Bulletin of Mathematical Biology

, Volume 79, Issue 1, pp 1–20 | Cite as

Space-Limited Mitosis in the Glazier–Graner–Hogeweg Model

Original Article
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Abstract

The Glazier–Graner–Hogeweg (GGH) model is a cellular automata framework for representing the time evolution of cellular systems, appealing because unlike many other individual-cell-based models it dynamically simulates changes in cell shape and size. Proliferation has seen some implementation into this modelling framework, but without consensus in the literature as to how this behaviour is best represented. Additionally, the majority of published GGH model implementations which feature proliferation do so in order to simulate a certain biological situation where mitosis is important, but without analysis of how these proliferation routines operate on a fundamental level. Here, a method of proliferation for the GGH model which uses separate cell phenotypes to differentiate cells which have entered or just left the mitotic phase of the cell cycle is presented and demonstrated to correctly predict logistic growth on a macroscopic scale (in accordance with experimental evidence). Comparisons between model simulations and the generalised logistic growth model provide an interpretation of the latter’s ‘shape parameter’, and the proliferation routine used here is shown to offer the modeller somewhat predictable control over the proliferation rate, important for ensuring temporal consistency between different cellular behaviours in the model. All results are found to be insensitive to the inclusion of active cell motility. The implications of these simulated proliferation assays towards problems in cell biology are also discussed.

Keywords

Contact inhibition of proliferation GGH model Logistic growth Single-cell-based model Monolayer formation 

Supplementary material

11538_2016_204_MOESM1_ESM.mp4 (1.7 mb)
Supplementary material 1 (mp4 1712 KB)
11538_2016_204_MOESM2_ESM.mp4 (342 kb)
Supplementary material 2 (mp4 341 KB)

