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Mathematical Modeling and Experimental Verification of the Proneural Wave

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Methods of Mathematical Oncology (MMDS 2020)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 370))

Abstract

Spatio-temporal pattern formation during development is regulated by interactions of multiple signaling pathways. To understand complex signaling networks, we used the Drosophila visual system as a model because neural differentiation progresses in a spatiotemporally ordered manner. During the development of the visual system, a wave of differentiation, called the proneural wave, sweeps across the brain surface and determines the timing of differentiation of neuroepithelial cells into neuroblasts, which are neural stem cells in Drosophila. Propagation of the proneural wave is regulated through a combination of signaling pathways, including the Notch, EGF, and JAK/STAT. We combined mathematical modeling with in vivo experiments, the results of which revealed that Notch-mediated lateral inhibition and EGF-mediated reaction diffusion determine the speed of progression of the proneural wave. We reported that JAK/STAT signaling has a noise-canceling function to assure robust neuroblast differentiation. Furthermore, we introduced a continuation method from spatially discretized models while conserving the cell size and lattice. This mathematical method enables us to introduce information from spatially discrete to spatially continuous models, rendering it suitable for applications in both experimental and mathematical analyses. Our interdisciplinary studies have revealed new functions of signaling pathways that have previously been difficult to address by conventional biological experiments.

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Acknowledgements

We thank Makoto Sato and Hiroshi Ishii for their critical reading of the manuscript. This work was supported by a Grant-in-Aid for Scientific Research on Innovative Areas (JP19H04956 and JP20H05030 to T.Y.), Grant-in-Aid for Scientific Research (C) (JP19K06674 to T.Y.), and Grant-in-Aid for Early-Career Scientists (JP20K14364 to Y.T.) from MEXT, Takeda Science Foundation (to T.Y.), and the Uehara Memorial Foundation (to T.Y.).

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Authors and Affiliations

  1. Department of Complex and Intelligent Systems, School of Systems Information Science, Future University Hakodate, 116-2 Kamedanakano-cho, Hakodate, Hokkaido, 041-8655, Japan

    Yoshitaro Tanaka

  2. Mathematical Neuroscience Unit, Institute for Frontier Science Initiative, Kanazawa University, 13-1 Takaramachi, Kanazawa-shi, Ishikawa, 920-8640, Japan

    Tetsuo Yasugi

Authors
  1. Yoshitaro Tanaka
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  2. Tetsuo Yasugi
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Correspondence to Tetsuo Yasugi .

Editor information

Editors and Affiliations

  1. Centre for Mathematical Modeling and Data Science, Osaka University, Toyonaka, Japan

    Takashi Suzuki

  2. Research Team MONC, Institut de Mathématiques de Bordeaux (CNRS UMR 5251), Talence, France

    Clair Poignard

  3. School of Mathematics and Statistics, MI, University of St Andrews, St Andrews, UK

    Mark Chaplain

  4. Quantitative Systems Biology Center, Vanderbilt University School of Medicine, Nashville, TN, USA

    Vito Quaranta

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Tanaka, Y., Yasugi, T. (2021). Mathematical Modeling and Experimental Verification of the Proneural Wave. In: Suzuki, T., Poignard, C., Chaplain, M., Quaranta, V. (eds) Methods of Mathematical Oncology. MMDS 2020. Springer Proceedings in Mathematics & Statistics, vol 370. Springer, Singapore. https://doi.org/10.1007/978-981-16-4866-3_3

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