A model for pattern formation on the shells of molluscs

Abstract

Models based on reaction-diffusion mechanisms are proposed for the generation of pigmentation and relief-like patterns on mollusc shells. They extend an earlier model to describe the formation of more complex patterns. Shell patterns are time records of a one-dimensional pattern forming process along the growing edge. Oblique lines result from travelling waves of activation (pigment production). Branches and crossings result from a temporary shift from an oscillatory into a steady state mode of pigment production. Checkerboard or meshwork-like patterns require systems with at least three components, one autocatalytic substance antagonized by two inhibitions, a diffusible inhibiting substance which generates the pattern in space and a non-diffusible one which is responsible for the pattern in time. Wavy lines, rows of dots and fish-bone like patterns can result from the superposition of two patterns: a pattern which is stable in time controls the oscillation frequency of the pigment-producing process. By computer simulations it is shown that the models reproduce not only fine details of the natural patterns but account also for pattern regulation such as observed on some species after injury.