References

  1. Abercrombie M, Heaysman JEM (1954) Observations of the social behaviour in tissue culture: II. ”Monolayering” of fibroblasts. Exp Cell Res 6:293–306CrossRefGoogle Scholar
  2. Barrandon Y, Green H (1987) Cell migration is essential for sustained growth of keratinocyte colonies: the roles of transforming growth factor-\(\alpha \) and epidermal growth factor. Cell 50:1131–1137CrossRefGoogle Scholar
  3. Bauer A, Jackson T, Jiang Y (2007) A cell-based model exhibiting branching and anastomosis during tumor-induced angiogenesis. Biophys J 92:3105–3121CrossRefGoogle Scholar
  4. Chaplain M, Stuart A (1993) A model mechanism for the chemotactic response of endothelial cells to tumour angiogenesis factor. IMA J Math Appl Med Biol 10:149–168CrossRefMATHGoogle Scholar
  5. Chaturvedi R, Izaguirre J, Huang C, Cickovski T, Virtue P, Thomas G, Forgacs G, Alber M, Hentschel G, Newman S, Glazier J (2003) Multi-model simulations of chicken limb morphogenesis. Lect Notes Comput Sci 2659:39–49CrossRefGoogle Scholar
  6. Chen C, Mirksch M, Huang S, Whitesides G, Ingber D (1997) Geometric control of cell life and death. Science 276:1425–1428CrossRefGoogle Scholar
  7. Cone C Jr, Tongier M Jr (1973) Contact inhibition of division: involvement of the electrical transmembrane potential. J Cell Physiol 82(3):373–386CrossRefGoogle Scholar
  8. Coomber B, Gotlieb A (1990) In vitro endothelial wound repair: interaction of cell migration and proliferation. Arteriosclerosis 10:215–222CrossRefGoogle Scholar
  9. Farooqui R, Fenteany G (2005) Multiple rows of cells behind an epithelial wound edge extend cryptic lamellipodia to collectively drive cell-sheet movement. J Cell Sci 118:51–63CrossRefGoogle Scholar
  10. Folkman J, Moscona A (1978) Role of cell shape in growth control. Nature 273:345–349CrossRefGoogle Scholar
  11. Graner F, Glazier J (1992) Simulation of biological cell sorting using a two-dimensional extended Potts model. Phys Rev L 69(13):2013–2016CrossRefGoogle Scholar
  12. Hanahan D, Weinberg R (2000) The hallmarks of cancer. Cell 100:57–70CrossRefGoogle Scholar
  13. Hogeweg P (2000) Evolving mechanisms of morphogenesis: on the interplay between differential adhesion and cell differentiation. J Theor Biol 203:317–333CrossRefGoogle Scholar
  14. Huang S, Ingber D (1999) The structural and mechanical complexity of cell growth control. Nat Cell Biol 1:E131–138CrossRefGoogle Scholar
  15. Huttenlocher A, Lakonishok M, Kinder M, Wu S, Truong T, Knudsen K, Horwitz A (1998) Integrin and cadherin synergy regulates contact inhibition of migration and motile activity. J Cell Biol 141(2):515–526CrossRefGoogle Scholar
  16. Jiang Y, Pjesivac-Grbovic J, Cantrell C, Freyer J (2005) A multiscale model for avascular tumor growth. Biophys J 89:3884–3894CrossRefGoogle Scholar
  17. Jones L, Gray M, Yue S, Haugland R, Singer V (2001) Sensitive determination of cell number using the CyQUANT cell proliferation assay. J Immunol Methods 254:85–98CrossRefGoogle Scholar
  18. Jorgensen P, Tyers M (2004) How cells coordinate growth and division. Curr Biol 14:R1014–R1027CrossRefGoogle Scholar
  19. Kippenberger S, Bernd A, Loitsch S, Guschel M, Mller J, Bereiter-Hahn J, Kaufmann R (2000) Signalling of mechanical stretch in human keratinocytes via MAP kinases. J Invest Dermatol 114:408–412CrossRefGoogle Scholar
  20. Knewitz M, Mombach J (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 36:59–69CrossRefGoogle Scholar
  21. Li J, Lowengrub J (2014) The effects of cell compressibility, motility and contact inhibition on the growth of tumor cell clusters using the Cellular Potts Model. J Theor Biol 343:79–91CrossRefGoogle Scholar
  22. Maini P, McElwain DLS, Leavesley D (2004) Travelling waves in a wound healing assay. Appl Math Lett 17:575–580MathSciNetCrossRefMATHGoogle Scholar
  23. Martz E, Steinberg M (1972) The role of cell-cell contact in contact inhibition of cell division: a review and new evidence. J Cell Physiol 79(2):189–210CrossRefGoogle Scholar
  24. Merks R, Perryn E, Shirinifard A, Glazier J (2008) Contact-inhibited chemotaxis in de novo and sprouting blood-vessel growth. PLoS Comput Biol 4(9):e1000163MathSciNetCrossRefGoogle Scholar
  25. Murrell M, Kamm R, Matsudaira P (2011) Tension, free space, and cell damage in a microfluidic wound healing assay. PLoS One 6:e24283CrossRefGoogle Scholar
  26. Ouchi N, Glazier J, Rieu J, Upadhyaya A, Sawada Y (2003) Improving the realism of the cellular Potts model insimulations of biological cells. Phys A 329:451–458MathSciNetCrossRefMATHGoogle Scholar
  27. Pardee A (1974) A restriction point for control of normal animal cell proliferation. Proc Natl Acad Sci USA 71:1286–1290CrossRefGoogle Scholar
  28. Pearl R (1927) The growth of populations. Q Rev Biol 2:532–548CrossRefGoogle Scholar
  29. Poplawski N, Agero U, Gens J, Swat M, Glazier J, Anderson A (2009) Front instabilities and invasiveness of simulated avascular tumors. Bull Math Biol 71:1189–1227MathSciNetCrossRefMATHGoogle Scholar
  30. Poplawski N, Swat M, Gens J, Glazier J (2007) Adhesion between cells, diffusion of growth factors, and elasticity of the AER produce the paddle shape of the chick limb. Phys A 373:521–532CrossRefGoogle Scholar
  31. Poujade M, Grasland-Mongrain E, Hertzog A, Jouanneau J, Chavrier P, Ladoux B, Buguin A, Silberzan P (2007) Collective migration of an epithelial monolayer in response to a model wound. Proc Natl Acad Sci USA 104(41):15988–15993CrossRefGoogle Scholar
  32. Puliafitoa A, Hufnagela L, Neveua P, Streichanb S, Sigalc A, Fygensond K, Shraimana B (2012) Collective and single cell behavior in epithelial contact inhibition. Proc Natl Acad Sci USA 109:739–744CrossRefGoogle Scholar
  33. Simpson M, Merrifield A, Landman K, Hughes B (2007) Simulating invasion with cellular automata: connecting cell-scale and population-scale properties. Phys Rev E 76:021918CrossRefGoogle Scholar
  34. Sisken J, Morasca L (1965) Intrapopulation kinetics of the mitotic cycle. J Cell Biol 25:179–189CrossRefGoogle Scholar
  35. Stott E, Britton M, Glazier J, Zajac M (1999) Stochastic simulation of benign avascular tumor growth using the Potts model. Math Comput Model 30:183–198CrossRefGoogle Scholar
  36. Timpe L, Martz E, Steinberg M (1978) Cell movements in a confluent monolayer are not caused by gaps: evidence for direct contact inhibition of overlapping. J Cell Sci 30:293–304Google Scholar
  37. Tremel A, Cai A, Tirtaatmadja N, Hughes B, Stevens G, Landman K, O’Connor A (2009) Cell migration and proliferation during monolayer formation and wound healing. Chem Eng Sci 64:247–253CrossRefGoogle Scholar
  38. Trepat X, Wasserman M, Angelini T, Millet E, Weitz D, Bulter J, Fredberg J (2009) Physical forces during collective cell migration. Nat Phys 5:426–430CrossRefGoogle Scholar
  39. Turner S, Sherratt J (2002) Intercellar adhesion and cancer invasion: a discrete simulation using the extended Potts model. J Theor Biol 216:85–100MathSciNetCrossRefGoogle Scholar
  40. Turner S, Sherratt J, Cameron D (2004) Tamoxifen treatment failure in cancer and the nonlinear dynamics of TGF-\(\beta \). J Theor Biol 229:101–111MathSciNetCrossRefGoogle Scholar
  41. Tyson J, Novak B (2001) Regulation of the eukaryotic cell cycle: molecular antagonism, hysteresis, and irreversible transitions. J Theor Biol 210:249–263CrossRefGoogle Scholar
  42. Ura H, Takeda F, Okochi H (2004) An in vitro outgrowth culture system for normal human keratinocytes. J Dermatol Sci 35:19–28CrossRefGoogle Scholar
  43. Zahm J, Kaplan H, Herard A, Doriot F, Pierrot D, Somelette P, Puchelle E (1997) Cell migration and proliferation during the in vitro wound repair of the respiratory epithelium. Cell Motil Cytoskelet 37:33–43CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2016

Authors and Affiliations

  1. 1.ARC Centre of Excellence for Mathematical and Statistical FrontiersQueensland University of Technology (QUT)BrisbaneAustralia

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