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

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.

[1]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[2]  H. Bode,et al.  Patterning processes in aggregates of Hydra cells visualized with the monoclonal antibody, TS19. , 1990, Developmental biology.

[3]  James A. Glazier,et al.  Coarsening in the two-dimensional soap froth and the large-Q Potts model: A detailed comparison , 1990 .

[4]  Denis Weaire,et al.  Computer simulation of a two-dimensional soap froth , 1983 .

[5]  P. Hogeweg,et al.  Modelling Morphogenesis: From Single Cells to Crawling Slugs. , 1997, Journal of theoretical biology.

[6]  L. Onsager Crystal statistics. I. A two-dimensional model with an order-disorder transition , 1944 .

[7]  G. Forgacs,et al.  Biological Physics of the Developing Embryo , 2005 .

[8]  Paulien Hogeweg,et al.  9 – Computing an organism: on the interface between informatic and dynamic processes , 2003 .

[9]  P. McClintock,et al.  Biological Physics of the Developing Embryo , 2005 .

[10]  M. S. Steinberg,et al.  Does differential adhesion govern self-assembly processes in histogenesis? Equilibrium configurations and the emergence of a hierarchy among populations of embryonic cells. , 1970, The Journal of experimental zoology.

[11]  P. Hogeweg,et al.  How amoeboids self-organize into a fruiting body: Multicellular coordination in Dictyostelium discoideum , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[12]  Erkki Ruoslahti,et al.  Stretching Is Good for a Cell , 1997, Science.

[13]  S. Brush History of the Lenz-Ising Model , 1967 .

[14]  J. Kermode,et al.  Computer simulation of a two-dimensional soap froth II. Analysis of results , 1984 .

[15]  P. Hogeweg,et al.  Evolving mechanisms of morphogenesis: on the interplay between differential adhesion and cell differentiation. , 2000, Journal of theoretical biology.

[16]  Peter J. Bentley,et al.  On growth, form and computers , 2003 .

[17]  Maciej Swat,et al.  Adhesion between cells, diffusion of growth factors, and elasticity of the AER produce the paddle shape of the chick limb. , 2006, Physica A.

[18]  Jesús A. Izaguirre,et al.  COMPUCELL, a multi-model framework for simulation of morphogenesis , 2004, Bioinform..

[19]  Paulien Hogeweg,et al.  Modelling Dictyostelium discoideum morphogenesis: The culmination , 2002, Bulletin of mathematical biology.

[20]  R. B. Potts Some generalized order-disorder transformations , 1952, Mathematical Proceedings of the Cambridge Philosophical Society.

[21]  Y. Sawada,et al.  Diffusion and deformations of single hydra cells in cellular aggregates. , 2000, Biophysical journal.

[22]  James A. Glazier,et al.  Non-turing stripes and spots: a novel mechanism for biological cell clustering , 2004 .

[23]  G. Grest,et al.  Effects of lattice anisotropy and temperature on domain growth in the two-dimensional Potts model. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[24]  Malcolm S. Steinberg,et al.  The Problem of Adhesive Selectivity in Cellular Interactions , 1964 .

[25]  Glazier,et al.  Simulation of the differential adhesion driven rearrangement of biological cells. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[26]  Denis Weaire,et al.  Monte Carlo simulation of the evolution of a two-dimensional soap froth , 1986 .

[27]  F Graner,et al.  Coarsening of three-dimensional grains in crystals, or bubbles in dry foams, tends towards a universal, statistically scale-invariant regime. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  Arpita Upadhyaya,et al.  Thermodynamic and fluid properties of cells, tissues and membranes , 2000 .

[29]  J. Ashkin,et al.  Two Problems in the Statistical Mechanics of Crystals. I. The Propagation of Order in Crystal Lattices. I. The Statistics of Two-Dimensional Lattices with Four Components. , 1943 .

[30]  T. Holstein,et al.  Cell sorting during the regeneration of Hydra from reaggregated cells. , 1992, Developmental biology.

[31]  L. Preziosi,et al.  Modeling the early stages of vascular network assembly , 2003, The EMBO journal.

[32]  Roeland M. H. Merks,et al.  A cell-centered approach to developmental biology , 2005 .

[33]  M. Takeichi,et al.  Experimental specification of cell sorting, tissue spreading, and specific spatial patterning by quantitative differences in cadherin expression. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[34]  E. Ising Beitrag zur Theorie des Ferromagnetismus , 1925 .

[35]  P. Hogeweg,et al.  Multilevel Selection in Models of Prebiotic Evolution: Compartments and Spatial Self-organization , 2003, Origins of life and evolution of the biosphere.

[36]  Samuel A. Safran,et al.  Kinetics of ordering in two dimensions. II. Quenched systems , 1983 .

