Stripe formation in juvenile Pomacanthus explained by a generalized Turing mechanism with chemotaxis

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Abstract
Current interest in pattern formation can be traced to a seminal paper by Turing, who demonstrated that a system of reacting and diffusing chemicals, called morphogens, can interact so as to produce stable nonuniform concentration patterns in space. Recently, a Turing model has been suggested to explain the development of pigmentation patterns on species of growing angelfish such as Pomacanthus semicirculatus , which exhibit readily observed changes in the number, size, and orientation of colored stripes during development of juvenile and adult stages, but the model fails to predict key features of the observations on stripe formation. Here we develop a generalized Turing model incorporating cell growth and movement, we analyze the effects of these processes on patterning, and we demonstrate that the model can explain important features of pattern formation in a growing system such as Pomacanthus. The applicability of classical Turing models to biological pattern formation is limited by virtue of the sensitivity of patterns to model parameters, but here we show that the incorporation of growth results in robustly generated patterns without strict parameter control. In the model, chemotaxis in response to gradients in a morphogen distribution leads to aggregation of one type of pigment cell into a striped spatial pattern.