Stripe formation in juvenile Pomacanthus explained by a generalized Turingmechanism with chemotaxis

Current interest in pattern formation can be traced to a seminal paper by T uring, who demonstrated that a system of reacting and diffusing chemicals, called morphogens, can interact so as to produce stable nonuniform concentr ation patterns in space. Recently, a Turing model has been suggested to exp lain the development of pigmentation patterns on species of growing angelfi sh such as Pomacanthus semicirculatus, which exhibit readily observed chang es in the number, size, and orientation of colored stripes during developme nt of juvenile and adult stages, but the model fails to predict hey feature s of the observations on stripe formation. Here we develop a generalized Tu ring model incorporating cell growth and movement, we analyze the effects o f these processes on patterning, and we demonstrate that the model can expl ain important features of pattern formation in a growing system such as Pom acanthus. The applicability of classical Turing models to biological patter n formation is limited by virtue of the sensitivity of patterns to model pa rameters, but here we show that the incorporation of growth results in robu stly generated patterns without strict parameter control. In the model, che motaxis in response to gradients in a morphogen distribution leads to aggre gation of one type of pigment cell into a striped spatial pattern.