[37]  F. Y. Wu The Potts model , 1982 .

[38]  Kevin J Painter,et al.  From a discrete to a continuous model of biological cell movement. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  S. Wong,et al.  A Cursory Study of the Thermodynamic and Mechanical Properties of Monte-Carlo Simulations of the Ising Model , 2004 .

[40]  G. Forgacs,et al.  Viscoelastic properties of living embryonic tissues: a quantitative study. , 1998, Biophysical journal.

[41]  Attila Szolnoki,et al.  Vertex dynamics during domain growth in three-state models. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[42]  Elizabeth A. Holm,et al.  The computer simulation of microstructural evolution , 2001 .

[43]  P. Brazdil,et al.  Analysis of results , 1995 .

[44]  G. Forgacs,et al.  Surface tensions of embryonic tissues predict their mutual envelopment behavior. , 1996, Development.

[45]  S. Kauffman Metabolic stability and epigenesis in randomly constructed genetic nets. , 1969, Journal of theoretical biology.

[46]  J. Davies,et al.  Molecular Biology of the Cell , 1983, Bristol Medico-Chirurgical Journal.

[47]  José C. M. Mombach,et al.  Quantitative comparison between differential adhesion models and cell sorting in the presence and absence of fluctuations. , 1995, Physical review letters.

[48]  James A. Glazier,et al.  Modelling Grain Growth and Soap Froth Coarsening: Past, Present and Future , 1992 .

[49]  P. Armstrong,et al.  A role for fibronectin in cell sorting. , 1984, Journal of cell science.

[50]  James A. Glazier Dynamics of Cellular Patterns , 1992 .

[51]  Glazier,et al.  Grain growth in three dimensions depends on grain topology. , 1993, Physical review letters.

[52]  Y. Sawada,et al.  Development of electrical activity in regenerating aggregates of hydra cells. , 1995, The Journal of experimental zoology.

[53]  Samuel A. Safran,et al.  Kinetics of ordering in two dimensions. I. Model systems , 1983 .

[54]  P. Armstrong,et al.  CELL SORTING IN THE PRESENCE OF CYTOCHALASIN B , 1972, The Journal of cell biology.

[55]  Michael Locke,et al.  Cellular membranes in development , 1964 .

[56]  D. Mattis,et al.  The Theory of Magnetism I , 1981 .

[57]  Paulien Hogeweg,et al.  Computing an organism: on the interface between informatic and dynamic processes. , 2002, Bio Systems.

[58]  Roeland M. H. Merks,et al.  Dynamic mechanisms of blood vessel growth , 2006, Nonlinearity.

[59]  Malcolm S. Steinberg,et al.  Reconstruction of Tissues by Dissociated Cells , 1963 .

[60]  Y. Sawada,et al.  Pattern formation in hydra tissue without developmental gradients. , 1989, Developmental biology.

[61]  Elizabeth A. Holm,et al.  Comparison of phase-field and Potts models for coarsening processes , 1998 .

[62]  Nicholas J Savill,et al.  Control of epidermal stem cell clusters by Notch-mediated lateral induction. , 2003, Developmental biology.

[63]  Steinberg,et al.  Liquid properties of embryonic tissues: Measurement of interfacial tensions. , 1994, Physical review letters.

[64]  Y Sawada,et al.  Minimum tissue size required for hydra regeneration. , 1993, Developmental biology.

[65]  Jesús A. Izaguirre,et al.  Multi-model Simulations of Chicken Limb Morphogenesis , 2003, International Conference on Computational Science.

[66]  P. S. Sahni,et al.  Kinetics of the Q-state Potts model in two dimensions , 1983 .

[67]  Y. Sawada,et al.  Regulation in the numbers of tentacles of aggregated hydra cells. , 1989, Developmental biology.

[68]  J. Sherratt,et al.  Intercellular adhesion and cancer invasion: a discrete simulation using the extended Potts model. , 2002, Journal of theoretical biology.

[69]  Glazier,et al.  Simulation of biological cell sorting using a two-dimensional extended Potts model. , 1992, Physical review letters.

[70]  J. Glazier,et al.  Solving the advection-diffusion equations in biological contexts using the cellular Potts model. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[71]  Yi-Tsann Jiang,et al.  Extended large-Q Potts model simulation of foam drainage , 1996 .

[72]  Yi Jiang Cellular pattern formation , 1998 .

[73]  Long-Qing Chen,et al.  Computer simulation of 3-D grain growth using a phase-field model , 2002 .

[74]  A Oikawa,et al.  Patterning in hydra cell aggregates without the sorting of cells from different axial origins. , 1992, Developmental biology.

[75]  Mombach,et al.  Mitosis and growth in biological tissues. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.