Summary
Mathematical modeling and computer simulation have become crucial to biological fields from genomics to ecology. However, multicell, tissue-level simulations of development and disease have lagged behind other areas because they are mathematically more complex and lack easy-to-use software tools that allow building and running in silico experiments without requiring in-depth knowledge of programming. This tutorial introduces Glazier—Graner—Hogeweg (GGH) multicell simulations and CompuCell3D, a simulation framework that allows users to build, test, and run GGH simulations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Because of lattice discretization and the option of defining long-range neighborhoods, the surface area of a cell scales in a non-Euclidian, lattice-dependent manner with cell volume, i.e., (see ref. 61 on bubble growth).
- 2.
In the text, we denote XML, CC3DML, and Python code using the Courier font. In listings presenting syntax, user-supplied variables are given in italics. Broken-out listings are boxed. Punctuation at the end of boxes is implicit.
References
Bassingthwaighte, J. B. (2000) Strategies for the Physiome project. Ann. Biomed. Eng. 28, 1043–1058.
Merks, R. M. H., Newman, S. A., and Glazier, J. A. (2004) Cell-oriented modeling of in vitro capillary development. Lect. Notes Comp. Sci. 3305, 425–434.
Turing, A. M. (1953) The chemical basis of morphogenesis. Philos. Trans. R. Soc. B 237, 37–72.
Merks, R. M. H. and Glazier, J. A. (2005) A cell-centered approach to developmental biology. Phys. A 352, 113–130.
Dormann, S. and Deutsch, A. (2002) Modeling of self-organized avascular tumor growth with a hybrid cellular automaton. In Silico Biol. 2, 1–14.
dos Reis, A. N., Mombach, J. C. M., Walter, M., and de Avila, L. F. (2003) The interplay between cell adhesion and environment rigidity in the morphology of tumors. Phys. A 322, 546–554.
Drasdo, D. and Hohme, S. (2003) Individual-based approaches to birth and death in avascular tumors. Math. Comput. Model. 37, 1163–1175.
Holm, E. A., Glazier, J. A., Srolovitz, D. J., and Grest, G. S. (1991) Effects of lattice anisotropy and temperature on domain growth in the two-dimensional Potts model. Phys. Rev. A 43, 2662–2669.
Turner, S. and Sherratt, J. A. (2002) Intercellular adhesion and cancer invasion: A discrete simulation using the extended Potts model. J. Theor. Biol. 216, 85–100.
Drasdo, D. and Forgacs, G. (2000) Modeling the interplay of generic and genetic mechanisms in cleavage, blastulation, and gastrulation. Dev. Dynam. 219, 182–191.
Drasdo, D., Kree, R., and McCaskill, J. S. (1995) Monte-Carlo approach to tissue-cell populations. Phys. Rev. E 52, 6635–6657.
Longo, D., Peirce, S. M., Skalak, T. C., Davidson, L., Marsden, M., and Dzamba, B. (2004) Multicellular computer simulation of morphogenesis: Blastocoel roof thinning and matrix assembly in Xenopus laevis. Dev. Biol. 271, 210–222.
Collier, J. R., Monk, N. A. M., Maini, P. K., and Lewis, J. H. (1996) Pattern formation by lateral inhibition with feedback: A mathematical model of Delta-Notch intercellular signaling. J. Theor. Biol. 183, 429–446.
Honda, H. and Mochizuki, A. (2002) Formation and maintenance of distinctive cell patterns by coexpression of membrane-bound ligands and their receptors. Dev. Dynam. 223, 180–192.
Moreira, J. and Deutsch, A. (2005) Pigment pattern formation in zebrafish during late larval stages: A model based on local interactions. Dev. Dynam. 232, 33–42.
Wearing, H. J., Owen, M. R., and Sherratt, J. A. (2000) Mathematical modelling of juxtacrine patterning. Bull. Math. Biol. 62, 293–320.
Zhdanov, V. P. and Kasemo, B. (2004) Simulation of the growth of neurospheres. Europhys. Lett. 68, 134–140.
Ambrosi, D., Gamba, A., and Serini, G. (2005) Cell directional persistence and chemotaxis in vascular morphogenesis. Bull. Math. Biol. 67, 195–195.
Gamba, A., Ambrosi, D., Coniglio, A., de Candia, A., di Talia, S., Giraudo, E., Serini, G., Preziosi, L., and Bussolino, F. (2003) Percolation, morphogenesis, and Burgers dynamics in blood vessels formation. Phys. Rev. Lett. 90, 118101.
