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

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.