Fibroblast cultures and dermatoglyphics: The topology of two planar patterns

This is a study of two, two dimensional biological patterns-the pattern created in a confluent dish of normal fibroblast and the dermatoglyphic pattern on the primate palm and sole. Both patterns are characterised by a small repertory of different types of interruptions or discontinuities in fields of otherwise parallel aligned elements. Because these discontinuities are invariant under plastic deformations as well as rigid motions, a topological treatment is appropriate. A quantitative topological characterisation shows the pattern in the two systems to be essentially identical. Regarding both systems as exercises in packing elongated elements in the plane subject to certain constraints, both can be modelled by a smooth, planar, nonoriented vector field. In neither case can the development of pattern be accounted for solely in terms of the aggregate of autonomously arising local detail; the whole constrains and influences the local situations. The interrelationship of global and local constraints on packing is quantified by the index theorem, which accounts for the range of patterns that may develop. The study shows that to understand pattern development in these systems, it is necessary to include topological considerations in addition to an analysis of cell behaviour.