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Spatiotemporal pattern in somitogenesis: A non-Turing scenario with wave propagation

Hiroki Nagahara1,*, Yue Ma2,†, Yoshiko Takenaka3,‡, Ryoichiro Kageyama4,5,§, and Kenichi Yoshikawa1,2,∥

  • 1Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
  • 2Spatio-Temporal Order Project, ICORP, Japan Science and Technology Agency (JST), Tokyo 102-0075, Japan
  • 3Venture Business Laboratory, Kyoto University, Kyoto 606-8501, Japan
  • 4Institute for Virus Research, Kyoto University, Kyoto 606-8507, Japan
  • 5CREST, Japan Science and Technology Agency, Kyoto 606-8507, Japan

  • *Present address: Mitsubishi UFJ Securities Co., Ltd., Tokyo 100-6317, Japan; nagahara-hiroki@sc.mufg.jp
  • †Corresponding author; dr.mayue@gmail.com
  • ‡Present address: RIKEN Advanced Science Institute, Saitama 351-0198, Japan; ytakenaka@riken.jp
  • §rkageyam@virus.kyoto-u.ac.jp
  • ∥yoshikaw@scphys.kyoto-u.ac.jp
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Phys. Rev. E 80, 021906 – Published 11 August, 2009

DOI: https://doi.org/10.1103/PhysRevE.80.021906

Abstract

Living organisms maintain their lives under far-from-equilibrium conditions by creating a rich variety of spatiotemporal structures in a self-organized manner, such as temporal rhythms, switching phenomena, and development of the body. In this paper, we focus on the dynamical process of morphogens in somitogenesis in mice where propagation of the gene expression level plays an essential role in creating the spatially periodic patterns of the vertebral columns. We present a simple discrete reaction-diffusion model which includes neighboring interaction through an activator, but not diffusion of an inhibitor. We can produce stationary periodic patterns by introducing the effect of spatial discreteness to the field. Based on the present model, we discuss the underlying physical principles that are independent of the details of biomolecular reactions. We also discuss the framework of spatial discreteness based on the reaction-diffusion model in relation to a cellular array, by comparison with an actual experimental observation.

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Phys. Rev. E 80, 021906– Published 11 August, 2009
  • Received 6 March 2009

© 2009 American Physical Society

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