Novak, B., Toth, A., Csikasz-Nagy, A., Gyorffy, B., Tyson, J. A., and Nasmyth, K. (1999) Finishing the cell cycle. J. Theor. Biol. 199, 223–233.
Peirce, S. M., van Gieson, E. J., and Skalak, T. C. (2004) Multicellular simulation predicts microvascular patterning and in silico tissue assembly. FASEB J. 18, 731–733.
Merks, R. M. H., Brodsky, S. V., Goligorksy, M. S., Newman, S. A., and Glazier, J. A. (2006) Cell elongation is key to in silico replication of in vitro vasculogenesis and subsequent remodeling. Dev. Biol. 289, 44–54.
Merks, R. M. H. and Glazier, J. A. (2005) Contact-inhibited chemotactic motility can drive both vasculogenesis and sprouting angiogenesis. q-bio/0505033.
Kesmir, C. and de Boer, R. J. (2003) A spatial model of germinal center reactions: Cellular adhesion based sorting of B cells results in efficient affinity maturation. J. Theor. Biol. 222, 9–22.
Meyer-Hermann, M., Deutsch, A., and Or-Guil, M. (2001) Recycling probability and dynamical properties of germinal center reactions. J. Theor. Biol. 210, 265–285.
Nguyen, B., Upadhyaya, A., van Oudenaarden, A., and Brenner, M. P. (2004) Elastic instability in growing yeast colonies. Biophys. J. 86, 2740–2747.
Walther, T., Reinsch, H., Grosse, A., Ostermann, K., Deutsch, A., and Bley, T. (2004) Mathematical modeling of regulatory mechanisms in yeast colony development. J. Theor. Biol. 229, 327–338.
Borner, U., Deutsch, A., Reichenbach, H., and Bar, M. (2002) Rippling patterns in aggregates of myxobacteria arise from cell–cell collisions. Phys. Rev. Lett. 89, 078101.
Bussemaker, H. J., Deutsch, A., and Geigant, E. (1997) Mean-field analysis of a dynamical phase transition in a cellular automaton model for collective motion. Phys. Rev. Lett. 78, 5018–5021.
Dormann, S., Deutsch, A., and Lawniczak, A. T. (2001) Fourier analysis of Turing-like pattern formation in cellular automaton models. Future Gener. Comput. Syst. 17, 901–909.
Börner, U., Deutsch, A., Reichenbach, H., and Bär, M. (2002) Rippling patterns in aggregates of myxobacteria arise from cell–cell collisions. Phys. Rev. Lett. 89, 078101.
Zhdanov, V. P. and Kasemo, B. (2004) Simulation of the growth and differentiation of stem cells on a heterogeneous scaffold. Phys. Chem. Chem. Phys. 6, 4347–4350.
Knewitz, M. A. and Mombach, J. C. (2006) Computer simulation of the influence of cellular adhesion on the morphology of the interface between tissues of proliferating and quiescent cells. Comput. Biol. Med. 36, 59–69.
Marée, A. F. M. and Hogeweg, P. (2001) How amoeboids self-organize into a fruiting body: Multicellular coordination in Dictyostelium discoideum. Proc. Natl Acad. Sci. USA 98, 3879–3883.
Marée, A. F. M. and Hogeweg, P. (2002) Modelling Dictyostelium discoideum morphogenesis: the culmination. Bull. Math. Biol. 64, 327–353.
Marée, A. F. M., Panfilov, A. V., and Hogeweg, P. (1999) Migration and thermotaxis of Dictyostelium discoideum slugs, a model study. J. Theor. Biol. 199, 297–309.
Savill, N. J. and Hogeweg, P. (1997) Modelling morphogenesis: From single cells to crawling slugs. J. Theor. Biol. 184, 229–235.
Hogeweg, P. (2000) Evolving mechanisms of morphogenesis: On the interplay between differential adhesion and cell differentiation. J. Theor. Biol. 203, 317–333.
Johnston, D. A. (1998) Thin animals. J. Phys. A 31, 9405–9417.
Groenenboom, M. A. and Hogeweg, P. (2002) Space and the persistence of male-killing endosymbionts in insect populations. Proc. Biol. Sci. 269, 2509–2518.
Groenenboom, M. A., Maree, A. F., and Hogeweg, P. (2005) The RNA silencing pathway: the bits and pieces that matter. PLoS Comp. Biol. 1, 155–165.
