Abstract
A wide variety of patterns can be observed in multicellular organisms. How these various spatial regularities are generated from the seemingly homogeneous field of an egg cell has been a great mystery, and various mathematical models have been proposed to provide a conceptual explanation of the underlying mechanism. Unlike other types of morphogenesis that involve three-dimensional processes, the patterns produced by pigment cells are simple in that they occur on the two-dimensional surface of the body. Therefore, they are relatively easy to reproduce using mathematical models. In addition, the ease with which the developmental process can be traced on a cell-by-cell basis without using special visualization techniques is also advantageous for studies linking experimental data to the models. Thus, pigment patterns have contributed significantly to the development of mathematical models of pattern formation and to the widespread recognition and acceptance of these models among experimental biologists. In this chapter, we discuss some of the important models that have been proposed and developed to understand the mechanisms of pigment pattern formation, including their relationship to patterns found in real organisms.
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Acknowledgements
This work was supported by JSPS KAKENHI Grant Numbers JP15H04415 and JP19H03283 (to SM) and 15KT0079 and 17H03683 (to MW), by the MEXT KAKENHI Grant Number 22127003 (to SK), and by the CREST program (to SK).
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Miyazawa, S., Watanabe, M., Kondo, S. (2021). Theoretical Studies of Pigment Pattern Formation. In: Hashimoto, H., Goda, M., Futahashi, R., Kelsh, R., Akiyama, T. (eds) Pigments, Pigment Cells and Pigment Patterns. Springer, Singapore. https://doi.org/10.1007/978-981-16-1490-3_9
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