Abstract
One of the reasons for the enormous success of the Glazier-Graner-HogewegGlazier-Graner-Hogeweg Model (GGH) model is that it is a framework for model building rather than a specific biological model. Thus new ideas constantly emerge for ways to extend it to describe new biological (and non-biological) phenomena. The GGH model automatically integrates extensions with the whole body of prior GGH work, a flexibility which makes it unusually simple and rewarding to work with. In this chapter we discuss some possible future directions to extend GGH modeling. We discuss off-lattice extensions to the GGH model, which can treat fluids and solids, new classes of model objects, approaches to increasing computational efficiency, parallelization, and new model-development platforms that will accelerate our ability to generate successful models. We also discuss a non-GGH, but GGH-inspired, model of plant development by Merks and collaborators, which uses the Hamiltonian and Monte-Carlo approaches of the GGH but solves them using Finite Element (FE) methods.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
U. Börner, A. Deutsch, H. Reichenbach, and M. Bär. Rippling patterns in aggregates of myxobacteria arise from cell-cell collisions. Phys. Rev. Lett., 89:078101, 2002.
A. B. Bortz, M. H. Kalos, and J. L. Lebowitz. A new algorithm for Monte Carlo simulation of Ising spin systems. J. Comp. Phys., 17:10, 1975.
F. P. Cercato, J. C. M. Mombach, and G. G. H. Cavalheiro. High performance simulations of the Cellular Potts model. In 20th International Symposium on High-Performance Computing in an Advanced Collaborative Environment, page 28, 2006.
N. Chen, J. A. Glazier, and M. S. Alber. A parallel implementation of the Cellular Potts model for simulation of cell-based morphogenesis. Lect. Notes Comput. Sci., 4173:58, 2006.
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.
R. O. Erickson. Symplastic growth and symplasmic transport. Plant Physiol., 82:1153, 1986.
K. A. Fichthorn and W. H. Weinberg. Theoretical foundations of dynamical Monte Carlo simulations. J. Chem. Phys., 95:1090, 1991.
M. C. Gibson, A. B. Patel, R. Nagpal, and N. Perrimon. The emergence of geometric order in proliferating metazoan epithelia. Nature, 442:1038, 2006.
D. T. Gillespie. A general method for numerically simulating the stochastic time evolution for coupled chemical reactions. J. Comp. Phys., 22:403, 1976.
P. Hogeweg. Evolving mechanisms of morphogenesis: on the interplay between differential adhesion and cell differentiation. J. Theor. Biol., 203:317, 2000.
P. Hogeweg. Computing an organism: on the interface between informatic and dynamic processes. Biosystems, 64:97, 2002.
P. Hogeweg and N. Takeuchi. Multilevel selection in models of prebiotic evolution: compartments and spatial self-organization. Orig. Life Evol. Biosph., 33:375, 2003.
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.
Y. Jiang, J. Pjesivac-Grbovic, C. Cantrell, and J. P. Freyer. A multiscale model for avascular tumor growth. Biophys. J., 89:3884, 2005.
K.-C. Lee. Rejection-free Monte Carlo technique. J. Phys. A, 28:4835, 1995.
J. A. Lockhart. An analysis of irreversible plant elongation. J. Theor. Biol., 8:264, 1965.
H. Meinhardt. Morphogenesis of lines and nets. Differentiation, 6:117, 1976.
R. M. H. Merks and J. A. Glazier. Dynamic mechanisms of blood vessel growth. Nonlinearity, 19, 2006.
R. M. H. Merks and J. A. Glazier. A cell-centered approach to developmental biology. Physica A, 352:113, 2005.
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., 289:44, 2006.
T. Nagai and H. Honda. A dynamic cell model for the formation of epithelial tissues. Philos. Mag., 81:699, 2001.
M. E. J. Newman and G. T. Barkema. Monte Carlo methods in statistical physics. Oxford University Press, Oxford, 3rd edition, 1999.
J. H. Priestley. Studies in the physiology of cambial activity. II. The concept of sliding growth. New Physiol., 29:96, 1930.
W.-J. Rappel, A. Nicol, A. Sarkissian, H. Levine, and W. F. Loomis. Self-organized vortex state in two-dimensional Dictyostelium dynamics. Phys. Rev. Lett., 83:1247, 1999.
T. Rudge and J. Haseloff. A computational model of cellular morphogenesis in plants. Lect. Notes Comput. Sci., 3630:78, 2005.
N. J. Savill and J. A. Sherratt. Control of epidermal stem cell clusters by Notch-mediated lateral induction. Dev. Biol., 258:141, 2003.
J. Starruß, T. Bley, and A. Deutsch. A new mechanism for swarming pattern formation of Myxococcus xanthus. Preprint, 2007.
M. Zajac, G. L. Jones, and J. A. Glazier. Model of convergent extension in animal morphogenesis. Phys. Rev. Lett., 85:2022, 2000.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Birkhäuser Verlag Basel/Switzerland
About this chapter
Cite this chapter
Balter, A., Merks, R.M.H., Popławski, N.J., Swat, M., Glazier, J.A. (2007). The Glazier-Graner-Hogeweg Model: Extensions, Future Directions, and Opportunities for Further Study. 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_7
Download citation
DOI: https://doi.org/10.1007/978-3-7643-8123-3_7
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8101-1
Online ISBN: 978-3-7643-8123-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)