On Pattern Formation Mechanisms for Lepidopteran Wing Patterns and Mammalian Coat Markings

J. D. Murray

Abstract

The patterns on wings of Lepidoptera can be generated with a few pattern elements, but no mechanism has been suggested for producing them. I consider two of the basic patterns, namely, central symmetry and dependent patterns. A biochemically plausible model mechanism is proposed for generating major aspects of these patterns, based on a diffusing morphogen that activates a gene or colour-specific enzyme in a threshold manner to generate a stable heterogeneous spatial pattern. The model is applied to the determination stream hypothesis of Kuhn & von Engelhardt (Wilhelm Roux Arch. Entw Mech. Org. 130, 660 (1933)), and results from the model compared with their microcautery experiments on the pupal wing of Ephestia kuhniella. In the case of dependent patterns, results are compared with patterns on specific Papilionidae. For the same mechanism and a fixed set of parameters I demonstrate the important roles of geometry and scale on the spatial patterns obtained. The results and evidence presented here suggest the existence of diffusion fields of the order of several millimetres, which are very much larger than most embryonic fields. The existence of zones of polarizing activity is also indicated. Colour patterns on animals are considered to be genetically determined, but the mechanism is not known. I have previously suggested that a single mechanism that can exhibit an infinite variety of patterns is a candidate for that mechanism, and proposed that a reaction-diffusion system that can be diffusively driven unstable could be responsible for the laying down of the spacing patterns that generates the prepattern for animal coat markings. For illustrative purposes I consider a practical reaction mechanism, which exhibits substrate inhibition, and show that the geometry and scale of the domain (part of the epidermis) play a crucial role in the structural patterns that result. Patterns are obtained for a selection of geometries, and general features are related to the coat colour distribution in the spotted Felidae, giraffe, zebra and other animals. The patterns depend on the initial conditions, but for a given geometry and scale are qualitatively similar, a positive feature of the model and a necessary model attribute in view of the pattern individuality on animals of the same species.