Individual-based models to growth and folding in one-layered tissues: Intestinal crypts and early development

In this paper we present individual-based models of the spat io-temporal dy namics in one-layered multicellular biological systems and outline how they can be adapted to experimental systems (individuum here: single cell). Mat hematically these systems present a now and interesting class of problems w hich allow to study how to link individual-based models with continuum theo ry in problems with internally growing manifolds. As model systems we mainly focus on intestinal crypts since they axe paradi gmatic in several regards: (i) they represent a simple, epithelial tissue, (ii) they contain only a small number of cells (N approximate to 300), (iii ) much is known about them and they are fairly well accessible to experimen ts, (iv) perturbations in their spatio-temporal dynamics have. been found t o result in folded patterns (crypt fission, polyps and adenoma) which are p ro-patterns of intestinal cancer. We show how the formation of folded patterns can be explained within a sing le-cell based, lattice-free model. We, further illustrate, that the, foldin g principles are expected to carry over to other tissue layers as well as t o a developing blastula or the oral mucosa, supported by computer simulatio ns and a simple field theory.