Skip to main content
SpringerLink
Log in
Book cover

Single-Cell-Based Models in Biology and Medicine pp 171–196Cite as

Center-based Single-cell Models: An Approach to Multi-cellular Organization Based on a Conceptual Analogy to Colloidal Particles

  • Chapter

Part of the book series: Mathematics and Biosciences in Interaction ((MBI))

Abstract

In this chapter we present a model framework for multi-cellular simulations which is built on conceptual analogies to colloidal particles. Cells are approximated as homogeneous isotropic elastic sticky objects, capable of migrating, growing, dividing and changing orientation. A cell is parameterized by biomechanical, cell-kinetic and cell-biological parameters. Each model parameter can in principle be determined experimentally. We show some simulation results for in-vitro systems and discuss the effect of model variants on simulated multi-cellular growth phenomena. The aim of this chapter is to provide an introduction and overview of the algorithms, technical concepts and the framework necessary to perform equivalent computational simulations with different model variants.

To Zoubida and Marvin

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

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Schienbein, K. Franke, and H. Gruler: Random walk and directed movement: comparison between inert particles and self-organized molecular machines, Phys. Rev. E 49, 5462 (1994).

    Article  Google Scholar 

  2. J. Mombach and J. Glazier: Single cell motion in aggregates of embryonic cells, Phys. Rev. Lett. 76, 3032 (1996).

    Article  Google Scholar 

  3. H. Othmer and A. Stevens: Aggregation, blowup and collapse: The abc’s of generalized taxis in reinforced random walks, SIAM J. Appl. Math. 57, 1044 (1997).

    Article  MATH  MathSciNet  Google Scholar 

  4. E. Palsson and H. Othmer: A model for individual and collective cell movement in dictyostelium discoideum, Proc. Natl. Acad. Sci. USA 12, 10448 (2000).

    Article  Google Scholar 

  5. A. Stevens: The derivation of chemotaxis equations as limit dynamics of moderately interacting stochastic many-particle systems, SIAM J. APPL. MATH. 61, 183 (2000).

    Article  MATH  MathSciNet  Google Scholar 

  6. Y.-S. C. et. al.: Johnson-kendall-roberts theory applied to living cells, Phys. Rev. Lett. 280, 312 (1999).

    Google Scholar 

  7. R. Carpick, D. F. Ogletree, and M. Salmeron: A gerneral equation for fitting contact area and friction vs load measurements, J. Colloid and Interface Sci 211, 395 (1999).

    Article  Google Scholar 

  8. D. Beysens, G. Forgacs, and J. Glazier: Cell sorting is analogous to phase ordering in fluids, Proc. Natl. Acad. Sci. USA 97, 9467 (2000).

    Article  Google Scholar 

  9. D. Drasdo, R. Kree, and J. McCaskill: Monte-carlo approach to tissue-cell populations, Phys. Rev. E 52, 6635 (1995).

    Article  Google Scholar 

  10. D. Drasdo: Different growth regimes found in a monte-carlo model of growing tissue cell populations, in Self organization of complex structures: From individual to collective dynamics, edited by F. Schweitzer (Gordon and Breach, 1996), pp. 281–291.

    Google Scholar 

  11. D. Drasdo: A monte carlo approach to growing solid non-vascular tumors, in Networks in Biology and Physics, edited by G. Forgacs (Springer, Berlin Heidelberg New York, 1998), pp. 171–185.

    Google Scholar 

  12. J. Galle, M. Loeffler, and D. Drasdo: On the temporal-spatial organization of epithelial cell populations in-vitro., in Mathematical Modelling & Computing in Biology and Medicine, edited by V. Capasso (Marcel Dekker Inc, 2003), pp. 375–385.

    Google Scholar 

  13. J. Galle, M. Loeffler, and D. Drasdo: Modelling the effect of deregulated proliferation and apoptosis on the growth dynamics of epithelial cell populations in vitro, Biophys. J. 88, 62 (2005).

    Article  Google Scholar 

  14. D. Drasdo and S. Hoehme: A single-cell based model to tumor growth in-vitro: mono-layers and spheroids, Physical Biology 2, 133 (2005).

    Article  Google Scholar 

  15. D. Drasdo: Coarse graining in simulated cell populations, Adv. Complex Syst. 8, 319 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  16. D. Drasdo, S. Hoehme, and M. Block: On the role of physics in the growth and pattern formation of multi-cellular systems: What can we learn from individual-based systems?, J. Stat Phys. (in press).