Kesmir, C., van Noort, V., de Boer, R. J., and Hogeweg, P. (2003) Bioinformatic analysis of functional differences between the immunoproteasome and the constitutive proteasome. Immunogenetics 55, 437–449.
Pagie, L. and Hogeweg, P. (2000) Individual- and population-based diversity in restriction-modification systems. Bull. Math. Biol. 62, 759–774.
Silva, H. S. and Martins, M. L. (2003) A cellular automata model for cell differentiation. Phys. A 322, 555–566.
Zajac, M., Jones, G. L., and Glazier, J. A. (2000) Model of convergent extension in animal morphogenesis. Phys. Rev. Lett. 85, 2022–2025.
Zajac, M., Jones, G. L., and Glazier, J. A. (2003) Simulating convergent extension by way of anisotropic differential adhesion. J. Theor. Biol. 222, 247–259.
Savill, N. J. and Sherratt, J. A. (2003) Control of epidermal stem cell clusters by Notch-mediated lateral induction. Dev. Biol. 258, 141–153.
Mombach, J. C. M., de Almeida, R. M. C., Thomas, G. L., Upadhyaya, A., and Glazier, J. A. (2001) Bursts and cavity formation in Hydra cells aggregates: Experiments and simulations. Phys. A 297, 495–508.
Rieu, J. P., Upadhyaya, A., Glazier, J. A., Ouchi, N. B., and Sawada, Y. (2000) Diffusion and deformations of single hydra cells in cellular aggregates. Biophys. J. 79, 1903–1914.
Mochizuki, A. (2002) Pattern formation of the cone mosaic in the zebrafish retina: A cell rearrangement model. J. Theor. Biol. 215, 345–361.
Takesue, A., Mochizuki, A., and Iwasa, Y. (1998) Cell-differentiation rules that generate regular mosaic patterns: Modelling motivated by cone mosaic formation in fish retina. J. Theor. Biol. 194, 575–586.
Dallon, J., Sherratt, J., Maini, P. K., and Ferguson, M. (2000) Biological implications of a discrete mathematical model for collagen deposition and alignment in dermal wound repair. IMA J. Math. Appl. Med. Biol. 17, 379–393.
Maini, P. K., Olsen, L., and Sherratt, J. A. (2002) Mathematical models for cell–matrix interactions during dermal wound healing. Int. J. Bifurcat. Chaos 12, 2021–2029.
Kreft, J. U., Picioreanu, C., Wimpenny, J. W. T., and van Loosdrecht, M. C. M. (2001) Individual-based modelling of biofilms. Microbiology 147, 2897–2912.
Picioreanu, C., van Loosdrecht, M. C. M., and Heijnen, J. J. (2001) Two-dimensional model of biofilm detachment caused by internal stress from liquid flow. Biotechnol. Bioeng. 72, 205–218.
van Loosdrecht, M. C. M., Heijnen, J. J., Eberl, H., Kreft, J., and Picioreanu, C. (2002) Mathematical modelling of biofilm structures. Antonie Van Leeuwenhoek Int. J. General Mol. Microbiol. 81, 245–256.
Pop awski, N. J., Shirinifard, A., Swat, M., and Glazier, J. A. (2008) Simulations of single-species bacterial-biofilm growth using the Glazier–Graner–Hogeweg model and the CompuCell3D modeling environment. Math. Biosci. Eng. 5, 355–388.
Chaturvedi, R., Huang, C., Izaguirre, J. A., Newman, S. A., Glazier, J. A., and Alber, M. S. (2004) A hybrid discrete-continuum model for 3-D skeletogenesis of the vertebrate limb. Lect. Notes Comput. Sci. 3305, 543–552.
Pop awski, N. J., Swat, M., Gens, J. S., and Glazier, J. A. (2007) Adhesion between cells, diffusion of growth factors, and elasticity of the AER produce the paddle shape of the chick limb. Phys. A 373, 521–532.
Glazier, J. A. and Weaire, D. (1992) The kinetics of cellular patterns. J. Phys.: Condens. Matter 4, 1867–1896.
Glazier, J. A. (1993) Grain growth in three dimensions depends on grain topology. Phys. Rev. Lett. 70, 2170–2173.
Glazier, J. A., Grest, G. S., and Anderson, M. P. (1990) Ideal two-dimensional grain growth, in Simulation and Theory of Evolving Microstructures (Anderson, M. P. and Rollett, A. D., eds.), The Minerals, Metals and Materials Society, Warrendale, PA, pp. 41–54.
