 

  70. S.-K. Wong. A cursory study of thermodynamic and mechanical properties of Monte-Carlo simulations of the Ising model. PhD thesis, University of Notre Dame, 2005.

    Google Scholar 

  71. F. Y. Wu. The Potts model. Rev. Mod. Phys., 54:235, 1982.

    Article  Google Scholar 

  72. K. Yosida. Theory of magnetism. Springer-Verlag, Heidelberg, 2006.

    Google Scholar 

  73. W. Zeng, G. L. Thomas, and J. A. Glazier. A novel mechanism for biological cell clustering. Physica A, 341:482, 2004.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Birkhäuser Verlag Basel/Switzerland

About this chapter

Cite this chapter

Glazier, J.A., Balter, A., Popławski, N.J. (2007). Magnetization to Morphogenesis: A Brief History of the Glazier-Graner-Hogeweg Model. 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_4

Download citation

Publish with us

Policies and ethics