    Google Scholar 

  17. D. Drasdo and S. Höhme: Individual-based approaches to birth and death in avascular tumors, Math. and Comp. Modelling 37, 1163 (2003).

    Article  MATH  Google Scholar 

  18. D. Drasdo and M. Löffler: Individual-based models on growth and folding in onelayered tissues: Intestinal crypts and blastulation, Nonl. Anal. 47, 245 (2001).

    Article  MATH  Google Scholar 

  19. J. Galle, G. Aust, G. Schaller, T. Beyer, and D. Drasdo: Single-cell based mathematical models to the spatio-temporal pattern formation in multi-cellular systems, Cytometry 69A, 704–710 (2006)

    Article  Google Scholar 

  20. D. Drasdo and G. Forgacs: Modelling the interplay of generic and genetic mechanisms in cleavage, blastulation and gastrulation, Dev. Dyn. 219, 182 (2000).

    Article  Google Scholar 

  21. D. Drasdo: Buckling instabilities in one-layered growing tissues, Phys. Rev. Lett. 84, 4244 (2000).

    Article  Google Scholar 

  22. H. Eagle: Nutriention needs of mammalian cells in tissue culture, Science 122, 43 (1955).

    Article  Google Scholar 

  23. R. Ham: Clonal growth of mammalian cells in a chemically defined, synthetic medium, Proc. Natl. Acad. Sci. 53, 288 (1965).

    Article  Google Scholar 

  24. I. Hayashi and G. Sato: Replacement of serum by hormones permits growth of cells in defined medium, Nature 239, 132 (1976).

    Article  Google Scholar 

  25. G. Sato, A. Pardee, and D. Sirbasku: Growth of Cells in Hormonally Defined Media (Cold Spring Harbour Laboratory, 1982).

    Google Scholar 

  26. B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, and P. Walter: The Cell (Garland Science Publ., New York, 2002).

    Google Scholar 

  27. D. Drubin and W. Nelson: Origins of cell polarity, Cell 84, 335 (1996).

    Article  Google Scholar 

  28. DSMZ: German collection of microorganism and cell cultures, http://www.dsmz.de/

    Google Scholar 

  29. G. Forgacs and S. Newmann: Biological Physics of the Developing Embryo (Cambridge University Press, Cambridge, 2005).

    Google Scholar 

  30. P. Rosen and D. Misfeldt: Cell density determines epithelial migration in culture, Proc. Natl. Acad. Sci. 77, 4760 (1980).

    Article  Google Scholar 

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

    Article  Google Scholar 

  32. M. Seinberg: Reconstruction of tissues by dissociated cells, Science 141, 401 (1963).

    Article  Google Scholar 

  33. M. Pfeiffer: Birds flock together, Nature 395, 324 (1998).

    Article  Google Scholar 

  34. S. Huang and D. Ingber: The structural and mechanical complexity of cell-growth control, Nature Cell Biol. 1, E131 (1999).

    Article  Google Scholar 

  35. L. Davidson, M. Koehl, R. Keller, and G. Oster: How do sea urchins invaginate? Using bio-mechanics to distinguish between mechanisms of primary invagination, Development 121, 2005 (1995).

    Google Scholar 

  36. M. Lekka, P. Laidler, D. Gil, J. Lekki, Z. Stachura, and A.Z. Hrynkiewicz: Elasticity of normal and cancerous human bladder cells studied by scanning force microscopy, European Biophysics Journal 28, 312 (1999).

    Article  Google Scholar 

  37. R. Mahaffy, C. Shih, F. McKintosh, and J. Kaes: Scanning probe-based frequency-dependent microrheology of polymer gels and biological cells, Phys. Rev. Lett. 85, 880 (2000).

    Article  Google Scholar 

  38. J. Alcaraz, L. Buscemi, M. Grabulosa, X. Trepat, B. Fabry, R. Farre, and D. Navajas.: Microrheology of human lung epithelial cells measured by atomic force microscopy, Biophys. J. 84, 2071 (2003).

    Google Scholar 

  39. S. Chesla, P. Selvaraj, and C. Zhu: Measuring two-dimensional receptor-ligand binding kinetics by micropipette, Biophys. J 75, 1553 (1998).