Glazier, J. A., Anderson, M. P., and Grest, G. S. (1990) Coarsening in the two-dimensional soap froth and the large-Q Potts model: a detailed comparison. Philos. Mag. B 62, 615–637.
Grest, G. S., Glazier, J. A., Anderson, M. P., Holm, E. A., and Srolovitz, D. J. (1992) Coarsening in two-dimensional soap froths and the large-Q Potts model. Mater. Res. Soc. Symp. 237, 101–112.
Jiang, Y. and Glazier, J. A. (1996) Extended large-Q Potts model simulation of foam drainage. Philos. Mag. Lett. 74, 119–128.
Jiang, Y., Levine, H., and Glazier, J. A. (1998) Possible cooperation of differential adhesion and chemotaxis in mound formation of Dictyostelium. Biophys. J. 75, 2615–2625.
Jiang, Y., Mombach, J. C. M., and Glazier, J. A. (1995) Grain growth from homogeneous initial conditions: Anomalous grain growth and special scaling states. Phys. Rev. E 52, 3333–3336.
Jiang, Y., Swart, P. J., Saxena, A., Asipauskas, M., and Glazier, J. A. (1999) Hysteresis and avalanches in two-dimensional foam rheology simulations. Phys. Rev. E 59, 5819–5832.
Ling, S., Anderson, M. P., Grest, G. S., and Glazier, J. A. (1992) Comparison of soap froth and simulation of large-Q Potts model. Mater. Sci. Forum 94–96, 39–47.
Mombach, J. C. M. (2000) Universality of the threshold in the dynamics of biological cell sorting. Phys. A 276, 391–400.
Weaire, D. and Glazier, J. A. (1992) Modelling grain growth and soap froth coarsening: Past, present and future. Mater. Sci. Forum 94–96, 27–39.
Weaire, D., Bolton, F., Molho, P., and Glazier, J. A. (1991) Investigation of an elementary model for magnetic froth. J. Phys.: Condens. Matter 3, 2101–2113.
Glazer, J. A., Balter, A., and Pop awski, N. (2007) Magnetization to morphogenesis: A brief history of the Glazier—Graner—Hogeweg model, in Single-Cell-Based Models in Biology and Medicine (Anderson, A. R. A., Chaplain, M. A. J., and Rejniak, K. A., eds.), Birkhauser Verlag, Basel, pp. 79–106.
Walther, T., Reinsch, H., Ostermann, K., Deutsch, A., and Bley, T. (2005) Coordinated growth of yeast colonies: Experimental and mathematical analysis of possible regulatory mechanisms. Eng. Life Sci. 5, 115–133.
Keller, E. F. and Segel, L. A. (1971) Model for chemotaxis. J. Theor. Biol. 30, 225–234.
Glazier, J. A. and Upadhyaya, A. (1998) First steps towards a comprehensive model of tissues, or: A physicist looks at development, in Dynamical Networks in Physics and Biology: At the Frontier of Physics and Biology (Beysens, D. and Forgacs, G., eds.), EDP Sciences, Berlin, pp. 149–160.
Glazier, J. A. and Graner, F. (1993) Simulation of the differential adhesion driven rearrangement of biological cells. Phys. Rev. E 47, 2128–2154.
Glazier, J. A. (1993) Cellular patterns. Bussei Kenkyu 58, 608–612.
Glazier, J. A. (1996) Thermodynamics of cell sorting. Bussei Kenkyu 65, 691–700.
Glazier, J. A., Raphael, R. C., Graner, F., and Sawada, Y. (1995) The energetics of cell sorting in three dimensions, in Interplay of Genetic and Physical Processes in the Development of Biological Form (Beysens, D., Forgacs, G., and Gaill, F., eds.), World Scientific, Singapore, pp. 54–66.
Graner, F. and Glazier, J. A. (1992) Simulation of biological cell sorting using a 2-dimensional extended Potts model. Phys. Rev. Lett. 69, 2013–2016.
Mombach, J. C. M. and Glazier, J. A. (1996) Single cell motion in aggregates of embryonic cells. Phys. Rev. Lett. 76, 3032–3035.
Mombach, J. C. M., Glazier, J. A., Raphael, R. C., and Zajac, M. (1995) Quantitative comparison between differential adhesion models and cell sorting in the presence and absence of fluctuations. Phys. Rev. Lett. 75, 2244–2247.
Cipra, B. A. (1987) An introduction to the Ising-model. Am. Math. Monthly 94, 937–959.
