Buckling Instabilities in one-layered growing tissue.

After exposure of tissues to radiation or growth factors or during tumor formation often an increased cell division rate is experimentally found. In tissue sheets as in intestinal crypts or the skin this is often accompanied by the folding of the sheet.

We suggest a generic mechanism which provides a potential explanation for this phenomenon.

Our studies partly base on a stochastic single cell Monte Carlo model and partly on a coarse grained analytic approach. For simplicity and in order to obtain a clear picture of the underlying folding principle we focus on one-dimensional cell chains in two-dimensional space.

The basic physical model assumptions are the existence of attractive nearest-neighbor interactions between cells to maintain the integrity of the one-layered tissue, a bending energy that models the polarity of the cells in a sheet and cell division that takes into account potential size changes of the sheet.

The effect of cell division on the tissue geometry and growth law is studied for different tissue geometries, bending rigidities (which measure the resistance of a tissue sheet against bending), cell division rates and division algorithms (daughter cells of the same size of mother cells or smaller than mother cells; the latter case corresponds to the situation found during blastula formation).

We find that as a tissue domain grows above a certain size the bending energy becomes too small to smooth local undulations that are stochastically created by local fluctuations in the growth of the layer hence the layer roughens.

If this occurs before cell deformations or compressions become so strong that cell division is hindered, the cell number increases exponentially (if the cycle time is large or the bending rigidity small) otherwise the growth law changes to sub-exponential growth before the folding occurs.