    Google Scholar 

  40. J. Piper, R. Swerlick, and C. Zhu: Determining force dependence of two-dimensional receptor-ligand binding affinity by centrifugation, Biophys. J. 74, 492 (1998).

    Article  Google Scholar 

  41. D. Landau: Theory of elasticity (Pergamon, 1975).

    Google Scholar 

  42. H. Hertz: über die berührung fester elastischer körper (on the contact of elastic solids)., J. Reine Angewandte Math. 92, 156 (1882).

    Article  Google Scholar 

  43. D. Landau and K. Binder: A Guide to Monte Carlo Simulations in Statistical Physics (Cambridge University Press, 2000).

    Google Scholar 

  44. Gardiner: Handbook of Stochastic medthods (Springer, New York, 1990).

    Google Scholar 

  45. D. Helbing: Traffic and related self-driven many particle systems, Rev. Mod. Phys. 73, 1067 (2001).

    Article  Google Scholar 

  46. F. Schweitzer: Brownian agents and active particles (Springer, Berlin, Heidelberg, 2003).

    MATH  Google Scholar 

  47. D. Elderfield: Field theories for kinetic growth models, J. Phys. A: Math. Gen. 18, L773 (1985).

    Article  MathSciNet  Google Scholar 

  48. M. Block, E. Schoell, and D. Drasdo: Classifying the expansion kinetics and critical surface dynamics of growing cell populations, Cond. mat. physics/0610146 (2006).

    Google Scholar 

  49. M. Allen and D. Tildersley: Computer Simulation of Liquids (Oxford Science Publ., Oxford, 1987).

    MATH  Google Scholar 

  50. J. Dhont: An Introduction to Dynamics of Colloids (Elsevier, Amsterdam, 1996).

    Google Scholar 

  51. H. Oettinger: Stochastic Processes in Polymeric Fluids (Springer, Berlin Heidelberg, 1993).

    Google Scholar 

  52. G. Schaller and M. Meyer-Hermann: Multicellular tumor spheroid in an off-lattice voronoi-delaunay cell model, Phys. Rev. E. 71, 051910 (2005).

    Article  MathSciNet  Google Scholar 

  53. G. Odell, G. Oster, P. Alberch, and B. Burnside: The mechanical basis of morphogenesis, Dev. Biol 85, 446 (1981).

    Article  Google Scholar 

  54. I. Bischofs and U. Schwarz: Cell organization in soft media due to active mechanosensing, Proc. Natl. Acad. Sci. (USA) 100, 9274 (2003).

    Article  Google Scholar 

  55. J. Honerkamp: Stochastic Dynamic Systems (Wiley, 1993).

    Google Scholar 

  56. A. Bru, J. Pastor, I. Fernaud, I. Bru, S. Melle, and C. Berenguer: Super-rough dynamics of tumor growth, Phys. Rev. Lett. 81, 4008 (1998).

    Article  Google Scholar 

  57. C. Potten and M. Loeffler: Stem cells: attributes, cycles, spirals, pitfalls and uncertainties. lessons for and from the crypt, Development 110, 1001 (1990).

    Google Scholar 

  58. S. Gilbert: Develoment (Sinauer Associates Inc., New York, 1997).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Rocquencourt, French National Institute for Research in Computer Science and Control (INRIA), B.P. 105, 78153, Le Chesnay Cedex, France

    Dirk Drasdo

  2. Mathematics Institute and Center for Systems Biology, University of Warwick, Coventry, CV4 7AL, UK

    Dirk Drasdo

  3. Interdisciplinary Centre for Bioinformatics, University of Leipzig, Härtelstr. 14-16, D-04107, Leipzig, Germany

    Dirk Drasdo

Authors
  1. Dirk Drasdo
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Division of Mathematics, University of Dundee, 23 Perth Road, Dundee, DD1 4HN, UK

    Alexander R. A. Anderson , Mark A. J. Chaplain  & Katarzyna A. Rejniak ,  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Birkhäuser Verlag Basel/Switzerland

About this chapter

Cite this chapter

Drasdo, D. (2007). Center-based Single-cell Models: An Approach to Multi-cellular Organization Based on a Conceptual Analogy to Colloidal Particles. 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_8

Download citation

Publish with us

Policies and ethics

Search

Navigation