Generative rules for the morphogenesis of epithelial tubes

A finite elements model imitating the morphogenesis of smoothly curved tubular epithelial rudiments is suggested. It is based upon the experimentally proved assumption of the lateral (tangential) pressure between adjacent epithelial cells. The main idea of the model is that under a non-zero local curvature the lateral cell-cell pressure acquires the radial components which are absent under zero curvature. In the framework of the model we investigate the roles of initial geometry, the different coefficients relating the local curvatures and radial cell shifts, and of visco-elastical cell-cell linkages in the shaping process. We also employ the different temporal regimes (both periodical and constant) of the lateral pressure exerted and the different overall durations of the modelling. As a result, we get a set of biologically realistical shapes, almost all of them belonging to the same basical "trefoiled" archetype. Among the variables explored, shaping was most affected by the changes in visco-elastical coefficients, in the temporal regimes and in the overall duration of the modelling. The model shows that rather complicated and realistical shapes of epithelial rudiments can be obtained without assuming any initial regional differences inside cell layers. The model may be useful for understanding the principles underlying both genetical and epigenetical regulation of the morphogenesis.