MODEL OF PATTERN-FORMATION IN ANIMAL COATINGS

One of the most universal phenomena in embryological morphogenesis is the formation of domains of morphologically polarized (apico-basally e longated) epithelial cells. It has been observed that cell polarizatio n precedes many ''obvious'' events in embryogenesis, such as invaginat ion and evagination, folding and curling of cell sheets, differentiati on of cells in eye development, emergence of skin derivates, and even the budding in Marine Hydrozoa. Domains of polarized and unpolarized c ells form ''reliefs'' in epithelial sheets that are the pre-patterns t o the above-mentioned patterns. This paper gives a model for the pigme nt pattern formation in animal coatings. The model simulates cell pola rization as a co-operative self-organized process of cells in an epith elial sheet. It is based upon the following experimentally proven prop erties of cells and their interactions: (i) each individual cell in an epithelial tissue is able to change shape from unpolarized to polariz ed and back. the transition being the ''all or none'' type (both forms are the only stable ones); (ii) polarization is transmitted from cell to cell via their contacts; (iii) local polarization forces generate tangential elastic tensions throughout the surrounding unpolarized cel ls which, in turn, inhibit further polarization, thus establishing a n egative feedback mechanism. These two types of force form the basis of the model, which is referred to as the PE model (polarization-elastic ity) for brevity.