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Coarse graining in simulated cell populations
The main mechanisms that control the organization of multicellular tissues are still largely open. A commonly used tool to study basic control mechanisms are in-vitro experiments in which the growth conditions can be widely varied. However, even in-vitro experiments are not free from unknown or uncontrolled influences.
One reason why mathematical models become more and more a popular complementary tool to experiments is that they permit to study hypotheses that were derived from biological experiments, free from unknown or uncontrolled influences.
Many model types have been considered so far to model multicellular organization ranging from detailed individual-cell based models with explicit representations of the cell shape to cellular automata models with no representation of cell shape, and continuum models, that consider a local density averaged over many individual cells.
However, how the different model description may be linked, and, how a description on a coarser level may be constructed based on the knowledge of the finer, microscopic level, is still largely unknown. Here we consider the example of monolayer growth in-vitro to illustrate how in a multi-step process starting from an single-cell based off-lattice-model that subsumes the information on the sub-cellular scale by characteristic cell-biophysical and cell-kinetic properties a cellular automaton may be constructed whose rules have been chosen based on the findings in the off-lattice model.
Finally we use the cellular automaton model as a starting point to construct a continuum model by a systematic coarse-graining procedure. The development of our models is guided by experimental observations on growing monolayers.