Models of growth and folding in tissues: From compact tumors to one-layered tissues.

The understanding of the principles underlying the complicated spatial-temporal processes during organismic development, the maintenence of tissues or perturbations of these require a model tool or a class of models capable to consider adequately the many degrees of freedom of these biological systems.

This includes the particular ability of biological cells to differentiate according to a program determined on the time scale of evolution. A differentiation often changes the physical properties of a cell and hence the way it is represented to its environment.

A successful model approach to multicellular systems must be able to include the spatial and temporal dynamics of cells as physical objects capable of changing their physical properties under certain stimuli. It must also be able to consider cell-type specific differences on small length scales of the order of the cell diameter.

Nevertheless, since it is hopeless to gain any insight from models with an endless number of parameters, a model approach must focus on those parameters that are essential to the effects of interest. To find an appropriate balance between these requirements is the challenge in modeling multicellular systems.

Starting from a (simple) single cell-based approach for cells in tissue culture it will be shown that this approach can easily be extended to describe (i) the growth of non-vascular tumor spheroids, (ii) blastula formation and gastrulation of sea urchin, and (iii) the buckling of one layered tissues as observed e.g. during the fission of intestinal crypts (pear-shaped pockets in the intestinal wall responsible for maintenence of the intestinal epithelium) after x-ray radiation.

Depending on the particular system studied cells are considered similar to Brownian particles with elastic interactions between them and the ability to divide and change their material or kinetic parameters by differentiation. >From these systems simple generic properties and effects can be extracted and analyzed separately by simple analytical models that allow to link the single-particle picture with a continuum description.