A common biomechanical model for the formation of stationary cell domains and propagating waves in the developing organisms

Many important morphogenetic processes that take place in the development of an animal start from the segregation of a homogeneous layer of cells into a different number of the domains of columnar and flattened cells. In many cases, waves of cell shape transformation travel throughout embryonic tissues. A biomechanical model is presented which embraces both kinds of event. The model is based on the idea of interplay between short- and long-range factors. While the former promote the spreading of a given cell state along a cell row in the recalculation direction, long-range factors are associated with self-generated tensions which, after exceeding a certain threshold, induce active cell extension and hence the rise of tangential pressure. Different kinds of biologically realistic stationary structures, as well as various kinds of the running waves, can be modelled under different parameter values. Moreover, the current model can be coupled with the previous one (Beloussov and Grabovsky, Comput. Methods Biomech. Biomed. Eng., 6: 53-63 (2003)) permitting a common causal chain to be created, moving from the state of an initial homogeneous cell layer towards the complicated shapes of embryonic rudiments.