“The leopard never changes its spots: realistic pigmentation pattern formation by coupling tissue growth with reaction-diffusion” by Malheiros, Fensterseifer and Walter

  • ©Marcelo de Gomensoro Malheiros, Henrique Fensterseifer, and Marcelo Walter

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    The leopard never changes its spots: realistic pigmentation pattern formation by coupling tissue growth with reaction-diffusion

Session/Category Title:   Simulating Natural Phenomena


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Abstract:


    Previous research in pattern formation using reaction-diffusion mostly focused on static domains, either for computational simplicity or mathematical tractability. In this work, we have explored the expressiveness of combining simple mechanisms as a possible explanation for pigmentation pattern formation, where tissue growth plays a crucial role. Our motivation is not only to realistically reproduce natural patterns but also to get insights into the underlying biological processes. Therefore, we present a novel approach to generate realistic animal skin patterns. First, we describe the approximation of tissue growth by a series of discrete matrix expansion operations. Then, we combine it with an adaptation of Turing’s non-linear reaction-diffusion model, which enforces upper and lower bounds to the concentrations of the involved chemical reagents. We also propose the addition of a single-reagent continuous autocatalytic reaction, called reinforcement, to provide a mechanism to maintain an already established pattern during growth. By careful adjustment of the parameters and the sequencing of operations, we closely match the appearance of a few real species. In particular, we reproduce in detail the distinctive features of the leopard skin, also providing a hypothesis for the simultaneous productions of the most common melanin types, eumelanin and pheomelanin.


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