Individual cell‐based models of the spatial‐temporal organization of multicellular systems—Achievements and limitations

Abstract

Computational approaches of multicellular assemblies have reached a stage where they may contribute to unveil the processes that underlie the organization of tissues and multicellular aggregates. In this article, we briefly review and present some new results on a number of 3D lattice free individual cell-based mathematical models of epithelial cell populations. The models we consider here are parameterized by bio-physical and cell-biological quantities on the level of an individual cell. Eventually, they aim at predicting the dynamics of the biological processes on the tissue level. We focus on a number of systems, the growth of cell populations in vitro, and the spatial-temporal organization of regenerative tissues. However, many processes on the sub-cellular scale do act cooperatively together and have a summary effect on a limited number of effective parameters on the cellular or the multicellular level. To unveil these hierarchies is one of the major issues of current research in systems biology (3). The parameters on the cellular scale are functions of characteristic quantities on the molecular scale, which are actively regulated by the cell (4,5). For example, although cells have a complex cytoskeleton they essentially behave as a viscoelastic, or on short time scales, as isotropic elastic body (6). Their biomechanical properties, therefore, may be characterized by a small number of material parameters, e.g. the Young modulus and the Poisson number. Further parameters are, for example, cell doubling time, cell mobility, and the cell-cell and cell-substrate adhesion.Because of recent advances in cell biophysics and cellbiology (7-10), the possibilities to collect new information on these parameters of cells and tissues are strongly improving. Nevertheless, an unique experimental identification of how the parameters on the cellular and subcellular level affect the organization on the multicellular level is often difficult. Many of the parameters cannot be directly modified and modifications of one property very often result in the modifications of other properties at the same time. This asks for new complementary methods that can deal with this complexity.Individual cell-based models (ICBM's, also called agentbased models) represent a recent trend in this context. These computer models use explicit representations of individual cells to model the organization of multicellular aggregates. One can distinguish two classes of them. In one class, the cellular automaton models, each cell is rep-

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