Metropolis, N., Rosenbluth, A., Rosenbluth, M. N., Teller, A. H., and Teller, E. (1953) Equation of state calculations by fast computing machines. J. Chem. Phys. 21, 1087–1092.
Forgacs, G. and Newman, S. A. (2005). Biological Physics of the Developing Embryo. Cambridge University Press, Cambridge.
Alber, M. S., Kiskowski, M. A., Glazier, J. A., and Jiang, Y. (2002) On cellular automation approaches to modeling biological cells, in Mathematical Systems Theory in Biology, Communication and Finance (Rosenthal, J. and Gilliam, D. S., eds.), Springer, New York, NY, pp. 1–40.
Alber, M. S., Jiang, Y., and Kiskowski, M. A. (2004) Lattice gas cellular automation model for rippling and aggregation in myxobacteria. Phys. D 191, 343–358.
Upadhyaya, A., Rieu, J. P., Glazier, J. A., and Sawada, Y. (2001) Anomalous diffusion in two-dimensional Hydra cell aggregates. Phys. A 293, 549–558.
Cickovski, T., Aras, K., Alber, M. S., Izaguirre, J. A., Swat, M., Glazier, J. A., Merks, R. M. H., Glimm, T., Hentschel, H. G. E., and Newman, S. A. (2007) From genes to organisms via the cell: A problem-solving environment for multicellular development. Comput. Sci. Eng. 9, 50–60.
Izaguirre, J. A., Chaturvedi, R., Huang, C., Cickovski, T., Coffland, J., Thomas, G., Forgacs, G., Alber, M., Hentschel, G., Newman, S. A., and Glazier, J. A. (2004) CompuCell, a multi-model framework for simulation of morphogenesis. Bioinformatics 20, 1129–1137.
Armstrong, P. B. and Armstrong, M. T. (1984) A role for fibronectin in cell sorting out. J. Cell Sci. 69, 179–197.
Armstrong, P. B. and Parenti, D. (1972) Cell sorting in the presence of cytochalasin B. J. Cell Sci. 55, 542–553.
Glazier, J. A. and Graner, F. (1993) Simulation of the differential adhesion driven rearrangement of biological cells. Phys. Rev. E 47, 2128–2154.
Glazier, J. A. and Graner, F. (1992) Simulation of biological cell sorting using a two-dimensional extended Potts model. Phys. Rev. Lett. 69, 2013–2016.
Ward, P. A., Lepow, I. H., and Newman, L. J. (1968) Bacterial factors chemotactic for polymorphonuclear leukocytes. Am. J. Pathol. 52, 725–736.
Lutz, M. (1999) Learning Python. O'Reilly & Associates, Sebastopol, CA.
Balter, A. I., Glazier, J. A., and Perry, R. (2008) Probing soap-film friction with two-phase foam flow. Philos. Mag. Lett. 88, 679–691.
Dvorak, P., Dvorakova, D., and Hampl, A. (2006) Fibroblast growth factor signaling in embryonic and cancer stem cells. FEBS Lett. 580, 2869–2287.
Acknowledgments
We gratefully acknowledge support from the National Institutes of Health, National Institute of General Medical Sciences, grants 1R01 GM077138–01A1 and 1R01 GM076692-01, and the Office of Vice President for Research, the College of Arts and Sciences, the Pervasive Technologies Laboratories and the Biocomplexity Institute at Indiana University. Indiana University's University Information Technology Services provided time on their BigRed clusters for simulation execution. Early versions of CompuCell and CompuCell3D were developed at the University of Notre Dame by J.A.G., Dr. Mark Alber and Dr. Jesus Izaguirre and collaborators with the support of National Science Foundation, Division of Integrative Biology, grant IBN-00836563. Since the primary home of CompuCell3D moved to Indiana University in 2004, the Notre Dame team have continued to provide important support for its development.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Humana Press
About this protocol
Cite this protocol
Swat, M., Hester, S., Balter, A., Heiland, R., Zaitlen, B., Glazier, J. (2009). Multicell Simulations of Development and Disease Using the CompuCell3D Simulation Environment. In: Maly, I. (eds) Systems Biology. Methods in Molecular Biology, vol 500. Humana Press. https://doi.org/10.1007/978-1-59745-525-1_13
Download citation
DOI: https://doi.org/10.1007/978-1-59745-525-1_13
Published:
Publisher Name: Humana Press
Print ISBN: 978-1-934115-64-0
Online ISBN: 978-1-59745-525-1
eBook Packages: Springer Protocols