Spatial patterns of cells in dividing epithelia

Early development of the feeding larva of the sea urchin Heliocidaris tuberculata: role of the small micromeres

The two modes of development in sea urchins are direct development, in which the adult develops directly from the gastrula to the adult and does not feed, and indirect development, in which the adult develops indirectly through a feeding larva. In this account of the indirect, feeding larva of Heliocidaris tuberculata, the question raised is whether an evolutionary difference of unequal cell divisions contributes to the development of feeding structures in the indirect larva. In indirect development, the cell divisions at the fourth and fifth cell cycles of the zygote are unequal, with four small micromeres formed at the vegetal pole at the fifth cell division. In direct development, these cell divisions are not unequal. From their position at the head of the archenteron, the small micromeres are strategically located to contribute to the feeding tissues of the larva and the adult of H. tuberculata.

A computer graphic simulation of squamous epithelium

An epithelium maintains its integrity through the organized growth and orderly differentiation of a transient cell population derived from stem cells. This organization is dependent upon both physical mechanisms such as cell adhesion and attraction and the relationship between differentiation and cell division. The interactions between these processes are complex and difficult to conceptualize from a purely mathematical approach. We have therefore set out to develop a graphic model of an epithelium controlled by rules that can be modified. We have chosen to model epidermis, the most superficial part of skin, with cells differentiating from a stem cell population and being lost from the surface of the model. The model is novel not only in the rules that govern cell behaviour, but also because it does not require a predefined lattice to assign the position of cells. Each cell assumes a position depending upon the balance of adhesive and repulsive forces that it experiences. Chemical factors which affect the differentiation of individual cell types are assumed to be produced both by cells within the model and externally from the underlying connective tissue. These "chemical factors" diffuse through the model with a concentration that declines as an inverse square with distance from the source. The rules allow the model to grow from a single stem cell to reach a steady state. At steady state the pattern and clonal structure is strikingly similar to that seen in a range of normal epithelia. Furthermore, if part of the model is removed it is capable of regenerating itself without additional rules. The model allows the visualization of the effects of introducing new rules and modifying the interaction between chosen rules. This study demonstrates that a set of simple rules can be used to make a dynamic flexible model resembling skin.