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From single cells to tissue architecture—a bottom-up approach to modelling the spatio-temporal organisation of complex multi-cellular systems

  • J. Galle
  • M. Hoffmann
  • G. Aust
Article

Abstract

Collective phenomena in multi-cellular assemblies can be approached on different levels of complexity. Here, we discuss a number of mathematical models which consider the dynamics of each individual cell, so-called agent-based or individual-based models (IBMs). As a special feature, these models allow to account for intracellular decision processes which are triggered by biomechanical cell–cell or cell–matrix interactions. We discuss their impact on the growth and homeostasis of multi-cellular systems as simulated by lattice-free models. Our results demonstrate that cell polarisation subsequent to cell–cell contact formation can be a source of stability in epithelial monolayers. Stroma contact-dependent regulation of tumour cell proliferation and migration is shown to result in invasion dynamics in accordance with the migrating cancer stem cell hypothesis. However, we demonstrate that different regulation mechanisms can equally well comply with present experimental results. Thus, we suggest a panel of experimental studies for the in-depth validation of the model assumptions.

Keywords

Individual cell-based model Epithelial monolayer Tumour invasion Cancer stem cell 

Mathematics Subject Classification (2000)

37N25 92C15 92C37 92C10 92C17 

Supplementary material

285_2008_172_MOESM1_ESM.mpg (6.6 mb)
Movies 1a, 1b (related to Fig.5 of the article): Population growth dynamics. Comparison of population growth dynamics according to scenarios: a) R1 and b) R2. Top views on growing colonies. Colour saturation indicates imminent cell division. b) Substrate adapted cells are shown in yellow. The two colonies regulated according to R1 and to R2 show nearly identical spreading. This is achieved by assuming different cell-substrate friction coefficients. For parameter sets ‘R1 vs. R2’, please, see Appendix.
285_2008_172_MOESM2_ESM.mpg (6.9 mb)
Movies 1a, 1b (related to Fig.5 of the article): Population growth dynamics. Comparison of population growth dynamics according to scenarios: a) R1 and b) R2. Top views on growing colonies. Colour saturation indicates imminent cell division. b) Substrate adapted cells are shown in yellow. The two colonies regulated according to R1 and to R2 show nearly identical spreading. This is achieved by assuming different cell-substrate friction coefficients. For parameter sets ‘R1 vs. R2’, please, see Appendix.
285_2008_172_MOESM3_ESM.mpg (22.4 mb)
Movies 2a, 2b (related to Fig.7 of the article): Cancer stem cell organisation. Top views on growing tumours (blue: migratory inactive, red: migratory active) within stroma (yellow). a) Environmentally regulated proliferation according to the plasticity scenario R3: Colour saturation indicates stem cells. The migratory cells at the tumour front (dark red) are considered to be quiescent stem cells. b) Intrinsically regulated proliferation according to the pedigree scenario R4: Colour saturation indicates differentiated cells. Most of the stem cells become confined in the tumour bulk. Stem cells located at the tumour periphery stay there and induce fast invasion. For parameter sets ‘R3 vs. R4’, please, see Appendix.
285_2008_172_MOESM4_ESM.mpg (22.6 mb)
Movies 2a, 2b (related to Fig.7 of the article): Cancer stem cell organisation. Top views on growing tumours (blue: migratory inactive, red: migratory active) within stroma (yellow). a) Environmentally regulated proliferation according to the plasticity scenario R3: Colour saturation indicates stem cells. The migratory cells at the tumour front (dark red) are considered to be quiescent stem cells. b) Intrinsically regulated proliferation according to the pedigree scenario R4: Colour saturation indicates differentiated cells. Most of the stem cells become confined in the tumour bulk. Stem cells located at the tumour periphery stay there and induce fast invasion. For parameter sets ‘R3 vs. R4’, please, see Appendix.

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Interdisciplinary Center for BioinformaticsUniversity LeipzigLeipzigGermany
  2. 2.Centre of Surgery, Research LaboratoriesUniversity LeipzigLeipzigGermany

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